Attention, Uncertainty Reduction and

Pre-announcement Premium in China

Rui Guo, Dun Jia, Xi Sun∗

This Draft: August 5, 2019

Abstract

This paper examines Chinese stock market returns in an environment in which the datesof central bank’s information supply through public announcements are not pre-fixed. Wedocument that positive excess returns accumulate for 3 days before China’s central bank releasesdata of monetary aggregates, which may be announced either early or late in a month. Thispre-announcement premium appears sizable, has a longer duration than that of the pre-FOMCpremium in the U.S., and is not driven by potential data leakages or expectation changes. Wepresent a model to account for this premium by highlighting the channel of investors’ informationdemand given unscheduled deliveries of announcements. As investors with limited attention findit optimal to learn about data ahead of announcements, increasingly focused attention drivesdown market uncertainty and boosts equity prices. We show that China’s setting of “quasi-scheduled” central bank announcements provides the exact data structure for us to test the keymodel mechanism of an information demand channel, which helps rationalize the empirics foundfor both China and the U.S.

JEL codes: E44, E52, G14

Key Words: Equity Premium, Macro Announcement, Monetary Policy, Inattention

∗Guo: Hanqing Institute of Economics and Finance, Renmin University of China. Email: rui.guo@ruc.edu.cn.Jia (Corresponding Author): Hanqing Institute of Economics and Finance, Renmin University of China. Email:dun.jia@ruc.edu.cn. Sun: Hanqing Institute of Economics and Finance, Renmin University of China. Email:xi.sun@ruc.edu.cn. We benefited from discussions with Hengjie Ai, Liyan Yang, Tao Zha, Jun Qian “QJ”, Christo-pher Polk, Xiaoji Lin, Howard Kung, Shiyang Huang, Grace Xing Hu, George Jiang, Zhigang Qiu, Hongda Zhong,and Jianyu Leyla Han. We thank comments from participants at various conferences and seminars. All errors areours. This paper was previously circulated under the title of “Monetary Announcement Premium in China”.

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1 Introduction

In this paper, we examine why stock markets react ex ante to an anticipated central bank’s

announcement on its monetary policy stance. In particular, we study the equity returns in an

environment in which the dates of central bank’s information supply through public announcements

are not pre-fixed. Lucca and Moench (2015) document a robust pre-drift of U.S. stock market

returns prior to the pre-scheduled dates and time of Federal Open Market Committee (FOMC)

statement releases, and labels this a puzzle for lack of data-consistent theories.1 We demonstrate

that by evaluating the implications of having “randomness” in announcement scheduling, we can

better clarify the mechanism behind the equity market’s pre-announcement responses.

Our exploration of the research question is framed within the Chinese context. To draw gen-

eral implications, we maintain that central banks’ periodical releases of the measures of domestic

monetary policy stance are comparable announcements: the monetary aggregates statistics pub-

lished by the People’s Bank of China (PBOC), the country’s central bank, and the U.S. FOMC

announcements of the federal funds rate targets.2 The data of monetary aggregates are announced

by the PBOC in a “quasi-scheduled” fashion with some randomness in announcement timing. In

other words, at the start of a month, the market expects monetary statistics to be released on a

day of that month with probability one, but the exact date and time of the announcement is largely

unknown.3 We first document a sizable pre-announcement premium in the Chinese equity market

before the PBOC’s announcement releases of monetary data, which more than triples the magni-

tude of the total equity premium in China. This pre-announcement premium of China and that of

U.S. share similar qualitative characteristics. However, quantitatively, we find the accumulation of

excess returns on Chinese equity market kicks off three days before announcements and exhibits a

much longer duration than that of its U.S. counterpart for a few hours.

1The Federal Reserve Board (FRB) pre-schedules the dates of eight FOMC meetings a year, and informs themarket of those dates ahead of time. On average, eight FOMC statements are issued per year right after the FOMCmeetings.

2The growth rate of M2 is one of the most critical monetary policy instruments in China (Chen, Ren, and Zha,2018).

3Note that the announcements of interest rate adjustments fall beyond our research focus, which is at least“quasi-scheduled” if announcements are not perfectly pre-scheduled. For example, often times, the benchmark ratesof loans and savings in China were changed by the PBOC and made public unexpectedly. Hence, investors can formexpectations of announcements of monetary aggregates data on a regular basis but cannot do the same for unexpectedbenchmark interest rate shifts.

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We then present a model to study the pre-announcement premium by featuring investors’ in-

formation demand decision, in the spirit of Sims (2003), focusing on the decision prior to a central

bank’s announcements. Specifically, we build a model of attention allocation in that an announce-

ment may arrive early or late in a month. In the model, investors are not able to draw highly

informative signals about the data to be released when it is too early to do so. When investors do

not pay attention and learn about monetary data, their forecast uncertainty about the growth of

aggregate money supply accumulates over time, which increases the opportunity cost of not paying

attention. Investors start to pay attention to learning about monetary data only when information

demand starts bringing value, that is, when uncertainty has accumulated excessively and very in-

formative signals can be drawn. As a result, the attentive learning among investors reduces their

forecast uncertainty of money growth, alleviates the aggregate market risk, and drives up the stock

prices. Our model highlights the importance of having endogenous information demand to account

for the pre-announcement premium.

We then test the key implications derived from our model. Importantly, we highlight the desir-

ability of exploiting the uniqueness of Chinese data, because China’s setting of “quasi-scheduled”

central bank announcements provides the exact data structure for us to test the key model mecha-

nism of an information demand channel, which helps rationalize the empirics found for both China

and the U.S. First, we show that uncertainty measures constructed from survey forecasts as well as s-

tock return volatility shrink as the date of the PBOC’s announcement of monetary aggregates draws

closer. Second, we provide direct evidence that across announcement events, the size of uncertainty

reduction is correlated with the magnitude of the pre-announcement premium. Third, the model

predicts that the timeliness of announcement arrival shifts the size of uncertainty reduction driven

by investors’ attention allocation. Empirically, we are able to show that the pre-announcement

premium in China is mainly driven by the delayed releases of monetary data. Finally, as proxied

by the web search intensity index, the size of attention allocated to monetary aggregates data and

monetary policy changes is found to be higher before the PBOC’s announcements of monetary ag-

gregates. We demonstrate that the size of uncertainty reduction prior to announcements increases

with the intensity of ex-ante attention allocation. We thus conclude that the information demand

channel of pre-announcement uncertainty reduction is critical for generating ex-ante reactions of

stock markets.

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To shed light on the U.S. pre-FOMC equity premium, our model suggests that only when it gets

close to the pre-scheduled FOMC date, investors see the possibility for policy changes. This raises

uncertainty and then triggers attentive learning, which leads to a quick reduction of uncertainty and

pre-announcement premium a few hours before the FOMC statement releases. As for China, the

lack of financial market sophistication for backing out the central bank’s policy moves gives room

to cycles of uncertainty accumulation between the PBOC’s announcements. With quasi-scheduled

announcements, investors with high cumulative uncertainty and more informative signals available

would start paying attention whenever learning brings value until the next announcement is made.

Therefore, it takes a few days for stock market investors in China to lower uncertainty to the

optimum, and equity prices keep climbing prior to the announcements.

This paper distinguishes itself from the large literature that aims to identify the impacts of

monetary policy shocks on equity markets and other dimensions of the economy (see Romer and

Romer (2004) and Bernanke and Kuttner (2005), etc.). Rather, we disentangle the ex-ante effects

of variation in uncertainty about monetary policy changes on stock market returns regardless of

the ex-post nature of the policy shocks. Our results show that the documented pre-announcement

premium in China is not driven by potential data leakages or expectation changes. In this respect,

this study contributes to the literature by theorizing the information demand channel through

which the stock market can be affected by uncertainty about monetary policy changes ahead of

time.

The rest of the paper is structured as follows. Section 2 is the literature review. We then discuss

the identification of announcement events and data sources in Section 3. Section 4 presents the

main empirical findings regarding the equity premium associated with monetary announcements.

Section 5 delivers a model that marks uncertainty reduction as the key driver of pre-announcement

premium. Section 6 summarizes the results of a series of empirical tests of the model predictions

and provides evidence consistent with our model. Section 7 discusses the relevance of our model

for rationalizing the characteristic features of pre-announcement premium observed both in China

and the U.S. given differences in the announcement scheduling. Section 8 concludes. In the Online

Appendix, we provide further technical details and additional empirical results of a wide range of

explorations.

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2 Related Literature

This paper is related to three strands of literature. First, this study is aligned with works that

explore the asset-pricing implications of macro announcements.

Empirically, Savor and Wilson (2013) find that the U.S. equity market exhibits larger excess

returns and Sharpe ratios on days of data releases for inflation, unemployment, and various interest

rates. Lucca and Moench (2015) detect a pre-announcement premium in response to issued FOMC

statements. They show that the U.S. stock market starts its pre-drift from the afternoon 1 day

before the FOMC meeting until hours before the FOMC statement releases on the FOMC day.

Brusa, Savor, and Wilson (2019) provides cross-country evidence that international stock markets

accrue high excess returns on the FOMC days. Altavilla, Giannone, and Modugno (2017), Balduzzi

and Moneta (2017), and Philippe, Alireza, and Vedolin (2017) study the announcement premium

in treasury markets, bond future markets, and foreign exchange markets, respectively. Our study

is the first to provide empirical evidence on the Chinese stock market’s ex-ante reactions to the

PBOC’s announcements of monetary aggregates data, a pre-announcement premium that shares

similar qualitative characteristics with the pre-FOMC premium of the U.S. markets. We thus

complement the international evidence on the effects of central bank’s announcements by showing

that the non-U.S. stock market may also react to the important information provided by its own

domestic central bank.

In theory, Ai and Bansal (2018) and Ai et al. (2019) theorize that the probability distortions

in the investor’s preference give room for the market to realize positive premium on announcement

days. Wachter and Zhu (2018) account for the announcement premium using a model whereby in-

vestors learn about disaster probabilities. While these theories aim to rationalize the announcement-

day stock returns, they implicitly entertain the possibility that central bank’s information has to

be somewhat leaked ex-ante in order to generate the pre-announcement pattern of excess returns.

Jiang, Pan, and Qiu (2019) introduce the informed trading prior to the central bank’s announce-

ment, by which the stock market incorporates the information ex-ante and realizes a positive

pre-announcement premium. With high frequency trading data, Bernile, Hu, and Tang (2016) and

Kurov et al. (2019) find that the market indeed moves in the same direction as the to-be-released

data a few minutes before announcements. However, their evidence suggests that various sources of

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information delivery including data leakages may lead to informed trading prior to announcements

but only up to a very short window prior to announcements. In this paper, by primarily focusing on

the pre-announcement period, we propose a model that features the information demand channel

relying on neither the ex-ante central bank’s information supply in form of a data leakage nor the

informed trading. In addition, we document that the pre-announcement drift of equity returns in

China is quite persistent, and carefully show that data leakage cannot be the main driver. More

importantly, while the theoretical works largely take the pre-scheduled announcements as given to

study the announcement effects, we delve into the asset-pricing implications in a model by having

announcement schedules not pre-fixed.

Importantly, our model highlights the role of endogenous decision of information demand such

that investors’ attentive learning prior to announcements reduces their forecast uncertainty about

monetary policy changes. By alleviating the aggregate market risk, the reduced uncertainty ex ante

boosts the stock market prices. The closest paper related to ours is Hu et al. (2019). They also

emphasize the uncertainty variation as the key driver of equity premium and provide a model in

which the arrival of a signal regarding the size of market risk resolves the uncertainty and raises

equity prices prior to announcements. In addition, Hu et al. (2019) along with Martello and Ribeiro

(2018) and Lakdawala, Bauer, and Mueller (2019) provide comprehensive evidence showing that

uncertainty reduction, regardless of whether it is measured by the VIX, the variance risk premium,

or the Libor rate volatility, is correlated with the stock returns around FOMC announcements.

Our paper differs from these works in two important dimensions. First, we provide the “micro-

foundation” in the model by endogenizing the attention allocation and information demand, which

endogenously determines the uncertainty cycles between announcements without resorting the ex-

ogenous delivery of signals that partly or completely resolves the uncertainty. Second, taking a

detour by studying China, we show that the setting of “quasi-scheduled” central bank announce-

ments provides the exact data structure for us to test the key model mechanism of an information

demand channel, which helps rationalize the empirics found for both China and the U.S.

Second, at the firm level, the rich literature dating back to Beaver (1968) documents high-

er excess returns on the announcement day of corporate earnings. In addition, both the pre-

announcement and post-announcement drifts of equity returns are identified around the day of cor-

porate earnings announcements (Bernard and Thomas, 1989; Frazzini, 2006; Barber et al., 2013).

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As the early announced information can be used to revise expectations about the late announce-

ments, Savor and Wilson (2016) detect the stock return differences on the earnings announcement

day between early announcer firms and the delayed ones. Our paper uncovers the differential

reactions of the aggregate stock market to the relative timeliness of the announcement arrivals

at the macro level. We rationalize such findings not from the perspective of risk-shifting across

firms but by having investors endogenously pay greater attention to more delayed central bank’s

announcements, which drives up the stock prices.

Third, this study is related to the literature that explores implications for asset pricing under

imperfect information and uncertainty. In the spirit of Sims (2003), models of investors with limited

attention and costly information-processing capacity show that asset values can be endogenously

shifted by the decision of attention allocation, which determines the optimal investment decisions

(Peng and Xiong, 2006; Kacperczyk, Nieuwerburgh, and Veldkamp, 2016; Kacperczyk, Nosal, and

Stevens, 2018). We show that the channel of attention-driven uncertainty reduction, that is, a

key result as implied by the class of rational inattention models, delivers the pre-announcement

drift of equity returns when triggered prior to the central bank’s announcement. By exploiting

the uniqueness of Chinese data structure, we thus provide direct evidence on the relationship of

uncertainty dynamics, attention allocation, and the equity premium, which is consistent with the

model of rational inattention. In addition, the extensive evidence suggests that attention as proxied

by web search and virtual clicks is a key driver of excess equity returns and may serve as the pre-

condition for CAPM to hold (Da, Engelberg, and Gao, 2011; Ben-Rephael, Da, and Israelsen, 2017;

Ben-Rephael et al., 2019). The empirical findings in this paper find that the pre-announcement

premium is an important example of the attention-driven premium. Our model gives the exact

theoretical account of the mechanism by which increased attention reduces forecast uncertainty

and raises the stock prices.

3 Data

In this section, we summarize the data used for identifying the response of China’s equity market

to announcements regularly published by the PBOC. By announcements, we refer to public news

that specifically delivers up-to-date statistics of a macroeconomic variable with regular publication

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frequency. In Section A.1 of the Online Appendix, we summarize and study the institutional details

of a range of macroeconomic announcements made by other statistical agencies of China along with

the FOMC statements issued by the U.S. FRB.

We are primarily interested in the announcements made by the PBOC on China’s monetary

aggregate data, which are indicative of the stance of China’s monetary policy and overall credit

condition. Data on the monetary aggregates, including levels and growth of M0, M1, and M2, are

all published on the website of the PBOC every month in a single announcement statement. Other

monetary and financial statistics are also published at the same time in the statement, including

the outstanding balance of total loans and deposits, monthly interest rate averages, and balance of

interbank loans.4 To avoid abuse of terminology, we simply label the announcements that publish

the most updated monetary aggregates data and other credit statistics as M2 announcements.5

3.1 Data Sources

Our sample ranges from January 2010 to June 2017. We made this choice for three reasons.

First, in the post-2010 period, the routine of PBOC’s publishing up-to-date macro data was formal-

ized. Statistics are promptly published on the PBOC’s website. Such internet information vendor

provides good precision to tell on what day and at what time a data point is initially accessible

by the market. Second, we abstract from a period of domestic and international financial market

turmoil, economic downturn, and massive policy interventions during 2007—2009. Many countries,

including China, suffered credit shortage and liquidity distress and implemented large fiscal and

monetary stimulus, all of which could be of first-order importance in shifting asset values in a

turbulent period. For example, China introduced a massive stimulus package of RMB 4 trillion

(roughly USD 586 billion) to its economy and has provided liquidity support to its financial mar-

4Since November 2012, these statistics have been published around the same time as the announcement of thebalance of total social financing (TSF), even though TSF data are made public via a separate statement issue. TSFdata could be online a few seconds or hours before or after the monetary aggregate data releases.

5We also note the quarterly publication of China’s Monetary Policy Report (MPR) by the PBOC and examineChina’s stock market reactions to these MPR announcements. Technically, the MPR does not square well withour research focus, that is, announcements that release updated statistics. Rather, the MPR is a comprehensivecollection of the PBOC’s assessments of the soundness of the credit market, macroeconomic and financial stability,and the necessity for the PBOC to fine tune monetary policy further. Therefore, the MPR is not directly comparableto other major central banks’ policy statements that specifically publish policy instrument targets or articulate thedecision of monetary policy moves, such as the FOMC statement by the U.S. FRB or the Monetary Policy Accountsof the European Central Bank. However, for completeness, we examine China’s stock market reactions to these MPRannouncements. The results are shown in Section B.5 of the Online Appendix.

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kets since 2008. Third, by focusing on recent years, China’s equity market could have increasingly

grown in sophistication through rounds of reforms. Market participants might have known how

to react to macro announcements and act upon information better than before. Therefore, our

sample selection helps isolate to the effects of macro announcements during a post-crisis period

reflecting China’s growing financial market sophistication and market participants’ familiarity with

the delivery process of key macro data. We discuss the empirical results using alternative sample

periods in Section B.1 of the Online Appendix.

To identify the pre-announcement reactions of the equity market, we extract a list of dates and

times of the PBOC’s announcements about monetary aggregates from the Bloomberg Economic

Calendar (BEC) database, which are verified to be consistent with the timing information published

on the PBOC’s website. Stock return data are constructed based on daily open and close price

series of the Wind A-Share Index. This index incorporates the A-shares of all firms listed on the

Shanghai Stock Exchange (SSE) and Shenzhen Stock Exchange (SZSE), and can be considered the

most comprehensive measure of stock performance of China’s equity market. We also examine the

robustness of our empirical results using the SSE Composite Index and the SZSE Component Index.

All these market index series are downloaded from Wind Data Feed Services. In addition, intra-day

price index data for both Shanghai and Shenzhen exchanges are sourced from the RESSET High

Frequency Database, which helps reaffirm our baseline findings using daily data.

To compute the excess equity returns, we take the 10-year treasury bond daily yield series as the

benchmark risk-free rate. The 1-year bank time deposit rate is treated as an alternative measure.

These risk-free rates are downloaded from the CSMAR Economic and Financial Database. Finally,

we exploit the forecast data from Bloomberg Economic Forecast Survey, and the series of daily

volatility of stock returns aggregated over high frequency price data from the RESSET database.

By doing this, we rationalize the pre-announcement equity premium through the lens of ex-ante

changes in market forecast uncertainty about economic fundamentals and monetary policy.

To measure the magnitude of investors’ attention allocation, we employ the keywords-based

search index complied by Baidu, Inc., a leading Chinese search engine conglomerate, to capture

the intensity of keywords search regarding monetary aggregates data and the PBOC’s policy moves

among Baidu users in China. The construction of proxies for attention echoes the exercise done for

the U.S. market in Da, Engelberg, and Gao (2011). Hence, we are able to identify the empirical

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relationship between the keywords search index and the size of uncertainty reduction prior to the

PBOC’s announcements as implied by our model that features the investors’ attention allocation

decision. We download the historical data of search index by keywords of interests from the website

of Baidu Search Index with the arranged authorization.

3.2 Timing of Announcements

Our sample covers 1819 trading days of China’s equity market, and 90 M2 announcement

events.6 We define the day of an announcement as the first trading day that China’s financial

markets have access to the PBOC’s updated statistics. 7

Figure 1 presents a histogram plot of the day of month distribution of M2 announcement days.

The vertical distance measures the percent of M2 announcements that fall into a 2-day bin. The

solid line approximates a probability density function of the discrete distribution. The graph shows

that about 50% of M2 announcements in our sample fall between the 11th and 14th days of a

month and the day mode for the PBOC releasing the monetary data is the 11th.

Therefore, no particular day of month is consistently chosen by the PBOC for releasing mone-

tary statistics. However, investors may still be able to figure out a window of days with greatest

probability of PBOC data release, for example, the 11th to 14th of a month. Note that the PBOC

does not pre-communicate with the market regarding the exact day of announcement. However,

market participants know with probability one that sooner or later, one announcement that pub-

lishes up-to-date monetary aggregate data will be made every month. Hence, we call this PBOC

routine of releasing monetary data “quasi-scheduled.” On the contrary, in the U.S., the FRB pre-

schedules the dates of eight FOMC meeting a year, and informs the market of those dates ahead

of time. In Section 7, we discuss the implications of announcement scheduling for equity premium.

6In Section A.2 of the Online Appendix, Table A.5 summarizes the degree of data co-releasing conditional on theday of announcements for a much wider range of macro announcement events. It shows that our identified events ofM2 announcements are largely independent events.

7In Section A.2 of the Online Appendix, we provide a summary of announcement days of a much wider rangeof macro announcements made by different statistical agencies according to the day-of-month of an announcement.Summaries of the announcement days by other timing classifications including day-of-week and time-of-day arerelegated to that section.

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Figure 1: Day of Month Distribution of M2 Announcements

Notes: Sample: January 2010 to June 2017. This figure plots the histogram distribution of day of month across allM2 announcements events in our sample. Each bin spans 2 consecutive calendar days. The vertical distance of the boxdenotes the percentage (%) of M2 announcement events with announcement days that fall into a 2-day bin. The solid lineapproximates the probability density function.

4 Pre-announcement Premium

In this section, we first document persistent pre-announcement drift of China’s stock market

returns in response to the PBOC’s announcements about monetary aggregate data. Then, we show

that the realized pre-announcement equity premium is large, and is not driven by potential data

leakage or expectation changes.

4.1 Evidence from High Frequency Data

To examine the reactions of China’s stock market to M2 announcements, we compute and plot

the average cumulative equity returns constructed from 5-minute trading blocks of the Shenzhen

and Shanghai market indexes in Figure 2.

Averaged across all M2 announcements for the period January 2010 to December 2016, the solid

lines denote the mean cumulative returns of the two indexes starting from i days after (before if i is

negative) the announcement.8 The day of the M2 announcement is marked by 0 on the x-axis and

8A slight shrinkage of our sample length of January 2010 to June 2017 is because the RESSET High Frequency

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shaded with grey color. ±1 standard deviation confidence bands are drawn along the cumulative

returns. For comparison, we insert dashed lines to capture the average cumulative returns across

all “non-announcement” 7-day windows, in which there is no announcement falling on any day of

the 7 days in the window.

Accordingly, this figure suggests that China’s equity returns, regardless of stock market ex-

changes, start accumulating 3 days prior to an average M2 announcement until reaching a peak on

the announcement day. The peak of mean cumulative returns of both markets is about 70–80 basis

points (bps). Conversely, returns stay flat for an average non-announcement window of the same

length and are significantly no different from zero. Hence, we confirm that China’s stock market

exhibits pre-announcement drift of equity returns in response to incoming releases of monetary

aggregates data.

Figure 2: Cumulative Chinese Stock Market Returns around M2 Announcements

(a) Shenzhen Stock Exchange (b) Shanghai Stock Exchange

Notes: Sample: January 2010 to December 2016. This figure shows the average cumulative returns over 5-minuteblocks on the SZSE Component Index and the SSE Composite Index of a 7-day announcement window. The solid line of aplot captures the average cumulative returns across all 7-day windows. The announcement day, that is, the first trading daywhen the market has access to the monetary data, is centered in the middle and is shown by the grey-shaded bar. The dashedline of a plot denotes the average cumulative returns of 7-day windows with no announcement day falling in between. Theshadow areas mark ±1 standard deviation confidence bands around the average cumulative returns.

Database stopped updating data after the end of 2016.

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4.2 Monetary Announcements: Pre-announcement Premium

We further identify the pre-announcement equity premium by estimating a baseline specification

given by

Exrett = γ +

T∑i=−T

βiItM2−i + βxXt + υt (1)

t corresponds to a trading day. Exrett denotes the daily difference of close-to-close stock returns

constructed from the Wind A-Share Market Index and the 10-year treasury daily yield, and thus,

is a measure of excess return. We show that open-to-close returns and use of alternative risk-free

rates would not affect our baseline results.

Our explanatory variables ItM2−i are dummy variables that equal 1 if day t is the i-th trading

day before (after if i is negative) an M2 announcement. With i = 0, ItM2 = 1 denotes the first

trading day on which an announcement is available to the public, that is, the announcement day.

In total, we include 2T + 1 day dummies to capture the duration of the announcement window.

Ceteris paribus, coefficient βi is interpreted as the mean excess return on the i-th day prior to

announcement relative to the average daily excess return outside an average non-announcement

window. We further include year, month, and weekday fixed effects in vector Xt to control for a

potential seasonality and calendar effect.

Table 1 reports the coefficient estimates of Equation (1). According to the results in column (1),

with T = 5 of an 11-day M2 announcement window, we find that most coefficient estimates βi are

statistically insignificant except for those associated with the 3-day dummies prior to announcement,

namely, IM2−1, IM2−2, and IM2−3. These point estimates range from 30 to 40 bps for a given trading

day, although the largest and most statistically significant daily equity premium is realized on the

day right before announcement tM2−1. It is important to note that we do not find a significant

premium on the M2 announcement day and the coefficient estimates associated with the second

to the fifth day after the announcements are not distinguishable from zero. Therefore, we confirm

that China’s equity market accrues a pre-announcement equity premium before the PBOC’s release

of monetary data. Thus, our findings for Chinese markets echo those for U.S. pre-FOMC drifts of

equity returns documented in Lucca and Moench (2015).

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For excess returns constructed using the open-to-close market index, the risk-free rate proxied

by the 1-year bank time deposit rate, and stock market raw returns as the dependent variable, the

findings on the 3-day pre-announcement premium are robust across columns (2), (3), and (4) of

Table 1. Column (5) presents similar estimates of the coefficient estimates when 7-day dummies of

announcement windows are included such that T = 3. In Section B.2 of the Online Appendix, we

demonstrate that directly using the Shenzhen or Shanghai stock exchange index for constructing

returns does not alter our baseline results.9

Table 1: Wind A-Share Index Returns in Windows of M2 Announcements

(1) (2) (3) (4) (5) (6) (7)VARIABLES Exret Open-Close Bank Rate Raw Returns Exret Exret Exret

ItM2−5 0.16 0.18 0.16 0.16 0.16 0.16(0.18) (0.15) (0.18) (0.18) (0.18) (0.18)

ItM2−4 -0.07 0.09 -0.07 -0.07 -0.07 -0.07(0.20) (0.16) (0.20) (0.20) (0.20) (0.20)

ItM2−3 0.29+ 0.31+ 0.29+ 0.29+ 0.28+ 0.29+

(0.19) (0.20) (0.19) (0.19) (0.19) (0.19)ItM2−2 0.25+ 0.25* 0.25+ 0.25+ 0.24+

(0.17) (0.15) (0.17) (0.17) (0.16)ItM2−1 0.39** 0.42*** 0.39** 0.39** 0.38**

(0.16) (0.16) (0.16) (0.16) (0.16)ItM2−1,2 0.32***

(0.12)ItM2−1,3 0.31***

(0.11)ItM2 0.22 0.13 0.22 0.22 0.21 0.22 0.22

(0.17) (0.16) (0.17) (0.17) (0.16) (0.17) (0.17)ItM2+1 -0.21 -0.13 -0.21 -0.21 -0.22 -0.21 -0.21

(0.17) (0.16) (0.17) (0.17) (0.17) (0.17) (0.17)ItM2+2 0.02 0.03 0.02 0.02 0.02 0.02 0.02

(0.19) (0.18) (0.19) (0.19) (0.19) (0.19) (0.19)ItM2+3 -0.02 -0.06 -0.02 -0.02 -0.03 -0.02 -0.02

(0.18) (0.17) (0.18) (0.18) (0.18) (0.18) (0.18)ItM2+4 0.01 0.02 0.01 0.01 -0.02 0.01

(0.19) (0.16) (0.19) (0.19) (0.18) (0.18)ItM2+5 0.03 0.02 0.03 0.03 0.03 0.03

(0.20) (0.19) (0.20) (0.20) (0.20) (0.20)

Year / Month / Weekday Dummies Yes Yes Yes Yes Yes Yes YesConstant -0.28 -0.07 -0.28 -0.27 -0.28 -0.28 -0.28

(0.21) (0.20) (0.21) (0.21) (0.20) (0.21) (0.21)

Observations 1,819 1,819 1,819 1,819 1,819 1,819 1,819R2 0.02 0.02 0.02 0.02 0.02 0.02 0.02

Notes: Sample: January 2010 to June 2017. Columns (1) to (5) report the regression results of Equation (1) for variousspecifications. Columns (6) and (7) list the estimation results of Equation (2). The dependent variable is the log close-to-closeexcess return constructed from the Wind A-Share Index except for column (4), which directly takes stock market returns asthe dependent variable. Announcement dummy ItM2−i equals 1 if it is the i-th trading day before (after if i is negative) anM2 announcement. Excess return data of the first trading day are aligned to the day on which the stock market first hasaccess to the monetary news with the dummy variable ItM2 = 1 when i = 0. Dummy variable ItM2−1,j equals 1 when atrading day t falls in a j-trading-day window before an M2 announcement. ***, **, *, and + denote significance at 1%, 5%,10%, and 15%, respectively. Robust standard errors are in parentheses.

9Apart from the Chinese equity markets, we further explore if other asset markets react to the PBOC’s announce-ments of monetary aggregates data in Section B.6 of the Online Appendix.

14

Given persistent accumulation of equity returns prior to monetary announcements, we run

the following regression to quantify the relative size of the mean daily excess return in the pre-

announcement window of j days.

Exrett = γ + θjItM2−1,j +T∑i=0

βiItM2+i + βxXt + υt (2)

Dummy variables ItM2−1,j = 1 denote those trading days that fall in a j-day window before an

M2 announcement. θj can be interpreted as the average daily excess return of those days that

fall into the j-day window, relative to daily returns outside these windows. The estimation results

are summarized in columns (6) and (7) of Table 1. Both columns suggest that relative to non-

announcement window length of j days for j = 2, 3 prior to monetary announcements, the realized

daily excess return, that is, the relative pre-announcement premium, is about 30 bps per day.

4.3 Pre-announcement Premium vs. Total Equity Premium

We then evaluate how quantitatively important the documented pre-announcement premium is

by examining the proportion of this premium to the total risk premium of China’s equity market.

Our measure of the magnitude of pre-announcement premium is the mean daily excess return of a

3-day window prior to an average M2 announcement. Table 2 summarizes the results.

Panel A of Table 2 presents the relative size of the pre-announcement premium using close-to-

close daily returns of China’s equity market. The first row indicates that the average daily excess

return of the Wind A-Share Market Index is about 1 bps, which can be aggregated up to an annual

return of approximately 3%. By contrast, the daily pre-announcement excess returns averaged over

all 3-day pre-announcement windows is about 27 bps, which can be annualized up to more than 10%

using a factor of 36 (12 times a year). Therefore, in annual terms, the monetary pre-announcement

premium in China scales the total equity premium of Chinese equity market by a multiple of 3.40.

In terms of the Sharpe ratio, a trading strategy of buy-and-hold for the Wind A-Share Index for 3

days prior to the M2 announcements 12 times a year amounts to 1.05. 10 This is a high number

— more than nine times the mean Sharpe ratio of 0.11 derived from the buy-and-hold strategy for

10Technically, this 3-day trading strategy is not implementable per se because investors are not pre-informed ofthe exact date of announcement every month. However, for comparative purposes, it is a way to compute the relativesize of this pre-announcement premium.

15

the market index throughout the year. In summary, our monetary pre-announcement premium is

large in both absolute and risk-adjusted terms.

Table 2: China’s Equity Premium and Monetary Pre-announcement Premium

A. Close-to-close Returns B. Open-to-close Returns

No.Obs Daily average Annualized S.R. Daily average Annualized S.R.

Whole Sample 1819 0.01 % 2.98 % 0.11 0.12 % 35.28 % 1.25PreAnns Days 270 0.27 % 10.14 % 1.05 0.38 % 14.55 % 1.51

Ratio 3.40 9.46 0.41 1.21

Notes: This table presents excess returns of the Wind A-Share Market Index earned in 3-day pre-M2windows relative to the size of China’s total equity premium. Columns “Annualized” stand for cumula-tive annual excess return, assuming there are 250 trading days in a calendar year. Row label “PreAnnsDays” presents the returns earned in 3-day pre-M2 trading windows. “Whole Sample” presents returnsearned in all trading days of the sample range: January 2010 to June 2017. “S.R.” denotes the annual-ized Sharpe ratio of pre-M2 window excess returns. Given 12 3-day windows per year, we calculate theannualized announcement Sharpe ratio as the per-day Sharpe ratio times

√36. “Scale/Ratio” shows

the multiple of returns earned in the 3-day pre-M2 trading windows to those earned in all trading days.Panel A summarizes the results based on close-to-close returns; Panel B lists the results based on open-to-close returns.

Panel B of Table 2 again confirms the quantitative relevance of this pre-announcement premium

using open-to-close returns. It shows that the monetary pre-announcement premium still accounts

for 41% of China’s total equity premium. The scale of the Sharpe ratio is greater than 1. This

is because the total premium of China’s equity market is much larger when returns are based on

open-to-close market prices. Hence, our results highlight the importance of studying strong market

reactions prior to monetary announcements.

4.4 The Unconditional Pre-announcement Premium

In this subsection, we examine if the documented pre-announcement premium depends on the

ex-post content of the PBOC’s announcement or the direction of expectation changes ex-ante. As a

result, these explanations are ruled out as the main drivers of the pre-announcement drift of equity

returns.

First, it is possible that the market reacts well to some pre-leaked data if there is data leakage to

some extent. Second, another possibility is that the stock market may rationally expect the direction

of monetary aggregates statistics to change ex-ante. If any one of the two or both channels hold,

in order to realize the positive equity premium ex-ante, the stock market should respond to the

PBOC’s data release that reflects the monetary expansion in the economy. Hence, both of the two

explanations predict that the pre-announcement premium should be conditional, which depends

16

on the nature of the to-be-delivered PBOC’s statistics. In the following, we implement a series

of empirical tests to show that our documented pre-announcement premium is orthogonal to the

announcement contents.

We first break our M2 announcement events into two groups according to the difference of the

announced year-over-year (YOY) M2 growth data of a month month and that of previous month

∆gM2,m = gM2,m−gM2,m−1. This measures if the PBOC’s up-to-date monetary data are indicative

of monetary expansion ∆gM2,m > 0 or monetary tightening if ∆gM2,m < 0. Then, we augment the

exercise carried out for Figure 2 by plotting the average cumulative stock market returns around

the M2 announcements conditional on whether ∆gM2,m is positive (dashed line) or negative (solid

line) in Figure 3.

Figure 3 shows that both the Shenzhen and Shanghai markets exhibit cumulative drifting of

returns 3 days prior to the announcement regardless of whether the monetary data are ex-post

suggestive of expansionary or tightened monetary policy stance. In addition, for both markets,

the cumulative returns of either scenario fall into the ±1 standard deviation confidence band of

the other. Therefore, in terms of magnitude, no statistically significant difference can be drawn

regarding the pre-announcement premium with or without the positive changes of M2 growth.11

By contrast, after the data announcements are made public, the post-announcement market index

moves in two opposite directions. The cumulative returns, conditional on ∆gM2,m > 0, keep

increasing whereas conditional on a decrease of the M2 growth rate, fluctuates and drops by the

end of the announcement day. This post-announcement market behavior then justifies our claim

that the data of monetary expansion raise the equity prices.

To formally test the null of the two explanations in the regression analysis, we use three different

proxies to characterize the content of an M2 announcement. First, monthly changes in YOY M2

growth rate ∆gM2,m serve as our baseline measure. Second, we construct the “unexpected” innova-

tions to the stance of monetary aggregates such that εM2,m = gM2,m− gM2,m, where gM2,m denotes

the market-expected M2 growth rate as proxied by the median forecast of Bloomberg Economic

Forecast Survey. Third, we take the difference of the surveyed forecast of M2 growth rate and the

11However, we note that the realized mean pre-announcement cumulative returns associated with ∆gM2,m > 0 arerelatively higher on day tM2 − 1 than that of the scenario on the same day with ∆gM2,m < 0 in case of the Shanghaiexchange. Hence, we do not completely rule out the possibility of data leakages, which may help account for suchsubtle differences.

17

Figure 3: Cumulative Returns around M2 Announcements by ∆gM2,t

(a) Shenzhen Stock Exchange (b) Shanghai Stock Exchange

Notes: Sample: January 2010 to December 2016. This figure shows the average cumulative returns over 5-minuteblocks on the SZSE Component Index and the SSE Composite Index of a 7-day announcement window. The two panels differby the announcement groups categorized by ∆gM2,m > 0 (dashed line) and ∆gM2,m < 0 (solid line). The average cumulativereturns across all 7-day windows are centered on the first trading day when the market has access to the M2 announcements,as shown by the grey-shaded bar. The dotted line at the bottom denotes the average cumulative returns of 7-day windows ofnon-announcement days. The shadow areas mark ±1 standard deviation confidence bands around average returns conditionalon data to be released in M2 announcements.

realized M2 growth of previous month E[∆gM2,m] = gM2,m − gM2,m−1 as the expectation-based

measure of announcement content. In summary, positive (negative) ∆gM2,m, εM2,m, or E[∆gM2,m]

can all be considered extra expansion (tightening) of monetary policy or overall credit condition.

We then estimate the following specification to examine if the pre-announcement premium is con-

ditional on the content of M2 announcements.

Exrett = γ + β1ItM2−1,j + β2 · ItM2−1,j · ContenttM2 + β3 · ContenttM2 + βxXt + υt (3)

We take j = 3 by focusing on the return reactions during the 3-day window prior to announcement.

ContenttM2 on the announcement day of a given month is measured by monthly data of ∆gM2,m,

εM2,m, or E[∆gM2,m]. The coefficient associated with the interaction term β2 gives the estimate of

additional gain or loss, if any, due to changes in the announcement content.

We summarize the key estimation results in columns (2) to (4) of Table 3. The results suggest

that the mean daily pre-announcement premium is not affected by the content of announcement

regardless of how we define the PBOC’s statistics are indicative of monetary expansion. That is,

18

the relative daily excess returns of 3-day windows prior to announcement are consistently around 30

bps and the coefficients of the interaction terms are statistically insignificant. Specifically, suppose

the market reacts to the leaked data ex-ante, the exact expansion of monetary aggregates changes

by ∆gM2,m > 0 or the pre-leaked “unexpected” component of monetary expansion by εM2,m > 0

should shift the size of pre-announcement premium. This rationale, however, is not supported

by results of columns (2) and (3). If the market responds to the monetary expansion only in

expectation such that E[∆gM2,m] > 0, the coefficient estimate related to the interaction term of

column (4) should be positive. This again is not consistent with the evidence. Hence, we rule out

the possibilities that potential data leakages or expectation changes are the main drivers behind

the documented pre-announcement drift of equity returns.

In addition, one might wonder if investors’ earned pre-announcement premium may be driven

by the announcement content associated with statistics other than M2 growth but are co-released

in the same PBOC’s statement. According to Section 3 of the Online Appendix, M1, total out-

standing loan balance (Loan), and deposit balance (Deposit) are jointly released. In addition, the

balance of Total Social Financing (TSF), which is later considered another key measure of monetary

policy stance, is published some time before or after the M2 announcement albeit in a separate

statement on the same day. 12 Columns (5) to (8) of Table 3 present coefficient estimates about the

interaction term between dummy ItM2−1,3 and measure of content associated with other data statis-

tics, also measured as monthly difference of YOY growth rates: ∆gM1,m, ∆gLoan,m, ∆gDeposit,m,

and ∆gTSF,m. The results show that none of these content measures shifts the magnitude of the

pre-announcement premium.

Our results show that the sizable equity premium prior to M2 announcements is not simply

driven by data leakages or expectation changes, which is independent of the to-be-released content

of the incoming PBOC’s monetary announcements. In the following section, we provide a model

to account for the mechanism behind the pre-announcement premium.

12However, TSF data are quarterly statistics before 2016. At the end of 2016 , TSF data started being publishedmonthly and jointly within the same data release statement of monetary aggregates data. Thus, there are fewer dayreturn observations for regressions involving TSF data, and these regressions find insignificant coefficients associatedwith the interaction terms about TSF data.

19

Table 3: Announcement Premium: Content of Announcements

VARIABLES (1) (2) (3) (4) (5) (6) (7) (8)

ItM2−1,3 0.30*** 0.31*** 0.32*** 0.32*** 0.30*** 0.31*** 0.30*** 0.28(0.11) (0.11) (0.12) (0.12) (0.11) (0.11) (0.11) (0.26)

ItM2−1,3 ·∆gM2,m 0.09(0.12)

ItM2−1,3 · εgM2,m 0.10(0.16)

ItM2−1,3 · E[∆gM2,m] -0.08(0.15)

ItM2−1,3 ·∆gM1,m -0.01(0.03)

ItM2−1,3 ·∆gLoan,m 0.01(0.12)

ItM2−1,3 ·∆gDeposit,m -0.01(0.09)

ItM2−1,3 ·∆gTSF,m 0.03(0.05)

Year / Month / Weekday Dummies Yes Yes Yes Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes Yes Yes Yes YesLevel Term Ctrls Yes Yes Yes Yes Yes Yes Yes YesConstant -0.28 -0.27 −0.35+ -0.28 −0.31+ −0.33+ −0.30+ 3.02

(0.21) (0.21) (0.21) (0.23) (0.21) (0.23) (0.21) (3.69)

Observations 1,819 1,819 1,819 1,819 1,819 1,819 1,819 540R2 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.06

Notes: Sample: January 2010 to June 2017. This table reports the dummy variable regression results of Equation (3). Thedependent variable is the close-to-close excess returns constructed from the Wind A-Share Index. Announcement dummyItM2−1,j equals 1 if a trading day falls in the j-day window before the announcement. ***, **, *, and + denote significanceat 1%, 5%, 10%, and 15%, respectively. Robust standard errors are in parentheses.

5 Model

In this section, we present a model that generates a positive pre-drift of market returns while

the investors anticipate an incoming announcement made by the central bank regarding the growth

of money supply. The key mechanism is that investors can learn about monetary data prior to

announcements, which helps mitigate their forecast uncertainty about economic fundamentals.

This further leads to decreased aggregate risk, which boosts the equity price. In the spirit of Sims

(2003), our model features the endogenous choice of information demand made by investors who

have limited attention to learn. By optimizing attention and learning, equity prices can increase

prior to announcements as uncertainty is lowered.

Specifically, our model accommodates “quasi-scheduled” public announcements. In other words,

even though investors, when entering a month, do not know the exact day of the central bank’s

data release announcement for that month, they are certain that some data will be released, sooner

or later, with probability one. In the model, an announcement with updated data may arrive early

20

or late in a month, and investors are not able to draw highly informative signals about the data

when it is too early to do so. Investors would pay attention to learning about monetary data

only when information demand starts bringing value. It follows that the size of the uncertainty

reduction driven by investors’ attention allocation depends on the timeliness of the announcement

arrival. Our model highlights the importance of having information demand to account for the

pre-announcement premium.

Ultimately, apart from rationalizing Chinese evidence, this model helps to explain the short-

lived pre-FOMC announcement premium even though the U.S. market is well informed of the

pre-fixed Fed’s announcement schedule ahead of time. Investors learn about the potential changes

in the federal funds rate target when it gets very close to the FOMC meeting days. Thus, jumps

of equity prices arise from increased information demand a few hours before the FOMC statement

release.

5.1 Environment

The model is discrete-time and each period t corresponds to a day.A central bank closely

monitors log changes in the balance of monetary aggregate for the economy on a daily basis,

that is, daily growth rate of money supply mt. For simplicity, mt is assumed to be evolving via a

stationary AR(1) process

mt = ρmt−1 + (1− ρ)µ+ et (4)

where ρ ∈ (0, 1) governs the persistence of money growth and et ∼ N(0, σ2e) captures the indepen-

dently and identically distributed (i.i.d.) innovations to the money growth process. µ ≥ 0 denotes

the unconditional mean of the daily growth rate of money supply.

We assume that the state of money growth can be perfectly known to market investors only

through the central bank’s monthly announcements, which are “quasi-scheduled”. This setup is

in line with the publication routine of the PBOC’s monetary announcements in China. Suppose

each month i for i = 0, 1, 2, ... has N > 0 days and ti denotes the end day of month i such that

ti = i ·N . We then lay out a formal definition of “quasi-scheduled” announcements as follows.

Definition 1 (Quasi-scheduled Announcements) Monthly announcements are quasi-

21

scheduled if: (1) every month, an announcement is to be made with probability one. The

announcement day tAi falls on a particular day of month i such that tAi = ti−1 + T with

T ∈ 1, ..., N; (2) T , unknown to investors entering month i until tAi , is independently and

identically drawn from a given distribution with cumulative density function F (T ) ∀ month i.

Then, we model the central bank’s announcements as monthly public signals informing investors

of the money growth rate realized on the announcement days tAi .13 Thus, signal stAiis given by

stAi= mtAi

. (5)

According to Equation (5), on the announcement day, the money supply growth rate is perfectly

revealed to the market.14 For illustrative purposes, we draw a time line in Figure 4 to recapitulate

the baseline environment of our model.

Figure 4: Time Line of Monetary Announcements

Date t

ti−1

end of month i− 1ti

end of month iti+1

end of month i+ 1

announcement about mtAiannouncement about mtAi+1

tAi tAi+1

5.2 Benchmark Results

We first derive the results of a benchmark case of the model when investors do not endogenously

acquire information apart from receiving central bank signals. Without loss of generality, suppose

investors stand on a day between two announcement dates of tAi and tAi+1. Conditional on the

13The daily growth rate can be easily converted to a lower-frequency growth rate in order to be aligned with thereality of announcement routines, by which monthly, quarterly, or yearly statistics are released.

14There are additional complexities associated with how we define an announcement signal. First, announcementscan be backward looking or may publish real-time statistics. For instance, the U.S. FOMC statement publishes thefederal funds rate target determined at the most recently convened FOMC meeting, which reflects the monetarypolicy moves around the announcement time. By contrast, a PBOC announcement publishes some statistics of theprevious observation cycle. For example, in May, the PBOC announces the YOY M2 grow rate of April. Second,data initially released are subject to measurement errors and rounds of ensuing revisions. Considering these factors,in Section C.2 of the Appendix, we redefine signals as backward looking containing measurement errors. We showthat our theoretical results are robust to extra complications.

22

information delivered through a previous announcement made on day tAi , we can compute investors’

expectation of the money growth rate of a day t prior to the announcement to be made on tAi+1 such

that t < tAi+1. mt denotes investors’ conditional expectation, that is, investors’ pre-announcement

forecast of money growth to be realized on day t. For ease of notation, we define ∆it = t− tAi ≥ 0,

the number of gap days between future day t and the previous announcement day tAi . By the Bayes’

rule and the AR(1) structure, the market-expected growth rate of money supply is

mt = ρ∆itmtAi

+ (1− ρ∆it)µ. (6)

Equation (6) suggests that investors’ forecast of money growth of future day t is a weighted average

of previously formed beliefs about mt, the true state revealed through previous announcement mtAi,

and the unconditional mean µ, the a priori mean of the growth rate of money supply. Investors

update mtAiover ∆i

t days by assigning weight ρ∆it < 1. As ∆i

t increases, investors’ confidence of

previously formed beliefs erode. At the same time, the forecast moves increasingly close to µ as

the weight attached to the a priori mean 1− ρ∆it gradually increases to 1.

Similarly, for the variance of money growth rate conditional on investors’ forecast, it follows

that

σ2m,t = (1− ρ2∆i

t)σ2e

1− ρ2(7)

σ2m,t measures the size of investors’ forecast uncertainty regarding the money growth rate of day

t. By Equation (7), forecast uncertainty up to day t takes a proportion of 1 − ρ2∆it ≤ 1 out of

the unconditional variance of money growth, σ2e

1−ρ2 . As time t evolves, larger ∆it makes investors’

forecasts about mt become increasingly uncertain over time. As a result, forecast uncertainty moves

closer to the a priori variance of money growth.

Equation (7) implies that investors’ forecast uncertainty about money growth keeps accumulat-

ing until the arrival of the next announcement. Given that the new announcement perfectly reveals

mtAi+1, accumulated forecast uncertainty then sharply drops to zero on the announcement day tAi+1.

Thus, we have the following proposition.

Proposition 1 In our baseline environment, for each monthly cycle, investors’ forecast uncertainty

23

accumulates over time from the previous announcement day tAi , peaks on day t = tAi+1 − 1, and

collapses to zero conditional upon the arrival of the next announcement made on day tAi+1 = ti + T

with T ∼ F (T ).

By Proposition 1, the exact announcement day tAi+1 = ti + T differs across months given the

random draw of T for each month. This implies that early or late arrivals of announcements for

different months are associated with different peak sizes of pre-announcement forecast uncertainty

on day tAi+1 − 1. Hence, investors develop greater uncertainty when it takes more days for the

central bank to release the next signal. For illustrative purposes, we plot an example evolution

of forecast uncertainty regarding money growth over months in Figure 5, which shows that the

pre-announcement peak of forecast uncertainty varies across months.

Figure 5: Example Path of Uncertainty Dynamics and Announcement Cycles

Notes: t corresponds to a day. Each month i is marked by two end points of ti−1 and ti, and has a duration of Ndays. tAi indicates the day on which an announcement is made.

We further explore the implications of this announcement environment for equity premium. We

work with the fundamental equation regarding the expected excess return of stock market portfolio

as follows:

EtRt+1 −Rft+1 = α · σ2x,t+1 (8)

where EtRt+1 − Rft+1 measures the expected return on the stock market portfolio relative to risk-

24

free rate Rft+1. The expectation operation is taken with information available up to day t. σ2x,t+1

denotes the conditional variance of market portfolio returns for day t+ 1. With α > 0, the equity

premium increases with the risk of the stock market.15 If follows that

∂[EtRt+1 −Rft+1]

∂σ2m,t+1

= α ·∂σ2

x,t+1

∂σ2m,t+1

(9)

We then take an assumption as follows

Assumption 1 The risk of the stock market increases with the conditional variance of money

growth for any day t such that∂σ2x,t

∂σ2m,t

> 0

Given the assumption, it yields that higher forecast uncertainty raises the equity premium by

incorporating larger market risk such that∂[EtRt+1−Rft+1]

∂σ2m,t+1

> 0. To establish the validity of the

assumption, we first show in Section A of the Appendix that evidence based on surveys of profes-

sional forecasts suggests that forecast uncertainty about money growth is more generally linked to

uncertainty about broader economic fundamentals in China. Then in Section C.1 of the Appendix,

we explicitly derive an equilibrium condition within a more elaborate model framework such that

the equity premium increases with the conditional variance of future money growth. Second, we

stress the fact that with the partial derivative expression in Equation (9), other macroeconomic

variables may also shift the aggregate market risk. We show in Section B.3 of the Appendix that

China’s equity market exhibits positive excess returns prior to some non-monetary macroeconomic

announcements, although the pre-announcement premium is more robustly associated with the

PBOC’s announcements of monetary aggregates data.

Thus, we obtain Proposition 2 governing the relationship between the equity premium and the

forecast uncertainty about money growth.

Proposition 2 If the aggregate market risk increases with the forecast uncertainty about money

growth, then lower forecast uncertainty about money growth leads to higher equity prices by reducing

the market risk.

Proposition 2 establishes a negative relationship between forecast uncertainty about money

15Equation (8) can be derived from various forms of capital market asset-pricing models. See Mehra and Prescott(1985), Fama and MacBeth (1993), and Section C.1 of the Appendix for a derivation of this equation with recursivepreference. For example, α can denote investors’ coefficient of relative risk aversion and is positive.

25

growth and the current level of stock prices. However, this baseline result is derived from an

environment in which investors have no other useful information in between announcements to

form better forecasts about money growth, by which the equity premium will be realized on the

announcement days only. In order to generate pre-announcement premium, we next enrich the

model structure by having investors optimally choose when and how much attention to pay to

learning about the growth rate of money supply prior to the incoming announcement. We show

that learning during the pre-announcement period drives down the forecast uncertainty over time,

which triggers an accumulation of excess equity returns.

5.3 Attention and Learning

In this subsection, we build in investors’ endogenous choice of acquiring information prior to

announcements, which results from investors weighing the marginal gain of learning against the

cost of doing so. We employ the framework of rational inattention to endogenize the decision of

information demand. In other words, subject to some constraint of information-processing capacity,

investors allocate an optimal amount of attention to learning about the money growth rate.

Specifically, we assume that on day t, money growth mt is realized and investors observe whether

or not the central bank makes the announcement. Then, if there is no announcement, investors

decide how much attention to pay to learning about money growth. By paying attention, investors

may draw an informative signal ft about mt with probability φt ∈ (0, 1) such that

ft = mt + ut. (10)

The noise term ut is orthogonal to the true state of money growth and is i.i.d. drawn from N(0, σ2u,t).

Equation (10) suggests that investors’ forecast uncertainty about mt conditional on exploiting the

information of ft is given by σ2u,t. The probability φt can be interpreted as the proportion of useful

information outstanding in the market accessible to investors for digesting and forming better

forecasts about money growth.

With probability 1−φt, investors may run into bad luck and draw a very noisy signal. We define

this noisy signal as f0,t = mt + ηt with ηt ∼ N(0, σ2η,t). For simplicity, we impose the regularity

condition σ2η,t = σ2

m,t such that the drawn signal, if it’s noisy, adds no extra information value

26

relative to the forecast variance about mt if no attention is paid, as denoted by σ2m,t.By Equation

(4), σ2m,t can be written as a function of ex-post forecast uncertainty of day t− 1 after the learning

decision of day t− 1 was taken, such that

σ2m,t = ρ2σ2

m,t−1 + σ2e (11)

For each day, investors solve the optimal attention allocation problem by minimizing the expect-

ed quadratic loss due to suboptimal belief relative to the true state mt:12φtE[mt − E(mt|ft)]2 +

(1 − φt)E[mt − E(mt|f0,t)]2.16 Substituting out the signal structures, investors choose optimized

signal noisiness σ2u,t to solve the constrained optimization problem as follows:

maxκt− 1

2[φtσ

2u,t + (1− φt)σ2

m,t]− vκt (12)

s.t. σ2u,t = 2−2κt σ2

m,t with 0 ≤ κt ≤ κ (13)

In particular, we assume that the optimized informative signal cannot be perfect such that

σ2u,t > 0 for any day t. This assumption can be rationalized by the constraint of Equation (13)

that the maximum amount of information inflow upon learning from the optimized informative

signal per day is bounded by an information-processing capacity. In models of rational inattention,

the entropy measure H(z) = 12 log2 σ

2z gauges the quantity of perceived uncertainty regarding a

normally distributed random variable z. It follows that the amount of information inflow can be

expressed using entropy notations as κt = H(mt) − H(E(mt|ft)) ∈ [0, κ], where κ denotes the

capacity bound. This yields σ2u,t = 2−2κt σ2

m,t and we observe σ2u,t < σ2

m,t as long as κt > 0. Thus,

κt is interpreted as the actual use of information capacity, that is, the optimized degree of attention

allocated to learning about mt, which then determines the size of σ2u,t. Therefore, endogenously

paying attention by exploiting informative signals helps mitigate the forecast uncertainty relative

to that of the no-attention scenario.

In addition, by Equation (12), optimizing attention is assumed to incur a marginal cost of

paying attention, v > 0. This cost may capture the opportunity cost when investors pay attention

16Quadratic loss minimization can be derived from utility maximization with a second-order approximation. Weprovide an example in Section C.3 of the Appendix.

27

to learning about money growth but remain inattentive to other variables of interest, which brings

in quadratic loss. Note that the marginal benefit of paying attention, φtσ2m,t log(2)2−2κt , decreases

with κt. It follows that the maximum marginal benefit at κt = 0, if dominated by the marginal cost

v, generates no value for attentive learning. Hence, learning is irrelevant when φt · σ2m,t < v = v

log(2) .

Thus, we can characterize the optimal degree of attention allocation using a step function depending

on the range of φt given σ2m,t such that

κ∗t =

κ if φt ∈ [ v

σ2m,t

22κ, 1]

12 log2[

φtσ2m,t

v ] if φt ∈ [ vσ2m,t, vσ2m,t

22κ)

0 if φt ∈ [0, vσ2m,t

)

(14)

Equations (14) suggest that larger φt and σ2m,t call for greater attention input from investors.

In other words, when investors have greater chance to draw precise information and when the

forecast uncertainty of no learning is too large, investors optimally devote more attention to learn

about money growth. Eventually, increased attention devotion reaches the information-processing

capacity, which results in constrained learning. We then obtain the following proposition.

Proposition 3 When information demand is endogenous, investors pay attention to learn about

money growth if (1) the probability of drawing useful information, φt, or (2) the forecast uncertainty

of no learning, σ2m,t, is sufficiently large such that φt · σ2

m,t ≥ v

We map the different types of learning decisions in a two-dimensional space of φt and σ2m,t in

Figure 6. It shows that φt and σ2m,t have to be jointly sizeable in order to trigger attentive learning,

regardless of whether it’s unconstrained (the medium-grey area) or constrained ( the dark grey

area). Given an extremely large probability of drawing informative signals or high level of forecast

uncertainty if learning is not applied, investors would do very intensive learning subject to the

capacity constraint.

28

Figure 6: Decision of Attentive Learning over Space of φt, σ2m,t

Notes: The y-axis denotes the forecast variance about mt if no learning is applied. Tickσ2e

1−ρ2 is the upper bound

of forecast variance of money growth rate mt given by Equation (7). The x-axis marks the probability of drawing informativesignals.

Accordingly, after the learning decision is incorporated, for all months i, the forecast variance

for money growth of day t can be summarized as follows:

σ2m,t =

(1− φt)σ2m,t + φtσ

2m,t2

−2κ if φt ∈ [ vσ2m,t

22κ, 1] and t 6= tAi

(1− φt)σ2m,t + v if φt ∈ [ v

σ2m,t, vσ2m,t

22κ) and t 6= tAi

σ2m,t if φt ∈ [0, v

σ2m,t

) and t 6= tAi

0 if t = tAi

(15)

Equation systems (11) and (15) fully characterize the dynamics of forecast uncertainty when

information demand via attention allocation is endogenous. In summary, when investors find

it unnecessary to be attentive, they let go of the accumulation of forecast variance over time.

Conditional on learning as 0 < κ∗t ≤ κ, the optimized noisiness associated with attentive learning

scales down the forecast uncertainty such that (1−φt)σ2m,t+φtσ

2m,t2

−2κ∗t < σ2m,t. Though, too large

φt or σ2m,t requires the maximum amount of attention and exploits the full information capacity of

the day.

We next discuss the relationship between the dynamics of forecast uncertainty about money

29

growth and the equity premium. By Proposition 2, lower forecast uncertainty about money growth

prior to announcements can generate the pre-announcement premium by raising the equity prices.

We offer the following proposition to highlight the key model mechanism that generates this pre-

announcement drift of excess returns.

Proposition 4 (Uncertainty Reduction and Pre-announcement Premium) When infor-

mation demand is endogenous, sufficiently large uncertainty and high probability of drawing in-

formative signals within a few days before the announcement lead to continuous reduction of un-

certainty and accumulation of excess returns.

To shed light on the dynamics of forecast uncertainty and the pre-announcement equity premi-

um, Equations (15) suggest that given sizable φt at any level of σ2m,t, the attentive learning results

in a lowered forecast uncertainty σ2m,t, which serves as the starting scale of uncertainty before the

learning decision of day t + 1 is taken. Therefore, according to Figure 6, as long as φt+1 and

σ2m,t+1 are still within the reasonable range that triggers the attentive learning, uncertainty will

be further contained on day t + 1. This dynamics carries over to future days until the arrival of

the next announcement when the true state of money growth supply is revealed. As a result, φt’s

that start trivial at the beginning of a monthly announcement cycle but become larger prior to

announcements can support a path of uncertainty accumulation when no learning is applied, as

followed by days of uncertainty reduction after attention is paid. A sequence of declining forecast

uncertainty is thus coupled with a series of equity price jumps.

A critical condition associated with Proposition 4 is that the probability of drawing informative

signals is high for days prior to announcement. Reasonably, as the announcement day draws closer

in a monthly announcement cycle, more information source could be available for investors to

aggregate and analyze, which necessarily increases the probability of drawing informative signals

about money growth.

In Figure 7, we plot an example path of forecast variance evolution of month i when informa-

tion demand is endogenous along with a baseline path of uncertainty dynamics without learning.

Specifically, starting from the first day of month i, the black-circled line denotes the baseline path

of forecast uncertainty. This is the case when the central bank’s announcements are the only source

of information. On announcement day tAi , uncertainty drops to zero and then kicks off another

30

round of accumulation into the next announcement cycle.

On the contrary, the blue dashed line captures the path of forecast uncertainty when information

demand is endogenous. To trigger learning, we feed in a series of probabilities of drawing informative

signals, which starts at a low level of 5 % on day 1 and increases at a constant daily rate of 30

% until being bounded by one. When the announcement is made on the 12-th day of the given

month, φt is again reset to 5 % and stays constant till the end of month. As t moves forward, it

shows that forecast uncertainty is reduced from the trigger-point day of day 6 when φt and forecast

uncertainty of no learning climb high. As a result, a series of uncertainty reduction follows until

the announcement day, during which either unconstrained learning or constrained learning can be

applied depending on parametrization. Once the announcement is made, forecast uncertainty again

collapses to zero. Thereafter, starting with low uncertainty and low probability of drawing useful

information, investors begin to stay rationally inattentive by letting uncertainty accumulate.

Figure 7: Example Path of Attention-driven Uncertainty Reduction

Notes: Under parametrization of increasing probabilities of drawing an informative signal φt+1 = (1 + g)φt withφ1 = 0.05, g = 0.3 and φtAi +j = 0.05 for j ≥ 0. The vertical red dotted line marks the day of monetary announcement.

The black solid line dotted with circles captures the initial accumulation and reduction of uncertainty conditional on theinformation delivered through announcement only. The blue dashed line denotes the path of uncertainty when learning is

endogenous. Tickσ2e

1−ρ2 is the upper bound of forecast variance of money growth rate mt, as given by Equation (7).

In summary, a model of investors with information demand choices may generate endogenous

reductions of forecast uncertainty and a pre-announcement drift of stock returns. Note that our

model does not rely on full or partial disclosure of central bank’s to-be-announced information in

31

the form of data leakage to deliver this ex-ante premium.

5.4 Testable Hypotheses

In this subsection, we discuss important implications derived from our model. These model

predictions are further tested against the data to establish the empirical relevance of our model

framework.

Uncertainty Dynamics Prior to Announcement. Our model highlights the key channel

through which attention-driven uncertainty reduction generates pre-announcement drift of equity

returns. Thus, we test the following two hypotheses.

Hypothesis 1 Measures of forecast uncertainty decline before the arrival of the PBOC’s monetary

announcements.

Hypothesis 2 Across announcement events, greater uncertainty reductions are associated with

larger cumulative excess equity returns.

Hypothesis 1 is tested against the data using measures of uncertainty constructed from professional

forecasts and China’s stock market volatility. We test whether Hypothesis 2 holds by examining the

cross-event correlation of the size of pre-announcement uncertainty reduction and the magnitude

of accumulated equity excess returns. These empirical tests provide the validity checks of the key

model mechanism behind the pre-announcement premium.

Early vs. Delayed Arrivals of Announcements. Assumptions that φt and σ2m,t are large

enough prior to announcements are pivotal for Proposition 4 to hold. With quasi-scheduled mon-

etary announcements, a key model implication is that greater size of daily uncertainty reduction

should be associated with more delayed announcements. To observe this, we express daily changes

in uncertainty ∆σ2m,t = σ2

m,t − σ2m,t−1 in the following according to Equations (11) and (15)

∆σ2m,t =

[1− φt(1− 2−2κ)]σ2

m,t − σ2m,t−1 if φt ∈ [ v

σ2m,t

22κ, 1]

(1− φt)σ2m,t + v − σ2

m,t−1 if φt ∈ [ vσ2m,t, vσ2m,t

22κ)

σ2e − (1− ρ2)σ2

m,t−1 ≥ 0 if φt ∈ [0, vσ2m,t

)

(16)

32

Equation (16) shows that uncertainty reduction ∆σ2m,t < 0 must be achieved via attentive learning.

Thus, the following proposition regarding the size of uncertainty reduction holds.

Proposition 5 With uncertainty reduction ∆σ2m,t < 0, larger probability of drawing informative

signals φt generates larger uncertainty reduction such that∂|∆σ2

m,t|∂φt

> 0.

In the data, more delayed announcement and investors’ extended time waiting for the announce-

ment make it possible for useful information about money supply growth to accumulate more, which

could raise φt. Thus, we expect the size of the equity premium and the magnitude of uncertainty

reduction before announcements to be more pronounced when the PBOC’s announcements are

delayed. Therefore, we test the following hypothesis.

Hypothesis 3 Larger pre-announcement premium is associated with more delayed announcement

arrival.

Then, we test if the size of the uncertainty reduction is also related to how much an announcement

is delayed.

Hypothesis 4 Across announcement events, greater uncertainty reductions are associated with

even more delayed announcement events.

Attentive Learning and Uncertainty Reduction. Our model highlights that investors’ atten-

tion allocation prior to central bank’s announcements helps reduce the forecast uncertainty about

money growth. To examine the link between attentive learning and uncertainty dynamics, the

keyword-based search index as constructed by Baidu, Inc., the leading Chinese search engine, is

adopted to proxy for the intensity of paid attention in China to learning about monetary aggregates

data and PBOC’s monetary policy. We continue testing the following two hypotheses.

Hypothesis 5 Measures of attention allocated to learning about monetary aggregates data and

monetary policy are higher prior to the PBOC’s monetary announcements than that of an average

day outside the announcement windows.

Hypothesis 6 Across announcement events, greater uncertainty reductions are associated with

larger intensity of attention.

33

6 Empirical Tests

In this section, we do a series of empirical tests for Hypotheses 1 to 6 and show that our model

implications are consistent with the data.

First, we demonstrate that uncertainty measures as constructed from the forecast data and stock

return volatility decline prior to M2 announcements. Second, we provide evidence that the size of

the pre-announcement premium is positively correlated with the degree of uncertainty reduction

prior to announcements. Third, our empirical results suggest that larger uncertainty reduction and

greater pre-announcement premium are associated with announcement events when the PBOC

delays releasing monetary data. In addition, we present the evidence that attention allocated to

learning about monetary aggregates data and monetary policy changes is higher before the PBOC’s

announcements. Finally, we show that the size of uncertainty reduction prior to announcements

increases with the intensity of attention allocation ex-ante.

6.1 Uncertainty Declines Before Announcements

We test Hypothesis 1 in the data by examining whether forecast uncertainty about the growth

of aggregate money supply declines before the PBOC’s monetary announcements. We construct

two empirical measures to proxy for investors’ uncertainty about money growth: first, the daily

dispersion of Bloomberg-surveyed forecast errors about M2 growth before M2 announcements;

second, daily stock return volatility aggregated over 5-minute returns in announcement windows.

The Bloomberg Economic Forecast Survey database records an unbalanced panel of individual

forecasts of various macroeconomic variables. In particular, we examine the dispersion of forecast

errors about M2 growth conditional on how close the surveyed day of forecasts is from the day of

the associated M2 announcement. We compute the dispersion of forecast errors instead of that of

forecast levels. This is because the distribution of individual forecasts of the M2 growth rate for a

given month made on the j-th day before the announcement does not maintain the same mean, that

is, the true state of M2 growth under the rational expectation assumption, across distributions of

different announcement events. This “demeaned” dispersion of pre-announcement j-th day forecast

errors helps identify the outstanding “average” uncertainty about the M2 growth rate ex-ante as a

function of how close forecasters are from perfectly being informed of the true state. In addition,

34

in Section A of the Appendix, we show that this forecast-based uncertainty about money growth is

correlated with uncertainty measures regarding a range of other macro variables. Thus, we argue

that uncertainty about the growth rate of money supply in China is linked to aggregate market

risk, which is more generally concerned with economic fundamentals.

Stock market volatility is conventionally treated as a measure of aggregate market risk that is

not necessarily tied to monetary policy (Bloom, 2014). However, given that a stock market itself is

an aggregator of future macroeconomic news (Beaudry and Portier, 2006), its return volatility when

situated within the window of monetary news can be the best measure among few alternatives. 17

6.1.1 Time Plots

Some suggestive evidence of time plots is first provided. Figure 8 plots the dynamics of fore-

cast uncertainty measured in the standard deviation of forecast errors over time. To smooth out

dispersion of forecast errors over days, we take 3-day (dashed line) and 5-day (solid line) centered

moving averages of daily standard deviations. These dispersion measures are computed based on

66 economists’ 1902 forecast points after we delete forecasters who made fewer than five forecasts

from the sample. Horizontally, we obtain the number of days that a given forecast survey day lags

the PBOC’s M2 announcement. Since there are few forecasts made on the day right before an

announcement day, we remove these observations that bias our measure of forecast uncertainty.

Time plots in Figure 8 clearly suggest that the forecast uncertainty first climbs, stays constant

if not fluctuating, and eventually starts declining a few days before the announcement is made.

Therefore, dynamics of forecast uncertainty before announcements is hump shaped. Qualitatively,

the path of this forecast-based uncertainty measure is consistent with our model’s predicted uncer-

tainty path when information demand is endogenous, as in Figure 7.18 Importantly, the evidence

shows that forecast uncertainty has to accumulate to higher levels before uncertainty reduction is

triggered.

17It is important to note that there is no option-based implied volatility index for China’s stock market exchangesspanning our entire sample coverage. In addition, text-based uncertainty proxies in the spirit of Baker, Bloom, andDavis (2016) are not readily available at the daily frequency for studying PBOC’s monetary policy uncertainty.

18In the data, forecasters are forecasting a single M2 growth number associated with a particular month. Theseforecasts may not correspond well to the forecast of daily money growth associated with a particular day in ourmodel. However, as long as we are focusing on the pre-announcement period when forecasters do not observe thetrue state of M2 growth before a PBOC’s announcement is made, uncertainty about future realization of M2 growth,no matter if it’s aggregated up to monthly or not, first accumulates and then declines once learning is applied.

35

Figure 8: Dispersion of Forecast Errors Prior to M2 Announcements

Notes: Sample: January 2010 to June 2017. This figure shows the dynamics of dispersion of forecast errors beforean M2 announcement. j marks the j − th calendar day before the announcement day, which is the first trading day that themarket has access to the updated monetary data. The dashed line and the solid line denote the centered 3-day and 5-daymoving averages of daily standard deviations of forecast errors regarding the to-be-released M2 growth statistics, respectively.

We then compute the mean daily return volatility aggregated over 5-minute trading blocks for an

average 11-day window centering the M2 announcement for both Shenzhen (SZSE) and Shanghai

(SSE) market indexes. These two volatility series are further normalized by dividing them by their

corresponding unconditional mean of daily volatility for days excluding all 11-day announcement

windows. If the relative volatility falls below one, it implies that the level of uncertainty on that

day is lower than that of an average non-announcement window.

In Figure 9, we plot the two relative return volatility series. The figure shows that regardless

of stock exchanges, across all M2 announcement windows in our sample, there is a clear trend

of uncertainty reduction before announcements. Strikingly, this continuous reduction of volatility-

based uncertainty measure initializes 3 days before announcements, which co-moves with the pre-

announcement drift of returns for a duration of 3 days. In addition, the decline of relative volatility

hits the bottom on the day right before announcement. This significantly lower degree of uncertainty

relative to that of an average day outside the announcement windows squares well with our findings

36

Figure 9: Stock Return Volatility in Windows of M2 Announcements

Notes: Sample: January 2010 to December 2016. This figure shows the average relative daily stock market returnvolatility to non-announcement window averages, which aggregates 5-minute return blocks per day on the SZSE ComponentIndex and the SSE Composite Index around an M2 announcement. t = 0 marks the first trading day on which the market hasaccess to the announcement as denoted by a vertical solid line. j captures the relative volatility |j| days after (before if j isnegative) the announcement. The solid line and the dashed line denote the relative return volatility of the SSE index and theSZSE index, respectively.

from Table 1 that the coefficient estimate associated with tM2 − 1 has the most significance. Lastly,

the relative volatility remains flat throughout the post-announcement period, which is aligned with

our findings that no significant post-announcement drift of returns is detected in Chinese markets.

6.1.2 Identifications

At the forecast level, Bloomberg forecast data enable us to estimate the size of forecast-specific

uncertainty directly, as measured by how far a particular forecast point about M2 growth is from

the released statistics, as a function of the number of days when this forecast is surveyed from the

associated M2 announcement day. We run the regression of the empirical specification as follows:

|FEi| = γ + α ·Distancei + β ·Distance2i + γLateDaysi + θLateDays2

i + τ ·X + ei (17)

37

To proxy for the forecast-level uncertainty, the absolute value of forecast error of a particular

forecast point i surveyed on day t, |FEi|, is taken as the dependent variable. Distancei captures

the number of gap days by which a survey day of forecast i lags its associated announcement day.

To capture the potential non-linearity, we have the squared term of day distance in the regression.

In addition, given that forecasts about an M2 number are routinely spread over dispersed days

before announcements, we are also concerned whether later forecasts are more precise than those

made earlier regardless of how close a forecast is from the announcement day. To control for timing

effect, we construct a measure called LateDaysi, which takes the day difference of the date of a

forecast i and the end date of the previous calendar month. Precisely, if a forecast of the to-be-

released M2 growth number this month is surveyed j days after (before if negative) the end of

the previous month, we label this forecast a relatively late (early) one such that LateDaysi = j.

LateDaysi along with its squared term LateDays2i are included for regression. We also have the

forecaster fixed effects, and year fixed effects included in the covariate vector X to ensure the

robustness of our main results.

The estimation results are shown in Table 4. By including the term of Distance2i , the estimation

gives a better fit, as both the coefficient estimates related to the linear and the squared terms are

significant, as shown in column (2). Considering the forecaster fixed effects, the results in column

(3) suggest that 1 day closer to the announcement day reduces the forecast-level uncertainty by

0.035. However, for some forecasts made much earlier than the announcement day, the forecast-

level uncertainty could also be small owing to the negative coefficient of the squared term. In

the middle range of distance, forecast-level uncertainty is higher. Hence, we find a similar hump-

shaped forecast-level uncertainty as a function of days from announcement, which is consistent with

Figures 7 and 8. The coefficient estimates of terms LateDaysi and LateDays2i are not statistically

significant according to column (4). This confirms that the hump-shaped uncertainty dynamics are

not driven by the lateness of a forecast relative to other forecasts but rather by its relative distance

from the arrival of the PBOC’s announcements.

Resorting to the measure of uncertainty as proxied by stock return volatility, we directly test

if return volatility prior to M2 announcement is lower than that of other days outside the pre-

announcement windows, which is a further test of Hypothesis 1 . We estimate the following model of

dummy regressions with ItM2−1,j = 1 denoting the day that falls into a pre-announcement window

38

Table 4: Hump-shaped Dynamics of Forecast-level Uncertainty

(1) (2) (3) (4)VARIABLES Pooled OLS Pooled OLS FE Model FE Model

Distancei -0.004 0.049*** 0.035** 0.035**(0.004) (0.017) (0.016) (0.016)

Distance2i -0.003*** -0.002*** -0.002**(0.001) (0.001) (0.001)

LateDaysi -0.010(0.013)

LateDays2i 0.002(0.001)

Forecaster FE Yes YesYear Dummies YesConstant 0.665*** 0.456*** 0.515*** 0.773***

(0.038) (0.079) (0.072) (0.257)

Observations 1,902 1,902 1,902 1,902R2 0.001 0.005 0.004 0.045

Notes: Sample: January 2010 to June 2017. This table reports the regres-sion results of Equation (17). The dependent variable is the absolute valueof forecast error of a particular forecast point i surveyed on day t, |FEi|. Atotal of 1902 forecast points of 66 forecasters are included in the sample af-ter we delete the forecasts of those professional forecasters who made fewerthan five forecasts. ***, **, *, and + denote significance at 1%, 5%, 10%,and 15%, respectively. Standard errors are clustered at the forecaster leveland are shown in parentheses.

of j days long for j = 1, 2, 3:

Ret V olt = γ + βjItM2−1,j + βxXt + υt (18)

where the estimate of βj captures the size of daily stock return volatility before an M2 announce-

ment day relative to a mean level of uncertainty for days outside these windows. We stack the

return volatility data of Shanghai and Shenzhen stock exchange indexes and include a dummy

variable to control for the mean difference of return volatility.19

Table 10 presents estimation results aligned with the key message from Figure 9. First,

volatility-based uncertainty is relatively smaller for a few days before the arrival of M2 announce-

ments. Second, we observe across columns that the closer the days of a window are to an announce-

ment, the lower is the average daily volatility. This precisely suggests that the forecast uncertainty

keeps declining from a higher level until reaching the bottom just 1 day prior to the announcement.

19Thereafter, we report the regression results when the return volatility data of the two exchanges are stackedtogether. We find that running estimations of individual stock exchange index separately does not change ourestimation results using stacked data.

39

Table 5: Relatively Low Uncertainty Prior to M2 Announcements

VARIABLES (1) (2) (3)

ItM2−1 -0.19***(0.04)

ItM2−1,2 -0.16***(0.04)

ItM2−1,3 -0.13***(0.03)

Year / Month / Weekday Dummies Yes Yes YesOther Anns Window Ctrls Yes Yes YesStock Exchange Dummy Yes Yes YesConstant 1.28*** 1.28*** 1.28***

(0.06) (0.06) (0.06)

Observations 3,400 3,400 3,400R2 0.29 0.29 0.29

Notes: Sample: January 2010 to December 2016. This table reports dummy variable regression results of Equation (18)for different specifications. The dependent variable is stacked daily stock return volatility data covering both Shanghai andShenzhen stock exchanges. The announcement day dummy ItM2−1,j equals one for the trading days in a j-day windowbefore an M2 announcement. “Other Anns Window Ctrls”: controls for the remaining day dummies of the announcementwindow of length of 2T +1 as T = 5. “Year/Month/Weekday Dummies”: controls for the year, month, and weekday effects.“Stock Exchange Dummy”: equals 1 if the return volatility data is constructed based on Shanghai Stock Exchange Index.***, **, *, and + denote significance at 1%, 5%, 10%, and 15%, respectively. Robust standard errors are in parentheses.

6.2 Correlations: Uncertainty Reduction and Premium

We have shown that our measures of uncertainty decline before M2 announcements. We now

test the null of Hypothesis 2 to evaluate whether the size of uncertainty reduction is associated with

the size of the pre-announcement equity premium by exploiting the variation across announcement

events. However, the limited number of forecast observations per announcement event is unable to

give us an unbiased account of uncertainty reduction for days right before the PBOC’s announce-

ment.Hereafter, we stick to the stock-market volatility as the proxy for forecast uncertainty when

identifications are done in the cross-event dimension.

Specifically, across announcement events, we estimate the partial effects of uncertainty reduction

on excess returns accumulated over the same duration of uncertainty declining. The empirical model

is specified as follows:

Cumretj,q = γ + β∆Ret V olj,q + βxX + eq (19)

where Cumretj,q denotes the cumulative equity excess return throughout the pre-announcement

window of j days associated with a given announcement q. ∆Ret V olj,q = Ret V oltM2−j,q −

Ret V oltM2−1,q measures the size of uncertainty change, that is, uncertainty reduction if

40

∆Ret V olj,q > 0, from the j-th day until the day right before the day of announcement q. With

the covariate vector X, we examine the robustness of the results by controlling for the mean level

of uncertainty in the j-day window.

We investigate the pre-announcement windows of 2 days and 3 days; the estimation results

are summarized in Table 6. Across columns, the results all suggest that uncertainty reduction

is positively correlated with cumulative excess returns over an duration of 2 to 3 days before

announcements regardless of additional controls. Therefore, evidence squares well with the model

implication that greater uncertainty reductions are associated with larger cumulative excess equity

returns.

Table 6: Uncertainty Reduction and Size of Pre-announcement Premium

(1) (2) (3) (4) (5) (6) (7) (8)VARIABLES 2-day 2-day 2-day 2-day 3-day 3-day 3-day 3-day

∆Ret V ol2,q 1.50*** 1.78*** 1.74*** 1.80***(0.52) (0.49) (0.49) (0.42)

∆Ret V ol3,q 1.81*** 1.69*** 1.74*** 2.19***(0.65) (0.58) (0.62) (0.44)

Ret V olq -0.48 -0.32 0.31 0.76(0.34) (0.29) (0.76) (0.65)

Stock Exchange Dummy Yes Yes Yes Yes Yes Yes Yes YesYear Dummies Yes Yes Yes Yes Yes Yes Yes YesMonth / Weekday Dummies Yes YesConstant 0.31* 0.28 0.84 -0.16 0.43* 0.12 -0.24 -3.50***

(0.18) (0.38) (0.55) (0.81) (0.25) (0.68) (0.90) (0.85)

Observations 168 168 168 168 168 168 168 168R2 0.10 0.19 0.21 0.46 0.08 0.18 0.18 0.53

Notes: Sample: January 2010 to December 2016. This table reports the regression results of Equation (19). The de-pendent variable is the cumulative excess equity returns over an interval of j days before the M2 announcement forj = 2, 3. Uncertainty is measured by the stock return volatility aggregated over 5-minute trading blocks for the dayof either the Shenzhen (SZSE) or Shanghai (SSE) stock exchange index. Return volatility data of both stock marketsare stacked. “Stock Exchange Dummy”: equals 1 if the return volatility data is constructed based on Shanghai StockExchange Index. ***, **, *, and + denote significance at 1%, 5%, 10%, and 15%, respectively. Robust standard errorsare in parentheses.

6.3 Timeliness of Announcement Arrival and Premium

In this subsection, we test Hypotheses 3 and 4 by exploring whether the size of the pre-

announcement premium and the size of the associated uncertainty reduction depend on the time-

liness of arrivals of M2 announcements. It is important to delve into this question given that

monetary announcements are quasi-scheduled in China and stock markets are very responsive to

the PBOC’s data releases.

41

6.3.1 Premium for More Delayed Announcements

First, we examine if the pre-announcement premium is more pronounced for more delayed

monetary announcements. We first select a number of reference days by which we divide our

announcement events into two groups: announcements made earlier, and those made on the day

and after. Then, we estimate the baseline specifications of Equations (1) and (2) using the daily

return samples of non-announcement days and the windows of selected groups of announcements.

Table 7 reports the estimation results. Coefficient estimates except for the pre-announcement

dummies are suppressed for the sake of space. In Panel A, the the estimations are associated with

PBOC announcements that are made relatively early in a month. The results from columns (1)

to (3) suggest that regardless of the length of pre-announcement windows, when the monetary

aggregate data are released too early in a month, no significant relative excess premium can be

obtained for days prior to the announcement. In addition, as the results in columns (4) and

(5) show, with announcements made on the 12th day and the 13th day of the month included,

coefficient estimates associated with 3-day pre-announcement windows turn trivially positive and

the magnitudes become larger.

Moving toward to Panel B, the results in columns (1) to (5) of Table 7 show that for those

announcements made late in a month, the coefficient estimates of pre-announcement excess returns

are significantly greater than zero. More importantly, across all the columns, we observe that the

magnitudes of estimated 1-day and 3-day ahead premiums become monotonically larger as data re-

leases are further postponed in a month. The evidence shows that the size of the pre-announcement

premium is strikingly dependent on the relative timeliness of the PBOC’s announcement arrival.

Compared to our baseline results shown in Table 1, the daily relative excess return of 30 bps of a

3-day window prior to announcement is then largely driven by those delayed announcements.

42

Table 7: Pre-announcement Premium: Early vs. Late Announcements

Panel A: Early Arrivals of Announcements

(1) (2) (3) (4) (5)VARIABLES Earlier than 10 Earlier than 11 Earlier than 12 Earlier than 13 Earlier than 14

ItM2−1,3 -0.20 -0.01 0.14 0.22* 0.29**(0.24) (0.20) (0.15) (0.12) (0.11)

Constant -0.15 -0.13 -0.25 -0.33 -0.30(0.30) (0.28) (0.25) (0.24) (0.23)

R2 0.04 0.03 0.03 0.02 0.02Observations 893 980 1,259 1,436 1,510

ItM2−1 0.17 0.02 0.13 0.22 0.23(0.42) (0.38) (0.27) (0.20) (0.18)

Constant -0.16 -0.13 -0.21 -0.30 -0.26(0.30) (0.28) (0.25) (0.23) (0.23)

R2 0.04 0.03 0.03 0.02 0.02Observations 893 980 1,259 1,436 1,510

Panel B: Late Arrivals of Announcements

(1) (2) (3) (4) (5)VARIABLES On and after 10 On and after 11 On and after 12 On and after 13 On and after 14

ItM2−1,3 0.34*** 0.37*** 0.47*** 0.48** 0.42*(0.12) (0.12) (0.15) (0.20) (0.24)

Constant −0.31+ −0.34+ -0.23 -0.15 -0.20(0.21) (0.22) (0.23) (0.25) (0.26)

R2 0.02 0.02 0.03 0.03 0.02Observations 1,755 1,668 1,389 1,212 1,138

ItM2−1 0.41** 0.47*** 0.63*** 0.73*** 0.83***(0.17) (0.17) (0.20) (0.26) (0.32)

Constant −0.31+ −0.34+ -0.23 -0.15 -0.19(0.21) (0.22) (0.23) (0.25) (0.26)

R2 0.02 0.02 0.03 0.03 0.02Observations 1,755 1,668 1,389 1,212 1,138

Notes: Sample: January 2010 to June 2017. This table reports dummy variable regression results of Equations(1) and (2). The dependent variable is the excess return constructed from the Wind A-Share Index. Announce-ment day dummy ItM2−1,j equals one for the trading days in a j-day window before an M2 announcement.Announcement day dummy ItM2−i equals one if the i-th trading day is before (or after if i is negative) an M2announcement. We align the return data of the first trading day that the equity market has access to the news tothe dummy variable ItM2 = 1 when i = 0. Each column summarizes the estimation results based on a restrictedsample that includes only trading days of non-announcement days and either 1-day or 3-day pre-announcementwindows of those selected announcement events that fall into either the early or the late group. Year, month,and weekday dummies along with the remaining day dummies of the announcement window of length of 2T + 1as T = 5 are included. ***, **, *, and + denote significance at 1%, 5%, 10%, and 15%, respectively. Robuststandard errors are in parentheses.

6.3.2 Uncertainty Reduction for More Delayed Announcements

Our empirical evidence is consistent with the model prediction that more delayed arrivals of

monetary announcement can generate larger pre-announcement premium by triggering larger re-

duction of uncertainty owing to more attentive learning. In this subsection, we test whether the

timeliness of announcement arrivals indeed affects the size of pre-announcement uncertainty reduc-

43

tion.

Specifically, across announcement events, we estimate the following specification

∆Ret V olj,q = γ + α ·DaytM2,q + β ·Day2tM2,q

+ βxX + eq (20)

where ∆Ret V olj,q again measures the size of uncertainty reduction over a j-day interval until the

day right before the day of announcement. Equation (19) also includes the linear and squared term

of DaytM2,q, which captures the day of month associated with the date of a given announcement q,

tM2,q. Thus, it measures the duration of time lapsed for investors from the start of a month to the

arrival of a PBOC monetary announcement.

Table 8 presents the estimation results of regressions with respect to uncertainty reduction

over the 3-day pre-announcement windows. Focusing on column (2), we find that 1 more day of

monetary announcement delay shrinks the stock market return volatility by about a maximum of

0.4 standard deviation for a given duration of 3 days. In addition, according to the statistically

significant coefficient associated with the squared term Day2tM2,q

, the magnitude of uncertainty

reduction owing to 1 more day of delay becomes smaller as the announcement day is further

postponed. However, this convexity effect is relatively trivial. For example, an announcement has

to be made on the 20th day of a month so as to completely nullify the positive effect of delays

on the size of uncertainty reduction. Columns (3) and (4) show that our estimation results are

robust even if the potential seasonality effects associated with given years, months and weekdays

are controlled for.

We thus conclude that more delayed announcements are associated with larger reduction of

uncertainty as well as more pronounced pre-announcement premium. In Section B of the Appendix,

we explore the correlation of relative timeliness of an announcement and the ex-post content of

monetary announcements. We rule out the claim that the delayed announcements, by signalling

monetary expansion, generate positive equity premium prior to announcements.

44

Table 8: Uncertainty Reduction across Announcements

VARIABLES (1) (2) (3) (4)

DaytM2,q 0.03** 0.41*** 0.38*** 0.34**(0.02) (0.13) (0.12) (0.15)

Day2tM2,q-0.01*** -0.01*** -0.01**

(0.00) (0.00) (0.01)Stock Exchange Dummy Yes Yes Yes YesYear Dummies Yes YesMonth / Weekday Dummies YesConstant -0.31 -2.61*** -2.36*** -1.81**

(0.20) (0.81) (0.79) (0.88)

Observations 168 168 168 168R2 0.02 0.05 0.09 0.15

Notes: Sample: January 2010 to December 2016. This table reports the regression results of Equation (20). The depen-dent variable is the size of uncertainty reduction, which is measured by the j-day difference in level regarding the intra-dayreturn volatility constructed from high-frequency return data of the SSE (Shanghai) and SZSE (Shenzhen) market indexes.Return volatility data are stacked. ***, **, *, and + denote significance at 1%, 5%, 10%, and 15%, respectively. Robuststandard errors are in parentheses.

6.4 Attentive Learning and Uncertainty Reduction

In this subsection, we test Hypotheses 5 and 6 and show that the theoretical link holds in the

data as our model predicts that uncertainty reduction is driven by investors’ attention allocation.

We propose that the keywords-based Baidu search index proxies well for the magnitude of average

attention allocation in China to learning about monetary aggregates data and monetary policy.

First, we evaluate the dynamics of attentive learning during announcement windows. The daily

Baidu search index associated with the keywords of “M2 growth rate” is taken as the baseline

measure of the intensity of attention allocation. In addition, we construct a composite measure

which is a simple average of search indexes associated with a broader range of terms including

“Credit”, “Monetary Policy”, “Money” along with “M2 growth rate”. To evaluate Hypothesis 5,

we run the estimation of the following specification:

Attnt = γ + θjItM2−1,j +

T∑i=0

βiItM2+i + βxXt + υt (21)

The coefficient θj is interpreted as the average size of daily attention of an interval of j days prior

to announcement relative to that outside the average non-announcement windows.

Since the keywords search data are traced in continuous time, which covers the off-trading hours

and weekends, we thus run our baseline estimation by first aligning the Baidu search index of the

45

first trading day on which the equity market has access to the news to the day of announcement, tM2.

This aligned timing makes our estimate of the size of the pre-announcement attention allocation

comparable to that of the equity premium according to Equation (2). However, for robustness, we

keep the original data structure of search timing without the realignment, and further focus on the

observations of the weekdays only as searches are relatively more intense during the weekends.

Table 9 summarizes the estimation results of regressions with respect to attention allocation

over the 3-day pre-announcement windows. Across columns of different timing restrictions, we

find that the coefficient estimate associated with the 3-day dummy θj for j = 3 are statistically

significant regardless of whether we consider search attention with respect to money growth only

or more generally to a series of monetary and credit statistics. These results indicate that learning

about monetary data and monetary policy changes becomes more intense a few days prior to the

PBOC’s announcement relative to the average size of attention allocation for a given day of the

non-announcement day windows. Importantly, other coefficient estimates suggest that conditional

on the made announcement, attention allocation is higher for days right after the announcement.

However, when it comes to day 4 or 5 after the announcement, the relative magnitude of higher

attention is lower.

Second, across announcement events, we estimate the partial effects of uncertainty reduction on

the size of search intensity over the same duration of uncertainty changes. We run the regression

of the following specification:

∆Ret V olj,q = γ + β ˆAttnj,q + βxX + eq (22)

where ∆Ret V olj,q measures the size of reduction of stock return volatility over a j-day interval until

the day right before the day of announcement. ˆAttnj,q is the normalized search index as divided by

the average daily search index of non-announcement days. The estimate of β, if positive, gives that

larger pre-announcement uncertainty reduction is associated with increased attention allocation.

Estimation results are shown in Table 10. The results suggest that over a 3-day pre-

announcement interval, larger intensive learning about either money growth rate or a range of

related monetary and credit statistics is coupled with greater size of uncertainty reduction. This

finding is robust regardless of how we define the scope of keywords search index and whether we

46

Table 9: Relatively High Attention Prior to M2 Announcements

Realigned Original Timing Weekdays OnlyVARIABLES Base Composite Base Composite Base Composite

(1) (2) (3) (4) (5) (6)

ItM2−1,3 17.18*** 37.81*** 11.28*** 30.61*** 13.30*** 36.90***(3.87) (9.42) (3.32) (8.22) (3.78) (9.43)

ItM2 64.25*** 54.25*** 51.13*** 36.54*** 49.89*** 42.73***(13.27) (13.89) (7.99) (12.88) (8.28) (13.70)

ItM2+1 34.89*** 38.57*** 65.64*** 32.31** 64.21*** 50.75***(6.48) (13.07) (13.12) (13.39) (14.10) (13.68)

ItM2+2 19.72*** 36.97*** 27.17*** 17.85 23.41*** 25.48**(5.02) (11.47) (5.47) (12.13) (5.95) (12.13)

ItM2+3 14.44*** 33.80*** 20.97*** 13.80 18.87*** 28.65**(4.68) (11.44) (4.45) (11.78) (5.06) (11.92)

ItM2+4 7.28* 33.33** 18.11*** 14.30 9.28* 22.26**(4.27) (13.46) (4.70) (10.79) (4.91) (11.30)

ItM2+5 4.90 39.15* 12.93*** 9.83 8.47* 28.39**(4.27) (21.93) (4.95) (10.98) (4.69) (14.12)

Constant 68.61*** 653.69*** 72.62*** 664.24*** 69.83*** 656.69***(5.06) (13.43) (4.77) (13.55) (4.96) (13.91)

Year / Month / Weekday Dummies Yes Yes Yes Yes Yes YesObservations 2,738 2,738 2,738 2,738 2,738 2,738R2 0.63 0.63 0.64 0.63 0.64 0.63

Notes: Sample: January 2011 to June 2017. This table reports the regression results of Equation (21). The de-pendent variable is the Baidu keywords-based search index. We consider search attention with respect to moneygrowth only (Base Measure), and more generally to a series of monetary and credit statistics (Composite Measure).Announcement dummy ItM2−1,j equals 1 for the trading days in a j-trading-day window before an M2 announce-ment. ***, **, *, and + denote significance at 1%, 5%, 10%, and 15%, respectively. Robust standard errors are inparentheses.

allow for timing realignment. Hence, we provide the evidence in support of the the key model

mechanism that learning can drive down the forecast uncertainty about money growth prior to the

PBOC’s monetary announcements.

7 Discussion: Quasi-scheduled vs. Pre-scheduled Announcements

In this section, we discuss the relevance of our model for rationalizing the characteristic features

of pre-announcement premium observed both in China and the U.S. despite their quantitative

differences.

Ultimately, our theory qualitatively squares well with the pre-announcement premium observed

in both China and the U.S. despite their quantitative differences. The U.S. stock market exhibits

very short-lived pre-FOMC announcement premiums, whereas for China, we find that the pre-

announcement drift takes a few days before reaching its peak. We argue that the institutional

differences in the routine of announcement scheduling, that is, quasi-scheduled and pre-scheduled

announcements, and the sophistication of financial markets of the two markets may jointly account

47

Table 10: Attentive Learning across Announcements

Realigned Original Timing Weekdays OnlyVARIABLES Base Composite Base Composite Base Composite

(1) (2) (3) (4) (5) (6)

ˆAttnj,q 0.24* 0.50** 0.32*** 0.39** 0.26** 0.48**(0.13) (0.23) (0.12) (0.18) (0.11) (0.21)

Stock Exchange Dummy Yes Yes Yes Yes Yes YesYear / Month / Weekday Dummies Yes Yes Yes Yes Yes YesConstant -0.21 -0.51** -0.21 -0.44** -0.22 -0.48**

(0.15) (0.21) (0.15) (0.19) (0.15) (0.20)Observations 168 168 168 168 168 168R2 0.20 0.21 0.21 0.20 0.20 0.21

Notes: Sample: January 2010 to December 2016. This table report the regression results of Equation (22).The dependent variable is the reduction of return volatility over an interval of j days before the M2 announce-ment for j = 3. ˆAttnj,q : search index divided by the average daily search index of non-announcement days.We consider search attention with respect to money growth only (Base Measure), and more generally to a se-ries of monetary and credit statistics (Composite Measure). “Stock Exchange Dummy”: equals 1 if the returnvolatility data is constructed based on Shanghai Stock Exchange Index. ***, **, *, and + denote significanceat 1%, 5%, 10%, and 15%, respectively. Robust standard errors are in parentheses.

for the characteristic differences, by which dynamics of φt and σ2m,t in our model are affected.

In particular, between pre-scheduled FOMC dates, investors know there is no probability of

the FRB unexpectedly changing the federal funds rate target. In addition, as federal funds rate

futures and derivatives are actively traded in the U.S. market, it can be very difficult for uncertain-

ty about monetary policy stance to accumulate between FOMC announcements. Mapping to our

model, this institutional background suggests that only when it is very close to the pre-scheduled

FOMC day, useful information about the FRB’s potential moves are accessible. This raises φt.

Moreover, between FOMC meetings, investors see trivial possibilities for policy changes and uncer-

tainty without attentive learning σ2m,t can be quite low. Therefore, it is very likely that suddenly

jumped uncertainty coupled with good chance of forming precise forecasts just a few hours before

the FOMC meeting provokes attentive learning, which leads to a quick reduction of uncertainty

and transient pre-announcement premium.

For China, the lack of financial market sophistication with regard to money supply creates

potential for cyclical uncertainty accumulation between the PBOC’s announcements. Importantly,

without knowing the exact day of announcement, investors with high cumulative uncertainty and

more informative signals available would start paying attention to the growth of money supply

whenever learning brings value until the next announcement is made. Therefore, it takes a few

days to lower uncertainty to the optimum, and equity prices keep climbing before announcements.

48

8 Conclusion

By studying China, this paper examines the stock market returns in an environment in which

the dates of central bank’s information supply through public announcements are not pre-fixed. We

document a “pre-announcement drift” of excess returns on the Chinese equity market in response

to the central bank’s monthly announcements of measures of monetary aggregates, which may

arrive early or late in a month. For the period 2010 to 2017, on average, Chinese A-share market

climbed and realized an excess return of 30 bps per day in the 3-day window prior to the day of

announcement, as shown by a flattening out after the announcement. In this paper, we demonstrate

that by evaluating the implications of having randomness in announcement scheduling, a model

that features investors’ endogenous learning characterizes the key mechanism behind the equity

market’s ex-ante reactions found both in China and the U.S., even though the U.S. FOMC dates

are pre-fixed whereas the PBOC’s announcements are quasi-scheduled.

We propose a theory for investors to acquire information endogenously to learn about the growth

rate of money supply given that announcements are not pre-scheduled. The pre-announcement

premium is driven by endogenous attention-driven information demand such that investors’ learning

helps reduce their forecast uncertainty prior to monetary announcements. We highlight that China’s

setting of scheduling its central bank’s announcements provides the exact data structure for us to

test the key model mechanism of attention-driven uncertainty reduction, which helps rationalize

the empirics found for both China and the U.S.

We then provide comprehensive evidence to show that the data are consistent with our model

predictions. First, measures of uncertainty decline prior to the PBOC’s announcements. Second,

more accumulated returns are associated with larger uncertainty reduction before announcements.

Third, by exploiting the timing variations across announcement events, we show that both the

size of uncertainty reduction and the pre-announcement premium are more pronounced when the

release of monetary data is more delayed. Finally, across announcements, we find that larger

pre-announcement uncertainty reduction is associated with increased attention for learning about

monetary aggregates and monetary policy changes.

49

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52

Appendices

A Forecast Uncertainty: M2 Growth and the Broader Economy

We show in this subsection that our forecast-based measure of uncertainty is more broadly

related to market uncertainty about the general economy, that is, aggregate market risk.

We first compute the standard deviation of forecast errors across all available forecasts per

month for a range of macro variables recorded in the Bloomberg Survey Database. Besides the

M2 growth, the forecast macro series are YOY growth rates of M1, exports, imports, CPI, PPI,

GDP, VAI, and PMI. Then, we compute pair-wise correlation coefficients of monthly forecast error

dispersion across the variables of forecast. The results are tabulated in Table A.1.T. Accordingly,

the first row shows that the forecast error dispersion of M2 growth forecasts is positively correlated

with all the other dispersion measures of the other macro variables of forecast except for the series

of M1 growth. In particular, the correlation coefficients are all statistically significant at the 5%

level.

Table A.1.T: Correlations: Monthly Dispersion of Forecast Errors

M2 M1 Exports Imports CPI PPI GDP VAI PMI

M2 1.00 -0.05 0.27 0.40 0.28 0.23 0.81 0.24 0.42(0.63) (0.01) (< 0.01) (0.01) (0.03) (< 0.01) (0.03) (< 0.01)

M1 1.00 0.66 0.55 0.27 -0.04 -0.08 0.12 -0.03(< 0.01) (< 0.01) (0.01) (0.71) (0.7) (0.33) (0.76)

Exports 1.00 0.74 0.50 0.15 0.35 0.68 0.30(< 0.01) (< 0.01) (0.17) (0.06) (< 0.01) (< 0.01)

Imports 1.00 0.46 0.30 0.54 0.63 0.39(< 0.01) (< 0.01) (< 0.01) (< 0.01) (< 0.01)

CPI 1.00 0.04 0.70 0.62 0.43(0.69) (< 0.01) (< 0.01) (< 0.01)

PPI 1.00 0.45 0.14 0.38(0.01) (0.23) (< 0.01)

GDP 1.00 0.76 0.77(< 0.01) (< 0.01)

VAI 1.00 0.44(< 0.01)

PMI 1.00

Notes: Sample: January 2010 to June 2017. This table shows the Pearson correlation matrix of standard de-viation of forecast errors regarding a series of macroeconomic variables. P-values are reported in parentheses.

Furthermore, at the forecaster level, we estimate the following specification to disentangle the

associations between the size of forecast error of a macro variable and that of M2 growth.

|FEij,m| = α+ γi|FEM2j,m |+ βi,xXm + υij,m (A.1.E)

53

In Equation (A.1.E), |FEij,m| denotes the absolute value of forecaster j’s forecast error regarding

a given macro variable i of month m. The absolute value proxies the magnitude of errors relative

to the true state of the variable. i = M2 captures the absolute forecast error for M2 growth. We

include year and forecaster dummies in covariate vector Xm.

The regression results are presented in Table A.2.T. Panel A shows the regression results re-

garding the correlations of absolute values of forecast errors at the forecaster level. Columns (1),

(3), and (4) suggest that a forecaster’s uncertainty about M1 growth, import growth, and growth of

value added are all positively correlated with the uncertainty about M2 growth, and have statistical

and economic significance. For robustness, we take the standard deviation of forecast errors about

M2 growth as the regressor, that is, our measure of uncertainty at the aggregate level. We examine

if an individual’s size of forecast errors about other macro variables is at least correlated with that

of a “representative” forecaster of M2 growth at the aggregate level. The estimation results are

shown in Panel B. Across columns, we observe that uncertainty about the growth of M1, VAI,

GDP, PMI, and CPI are all correlated with uncertainty about M2 growth.

54

Table A.2.T: Forecast-level Regressions: Forecast Errors across Macro Variables

Panel A : Baseline

(1) (2) (3) (4) (5) (6) (7)VARIABLES M1 Exports Imports VAI GDP PMI CPI

|FEM2j,m| 0.27* 0.42 1.12*** 0.09** 0.07 0.01 0.01

(0.15) (0.38) (0.39) (0.05) (0.05) (0.03) (0.01)Year/Forecaster Control Yes Yes Yes Yes Yes Yes YesConstant 0.51+ 12.73*** 26.80*** 2.06*** 0.35** 0.53*** 0.57***

(0.34) (2.71) (3.73) (0.34) (0.14) (0.07) (0.09)

Observations 588 1,781 1,774 1,412 542 1,119 1,638R2 0.12 0.09 0.22 0.16 0.39 0.32 0.13

Panel B : Alternatives

(1) (2) (3) (4) (5) (6) (7)VARIABLES M1 Exports Imports VAI GDP PMI CPI

S.D. of FEM2j,m 0.68*** 0.21 1.25 0.30*** 0.12** -0.07 0.06**

(0.21) (0.39) (0.92) (0.07) (0.06) (0.06) (0.02)Year/Forecaster Control Yes Yes Yes Yes Yes Yes YesConstant -0.25 12.79*** 26.66*** 1.53*** 0.32*** 1.06*** 0.48***

(0.21) (2.47) (2.94) (0.31) (0.10) (0.20) (0.07)

Observations 963 1,896 1,884 1,576 686 1,666 1,827R2 0.11 0.09 0.21 0.16 0.41 0.31 0.13

Notes: Sample: January 2010 to June 2017. The table displays the regression results regarding coef-ficient estimates of βi as per Equation (A.1.E), where i refers to the YOY growth rate of M1, Exports,Imports, VAI, GDP, PMI, and CPI. |FEij,m| denotes the absolute value of forecaster j’s forecast error re-garding a given macro variable i of month m. i = M2 captures the absolute forecast error for M2 growth.***, **, *, and + denote significance at 1%, 5%, 10%, and 15%, respectively. Standard errors are clus-tered at forecaster level and shown in parentheses.

In summary, both the correlation analysis and the regression results suggest that our measure

of uncertainty about M2 growth represents general uncertainty about the broader economy. As

shown in Figure 8, a decline of uncertainty before M2 announcements reflects that learning among

investors, which reduces uncertainty about M2 growth, also helps to resolve market uncertainty

about a range of other macroeconomic variables and thereby the aggregate market risk.

B Early vs. Late Arrivals: the Predictability of News Content

We show that the pre-drift of excess returns prior to M2 announcements are mostly driven by

the delayed PBOC’s announcements. In this subsection, we check if the announcement delays are

indicative of monetary expansion. If so, then the delayed announcements, by signalling the lax of

monetary policy, could have triggered the positive excess returns before an announcement.

We thus run the following regression in order to examine if the delayed announcements, as

measured by the day-of-month of a given announcement day, DayM2,q is associated with the size of

55

our baseline measure of announcement content, the monthly changes of M2 YOY growth ∆gM2,m.

Across announcement events, we specify

∆gM2,q = α+ γDayM2,q + ζX + eq (B.2.E)

For the robustness, we substitute out the day-of-month measure using a dummy variable of

DelayM2,q that equals 1 if an announcement q is made after the 12th of a month. In the control

covariates vector X, we include the one month lag of the delay measurement DayLagMonthM2,q

or DelayLagMonthM2,q along with the statistics including monthly changes in the growth rates of

M2, loan balance, deposit balance, M1, CPI, VAI, and exports for the previous month. In addition,

the year, month and weekday effects are controlled for for some specifications.

Table B.3.T summarizes the estimation results. First, we see that regardless of having additional

control variables, either one of the two announcement delay measures is not correlated with the

ex-post M2 growth data. If any, the negative sign of the coefficient estimate suggests that the more

delayed announcements is associated with greater monetary contraction rather than expansion,

though statistically this association is not significant. Second, across the coefficient estimates of

the control variables, we observe that the best predictor of the ex-post M2 growth for this month

is the one that realized in the previous month rather than how much an announcement is delayed.

Hence, our empirical evidence does not support the claim that the more delayed announcements,

by signalling the lax of monetary policy, generate the positive pre-announcement premium.

56

Table B.3.T: Early vs. Late Arrivals: the Predictability of News Content

VARIABLES (1) (2) (3) (4) (5) (6) (7) (8)

DayM2,q -0.08 -0.08 -0.15 -0.15(0.05) (0.05) (0.10) (0.10)

DayLagMonthM2,q 0.02 -0.02 -0.05(0.05) (0.09) (0.10)

DelayM2,q -0.21 -0.21 -0.26 -0.18(0.20) (0.20) (0.33) (0.31)

DelayLagMonthM2,q 0.06 -0.05 -0.16(0.20) (0.30) (0.33)

∆gM2,m−1 -0.01 -0.39** -0.50*** -0.02 -0.39** -0.50***(0.11) (0.16) (0.17) (0.10) (0.16) (0.18)

∆gloan,m−1 0.14 0.18 0.17 0.21(0.17) (0.19) (0.17) (0.19)

∆gdeposit,m−1 0.13 0.22 0.11 0.21(0.14) (0.17) (0.14) (0.17)

∆gM1,m−1 0.02 -0.02 0.01 -0.03(0.04) (0.05) (0.04) (0.05)

∆gCPI,m−1 0.06 0.06(0.28) (0.30)

∆gV AI,m−1 0.04 0.04(0.03) (0.03)

∆gexport,m−1 0.01 0.01(0.01) (0.01)

Year / Month / Weekday Dummies Yes Yes Yes YesConstant 0.71 0.51 1.45 1.68 -0.14 -0.17 -0.49 -0.48

(0.61) (0.82) (1.84) (1.99) (0.13) (0.16) (0.47) (0.55)

Observations 90 90 90 90 90 90 90 90R2 0.03 0.03 0.38 0.42 0.01 0.01 0.36 0.40

Notes: Sample: January 2010 to June 2017. The table displays the regression results regarding coefficient estimatesper Equation (B.2.E). ***, **, *, and + denote significance at 1%, 5%, 10%, and 15%, respectively. Robust standarderrors are in parentheses. Standard errors are clustered at forecaster level and shown in parentheses.

57

Part I

Online Appendix

Attention, Uncertainty Reduction and

Pre-announcement Premium in China

A Additional Summaries

A.1 List of Other Announcements

We select and consider a wider range of macroeconomic variables that have data regularly

published by different agencies through public announcements. Apart from the monetary-related

statistics published by PBOC, other macroeconomic statistics can be broadly categorized into three

groups based on their data coverage: trade data, real-sector productivity measures, and aggregate

price indexes. The associated announcements of these data are grouped correspondingly. The U.S.

FOMC statement issuance, labelled FOMC announcements, belongs to a fourth category. In the

following, we discuss details of these selected announcements that span the four categories.

1. Trade Data Announcements. Statistics regarding total imports and exports of China are

published monthly by the General Administration of Customs of the People’s Republic of

China (GACC) via a single statement on its website. We label these data release news as

TRD announcements.

2. Real-sector Productivity Announcements. We also examine four important data se-

ries measuring the functioning of the production side of the Chinese economy: fixed asset

1

investment excluding rural households (FAI), value added of industrial enterprises above

the designated size (VAI), profits of industrial enterprises above the designated size (INP),

and the manufacturing purchasing managers index (PMI). Each month, these statistics are

published by the National Bureau of Statistics of China (NBS).1

3. Aggregate Price Index Announcements. NBS announcements of three other statistics of

aggregate prices are also considered: the consumer price index (CPI) released simultaneously

with the producer price index (PPI), and the sales price index of residential real estate in 70

large and medium-sized cities (RST).2

4. FOMC Announcements. FOMC meetings that discuss the relevance of U.S. monetary

policy changes are held regularly eight times a year. Each FOMC statement is issued right

after each meeting.3 We explore whether China’s market is responsive to important macro

announcements originating from other country.

In total, we examine nine announcements including PBOC’s M2 announcements, each releasing

at least one important set of statistics. Important to note that a Chinese announcement given in

one month might not be releasing the data points for that month but some statistics spanning the

previous month. For example, the M2 growth statistics of month m − 1 are released in month m

announcement. In addition, for certain statistics of some unusual periods, the monthly statistics

can be published by the end of that month. For instance, China’s manufacturing PMI data of a

month are occasionally made public on the 30th of a month.

Table A.1 summarizes all these selected announcements with their publishing agencies, statistics

published at the same time in the same statement online, and the number of statement issues per

year. First, besides the FOMC announcements, other agencies release critical data about the

Chinese economy. Second, for our sample coverage of January 2010 to June 2017, a given Chinese

1FAI and VAI data are routinely published around the same time on an announcement day through separatestatements on the NBS’s website. Other important statistics, including retail sales of consumer goods, developmentand sales statistics of national real estate, energy production, and private fixed asset investment, are all publishedon the same day about the same time, albeit in separate statements. The quarterly GDP growth rate, however, isannounced together with all these aforementioned statistics every 3 months.

2Since 2009, CPI and PPI data are released simultaneously in the same public statement. PPI data releasespreceded CPI data releases by 1 day before 2009.

3In rare circumstances, more than eight FOMC statements a year can be issued. For example, during the recessionyears of 2001, 2007, and 2008, the FOMC Committee issued more than one statement in a given month of criticaltimes.

2

announcement may release more than one set of statistics. Third, statistics of China are routinely

published monthly. However, a subtlety should be noted. In any year, there are at most 11

announcements for data releases of FAI, FAI, and INP. This is because data for both January

and February of the year are released in the March statements, that is, the NBS does not publish

any statistics in February. This may be because the Chinese Spring Festival holidays normally fall

in February. Finally, the U.S. FOMC Committee may issue more than eight statements in recession

years under rare circumstances.

Table A.1: List of Announcements

Announcement Label Publishing Agency Released Statistics No. of Routine Issues per Year

M2 PBOC M0/M1/M2 Level and Growth 12Loan and Savings Balance: Level and GrowthInterbank Loan: Interest Rate and Balance

TRD GACC Import/Export Level and Growth 12FAI NBS Fixed Asset Investment 11VAI NBS Value Added of Industrial Enterprises 11INP NBS Profits of Industrial Enterprises 11PMI NBS Manufacturing/Non-manufacturing PMI 12CPI NBS CPI & PPI 12RST NBS Price Indexes of Residential Buildings 12FOMC U.S. FRB FOMC Statement 8

A.2 Summaries of Announcement Timing

Apart from the M2 announcements, dates and times information of other announcement events

are obtained from the Bloomberg Economic Calendar (BEC) database too.

Table A.2 provides a summary of announcement days by their day-of-month for the M2 an-

nouncements along with other announcements. It shows that 75% of the monetary aggregate data

published by the PBOC are announced between the 8th and 14th days of a month. There is only

a one-fourth chance of a monetary announcement being delayed beyond the 14th of a month. As

for announcements made by other statistical agencies, the TRD announcements are typically pub-

lished by the 15th day of a month. Three-fourths of FAI and VAI data are published in the first

half of a month. Three-fourths of INP announcements are available by the end of a month. The

PMI announcements are routinely published on the first day of a month. The CPI announcements

are mostly published before the 11th day of a month. The RST data are made public mostly on

the 18th day of a month. 75% of the FOMC statements are issued later than the 14th of a month.

3

Table A.2: Day of Month Distribution of Announcements

M2 TRD FAI VAI INP PMI CPI RST FOMC

Min 8 8 9 9 3 1 8 17 125.Perctl 11 8 11 11 27 1 9 18 14Median 12 10 13 13 27 1 10 18 1975.Perctl 14 10 15 15 27 1 11 18 28Max 18 15 21 21 29 31 21 26 31Mode 11 10 13 13 27 1 9 18 28

No. Events 90 90 82 76 42 91 90 76 60

Notes: Sample: January 2010 to June 2017. This table shows the day of month distribu-tion of announcements by their percentile cut-off days of a month. Number i in a cell denotesthe i-th day of a month. Min: the earliest day of a month for an announcement day event;Max: the latest day of month for a data release; Percentiles: percentiles of the day of monthdistribution; Median: 50% percentile cut-off. Mode: day of month on which largest numberof announcement events falls. Data reported are rounded off in the case of decimal ratios.

Table A.3 summarizes announcement days by the day of week distribution for all announce-

ments. The table shows that M2 announcements are often made public on weekdays and 33% of

them fall on Fridays. While most of the announcements have greater chance of being made public

on Thursdays and Fridays, announcements of TRD and PMI are more evenly distributed within

a week.

Table A.3: Day of Week Distribution of Announcements

M2 TRD FAI VAI INP PMI CPI RST FOMC

Mon .10 .16 .11 .12 .12 .13 .09 .18Tue .17 .12 .17 .17 .14 .14 .17 .13Wed .13 .16 .18 .18 .07 .15 .12 .14 .13Thu .19 .17 .15 .14 .17 .13 .22 .12 .83Fri .32 .14 .23 .24 .24 .16 .23 .21 .03Sat .03 .13 .11 .09 .10 .12 .10 .12Sun .06 .12 .05 .05 .17 .15 .07 .09

No. Events 90 90 82 76 42 91 90 76 60

Notes: Sample: January 2010 to June 2017. This table shows the percentage of announce-ments (in decimals) made on each day of the week for a given announcement. Due to round-ing off, column numbers might not add up precisely to one.

Table A.4 summarizes the distribution of announcement days by the point of time for data

release across events. In general, except for FOMC announcements that always fall on weekdays

before the trading hours of Beijing Local Time, the rest of the announcements are made public on

either weekdays or weekends at any time, that is, regardless of whether it falls within, before, or

after the trading hours. For about one-third of all times in the sample, monetary aggregate data

(M2 announcements) are published after trading hours on weekdays. Another one-third falls on

weekends, that is, post-trading hours on Friday until the end of Sunday. Announcements about

international trade data, real-sector statistics, and price indexes are routinely made available within

4

trading hours, although sometimes data may be released over weekends. The PMI data are released

promptly at 9:00 AM although the announcement day can be any day of the week or weekend.

Table A.4: Timing Distribution of Announcements

M2 TRD FAI VAI INP PMI CPI RST FOMC

Weekday beforetrading hours

No. Anns. 3 66 60Avg. Time 8:40 9:00 2:07

Weekday withintrading hours

No. Anns. 26 66 68 64 31 75 60Avg. Time 10:30 10:38 11:08 11:02 9:41 9:39 9:32

Mon-Thur aftertrading hours

No. Anns. 30 1 1 1Avg. Time 15:58 15:34 15:40 15:40

Onweekends

No. Anns. 31 23 13 11 11 25 15 16Avg. Time 15:19 10:40 12:55 12:49 9:43 9:00 9:34 9:33

Total 90 90 82 76 42 91 90 76 60

Notes: This table reports the number of announcement events by categorized groups of announcement timingand the averaged point of time for data releases within each group. The four groups are: (1) announcements re-leased before trading hours on weekdays; (2) announcements released within trading hours (including announce-ments with data released between the morning and afternoon sessions); (3) announcements released after tradinghours from Monday to Thursday; and (4) announcements released between market closure on Friday until mid-night of Sunday. The SZSE and SSE are normally open for trading from Monday to Friday, with call auctionduring 9:15–9:25, and continuous auction during 9:30–11:30 and 13:00–15:00. Intent orders for block trades areaccepted during 9:30–11:30 and again 13:00–15:30, while execution orders and fixed-price orders for block tradesare accepted during 15:00–15:30. Special block trade sessions are held on an ad-hoc basis during 15:00–17:00.

We make a few points here through comparing M2 and FOMC announcements. The PBOC’s

announcements are made public on any day of a week, whereas the FOMC statement releases

predominantly fall on early Thursday mornings in Beijing time (Wednesday afternoons in U.S.

Eastern Time). In addition, a greater proportion of M2 announcements are publicly available

during off-trading sessions, including post-trading hours and on weekends. However, the FOMC

statements are issued routinely within trading hours around 2:15 PM using U.S. Eastern time.

Accounting for China–U.S. time differences, this FOMC news is initially accessible by the Chinese

market around 2:15 to 3:15 AM on Thursdays using Beijing Time, depending on whether U.S.

daylight-saving time applies.

A.3 Summary of Co-released Announcements

Table A.5 summarizes the number of labeled announcements that are made public on a day on

which some other selected announcements are also published, that is, co-released announcements.

Out of the 90 M2 announcements, monetary data are co-released with FAI, VAI, and CPI data

about 20 times. Furthermore, FAI and VAI statistics are routinely released together.

5

Table A.5: Co-released Announcements

M2 TRD FAI VAI INP PMI CPI RST FOMC

M2 90 7 20 19 18 2TRD 90 1 1FAI 82 76 31 3 1VAI 76 29 3 1INP 42PMI 91 2CPI 90 1RST 76 4FOMC 60

Notes: Sample: January 2010 to June 2017. A number in the cell indicates the numberof row announcement events that overlap the column announcement events. An overlapis counted if both types of labeled announcements fall on the same day. Note that thesum of row or column numbers does not have to equal the total number of announce-ment events of a given announcement label.

B Additional Empirical Results

B.1 Return Responses: Alternative Sample Periods

Here, we examine the Chinese stock market’s reactions to M2 announcements when other

periods of time are considered. According to columns (1), (2), (4), and (5) of Table B.1, the

estimation results suggest that the pre-announcement premium is robust regardless of whether the

sample starts 1 year earlier or later than 2010, our baseline starting point. The relative excess return

is consistently at around 30 bps per day of a 3-day window before an announcement. However, when

we exclusively focus on a sample period of pre-2010 years, little evidence is detected to argue for the

existence of a pre-announcement premium regardless of how long the pre-announcement window is.

This can be explained by the fact that at that stage, the stock market was relatively unsophisticated

when incorporating macroeconomic news, let alone the irregularity and the non-fixed information

vendor of the PBOC starting to release monetary aggregate data in those years.

6

Table B.1: Alternative Samples and Reactions to M2 Announcements

(1) (2) (3) (4) (5) (6)VARIABLES 2011–2017 2009–2017 2002–2010 2011–2017 2009–2017 2002–2010

ItM2−1 0.44** 0.31** −0.25+

(0.18) (0.15) (0.17)ItM2−1,3 0.34*** 0.24** -0.14

(0.12) (0.11) (0.13)

Year/Month/Weekday Dummies Yes Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes Yes YesConstant -0.28 0.08 -0.03 -0.28 0.08 -0.03

(0.22) (0.22) (0.25) (0.22) (0.22) (0.25)

Observations 1,577 2,063 1,928 1,577 2,063 1,928R2 0.02 0.02 0.03 0.02 0.02 0.03

Notes: This table reports the dummy variable regression results of Equations (1) and (2) for different sample periods.The dependent variable is the close-to-close excess return constructed from the Wind A-Share Index. We align the returndata of the first trading day on which the equity market has access to the monetary aggregate data to the dummy variableItM2 = 1 when i = 0. Announcement dummy ItM2−1 equals one for the day that is 1 day before an M2 announcement.Announcement dummy ItM2−1,3 equals one for the trading days in a 3-trading-day window before an M2 announcement.“Other Anns Window Ctrls” controls the remaining day dummies of the announcement window of length of 2T+1 as T = 5.“Year/Month/Weekday Dummies” control the year, month, and weekday effects. ***, **, *, and + denote significance at1%, 5%, 10%, and 15%, respectively. Robust standard errors are in parentheses.

B.2 Return Responses: Alternative Market Indexes

We discuss the robustness of our baseline results when returns are constructed from other

market indexes of the SZSE and SSE. We run regressions of baseline specification of Equation (1).

In Table B.2, our results show that even if we remove potential seasonality of equity premium by

controlling for year, month, and weekday dummies, coefficients associated with the first, second,

and third days prior to announcement are all positive and large in size despite the coefficient

of ItM2−1 gives the most significance, whereas those of post-announcement dummies are trivial.

Return accumulation of 3 consecutive days are most noted when the Wind A-Share market index

is considered in column (4). However, jumps in excess returns are statistically significant on the

day right before the announcements when a particular stock exchange is examined, according to

columns (5) and (6). In addition, we observe that the size of the pre-announcement premium is

more pronounced for the SZSE than for the SSE.

7

Table B.2: Alternative Market Index: Returns in Windows of M2 Announcements

(1) (2) (3) (4) (5) (6)VARIABLES Wind A SZSE Index SSE Index Wind A SZSE Index SSE Index

ItM2−5 0.16 0.15 0.11 0.16 0.15 0.11(0.18) (0.19) (0.15) (0.18) (0.19) (0.15)

ItM2−4 -0.04 -0.09 -0.04 -0.07 -0.12 -0.06(0.19) (0.17) (0.17) (0.20) (0.17) (0.17)

ItM2−3 0.30+ 0.19 0.20 0.29+ 0.17 0.18(0.19) (0.19) (0.16) (0.19) (0.19) (0.16)

ItM2−2 0.23 0.16 0.14 0.25+ 0.19 0.16(0.17) (0.16) (0.14) (0.17) (0.16) (0.14)

ItM2−1 0.41*** 0.34** 0.25** 0.39** 0.32* 0.23*(0.16) (0.16) (0.13) (0.16) (0.17) (0.13)

ItM2 0.21 0.14 0.18 0.22 0.16 0.18(0.16) (0.18) (0.14) (0.17) (0.18) (0.14)

ItM2+1 -0.19 −0.26+ -0.17 -0.21 −0.29+ -0.19(0.17) (0.18) (0.14) (0.17) (0.18) (0.14)

ItM2+2 0.04 -0.11 -0.04 0.02 -0.12 -0.05(0.19) (0.20) (0.18) (0.19) (0.20) (0.18)

ItM2+3 -0.04 -0.09 -0.08 -0.02 -0.07 -0.06(0.18) (0.19) (0.15) (0.18) (0.19) (0.15)

ItM2+4 0.03 -0.02 -0.04 0.01 -0.04 -0.07(0.19) (0.21) (0.17) (0.19) (0.21) (0.17)

ItM2+5 0.02 -0.04 -0.06 0.03 -0.02 -0.05(0.19) (0.19) (0.16) (0.20) (0.19) (0.16)

Year/Month/Weekday Dummies Yes Yes YesConstant -0.04 -0.04 -0.03 -0.28 -0.24 -0.26

(0.06) (0.06) (0.05) (0.21) (0.22) (0.19)

Observations 1,819 1,819 1,819 1,819 1,819 1,819R2 0.01 0.01 0.01 0.02 0.02 0.02

Notes: Sample: January 2010 to June 2017. This table reports the dummy variable regression results of Equation(1). The dependent variable is the excess equity return constructed from a given market index. Announcement dum-my ItM2−i equals 1 if it is the i-th trading day before (after if i is negative) an M2 announcement. We align thereturn data of the first trading day that the equity market has access to the news to the dummy variable ItM2 = 1when i = 0. ***, **, *, and + denote significance at 1%, 5%, 10%, and 15%, respectively. Robust standard errorsare in parentheses.

B.3 Return Responses: Other Macro Announcements

We examine if the pre-announcement premium associated with releases of monetary aggregates

data carries over to other macro announcements summarized in subsection A.1 of the Appendix.

Table B.3 reports the results based on our baseline dummy regression of Equation (1) by considering

windows of other announcement events. Importantly, focusing on a window length of 5 days before

announcements, we find that China’s stock market also exhibits statistically significant reactions to

announcements of VAI, FAI, and CPI. Specifically, a similar positive pre-announcement premium

is found. We regard this as additional evidence in support of the channel of attention-driven

uncertainty reduction. As the aggregate market risk can be shifted by a range of macro statistics

beyond monetary aggregates data, pre-announcement learning of these data helps to reduce market

8

risk, which can push up equity prices ex-ante.

We discuss some findings of interest in the following part. First, for the coefficient estimate

of post-announcement day tAnns+3 regarding the INP news about industrial production data, the

partial effect is significantly different from zero. In addition, in response to the TRD announce-

ments of China’s trade statistics on the announcement day, the stock market reacts with a large 40

bps of excess returns relative to no-announcement daily returns. However, we should not confuse

these coefficients with those suggested for a pre-announcement premium. Rather, this evidence

suggests that the market is simply reacting to these updated statistics conditional on the release of

data. Furthermore, we note that the equity market exhibits trivial or even negative excess returns

in response to incoming announcements of PMI and RST.

Table B.3: Returns in Windows of Other Macro Announcements

(1) (2) (3) (4) (5) (6) (7) (8)VARIABLES M2 TRD VAI FAI INP PMI CPI RST

ItAnns−5 0.16 0.20 0.00 0.01 -0.29+ -0.31 0.02 -0.06(0.18) (0.17) (0.21) (0.20) (0.19) (0.22) (0.20) (0.20)

ItAnns−4 -0.07 0.28 0.40** 0.39** 0.11 -0.20 0.39** 0.13(0.20) (0.20) (0.20) (0.19) (0.24) (0.18) (0.19) (0.17)

ItAnns−3 0.29+ 0.21 0.38* 0.25 -0.22 -0.23 0.17 -0.38**(0.19) (0.18) (0.20) (0.20) (0.20) (0.21) (0.14) (0.19)

ItAnns−2 0.25+ 0.25 0.28 0.23 -0.15 -0.22 -0.06 0.00(0.17) (0.19) (0.20) (0.19) (0.18) (0.20) (0.19) (0.21)

ItAnns−1 0.39** 0.24 -0.02 -0.01 -0.23 0.12 -0.05 -0.01(0.16) (0.18) (0.18) (0.17) (0.18) (0.16) (0.19) (0.21)

ItAnns 0.22 0.37** 0.10 0.14 -0.00 0.21 0.09 -0.35*(0.17) (0.18) (0.21) (0.20) (0.22) (0.20) (0.20) (0.21)

ItAnns+1 -0.21 0.08 -0.02 -0.05 0.06 0.23 0.07 0.03(0.17) (0.17) (0.19) (0.18) (0.19) (0.19) (0.17) (0.21)

ItAnns+2 0.02 0.03 -0.07 -0.03 -0.21 0.19 -0.01 0.01(0.19) (0.19) (0.22) (0.21) (0.21) (0.17) (0.19) (0.18)

ItAnns+3 -0.02 0.17 0.08 0.10 0.51*** 0.06 0.03 -0.15(0.18) (0.14) (0.18) (0.18) (0.16) (0.16) (0.17) (0.20)

ItAnns+4 0.01 0.02 0.10 0.13 -0.01 0.03 0.12 -0.21(0.19) (0.19) (0.21) (0.20) (0.18) (0.16) (0.19) (0.22)

ItAnns+5 0.03 0.06 -0.03 0.00 0.19 -0.05 -0.10 -0.42+(0.20) (0.19) (0.20) (0.19) (0.18) (0.20) (0.19) (0.27)

Year/Month/Weekday Dummies Yes Yes Yes Yes Yes Yes Yes YesConstant -0.28 -0.35* −0.32+ −0.31+ -0.26 -0.23 -0.29 -0.28

(0.21) (0.20) (0.21) (0.20) (0.20) (0.20) (0.20) (0.20)

Observations 1,819 1,819 1,819 1,819 1,819 1,860 1,819 1,819R2 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

Notes: Sample: January 2010 to June 2017. This table reports dummy variable regression results of Equation (1)for announcement windows associated with both monetary and a wider range of macro data releases. The depen-dent variable is the close-to-close excess return constructed from the Wind A-Share Index. Announcement dummyItAnns−i equals one if the i-th trading day is before (or after if i is negative) a particular type of announcement.We align the return data of the first trading day that the equity market has access to the news to the dummy vari-able ItAnns = 1 when i = 0. ***, **, *, and + denote significance at 1%, 5%, 10%, and 15%, respectively. Robuststandard errors are in parentheses.

9

B.4 Return Responses: FOMC Statements

We further evaluate if China’s stock market reacts to the U.S. FOMC statement releases. Table

B.4 summarizes the key results. Columns (1) and (4) list the coefficients of pre-announcement

dummies of Equations (1) and (2), which suggest that a pre-announcement premium exists when

the PBOC is about to release the monetary aggregate data. However, from columns (2) and (5), we

find no evidence that China’s equity market reacts to FOMC statement releases ex-ante. In other

words, for all lag and lead terms relative to FOMC announcement days, no daily excess return is

statistically different from zero. This finding differs from the evidence documented in Lucca and

Moench (2015) and Brusa, Savor, and Wilson (2019) whereby the stock markets of a number of

economies exhibit positive pre-drifts of returns in response to incoming FOMC announcements.

Importantly, we note the sample difference of our study years of 2010–2017 against the pre-2011

period in Lucca and Moench (2015). Hence, our sample captures a period when the U.S. federal

funds rate was mostly near a zero lower bound after the end of 2008.It is possible that the U.S. FRB

guided expectations of domestic and international market investors by minimizing the potential

changes in U.S. monetary policy (Yellen, 2015). Thus, the market hardly responded, because there

is assumed to be little risk from U.S. monetary policy for Chinese market to incorporate into its

own markets. The implication is that for a sample with more volatile interest rate changes, like

pre-2011, we should observe Chinese markets’ reaction to FOMC news.

However, the estimation results using the sample years of 2002–2009 do not provide sufficient

evidence to support the claim that China’s equity market significantly responded to FOMC an-

nouncements, as shown in column (6). From column (3), we observe very marginal positive and

negative coefficient estimates associated with daily excess returns 2 and 3 days before the FOM-

C statement release. Some excess return drops are observed for days after the statement with a

significance level of 10%, as shown in columns (3) and (6).

Therefore, it is safe to conclude that China’s equity market does not price in the risk of incoming

U.S. monetary policy changes as delivered through FOMC statements. Moreover, a constant close-

to-zero U.S. federal funds rate indicating limited U.S. monetary policy risk does not help to explain

the muted reaction of the Chinese equity market to FOMC announcements. In general, the non-

sophistication of Chinese markets, limited participation of Chinese investors in foreign capital

10

markets, and actively managed exchange rate, restrictions on the capital accounts, and trade flow

limits could all prevent China from being affected by market risk originating outside China.

Table B.4: China’s Stock Market Responses to FOMC Announcements

(1) (2) (3) (4) (5) (6)VARIABLES M2 FOMC FOMC M2 FOMC FOMC

2010-2017 2010-2017 2002-2009 2010-2017 2010-2017 2002-2009

ItAnns−5 0.16 -0.04 -0.06 0.16 -0.05 -0.05(0.18) (0.18) (0.28) (0.18) (0.18) (0.28)

ItAnns−4 -0.07 -0.14 0.01 -0.07 -0.14 0.02(0.20) (0.21) (0.22) (0.20) (0.21) (0.22)

ItAnns−3 0.29 -0.30 -0.59*(0.19) (0.29) (0.33)

ItAnns−2 0.25 -0.27 0.44*(0.17) (0.26) (0.23)

ItAnns−1 0.39** 0.06 -0.27(0.16) (0.20) (0.28)

ItAnns−1,3 0.31*** -0.17 -0.14(0.11) (0.15) (0.17)

ItAnns 0.22 -0.09 -0.15 0.22 -0.10 -0.14(0.17) (0.22) (0.24) (0.17) (0.22) (0.24)

ItAnns+1 -0.21 0.00 -0.39* -0.21 0.00 -0.38*(0.17) (0.22) (0.22) (0.17) (0.22) (0.22)

ItAnns+2 0.02 -0.09 0.14 0.02 -0.07 0.15(0.19) (0.23) (0.32) (0.19) (0.23) (0.32)

ItAnns+3 -0.02 0.16 -0.36 -0.02 0.16 -0.38*(0.18) (0.19) (0.23) (0.18) (0.19) (0.23)

ItAnns+4 0.01 -0.11 -0.16 0.01 -0.13 -0.16(0.19) (0.19) (0.24) (0.19) (0.19) (0.24)

ItAnns+5 0.03 -0.20 0.22 0.03 -0.21 0.22Year / Month / Weekday Dummies Yes Yes Yes Yes Yes YesConstant -0.28 -0.22 -0.04 -0.28 -0.23 -0.01

(0.21) (0.20) (0.24) (0.21) (0.21) (0.24)

Observations 1,819 1,819 2,037 1,819 1,819 2,037R2 0.02 0.01 0.03 0.02 0.01 0.03

Notes: Sample: January 2010 to June 2017. This table reports dummy variable regression results for specificationsof Equations (1) and (2). The dependent variable is the close-to-close excess return constructed from the Wind A-Share Index. We align the return data of the first trading day on which the equity market has access to the FOMCnews to the dummy variable ItAnns = 1 when i = 0. Announcement dummy ItAnns−i equals one if the i-th tradingday is before (or after if i is negative) an FOMC announcement. Announcement dummy ItAnns−1,3 equals one forthe trading days in a 3-trading-day window before an FOMC announcement. “Other Anns Window Ctrls” controlsfor the remaining day dummies of the announcement window of length of 2T + 1 as T = 5. “Year/Month/WeekdayDummies” control the year, month, and weekday effects. ***, **, *, and + denote significance at 1%, 5%, 10%, and15%, respectively. Robust standard errors are in parentheses.

B.5 Return Responses: Monetary Policy Reports

Besides the monthly announcements of monetary aggregates data, the MPR is issued every

quarter by the PBOC, namely, MPR announcements. We check whether the stock market reacts

to the issuance of this policy report. Table B.5 summarizes the key findings. According to column

(2), the relative excess return per day for a 3-day pre-announcement window is 28 bps, which is

positive and statistically significant at 10%. Column (4) presents the estimated coefficient of a 1-day

daily relative premium of 31 bps, which is not distinguishable from zero in spite of its comparable

magnitude to the coefficient in column (1) of Table 1. We conclude that the equity market responds

11

to the issuance of MPRs ex-ante although the estimated size of the positive premium contains

larger standard errors. In addition, the results of columns (3) and (6) show the estimates of the

pre-announcement coefficients when all events of M2 and MPR announcements are considered.

The coefficients in these columns suggest that given the similar magnitude, the predominant driver

of the pre-announcement premium is the anticipation of announcements of monetary aggregates

data, not the incoming policy reports.

However, greater noise associated with the estimation of the pre-announcement premium in the

case of MPR announcements may be due to the following. First, China’s MPR, although inclusive

of statistics about the conduct of Chinese monetary policy, delivers much more comprehensive

information and the PBOC’s market assessment with little focus on releasing the updated data.

Second, monetary aggregates data are published monthly, which could be more useful for investors

to draw real-time investment implications than an encyclopedia style of quarterly issues of the

MPR.

Table B.5: Returns in Windows Prior to MPR Announcements

(1) (2) (3) (4) (5) (6)VARIABLES M2 Ann. MPR Ann. M2 and MPR Ann. M2 Ann. MPR Ann. M2 and MPR Ann.

ItAnns−1,3 0.31*** 0.28* 0.34***(0.11) (0.17) (0.10)

ItAnns−1 0.39** 0.31 0.37***(0.16) (0.27) (0.14)

Year / Month / Weekday Dummies Yes Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes Yes YesConstant -0.28 -0.27 -0.32 -0.28 -0.27 -0.32

(0.21) (0.20) (0.21) (0.21) (0.20) (0.21)

Observations 1,819 1,819 1,819 1,819 1,819 1,819R2 0.02 0.02 0.02 0.02 0.02 0.02

Notes: Sample: January 2010 to June 2017. This table reports dummy variable regression results for specifications of Equations (1) and(2). The dependent variable is the close-to-close excess return constructed from the Wind A-Share Index. We align the return data of thefirst trading day on which the equity market has access to the MPR reports to the dummy variable ItAnns = 1 when i = 0. Announcementdummy ItAnns−1 equals one for the day that is 1 day before an MPR announcement. Announcement dummy ItAnns−1,3 equals one forthe trading days in a 3-trading-day window before an MPR announcement. “Other Anns Window Ctrls” controls for the remaining daydummies of the announcement window of length of 2T + 1 as T = 5. “Year/Month/Weekday Dummies” controls for the year, month, andweekday effects. ***, **, *, and + denote significance at 1%, 5%, 10%, and 15%, respectively. Robust standard errors are in parentheses.

B.6 Return Responses: Other Markets

We further explore the responses of other asset markets of China to the PBOC’s announcements

of monetary aggregates data. As response variables, we take the daily returns of 10-year government

bond yields, that is, risk-free rates, and the daily excess returns for Chinese A-share futures of 300

big stocks, gold futures, and Chinese Yuan exchange rates against major currencies, including

12

the U.S. Dollar, Japanese Yen, and Euro. According to Table B.6, we find no excess returns for

most asset markets relative to no-announcement windows except for stock futures, despite a 10%

significance level. This evidence confirms our main findings that the excess return of stock market

portfolios, regardless of whether it is computed based on spot or future prices, is particularly

responsive to monetary data releases.

Table B.6: Other Markets’ Reactions to M2 Announcements

(1) (2) (3) (4) (5) (6)VARIABLES R10Y,bond FurtureCSI300 FurtureGold EXUSD EXJPY EXEUR

ItM2−1,3 0.12 0.18* 0.04 -0.00 -0.01 -0.03(0.20) (0.11) (0.07) (0.01) (0.05) (0.04)

Year/Month/Weekday Dummies Yes Yes Yes Yes Yes YesOther Anns Window Ctrls Yes Yes Yes Yes Yes YesConstant 0.18 -0.29 0.20* -0.03** 0.14* -0.04

(0.30) (0.24) (0.11) (0.01) (0.07) (0.07)

Observations 1,819 1,750 1,819 1,819 1,817 1,818

Notes: Sample: January 2010 to June 2017 (Series of FurtureCSI300 starts from April 2010). This table reports dum-my variable regression results of Equation (1) using different dependent variables. Announcement dummy ItM2−1,3 e-quals one for the trading days in a 3-trading-day window before an M2 announcement. “Other Anns Window Ctrls” con-trols for the remaining day dummies of the announcement window of length of 2T +1 as T = 5. “Year/Month/WeekdayDummies” controls for the year, month, and weekday effects. ***, **, *, and + denote significance at 1%, 5%, 10%,and 15%, respectively. Robust standard errors are in parentheses.

C Alternative Model with Recursive Preference

C.1 Expected Return and Uncertainty about Money Growth

Alternatively, we work with a more elaborated model when investors have recursive preference in

the form of Kreps–Porteus and Epstein–Zin utilities. An explicit relationship between the expected

excess return of stock market portfolio and the risk-aversion weighted forecast uncertainty about

money supply growth can be derived.

This model is discrete-time and each period t corresponds to a day. A representative household

maximizes its lifetime utility Vt(ct, zt) for day t, which is defined over real consumption ct and the

certainty equivalent of day t expected continuation value zt such that

Vt(ct, zt) = maxct,xt,bt∞t=0

[(1− β)c1−ξt + β(EtV 1−α

t+1 )1−ξ1−α ]

11−ξ . (C.1)

where zt = (EtV 1−αt+1 )

11−α . ξ and α index the inverse of a household’s elasticity of inter-temporal

substitution and the coefficient of relative risk aversion, respectively. We work with parameter

13

values of α > 1 > ξ such that the household prefers early resolution of uncertainty.

The household chooses consumption ct, equity holding xt, and holding of risk-free bond bt,

which pays one unit of consumption good in period t + 1. β ∈ (0, 1) is the subjective discount

factor. Utility maximization is subject to a daily budget constraint

ct + qtxt +bt

Rft+1

= (qt + yt)xt−1 + bt−1 (C.2)

where qt is the per-share equity price. yt is the per-share dividend payout. The gross rate of risk-

free bond return is given by Rft+1 known as of day t. By definition, the rate of return from risky

equity investment is Rt = qt+ytqt−1

. A portfolio investment with share of holdings φt invested in equity

and 1− φt in the riskless bond on day t gives an aggregate market rate of return for the next day

RW,t+1 = Rft+1 +φt(Rt+1−Rft+1). With the beginning-of-day total wealth Wt = (qt+yt)xt−1 +bt−1,

the budget constraint is equivalently given by Wt+1 = (Wt − ct)RW,t+1.

In addition, we impose the constraint of cash-in-advance, which necessarily binds in equilibrium

such that the total consumption is financed by holding of real balance of monetary aggregate

Mt with ct = ψMt.4 Given that a household’s dividend income is consumed in every period

yt = ct, it follows that yt = ψMt. Now, define mt as the growth rate of real money balance in

log, mt = log(Mt) − log(Mt−1). Thus, we obtain ct+1

ct= emt+1 . In addition, in equilibrium, the

aggregate holding of risk-free bond bt has to be zero with φt = 1 and thus, RW,t+1 = Rt+1.

Imposing constant equity price-dividend ratio χ = qtyt

for simplicity, we derive the first-order

condition which gives the key asset pricing equation in the following

1 = Et[βθe−ξθmt+1Rθt+1] (C.3)

where related terms can be factored into a stochastic discount factor Ωt|t+1 = βθe−ξθmt+1Rθ−1t+1

such that 1 = Et[Ωt|t+1Rt+1] and θ = 1−α1−ξ . According to this equation, by affecting the stochastic

discount factor, investors’ forecast of money supply growth mt+1 can shift the expected equity

returns.

We show that the expected excess equity return in log EXt+1|t is determined by the risk-aversion

4Alternatively, we can reinterpret this equilibrium condition as the quantity theorem of money. Thus, constantψ > 0 measures the velocity of money.

14

α-weighted investors’ forecast uncertainty about future money supply growth as of day t, σ2m,t+1.

EXt+1|t = log(EtRt+1)− log(Rft+1) = α · σ2m,t+1 (C.4)

Equation (C.4) suggests that forecast uncertainty about money supply growth amounts to total

aggregate market risk, which determines the size of the equity premium. Larger uncertainty raises

the expected excess return.

Note that Equation (C.4) holds regardless of whether we are working with a recursive utility

or not. For example, α = ξ makes the recursive preference time separable, which gives investors

optimization over conventional expected utility. Therefore, the expected excess return of stock

market portfolios increases with aggregate market risk, which is shifted by investors’ uncertainty

about future money supply growth. Necessarily, lowered forecast uncertainty reduces the expected

risk premium by raising current stock prices and current returns.

C.2 Signal is Backward Looking and Imperfect

In this subsection, we consider a more complex structure of central bank’s signals. In other

words, money supply growth is announced with time lags and measurement errors. Specifically,

the central bank makes an announcement on day tAi of month i about the money supply growth

realized at the end of previous month i− 1 such that

stAi= mti−1 + ηtAi

(C.5)

where ηtAi∼ N(0, σ2

η) captures the innovations to measurement errors of the signal. This signal

structure sharply differs from the real-time signal modeled in the main section, by which the

announcement releases data about the realization on the announcement day tAi .

We start with a scenario in which investors’ learning is not endogenous. It follows that only the

arrival of the central bank’s announcements affects investors’ conditional expectation and forecast

variance about money supply growth. Upon the arrival of an announcement on day tAi+1 = ti + T ,

15

investors’ forecast of mti+j for j ≥ T with new information incorporated is given by

mti+j|tAi+1= ρjmti|tAi+1

+ (1− ρj)µ (C.6)

Note that the new announcement directly revises the back-cast of mti by updating mti|tAiwith

mti|tAi+1. According to Equation (C.6), the forecast of mti+j is some weighted average of prior belief

and unconditional mean of money supply growth. Similarly, the expected variance of money supply

growth is given by

σ2m,ti+j|tAi+1

= ρ2j σ2m,ti|tAi+1

+ (1− ρ2j)σ2e

1− ρ2(C.7)

Consistent with the implications suggested by Equations (6) and (7), the mean forecast and forecast

uncertainty further in the future become increasingly closer to the unconditional moments of µ and

σ2e

1−ρ2 as j increases.

Now, we consider how mti|tAiis updated to mti|tAi+1

. Applying Bayes’ rule, the updated forecast

linearly combines the forecast that is carried over and the announcement signal weighted by their

relative informativeness. It yields

mti|tAi+1= (1− κ)mti|tAi

+ κstAi+1(C.8)

where κ =1/σ2

η

1/σ2η+1/σ2

m,ti|tAi

captures the Kalman gain of information, which measures how much

the updated forecast should be weighted toward the new signal. Equation (C.8) shows that a

more precise signal of smaller σ2η or a rough forecast of greater σ2

m,ti|tAiraises the Kalman gain.

Consequently, the updated forecast uncertainty must satisfy

1

σ2m,ti|tAi+1

=1

σ2m,ti|tAi

+1

σ2η

(C.9)

Equation (C.9) implies that given a more informative signal of smaller ση, forecast uncertainty

about money supply growth at the end of the previous month is further reduced.

Hence, uncertainty about money supply growth up to day tAi+1 = ti + T is consequently lower

conditional on arrivals of announcements. The size of uncertainty reduction ∆σ2m,tAi+1

can be derived

16

as

∆σ2m,tAi+1

= ρ2T [σ2m,ti|tAi

− σ2m,ti|tAi+1

]

= ρ2Tσ2m,ti|tAi

σ2m,ti|tAi+1

σ2η

(C.10)

The second equality comes directly from Equation (C.9). It is important to note that given perfect

signals similar to the baseline model environment such that ση → 0, uncertainty reduction is infinity,

which leads to ex-post uncertainty of σ2m,tAi+1

→ 0.

Then, considering endogenous learning, similar attention allocation rules of equation system

(14) apply. The associated forecast uncertainty dynamics can be similarly summarized by equation

systems (C.11) and (C.12)

σ2m,t =

(1− φt)σ2m,t + φtσ

2m,t2

−2κ if φt ∈ [ vσ2m,t

22κ, 1] and t 6= tAi

(1− φt)σ2m,t + v if φt ∈ [ v

σ2m,t, vσ2m,t

22κ) and t 6= tAi

σ2m,t if φt ∈ [0, v

σ2m,t

) and t 6= tAi

min 1σ−2m,t+σ

−2η, (1− φt)σ2

m,t + φtσ2m,t2

−2κ∗ if t = tAi

(C.11)

where σ2m,t can be written as a function of forecast uncertainty of day t − 1 after the learning

decision of the previous day is taken.

σ2m,t = ρ2σ2

m,t−1 + σ2e (C.12)

Note that contrary to equation system (15), on announcement days, the forecast uncertainty will

not be zero, but is updated according to Equation (C.9) given imperfect signals.

In summary, regardless of whether we have a simple or a more complex signal structure, learning

can trigger uncertainty reduction, which leads to reduced expected risk premium and higher current

returns.

17

C.3 Derivation of the Loss Function of Learning for Investors

In this subsection, with recursive preference, we explicitly derive an objective function of

quadratic form for investors’ optimization of attention allocation. Investors’ value function at

optimum Vt(ct, zt) is homogeneous of degree one in arguments ct and zt. Conditional on optimized

consumption of previous period ct−1 > 0, we derive

Vt(ct, zt) = ct−1Vt(ctct−1

,ztct−1

) = ct−1Vt(ect , ezt)

where ct = log[ ctct−1

] and zt = log[ ztct−1

]. Up to a second-order Taylor expansion of Vt(ct, zt) around

any arbitrary couplet point of (ct, zt), we obtain

Vt(ect , ezt) = Vt(e

ct , ezt) + Vt,1ect(ct − ct) + Vt,2e

zt(zt − zt)

+Vt,11

2ect(ct − ct)2 +

Vt,22

2ezt(zt − zt)2 + Vt,12e

ctezt(ct − ct)(zt − zt) (C.13)

where Vt,1 and Vt,2 are partial derivatives of Vt with respect to the first and second arguments

evaluated at the centering couplet (ct, zt), respectively. Vt,11, Vt,22, and Vt,12 are the associated

second-order partials and cross-partials. Given Equation (C.13), optimization over current con-

sumption ct yields the first-order condition:

Vt,1 + Vt,11(ct − ct) + Vt,12ezt(zt − zt) = 0

Hence, in the following identity, it holds that ct and zt are linearly related at optimum:

ct = a+ bzt (C.14)

where a = ct − Vt,1Vt,11

+Vt,12ezt ztVt,11

, b = −Vt,12Vt,11

ezt > 0.

Therefore, when evaluating Vt(ect , ezt) up to the second-order around the real optimum couplets

(c∗t , z∗t ), we derive

Vt(ect , ezt) = Vt(e

c∗t , ez∗t )− φt,c(ct − c∗t )2 − φt,z(zt − z∗t )2 + φt,cz(ct − c∗t )(zt − z∗t )

18

Note that first-order conditions about ct and zt hold at the optimum such that the first-order terms

cancel out to zeros because V ∗t,1 = 0 and V ∗t,2 = 0. Other partials and cross-partials evaluated at

the optimum couplets are absorbed into terms φt,c = −ec∗t V∗t,11

2 > 0, φt,z = −ez∗t V∗t,22

2 > 0, and

φt,cz = V ∗t,12ec∗t ez

∗t > 0.

Define loss function L(ct, zt) = ct−1L(ct, zt) where

L(ct, zt) = Vt(c∗t , z∗t )− Vt(ct, zt)

=λt2

(ct − c∗t )2

The second equality directly follows from the fact that investors choose ct and zt according to

Equation (C.14) for any chosen couplets. Hence, after substituting zt and z∗t , we have λt =

2(φt,c +φt,zb2− φt,cz

b ) ≥ 0 as some time-varying constant depending on the true states, which makes

the loss non-negative. Imposing the equilibrium condition of ct = ψMt yields log[ ctct−1

] = log(Mt)−

log(Mt−1) = mt, and we can express the loss function in the form of volatility of the money supply

growth rate due to suboptimal beliefs.

In other words, abstracting from constant λt which is independent of investors’ beliefs, in-

vestors optimize the attention allocation in order to minimize the expected gap of real state and

all perceived states of mt such that

1

2E(mt −m∗t )2

D Proofs

D.1 Proof of Equation (C.3)

For ease of notations, we first define mct and mVt+1 as follows:

mct =∂Vt∂ct

= (1− β)V ξt c−ξt

mVt+1 =∂Vt∂Vt+1

= βV ξt (EV 1−α

t+1 )α−ξ1−αV −αt+1

19

By the fact that V (ct, zt) is homogeneous of degree one in ct and zt, we can show that the following

equation holds at the optimum.

Vt = mct · ct + E[mVt+1 · Vt+1]

Defining Wt = Vtmct

, it follows that

Wt = ct + E[mVt+1 ·mct+1

mct· Wt+1]

Rearranging, we obtain

1 = E[mVt+1 ·mct+1

mct· Wt+1

Wt − ct]

In the following part, we show that the stochastic discount factor can be defined as Ωt|t+1 =

mVt+1·mct+1

mctand RW,t+1 = Wt+1

Wt−ct such that Wt = Wt at optimum. Maximizing equation (C.1)

subject to Equation (C.2) when expressed in the function of beginning-of-day wealth Wt yields the

first-order condition regarding optimal wealth level of t+ 1:

E[mVt+1 ·∂Vt+1

∂Wt+1·RW,t+1] = mct

with marginal value of wealth at t given by ∂Vt∂Wt

= mct according to the envelope theorem. This

yields

1 = E[mVt+1 ·mct+1

mct·RW,t+1]

and we have Wt = Wt = Vtmct

at optimum. Thus, the stochastic discount factor is

Ωt|t+1 =βV ξ

t (EV 1−αt+1 )

α−ξ1−αV −αt+1(1− β)V ξ

t+1c−ξt+1

(1− β)V ξt c−ξt

=β[ct+1

ct]−ξ[

Vt+1

[EV 1−αt+1 ]

11−α

]ξ−α

20

The equilibrium return of the market portfolio RW,t+1 can be expressed as

RW,t+1 =Wt+1

Wt − ct

=Vt+1/[(1− β)V ξ

t+1c−ξt+j ]

Vt/[(1− β)V ξt c−ξt ]− ct

= β[ct+1

ct]−ξ[

Vt+1

[EV 1−αt+1 ]

11−α

]ξ−1−1

Now, substitute the ratio of future value relative to the certainty equivalence Vt+1

[EV 1−αt+1 ]

11−α

as function

RW,t+1 from the stochastic discount factor. We obtain the following for all states:

Ωt|t+1 = β[ct+1

ct]−ξ[R−1

W,t+1/(β[ct+1

ct]−ξ)]

ξ−αξ−1

= βθ[ct+1

ct]−ξθRθ−1

W,t+1

where θ = 1−α1−ξ .

Hence, in equilibrium, the stock market portfolio return satisfies Rt+1 = Rw,t+1 such that

1 = E[mVt+1 ·mct+1

mct·Rt+1]

Similarly, the following holds for the risk-free rate Rft+1.

1 = E[Ωt|t+1 ·Rft+1] (D.1)

D.2 Proof of Equation (C.4)

By Equation (C.3), we exploit the assumption that the price-dividend ratio is constant χ.

1 = E[(β(1 + χ)

χ)θ · e(1−α)mt+1 ]

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Given that the AR(1) process governing real money supply growth has lognormal structure, we

obtain the following

log[1 + χ

χ] = −[log β + (1− ξ)mt+1 +

(1− ξ)(1− α)

2σ2m,t+1]

By Equation (D.1), it follows that

1 = E[βθe−ξθmt+1(1− χχ

emt+1)θ−1 ·Rft+1]

Rft+1 can be solved as

log(Rf ) = − log β + ξmt+1 +ξ − α− αξ

2σ2m,t+1)

Based on the fact that Rt+1 = 1+χχ

ct+1

ct, the expected equity return is as follows:

ERt+1 = E((1 + χ)

χemt+1)

This is solved as

log(ERt+1) = − log β + ξmt+1 +ξ + α− αξ

2σ2m,t+1

Hence, EXt+1|t = log(ERt+1)− log(Rft+1) follows.

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