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NBP Working Paper No 983089983097983092

How frequently should we re-estimate

DSGE models

Marcin Kolasa Michał Rubaszek



Economic InstituteWarsaw 983090983088983089983092



DSGE models




Published byNarodowy Bank PolskiEducation amp Publishing Departmentul Świętokrzyska 112100-919 Warszawa Polandphone +48 22 185 23 35wwwnbppl

ISSN 2084-624X

copy Copyright Narodowy Bank Polski 2014

Marcin Kolasa ndash corresponding author Narodowy Bank Polski and Warsaw Schoolof Economics Narodowy Bank Polski ul Świętokrzyska 1121 00-919 Warsaw Polandtel +48 22 185 24 65 fax +48 22 185 43 74 marcinkolasanbpplMichał Rubaszek ndash Narodowy Bank Polski and Warsaw School of Economicsmichalrubaszeknbppl

We are grateful to the participants of the International Symposium on Forecasting in Seouland the seminar at the Narodowy Bank Polski as well as three anonymous referees for useful

comments The views expressed in this paper are those of the authors and not necessarily ofthe institutions they represent



983091NBP Working Paper No 983089983097983092

1 Introduction

2 Model

3 Forecasting contest

4 Results

41 Point forecasts

42 Density forecasts

43 Robustness checks

5 Conclusions

References

Tables

Appendix

A List of model equations

B Data

C Measurement equations

D Calibration and prior assumptions

E Introducing financial frictions

5

7

8

10

10

11

13

14

16

18

23

23

25

26

26

28

Contents



Narodowy Bank Polski983092

Abstract

Abstract

A common practice in policy making institutions using DSGE models for forecasting

is to re-estimate them only occasionally rather than every forecasting round In

this paper we ask how such a practice affects the accuracy of DSGE model-based

forecasts To this end we use a canonical medium-sized New Keynesian model

and compare how its quarterly real-time forecasts for the US economy vary with

the interval between consecutive re-estimations We find that updating the model

parameters only once a year usually does not lead to any significant deterioration

in the accuracy of point forecasts On the other hand there are some gains from

increasing the frequency of re-estimation if one is interested in the quality of density

forecasts

Keywords forecasting DSGE models parameter updating

JEL Classification C53 E37




Chapter 1048625

1 Introduction

Dynamic stochastic general equilibrium (DSGE) models are currently the workhorse

framework in macroeconomic analyses and forecasting Their use is widespread in policy

making institutions and central banks in particular One of the reasons for the popular-

ity of DSGE models is that their forecasting performance has been found to be relatively

good in comparison to standard time series models as well as expert judgment (see eg

Smets and Wouters 2003 Adolfson Linde and Villani 2007 Rubaszek and Skrzypczyn-

ski 2008 Edge Kiley and Laforte 2010 Kolasa Rubaszek and Skrzypczynski 2012

Wieland and Wolters 2012 Del Negro and Schorfheide 2012)

A common practice in institutions using DSGE models for forecasting is to re-estimate

them only occasionally rather than every time a new forecast is produced The main

reason applying also to other econometric models is that re-estimation complicates com-

munication between the modelers and policy makers as the difference between consecutive

forecasts is affected both by new data release and changes in parameter estimates Infre-

quent re-estimation decreases the number of forecasting rounds during which this second

source of the difference has to be taken into account Also the policy makers can get

used to certain model properties the response of the economy to a monetary shock for

instance hence do not want to see them change every time a new forecast is produced

Another argument supporting this practice though its relevance is certainly diminishing

due to increasing computing power of multi-core processors is that the estimation process

of large DSGE models can be very time consuming Needless to say if every change in

model properties needs to be documented and communicated to the policy makers fre-

quent re-estimations eat up even more time and prevent modelers from getting involved

in potentially more productive projects The final argument is that to our best knowl-

edge there are no clear guidelines in the literature on how frequently models should be

re-estimated so that the accuracy of forecasts they generate is unaffected




In contrast to real-life applications most of the literature investigating performance of

DSGE model-based forecasts is based on out-of-sample exercises where model parameters

are updated quarterly Only few studies re-estimate the model parameters at longer in-

tervals eg every four quarters (Adolfson Linde and Villani 2007 Smets and Wouters

2007 Christoffel Coenen and Warne 2010) or even only once at the beginning of the

evaluation sample (Giannone Monti and Reichlin 2010) None of the above papers dis-

cuss how infrequent model re-estimation affects forecast accuracy While it is possible that

using most recent data does not necessarily improve forecasts obtained with economet-

ric models (see eg Swamy and Schinasi 1986) one can also be concerned that obsolete

parameter estimates may have non-negligible costs in terms of the quality of predictions

generated for some macroaggregates influencing the policy decisions

To provide some guidelines for practitioners in this study we ask the following ques-

tion how often should we update DSGE model parameters to obtain efficient predictions

about the main macrovariables To answer it we take a canonical medium-sized New

Keynesian model and compare how its quarterly real-time forecasts for the US economy

vary with the interval between consecutive re-estimations Our main results based on

three key macroeconomic variables (output inflation and the interest rate) can be sum-

marized as follows We find that updating the model parameters only once a year does

not lead to any significant deterioration in the accuracy of point forecasts Even though

there are some gains from increasing the frequency of re-estimation if one is interested in

the quality of density forecasts these gains are rather small These general conclusions

are robust to using looser priors in our benchmark model or augmenting it with finan-

cial frictions Finally much of the decrease in forecast precision that is observed when

re-estimations become less frequent is because of shorter sample rather than due to data

revisions

The rest of this paper is organized as follows Section two presents the benchmark




Chapter 983090

model that we use in our investigation Section three describes the settings of the fore-

casting contest The main results and robustness checks are discussed in section four

The last section concludes

2 Model

Our investigation is based on the canonical medium-sized New Keynesian framework of

Smets and Wouters (2007) It features utility maximizing households profit maximizing

firms a fiscal authority financing exogenous spending with lump sum taxes and a central

bank setting short term interest rates according to a Taylor-like rule The model incorpo-

rates a number of real and nominal rigidities including habits in consumption investment

adjustment costs time-varying capacity utilization as well as wage and price stickiness

with indexation

The exact specification we use differs from Smets and Wouters (2007) only in that we

additionally allow for trend investment-specific technological progress This modification

is aimed to account for the deviation between the average growth rate of real investment

and that of other GDP components1 A full list of log-linearized model equations can be

found in the Appendix

All estimations are done using Bayesian methods and seven standard quarterly macroe-

conomic variables for the US output consumption investment wages hours worked

inflation and the interest rate Full definitions and sources of the real-time data used

are given in the Appendix The prior assumptions are identical to those in Smets and

Wouters (2007) and also listed in the Appendix The posterior distributions are approx-

imated using the Metropolis-Hastings algorithm with 250000 replications out of which

we drop the first 50000

1Smets and Wouters (2007) deal with this discrepancy in long-run trends by defining real investmentas nominal investment deflated with the GDP deflator We cannot follow this path since there is nonominal investment series in our real-time database




Chapter 983091


We compare the accuracy of forecasts generated by the DSGE model the parameters of

which are re-estimated according to the following five schemes2

update 1Q the model is re-estimated each quarter (baseline variant)

update 2Q estimation is repeated when the data for the 2nd or 4th quarter are available

update 1Y the model is re-estimated when full-year data are available

update 2Y the model is re-estimated only in even years

fixed the parameters are estimated once at the beginning of the forecast evaluation

sample

Our investigation proceeds in three steps First we collect quarterly real time data

(RTD) describing the US economy in the period between 19661 and 20114 The data

are taken from the Philadelphia Fed ldquoReal-Time Data Set for Macroeconomistsrdquo which

is described in more detail by Croushore and Stark (2001) The use of RTD enables us

to control for both reasons that support frequent re-estimation which we call sample and

vintage effects To be more precise let θvT be the vector of parameter estimates based on

the sample 1 T from vintage date v The difference between the current estimates and

those done q quarters ago using the data vintage available at that time can be decomposed

into

θvT minus θ

vminusq

T minusq = (θvT minus θv

T minusq)

sample effect

+ (θvT minusq minus θ

vminusq

T minusq)

vintage effect

(1)

Hence our main forecasting contest that uses RTD captures both sample and vintage

effects In the case in which we use the latest available data (LAD) the differences in

2In practice some of re-estimations might be carried out in response to changes in model structure

or data definitions rather than according to fixed schedule Our alternative schemes do not account forsuch a possibility




Forecasting contest

forecast accuracy between the five schemes is only due to the sample effect

In the second step for each moment of forecast formulation t from the period 19894

- 20113 horizon h and forecasting scheme j we compute point forecasts - yf t+h|t j - as

well as the predictive scores p(yt+h|t j) More precisely out of 200000 posterior draws for

parameter vector θ obtained with the Metropolis-Hastings algorithm we select N = 5 000

equally spaced subdraws θ(n) for n = 1 2 N For each θ(n) we calculate the first

two moments of the predictive density p(Y t+h|tjθ(n)) which has Gaussian distribution3

Subsequently following Geweke and Amisano (2014) the point forecast is computed as

the mean of the first moments

yf t+h|t j =

1

N

N sum

n=1

E (Y t+h|tjθ(n)i ) (2)

whereas the predictive score is obtained as the average of the predictive densities evaluated

at the realization yt+h of Y t+h

p(yt+h|t j) = 1

N

N sum

n=1

p(yt+h|tjθ(n)i ) (3)

The forecasting scheme is recursive4 the evaluation sample spans from 19901 to 20114

and the maximum forecast horizon is twelve quarters Thus the first set of forecasts is

generated for the period 19901-19924 with the model estimated on the sample span-

ning 19661-19894 The second set of forecasts is for the period 19902-19931 with the

model estimated on the sample 19661-19901 (baseline scheme) or 19661-19894 (remain-

ing schemes) The third set of forecasts is for the period 19903-19932 with the model

estimated on the sample 19661-19902 (baseline and update 2Q) or 19661-19894 (re-

3For each parameter draw the Kalman filter is used to obtain smooth estimates of unobservable modelstates given the data available at the time the forecast is formulated (RTD variant) or the latest availabledata (LAD variant)

4The results for the rolling forecasting scheme which are available upon request lead to broadly thesame conclusions as those presented in Section 4



Narodowy Bank Polski 983089983088

Chapter 1048628

maining schemes) etc Since our dataset ends in 20114 the number of forecasts that we

can use in evaluation ranges from 77 (for 12-quarter ahead forecasts) to 88 (for 1-quarter

ahead forecasts)

In the third stage we assess the quality of forecasts for the key three US macroeconomic

time series output inflation and the interest rate Given that the maximum forecast

horizon is relatively long the comparisons are for output and price levels rather than

growth rates The realizations which we call actuals are taken from the latest available

vintage ie the data released in 20121

4 Results

In this section we report the relative accuracy of point and density forecasts which is eval-

uated with the root mean squared forecast error (RMSFE) and the average log predictive

scores (LPS) respectively

41 Point forecasts

We begin our comparison by analyzing point forecasts Table 1 reports the values for

the RMSFEs both using real-time and latest available data As discussed above the

former case allows us to capture both sample and vintage effects while the latter distills

the sample effect The numbers for the update 1Q scheme (our baseline) represent the

values of the RMSFEs while the remaining numbers are expressed as ratios so that

values above (below) unity indicate that a given scheme underperforms (overperforms)

the baseline Moreover to provide a rough gauge of whether the RMSFE ratios are

significantly different from unity we report the results of the Diebold-Mariano test

The RTD results show that the accuracy of update 2Q and update 1Y schemes are not

significantly different from the baseline For the update 2Y variant the ratios for output

inflation and the interest rate tend to be above unity and in many cases significantly




Results

so This brings us to the first conclusion the parameters of the canonical medium-sized

DSGE model can be re-estimated once a year without a significant loss of point forecasts

accuracy for the main macrovariables However less frequent re-estimation leads to a

significant deterioration in the quality of predictions for these variables

As regards the fixed scheme the loss in forecast precision is very large For instance

the RMSFEs for the interest rate go up by as much as 30 compared to the baseline The

ratios are even larger for output and the price level exceeding 15 and 18 for the 3-year

horizon Hence our second conclusion is that evaluating the forecasting performance of

DSGE models without updating their parameters can give a distorted picture

The comparison of the RTD and LAD results for the baseline scheme indicates that

the use of RTD generates the RMSFEs for output and inflation that are about 10 higher

than in the LAD case For the remaining updating schemes except for the fixed one the

RMSFE ratios are very similar Since there is no vintage effect for LAD our third finding

is conclusion one (re-estimate the model at least once a year) is driven mainly by the

sample effect


We complement the discussion of point forecasts accuracy with an evaluation of density

forecasts The aim is to check to what extent the analyzed forecasts provide a realistic

description of actual uncertainty The quality of the density forecast is assessed with

the average log predictive score statistic which for h-step ahead forecasts from the j-th

scheme is equal to the mean value of log of p(yt+h|t j) computed with formula (3)

In Tables 2 and 3 we report the values of average LPS for each of the three key

macroeconomic variables separately and for their joint distribution respectively As

before we present the results for models estimated with RTD as well as with LAD The

numbers for the baseline represent the levels whereas the remaining numbers are expressed




as differences so that values below zero indicate that a given scheme underperforms the

baseline To provide a rough gauge of whether these differences are significantly different

from zero we report the results of the Amisano and Giacomini (2007) test

The RTD results for individual variables show that decreasing the frequency of model

re-estimation leads to a deterioration in the quality of density forecasts However the

decrease in the fit although in some cases statistically significant is not large for the

update 2Q and update 1Y schemes the average value of the predictive likelihood is up

to 13 lower than for the baseline depending on the variable and horizon For the

multivariate forecasts which take into account the covariances the differences in the

average LPSs for the upadete 1Y scheme are somewhat higher amounting up to 26

and statistically significant For the update 2Y and fixed schemes the LPS differences are

significantly negative for most variables and horizons Moreover their values indicate a

sizeable decline in the average predictive likelihood amounting in the update 2Y scheme

to around 7 for the joint density of all three macrovariables The loss under the fixed

scheme is even larger reaching 80 in the multivariate case We interpret these results

as confirming our conclusions formulated for point forecasts ie that DSGE models

should be re-estimated at least once a year Moreover they also show that there are some

gains from re-estimating the model more frequently than once a year especially if one is

interested in the quality of multivariate density forecasts

The comparison of the RTD and LAD results for the baseline scheme shows that the

use of RTD decreases the accuracy of density forecasts for output and inflation with the

fall in the average LPSs ranging from 5 to 15 The decline is most sizable for the short-

term inflation forecasts The comparison of the LPS differences for the remaining schemes

indicates that they are broadly the same for the RTD and LAD cases This confirms our

earlier finding that the sample effect dominates the vintage effect




Results


The results presented above suggest that the parameter estimates of our benchmark model

are quite stable At least to some extent this may be due to the prior assumptions bor-

rowed from the original Smets and Wouters (2007) model which are sometimes considered

to be rather tight To check if this is the case we repeat our calculations with looser pri-

ors More specifically we increase the standard deviations of prior distributions for all

structural parameters by 50 except for the degree of indexation and capacity utilization

cost curvature for which the standard deviations are raised by 335

The results of this robustness check are presented in Table 4 They show that loos-

ening the priors usually slightly improves the quality of short-term forecasts and quite

sizeably decreases it for longer horizons Looking at a comparison across alternative up-

dating schemes this variant suggests that re-estimations can be carried out every two

years without significantly affecting the quality of point forecasts for output and infla-

tion As regards the density forecasts the main conclusions are broadly the same as those

formulated using our baseline results

Our next check is motivated by the absence of a financial sector in the benchmark

Smets and Wouters (2007) model even though one might argue that risk premium shocks

can capture at least to some extent disruptions in financial intermediation This simpli-

fied description of financial markets may significantly affect the forecasting performance

especially during times of financial stress We address this concern by augmenting the

benchmark model with the financial accelerator mechanism in the spirit of Bernanke

Gertler and Gilchrist (1999) The exact implementation of this extension follows Del Ne-

gro Giannoni and Schorfheide (2014) and uses corporate bond spreads as an additional

observable variable The details can be found in the Appendix

Table 5 summarizes the results of this robustness check In the short-run the quality

5For these parameters increasing the standard deviations of the prior (beta) distributions by 50would result in bimodality




Chapter 983093

of point forecasts for output and the interest rate improve However if we focus on longer

horizons the picture is reversed and the accuracy of predictions for prices clearly deteri-

orates across the board Similar patterns emerge for density forecasts These findings are

in line with Del Negro and Schorfheide (2012) and Kolasa and Rubaszek (2015) who show

that including financial frictions in the corporate sector usually generates less accurate

forecasts even though their quality improves during the Great Recession As regards the

frequency of re-estimation in this alternative specification the results suggest to do it

twice rather than once a year if the main focus is on point forecasts for output and prices

Otherwise and especially if the quality of density forecasts is the main target the results

are consistent with our baseline conclusions

Finally one might be concerned that our recommended interval between consecutive

model re-estimations might be driven by choosing the first quarter of the year in the 1Y

and 2Y schemes as the time of parameter update or by some special events occurring just

before re-estimation in the 1Y schedule (and hence one year before that done according to

the 2Y scheme) The additional checks (not reported but available upon request) prove

that this is not the case and that our main conclusions are based on the intrinsic features

of the alternative updating schemes

5 Conclusions

The results of this study show that the common practice used by the policy making in-

stitutions to re-estimate DSGE models only occasionally is justified and does not lead

to any sizable loss in forecast accuracy for the main macrovariables as long as the in-

terval between consecutive re-estimations does not exceed one year Such a frequency of

updating the model parameters facilitates the communication between the modelers and

policy makers and allows to save on model maintenance costs without coming at the

expense of forecast quality The main source of deterioration in forecast precision when




Conclusions

re-estimations become less frequent is related to new data arrival (sample effect) rather

than data revisions (vintage effect) Finally according to our results while assessing

the forecasting performance of DSGE models it might matter whether real-time or latest

available data are used




References

References

Adolfson Malin Jesper Linde and Mattias Villani 2007 ldquoForecasting Performance of

an Open Economy DSGE Modelrdquo Econometric Reviews 26 (2-4)289ndash328

Amisano Gianni and Raffaella Giacomini 2007 ldquoComparing Density Forecasts via

Weighted Likelihood Ratio Testsrdquo Journal of Business amp Economic Statistics 25177ndash

190

Bernanke Ben S Mark Gertler and Simon Gilchrist 1999 ldquoThe financial accelerator in

a quantitative business cycle frameworkrdquo In Handbook of Macroeconomics Handbook

of Macroeconomics vol 1 edited by J B Taylor and M Woodford chap 21 Elsevier

1341ndash1393

Christoffel Kai Gunter Coenen and Anders Warne 2010 ldquoForecasting with DSGE

modelsrdquo Working Paper Series 1185 European Central Bank

Croushore Dean and Tom Stark 2001 ldquoA real-time data set for macroeconomistsrdquo

Journal of Econometrics 105 (1)111ndash130

Del Negro Marco Marc Giannoni and Frank Schorfheide 2014 ldquoInflation in the GreatRecession and New Keynesian Modelsrdquo NBER Working Papers 20055 National Bureau

of Economic Research Inc

Del Negro Marco and Frank Schorfheide 2012 ldquoDSGE Model-Based Forecastingrdquo In

Handbook of Economic Forecasting Handbook of Economic Forecasting vol 2 edited

by G Elliott and A Timmermann Elsevier

Edge Rochelle M Michael T Kiley and Jean-Philippe Laforte 2010 ldquoA comparison

of forecast performance between Federal Reserve staff forecasts simple reduced-form

models and a DSGE modelrdquo Journal of Applied Econometrics 25 (4)720ndash754

Geweke John and Gianni Amisano 2014 ldquoAnalysis of Variance for Bayesian Inferencerdquo

Econometric Reviews 33 (1-4)270ndash288

Giannone Domenico Francesca Monti and Lucrezia Reichlin 2010 ldquoIncorporating con-

junctural analysis in structural modelsrdquo In The Science and Practice of Monetary

Policy Today edited by Volker Wieland Springer Berlin Heidelberg 41ndash57

Kolasa Marcin and Michal Rubaszek 2015 ldquoForecasting using DSGE models with finan-

cial frictionsrdquo International Journal of Forecasting 31 (1)1ndash19




References

Kolasa Marcin Michal Rubaszek and Pawel Skrzypczynski 2012 ldquoPutting the New

Keynesian DSGE model to the real-time forecasting testrdquo Journal of Money Credit

and Banking 44 (7)1301ndash1324

Rubaszek Michal and Pawel Skrzypczynski 2008 ldquoOn the forecasting performance of a

small-scale DSGE modelrdquo International Journal of Forecasting 24 (3)498ndash512

Smets Frank and Raf Wouters 2003 ldquoAn Estimated Dynamic Stochastic General Equi-

librium Model of the Euro Areardquo Journal of the European Economic Association

1 (5)1123ndash1175

Smets Frank and Rafael Wouters 2007 ldquoShocks and Frictions in US Business Cycles A

Bayesian DSGE Approachrdquo American Economic Review 97 (3)586ndash606

Swamy PAVB and Garry J Schinasi 1986 ldquoShould fixed coefficients be reestimated

every period for extrapolationrdquo International Finance Discussion Papers 287 Board

of Governors of the Federal Reserve System (US)

Wieland Volker and Maik H Wolters 2012 ldquoForeacasting and Policy Makingrdquo In






Tables

Tables

Table 1 Root Mean Squared Forecast Errors (RMSFE)H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data results

Output

update 1Q 066 117 202 261 308 414update 2Q 100 100 100 100 100 101lowast

update 1Y 101 101 101 101 102 101update 2Y 103 102 103lowast 104lowastlowast 104lowastlowastlowast 104lowastlowast

fixed 101 099 114 135 151lowastlowast 155lowastlowast

Prices

update 1Q 026 047 087 130 177 277update 2Q 100 099 099 099 100 101update 1Y 100 099 099 100 100 102update 2Y 100 100 101 102 104 107lowastlowast

fixed 101 110 138lowastlowast 161lowastlowastlowast 173lowastlowastlowast 181lowastlowastlowast

Interest rate

update 1Q 012 022 038 046 052 057update 2Q 100 100 100 100 100 100update 1Y 100lowast 100 100 100 100 099

update 2Y 102

lowastlowast

103

lowastlowast

102

lowast

101 101 098fixed 127lowastlowastlowast 129lowastlowastlowast 130lowastlowastlowast 127lowastlowastlowast 122lowastlowastlowast 116lowastlowastlowast

Latest available data results

Output

update 1Q 061 107 192 250 288 365update 2Q 101 101 101 100 101 101update 1Y 101 102 101 101 102lowast 101update 2Y 103 103 103 103 104 103fixed 113lowast 111lowast 102 097 094 092

Prices

update 1Q 021 039 077 120 172 285

update 2Q 101 101 101 100 099 099update 1Y 102 103 102 102 102 103update 2Y 103 105 105 104 104 105fixed 106 110 120lowastlowast 131lowastlowastlowast 139lowastlowastlowast 148lowastlowastlowast

Interest rate

update 1Q 012 023 039 048 054 059update 2Q 100 100 100 100 100 100update 1Y 102lowast 102 101 100 100 100update 2Y 101 102 102 102 101 099fixed 122lowastlowast 123lowastlowast 124lowastlowastlowast 126lowastlowastlowast 129lowastlowastlowast 135lowastlowastlowast

Notes For the baseline (update 1Q) the RMSFEs are reported in levels whereas for the remaining

schemes they appear as the ratios so that the values above unity indicate that a given scheme has ahigher RMSFE than the baseline Asterisks lowastlowastlowast lowastlowastand lowastdenote the 1 5 and 10 significance levelsof the Diebold-Mariano test where the long-run variance is calculated with the Newey-West method




Tables

Table 2 Average univariate Log Predictive Scores (LPS)H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

Output

update 1Q -1121 -1660 -2197 -2461 -2628 -2895update 2Q -0004 -0002 -0003 -0003 -0004 -0008lowast

update 1Y -0010lowastlowastlowast -0009 -0012lowast -0013lowast -0012 -0010update 2Y -0022lowastlowastlowast -0023lowastlowast -0032lowastlowastlowast -0032lowastlowastlowast -0030lowastlowast -0026lowast

fixed -0123lowastlowast -0099 -0132 -0231 -0323lowast -0422lowastlowast

Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast

update 1Y -0002 0000 -0001 -0001 -0003 -0008update 2Y -0008lowast -0005 -0008 -0012lowast -0016lowastlowast -0029lowastlowastlowast

fixed -0134lowastlowastlowast -0204lowastlowastlowast -0297lowastlowastlowast -0355lowastlowastlowast -0392lowastlowastlowast -0439lowastlowastlowast

Interest rate

update 1Q 0324 -0128 -0549 -0738 -0841 -0941update 2Q -0004lowastlowast -0004lowastlowast -0003 -0003 -0002 0001update 1Y -0008lowastlowastlowast -0009lowastlowastlowast -0009lowastlowastlowast -0006 -0003 0003update 2Y -0019lowastlowastlowast -0023lowastlowastlowast -0024lowastlowastlowast -0021lowastlowast -0018 0006fixed -0175lowastlowastlowast -0202lowastlowastlowast -0211lowastlowastlowast -0194lowastlowastlowast -0162lowastlowastlowast -0108lowastlowastlowast

Latest available data

Output

update 1Q -1082 -1599 -2148 -2420 -2574 -2799update 2Q -0005 -0007 -0006 -0003 -0004 -0004update 1Y -0010lowast -0013 -0012 -0012lowast -0015lowastlowast -0011lowast

update 2Y -0020lowast -0024 -0028lowast -0030lowastlowast -0035lowastlowast -0028lowastlowast

fixed -0139lowastlowastlowast -0124lowastlowastlowast -0076 -0055 -0057 -0042

Prices

update 1Q 0013 -0673 -1431 -1883 -2202 -2633update 2Q -0004 -0004 -0002 -0001 0000 0000update 1Y -0009 -0010 -0010 -0009 -0010 -0014update 2Y -0016 -0020lowast -0023lowastlowast -0023lowastlowast -0023lowastlowast -0028lowastlowast


Interest rate

update 1Q 0334 -0122 -0551 -0742 -0843 -0933update 2Q -0004lowast -0004 -0003 -0001 0000 0002update 1Y -0012lowastlowastlowast -0014lowastlowast -0009 -0003 -0001 0001update 2Y -0015lowastlowastlowast -0019lowastlowastlowast -0021lowastlowast -0020 -0018 0004fixed -0162lowastlowastlowast -0172lowastlowastlowast -0183lowastlowastlowast -0204lowastlowastlowast -0229lowastlowastlowast -0268lowastlowastlowast

Notes For the baseline (update 1Q) LPSs are reported in levels whereas for the remaining schemes theyappear as the differences so that the values below zero indicate that a given scheme has a lower LPS thanthe baseline Asterisks lowastlowastlowast lowastlowastand lowastdenote the 1 5 and 10 significance levels for the Amisano andGiacomini (2007) test where the long-run variance is calculated with the Newey-West method




Table 3 Average multivariate Log Predictive Scores (LPS) for output prices and iterestrate

H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246

update 2Q -0007lowast -0004 -0006 -0007 -0010lowast -0014lowastlowast

update 1Y -0020lowastlowastlowast -0018lowastlowast -0025lowastlowastlowast -0026lowastlowast -0025lowastlowast -0015

update 2Y -0050lowastlowastlowast -0052lowastlowastlowast -0070lowastlowastlowast -0073lowastlowastlowast -0068lowastlowastlowast -0044lowast



update 1Q -0679 -2300 -3962 -4847 -5404 -6122

update 2Q -0012lowast -0014lowast -0011 -0007 -0007 -0006update 1Y -0027lowastlowast -0031lowastlowast -0027lowastlowast -0024lowast -0027lowastlowast -0022

update 2Y -0047lowastlowastlowast -0057lowastlowastlowast -0064lowastlowastlowast -0068lowastlowast -0071lowastlowast -0045lowast


Notes See notes to Table 2




Tables

Table 4 Relative forecast accuracy of model with loose priorsH = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Root Mean Squared Forecast Errors

Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102

fixed 106 104 115 131 139lowast 134lowastlowast

Prices

update 1Q 025 046 091 145 207 343

update 2Q 100 100lowast

100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102

fixed 109 126lowastlowast 156lowastlowastlowast 171lowastlowastlowast 174lowastlowastlowast 171lowastlowastlowast

Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100

update 1Y 101lowastlowast 101lowast 101lowast 101lowast 101 100

update 2Y 102lowast 102lowastlowast 102lowastlowast 102lowast 101 100

fixed 141lowastlowastlowast 145lowastlowastlowast 143lowastlowastlowast 137lowastlowastlowast 130lowastlowastlowast 121lowastlowastlowast

Average Log Predictive Scores

Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005

update 1Y -0008lowastlowastlowast -0007lowastlowast -0007 -0006 -0005 -0002

update 2Y -0013lowastlowastlowast -0013lowastlowast -0018lowastlowastlowast -0023lowastlowast -0023lowast -0024lowast

fixed -0139lowastlowastlowast -0120 -0147 -0218 -0267lowastlowast -0287lowastlowast

Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972

update 2Q -0004lowastlowast -0005lowastlowast -0004 -0003 -0002 0002

update 1Y -0011lowastlowastlowast -0012lowastlowastlowast -0012lowastlowastlowast -0011lowastlowastlowast -0008lowast 0001

update 2Y -0018lowastlowastlowast -0018lowastlowastlowast -0018lowastlowastlowast -0018lowastlowastlowast -0016lowastlowast -0003


3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast

-0012 -0010 -0004update 2Y -0035lowastlowastlowast -0027lowastlowastlowast -0027lowastlowast -0031lowastlowast -0032lowast -0035lowast


Notes See notes to Tables 1 and 2




Table 5 Relative forecast accuracy of model with financial frictionsH = 1 H = 2 H = 4 H = 6 H = 8 H = 12


Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast

update 1Y 102lowastlowast 101lowastlowast 102lowastlowastlowast 103lowastlowastlowast 102lowastlowast 102lowastlowast


fixed 122lowast 136lowast 147lowastlowast 154lowastlowast 157lowastlowast 157lowastlowastlowast

Prices

update 1Q 026 052 120 212 325 586

update 2Q 100 100 101 101 101 102update 1Y 101lowast 102lowast 103lowast 104lowast 105lowastlowast 105lowastlowast

update 2Y 104lowastlowastlowast 106lowastlowastlowast 110lowastlowastlowast 111lowastlowastlowast 111lowastlowastlowast 110lowastlowastlowast

fixed 121lowastlowast 148lowastlowastlowast 191lowastlowastlowast 215lowastlowastlowast 228lowastlowastlowast 243lowastlowastlowast

Interest rate

update 1Q 011 020 037 052 065 083

update 2Q 100lowastlowast 100 100 100 100 100

update 1Y 100 100 101 102lowast 102lowast 102lowast

update 2Y 101 102 102 102 102 103lowastlowast


Log Predictive Scores

Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022

update 2Q -0004 -0001 -0006lowast -0006 -0006 -0012lowast

update 1Y -0009lowastlowastlowast -0010lowastlowastlowast -0020lowastlowastlowast -0021lowastlowastlowast -0018lowastlowast -0021lowast

update 2Y -0015lowastlowastlowast -0015lowastlowastlowast -0025lowastlowastlowast -0022lowastlowast -0016 -0023

fixed -0138lowastlowast -0203lowastlowast -0308lowast -0425lowastlowast -0557lowastlowast -0877lowastlowastlowast

Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007

update 1Y -0022lowast -0025lowast -0030lowastlowast -0032lowastlowast -0031lowastlowast -0031lowastlowast

update 2Y -0079lowastlowast -0100lowastlowast -0108lowastlowast -0096lowastlowastlowast -0090lowastlowastlowast -0076lowastlowastlowast


Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271

update 2Q -0002lowastlowastlowast -0002lowastlowastlowast -0002lowast -0002 -0001 -0002

update 1Y -0006lowastlowastlowast -0007lowastlowastlowast -0010lowastlowast -0009 -0008 -0009

update 2Y -0018lowastlowastlowast -0021lowastlowastlowast -0021lowastlowast -0017lowastlowast -0016lowastlowast -0024lowast


3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897

update 2Q -0009 -0005 -0017 -0019lowast -0019lowast -0026lowast

update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast

update 2Y -0095lowastlowastlowast -0090lowast -0117lowast -0115lowastlowast -0114lowastlowast -0126lowastlowastlowast






Appendix

Appendix


This section lays out the full system of log-linearized equations that make up the DSGE

model analyzed in the main text The specification is the same as used by Smets and

Wouters (2007) The only difference concerns trend investment specific technological

progress which we include to account for a secular trend in the real investment to output

ratio observed in the data

This modification means that for the model to have a well defined steady statethe trending real variables need to be normalized both with neutral (γ ) and invest-

ment specific (γ i) technological progress (see eg Greenwood Herzowitz and Krus-

sel 1997) In particular if we define γ y = γγ α

1minusα

i the stationarization is as follows

yt = Y tγ ty y pt = Y pt γ

ty ct = C tγ

ty it = I t(γ yγ i)

t kt = K t(γ yγ i)t kst = K st (γ yγ i)

t

wt = W t(P tγ ty) rkt = Rk

t γ tiP t and q t = Qtγ

ti where Y t is output Y pt is potential output

C t is consumption I t is investment K t is capital K st is capital services W t is nominal

wage Rkt is the nominal rental rate on capital Qt is the real price of capital and P t is the

price level As regards the remaining endogenous variables showing up in the equations

below lt stands for labor rt is the nominal interest rate πt is inflation micro pt is price markup

microwt is wage markup and z t is capital utilization

The model is driven by seven stochastic disturbances total factor productivity εat

investment specific technology εit risk premium εbt exogenous spending εgt price markup

ε pt wage markup εwt and monetary policy εrt The two markup shocks are assumed to

follow ARMA(11) processes All remaining disturbances are modeled as first-order au-

toregressions except that the government spending shock additionally depends on the

current innovation to total factor productivity All variables presented in the equations

below are expressed as log deviations from the non-stochastic steady state The param-eters are defined in section D Stars in subscripts indicate the steady state values which

are functions of deep model parameters

Aggregate resource constraint

yt = (1 minus (γ yγ i minus 1 + δ )klowastyminus1

lowast minus gy)ct + (γ yγ i minus 1 + δ )kyit + rk

lowastklowasty

minus1

lowast z t + gyε

gt (A1)

Consumption Euler equation




ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +

γ y(σc minus 1)wlowastllowastclowast

σc(γ y + λ)(1 + λw)(lt minusE tlt+1)

minus

γ y minus λ

σc(γ y + λ)(rt minus E tπt+1) + εbt (A2)

Investment Euler equation

it = 1

1 + βγ 1minusσcy

itminus1 +βγ 1minusσc

y

1 + βγ 1minusσcy

E tit+1 + 1

(1 + βγ 1minusσcy )γ 2yγ

2i ϕ

q t + εit (A3)

Value of capital

q t = β (1 minus δ )

γ σcy γ iE tq t+1 +

γ σcy γ i minus β (1 minus δ )

γ σcy γ iE tr

kt+1 minus (rt minus E tπt+1) +

σc(γ y + λ)

γ y minus λ εbt (A4)

Aggregate production function

yt = φ p(αkst + (1 minus α)lt + εat ) (A5)

Capital services

kst = ktminus1 + z t (A6)

Optimal capacity utilization

z t = 1 minus ψ

ψ rkt (A7)

Capital accumulation

kt = 1 minus δ

γ yγ iktminus1 +

γ yγ i minus 1 + δ

γ yγ iit + (γ yγ i minus 1 + δ )(1 + βγ 1minusσc

y )γ yγ iϕεit (A8)

Price markup

micro pt = α(ks

t minus lt) + εat minus wt (A9)

Phillips curve

πt = ι p

1 + βγ 1minusσcy ι p

πtminus1 +βγ 1minusσc

y


E tπt+1

minus

(1 minus βγ 1minusσcy ξ p)(1 minus ξ p)

(1 + βγ 1minus

σcy ι p)ξ p((φ pminus

1)ε p + 1)micro pt + ε

pt (A10)




Appendix

Input cost minimization

rkt =minus

(ktminus

lt) + wt (A11)

Wage markup

microwt = wt minus (σllt +

1

γ y minus λ(γ yct minus λctminus1)) (A12)

Real wage dynamics

wt = 1

1 + βγ 1minusσcy

wtminus1 +βγ 1minusσcy

1 + βγ 1minusσcy

(E twt+1 minus E tπt+1)minus 1 + βγ 1minusσcy ιw

1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus

(1minusβγ 1minusσcy ξ w)(1

minusξ w)

(1 + βγ 1minusσcy )ξ w((φw minus 1)εw + 1)microwt + εwt (A13)

Taylor rule

rt = ρrtminus1 + (1 minus ρ)[rππt + ry(yt minus y pt )] + r∆y(∆yt minus∆y

pt ) + εrt (A14)

B Data

The source of all data used to estimate the model is the ldquoReal-Time Data Set for Macroe-

conomistsrdquo (RTDSM) database maintained by the Federal Reserve Bank of Philadelphia

The only exception is the short-term interes rate which is not subject to revisions and

taken from the Federal Reserve Board statistics The exact definitions follow below

(RTDSM codes in parentheses)

Ouptut Real gross domestic product (ROUTPUT) divided by civilian noninstitutional

population (POP)

Consumption Real personal consumption expenditures (RCON) divided by civilian

noninstitutional population (POP)

Investment Real gross private domestic nonresidential investment (RINVBF) divided

by civilian noninstitutional population (POP)

Hours Aggregate weekly hours (H) divided by civilian noninstitutional population (POP)

normalized to average one over the estimation sample

Wages Nominal wage and salary disbursements (WSD) divided by civilian noninsti-

tutional population (POP) and deflated by the price index for gross domestic product

(P)




Price level Price index for gross domestic product (P)

Interest rate Federal funds rate


The following equations relate the model variables to their empirical conterparts defined

in section B

∆logOutputt = γ y minus 1 + yt minus ytminus1 (C1)

∆logConsumptiont = γ y minus 1 + ct minus ctminus1 (C2)

∆log Investmentt = γ yγ i minus 1 + it minus itminus1 (C3)

logHourst = l + lt (C4)

∆logWagest = γ y minus 1 + wt minus wtminus1 (C5)

∆logPriceLevelt = π + πt (C6)

InterestRratet = β minus1γ σcy (1 + π)minus 1 + rt (C7)


The calibrated parameters are reported in Table D1 while Tables D2 and D3 describe

the prior assumptions used in Bayesian estimation




Appendix

Table D1 Calibrated parametersParameter Value Description

δ 0025 Depreciation rategy 018 Exogenous spending share in outputλw 15 Steady-state wage markupε p 10 Kimball aggregator curvature in the goods marketεw 10 Kimball aggregator curvature in the labor market

Table D2 Prior assumptions - structural parameters

Parameter Type Mean Std Descriptionϕ normal 4 15 Investment adjustment cost curvatureσc normal 15 037 Inv elasticity of intertemporal substitutionh beta 07 01 Habit persistanceξ w beta 05 01 Calvo probability for wagesσl normal 2 075 Inv Frisch elasticity of labor supplyξ p beta 05 01 Calvo probability for pricesιw beta 05 015 Wage indexationι p beta 05 015 Price indexationψ beta 05 015 Capacity utilization cost curvatureφ normal 125 012 Steady-state price markuprπ normal 15 025 Weight on inflation in Taylor ruleρ beta 075 01 Interest rate smoothingry normal 012 005 Weight on output gap in Taylor ruler∆y normal 012 005 Weight on output gap change in Taylor ruleπ gamma 062 01 Steady-state inflation rate

100(β minus1 minus 1) gamma 025 01 Rate of time preferencel normal 0 2 Steady-state hours worked

100(γ y minus 1) normal 04 01 Trend growth of output100(γ i minus 1) normal 03 01 Trend growth of relative price of investment

α normal 03 005 Capital share




Table D3 Prior assumptions - shocksParameter Type Mean Std Description

σa inv gamma 01 2 Volatility of productivity shockσb inv gamma 01 2 Volatility of risk premium shockσg inv gamma 01 2 Volatility of exogenous spending shockσi inv gamma 01 2 Volatility of investment specific shockσr inv gamma 01 2 Volatility of monetary policy shockσ p inv gamma 01 2 Volatility of price markup shockσw inv gamma 01 2 Volatility of wage markup shockρa beta 05 02 Persistence of productivity shockρb beta 05 02 Persistence of risk premium shock

ρg beta 05 02 Persistence of exogenous spending shockρi beta 05 02 Persistence of investment specific shockρr beta 05 02 Persistence of monetary policy shockρ p beta 05 02 Persistence of price markup shockρw beta 05 02 Persistence of wage markup shockmicro p beta 05 02 Moving average term in price markupmicrow beta 05 02 Moving average term in wage markupρga beta 05 02 Impact of productivity on exogenous spending


As one of the robustness checks considered in the paper we augment the benchmark

Smets and Wouters (2007) model with financial frictions as in Bernanke Gertler and

Gilchrist (1999) They introduce an additional type of agents called entrepreneurs who

manage capital finance their operations by borrowing from banks owned by households

and are subject to idiosyncratic risk that can be observed by lenders only at a cost This

contracting friction results in an endogenous and time-varying wedge between the rate of

return on capital and the risk-free rate

Our exact specification follows Del Negro Giannoni and Schorfheide (2014) and is

implemented by replacing the value of capital equation (A4) with

E t983163ret+1 minus rt

983165 = ζ prb(q t + kt minus nt)minus

σc(γ y + λ)

γ y minus λ εbt + εσt (E1)

where εσt is a shock to the standard deviation of idiosyncratic risk faced by entrepreneurs

ret is the rate of return on capital defined as

ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast

+ 1minus δ q t minus q tminus1 + πt (E2)




Appendix

and the law of motion for entrepreneursrsquo net worth nt can be written as

nt = ζ nre(ret minus πt) minus ζ nr(rtminus1 minus πt) + ζ nqk(q tminus1 + ktminus1) + ζ nnntminus1 minus ζ nσωζ prσω

εσtminus1 (E3)

The family of parameters ζ showing up in the new equations depend on the deep

parameters of the augmented model including the following four describing the financial

frictions block the survival rate of entrepreneurs ν steady-state standard deviation of id-

iosyncratic productivity monitoring costs and transfers from households to entrepreneurs

Conditional on other model parameters the last three of the four new parameters can be

uniquely pinned down by the debt elasticity of the external finance premium ζ prb and twosteady-state proportions ie the quarterly bankruptcy rate F lowast and the premium re

lowastminus rlowast6

As in Del Negro Giannoni and Schorfheide (2014) we fix F lowast at 0008 ν at 099 and esti-

mate ζ prb relowastminus r

lowast as well as the standard deviation and autocorrelation of εσt Our prior

assumptions are summarized in Table E4 They are taken from Del Negro Giannoni

and Schorfheide (2014) except for the risk shock characteristics which we parametrize

identically to other AR(1) shocks in the benchmark model

Table E4 Prior assumptions - financial frictions blockParameter Type Mean Std Descriptionrelowastminus r

lowast gamma 05 0025 Steady-state external finance premiumζ prb beta 005 0005 Premium elasticity wrt debtσσ inv gamma 01 2 Volatility of risk shockρσ beta 05 02 Persistence of risk shock

Finally while estimating the augmented model we additionally use the time series on

credit spreads defined as the difference between the Moodyrsquos seasoned Baa corporate bond

yields and the 10-year treasury note yields (source Federal Reserve Board statistics) andlinked to the model concept of the external finance premium via the following measurement

equation

Spreadt = relowastminus r

lowast + E t

983163ret+1 minus rt

983165 (E4)

6See technical appendix to Del Negro and Schorfheide (2012) for derivations



wwwnbppl



Economic InstituteWarsaw 983090983088983089983092



DSGE models





ISSN 2084-624X








1 Introduction

2 Model


4 Results

41 Point forecasts



5 Conclusions

References

Tables

Appendix


B Data




5

7

8

10

10

11

13

14

16

18

23

23

25

26

26

28

Contents




Abstract

Abstract










forecasts






Chapter 1048625

1 Introduction





















































revisions





Chapter 983090




2 Model







with indexation

















Chapter 983091









sample









into

θvT minus θ

vminusq


T minusq)

sample effect


vminusq

T minusq)

vintage effect

(1)








Forecasting contest










yf t+h|t j =

1

N

N sum

n=1




p(yt+h|t j) = 1

N

N sum

n=1














Chapter 1048628



ahead forecasts)






4 Results




41 Point forecasts















Results















sample effect










































Results






























Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




ISSN 2084-624X








1 Introduction

2 Model


4 Results

41 Point forecasts



5 Conclusions

References

Tables

Appendix


B Data




5

7

8

10

10

11

13

14

16

18

23

23

25

26

26

28

Contents




Abstract

Abstract










forecasts






Chapter 1048625

1 Introduction





















































revisions





Chapter 983090




2 Model







with indexation

















Chapter 983091









sample









into

θvT minus θ

vminusq


T minusq)

sample effect


vminusq

T minusq)

vintage effect

(1)








Forecasting contest










yf t+h|t j =

1

N

N sum

n=1




p(yt+h|t j) = 1

N

N sum

n=1














Chapter 1048628



ahead forecasts)






4 Results




41 Point forecasts















Results















sample effect










































Results






























Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




1 Introduction

2 Model


4 Results

41 Point forecasts



5 Conclusions

References

Tables

Appendix


B Data




5

7

8

10

10

11

13

14

16

18

23

23

25

26

26

28

Contents




Abstract

Abstract










forecasts






Chapter 1048625

1 Introduction





















































revisions





Chapter 983090




2 Model







with indexation

















Chapter 983091









sample









into

θvT minus θ

vminusq


T minusq)

sample effect


vminusq

T minusq)

vintage effect

(1)








Forecasting contest










yf t+h|t j =

1

N

N sum

n=1




p(yt+h|t j) = 1

N

N sum

n=1














Chapter 1048628



ahead forecasts)






4 Results




41 Point forecasts















Results















sample effect










































Results






























Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Abstract

Abstract










forecasts






Chapter 1048625

1 Introduction





















































revisions





Chapter 983090




2 Model







with indexation

















Chapter 983091









sample









into

θvT minus θ

vminusq


T minusq)

sample effect


vminusq

T minusq)

vintage effect

(1)








Forecasting contest










yf t+h|t j =

1

N

N sum

n=1




p(yt+h|t j) = 1

N

N sum

n=1














Chapter 1048628



ahead forecasts)






4 Results




41 Point forecasts















Results















sample effect










































Results






























Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Chapter 1048625

1 Introduction





















































revisions





Chapter 983090




2 Model







with indexation

















Chapter 983091









sample









into

θvT minus θ

vminusq


T minusq)

sample effect


vminusq

T minusq)

vintage effect

(1)








Forecasting contest










yf t+h|t j =

1

N

N sum

n=1




p(yt+h|t j) = 1

N

N sum

n=1














Chapter 1048628



ahead forecasts)






4 Results




41 Point forecasts















Results















sample effect










































Results






























Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




























revisions





Chapter 983090




2 Model







with indexation

















Chapter 983091









sample









into

θvT minus θ

vminusq


T minusq)

sample effect


vminusq

T minusq)

vintage effect

(1)








Forecasting contest










yf t+h|t j =

1

N

N sum

n=1




p(yt+h|t j) = 1

N

N sum

n=1














Chapter 1048628



ahead forecasts)






4 Results




41 Point forecasts















Results















sample effect










































Results






























Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Chapter 983090




2 Model







with indexation

















Chapter 983091









sample









into

θvT minus θ

vminusq


T minusq)

sample effect


vminusq

T minusq)

vintage effect

(1)








Forecasting contest










yf t+h|t j =

1

N

N sum

n=1




p(yt+h|t j) = 1

N

N sum

n=1














Chapter 1048628



ahead forecasts)






4 Results




41 Point forecasts















Results















sample effect










































Results






























Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Chapter 983091









sample









into

θvT minus θ

vminusq


T minusq)

sample effect


vminusq

T minusq)

vintage effect

(1)








Forecasting contest










yf t+h|t j =

1

N

N sum

n=1




p(yt+h|t j) = 1

N

N sum

n=1














Chapter 1048628



ahead forecasts)






4 Results




41 Point forecasts















Results















sample effect










































Results






























Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Forecasting contest










yf t+h|t j =

1

N

N sum

n=1




p(yt+h|t j) = 1

N

N sum

n=1














Chapter 1048628



ahead forecasts)






4 Results




41 Point forecasts















Results















sample effect










































Results






























Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Chapter 1048628



ahead forecasts)






4 Results




41 Point forecasts















Results















sample effect










































Results






























Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Results















sample effect










































Results






























Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl
































Results






























Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Chapter 983093


















5 Conclusions











Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Conclusions








References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




References

References





190




1341ndash1393























References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




References








1 (5)1123ndash1175












Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Tables

Tables



Output




Prices



Interest rate


update 2Y 102

lowastlowast

103

lowastlowast

102

lowast



Output


Prices

update 1Q 021 039 077 120 172 285


Interest rate







Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Tables


Real time data

Output




Prices

update 1Q -0144 -0797 -1506 -1933 -2232 -2635

update 2Q 0000 0002 0002 0001 0000 -0004lowast



Interest rate



Output




Prices



Interest rate







H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl





H = 1 H = 2 H = 4 H = 6 H = 8 H = 12

Real time data

update 1Q -0889 -2503 -4108 -4960 -5507 -6246






update 1Q -0679 -2300 -3962 -4847 -5404 -6122








Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Tables



Output

update 1Q 064 112 195 259 321 465

update 2Q 100 100 100 100 100 100

update 1Y 101 100 101 101 100 100

update 2Y 101 100 101 102lowast 102 102


Prices

update 1Q 025 046 091 145 207 343


100 100 100 100update 1Y 100 100 100 099 099 099

update 2Y 100 100 100 101 101 102


Interest rate

update 1Q 011 021 036 046 052 060

update 2Q 100 100 100 100 100 100





Output

update 1Q -1098 -1636 -2172 -2454 -2652 -2979

update 2Q -0003 -0001 -0002 -0003 -0003 -0005




Prices

update 1Q -0112 -0755 -1474 -1930 -2265 -2731

update 2Q 0000 0002 0001 0002 0002 0001

update 1Y -0003 0000 0000 0001 0003 0004

update 2Y -0007 -0002 -0003 -0004 -0003 -0006


Interest rate

update 1Q 0345 -0107 -0529 -0724 -0840 -0972





3 variables

update 1Q -0810 -2404 -3990 -4854 -5435 -6256

update 2Q -0008lowast -0004 -0003 -0004 -0006 -0005

update 1Y -0020

lowastlowastlowast

-0014

lowastlowast

-0012

lowast









Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl






Output

update 1Q 061 107 197 276 351 493

update 2Q 101 100 101 101 101 101lowast




Prices

update 1Q 026 052 120 212 325 586




Interest rate

update 1Q 011 020 037 052 065 083






Output

update 1Q -1071 -1587 -2139 -2457 -2682 -3022





Prices

update 1Q -0157 -0891 -1699 -2210 -2591 -3133

update 2Q -0004 -0003 -0005 -0006 -0006 -0007




Interest rate

update 1Q 0316 -0127 -0586 -0852 -1037 -1271





3 variables

update 1Q -0902 -2633 -4388 -5346 -5989 -6897


update 1Y -0033

lowastlowast

-0030

lowast

-0046

lowast

-0054

lowastlowast

-0056

lowastlowast

-0059

lowastlowast







Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Appendix

Appendix










1minusα



ty ct = C tγ



t




















lowastklowasty

minus1

lowast z t + gyε

gt (A1)





ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




ct = λ

λ + γ yctminus1 +

γ y

λ + γ yE tct+1 +



minus

γ y minus λ



it = 1

1 + βγ 1minusσcy


y

1 + βγ 1minusσcy

E tit+1 + 1


2i ϕ

q t + εit (A3)

Value of capital




γ σcy γ iE tr


σc(γ y + λ)




Capital services



z t = 1 minus ψ

ψ rkt (A7)


kt = 1 minus δ

γ yγ iktminus1 +




Price markup

micro pt = α(ks


Phillips curve

πt = ι p



y


E tπt+1

minus


(1 + βγ 1minus



pt (A10)




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Appendix


rkt =minus

(ktminus

lt) + wt (A11)

Wage markup


1


Real wage dynamics

wt = 1

1 + βγ 1minusσcy


1 + βγ 1minusσcy


1 + βγ 1minusσcy

πt

+ ιw

1 + βγ 1minusσcy

πtminus1 minus


minusξ w)


Taylor rule


pt ) + εrt (A14)

B Data







population (POP)









(P)








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl








in section B














Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Appendix


























σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl



















σc(γ y + λ)




ret = rklowast

rklowast

+ 1minus δ rkt + 1

minusδ

rklowast





Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl




Appendix



εσtminus1 (E3)



















equation


lowast + E t


983165 (E4)




wwwnbppl



wwwnbppl

NBP Working Papers

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Transcript of NBP Working Papers