Cravino Levchenko Devaluations

The Distributional Consequences of Large Devaluations

Javier CravinoUniversity of Michigan

and NBER

Andrei A. LevchenkoUniversity of Michigan

NBER and CEPR

May 1, 2015

Abstract

We study the differential impact of large exchange rate devaluations on the cost ofliving at different points on the income distribution. Across product categories, thepoor have relatively high expenditure shares in tradeable products. Within tradeableproduct categories, the poor consume lower-priced varieties that are bundled withless local distribution services. A devaluation raises the relative price of tradeables,increasing the price of the basket of goods consumed by poor households relative tothe one consumed by rich households. We quantify these effects following the 1994Mexican peso devaluation and show that their distributional consequences can belarge. Following the devaluation, the cost of the consumption basket of those in thebottom decile of the income distribution rose between 1.4 and 1.63 times more thanthe cost of the consumption basket for the top income decile. We supplement thedetailed results for Mexico using cross-country evidence.

Keywords: exchange rates, large devaluations, distributional effects, consumptionbaskets

JEL Codes: F31, F61

We are grateful to seminar participants at CREI, Bank of Italy, Michigan, and CESifo for helpful sugges-tions and to Nitya Pandalai-Nayar for excellent research assistance. We are especially grateful to ChristianAhlin andMototsugu Shintani for sharing the digitized pre-April 1995Mexican consumer price data. Email:[email protected], [email protected].

1 Introduction

Large exchange rate devaluations are associated with dramatic changes in relative prices.In the aftermath of a devaluation, the price of tradeable goods at the dock moves one-for-one with the exchange rate, the retail price of tradeable goods increases, though lessthan the exchange rate, while non-tradeable goods prices are relatively stable.1 A clearillustration of such relative price movements is presented in Figure 1, which plots theevolution of these prices following the 1994 Mexican devaluation. The retail price oftradeables is much closer to the price of non-tradeables than to prices of tradeables at thedock, consistent with the importance of local distribution costs in retail prices.2

Figure 1: Price changes during the 1994 Mexican devaluation

1.00

1.50

2.00

2.50

Nov94 Jan95 Apr95 Jul95 Oct95

Trade weighted exchange rate Price of Non TradeablesRetail price of Tradeables Price of Tradeables at the dock (IPI)

Notes: This figure plots the trade-weighted nominal exchange rate, the import price index, and the con-sumption price indices of tradeables and non-tradeables following the November 1994 peso devaluation,each rebased to November 1994.

This paper studies the distributional consequences of such relative price movements.It is well known that households at different income levels consume very different baskets

1These patterns were first documented by Burstein et al. [2005] for 5 large devaluations. In summarizingthe literature, Burstein and Gopinath [2015] extend these findings to include more devaluation episodes.

2Burstein et al. [2003] estimate that local distribution margins comprise about 50 percent of the retailprice of tradeable goods.

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of goods.3 We distinguish two sources for these differences, which we label Across andWithin. Across product categories, the poor spend relatively more on tradeables (such asfood), while the rich spend relatively more on non-tradeables (such as personal services).Within product categories, the rich spend relatively more on higher-end goods purchasedfrom higher-end retail outlets. To the extent that the non-tradeable component of con-sumer prices varies along these dimensions, rich and poor households will face differentchanges in the retail price of tradeable goods. The changes in relative prices following alarge devaluation will thus affect households differentially, generating a distributional aswell as an aggregate impact on welfare.

We measure the magnitude of these two effects during the 1994 Mexican devaluation.For this episode, we combine two sources of detailed microdata that are key for study-ing these mechanisms. The first is household-level expenditure data on detailed productcategories from the Mexican household surveys both immediately before and after thecrisis. The second is monthly data on unique product-outlet level prices that the Bankof Mexico uses to construct the consumer price index. In what follows, we refer to aunique product-outlet combination as a variety. Crucially, the product categories in thehousehold survey can be matched to the consumption categories for which the Bank ofMexico computes consumer price indices. Indeed, these datasets are the two principalinputs underlying the official Mexican CPI. We supplement the results for Mexico usingthe Economist Intelligence Unit CityData on store prices in a sample of several emergingmarket devaluations.

We first calculate an income-specific price index that captures the Across effect byweighting price indices for disaggregated consumption categories with income-specificexpenditure shares from the 1994 household expenditure survey. According to this in-dex, in the 2 years following the devaluation, the consumers in the bottom decile of theMexican income distribution experienced increases in the cost of living about 1.26 timeslarger than the consumers in the top income decile. The increase in the price index was97% for households in the poorest decile, compared to 77% for households in the richestdecile. The effect is monotonic across all income deciles.

We then compute an income-specific price index that captures theWithin effect usingthe unique product-outlet level price data and household expenditure data. First, weuse the household survey data to show that high-income households tend to pay higherunit values within detailed product categories (i.e. both the rich and the poor buy bread,

3This was documented as early as the 19th century by Engel [1857, 1895, "Engels Law"], and confirmedrepeatedly in micro data. For recent evidence using household surveys from multiple countries, see Alms[2012].

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but the rich pay more per kilo). This evidence supports the notion that rich householdspurchase higher-priced varieties. We then compute a Within price index by assumingthat all consumers have the same expenditure shares across product categories, but thatwithin each category, the rich consume the more expensive varieties, and the poor the lessexpensive ones. In our benchmark index, the Within effect implies that inflation for thelower-income consumers was between 11 and 25 percentage points higher than for thehigher-income consumers.

The Across and Within effects are roughly additive, reinforcing each other. Our pre-ferred estimate of the price index that combines these two effects implies that the house-holds in the bottom decile of the Mexican income distribution experienced increases inthe cost of living between 1.4 and 1.63 times higher than the households in the top decilein the two years that follow the devaluation. Absent any changes in nominal income,our combined price index implies a decline in real income of 50-54% for poor householdscompared to 40-42% for rich households. The main finding is thus that both the Acrossand the Within distributional effects were large and economically significant in the 1994Mexican devaluation.

We then provide a unified explanation for why the devaluation is anti-poor. Namely,at different levels of product disaggregation, the poor spend a higher fraction of their in-come on tradeable product categories, and among tradeables, on products with system-atically lower distribution margins. Since distribution costs are largely non-tradeable, asthe relative price of tradeables to non-tradeables increases following the devaluation, theprices paid by the poor rise by proportionally more than those paid by the rich.4

We present novel empirical evidence of the two premises behind this explanation.First, both across and within product categories, differences in distribution margins canexplain the observed price changes following the devaluation. Across product categories,the relative price of the categories with lower distribution margins increased after the de-valuation. Within product categories, we show in a simple flexible price framework thatdifferences in distribution margins alone can account for the observed differences in pricechanges across varieties. These exercises also provide a tighter link between the observedprice changes and the devaluation itself. Second, there is a systematic relationship be-tween the non-tradeable component in retail prices and expenditure shares of the rich

4We focus on the role of local distribution costs because they are key for accounting for the aggregatechange in consumer price indices for tradeable goods after large devaluations [Burstein et al., 2005, Bursteinand Gopinath, 2015]. Our contribution is to provide new evidence that cross-sectional heterogeneity inthese costs can also account for differential price changes across goods and varieties, and therefore carriesdistributional consequences across consumers.

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and the poor: the poor spend less on goods with a high non-tradeable component.5

Finally, we provide an independent piece of evidence on theWithin effect, based on anentirely different data source and empirical strategy. Namely, we use the Economist Intel-ligence Unit CityData on store prices. This database reports, at a 6-monthly frequency, theprices of about 160 goods in 140 cities all over the world, from 1990 until today. Cruciallyfor the Within effect identification, for goods bought in stores such as food, alcohol,toiletries, and clothing CityData contains 3 price quotes: a supermarket/chain store,mid-level/branded store, and a high-end store. We examine whether in several largedevaluation episodes including Mexico in 1994, prices in higher-end outlets rose by lessthan in lower-end outlets.

This empirical exercise has two advantages. First, it uses no information on pre-crisisprices. The independent variable is the binary indicator for the type of store in which thegood is sold, controlling for good fixed effects. Thus, we can be sure that the differentialchanges in the price of high end vs low end varieties is not due to some mean reversionin prices. Second, we can examine devaluation episodes in countries other than Mexico.Our main finding is that prices in higher-end stores rose by significantly less than pricesin lower-end stores in the aftermath of the devaluations that we study. In Mexico, relativeto the lower-end stores, prices in the mid-level stores rose by 7% less, and in the high-end stores by 12% less between 1994 and 1996. The pattern holds for other devaluationsas well. We take the sample of devaluations from Burstein et al. [2005]: Mexico 1994,Thailand and Korea 1997, Brazil 1998 and Argentina 2001. To this sample we add Icelandin 2007-8. The above pattern is statistically and economically significant in 5 of these6 episodes. Only in Thailand do we not find that prices in higher-end stores rose bysignificantly more.

Our analysis is expressly about the differences in consumption price levels for house-holds of different incomes, and is silent on how nominal income itself changed for thepoor and the rich. As such, our results can be interpreted as differences in compensatingvariation of changes in the consumption price level across the income distribution. Thatis, we answer the question, by how much should the nominal income of the poor havechanged relative to the rich to leave both groups relatively as well off as before? Ourresults can be benchmarked to existing studies of how incomes changed during the Mexi-can devaluation. For example, Maloney et al. [2004] report that median real wages fell by30%, but that there was not much differential impact across education groups (which can

5In a recent paper, Jaimovich et al. [2014] document that lower-end retail outlets where the poor aremore likely to shop generate relatively less value added. We provide our own evidence of this regularityin Section 5.2.

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serve as a rough proxy for income). Changes in asset values/incomes are more difficultto ascertain, but available evidence suggests that assets of the poor suffer larger lossesthan those of the rich. Halac and Schmukler [2004] document that in a sample of LatinAmerican crises that includes Mexico in 1994, larger depositors and larger borrowers suf-fered less than small ones, though these results cannot be linked directly to householdsby income.

Our paper belongs to the literature on large devaluations, surveyed by Burstein andGopinath [2015]. This literature has highlighted that pass-through into retail prices isimperfect because consumer prices include a large non-traded component (sometimescalled distribution margins). Goldberg and Campa [2010] document the heterogeneityof distributionmargins across sectors. We study a pattern that has until now been ignoredin the exchange rate literature: the importance of the non-traded component in the totalconsumption basket varies systematically along the income distribution, both across andwithin detailed product categories. Some evidence on what we label the Across effect isprovided by Friedman and Levinsohn [2002] and Levinsohn et al. [2003] for Indonesias1998 depreciation, and by Kraay [2008] for the Egyptian 2000-05 depreciation. Our pa-per examines the Across effect more systematically and relates it the interaction betweendistribution margin heterogeneity and differences in consumption baskets.

Our paper is also related to a large and growing literature in international trade thatmodels demand non-homotheticities and examines the distributional impact of trade in-tegration across consumers [see, e.g. Fajgelbaum et al., 2011, Fajgelbaum andKhandelwal,2014]. The closest to ours are papers by Porto [2006] and Faber [2014]. Porto [2006] useshousehold consumer expenditure data in Argentina following Mercosur to trace the dis-tributional impact of this regional trade agreement on different consumers. The analysisincorporates the Across effect but not the Within effect. Faber [2014] shows that follow-ing NAFTA, intermediate inputs used in production of higher-quality varieties becamecheaper in Mexico, and richer consumers benefited more a type of Within effect thatis differential across product categories according to their intensity of imported inputuse. Relative to these papers, that focus on long-run changes, we examine the relativelyshort-run effects following large devaluations. Our paper is the first, to our knowledge, tocombine the analysis of Across andWithin effects and relate them to distributionmargins.

The rest of this paper is organized as follows. Section 2 illustrates the distributional ef-fects of relative price changes when consumption baskets differ across consumers. Section3 describes the data and the main results. Section 4 provides an explanation for the mainfindings by relating them to distribution margins. Section 5 presents the cross-countryevidence, and Section 6 concludes.

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2 Conceptual framework

We focus on a setting in which the indirect utility of a household h is proportional to realincome:

Vht WhtPht

,

where Wht is nominal income and Pht is the household-specific ideal price index. A pro-portional welfare change due to a shock for instance, a large exchange rate devaluation is then equal to bVth = bWht bPht , (1)where bxt = xt/xt0 1 denotes the cumulative growth rate of variable xt between somebase period t0 and year t. The change in the ideal price index can be approximated by

bPht g2G

whg bPg,t = bPht ,where g indexes goods, whg are household-specific expenditure shares, bPg,t are good-specific price changes, and bPht is a measured household-specific aggregate price index.To relate the distributional effects of a change in prices across households, it helps towrite (1) as: bVht = bWht

g2Gwg bPg,t| {z }

homothetic-utility bV

g2GbPg,t(whg wg)| {z }

Cov(bPg,t,whgwg), (2)

where wg is the economy-wide share of spending on good g. The first term of this expres-sion is change in welfare that we would obtain if utility were homothetic and every h hadthe same consumption basket. The second term captures the distributional impact acrosshouseholds. The term is reminiscent of a (negative) covariance between price changesand household-level relative spending shares. If the pattern of price changes across g ispositively correlated with hs relative spending shares, then h suffers more from this vec-tor of price changes than the average household, because prices go up on average morein goods that the household consumes more of.

Consider an example in which there are two households, rich and poor, h = r, p, andtwo goods, tradeables and non-tradeables: g = T,NT. Suppose further that the poor havehigher expenditure shares in tradeables: wpT > wT > w

rT. If an exchange rate depreciation

leads to a higher increase in the price of tradeables than in the price of non-tradeables bPT,t > bPNT,t then the last term in (2) will be negative for the poor and positive for the6

rich. This is the simplest version of what in the empirical analysis below we refer to asthe Across effect.

Suppose instead that instead of tradeables and non-tradeables, the two goods were anexpensive variety and a cheap variety: g = E,C, and the poor consumed a higher share ofthe cheap variety than the rich, wpC > wC > w

rC. If the price of the cheap variety increased

by more after a devaluation, bPC,t > bPE,t, we once again have an anti-poor distributionaleffect.

The discussion above underscores the point that there is no fundamental differencein how the Across and Within effects work. Both are driven by the covariance of pricechanges and relative spending shares across the income distribution. Because they relyon different measurement strategies, it is still convenient to separate them in the empiricalanalysis. Note also that the expression (1) has a natural compensating variation interpre-tation: in response to a given vector of price changes bPg,t, a compensating variation forhousehold h is a change in income bWht that leaves welfare unchanged (bVht = 0). Thus,while we state the empirical results in terms of changes in household-level costs of livingindices bPht , they can equivalently be stated in terms of the heterogeneity in the compen-sating variation across households.

2.1 Within and Across effects: definitions and measurement

This section defines the Across, Within, and Combined price indices. Let there be G goodscategories indexed by g, and let each g contain varieties indexed by vg. Households willhave different expenditure shares both across goods categories g, and across varieties vgwithin each g. The change in the aggregate price index is defined by:

bPt g2G

wg bPg,t, (3)where wg h P

hg,t0

qhg,t0h g Phg,t0q

hg,t0

is the economy-wide expenditure share on good g at some base

year t0, and bPg,t 1Vg vg2g bPvg,t is the aggregate price index for good category g that hasVg varieties. bPt is the change in the CPI as it would be constructed by national statisticalagencies.

The change in the household-specific price index is given by:

bPht g2G

whg bPhg,t, (4)

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where whg Phg,t0q

hg,t0

g Phg,t0qhg,t0

is now the share of household hs expenditures that go towards

good category g, and the change in the price sub-index of good g varies across householdsbecause they consume different varieties:

bPhg,t vg

shvg bPvg,t, (5)where shvg is household hs share of expenditures in variety v within the good category g,and bPvg,t is the (non-household-specific) change in the price of variety v of good g. bPhg,tcan vary across households if households of different incomes consume different goodswithin each good category g. This would happen, for instance, if the richer householdsconsume systematically higher-priced varieties within each g.

We define the Across change in the price index for household h as:

bPhAcross,t g2G

whg bPg,t, (6)and theWithin change in the price index for household h as:

bPhWithin,t g2G

wg bPhg,t. (7)In words, bPhAcross,t is the change in the cost of living for a hypothetical household that hashs expenditure shares across g, and faces the unweighted average price change across allvarieties within each g. By contrast, bPhWithin,t is the change in the cost of living for a hypo-thetical household that has aggregate consumption shares across goods g, but consumeshousehold hs varieties within each good g.

Using these expressions, the change in the price index of household h is:6

bPht = g2G

whg bPg,t| {z }bPhAcross,t+

g2Gwg bPhg,t| {z }bPhWithin,t

+ g2G

whg wg

bPhg,t bPg,t| {z }bPhCov,t

g2Gwg bPg,t| {z }bPt

.

6In particular, note that

bPht g2G

whg bPhg,t = g2G

whg bPg,t + g2G

whg

bPhg,t bPg,t=

g2Gwhg bPg,t +

g2Gwg bPhg,t +

g2G

whg wg

bPhg,t bPg,t g2G

wg bPg,t.

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The third term, labeled bPhCov,t, is a covariance across goods between how different pricechanges are for h relative to the average and how different hs expenditure share relativeto the average. It is not formally a covariance because bPg,t is not the mean across goods,but rather the mean across varieties within g, and wg is not the mean across goods butan expenditure-weighted average across households. The covariance will be positivewhen h experiences large deviations from the mean in its household-specific price in itsrelatively large expenditure categories.

The difference in the change of the price indices of two households h and h0 at differentpoints in the income distribution (where Dxt xht xh0t denotes a cross-sectional ratherthan a time difference) is then given by

DbPt = DbPAcross,t + DbPWithin,t + DbPCov,t.The difference in bPth is the sum of the differences in the Across and Within indices andthe covariance term. In Section 3 we calculate DbPt, DbPAcross,t and DbPWithin,t following the1994 Mexican devaluation and show that the covariance term is quantitatively small.

3 Price changes during the 1994 Mexican devaluation

This section quantifies the distributional consequences of the 1994 Mexican devaluationthat arise from changes in the relative prices of the consumption baskets purchased bydifferent households across the income distribution. After introducing the data sources,we proceed in three steps. First we compute the differences in household-specific priceindices that arise from differences in expenditure shares across product categories theAcross effect. Second, we compute the differences in price indices arising from differencesin expenditure shares within product categories the Within effect. Third, we let thesetwo mechanisms interact, and compute the Combined effect. We conclude this section byrecalculating price indices under alternative assumptions to show the robustness of theresults.

3.1 Data description

We employ two complementary pieces of data to build and analyze the household-specificprice indices during theMexican devaluation. The first is monthly data on unique product-outlet level prices that the Bank of Mexico uses to construct the consumer price index.The second is household-level expenditure data on detailed product categories from the

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Mexican household surveys both immediately before and after the crisis.

3.1.1 Mexican data on consumer prices

The Mexican micro data on consumer prices is collected by the Banco de Mexico withthe purpose of computing the Consumer Price Index. Since January 1994, the prices thatunderlie the construction of the CPI are published in the Diario Oficial de la Federacion(DOF), the official bulletin of the Mexican government published monthly. Each pricequote in the DOF corresponds to a specific product, which is a unique product-city-outlet combination that can be traced through time. An exact product description -i.e.Kelloggs, Corn Flakes, 500gr box- for each specific product was published in the April1995 DOF. Unfortunately, outlet identifiers are not available in the data for this time pe-riod. The specific products are grouped into 313 generic categories -i.e. Cereal in Flakes-,representing the goods and services consumed in Mexico. For most generic product cate-gories, the price quotes for the specific goods are expressed in common units -for example,the prices of specific products within the category Cereal in Flakes are quoted per Kilo ofCereal-. These micro price data from the DOF have been used previously by Ahlin andShintani [2007] and Gagnon [2009].

We focus on a sample of 26,426 specific products grouped into 284 generic categoriesthat can be observed continuously from January 1994 to December 1996.7 For each specificproduct, we observe its monthly price, its generic category, the city in which it is soldand the units in which prices are quoted. The DOF also publishes the specific productsthat are added because of product substitutions, or changes in the outlets that are beingsampled by the price inspectors. We focus on the specific products that can be observedcontinuously through our sample.

Finally, in addition to the micro price data, we also obtain the price indices computedby the Bank of Mexico for each generic category, as well as consumption price indicesfor more aggregated categories. We also obtain the weight that each generic category isassigned in the aggregate CPI from the household surveys (see below).

3.1.2 Mexican household surveys

We use theMexican household surveys, Encuesta Nacional the Ingresos y Gastos de Hog-ares, (ENIGH) for 1994 and 1996 to obtain consumption expenditures across consumptioncategories by household. The key variables that we use from this dataset are the house-holds city, households income, households total expenditures in 547 detailed product

7There was a revision in April 1995, in which some of the generic categories were changed.

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categories. Crucially, the product categories in the ENIGH can be mapped in the 313generic good categories that are used to calculate the CPI in fact, the weights used tocompute the CPI are derived from the ENIGH. In addition, for some product categoriesthe ENIGH reports the total quantity of the good consumed by each household. We com-bine the total quantities with the expenditure data to compute the unit value paid by eachhousehold in each product category.

3.2 The Across effect

We calculate the Across price index in equation (6), reproduced here to facilitate the ex-position:

bPhAcross,t = g2G

whg bPg,t.We obtain the price indices bPg,t for the aggregate product categories from the Bank ofMexico. We define the product categories G for two alternative levels of disaggregationfor which the Bank of Mexico computes consumer price indices: at the 1-digit (8 goodcategories), and at 6 digits (37 categories). Appendix Table A1 reports the product cate-gories for different levels of disaggregation. We compute the expenditure shares whg forthe product categories from the 1994 household expenditure survey. In particular, wesort households into income deciles and compute the expenditure shares of each decile ineach of the G product categories. We normalize the price indices to equal 100 in October1994, the month before the devaluation.

Tables 1a and 1b report the resulting price indices for different deciles of the incomedistribution when the product categories are defined at the 1 and 6 digit levels of dis-aggregation. Changes in the across price indices bPhAcross,t differ dramatically across theincome distribution. Table 1a shows that when the across price index is computed atthe 1-digit level of disaggregation, the price index increased by 91 percent for the house-holds in poorest decile, compared to only 80 percent for households in the top decile. Therelation between the change in the indices and household income decile is monotonic,households of lower income experienced higher inflation in the two years following thedevaluation.

This difference in the price indices is even more dramatic when bPhAcross,t is computedat the 6-digit level of disaggregation. Table 1b reports that the change in the 6-digit acrossprice index was 97 percent for households in the bottom decile, relative to 77 percent forhouseholds in the top decile. Two years after the devaluation, inflation for the bottom

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Table 1: The Across price index by income decile, 1994 weights

(a) 1-Digit

Income Decile1 2 3 4 5 6 7 8 9 10 Aggregate Official

Oct. 94 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00April 95 1.24 1.25 1.24 1.25 1.24 1.25 1.24 1.24 1.24 1.23 1.24 1.25Oct. 95 1.46 1.46 1.46 1.46 1.45 1.45 1.45 1.44 1.44 1.42 1.44 1.49April 96 1.74 1.73 1.73 1.72 1.71 1.71 1.70 1.69 1.68 1.65 1.69 1.72Oct. 96 1.91 1.90 1.89 1.89 1.87 1.87 1.87 1.85 1.84 1.80 1.85 1.88

(b) 6-Digit

Income Decile1 2 3 4 5 6 7 8 9 10 Aggregate

Oct. 94 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00April 95 1.26 1.26 1.25 1.25 1.25 1.25 1.24 1.24 1.24 1.22 1.24Oct. 95 1.50 1.49 1.48 1.47 1.46 1.46 1.45 1.44 1.43 1.40 1.44April 96 1.79 1.77 1.76 1.75 1.73 1.72 1.71 1.70 1.67 1.62 1.69Oct. 96 1.97 1.94 1.93 1.91 1.89 1.88 1.87 1.85 1.83 1.77 1.85

Note: These tables report the Across price indices defined in equation (6) for different income deciles. Table1a computes the price index using 8 1-Digit product categories for G, while Table 1b computes the priceindex using 37 6-Digit product categories for G. The expenditure weights come from the 1994 householdsurvey.

decile was 1.26 times higher than inflation for the top decile due to the fact expenditureshares of rich and the poor households differ across product categories.

We next compute the across price indices at the household level. Figure 2 plots aquadratic fit of bPhAcross for October 1996 computed at a 6-digit level of disaggregation,for households of different income levels. The figure confirms that the relation shown inTables 1a and 1b between inflation and income is monotonic, while also showing that theprice difference between the richest and poorest household exceeds 25 percentage points.

One well-known limitation of Laspeyres price indices is that they overstate how pricechanges affect welfare because they are subject the substitution bias.8 In particular, differ-ences in the change of the price indices for rich and poor households may not necessarilytranslate into differences in welfare if poor households are better able to substitute con-sumption in response to price changes. With this in mind, we recalculate the across priceindices using expenditure weights from the 1996 household survey. By using end-of-

8See Hausman [2003].

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Figure 2: The Across price index by household income

Quadratic Fit Local Polynomial Fit16

018

020

022

0

4 6 8 10 12Ln(Income)

170

180

190

200

210

Chan

ge in

Con

sum

ptio

n Pr

ice L

evel

4 6 8 10 12Ln(Income)

Note: This figure reports the quadratic and local polynomial fits of the household-specific price levelchanges against log income, together with 95% confidence intervals. The household-specific price indicesare calculated based on the 37 6-digit consumption categories and 1994 expenditure weights. Income istaken from the 1994 household survey.

period weights, the price index is likely to understate the true welfare effects of the pricechanges. The true welfare change lies between the change predicted by the Laspeyres(1994 weights) price index and the Paasche (1996 weights) price index.

The resulting price indices using 1996 weights are reported in Tables 2a and 2b. Thetables show that the magnitude of the observed inflation differences between incomedeciles is similar to what we obtain under the 1994 weights: inflation for the poorestdecile is 19 percentage points higher than inflation for the richest decile. We concludethat the ability to substitute towards cheaper products does not substantially mitigate thedisparity in the welfare losses between rich and poor households arising from differencesin expenditure shares across product categories.

3.3 The Within effect

In the previous section, we computed theAcross price indices from observed price changesand observed expenditure weights. While we can observe price changes for individualvarieties within product categories, the expenditure weights shvg needed to compute theWithin effect are not directly observable. In this section, we document expenditure pat-terns within categories across the income distribution using data from the household ex-penditure survey, before computing the Within price index.

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Table 2: The Across price index by income decile, 1996 weights

(a) 1-Digit



(b) 6-Digit



Note: These tables report the Across price indices defined in equation (6) for different income deciles. Table2a computes the price index using 8 1-Digit product categories for G, while Table 2b computes the priceindex using 37 6-Digit product categories for G. The expenditure weights come from the 1996 householdsurvey.

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3.3.1 Expenditure differences within product categories

This section uses data from the 1994 household expenditure survey to document thatwithin narrow product categories, richest households tend to purchase more expensivevarieties. For this purpose, we define the unit values paid by household h in category gas:

uhg,t vg2g Pvg,tq

hvg,t

vg2g qhvg,t=

v2gwq,hvg Pvg,t.

Households that purchase higher quantity shares wq,hvg qhvg ,t

vg2g qhvg ,tof more expensive

varieties will pay higher higher unit values uhg within product categories g.We use the 1994 household expenditure survey to study how uhg,t changes across

households of different incomes. The 1994 household expenditure survey contains unitvalue data for 439 detailed product categories. The product categories in the householdsurvey are more disaggregated than the 313 generic product categories for which theBank of Mexico computes the CPI.9 We use the unit value data and the income data fromthe 1994 household survey to estimate the following relationship:

ln uhg,94 = b1 ln Inch94 + dg + e

hg,94, (8)

where lnInch94

is the log of household income, and dg denotes good-level fixed effects.

The coefficient of interest b1 is the elasticity of the unit value paid with respect to house-hold income. In an alternative specification, we sort households into income deciles andestimate:

ln uhg,94 =10

j=1

ajI[h2Dec. j] + dg + ehg,94. (9)

where I[h2Dec. j] is the indicator function for whether h is in income decile j = 1, ..., 10.Table 3 reports the results of estimating equations (8) and (9) using two alternative

samples: (i) the entire sample of products for which we observe unit values in the expen-diture survey (columns 1 and 2) and (ii) good categories that correspond to food products(columns 3 and 4). The table shows a strong positive correlation between unit values paidand household income: richer households pay higher unit values for varieties within nar-row product categories. The first column reports an estimated coefficient of b1 = 0.211

9It is possible to aggregate the categories in the survey into the CPI categories. See Section 3.1.1.

15

Table 3: Unit values by income

(1) (2) (3) (4)All product categories Food categories

logInch94

0.211*** 0.0712***

(0.00168) (0.00144)Decile 2 0.0654*** 0.0267***

(0.00474) (0.00406)Decile 3 0.117*** 0.0473***

(0.00474) (0.00411)Decile 4 0.152*** 0.0619***

(0.00492) (0.00429)Decile 5 0.180*** 0.0593***

(0.00493) (0.00429)Decile 6 0.237*** 0.0810***

(0.00508) (0.00446)Decile 7 0.282*** 0.0898***

(0.00524) (0.0046)Decile 8 0.350*** 0.118***

(0.00541) (0.00473)Decile 9 0.434*** 0.134***

(0.00573) (0.00488)Decile 10 0.666*** 0.216***

(0.00679) (0.00571)

Number of categories 439 439 210 210Observations 290,989 287,588 196,157 192,756R2 0.832 0.834 0.797 0.803

Notes: Robust standard errors in parentheses. ***: significant at 1%; **: significant at 5%; *: significant at10%. All specifications include product fixed effects. This table reports the results of estimating equations(8) (columns 1 and 3) and (9) (columns 2 and 4).

that is highly significant. The second column shows that unit values increase monotoni-cally with household income, as the decile dummies get progressively higher as incomeincreases, with the biggest jump in the last decile. Households at the richest decile payunit values that are 0.66 log points higher than the unit values the paid by poorer house-holds. This finding is robust to limiting the sample to the food product categories.

Finally, Figure 3 plots a local polynomial fit of log deviations from mean log unit val-ues within each product against log household income, together with 95% confidenceintervals. The figure shows a strong positive relation between household income andunit value paid within each product categories. A household with income that is two logpoints higher than average pays unit values that are 0.5 log points higher than average in

16

Figure 3: Unit values by household income

.5

0.5

1Ln

(Unit

Valu

e)

4 2 0 2 4Ln(Income)

Notes: This figure reports the local polynomial fit of log deviations from mean log unit values within eachproduct against log household income, together with 95% confidence intervals.

the average product category category.

3.3.2 The Within price index

The Within price index is given by equation (7), reproduced here for convenience:

bPhWithin,t = g2G

wg bPhg,t.We weight the generic product categories g with aggregate expenditure weights, wg, thatwe compute from the household expenditure survey, and allow for differences in the priceindices that households face for each generic category: bPhg vg2g shvg bPvg . Differences inthe price indices bPhg stem from differences in the expenditure shares shvg across the differentvarieties vg within each product category g. While we can observe the price change bPvgof every specific variety sampled in the Diario, the expenditure shares of each differenthousehold shvg are not observable.

We link expenditure shares shvg to household income following the evidence from Sec-

17

tion 3.3.1 that richer households tend to purchase more of the most expensive varietieswithin each product category, and assume that rich households consume high-priced va-rieties while poor households consume low-priced varieties. We classify varieties as high-or low-priced using three alternative criteria.

First, we split varieties according to whether their average price between January 1994and October 1994 the 10 months prior to the devaluation for which we have data wasabove or below the average price of the median good in the generic category. Second, wesplit the January 1994-October 1994 average prices into quartiles in each generic category,and focus on products that are in the highest vs. the lowest quartiles. Third, we focus onthe maximum vs. the minimum average prices in each generic category. Focusing on the10-month average (January 1994-October 1994) as the base period in which we classifyvarieties into high or low price, as opposed to the price in one particular month, has theadvantage that temporary sales are less likely to be identified as low prices. In Section3.5, we show that using January 1994 as our base period does not significantly affect ourresults.

One potential concern with this procedure is that high and low pre-devaluation pricesmay not reflect differences in product attributes (such as the type of retail outlet), buymaycome simply from price dispersion due to staggered price adjustment. If some prices arelow at the beginning of the sample because they have not been adjusted in a long time,a large increase in these prices may simply reflect that the price is finally being adjusted.To avoid this concern, we limit our analysis to specific varieties for which we see a pricechange between January 1994, our base month, and October 1994, the month prior to thedevaluation. For this sample of products, we can be sure that changes in prices that occurafter October 1994 are not due to the firms resetting old prices.

Finally, theWithin price index from equation (7) can only be computed for those prod-uct categories in which identical goods can be observed continuously through time. Un-fortunately, this does not encompass every category, since some categories were discon-tinued in the April 1995 revision of the consumer price index. As a consequence, only 284of the 313 generic categories can be traced before March 1995. The continuing categoriesaccount for 82 percent of the expenditures. In addition, there are some generic categories,focusing on apparel, for which the specific product quotes are based on samples of prod-ucts, as opposed to unique individual products. After excluding these product categories,the remaining categories for which identical products that can be observed continuouslythrough time account for 65% of total consumption expenditures. To compute a priceindex that reflects the importance of the Within effect for the entire economy we need totake a stand on how the relative price of cheap vs. expensive varieties changed for the

18

missing categories.With this inmind, we compute thewithin price index under two limiting assumptions.

First, we take a conservative approach and assume that the relative price of cheap versusexpensive varieties remained constant for the missing generic categories. In this case, theWithin price index is given by:

bPhWithin,t = g2GM

wg bPhg,t + g2GU

wg bPg,t, (10)where GM is the set of categories for which identical varieties that are measured contin-uously through time, GU is the sets of categories for which identical goods that cannotbe measured continuously through time, and bPg,t is the change in the aggregate price in-dex for the goods in category g. Second, we make the opposite assumption and that thechange in the price of cheap and expensive goods for the missing categories was equalto the (weighted) average change of the price of cheap and expensive varieties that wedo observe. In particular, we assume that for each category g 2 GU, the price index isbPhg,t = g2GM wg bPhg,tg2GM wg . In this case, the within price index is given by:

bPhWithin,t = g2GM

wg bPhg,t + g2GU

wgg2GM wg bPhg,tg2GM wg

= g2GU

wg bPhg,t"1g2GM wgg2GM wg

+ 1

#=g2GM wg bPhg,tg2GM wg

. (11)

Figure 4 plots the month-to-month evolution of the price indices computed both whenwe sort goods according to the median price or whenwe focus onmaximum vsminimumprices within each product category. Note that the price indices for high vs low prices arevery close to each other before the October 1994 devaluation. Following the devaluation,the price indices start to diverge. The pattern is evident both whenwe focus on prices thatare above vs. below the median and when we focus on maximum vs. minimum prices.

The exact values for the resulting price indices are reported in Tables 4a and 4b. Thefirst two columns report the price indices when we sort goods depending on whethertheir average price prior to the devaluation were below and above the median. Evenaccording to our most conservative price index (Tables 4a), inflation was substantiallyhigher for the products that were initially below the median: by October 1996, prices forthese goods increased by 11 percentage points more than for the goods that were initiallyabove the median. According to the liberal index, the difference in inflation between

19

Figure 4: The Within price indices

Conservative LiberalMaximum vs. Minimum Maximum vs. Minimum

11.

21.

41.

61.

82

1994

m1

1994

m4

1994

m7

1994

m10

1995

m1

1995

m4

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m7

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m10

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m1

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m10

P_within_Low P_within_High

11.

21.

41.

61.

82

1994

m1

1994

m4

1994

m7

1994

m10

1995

m1

1995

m4

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m7

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m10

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m1

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m4

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m7

1996

m10

P_Within_High P_Within_Low

Above vs. below median Above vs. below median

11.

21.

41.

61.

82

1994

m1

1994

m4

1994

m7

1994

m10

1995

m1

1995

m4

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m10


11.

21.

41.

61.

82

1994

m1

1994

m4

1994

m7

1994

m10

1995

m1

1995

m4

1995

m7

1995

m10

1996

m1

1996

m4

1996

m7

1996

m10

P_Within_High P_Within_Low

Notes: This figure plots the Within price indices. The Conservative price indices are defined in (10), and theLiberal indices in (11). The plots labeled Maximum vs. Minimum plot the Within indices for consumersthat consume the highest- and the lowest-priced varieties within each product category. The plots labeledAbove vs. below median plot the Within indices for consumers that buy the varieties priced above andbelow the median price within each product category.

20

Table 4: The Within price index

(a) Conservative

BelowMedian

AboveMedian

Quart. 1 Quart. 2 Quart. 3 Quart. 4 Min Max

Oct. 94 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00April 95 1.27 1.22 1.29 1.25 1.23 1.24 1.29 1.23Oct. 95 1.49 1.43 1.51 1.45 1.43 1.45 1.52 1.43April 96 1.72 1.63 1.74 1.67 1.63 1.65 1.76 1.64Oct. 96 1.87 1.76 1.88 1.81 1.75 1.76 1.91 1.75

(b) Liberal

BelowMedian

AboveMedian

Quart. 1 Quart. 2 Quart. 3 Quart. 4 Min Max

Oct. 94 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00April 95 1.30 1.24 1.33 1.27 1.23 1.24 1.34 1.24Oct. 95 1.52 1.44 1.56 1.47 1.43 1.46 1.57 1.43April 96 1.78 1.65 1.81 1.70 1.63 1.67 1.85 1.66Oct. 96 1.93 1.76 1.96 1.85 1.75 1.76 2.00 1.75

Note: These tables report the Within price indices defined in equation (7). Table 4a reports the price in-dices under the Conservative assumptions (equation 10), while Table 4b reports the Liberal price indices(equation 11). Columns labeled Below/Above Median report the price indices for consumers that buy thevarieties priced above/below the median price in each product category. Columns labeled Quart. 1/2/3/4report the price indices for consumers buy varieties with prices in the 1/2/3/4th quartiles of the price dis-tribution within each product category. Columns labeled Min/Max report the price indices for consumersthat buy the maximum and minimum priced varieties in each product category.

these price indices was 17 percent. Columns 3 to 7 show that price indices for goods thatwere in different quartiles of the price distribution as of the January-October 1994 period.By October 1996, inflation was between 14 and 20 points higher, depending on the choiceof the price index, for varieties in the cheapest quartile relative to varieties in the mostexpensive quartile. The relation tends to be monotonic, the change in the price index islower for goods that are in lower quartiles. Finally, the last two columns report the priceindex for the maximum and minimum price in each generic product category. Again,lower-priced varieties increased significantly faster than the most expensive varieties fol-lowing the devaluation. If we focus on the liberal index, the inflation for the lowest priceswas about 1.3 times higher (100 vs 75 percent inflation) than for the highest prices. Thisshows that the welfare losses of exchange rate depreciations for poor households can besignificantly higher due to the Within effect.

21

These calculations do not account for substitution effects across varieties within goods.Conventional wisdom and recent evidence [Bems and di Giovanni, 2014] suggest that incrises there is expenditure switching away from more expensive towards cheaper vari-eties within each good. In our context, this would involve the rich switching to cheapervarieties, but as we show those cheaper varieties also experienced higher price increases,most likely dampening the importance of the expenditure switching effect for the rich.For the poor it is not clear how such expenditure switching will work, as they alreadyconsume the cheapest varieties. While it is possible that the poor switch to products thatare outside the scope of Mexicos price data collection, we currently have no way of as-sessing the potential importance of this effect. Alternatively, it is possible that the poorswitch to higher-priced varieties as their price rises by less than for the cheap varieties.While theoretically possible, this appears implausible in the context of a large fall in realincomes.

3.4 The Combined effect

In this section we compute the Combined price index, defined in equation (4), reproducedhere for convenience:

bPht = g2G

whg bPhg,t.This index combines the twomechanisms captured by the Across andWithin price indicescomputed above. Since we do not observe the varieties consumed by each household, wereport the comparison of a hypothetical poor and a hypothetical rich household. The poorhousehold is defined as one that has across-goods expenditure shares whg of a householdin the bottom income decile, and on top of that consumes the cheaper varieties withineach g. The rich household has whg of the top income decile, and within each g consumesthe more expensive varieties.

We follow the procedure described in Section 2.1 to compute the indices bPhg. As dis-cussed in Section 2.1, the indices bPhg cannot be computed for all product categories. Weproceed as above, and compute the Overall price index under the two limiting assump-tions from the previous section. In particular, we compute the conservative version underwhich there is no Within effect in categories where it cannot be directly measured:

bPht = g2GM

whg bPhg,t + g2GU

whg bPg,t, (12)

22

Figure 5: The Combined price indices

Conservative LiberalMaximum vs. Minimum Maximum vs. Minimum

11.

52

2.5

1994

m1

1994

m4

1994

m7

1994

m10

1995

m1

1995

m4

1995

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1995

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1996

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11.

52

2.5

1994

m1

1994

m4

1994

m7

1994

m10

1995

m1

1995

m4

1995

m7

1995

m10

1996

m1

1996

m4

1996

m7

1996

m10

P_all_Low P_all_High

Above vs. below median Above vs. below median

11.

21.

41.

61.

82

1994

m1

1994

m4

1994

m7

1994

m10

1995

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1995

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11.

52

1994

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1994

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m1

1995

m4

1995

m7

1995

m10

1996

m1

1996

m4

1996

m7

1996

m10

P_all_Low P_all_High

Notes: This figure plots the Combined price indices. The Conservative price indices are defined in (12),and the Liberal indices in (13). The plots labeled Maximum vs. Minimum plot the Combined indices forconsumers that consume the highest- and the lowest-priced varieties within each product category. Theplots labeled Above vs. below median plot the Combined indices for consumers that buy the varietiespriced above and below the median price within each product category.

and a liberal version in which the Within effect is equally strong in the unmeasured cate-gories as it is in measured ones:

bPht = g2GM

whg bPhg,t + g2GU

whgg2GM w

hg bPhg,t

g2GM whg. (13)

Figure 5 plots the month-to-month evolution of the Combined price index under ourtwo alternative assumptions, computed both when we sort goods relative to the medianprice and when we focus on maximum vs minimum prices within each product category.Note that the price indices for high vs low prices are very close to each other before theOctober 1994 devaluation, after which the price indices start to diverge.

23

Table 5: The Overall price index

(a) Conservative

BelowMedian

AboveMedian

Quart. 1 Quart. 4 Min Max

Oct. 94 1.00 1.00 1.00 1.00 1.00 1.00April 95 1.31 1.22 1.33 1.23 1.35 1.23Oct. 95 1.56 1.40 1.58 1.42 1.61 1.41April 96 1.84 1.58 1.86 1.59 1.91 1.60Oct. 96 2.00 1.71 2.03 1.72 2.10 1.73

(b) Liberal

BelowMedian

AboveMedian

Quart. 1 Quart. 4 Min Max

Oct. 94 1.00 1.00 1.00 1.00 1.00 1.00April 95 1.33 1.22 1.36 1.24 1.38 1.23Oct. 95 1.58 1.41 1.63 1.43 1.66 1.42April 96 1.88 1.59 1.92 1.60 1.98 1.61Oct. 96 2.04 1.70 2.09 1.69 2.16 1.71

Note: These tables report the Overall price indices defined in equation (4). Table 5a reports the price indicesunder the Conservative assumptions (equation 12), while Table 5b reports the Liberal price indices (equation13). Columns labeled Below/Above Median report the price indices for consumers that buy the varietiespriced above/below the median price in each product category. Columns labeled Quart. 1/4 report theprice indices for consumers buy varieties with prices in the 1/4th quartiles of the price distribution withineach product category. Columns labeled Min/Max report the price indices for consumers that buy themaximum and minimum priced varieties in each product category.

The corresponding price indices are reported in Tables 5a and 5b. Overall, the differ-ence in inflation faced by rich and poor households is startling. According to our mostconservative index, if we split goods according to median prices, the change in price twoyears after the devaluation was more than 1.4 times higher for the poorest householdscompared to the richest ones. In the other extreme, under the liberal index and usingmaximum vs. minimum prices, inflation for the poorest households was 45 percentagepoints, or about 1.63 times, higher than for the richest households. In the following sec-tion, we show that the magnitude of these results is robust to a number of alternativeassumptions that we can use to build the price indices.

24

3.5 Robustness

In this Section we conduct a battery of robustness checks on our results for the Withineffect estimated in Sections 3.3.2. We proceed in three steps. First, we conduct placeboexperiments to show that the Within effect is not present in non-devaluation periods.Second, we show that the details of the assumptions used to calculate the baseline Withineffect are not crucial for the findings. Third, we recalculate the Within price index usingthe unit value data from the expenditure survey to distinguish the goods purchased bypoors vs rich households.

3.5.1 The Within effect following non-devaluation periods

TheWithin effect presented in Section 3.3.2 arises from the fact that the price of cheap vari-eties increased relative to the price of expensive varieties following the 1994 devaluation.In this section, we provide evidence that this change in relative prices is related to thedevaluation itself, and does not arise mechanically from some mean reversion in prices.10

With this in mind, we compute a liberal within effect for two periods during which theMexican nominal exchange rate was remarkably stable, the October 2005September 2007period and the October 2006September 2008 period. For each of these periods, we followthe procedure described in Section 3.3.2 to compute the liberal within effect.11

Table 6 reports the resulting Within effect 1 year and 2 years after the initial month foreach of the periods (i.e. the cell 2005 - 2 years shows the difference in the price index forcheap vs expensive varieties as of October 2007, where the cheap and expensive varietiesare classified using the average price of the variety during the 10 months preceding Oc-tober 2005). The resulting Within effect is almost non-existent in both periods when weclassify varieties using the above/below the median criterion, and an order of magnitudesmaller than the within effect that we compute following the devaluation if we use themax/min criterion.

3.5.2 Alternative assumptions for the Within price index

We now show that the baseline assumptions used to calculate the Within effects are notcrucial for the findings in the previous two sections. In particular, we recalculate the priceindices under three alternative approaches. First, we change the base period, and classify

10This concern should be at partially mitigated by noting that the price indexes from Section 3.3.2 showno differential trends in the months before the devaluation, as well as by our approach of only computingthe Within effect using prices that already experienced a price change between January and October 1994.

11In particular, we classify varieties as cheap or expensive according their average price in first the 10months of the years 2005 and 2006 respectively.

25

Table 6: Robustness: Within effect in alternative years

Above/ below median Max/ min prices2005 2006 2005 2006

1 year 0.01 0.00 0.04 0.002 years 0.01 0.00 0.03 0.02

Note: These tables report the difference in the liberal within price indexes for high and low prices definedin equation (11). We compute the Within price index following the procedure used in Table (4b) starting inOctober of each of the years displayed in the alternative columns. The rows 1 year and 2 years reportthe liberal Within effect one and two years after the baseline month.

varieties as high- and low-priced according to their relative position in January 1994. Theadvantage of this alternative is that it pushes back the date at which goods are classifiedas either cheap or expensive as far back from the devaluation date as possible (our datastarts in January 1994, so we cannot go back farther). The disadvantage is that, to theextent that prices are affected by temporary sales, observations in any individual monthwill be inherently more noisy than a 10-month average.

Another potential concern is that there may be substantial product heterogeneity evenwithin product categories, so that comparing high- vs. low-priced products may not be ameaningful exercise. To alleviate this concern, we re-calculate the Within effect for thoseproducts inwhich prices are quoted in themost comparable units: kilos and liters. Finally,we recompute our results focusing on the entire set of varieties, instead of limiting oursample to the set of varieties that experienced a price change prior to the devaluation.

Table 7 reports these alternative results. To facilitate exposition, we report the changein the Overall price index one year and two years after the devaluation, and omit theversion of the price index in which prices are sorted into quartiles. We continue to findlarge differences between the price changes faced by poor vs. rich households for all thesealternative price indices. The difference in the price changes is somewhat smaller whenwe use January 94 as the base period. This is not surprising, since focusing on any oneparticular month would lead us to identify temporary sales as low prices. The differencebecomes larger than the baseline if we focus on goods for which prices are denominatedin kilos or liters, or if we do not condition on prices changes.

3.5.3 Estimating difference in prices between rich and poor households

Finally, we revisit the Within price indexes presented in Sections 3.3.2 under an alterna-tive classification of which varieties are consumed by the rich vs. the poor. In particular,

26

Table 7: Robustness: the Overall price index under alternative assumptions

Conservative LiberalBelowMedian

AboveMedian

Min Max BelowMedian

AboveMedian

Min Max

Base period: January 94

Oct. 94 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00Oct. 95 1.54 1.41 1.56 1.42 1.56 1.42 1.59 1.43Oct. 96 1.96 1.72 1.98 1.73 2.00 1.72 2.02 1.73

Including only prices quoted per Kg or per Liter

Oct. 94 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00Oct. 95 1.55 1.42 1.60 1.41 1.62 1.48 1.75 1.47Oct. 96 1.99 1.76 2.10 1.75 2.16 1.91 2.39 1.88

Including products with no price changes 10 months prior to the devaluation

Oct. 94 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00Oct. 95 1.55 1.39 1.63 1.39 1.56 1.38 1.65 1.36Oct. 96 1.97 1.71 2.13 1.73 1.96 1.68 2.13 1.68

Note: These tables report the Overall price indices defined in equation (4) under alternative assumptions.Table 5a reports the price indices under the Conservative assumptions (equation 12), while Table 5b reportsthe Liberal price indices (equation 13). Columns labeled Below/Above Median report the price indices forconsumers that buy the varieties priced above/below the median price in each product category. Columnslabeled Min/Max report the price indices for consumers that buy the maximum and minimum pricedvarieties in each product category.

27

we use data from the household expenditure surveys to more closely match which are thevarieties are consumed by rich vs. poor households. We proceed in two steps. First, foreach product category for which we have unit value data in the expenditure survey, weobtain the log difference in unit values paid by households in the highest vs the lowest in-come decile by estimating the dummies a10g s from equation 9 in each product category.12

Second, we combine these estimates with the Diario data and, starting from the varietythat has the median price in each category, we find the two prices that are closest from be-ing at a log-distance of a10g from each other.13 This procedure has the advantadge of beingbased on the actual differences in unit values paid by rich vs. poor households in eachg. As such, it captures the heterogeneity in the consumption patterns of the rich and thepoor across goods: there may be some g in which the rich and the poor consume similarunit values on average, while in other g the unit values of the rich and the poor are vastlydifferent.

There are two caveats, however. First, while there are infinitelymany bundles of goodsthat would give the same unit values, this procedure assumes that rich and poor house-holds consume only the two goods that are a log distance of a10g apart from each other.Second, since we the expenditure survey only contains unit value data for a limited set ofproducts, we can only compute the indexes for a bundle of goods that accounts for 50 per-cent of consumption expenditures (as opposed to 65 percent in our baseline procedure).

Table 8 reports the resultingWithin price indices. Themagnitude of theWithin effect isclose to the baseline when using the above/below the median prices of the varieties. Notethat the conservativeWithin effect is mechanically slightly lower than in the baseline (0.09two years after the devaluation vs 0.11 in Table 4b), since the categories for which we cancompute the Within effect with this alternative methodology comprises a lower share ofconsumption expenditures (0.5 vs 0.65), and the conservative calculation atttributes zeroWithin effect to unmeasured categories.

12That is, we estimate equation 9 separately for each product category g and recover the a10g s.13Formally, in each category, we define the high- and low-priced varieties as the varieties in the Diario that

have a price that is closest to Pmediang expa10g /2

and Pmediang exp

a10g /2

respectively, where Pmediang

is the median price of a variety in product category g. For product categories for which there numbers areabove (below) the maximum (minimum) prices in the category, we define the high (low) priced varieties asthat with the maximum (minimum) price.

28

Table 8: Robustness: Within price index matching unit value data

Conservative LiberalLowprices

Highprices

Lowprices

Highprices

Oct. 94 1.00 1.00 1.00 1.00Oct. 95 1.54 1.45 1.65 1.49Oct. 96 1.89 1.80 2.01 1.83

Note: These tables report the Within price indices defined in equation (7) under alternative assumptions.Columns labeled low/high report the price indices for consumers that buy the varieties priced a10g /2 lowerand a10g /2 log points higher, respectively, than the median variety in g.

4 Distribution margins, price changes, and consumptionpatterns

The previous section shows that the patterns of price changes following the 1994 Mex-ican devaluation were strongly anti-poor. This section provides a unified explanationand novel empirical evidence linking the observed price changes to the devaluation it-self. Namely, at different levels of product disaggregation, the poor spend a higher frac-tion of their income on tradeable product categories, and among tradeables, on productswith systematically lower distribution margins. Since distribution costs are largely non-tradeable, as the relative price of tradeables to non-tradeables increases following thedevaluation, the prices paid by the poor rise by proportionally more than those paid bythe rich.

We focus on the role of local distribution costs because they are key for accountingfor the aggregate change in consumer price indices for tradeable goods after large de-valuations [Burstein et al., 2005, Burstein and Gopinath, 2015]. Our contribution in thefollowing sections is to provide new evidence that cross-sectional heterogeneity in thesecosts can also account for differential price changes across goods and varieties, and there-fore carries distributional consequences across consumers. This mechanism applies toboth the Across and Within effects, which we take up in turn.

4.1 A simple framework for understanding price changes

We start by setting up a framework for understanding retail price changes following a de-valuation, based on the simple flexible-price model with distribution margins of Bursteinet al. [2005]. Competitive retailers combine physical goods with distribution services in

29

fixed proportions in order to sell the goods to consumers. The retail price of variety vg isgiven by:

Pvg,t = PTvg,t + nvgP

Dt , (14)

where PTvg,t and nvg denote the price of the physical good and the quantity of distributionservices that are used to provide one unit of the retail variety vg, and PDt denotes the priceof non-tradeable distribution services. At any time t, the proportional price change forretail variety vg is given by

bPvg,t = 1 hvg,t1 bPTvg,t + hvg,t1 bPDt , (15)where hvg,t nvgPDt /Pvg,t is the distribution margin for variety vg.

We are interested in understanding how retail prices change in response to exchangerate shocks. In what follows, we make the simplifying assumption that the price of non-tradeable services does not move with the exchange rate, bPDt = 0,14 and that the price ofthe tradeable good moves in proportion to the exchange rate, bPTvg,t = abEt.15 The changein the retail price of variety vg is then given by:

bPvg,t = 1 hvg,t1 abEt. (16)Aggregating up to the good category, the change in the price index for category g, bPg,t 1Vg vg2g bPvg,t, is given by:

bPg,t = 1 hg,t1 abEt. (17)where hg,t 1Vg vg2g hvg,t is the average share of distribution services in g.

Equations (16) and (17) relate changes in retail prices following a devaluation to localdistribution margins. They state that varieties and product categories for which distri-bution margins are high will experience smaller proportional price changes. To the ex-tent that expenditure patterns across the income distribution are systematically related tothese distribution margins, large devaluations will have distributional consequences.

14This approximation is in line with observed price changes after large devaluations. See Burstein et al.[2005] and Figure 1.

15This could be, for example, because the production of tradeable goods uses tradeable and non-tradableinputs, PTt =

EtPTt

a PNt 1a where PTt is the foreign currency-denominated price.

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4.2 Distribution margins and the Across effect

Our explanation for the Across effect relies on two premises: (i) the differences in the non-tradeable component of different product categories explain the good-level price changesfollowing the devaluation; and (ii) there is a systematic relationship between the non-tradeable component and expenditure shares of the rich and the poor: the poor havehigher effective expenditure shares in tradeables. We now provide empirical evidence oneach of these in turn.

Distribution margins and price changes Figure 1 has already documented that the rel-ative price of tradeable to non-tradeables increased following the devaluation.16 We nowshow that among the categories classified as tradeables, the prices of goods with higherdistribution margins increase by less, as postulated by equation (17). To take this equa-tion to the data, however, we need to know the distribution margins in for disaggregatedproduct categories. Unfortunately, these data are not available for Mexico for a periodclose to the 1994 devaluation. Thus, we use data on US distribution margins, obtainedfrom the 1992 US Benchmark Input-Output Tables provided by the BEA. In particular,the BEA reports distribution margins (transportation, wholesale, and retail) for the mostdetailed IO classification categories (about 450 sectors). We match these categories byhand to the consumption categories in the Mexican consumer price data. The underly-ing assumption behind the exercise is that the variation in distribution margins acrossproduct categories is at least partly technologically determined, and thus the US data areinformative of the cross-category variation in distribution margins in Mexico. To the ex-tent this measure provides a noisy indicator of Mexican distribution margins, the noisewill likely bias us towards finding no patterns in the data.

According to these data, the distribution margins range from about 0.25 to about 0.6across tradeable sectors, with the mean of 0.43 and the median of 0.41. Appendix TableA2 reports the 10 products with the lowest and highest distribution margins in our data.The group with the highest margins is heterogeneous, including items as diverse as oph-thalmic and orthopedic equipment, tires, gasoline, and jewelry and watches. Thegroup with the lowest margins is more homogeneous, with various food items taking up8 out of 10 lowest distribution margin categories.

Figure 6 reports the scatterplot of the good-level price changes bPg,t following the de-valuation (the change from October 1994 to October 1996) against the one minus the dis-tribution margin (1 hg,t1) as in (17). Each dot represents a tradeable product category.

16See Burstein et al. [2005] for evidence from other countries.

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Figure 6: Price changes and distribution margins

Coeff = 1.293Std.Err. = .357R2 = .085

01

23

P g,O

ct96

/Pg,

Oct

94

1

.3 .4 .5 .6 .7 .81 Distribution margin (1 g)

Note: This figure presents the scatterplot of the price change in each good against oneminus the distributionmargin (1 hg) together with an OLS fit following the 1994 Mexican devaluation. The box in the top leftcorner reports the coefficient, robust standard error, and the R2 in that bivariate regression.

There is a positive and statistically significant relationship between these variables: theproduct categories with lower distribution margins experienced larger price increases,exactly as implied by (17). In spite of the fact that our data on distribution margins comefrom the US Input-Output tables, the relationship is strongly significant, with a t-statisticof 3.6 and the R2 in this bivariate regression of 8.5%.17

To establish more firmly that this pattern is due to the devaluation, Figure 7 plots thesame relationship in two placebo periods: one immediately pre-devaluation and one inthe mid-2000s. The picture is very different, and the point estimates are close to zero andinsignificant. Indeed, for the early 1990s placebo, the point estimate is actually negative.The R2s, at 0.014 and 0.001, correspondingly show that distribution margins have noexplanatory power for price changes outside of large devaluations.

17The two outliers with a nearly 300% price increase are wheat flour (harina de trigo) and white bread(pan blanco). Dropping those two goods, the coefficient is 1.03, with the t-statistic of 3.39 and R2 of 7.4%.

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Figure 7: Placebo: price changes and distribution margins

October 1992 October 1994 October 2004 October 2006

Coeff = .202Std.Err. = .128R2 = .014

.5

0.5

1P g

,Oct

94/P

g,O

ct92

1


Coeff = .048Std.Err. = .06R2 = .002

.2

0.2

.4

.6

.8

P g,O

ct06

/Pg,

Oct

04

1


Note: This figure presents the scatterplot of the price change in each good against oneminus the distributionmargin (1 hg) together with an OLS fit for two placebo periods. The box in the top left corner reports thecoefficient, robust standard error, and the R2 in that bivariate regression.

Distribution margins and consumption patterns We now evaluate how expenditureshares across product categories are related to observed distribution margins. Combining(6) and (17), the Across price index for household h following a devaluation can bewrittenas:

bPhAcross,t = g2G

whg bPg,t == (1whN)

1

g2Tewhghg,t1

! abEt. (18)

Here, whN 1g2T whg denotes the share of non-tradeable goods consumed by house-hold h, and ewhg g2T whgg2T whg denotes the share of spending on tradeable category g intotal tradeables expenditure.

According to equation (18), changes in the Across price index are driven by: i) theshare of expenditure on non-tradeable product categories, whN, and ii) expenditure sharesacross tradeable product categories with different distributionmargins,g2T ewhghg,t1. Tothe extent that the poor consume relativelymore of the tradeable categories,wpoorN < w

richN ,

or if the tradeables they consume tend to have lower distributionmargins,g2T ewpoorg hg,t1

Cravino Levchenko Devaluations

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