The Cyclicality of Sales, Regular and Effective Prices
Business Cycle and Policy Implications
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund

Contributor Notes

We study the cyclical properties of sales, regular price changes and average prices paid by consumers ("effective" prices) in a dataset containing prices and quantities sold for numerous retailers across a variety of U.S. metropolitan areas. Both the frequency and size of sales fall when local unemployment rates rise and yet the inflation rate for effective prices paid by consumers declines significantly with higher unemployment. This discrepancy can be reconciled by consumers reallocating their expenditures across retailers, a feature of the data which we document and quantify. We propose a simple model with household shopping effort and store-switching consistent with these stylized facts and document its implications for business cycles and policymakers.

Abstract

We study the cyclical properties of sales, regular price changes and average prices paid by consumers ("effective" prices) in a dataset containing prices and quantities sold for numerous retailers across a variety of U.S. metropolitan areas. Both the frequency and size of sales fall when local unemployment rates rise and yet the inflation rate for effective prices paid by consumers declines significantly with higher unemployment. This discrepancy can be reconciled by consumers reallocating their expenditures across retailers, a feature of the data which we document and quantify. We propose a simple model with household shopping effort and store-switching consistent with these stylized facts and document its implications for business cycles and policymakers.

I. Introduction

Explaining the apparent non-neutrality of money has led macroeconomists to study a variety of frictions, such as nominal and real wage rigidities or information rigidities. But the most commonly emphasized potential source of monetary non-neutrality remains “sticky prices” as epitomized by Woodford (2003). In part, this likely reflects the ubiquitousness of sticky prices in daily life. For example, Starbucks has raised its brewed coffee prices only once per year since the 2007-2009 recession began, despite the fact that the spot price of (Robusta) coffee bean rose 50 percent between February of 2007 and February of 2008, then fell 33 percent from February of 2008 to February 2010, before again rising 50 percent by February 2011.2 This annual frequency of updating prices is not uncommon, and the notion that many prices change only infrequently has been well-documented in the literature.3

Yet while firms may choose to change their prices only infrequently, this need not imply that the “effective” prices actually paid by households are themselves sticky. Chevalier and Kashyap (2011), for example, argue that if households respond strongly to sales, then “effective” price flexibility due to consumers reallocating their expenditures across goods or time could potentially undo much of the macroeconomic effects of the underlying price rigidities commonly observed in regular prices. While a significant body of work now exists which quantifies how the treatment of sales affects the degree of price rigidity (e.g. Bils and Klenow 2004, Nakamura and Steinsson 2008, Eichenbaum, Jaimovic and Rebelo 2011, and Kehoe and Midrigan 2011), evidence on the extent to which sales prices affect the effective prices paid by households remains limited. In large part, this shortcoming reflects data limitations: measuring effective prices paid by households requires data on both quantities and prices, whereas most data-sets include only the latter.

Using a panel dataset of both prices and quantities sold at the universal product code (UPC) level across different stores in 50 U.S. metropolitan areas from 2001 to 2007, we build on this literature by studying the cyclicality in both the prices posted by retailers as well as the effective prices actually paid by consumers. Consistent with Gali and Gertler (1999), Williams (2006), Roberts (2006) and others documenting the lack of a strong negative relationship between inflation and unemployment in U.S. macroeconomic data, we find little cyclical sensitivity in the inflation rate of prices posted by retailers. In contrast, and consistent with the notion of significant consumer reallocation of expenditures in response to economic conditions, we document that effective price inflation is indeed more cyclically sensitive than inflation in posted prices. Furthermore, the difference is quantitatively large: a 2 percent point increase in the local unemployment rate lowers the local inflation rate in effective prices by 0.5 percent relative to the inflation rate in posted prices for a given UPC.

To assess whether this sensitivity of effective prices paid by households is driven by sales, we also measure the cyclicality of regular and sales price changes, as well as the proportion of a given good bought on sale. While regular price changes exhibit little cyclical sensitivity, we find that the frequency and size of sales, as well as the share of goods bought on sale, decline when unemployment rates rise. Thus, the greater flexibility in prices paid by households relative to the prices charged by firms does not stem from the cyclical response of sales. Indeed, the cyclical behavior of sales is precisely the opposite of what one would expect if sales were used in the same manner as regular price changes: for sales to undo the effects of price rigidities in terms of monetary non-neutrality, we would expect them to be systematically more frequent when local unemployment rates rise. Thus, these results provide new evidence consistent with Eichenbaum et al. (2011), Kehoe and Midrigan (2010) and Guimaraes and Sheedy (2011) that sales are fundamentally different from regular price changes.

If sales are not the source of the observed flexibility in the prices actually paid by households for a given good in a given metropolitan area, what is? We argue that both the counterintuitive cyclical behavior of sales prices and the discrepancy between the cyclical changes in posted and paid prices can be accounted for by consumers switching across stores in response to economic conditions. Intuitively, given considerable dispersion of prices across stores in any given time period, a deterioration in local economic conditions should lead some price-sensitive consumers to reallocate some of their consumption expenditures toward low-price retailers, thereby lowering the average price paid for any given good. At the same time, this store-switching behavior on the part of price-sensitive consumers should reduce the incentive of high-price stores to attract these price-sensitive consumers through sales, which could account for the counter-intuitive cyclical behavior of sales prices that we identify.

We document two pieces of evidence consistent with this mechanism. First, because we have data for a variety of identical goods sold across different stores within a given geographic area, we can quantify the extent to which some stores are systematically more expensive than others. High-price stores experience larger a decline in the importance of sales than low-price stores when local unemployment rates rise, consistent with the mechanisms described above. We also show that, when the unemployment rate increases, the growth rate of revenues in high-price stores declines more than in low-price stores, consistent with significant expenditure reallocation across retailers by households. Second, we exploit a detailed panel dataset tracking individual households’ expenditures at the UPC level for each store. Given that we can characterize the degree to which some stores are more expensive than others, these data allow us to quantify the extent to which individual households reallocate their expenditures across different retailers in response to economic conditions. We find robust evidence that individual households do indeed reallocate their consumption expenditures toward low-price retailers when local economic conditions deteriorate and that this reallocation is most pronounced for households near the middle of the income distribution.

In short, our empirical results point to significantly more flexibility in the prices paid by households relative to the prices charged by firms, but this flexibility appears to be driven by the reallocation of household expenditures across retailers rather than by sales. While previous work has considered the macroeconomic consequences of effective price flexibility due to sale pricing by retailers, the potential implications of retail-switching remain unexplored. As a result, we build on the effective price literature by integrating store-switching by households into a basic New Keynesian model. In this model, two retailers each purchase intermediate goods from monopolistic competitors, who are subject to sticky-prices, and convert these goods into an identical final good. One “local” retailer charges a premium over the “discount” retailer. However, household expenditures at the latter are subject to iceberg costs which can be reduced by time-intensive shopping on the part of households. When the return to shopping effort is diminishing, shopping effort on the part of households will be countercyclical. As a result, periods of low employment are also periods of high shopping effort activity. This effort leads to lower effective prices at the “discount” retailer and households therefore reallocate more of their expenditures toward this retailer when employment is low. We show that time-intensive shopping effort and expenditure reallocation lead to three testable predictions: 1) effective prices are high relative to posted prices when the level of economic activity is high, 2) high-price retailers of otherwise identical goods account for a larger share of total retail revenues when the level of economic activity is high, and 3) the unconditional Phillips curve relationship between inflation and economic activity is steeper when measured in terms of effective rather than posted prices. Consistent with household expenditure-reallocation, we find that all three predictions hold in our data even when aggregated across all categories and regions.

In the model, the effective prices paid by households are much more flexible than the underlying posted prices, as suggested by Chevalier and Kashyap (2011). However, this effective price flexibility stems not from the presence of sales, as in Chevalier and Kashyap (2011), but from the reallocation of household expenditures across retailers and the time-variation in shopping effort. In response to monetary policy shocks, for example, nearly 50 percent of the total adjustment in the price of the final consumption good paid by households occurs in the first quarter, while only this ratio is less than 20 percent for underlying posted prices. As a result, the contemporaneous effect of monetary policy shocks on output is smaller, i.e. there is less monetary non-neutrality than one would expect based on the frequency of posted price changes. However, the effect is relatively small on impact and most importantly does not qualitatively affect the persistence of the response of the output gap to monetary policy shocks. Hence, the response of output to a monetary policy shock looks much more like that of a typical New Keynesian model with high levels of price stickiness than one with low levels of price-stickiness. In short, despite significant flexibility in the effective prices faced by households, the dynamics of the model are dominated by the underlying level of price-stickiness in posted prices. In this sense, our results are similar in spirit to those of Eichenbaum et al. (2011), Guimaraes and Sheedy (2011) and Kehoe and Midrigan (2011) but whereas they focus on effective price flexibility due to sales, we emphasize the role of the reallocation of expenditures across stores by households as the source of effective price flexibility.

Despite the fact that the quantitative implications of store-switching are limited in terms of the degree of monetary neutrality, the presence of shopping effort and store-switching does have several novel business cycle and policy implications. For example, the presence of shopping effort and store-switching alters the effective Frisch labor supply elasticity and the effective elasticity of the output gap with respect to real interest rates, when the latter are expressed in terms of input prices rather than final consumption goods prices. For the labor supply elasticity, when the utility return to labor is high, then the return to shopping effort must also be high since the marginal disutilities of labor and shopping effort are identical. High returns to shopping effort require low shopping intensity under diminishing returns. But if less time is spent on shopping, then the marginal disutility of labor is low so households will be willing to supply more labor. For the sensitivity of the output gap to real interest rate changes expressed in terms of posted prices, if real interest rates rise, then output will fall but be expected to rise via the dynamic IS curve. With countercyclical shopping effort, the time spent on shopping will therefore be expected to rise thereby lowering expected inflation in final goods prices. The latter will lead to relatively more consumption and output, thereby mitigating the initial decline in output.

The presence of store-switching and shopping effort also leads to new insights into some traditional measurement issues regarding inflation. For example, the Boskin Commission report (1996) and Shapiro and Wilcox (1996) discussed the potential for store-substitution to cause biased estimates of inflation. Reinsdorf (1993), Hausman and Leibtag (2007) and Diewart, Greenlees and Hulten (2009) try to assess the average inflation bias in the U.S. from store-switching, but focus primarily on the entry of new potentially low-price outlets and the fact that these entrants will only gradually be included in the CPI sample of stores. Triplett (2003) also highlights retail-switching behavior on the part of households as well as the related costs faced by households due to shopping effort. As emphasized in Triplett (2003), the difference in our model between the final consumption price index faced by households and a fixed-expenditure weight index will reflect two sources: the reallocation of expenditures by households across retailers as well as the time-varying intensity of shopping effort on the part of households. One contribution of the paper is to show that the “effective” price index in our model, which uses time-varying expenditure weights across retailers, will generally track the final consumption price index despite not directly including the household costs stemming from shopping effort. Another contribution to the inflation measurement literature is documenting how store-switching also leads to a cyclical mismeasurement of inflation both in the data and in the model. We further document that substitution across similar goods within stores also varies with business cycle conditions, so that the well-known “substitution bias” will occur not just in the long-run but also over the course of the business cycle. These two forms of cyclical biases suggest that to more precisely measure the cost-of-living, statistical agencies would be well-served by tracking actual prices paid by consumers rather than prices charged by retail outlets, as emphasized in Triplett (2003).

We also show that shopping effort and store-switching have policy implications above and beyond that for the measurement of inflation. First, the loss function derived from the household’s expected utility over consumption and leisure displays a larger relative weight on output gap stabilization. This primarily reflects a reduced welfare cost of inflation volatility in the presence of shopping effort. Inflation volatility implies higher price dispersion which requires more labor, and therefore less leisure, due to the convexity of labor supply. However, countercyclical shopping effort implies reduced shopping intensity when hours worked are high, thereby mitigating the decrease in leisure and therefore the welfare costs of inflation volatility. Finally, we consider whether welfare would be enhanced if central banks responded to effective price measures rather than posted prices. The results vary with the regime: an inflation-targeting central bank is generally well-served by responding to posted price inflation rather than measures of effective price inflation, but in price-level targeting regimes, significantly higher welfare can be obtained by targeting deviations of effective prices from a target level than from targeting traditional posted price gaps. This again suggests that devoting more resources to constructing aggregate measures of effective prices paid by households could potentially lead to improved policy rules and therefore greater economic stability and welfare.

The structure of the paper is as follows. Section 2 discusses the dataset used for the empirical analysis. Section 3 presents baseline empirical results on the cyclicality of regular, sales and effective prices while section 4 documents evidence supporting the cyclicality of store-switching by consumers. Section 5 presents equivalent results for the cyclicality of within-store cross-good substitution. Section 6 develops the model with store-switching and household shopping effort and derives policy and business cycle implications. Section 7 concludes.

II. Data Description

We use a very extensive data set assembled by Symphony IRI, a marketing and market research agency,4 and discussed in more detail in Bronnenberg, Kruger and Mela (2008). This data set contains weekly scanner price and quantity data covering a panel of stores in 50 metropolitan areas and 31 product categories from January 2001 and December 2007. Importantly, the date set covers multiple chains of retailers for each market. In addition, the data includes a panel of households in two of the metropolitan areas in which households provided detailed information on their characteristics and purchases. This household dimension can be linked to the store-level information of the data set.

The metropolitan areas are typically defined at the Metropolitan Statistical Area (MSA) level. In four cases (West Texas/New Mexico, South Carolina, New England, and Mississippi), the areas identified in the data set offer a greater coverage than a city. Two of the metropolitan areas are smaller than typical (Eau Claire, WI and Pittsfield, MA) but the household panel data were constructed only for these two areas. Within each metropolitan area, the data includes price and quantity data from a panel of stores, defined either as drug stores or grocery stores. Grocery stores outnumber drug stores within each metropolitan area. For example, data from San Francisco in 2005 cover 44 grocery stores and 14 drug stores. Each outlet has an identifier which is constant over time so one can track the prices and revenues at each retailer over time. However, retailers (or chains of retailers) are deliberately not identified by name.

For each retail outlet, weekly data are available at the UPC (universal product code) level. Goods are classified into 31 general product categories (e.g., Beer, Coffee, Deodorant) as well as more refined categories. Brand information is included (e.g., Budweiser, Heineken, Coors) but all private-label UPC’s have the same brand identification so that the identity of the retailer cannot be recovered from the labeling information. Detailed information about each good is included, such as whether a product is low-fat, as is information about the volume of the product (e.g., 6-packs vs. 12-packs, volume per container). Unfortunately, no data on costs are available.

Retailers report the total dollar value of weekly sales (TR) for each UPC code, as well as total units sold (TQ). The combination of the two yields the average retail price during that week which is computed as follows:

Pmsctj=TRmsctjTQmsctj(2.1)

where m, s, c, t, and j index markets, stores, product categories, time, and UPC. This retail price includes retail features, displays and retailer coupons, but does not incorporate manufacturer coupons. In addition, retailers flag goods on sale. Thus, the dataset provides the average price of a good paid by consumers at a given store during the course of the week, as well as whether this price is identified as a sales price.

Because we are interested in differentiating between regular price changes and those due to sales, we adopt the following conventions. First, any change in prices between two periods when neither period has a sales flag is defined as a “regular” price change if the price difference exceeds 1 percent in value. Second, when a sales flag is listed and the price after the sale expires is the same as prior to the sale, we assume no change in regular prices in intermittent periods. Third, in addition to the sales flag provided in the data set, we apply an additional filter similar to the filter in Nakamura and Steinsson (2008). Specifically, we consider a good on sale if a price reduction is followed by a price increase of the same magnitude within four weeks.5

Table 1 presents basic statistics about the weekly frequency and size (in log-percentage terms) of both sales price changes and regular price changes across goods and for each of the main categories. We also present data on the average share of goods bought on sale.6 The frequency of sales and regular price changes are computed at the individual UPC level in a given month, then averaged across all UPC labels within a category in a given city and month, and finally averaged across time and cities. To aggregate across the individual UPCs within each product category, we use several weighting schemes: i) equal weights; ii) expenditure shares for a given city and year (“city specific”); iii) cross-city expenditure shares for a given year (“common”).7

Table 1.

Descriptive Statistics

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Notes: The table reports basic statistics about sales and regular price changes at the city/category level at the weekly frequency from 2001 to 2007.

The average size of sales is approximately 25 percent across all goods. While less than 20 percent of goods are on sale in any given week, more than 30 percent of all goods purchased are done so when goods are on sale. Frozen dinners and frozen pizzas are the goods which are proportionally most bought on sale, while cigarettes are the least frequently bought on sale (Appendix Table A1). It is also the case that frozen dinners and pizzas are among the goods which are most frequently on sale while cigarettes are only rarely on sale. Cigarettes and beer are the goods for which sales, when they do occur, tend to be smallest while frozen dinners and pizzas are, again, at the other extreme. Panel A of Figure 1 documents that there is a strong positive correlation between the frequency and size of sales across categories, while Panel C illustrates the fact that categories of goods with a higher frequency of sales also have a larger fraction of goods bought on sale.

Figure 1.
Figure 1.

Correlations between key moments

Citation: IMF Working Papers 2012, 207; 10.5089/9781475505573.001.A001

Notes: Figures report average (across time and goods) moments at the category level. Expenditure shares are used as weights to aggregate goods. Red line shows the best fit linear projection. See section 2 for details.

Rows (4) through (9) in Table 1 focus on the properties of regular price changes. Across all goods, increases in regular prices are more frequent than price decreases. The average size of price changes is 3.5 percent and the average size of absolute price changes is 12 percent. The average weekly frequency of regular price changes is 5 percent, so that the average duration between regular price changes is approximately 5 months. While lower than the frequency found by Nakamura and Steinsson (2008), our data is sampled at the weekly frequency which can lead to higher estimates of the frequency of price changes than when data is sampled at the monthly frequency, as documented in Kehoe and Midrigan (2010). Panel B of Figure 1 illustrates that, in contrast to sales, categories of goods with more frequent regular price changes tend to have smaller price changes.

Figure 1 also examines whether there is any systematic link between the properties of regular price changes and sales across categories. Panel D, for example, shows that there is little link between the frequencies of sales and regular price changes across categories, while Panel E documents instead a positive relationship between the average size of sales (in percentage terms) and the average change in regular prices across categories. Finally, Panel F illustrates a weak positive relationship between the frequency of sales and the average size of regular price changes across categories.

III. The Cyclicality of Effective, Regular and Sales Price Changes

While a significant literature now exists on measuring and quantifying different forms of price changes, our primary interest is in examining the cyclicality of different prices in the data. In particular, we distinguish between two forms of prices: posted prices are those provided at the store-level and consist of both regular and sales prices, and “effective” prices are the average (weighted by quantities) prices paid by households across retailers for a given good.

3.1 The Cyclicality of Posted and Effective Prices

To first characterize whether the prices that households pay differ in a systematic manner from the prices charged by retailers, we examine the cyclicality of the two. Measuring the effective prices paid by households exploits the fact that our data includes quantities sold as well as prices. It further exploits the fact that we have data for a large number of retailers within each metropolitan area. Specifically, we first construct the quantity-weighted average “effective” price of a specific good j in category c across stores in geographic area m as

P¯mcjteff=ΣsmTRmsctjΣsmTQmsctj.(3.1)

This measure can change because individual prices change or because consumers reallocate their consumption of the good across stores. For each good j in category c and market m, we then compute the monthly inflation rate log(P¯mcj,teff/P¯mcj,t1eff). Then, using weights ωmcjt for UPCs, we aggregate across all goods j within a category c to get the average category-level inflation rate across stores. In aggregating across goods, we consider the use of equal weights, city-specific weights, and common weights across UPC’s within each product category. Because these weights are held fixed within each calendar year, our measure of “effective” price inflation does not include substitution across goods, a question to which we return in section 5. Finally, we cumulate monthly inflation rates into the annual inflation rate π¯mcteff. which we refer to as the “across-store effective inflation rate”. Using prices constructed in (2.1), we also construct posted inflation price measures π¯mctpost in an equivalent manner, except for the fact that weighting across retailers is based on fixed-expenditure weights rather than time-varying expenditure-weights.8

To assess the cyclicality of price changes with respect to economic conditions, we adopt the following baseline empirical specification:

Ymct=βURmct+λt+θm,c+error(3.2)

where m, c, and t index markets (e.g., Atlanta, Detroit), the category of the good (e.g., beer, yogurt), calendar time (i.e., month); Ymct is a variable of interest (e.g., effective inflation rate); URmct is the local seasonally-adjusted unemployment rate;9 θm,c denotes the fixed effect for each market and category of good while λt denotes time fixed effects. Because the unemployment rate at the metropolitan level is only available at the monthly frequency, we estimate specification (3.2) at the monthly frequency as well. Since the error term in specification (3.2) is likely to be serially and cross-sectionally correlated, we use the Driscoll and Kraay (1998) method to construct standard errors.10

Estimates of β in specification (3.2) show the strength of correlations between local business conditions and various pricing moments and thus are informative about cyclical properties of these moments. One may, however, entertain a causal interpretation of the estimates. Because most goods sold in stores are not produced locally, specification (3.2) should not suffer from endogeneity issues typically associated with regressions of prices on real economic activity. For example, unobserved productivity innovations for a specific product, like razors, are unlikely to be correlated with local unemployment rates. While aggregate shocks could lead to simultaneous movements in prices of goods and local economic conditions, controlling for time fixed-effects should eliminate this endogeneity issue. Hence, the causal interpretation of β in specification (3.2) can stem from the fact that almost all products sold at a given retailer will be produced in other geographic areas so that local variation in unemployment rates will serve as proxies for shocks to the local demand for consumer goods.

Given these measures of posted price and effective price inflation rates at the category/market level, we estimate their cyclical sensitivity to local economic conditions using equation (3.2). The results are presented in Table 2. Focusing on the results with both city-category and time fixed-effects, we find little cyclical sensitivity of posted price inflation measures to local economic conditions. While the coefficients on unemployment rates are mostly negative, we cannot reject the null of zero response. This acyclicality in posted price inflation to economic conditions is consistent with Gali and Gertler (1999), Williams (2006), Roberts (2006) and others documenting the lack of a strong negative relationship between inflation and real economic activity in U.S. macroeconomic data, albeit that our results obtain at a microeconomic level. However, the results for inflation in effective prices are quite different: the inflation rate of prices actually paid by consumers drops significantly when local economic conditions worsen. Furthermore, the difference between the two sets of coefficients is economically large: a 2 percent point increase in the local unemployment rate lowers the effective price inflation rate by 0.5 percent at an annual rate below the inflation rate of posted prices. Hence, the key finding is that effective prices paid by households are significantly more flexible and sensitive to economic conditions than the underlying prices charged by retailers.11

Table 2.

Cyclical properties of selected moments of price changes.

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Notes: The table reports estimated coefficients on local seasonally-adjusted unemployment rate in specification (3.2). Number of observation is 127,224. Estimated specification is given by equation (1). Driscoll and Kraay (1998) standard errors are in parentheses.***, *** denote significance at 0.01, 0.05, and 0.10 levels.

3.2 The Cyclicality of Sales and Regular Price Changes

The greater flexibility in the effective prices paid by households relative to those charged by firms is consistent with the logic of Chevalier and Kashyap (2011) in which the reallocation of consumer expenditures leads not just to greater effective price flexibility for households but ultimately to diminished monetary non-neutralities. To investigate the source of this flexibility, we now consider whether sales are the key driver of this behavior. Thus, we again estimate (3.2) but now use the frequency and size of sales for each UPC aggregated to the category/market level, as well as the share of monthly expenditures for each UPC done on sale, again aggregated to the category/market level. For comparison, we also assess the cyclicality of regular price changes, both in terms of their frequency and size. Note that since posted price inflation rates depend on both the frequency and size of price changes, this can be interpreted as a decomposition of the results for inflation rates.

The first column of Table 2 documents results from estimating specification (3.2) at the category/market level using a simple average across all UPC products within a category, excluding all fixed effects in specification (3.2). The results indicate that a higher local unemployment rate is associated with more frequent sales and a larger share of goods on sales. However, it is unclear whether this larger role played by sales reflects the fact that sales become more prevalent within a market when i) the unemployment rises (i.e. business cycle effects), ii) regions with higher unemployment rates on average also experience more frequent sales for other reasons (i.e. systematically more depressed areas may have on average more frequent sales), or iii) there is a comovement of trends in unemployment and properties of sales. As a result, columns (2) and (3) present equivalent results controlling for geographic/category specific effects and time fixed effects to address ii) and iii). Introducing geographic/category level fixed effects eliminates much of the positive effect of unemployment on sales found in the previous specification, leaving little evidence of cyclical sensitivity of pricing behavior to economic conditions. However, this lack of sensitivity to economic conditions could also reflect macroeconomic shocks (or other omitted variables) which induce variation in both unemployment rates and the dependent variables and thus lead to potentially spurious correlations. As a result, our preferred specification includes both geographic/category fixed effects and time fixed effects. As illustrated in column (3), controlling for time fixed effects alters the results: higher unemployment rates within an area become associated with significantly less frequent sales and those sales which do occur are smaller in size (the positive coefficient points to smaller sales since these are measured as negative values). Although consumers may time their purchases to exploit scarcer sales and thus offset some of the decline by purchasing more goods on sale whenever there is a sale, we find no support for this channel. Specifically, the share of goods bought on sale declines with increases in the rate of unemployment.12 Hence, these results indicate that once one controls for aggregate conditions, a worsening in local economic conditions reduces the size, frequency, and relative importance of sales.13

In addition, column (3) documents the cyclicality of regular price changes. These results point to a slightly reduced frequency in regular price changes. This reduced frequency of price changes obtains for both price increases and price decreases, although the results are only marginally statistically significant for the former. However, when we measure category averages using expenditure weights, either city-specific (column (4)) or common across cities (column (5)), cyclical changes in the frequency of regular price changes are no longer significantly different from zero. Furthermore, we find little evidence that the size of regular price changes varies with local economic conditions, regardless of the category aggregation method. The cyclicality of sales behavior, on the other hand, is very robust to the aggregation method. The frequency and average size of sales, as well as the share of goods bought on sale, are robustly lower when local unemployment rates are higher.14

In short, these results suggest that the properties of regular price changes are close to acyclical: neither the frequency nor size of these types of price changes vary in a systematic manner with local economic conditions. Similarly, we find little evidence that category-level inflation rates are significantly reduced by higher local unemployment rates. In contrast, sales prices appear to be much more cyclical: sales are smaller and less frequent when local unemployment rates are high, and the share of goods bought on sale declines with worsening local economic conditions. This counter-intuitive cyclical behavior of sales strongly suggests that sales prices are unlikely to have the same macroeconomic implications as regular price changes since one would then expect more frequent and larger sales in the face of economic downturns accounting for the decline in aggregate inflation. Thus, the pro-cyclicality of sales suggests that the relevant degree of price stickiness is closer to that of Nakamura and Steinsson (2008) than Bils and Klenow (2004), consistent with Eichenbaum et al. (2011), Kehoe and Midrigan (2010) and Sheedy and Guimaraes (2011).

3.3 Implications of Sales and Effective Price Cyclicality

The pro-cyclicality of both sales and effective prices identified in the previous two sections raises two questions. The first is whether the two are related phenomena. The pro-cyclicality of effective prices means that when local economic conditions deteriorate, households pay lower prices (or price increases are smaller) for a given good. The acyclicality of regular price changes means that the regular prices of the goods do not change, on average, when local economic conditions deteriorate while the pro-cyclicality of sales means that goods are less frequently on sale and that sales are smaller on average. One way to reconcile these sets of facts is through the reallocation of expenditures by households across retailers: when local economic conditions worsen, households purchase relatively more of their expenditures at low-price retailers, thereby lowering effective prices paid even in the absence of decreases in prices charged by retailers.

While the pro-cyclicality of sales may seem counterintuitive when these are viewed primarily as just another form of price changes, interpreting it in the context of a setting in which consumers can switch across retailers delivers a natural link between the two. Intuitively, a deterioration in local economic conditions should lead more price-sensitive consumers to reallocate some of their consumption expenditures toward low-price retailers, thereby lowering the average price paid for any given good. At the same time, this store-switching behavior on the part of price-sensitive consumers should reduce the incentive of high-price stores to attract these price-sensitive consumers through sales, which could account for the counter-intuitive cyclical behavior of sales prices that we identify. In addition, these two effects should reinforce each other. To the extent that high-price stores reduce the frequency and size of sales, then this should induce additional store-switching behavior on the part of price-sensitive consumers, which in turn should again reduce the incentive of high-price stores to do sales, etc.

In Appendix B, we present a simple model building on Lal and Rao (1997) which illustrates this mechanism and the multiplier effect of store-switching on sales and vice-versa. There are two retailers in the model. One sets “everyday low prices” (EDLP) and does no sales while the other retailer, referred to as “HiLo”, follows a pricing strategy that incorporates intermittent sales. The coexistence of the two types of retailers is a unique Nash equilibrium and ensures a segmentation of the market. The two stores compete over two different types of consumers: “bargain hunters” and “loyal” consumers. These consumers differ in their transportation costs and in whether they observe sales prices. Bargain hunters have low transportation costs and always observe all prices, hence they purchase from the store that offers the lowest cost that period (including transportation cost). Loyal consumers have higher transportation costs and do not observe current prices. As a result, they buy a single unit from the retailer which offers the lowest price (net of transportation costs) in expectation. An increase in the share of bargain hunters (which we interpret as similar to an increase in local unemployment rate) leads to relatively more consumers buying from the low-price EDLP retailer. This reduces the incentive of the HiLo retailer to do sales thereby increasing the relative price of HiLo stores by decreasing the optimal size of sales. This simple model illustrates how variation in local economic conditions can, in the presence of store-switching on the part of households, naturally account for the pro-cyclicality of sales observed in the data. In section 4, we provide additional empirical evidence in support of this mechanism.

The second question which follows from store-switching by households is whether the flexibility that it implies for effective prices paid by households matters for macroeconomic dynamics. Chevalier and Kashyap (2011) argue that effective price flexibility due to sales could potentially undo the monetary non-neutralities typically associated with rigid prices. Our evidence suggests that while the prices paid by households are indeed significantly more flexible than implied by changes in posted prices, this flexibility stems from the reallocation of household expenditures across retailers rather than from counter-cyclical sales. An important question, therefore, is quantifying the extent to which effective price flexibility due to store-switching affects the degree of monetary non-neutrality as well as assessing other business cycle and policy implications of store-switching. To this end, we build a model in section 6 with shopping effort and store-switching on the part of households which allows us to quantify the implications of store-switching behavior for macroeconomic dynamics.

IV. Household Store-Switching

To provide more direct evidence on whether consumers reallocate their expenditures across retailers as their incomes change, we pursue two complimentary approaches. The first approach establishes that the pro-cyclicality of sales is particularly pronounced for high-price retailers. The second approach employs household panel data and documents that households do indeed reallocate their consumption expenditures toward low-price retailers when local economic conditions worsen.

4.1 Cross-sectional variation in the sensitivity of pricing to business conditions

To quantify expenditure switching across retailers, we construct a time-varying ranking of stores’ relative prices as follows. First, for each UPC-level good j in category c and market m, we rank each store s in a given market and period t by the price charged for that good. The rank R is 1 when a store has the lowest price, R = 2 for the second lowest price, and so on. We normalize the rank by (Rmax + 1), i.e., the number of stores selling this good plus one, so that the resulting rank Rmcstj ∈ (0,1).15 Second, we compute the average rank for a store across the set of UPC products Ω. We consider several versions of Ω because different stores sell different goods: i) Ω includes all UPCs that are sold in every store in a given market (Ωmax); ii) Ω includes UPCs sold in 90 percent of stores in a market (Ω90); iii) Ω includes UPCs sold in 75 percent of stores (Ω75).16 The average rank of a store for a given Ω is Rmst,Ω ΣcΣjΩ ωmcstj Rmcstj where ω is a weight (equal, city-specific, or common). Finally, we rank stores based on Rmst,Ω to determine stores with consistently low and high prices. To make ranks comparable across cities, we normalize Rmst,Ω by the number of stores in a city plus one to have the resulting rank Rmst,Ω ∈ (0,1), where 0 is the lowest-price and 1 is the highest-price store. A store’s price ranking tends to be highly persistent over time, with an autocorrelation parameter of 0.90 at the annual frequency.17

To quantify how the cyclicality of price changes varies with the relative price rank of the store, we perform the analysis at the store-level using the following empirical specification

Ymst=qsm+a1URmt+a2URmt×R¯mst,Ω+λt+error(4.1)

where Ymst is a price moment considered for store s in market m at time t, qsm is the store s fixed effect in market m, and λt is the time fixed effect. The aggregation of the price measures across goods is done via expenditure shares of each UPC product across all stores.

In Table 3, we present results using the three different definitions of Ω applied to the size and frequency of sales, the share of goods bought on sale, and the size and frequency of regular price changes. The results are consistent with the notion that a store’s price rank has significant effects on the cyclicality of price changes. Specifically, more expensive stores (those with a higher rank) exhibit much more pronounced declines in the frequency of sales. This is accompanied by a significant decline in the share of goods bought on sale in more expensive stores. The size of sales in more expensive stores and the size of sales in less expensive stores have similar reactions to the unemployment rate. Finally, when the unemployment rate increases, the growth rate of revenues declines more strongly in expensive stores than in cheap stores. In fact, the least expensive stores may experience an increase in the growth rate of revenue when unemployment increases. These results hold for all definitions of Ω and are therefore consistent with the notion that higher unemployment leads to store-switching by price-sensitive consumers and a reduction in the incentive of high-price stores to offer discounts and sales to attract them.

Table 3.

Cyclicality of pricing moments by store rank.

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Notes: The table reports estimates of specification (4.1). Number of observation is 144,270. UR is the local seasonally-adjusted unemployment rate. Rank is the rank of the store in terms of level of prices (Rmst,Ω). Ω indicates what universe of goods is used to rank stores. Expenditure shares are used to aggregate ranks across UPCs. Driscoll and Kraay (1998) standard errors are in parentheses.***, **, * denote significance at 0.01, 0.05, and 0.10 levels. See text for further details.

4.2 Households’ choices of shopping outlets as a function of business conditions

We also consider an alternative and more direct approach to quantifying the extent of consumers’ reallocation of their expenditures across stores. The household panel data developed by IRI Symphony tracks between 5,000 and 10,000 households in Eau Claire, WI and Pittsfield, MA from 2001 to 2007. About 2,000 households are continuously present between 2001 and 2007. During this time, households’ expenditures on each UPC product were tracked, including the location of each purchase. Hence, these detailed data allow us to directly measure the extent of the store-switching phenomenon at the level of individual households in light of changing economic conditions.

To do so, we first construct a household-specific time-varying measure of the pricing rank of the stores in which each household does its shopping. Specifically, we construct an average rank of stores at which household h shopped in month t and market m (either Eau Claire, WI or Pittsfield, MA)

R˜hmt=ΣsmψmhstR¯mst,Ω(4.2)

where Rmst,Ω is the average price rank of store s in market m at time t across the set of goods Ω as defined before and ψmhst denotes the share of the household’s expenditures spent at store s in market m and month t. A low (high) value of R˜hmt means that household h made purchases in low (high) price stores in month t. Using R˜hmt therefore provides a way to quantify the extent to which each household is allocating their expenditures across retailers of different average price levels.

To assess whether individual households reallocate their expenditures across stores as local economic conditions change, we estimate the following specification across households in the two markets

R˜hmt=qhm+a1URmt+λt+error(4.3)

where qhm is a household h in city m fixed effect and λt is a time fixed effect. The results are presented in Table 4 using both a simple average across all UPC’s consumed by a household as well as using a household’s average expenditure-weights across UPCs. Because store price ranks can vary with the set of UPC’s used in their construction, we produce these results for each of the definitions of Ω considered before. The results are similar regardless of the choice for Ω or weights used to construct each household’s average expenditure-rank: the coefficient on unemployment is negative and statistically significantly different from zero at standard levels. Thus, higher local unemployment rates are associated with households substituting more of their expenditures towards low-price retailers. In addition, the estimated magnitudes are relatively large: a 1 percent point increase in the local unemployment rate is associated with a decrease in the average rank at which households shop of between 0.05 and 0.13 depending on the specific measures used.18

Table 4.

Rank of the shore where households shop as a function of local unemployment rate.

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Notes: The table reports estimates of specification (4.3). The dependent variable is the average rank of stores where a household shops in a given month. The table reports estimated coefficients on the local seasonally-adjusted unemployment rate. Each regression has 471,615 observations. Driscoll and Kraay (1998) standard errors are in parentheses.***, **, * denote significance at 0.01, 0.05, and 0.10 levels.

The household data also includes detailed characteristics of each household for that year, such as age of the head of household, income, and the number of household members. As a result, we can also investigate which types of households are most likely to engage in store-switching behavior. Specifically, we focus on the relationship between household income and store-switching via the following empirical specification:

R˜hmt=qhm+a1URmt+ΣgagURmt×Dhmg+λt+error(4.4)

where Dhmg is the dummy variable equal to one if the average annual income of household h in market m falls into g-th quintile of the income distribution we have in the IRI sample of households.19 Hence, a1 indicates the degree of store switching for the lowest-income quintile. Using a1 as the benchmark, we explore how the degree of store-switching varies with income quintile. The results are presented in Table 5 for different measures of Ω and using both equal and expenditure-share weighting of different goods. In each case, the strongest store switching is observed for households in the second and third income quintiles (annual income between $22,600 and $50,000). This seems intuitive: most low-income households are likely to shop in less expensive stores most of the time, while high-income households are more likely to consistently shop in the most expensive stores. Hence, sales by high-price stores are likely to be designed to attract the middle of the income distribution, and it is these consumers whose switching behavior is most significant over the course of the business cycle.

Table 5.

Rank of the shore where households shop as a function of local unemployment rate and household’s income.

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Notes: The table reports estimates of specification (4.4). The dependent variable is the average rank of stores where a household shops in a given month. The table reports estimated coefficients on the local seasonally-adjusted unemployment rate. Dg is the dummy variable equal to one if a household is in gth income quintile and zero otherwise. Each regression has 471,615 observations. Driscoll and Kraay (1998) standard errors are in parentheses.***, **, * denote significance at 0.01,0.05, and 0.10 levels.

V. Cross-Good Substitution

While we have so far limited our attention to expenditure-switching across stores by households for a given UPC product, the literature on price measurement has long emphasized another margin of substitution, namely across goods. Our primary motivation for focusing on switching across stores for a given good is that, as in the construction of the CPI, it is helpful to consider the cost of a fixed basket of goods for welfare purposes. The substitution bias long emphasized in the literature, in which CPI inflation will be overstated because it ignores the possibility of consumers switching to substitute goods when relative prices change, instead involves a change in the composition of the basket which will have implications for welfare. Nonetheless, we also consider this additional margin here for two reasons. First, the substitution bias has primarily been considered as a source of a long-run bias in inflation measurements, while the cyclical properties of this margin have been ignored. Second, comparing the degree of store-switching to the amount of across-goods substitution provides one metric to quantify the relative importance of store-switching for the measurement of inflation.

To quantify the degree of substitution across goods, we first construct the quantity-weighted average “effective” price across all goods j within category c in store s and geographic area m as

P¯mctseq=ΣjcTRmsctjΣjcTRmsctj×EQj.(5.1)

where EQj is the quantity equivalent of good j. Hence, in calculating P¯mctseq, all prices are converted into quantity-equivalent measures so that e.g. the price of a 6-pack of beer is comparable to a 12-pack. P¯mctseq can change because individual prices change or because consumers reallocate their consumption of goods within a given category. For category c, store s and market m, we compute the monthly inflation rate log(P¯mctseq/P¯mcts,t1eq). Then, we aggregate across all stores in market m to get the average category-level inflation rate. Similar to the aggregation above, we consider the use of equal weights or expenditure-weights to aggregate across stores.20 Finally, we cumulate monthly inflation rates into annual inflation rate π¯mcteq which we refer to as the “within-category effective inflation rate”.

Because some categories include much more heterogeneity in goods than others, we consider two classification schemes for measuring the substitution of goods within categories. The first (and broadest) includes all UPCs within a category. The second allows substitution only within subcategories which approximately corresponds to adding another digit to the level of disaggregation. For example, we use all types of milk when we calculate P¯mctseq for the first classification. In contrast, the second classification considers separately such subcategories as whole milk, skimmed milk, 2 percent milk, etc. Inflation rates for subcategories are aggregated to the category level using equal or expenditure-based weights.

The sensitivity of these inflation rates to local unemployment is then assessed using

π¯mcteq=βURmt+λt+θm,c+error(5.2)

which is equivalent to the specification used to measure the sensitivity of effective across-store inflation rates to economic conditions. The results, presented in Table 6, point to a statistically significantly negative relationship between unemployment rates and cross-good inflation rates. Thus, as in our baseline results, this indicates that there is significant substitution of expenditures by households in response to changing local economic conditions, but along a different margin, namely substituting across different goods within a category. Not surprisingly, the effect is stronger when we allow a larger set of goods within each category. Importantly, the quantitative magnitudes are of the same order as those identified for across-store substitution.

Table 6.

Within category substitution.

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Notes: The table reports estimates of specification (5.2). The dependent variable is the within-category effective inflation rate. The table reports estimated coefficients on the local seasonally-adjusted unemployment rate. Number of observations is 94,851. Driscoll and Kraay (1998) standard errors are in parentheses.***, **, * denote significance at 0.01, 0.05, and 0.10 levels.

VI. Aggregate Implications of Store-Switching

The key message from our empirical results is that while significant flexibility is present in the prices paid by households relative to those charged by retailers, this flexibility is driven primarily by store-switching on the part of households rather than sales. To what extent should macroeconomists care about store-switching behavior? In this section, we present a stylized New Keynesian model in which households can reallocate their expenditures across stores in light of changing economic conditions. The model delivers testable predictions which are confirmed in the data. We then present and discuss some business cycle and policy implications of the model.

6.1 New Keynesian Model with Expenditure Reallocation across Retailers

To assess the implications of the reallocation of expenditures across stores, we incorporate a decision on the part of households over how much to purchase from different retailers into an otherwise standard New Keynesian model as in Clarida, Gali and Gertler (1999) and Woodford (2003). Retailers sell identical composite goods but at potentially different prices. The “local” retailer charges a higher price to consumers, but purchases at the “discount” retailer come with an iceberg cost. This cost can be reduced by households via time-intensive shopping effort. Thus, households can reduce the effective price of their aggregate consumption at the expense of leisure time. Intermediate goods are produced under monopolistic competition subject to infrequent price adjustment. We abstract from sales in the model and focus primarily on the expenditure reallocation decision of households, but including sales would tend to strengthen the expenditure reallocation process given the cyclical properties of sales documented in sections 3 and 4.

6.1.1 Household Problem

The representative household maximizes lifetime utility over consumption and leisure

E0Σt=0βt{logCt+log(1LtSt)}(6.1)

where Ct is the consumption bundle of goods, Lt is labor supply, St is the shopping effort or time spent searching for better prices, and β is the discount factor. Labor is freely mobile across employers. Households live in location A and can purchase consumption goods CA,t from the “local” retailer and purchase CB,t from the “discount” retailer in location B. We assume that the total consumption bundle Ct is given by

Ct=(CA,tγ1γ+CB,tγ1γ)γ/(γ1)(6.2)

where γ measures the elasticity of substitution across stores (or rather locations). The imperfect substitution among retailers guarantees positive purchases at each retailer and will be used to calibrate the degree of store-switching to what we observe in the data. The budget constraint of the household is

PA,tCA,t+τtPB,tCB,t+Ht=(1+it1)Ht1+WtLt+Πt(6.3)

where τt is the iceberg cost of traveling to another location (or searching another location), Ht is the bond holding, Wt is wages, and Πt represents profits from ownership of all firms.

We will assume that the iceberg cost is a function of St

τt=τ(St),τ1,τ(0)>1,τ<0.

To simplify algebra, we will assume that τ(St) has constant elasticity ϕ

(StτtτtSt)=ϕ0.

Intuitively, one can think of τ as e.g. an information cost associated with shopping at the “discount” retailer which is reduced as the household devotes more time to search at this retailer. For example, households typically do their shopping in one primary retailer at which they may accumulate substantial store-specific knowledge, such as the location of different goods (Rhee and Bell 2002). Shopping at other retailers will require more time and effort in the absence of this information, which is captured by τ. However, households can reduce this additional cost via the time-intensive shopping process in which information about other retailers is acquired.

Both retailers face the same marginal cost over consumption goods given by Pt. The “discount” retailer sells at cost PB,t = Pt, whereas the price at the “local” retailer is assumed to be a constant markup over this input price PA,t = μPt, possibly reflecting higher local taxes, high-quality service, the use of an additional scarce input (such as more expensive local real estate), or a lower level of productivity. Thus, the relative posted prices of the two retailers are assumed to be constant (PA,tPB,t=μ), but the relative expenditure costs faced by households will vary with τt:PA,tτtPB,t=μ/τt. The efficient allocation of consumption by the household across retailers implies

CA,tCB,t=(τtPB,tPA,t)γ={τtμ}γ(6.4)

such that the demand for goods from the “local” retailer at location A relative to the demand for goods from the “discount” retailer at location B will fall when the iceberg costs associated with the “discount” store are low. With iceberg costs a function of shopping effort, time variation in shopping intensity will affect the relative prices at the two stores faced by households and will therefore underlie the reallocation of household expenditures across retailers. The efficient allocation of consumption expenditures on the part of the household also implies that the price of the final consumption bundle Ptc is

Ptc=({PA,t}1γ+{τtPB,t}1γ)1/(1γ)=μPt(1+{CA,tCB,t}1γγ)1/(1γ).(6.5)

Because the final goods sold at the two retailers are identical, log changes in Pt will be equivalent to those of a fixed-expenditure-weighted price index like the CPI. Changes in the price of the final consumption good (i.e. “cost-of-living” index), however, will systematically differ from changes in Pt for two reasons. First, as emphasized by Triplett (2003), the price of final consumption good depends on the time-varying effort devoted to shopping, which is a relevant cost from the household’s point of view but is clearly not captured in standard price indexes. Second, the price of the final consumption good will vary with the reallocation of expenditures across the two retailers on the part of the household, even when the household buys identical individual goods at the two retailers, as long as prices differ across retailers.

Note also that the household budget constraint can be rewritten more simply in terms of the price of the final consumption good as

PtCCt+Ht=(1+it1)Ht1+WtLt+Πt.(6.6)

As a result, the first-order conditions with respect to aggregate consumption and bond holdings will be standard conditional on being expressed in terms of the final consumption good and its price index Ptc:

Consumption¯:Ct1=qtPtcq̆=ČtP̆tC(6.7)
Bonds¯:qt=Etqt+1β(1+it)q̆t=Etq̆t+1+it(6.8)

where “checks” denote log-linearized deviations from steady-state values. The optimality condition for labor is

Labor¯:(1LtSt)1=WtqtηLL̆t+ηSŠt=W̆t+q̆t(6.9)

where

ηLL¯1L¯S¯andηSS¯1L¯S¯

is the steady-state ratio of labor supply to leisure and equivalently for ηS, and bars indicate steady-state levels of variables. Note that ηL and ηS are the steady-state elasticities of the marginal disutility of reducing leisure hours with respect to labor and shopping hours respectively. The first-order condition for labor includes shopping effort St since the latter also affects the marginal disutility of labor.

The optimality condition with respect to shopping effort is

ShopingEffort¯:(1LtSt)1=ϕ(τt1γμ1γ+τt1γ)1St{ηLL̆t+ηSŠt}=ωSŠt(6.10)

where

ωSϕ(1γ)(μ1γμ1γ+τ¯1γ)1

and τ is the steady-state level of iceberg costs. This optimality condition states that the marginal disutility of shopping effort (the LHS) must equal the marginal benefit of shopping time (the RHS), which is the utility flow from the reduction in expenditures associated with lower effective prices at the “discount” retailer. The parameter ωS denotes the steady-state elasticity of this utility flow with respect to shopping. A steady state with an interior solution for shopping requires the marginal return to shopping effort to be diminishing in the hours spent shopping, i.e. ωS < 0 which, as we document later, is consistent with the data.

Because the marginal disutility of labor and shopping effort are equal, an optimizing household will therefore also equalize the marginal returns to labor and shopping hours:

W̆t+q̆t=ωsŠt(6.11)

so that with diminishing returns to shopping effort, hours spent shopping will tend to be low when the utility return to labor is high. A direct relationship between hours worked and hours spent shopping also follows directly from the first-order condition with respect to shopping:

ηLL̆t=εSŠt(6.12)

where, given ηS=ϕτ¯1γμ1γ+τ¯1γ,

εSωSηS=ϕγϕμ1γμ1γ+τ¯1γ1.

The parameter εS represents the steady-state elasticity of the net utility cost from higher shopping effort, combining the fact that shopping hours above the steady-state both increase the marginal disutility of hours worked or spent shopping and lead to lower marginal expenditure reductions from shopping effort. Note that diminishing marginal return to shopping (ωS < 0) is sufficient (but not necessary) for this net utility elasticity to be negative, so that shopping intensity will be countercyclical with respect to hours: εS < 0.21 Intuitively, if labor hours are low, the marginal disutility to shopping is low, so the household will increase shopping effort which will both increase the disutility of shopping and lower its marginal return.

One can use this relationship between hours worked and shopping time to eliminate shopping effort from the first-order condition with respect to labor, yielding

ηL(1+ηSεS)L̆t=W̆t+q̆t.(6.13)

Shopping effort being countercyclical with respect to labor increases the effective Frisch labor supply elasticity.22 This reflects the fact that when the utility return to labor is high, shopping intensity will tend to be low so that the return to shopping is also high. But if the household spends fewer hours shopping, then the marginal disutility of labor will be lower, and the household will therefore be willing to supply more labor than it would in the absence of a time-varying shopping effort.

6.1.2 Firms

Retailer j for j ϵ {A, B} purchases intermediate goods along a continuum of mass one and assembles them into a consumption good:

Cj,t=(01yj,t(i)σ1σdi)σ/(σ1)

where yj,t(i) is an individual good i (think of this as a UPC) bought by the retailer in location j, and σ is the elasticity of substitution across individual goods (varieties). Note that because the aggregator is the same across locations, the composition of goods in the basket is exactly the same across locations and buyers. Cost minimization implies that the marginal cost paid by both retailers for producing one consumption good is given by

Pt=(01pt(i)1σdi)1/(1σ).

Intermediate goods are produced by a continuum of monopolistic competitors, each of which sells to both retailers. Producer i therefore faces the following total demand:

yt(i)=yA,t(i)+yB,t(i)=(pt(i)Pt)σCA,t+(pt(i)Pt)σCB,t=(pt(i)Pt)σYt

where Yt = CA,t + CB,t. The production function for each intermediate goods producer i is given by

yt(i)=ZtNt(i)α,α(0,1)

where yt(i) is the output of variety i, Zt is the aggregate level of technology, and Nt(i) is employment of firm i. Technology follows a stationary AR(1) process in logs with i.i.d. innovations denoted by ϵtz and persistence ρz:

Žt=ρzŽt1+ϵtz.

Workers are hired from a common labor market at nominal wage Wt. Firms can reset prices as in Calvo (1983) with the probability of being able to reset their price denoted by 1 – θ When able to reset prices, firm i therefore choose a reset price Pt*(i) to maximize profits

maxPt*EtΣk=0θk{Ξt,t+k(Pt*(i)yt+k|k(i)Wt+kNt+k|k(i))}

where yt+k|k(i) is the level of output in period t + k of the firm that reset its price in period t, Ξt,t+k is the stochastic discount factor, subject to their demand curve and the production function. Combined with the evolution of the intermediate goods price level Pt

Pt=(θPt11σ+(1θ)Pt*1σ)11σ

this yields the log-linearized New Keynesian Phillips Curve in terms of input prices Pt for retailers

πt=βEtπt+1+kMCt(6.14)

where k=(1θ)(1βθ)θΘ,Θ=1α1α+ασ,πt=P̆tP̆t1, and real marginal costs are given by MC=WtP̆tY̆t+N̆t. In the absence of sticky-prices, output in the model would simply track technology, so the log-linearized output gap is defined as X̆tY̆tY̆tn=Y̆tZ̆t.

6.1.3 The Central Bank

Monetary policy follows an interest rate rule in which interest rates respond to inflation, output growth and the output gap such that, after-log-linearization,

it=ρrit1+(1ρr)[χππt+χxX̆t+χΔyΔY̆t]+ϵtr(6.15)

where ρr is the degree of interest-smoothing, Χπ is the long-run response to inflation, Χx is the long-run response to the output gap, ΧΔy is the long-run response to output growth, ϵtr is an i.i.d. monetary policy shock.

6.1.4 Parameter Values

To the extent possible, we rely on typical values of parameters in the model. For example, we set β = 0.99 and θ, the degree of price rigidity, to 0.70 such that firms update their prices every 10 months on average, as in Nakamura and Steinsson (2008). This rate of price-stickiness obtains empirically from focusing only on regular price changes. This is consistent with our empirical results documenting the pro-cyclicality of sales prices. However, we subsequently experiment with lower values of θ to explore the quantitative importance of store-switching relative to the effects of not treating sales as regular price changes. We set θ to be 0.66 and σ, the elasticity of substitution across intermediate goods, to be 10. Coefficients for the interest rate rule follow Coibion and Gorodnichenko (2011), such that long-run responses to inflation (Χπ), output growth (ΧΔy) and the output gap (Χx) are equal to 1.5, 0.5, and 0.1 respectively while the degree of interest smoothing θr is 0.9. The persistence of technology shocks is 0.95. Following Coibion, Gorodnichenko and Wieland (2011), the standard deviation of technology shocks is set to 0.0090 while that of monetary policy shocks is 0.0024.

With respect to the parameters governing store-switching and shopping effort, we first normalize the iceberg cost such that ττ(S) = μ. As a result, steady-state consumption of “local” versus “discount” stores is equalized. This appears to be in line with data since the 1990s. For example, in the 2002 Economic Census, discount stores and supercenters accounted for 73 percent of sales at general merchandise stores and 41 percent of sales at both general merchandise and food stores (Annual Benchmark Report for Retail Trade and Food Services (2005)). Discount stores and supercenters are also significantly cheaper on average. Cleeren et al. (2010) report that discount stores often charge up to 60 percent less than regular grocery stores for leading brands. Hausman and Leibtag (2007) report that supercenters are on average 27 percent cheaper than other grocery stores for selected food products. We set a slightly higher value of μ = 1.5, such that “discount” stores in the model are 33 percent cheaper on average, because the ability of superstores and discount stores to achieve price discounts is likely to be even larger for non-grocery products (which are more durable and hence more amenable to bulk purchases) than for the grocery goods which Hausman and Leibtag (2007) focus on. These parameters imply a steady-state labor-leisure ratio of 0.4. The 2005 American Time Use Survey reports that the average American age 15 and older worked 3.7 hours a day while spending 5.7 hours on leisure and 8.6 hours on sleep. These values imply average labor-leisure ratios of 0.65 (not counting sleep as leisure) or 0.26 (counting sleep as leisure).

Evidence on the elasticity of substitution across stores is limited. Walters (1991) examined both within and across-store substitution and found relatively low rates for the latter relative to the former. Kumar and Leone (1988) found cross-store elasticities of substitution to be two to three times smaller than within-store elasticities for narrow product categories. Rhee and Bell (2002) similarly document limited switching by households in terms of their primary store of choice. As a result, we set γ = 4, less than half the elasticity of substitution across varieties. For the elasticity of iceberg costs to shopping effort, Aguiar and Hurst (2005) report that retired households spend 42 percent more time shopping than pre-retired households, leading to a 17 percent decline in total food expenditures (with no change in food consumption). We use a slightly lower elasticity of ϕ = –0.3 (rather than ϕ = –0.4 = –17 percent/42 percent) since some of the reduction in expenditures documented in Aguiar and Hurst also reflects a rise in time spent preparing food. Note that with ϕ = 4 and τ = μ, diminishing marginal return to shopping effort will obtain for –2/3 > ϕ > 0, so our baseline value of ϕ is squarely in the middle of the admissible range.

While there is only limited evidence on empirical values for γ and ϕ, we can use our estimates of household-switching to assess how well our baseline parameter values conform to our empirical estimates. For example, Table 4 indicates that a 1 percent point increase in the unemployment rate is associated with a decrease in the average rank at which households shop of approximately 0.13 when counting goods sold at all stores, with a standard error of almost 0.04. Using Okun’s Law such that a 1 percent point increase in the unemployment rate is associated with a 2 percent decline in the output gap as in Knotek (2007), this delivers a semi-elasticity of the average rank at which households shop with respect to the output gap of approximately 0.065 with a 95 percent confidence interval of [0.028 0.102]. In our model with two retailers, the average price rank at which the household shops is

Rtc=(CA,tPA,tCA,tPA,t+CB,tPB,t)×23+(CA,tPB,tCA,tPA,t+CB,tPB,t)×13

where the 2/3 and 1/3 values reflect our ranking algorithm of section 4. It follows that the steady-state semi-elasticity of the average price rank at which the household shops with respect to the output gap can be expressed as

dRc=13SA(1SA)γϕζX̆t

where ζ(σ1σμ)1εS<0 is the steady-state elasticity of shopping effort with respect to the output gap and SA=μ1+μ is the steady-state share of household expenditures at high-price retailers. Our baseline parameter values then imply an elasticity of the average price rank at which households shop relative to the output gap of approximately 0.082, which is close to the empirical estimate and well within the confidence interval. Hence, our baseline parameter choices for γ and ϕ yield a rate of expenditure reallocation across retailers which is in line with our empirical estimates of actual household behavior.

6.1.5 The Simplified Log-Linearized Model

A convenient property of the model is that it can be reduced to the same three equations typical of New Keynesian models. The assumption that τ = μ, which is not out of line with current expenditure shares in the U.S., is particularly convenient in simplifying expressions in the model. Under this condition, the standard New Keynesian Phillips Curve for input prices can be expressed in terms of the output gap

πt=βEtπt+1+k˜X̆t(6.16)

where k˜(1θ)(1βθ)θ(1α1α+ασ){(σ1σμ)+1α}. The policy rule is unchanged. The Euler equation for the output gap is

Xˇt=EtX̆t+111+12ϕζ(itEtπt+1rtn)(6.17)

where ζ < 0 whenever shopping effort is countercyclical with respect to hours (εS < 0). Furthermore, one can verify that ϕζ is increasing in ϕ as long as σ > 1. Thus, larger elasticities of iceberg costs to shopping effort (more negative ϕ) effectively decrease the elasticity of the output gap, holding future gaps constant, to contemporaneous real interest rates. This effect reflects the countercyclicality of the shopping effort: if consumption prices are expected to rise, then the output gap should be high but falling and therefore the shopping intensity should be low but expected to rise. The expected increase in shopping time will therefore offset part of the increase in the rise in consumption prices which reduces the expected decline in gaps. As a result, when the Euler equation is expressed in terms of input prices, the sensitivity of the output gap to changes in real interest rates is diminished.

6.2 Testable Predictions of the New Keynesian Model with Store-Switching

In this section, we focus on the empirical validity of the key mechanism of the model with store-switching that underlies the subsequent business cycle and policy implications of the model. Specifically, low economic activity is associated with more shopping activity and therefore lower relative consumption prices, as illustrated by:

P̆tCP̆t=ϕ2Št=ϕ2ζX̆t.(6.18)

When the output gap is low, shopping effort will be high (ζ < 0), thereby reducing the relative price of the final consumption good relative to input prices. Because the price of the final consumption good, rather than intermediate prices, is what matters ultimately for household welfare, the novel channel in this model is how the ratio of the two evolves with economic conditions. P̆t in the model is equivalent, when log-linearized, to the CPI price index in the data. Unfortunately, there is no direct empirical equivalent to the effective price of the final consumption good P̆tC since it incorporates both the iceberg cost, which is unobservable, as well as the reallocation of expenditures across retailers.

However, we can construct an alternative effective price index PtE equivalent to that considered in sections 3 and 4, which incorporates the reallocation of expenditures across stores:

PtE(PA,tCA,t+PB,tCB,t)(CA,t+CB,t).

After log-linearization, this price index evolves according to:

P̆tEP̆t=(μ1)(μ+1)γϕ2ζX̆t=(μ1)(μ+1)γ(P̆tCP̆t).(6.19)

Thus, our alternative measure of effective prices P̆tE should be high relative to the CPI price index P̆t when the level of economic activity is high (X̆t>0), exactly as would be the case with the measurable final consumption price index P̆tC. Only the magnitude of the elasticity of relative price movements with respect to economic conditions will differ. Given our calibration of the model, (μ1)(μ+1)γ=0.8 so P̆tE will capture 80 percent of the movements in the final consumption price index, despite the fact that iceberg costs are not directly observable. Thus, our “effective” price measure P̆tE which reflects the prices consumers actually pay will, at least in our calibration, closely track the final consumption price index P̆tC.

We can assess the validity of this prediction in our dataset by constructing a measure of the gap between the average effective price level and the average posted price level. The average effective price level is based on the average price paid by households for a given UPC in a metropolitan area, then aggregated across UPCs and geographic areas using constant expenditure weights. Changes in this index therefore reflect both changes in the individual prices as well as consumer reallocation of expenditures across retailers. The posted price index is constructed using fixed expenditure-weights over all individual UPC products and geographic areas. Panel A of Figure 2 plots the difference between these two series and the aggregate unemployment rate. As predicted by the theory, the average effective price index declines sharply relative to the posted price index when the U.S. unemployment rate rises, while the reverse happens when the unemployment rate declines. Hence, this figure illustrates how, even after aggregating across all regions and product categories, the effects of consumer reallocation across retailers leads to a non-trivial mis-measurement of the household consumption price index.

Figure 2.
Figure 2.

Economic Conditions and the Reallocation of Consumption Expenditures across Retailers.

Citation: IMF Working Papers 2012, 207; 10.5089/9781475505573.001.A001

Notes: Panel A plots the difference between the “effective” price index and the “posted” price index. The latter is a fixed-expenditure-weighted average of all UPC prices in each store and metropolitan areas in the data, where weights are average expenditure share of each UPC in each geographic area relative to total household expenditures. The former is the fixed-expenditure-weighted average of average price paid by households for each UPC across all retailers in a metropolitan area. Panel B plots the share of total retailer revenues arising from revenues at high-price retailers in the data. “High-price” retailers are defined as in the text for each metropolitan area. Total share is a fixed expenditure-weighted average across metropolitan areas of shares in each metropolitan area. See section 6.2 for details.

Furthermore, the quantitative magnitudes implied by the series shown in the figure are in line with the predictions of the model. At our baseline parameters, the elasticity of the difference between effective prices and posted prices (P̆tEP̆t) with respect to the output gap is approximately 0.15. Between 2001 and 2003, the U.S. unemployment rate rose by approximately 2 percentage points, which via Okun’s Law, translates to an approximate 4 percentage point decline in the output gap. The theory predicts that such a decline in the gap would be associated with a decline in the effective price index of 0.60 percentage points relative to the posted price index. The figure points to a decline in this price differential which is very close to this value. Thus, both the qualitative and quantitative implications of this dimension of the model appear to be consistent with the data.

The potential for mismeasurement by fixed-expenditure-weight prices indexes of the effective prices paid by households due to store-switching has long been recognized by the literature on inflation measurement (e.g. Boskin Commission Report 1996, Shapiro and Wilcox 1996, Reinsdorf 1993, Triplett 2003, Hausman and Leibtag 2007) but little progress has been made in quantifying it. Our model and empirical estimates suggest that the cyclical mismeasurement is relatively large. Because it would be difficult for statistical agencies to construct time-varying expenditure weights across retailers in real-time, one implication of these results is that better measurement of the “cost-of-living” should focus on tracking the prices paid by households rather than those charged by specific retailers, as suggested in Triplett (2003).

A second approach to assessing the store-switching channel and its effect on relative prices is to focus on quantities purchased rather than prices. In our model, the relative quantities purchased at “local” retailers versus “discount” retailers follow

ČtAČtB=γϕζX̆t(6.20)

such that when the output gap is low, households will tend to purchase relatively more goods from low-price stores than high-price stores. Again, this reallocation of expenditures will reflect the higher degree of shopping effort when economic activity is low. Given that the relative posted prices at the two stores are constant in the model, the cyclical reallocation in goods purchased will be mirrored in terms of relative dollar expenditures across the two retailers. Specifically, defining the share of total revenues going to “local” retailers as SA,t(CA,tPA,t)/(CA,tPA,t + CB,tPB,t), the cyclicality of the revenue share of high-price retailer is

ŠA,t=(25)γϕζX̆t.(6.21)

To evaluate this additional prediction, we construct the share of total retailer revenues going to “high-price” retailers in our data-set, where “high-price” retailers are defined as in section 4.1 and have the rank above 0.5. Panel B of Figure 2 plots the time series for this share, aggregated across all metropolitan areas, as well as the unemployment rate. Consistent with the prediction of the model, the revenue share of “high-price” retailers declined sharply during the 2001-2003 recession, before gradually recovering. Thus, the cyclical behavior of relative revenues of “high-price” and “low-price” retailers in the data is also consistent with the predictions of the model with time-varying shopping effort and store-switching. One caveat is that the figure also illustrates how the revenue share of “high-price” retailers never recovers fully after the 2001-2003 recession, which reflects the trend growth of discount retail stores in the U.S. during this time period.

The third approach is with respect to the slope of the Phillips curve, i.e. the relationship between inflation and real economic activity. While the New Keynesian Phillips curve (NKPC) is unchanged in the presence of endogenous shopping effort when expressed in terms of input prices, the relevant measure from households’ point of view is the price of the final consumption bundle. We can rewrite the NKPC in terms of consumption price inflation as

πtC=βEtπt+1C+(k˜+12ϕζ(1+β))X̆t12ϕβζEtX̆t+112ϕζX̆t1.(6.22)

such that consumption price inflation depends on expected inflation in the next quarter, the current output gap, as well as the previous period’s gap and the next quarter’s expected gap. The presence of shopping effort increases the coefficient on the contemporaneous output gap, which suggests a steeper short-run Phillips curve relationship between effective price inflation and real economic activity. This seems intuitive since the ability of households to reallocate their expenditures across stores suggests that the effective price of consumption goods paid by consumers should be more flexible than that of input prices.

To assess the manner in which the relationship between inflation and real economic activity is affected by store-switching, we first simulate the model with time-varying shopping effort. We then plot the unconditional relationship between CPI inflation πt and employment, as well as that between measured effective price inflation πtE, in Panel A of Figure 3. The lines show the slopes of the average relationship between employment and each measure of inflation in the model: as suggested by the coefficients on the output gap in the NKPC, the slope is steeper when using effective consumption prices rather than CPI measures.

Figure 3.
Figure 3.

Correlation between unemployment rate and measures of inflation.

Citation: IMF Working Papers 2012, 207; 10.5089/9781475505573.001.A001

Notes: The top figure plots the unconditional relationship between the negative employment gap (Ľt) and both posted (CPI) inflation and “effective” price inflation, both annualized, from simulating the model in section 6.1. The solid lines plot the estimated linear relationship between each. The bottom figure presents relationships between the unemployment rate the same two measures of inflation in the data. See section 6.2 for details.

Panel B of Figure 3 shows the equivalent unconditional correlations between each form of inflation and unemployment from aggregating our monthly micro-level data. Specifically, Figure 3 plots posted price inflation πtpost and effective price inflation πteff. In each case, the inflation measures are constructed as weighted (by expenditure shares) averages of π¯mctpost and π¯mcteff across metropolitan areas and categories. The figure reveals that, with higher aggregate levels of unemployment, both fixed-weighted inflation and effective price inflation measures are lower, but the decline is larger for effective price inflation measures as predicted by the model with store substitution, with the difference between the two being statistically significant at the 1 percent level.

In short, these results suggest that the key predictions of the model with store-switching and shopping effort are apparent not only in micro-data but also in more aggregate series. The counter-cyclicality of consumer shopping effort leads to effective prices paid by consumers that are countercyclical with respect to standard price measures such as the CPI index, reallocation of consumer expenditures toward low-price outlets during economic downturns, and steeper Phillips curves in terms of effective prices paid by consumers than typically found.

6.3 Business Cycle and Policy Implications of Store-Switching

In this section, we turn to the implications of shopping effort and store-switching for business cycle dynamics and policy in the model. We focus on three questions: 1) how does the presence of shopping effort and store-switching affect the degree of monetary neutrality, 2) how does it affect the relative importance of stabilizing inflation and output gap volatility for welfare, and 3) does it matter whether monetary policy-makers target traditional inflation measures or are there welfare gains from targeting “effective” price measures which incorporate store-switching on the part of households? We address each question in turn.

6.3.1 Effective Price Flexibility and the Degree of Monetary Non-Neutrality

The first question is whether, with prices being effectively more flexible than suggested by posted prices, the degree of monetary neutrality will be lower than expected from the degree of price stickiness. This logic was suggested by Chevalier and Kashyap (2011) in the context of sales, but store-switching similarly generates flexibility in the effective prices paid by households which could potentially undo the stickiness in regular price changes. To assess the implications of store-switching for the degree of monetary neutrality, we consider the dynamic effects of a contractionary monetary policy shock in our model. Panel A in Figure 4 plots the impulse responses of inflation and the output gap from our model after a contractionary monetary policy shock. The responses include those from a standard New Keynesian model without store-switching (ϕ = 0), as well as in the case of endogenous shopping effort (ϕ = −0.3). These responses illustrate a key implication of endogenous shopping effort: an equivalent contractionary monetary policy shock has smaller real effects in the presence of store-switching. At our baseline parameter values, the reduction in real effects for a monetary policy shock is approximately 10 percent on impact. This reflects the reduced elasticity of output with respect to real interest rates in the dynamic IS equation (6.17). The higher real interest rate after a contractionary monetary policy shock contracts contemporaneous demand for consumption goods and therefore leads to a decline in labor demand and wages. Because households want to equalize the return to shopping effort and labor, the lower return to labor leads to an increase in shopping effort and a reallocation of consumption expenditures across retailers which reduces the effective prices faced by consumers. With effective prices lower than they would be in the absence of store-switching, consumption does not fall by as much as in the model without store-switching. The reduced effect on output then also implies smaller effects on inflation via the NKPC.

Figure 4.
Figure 4.

Business Cycle and Policy Implications of Endogenous Shopping Effort and Store-Switching.

Citation: IMF Working Papers 2012, 207; 10.5089/9781475505573.001.A001

Notes: The top panel displays impulse responses of inflation, output gap and shopping effort to a contractionary monetary policy shock in the model described in section 6.1. θ is the degree of price stickiness and ø is the elasticity of iceberg costs to shopping effort. The middle panel plots the impulse responses of inflation rates for final consumption goods (πc), effective prices (πE), and posted prices (π) in the left figure, price levels for consumption goods (Pc), effective prices (PE) and posted prices (P) in the middle figure, and total consumption (C), consumption at the high-price retailer (CA) and consumption at the low-price retailer (CB) in the right figure. The bottom panel plots the coefficients on inflation volatility (left) and output gap volatility (middle) from the second-order approximation to utility in the model of section 6.1 and the right figure plots the ratio of the two. See section 6.3 for details.

In addition, Panel A plots the impulse responses of inflation and the output gap in the model without store-switching and the levels of price flexibility from Bils and Klenow (2004): θ = 0.40 such that firms update prices every five months on average. This is a useful benchmark because it illustrates dynamics when sales are treated as regular price changes. Hence, the figures allow us to assess the relative importance of the two results from section 3: sales are not like regular price changes (so prices are less flexible than implied by average frequencies) and store-switching on the part of households is present (so effective prices are more flexible than implied by posted prices). The former implies larger real effects of monetary policy while the latter suggests smaller real effects. On balance, the results in Figure 3 suggest that incorporating both less flexible posted prices and store switching leads to approximately the same contemporaneous response of the output gap as in the more flexible-price model without store-switching. However, the dynamic response of the output gap is much more persistent than with more flexible prices and no store switching. Thus, the medium-run effects of monetary policy shocks on real economic activity are much more affected by the increased price stickiness when sales are not being treated like regular price changes than by the household’s store-switching/shopping-effort mechanism.23,24

Panel B of Figure 4 illustrates how store-switching affects relative consumption across retailers in the baseline case of ϕ = −0.3. While consumption at “local” stores falls very sharply, consumption at “discount” stores is nearly unaffected. This pattern reflects the extent of consumer reallocation of household expenditures in response to economic conditions. This pattern is also consistent with the empirical response of the growth rate of revenue in high-and low-price stores to the local unemployment rate reported in Table 3. Panel B also illustrates the response of different price and inflation measures to the contractionary monetary policy shock. The price of the final consumption bundle P̆C declines much more sharply on impact than CPI/input prices P̆ as a result of the increased shopping effort. Our measure of effective prices P̆E tracks the price of final consumption bundle P̆C closely. In terms of inflation rates, shopping-effort/store-switching leads to a dramatic difference in the behavior of inflation rates: final good inflation drops substantially on impact but is very low in subsequent periods. A simple way to gauge how much more flexible final goods prices are than posted prices is to note that, in the period of the shock, posted prices P̆ fall by only 1/6th of the cumulative decline in prices while almost 1/2 of the cumulative adjustment in final goods prices P̆C happens in the first quarter. Despite this much greater flexibility in the effective prices paid by households due to store-switching than would be expected from the underlying degree of price stickiness, the implications for monetary neutrality are limited. In this sense, our results are in the same spirit as Eichenbaum et al. (2011), Kehoe and Midrigan (2010) and Guimaraes and Sheedy (2011), but whereas they focus on sales pricing as a sources of effective price flexibility for households, our results stem from the shopping effort and store-switching margins. But the common finding is that even with high effective price flexibility for households, the degree of monetary neutrality in the models hinges primarily on the underlying degree of rigidity in regular prices.

6.3.2 Welfare Objective Function with Endogenous Shopping Effort and Store-Switching

The difference between posted and effective price movements induced by the shopping effort and store-substitution margins also implies that standard approximations of household welfare in New Keynesian models will be affected. The most common approach to quantifying welfare is through 2nd order approximations of utility, as in Woodford (2003), which deliver a loss function in terms of inflation and output gap volatility. But since household welfare with shopping effort depends on effective prices rather than posted prices, this suggests that the relative importance of the two forms of volatility will be affected. To formally assess this effect, we derive the 2nd order approximation to utility in the model and express it in terms of posted inflation volatility and output gap volatility (Appendix C):

E(Ut)12(σ1σμ){Cπ(ϕ)E(πt2)+cx(ϕ)E(X̆t2)},(6.23)cπ(ϕ)σΘθ(1θ)2(ωSϵS),cx(ϕ)1α+(σ1σμ)γ4ϕ2ϕ2+ωS2ϵS2.

Panel C of Figure 4 illustrates how the coefficients on inflation and output gap volatility vary with the elasticity of costs to shopping time ϕ. Higher elasticities systematically lower the coefficient on inflation volatility, i.e., Cπϕ<0. The latter reflects the elasticity of leisure with respect to price dispersion: without shopping effort, high price dispersion requires high levels of labor supply and therefore less leisure, which reduces welfare. However, when shopping effort is present and countercyclical, higher levels of labor supply associated with price dispersion are offset by fewer hours spent shopping, so the sensitivity of leisure to inflation volatility is reduced. The coefficient on output gap volatility reflects the loss from volatility in leisure, which depends on the variance in labor supply, shopping effort, the covariance between the two, and changes in the dispersion of consumption across the two retailers. The interaction of these effects is nonlinear, such that low elasticities of shopping reduce the cost of a given level of output gap volatility but this effect is reversed at high elasticities. The overall effect is to make welfare relatively more sensitive to output gap volatility relative to inflation volatility as the steady-state level of shopping effort increases. Thus, the presence of store-switching and shopping effort suggests that stabilizing output gap volatility should play a more prominent role in the objective function of policymakers than implied by standard models omitting this channel.

6.3.3 What Price Measure Should Policymakers Target?

A third question of practical interest implied by the model is whether policymakers should focus on standard fixed-expenditure weight price measures or one that reflects the shopping effort, and therefore expenditure-reallocation, activities of households. While household welfare is explicitly associated with the price of the final consumption good PtC, the fact that these prices are effectively more flexible than posted prices Pt might suggest that responding to the latter will be welfare-improving via the logic of Aoki (2001).

To address this question, we quantify household welfare (6.23) when the central bank responds either to posted price inflation πt in the standard interest rate rule, final good price inflation πtC or the closely related expenditure-weighted final goods inflation rate πtE holding the other parameters in the model (including those in the policy rule) constant. The resulting inflation and output gap variances are plotted in Panel A of Figure 5 for different long-run inflation response coefficients ϕπ. Responding to posted price inflation πt, as assumed in our baseline, leads to lower volatility in posted price inflation but higher levels of output gap volatility, with the latter effect being particularly strong when the inflation response is high. Given that inflation volatility is more heavily weighted in the loss function, these results lead to utility being higher in most cases when the central bank targets posted price inflation rather than final goods price inflation or the expenditure-weighted inflation measure. Thus, this result suggests that, even in the presence of store-switching and time-varying shopping effort, policy-makers may be better served by responding to traditional measures of inflation than to measures of effective price inflation.

Figure 5.
Figure 5.

Which Inflation Measure Should Policymakers Target?

Citation: IMF Working Papers 2012, 207; 10.5089/9781475505573.001.A001

Notes: The top panel displays the variance of inflation (left) and the variance of the output gap (middle) for different long-run responses to inflation by the central bank when the central bank responds to either posted price inflation (π), effective price inflation (πE), or inflation of final goods prices (πc). The right panel shows expected utility loss in each case. The bottom panel plots equivalent figures in the case of price-level targeting when the central bank responds to either posted prices (P), effective prices (PE), or final consumption goods prices (Pc). See section 6.3 for details.

However, this result appears to be specific to inflation targeting. For example, this result does not obtain if we consider price-level targeting (PLT) regimes, which—as we know from Woodford (2003), Gorodnichenko and Shapiro (2007), Coibion et al. (forthcoming), and others—are closer to replicating the optimal policy under commitment than inflation targeting. Specifically, we replace the baseline interest rate rule with one that allows for responses to deviations of price-levels from their targets:

it=ρrit1+(1ρr)[χpP̆tm+χxX̆t+χΔyΔY̆t]+ϵtr(6.24)

where P̆tm denotes the deviation of posted prices P̆t, final goods prices P̆tC, or expenditure-weighted prices P̆tE from a target path. Panel B of Figure 5 plots the implied inflation and output volatilities for different response coefficient χp to each price level, as well as expected utility losses for different values of χp. While output gap volatility is still higher when the central bank responds to posted prices, posted price inflation volatility is now also higher in this case. This reflects the fact that much of the price response is immediate for P̆tC and P̆tE and more delayed for P̆t. Under price level targeting, the large immediate decline in effective prices after a disinflationary shock must be reversed when the central bank targets the level of effective prices. This requires significant declines in nominal and real interest rates on the part of monetary policy-makers, which will tend to immediately raise contemporaneous output gaps via the dynamic IS curve relative to how they otherwise would have responded. This, in turn, offsets some of the initial disinflation via the New Keynesian Phillips Curve. As a result, both inflation and output gap volatility will be significantly reduced when the central bank targets the “effective” or final consumption price level. This effect does not occur under inflation-targeting because the latter does not require the policy-maker to undo the immediate decline in effective prices and therefore does not require the significant declines in nominal and real interest rates which serve to stabilize both inflation and output volatility under PLT. Hence, expected utility is now strictly greater when the central bank targets deviations of effective final goods price deviations rather than posted price levels.

VII. Conclusion

A key question for macroeconomists is quantifying both the degree of price rigidities and the implications of these rigidities for macroeconomic dynamics. How to interpret temporary sales is a central ingredient in characterizing whether price-stickiness is large enough to qualitatively affect business cycle dynamics. We shed new light on this question by studying the cyclicality of sales and regular price changes using detailed micro-level data. We find that sales are pro-cyclical: higher unemployment rates lead to declines in both the frequency and absolute size of sales, as well as to declines in the share of goods bought on sale. This suggests that sales prices differ in a fundamental way from regular price changes, and are therefore unlikely to undo the high levels of price-stickiness apparent among regular price changes.

At the same time, we show that actual prices paid by households for a given good are significantly more flexible than what is implied by the behavior of posted prices. This pattern reflects store-switching on the part of households in light of changing economic conditions. In a simple model of shopping effort and store-switching, the ability of consumers to reallocate their expenditures across retailers charging different prices provides an additional force toward price flexibility which leads to smaller real effects of monetary policy shocks. Furthermore, store-switching by households can rationalize the pro-cyclicality of sales: economic downturns increase the incentive of households to search for bargains at low-price retailers, thereby reducing the incentive of high-price retailers to try and attract these households via sales. However, despite the increased flexibility in the prices that households actually pay in light of store-switching, the quantitative implications of store-switching for monetary neutrality are relatively small. Thus, our results are similar in spirit to those of Eichenbaum et al. (2011), Kehoe and Midrigan (2010), and Guimaraes and Sheedy (2011), but whereas they focus on the role of sales in generating increased flexibility in prices paid by households, we focus on the store-switching margin for effective price flexibility. Nonetheless, store-switching does have non-trivial implications for the relative importance of stabilizing output gap versus inflation variation in welfare calculations, the question of which price measures should be targeted by policymakers, and the interpretation of estimated relationships in terms of structural parameters.

Another implication of store-switching and time-varying shopping effort is that there is a cyclical mismeasurement of the price of households’ final consumption basket in standard aggregate inflation measures. This points towards a need for statistical agencies to devote more resources toward measuring the reallocation of household expenditures, not just across goods as commonly emphasized with respect to the substitution bias, but also across retailers. While the construction of time-varying expenditure weights in real-time is unlikely to be feasible for statistical agencies, one approach would be to track the prices paid by households in real-time rather than the prices charged by a fixed set of retailers, as suggested by Triplett (2003). To this end, scanner price data, which provide prices and quantities, may be a useful tool for constructing cost-of-living indexes although a number of challenges remain to be addressed in this area (see Feenstra and Shapiro (2003)).

A related implication is that the ideal price index in the presence of time-varying shopping effort should measure not only the reallocation of expenditures across stores but also the shopping effort intensity of households, since this represents a component of the cost of the consumption basket. Further work on how this could be measured in practice would be of immediate practical relevance. One implication of our results, however, is that shopping effort and store-switching are closely related, so that a price-measure which incorporates the reallocation of expenditures across retailers will generally capture most of the missing cyclical variation in the final consumption price index.

Another fruitful extension would be to consider the impact of the rise in online retailing: the latter likely reduces shopping costs substantially and therefore facilitates the reallocation of expenditures across retailers by households. With online retailing growing rapidly, expenditure-reallocation across retailers is likely to become increasingly important. Just as Walmart reshaped the retailing industry in the U.S., the rise of Amazon.com and other online retailers will similarly transform household expenditure decisions. Our results suggests that the ways in which households reallocate their expenditures, as well as the intensity of their shopping search, will not be innocuous for macroeconomic dynamics and optimal policy responses to economic fluctuations.

One may also use this idea to shed new light on the puzzle of the missing disinflation during the 2007-2009 downturn. As documented in Ball and Mazunder (2011), the magnitude of the output gap in the recent recession would have been expected to lead to significantly more disinflation than actually occurred, based on historical Phillips curve correlations. One potential explanation is that the slope of the Phillips curve is non-linear, becoming flatter at low levels of economic activity and inflation levels. This could follow from downward wage rigidity, for example. Such a result could also follow from cyclical changes in price rigidities. For example, if prices become increasingly rigid due to store-switching as economic conditions worsen, as suggested by the results in Table 2, then this could lead to a flattening of the Phillips curve at lower levels of economic activity. Estimates of the slope of the Phillips curve during regular times would therefore lead to an over-prediction of the decline in inflation during periods of economic crisis.

The Cyclicality of Sales, Regular and Effective Prices: Business Cycle and Policy Implications
Author: Mr. Olivier Coibion, Mr. Yuriy Gorodnichenko, and Mr. Gee Hee Hong
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    Correlations between key moments

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    Economic Conditions and the Reallocation of Consumption Expenditures across Retailers.

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    Correlation between unemployment rate and measures of inflation.

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    Business Cycle and Policy Implications of Endogenous Shopping Effort and Store-Switching.

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    Which Inflation Measure Should Policymakers Target?