Measuring price selection in microdata: it’s not there

Peter Karadi, Raphael Schoenle, Jesse Wursten

Working Paper Series

Measuring price selection in microdata:

it's not there

No 2566 / June 2021

Disclaimer: This paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB.

Abstract

We use microdata to estimate the strength of price selection { a key metric for the eect of monetary policy on the real economy. We propose a product-level proxy for mispricing and assess whether products with larger mispricing respond with a higher probability to identied monetary and credit shocks. We nd that they do not, suggesting selection is absent. Instead, we detect state-dependent adjustment on the gross extensive margin. Our results are broadly consistent with second-generationstate-dependent pricing models and sizable eects of monetary policy on the real economy.

JEL codes: E31, E32, E52

Keywords: monetary non-neutrality,state-dependent pricing, identied credit and monetary policy shocks, price-gap proxy, scanner data, PPI microdata

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• Non-TechnicalSummary

The ability of monetary policy to stabilize business cycles depends on the exibility of the price level. If prices are very exible, they will absorb shocks, if they are sticky, activity will adjust instead. However, the price level can be exible even if only a few prices adjust, as long as the prices that react do so in a disproportionate manner. Such 'self-selection' of large price changes tends to reduce the real e ects of monetary policy shocks in realistic price-setting frameworks. In this paper, we use micro price data to measure the strength of price selection.

We carefully measure the selection e ect in the data. In our main analysis, we use a detailed, weekly panel of barcode-level prices in U.S. supermarkets between 2001 and 2012. The granularity of the data in the cross- section allows us to identify product-level pricing pressures, while the long time series dimension allows us to identify aggregate shocks. Selection is present if, following an aggregate shock, prices that are further away from their optima respond with higher probability than those that are closer. There are two key challenges. First, optimal prices and therefore price gaps are unobserved. Our approach is to rely on the pricing behavior of close substitutes to measure unobserved optimal prices (Gagnon et al., 2012). In particular, we measure the di erence between a price and the average price of the exact same good sold by competing supermarkets, after we control for permanent store-level characteristics (coming from heterogeneity among regions and amenities). We show that our price gap proxy indeed predicts future price changes indicating that it is a valid measure of product-level price pressures. The second challenge is to identify aggregate shocks. We identify aggregate credit shocks using conventional timing restrictions (Gilchrist and Zakrajsek, 2012). We show that the aggregate shocks also a ect the probability of price changes, indicating that the shock we identify is relevant for price setting.

To measure the strength of selection, we assess whether our price-gap proxies interact with identi ed aggregate shocks to inuence the probability of price adjustment. We approach this question in a linear- probability panel-regression framework. Our dependent variables are respectively the probability of price increases and the probability of price decreases over the 24 months following the aggregate shock. We test whether the interaction term of the price gap and the aggregate shock signi cantly inuences the probability of those price changes. If the coecient of the interaction term is high, then, conditional on an aggregate shock, prices with higher price gaps respond with higher probability. As controls, we add the direct e ects of both the price gap and the aggregate shock as well as the age of the price and numerous xed e ects.

Our main nding is that selection appears to be absent in the data as the interaction term stays insignificant in all of our regressions. These results do not change if we use alternative price-gap proxies, di erent aggregate shocks, di erent datasets, and di erent speci cations. This is true, even though prices do respond directly to both aggregate and product-level price pressures in all our speci cations. Our evidence support frameworks with a micro-macro dichotomy: even though prices respond to product-level pressures quite exibly, the aggregate price level is sticky and monetary policy can stabilize business cycles.

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• Introduction

The ability of monetary policy to stabilize business cycles depends on the exibility of the price level. If prices are very exible, they will absorb shocks, if they are sticky, activity will adjust instead. However, the price level can be exible even if only a few prices adjust, as long as the prices that react do so in a disproportionate manner. Such 'self-selection' of large price changes tends to reduce the real e ects of monetary policy shocks in price-setting frameworks where frictions to price adjustment are microfounded by small, xed (menu) costs (Golosov and Lucas, 2007). In this paper, we use micro price data to measure the strength of price selection.

Our model-free nding is that selection is absent in the data. We arrive at this result by analyzing the probability of price adjustments in response to an identi ed aggregate shock. Even though prices do respond to the shock directly, the probability of adjustment in response to a shock is not a function of the extent of their mispricing, which selection would require. Instead, we detect a uniform shift from price increases towards price decreases after a policy tightening. These results imply that price adjustment in macroeconomic models generally should feature a state-dependent adjustment through the gross extensive margin and weak selection, implying a sizable monetary non-neutrality. We characterize conditions which state-dependent pricing models with random menu cost (such as Dotsey et al., 1999; Luo and Villar, 2017; Alvarez et al., 2020) or rational inattention (Woodford, 2009) are consistent with our ndings.

We measure selection by considering how the probability of price adjustment depends on an interaction of a macro-level and a micro-level component. The macro-level component is an aggregate shock which hits the economy and exerts a general adjustment force. The micro-level component is the pre-existingproduct-level mispricing, which is present because sticky prices failed to keep up with changes in their optimal levels. A non-zero interaction term of the second kind implies that prices of goods with large mispricing are more likely to adjust when a shock hits the economy. Such a relation would indicate the presence of a selection e ect: Prices respond to a shock disproportionately strongly to make up for any already existing product- level mispricing. As a result, the aggregate price level becomes disproportionately exible. If the prices of goods with larger mispricing do not react with a higher probability to a shock, then selection is absent. This de nition of selection can be formalized by a suitable generalization of the accounting framework of Caballero and Engel (2007), as we explain below.

The empirical implementation of our approach to measure selection is straightforward. We use micro price data and regression analysis. There are two key challenges. The rst is to obtain a suitable proxy for mispricing. We achieve this by using the information on the price-setting of close substitutes, as we explain below. The second is to identify an aggregate shock, which generates an uniform price-adjustment impetus. Our baseline aggregate shock is a credit shock, which we identify using timing restrictions as in Gilchrist and Zakrajsek (2012). Our results are also robust to monetary policy shocks identi ed using high- frequency surprises in interest rates around policy announcements (Gertler and Karadi, 2015; Jarocinski and Karadi, 2020). With these proxies in hand, we can measure selection by estimating how the probability of price adjustment statistically depends on the interaction of the aggregate shock and the product-level price- gap proxy. We approach our question in a linear-probabilitypanel-regression framework. Our dependent variables are the probability of price increases and price decreases, respectively, over the 24 months following a credit shock. Besides the interaction term of the current aggregate shock and the lagged price gap proxy that is the focus of our analysis, we also include the previous-periodproduct-level price gap and the current-

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period aggregate shock as explanatory variables. Furthermore, we satiate the regressions with a rich set of xed e ects, control for the age of prices, and cluster the standard errors across time and across product categories.

On the data side, we construct our baseline measure of the price gap using a detailed, weekly panel of barcode-level prices in U.S. supermarkets between 2001 and 2012, compiled by the marketing company IRi.1 In a complementary analysis, we also show that our results are robust to using the producer-price microdata that underlies the U.S. producer-price index (PPI).

Our baseline measure of the price gap calculates the distance of the price from the average of close competitors, after controlling for permanent di erences in prices coming from variation in geography and amenities (Gagnon et al., 2012). This 'competitor-price gap' is a relevant measure of product-level price pressures as long as sellers strive to keep their prices close to competitors' prices to maintain pro tability and market share. We show that our results are robust to using an alternative 'reset-price' gap measure. Here, we build on the approach proposed by Bils, Klenow and Malin (2012), who de ne reset prices as the unobserved optimal prices that a store would set if pricing frictions were temporarily removed. We follow the algorithm of Bils, Klenow and Malin (2012) to approximate these.

We nd that our price gap measure is a valid proxy of product-level price pressures because rst, they raise the probability of future price adjustments and second, the average size of the adjustment is proportional to the distance between optimal and actual prices. Furthermore, the aggregate shocks are also relevant, because they signi cantly change the probability of price increases and decreases. However, we nd no evidence of price selection because the interaction term is consistently insigni cant in all of our regressions. These results are robust to using the di erent price gap proxies (competitor price gaps or reset-price gaps), di erent aggregate shocks (credit shock versus monetary policy shock), di erent datasets (supermarket scanner versus producer-price microdata) and di erent speci cations (linear versus non-linear probability models). Selection is always absent.

Our results pose a challenge to conventional price-setting models. This result arises as we interpret our evidence through a suitable generalization of the exible accounting framework of Caballero and Engel (2007). According to this generalization, the price-level response to an aggregate shock can be decomposed into three adjustment margins. The rst is the intensive margin which is the only one present in time-dependent models. It accounts for the change in the magnitude of price changes, when adjusting rms incorporate the impact of the aggregate shock to their price changes. The second is a gross extensive margin, which measures the adjustment through the uniform shift between price increases versus price decreases. The third is a selection e ect, which measures whether goods with larger mispricing respond with higher probability to the aggregate shock. The second and the third margins can be jointly referred to as the extensive margin e ects (as in Caballero and Engel, 2007). Our evidence, on the one hand, points to the presence of the gross extensive margin, as we nd robust evidence on the uniform shift between price increases versus price decreases after an aggregate shock. These results are inconsistent with standard time-dependent pricing models (Calvo, 1983), where the gross extensive margin is absent,2 and implies state-dependence of price changes. On the other hand, our results show no evidence for the selection e ect. This is inconsistent with standard menu

1We would like to thank IRI for making the data available. All estimates and analysis in this paper, based on data provided by IRI, are by the authors and not by IRI.

• As we clarify in Section 8, there is a change in the relative share of measured increases vs decreases in the Calvo (1983) model. However, this is a side-eect of the intensive margin eect, and it is not uniform across levels of mispricing, which would be a requirement of the presence of the gross extensive margin.

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