# RDP 2010-01: Reconciling Microeconomic and Macroeconomic Estimates of Price Stickiness 1. Introduction

The degree of price stickiness has a major influence on the behaviour of inflation and is an important determinant of the effects of monetary policy; all else equal, the stickier are prices, the larger is the response of economic activity to a monetary policy shock.

A common way of modelling price stickiness is to assume that the opportunity for firms to reset their prices in any particular period is a random event. The probability that they are unable to do so is known as the Calvo probability (Calvo 1983), which provides a natural measure of the degree of price stickiness. Aggregate measures of the Calvo probability have been estimated using both macroeconomic and microeconomic data. The two types of data tend to deliver very different estimates of the degree of aggregate price stickiness. The aim of this paper is to understand how and why these differences occur.

One approach to making inferences about an economy-wide Calvo probability is to estimate a New-Keynesian Phillips Curve (NKPC) using aggregate data on inflation and either output or real marginal costs. When prices are stickier, larger changes in output are required to change the rate of inflation. In other words, the Calvo probability is inversely related to the slope of the Phillips Curve. We will refer to an estimate of the Calvo probability obtained from the NKPC as ; typically this is estimated using quarterly data to be at least 0.75, which implies that the average duration between price changes is at least four quarters.[1]

A second approach is to use data from surveys of firms or microeconomic-level price data (for example, see Blinder et al 1998). By measuring the average time that a price remains unchanged within a sector and taking a weighted average of these durations across sectors, it is possible to calculate an economy-wide average duration of prices. An aggregate measure of the Calvo probability can then be inferred from the average duration of prices, which we refer to as θmicro. Microeconomic studies using the data which underlie the United States' CPI suggest that prices remain fixed on average for between one to three quarters (Bils and Klenow 2004; Klenow and Kryvtsov 2008; Nakamura and Steinsson 2008). This duration implies that the quarterly θmicro is around 0.5.

The microeconomic data also reveal that considerable heterogeneity exists in the frequency with which prices are reset across sectors – see Klenow and Kryvtsov (2008). We show that in the presence of this heterogeneity, aggregate estimates of the Calvo probability from microeconomic and macroeconomic studies should not be expected to be equal. Further, we derive an aggregate measure of the Calvo probability that should be obtained from the aggregate data and used in macroeconomic modelling when heterogeneity exists, which we label .

A stark finding of our paper is that is lower than θmicro, whereas (as already noted) is typically much higher than θmicro. We argue that is a poor estimator of due to econometric problems stemming from the heterogeneity in price stickiness evident in the microeconomic data.

Imbs, Jondeau and Pelgrin (2007) also suggest that the divergence between the macroeconomic and microeconomic estimates of the frequency of price resetting could reflect heterogeneity across sectors, but focus on estimating an aggregate Calvo probability using sectoral panel data. Our alternative approach is to introduce various types of heterogeneity into a structural model.

The introduction of heterogeneity raises the issue of how firms interact with each other and consumers. One approach, which we adopt, is to allow firms to use the output of all other firms as intermediate inputs, which is known as roundabout production (Basu 1995). We show that in economies with both roundabout production and heterogeneity, the conventional measure of real marginal costs, namely labour's share of income, is no longer suitable and ignoring this contributes to the upwards bias of .

Because the standard NKPC is often unable to capture the persistence evident in inflation, a lag of inflation is often included. This is motivated by the possibility that some firms index their prices to past inflation instead of setting their prices optimally when they have the opportunity to reset prices (see, for example, Galí and Gertler 1999). These indexation assumptions are used despite there being no empirical microeconomic evidence of such behaviour. The resulting Phillips curve is referred to as the hybrid NKPC; estimates of these suggest that 80 per cent of firms index their prices to past inflation (see Schorfheide 2008). We show that a more realistic model with roundabout technology can generate the persistence in inflation evident in the data without resorting to ad hoc assumptions about the behaviour of prices. Further, if heterogeneity is also present, estimates of the hybrid NKPC will falsely suggest that the indexation of some prices exists when in reality there is none.

In the next section, the relationship between estimates of the Calvo probability obtained using macroeconomic and microeconomic data is clarified. Section 3 briefly describes the model used to generate data for the econometric analysis presented in Section 4. The macroeconomic implications of those estimates are discussed in Section 5 and Section 6 concludes.

## Footnote

For a range of values, see Dennis (2006) and Schorfheide (2008). [1]