Title: Essays on Sticky Prices and High Inflation Environments
Description: It has been well established for a long time that sticky prices are fundamental to our understanding of monetary policy. Indeed, sticky prices are a common micro-foundation in models of monetary policy and nominal aggregate fluctuations, as monetary variables typically do not have real economic effects if prices are fuly flexible. This is why price stickiness has been the focus of much research, both theoretical and empirical. A particularly exciting development in this literature has been the recent availability of large, detailed, micro data sets of individual prices, which allow us to observe when and how often the prices of individual goods and sevices change. This type of data has greatly improved our ability to discipline the theoretical models that are used to analyze monetary policy, and advances in sticky price modelling have also provided important questions to ask of the data. The most common data set used in this literature has been the micro data underlying the U.S. Consumer Price Index.

While work with this data has produced important results, an important limitation is that it has, until recently, only been available going back to 1988. This is a limitation because it means that the data set only cover periods of low and stable inflation, which limits the types of questions that the price data can help answer. In this dissertation, I present an extension to this data set: in work carried out with Emi Nakamura, Jón Steinsson and Patrick Sun, we re-constructed an older portion of the data to extend it back to 1977. With this new sample, we can study the high inflation periods of the late 1970's and early 1980's, and in this dissertation I explore various questions related to monetary policy, and show that several important insights can be gained from this new data set. Chapter 1, ``The Elusive Costs of Inflation: Price Dispersion during the U.S. Great Inflation", presents the extended CPI data set and addresses a key policy question: How high an inflation rate should central banks target? This depends crucially on the costs of inflation.

An important concern is that high inflation will lead to inefficient price dispersion. Workhorse New Keynesian models imply that this cost of inflation is very large. An increase in steady state inflation from 0% to 10% yields a welfare loss that is an order of magnitude greater than the welfare loss from business cycle fluctuations in output in these models. We assess this prediction empirically using a new dataset on price behavior during the Great Inflation of the late 1970's and early 1980's in the United States. If price dispersion increases rapidly with inflation, we should see the absolute size of price changes increasing with inflation: price changes should become larger as prices drift further from their optimal level at higher inflation rates. We find no evidence that the absolute size of price changes rose during the Great Inflation. This suggests that the standard New Keynesian analysis of the welfare costs of inflation is wrong and its implications for the optimal inflation rate need to be reassessed.

We also find that (non-sale) prices have not become more flexible over the past 40 years. Chapter 2, ``The Skewness of the Price Change Distribution: A New Touchstone for Sticky Price Models", documents the predictions of a broad class of existing price setting models on how various statistics of the price change distribution change with the rate of aggregate inflation. Notably, menu cost models uniformly feature the price change distribution becoming less dispersed and less skewed as inflation rises, while in the Calvo model both relations are positive. Using a novel data set, the micro data underlying the U.S. CPI from the late 1970's onwards, we evaluate these predictions using the large variation in inflation over this period. Price change dispersion does indeed fall with inflation, but skewness does not, meaning that menu cost models are at odds with these empirical patterns. The Calvo model's prediction on price change skewness are consistent with the data, but it fails to match the positive relationship between inflation and the frequency of price change, and the negative relationship between inflation and price change dispersion.

Since the negative correlations for dispersion and skewness are driven by the selection effect in menu cost models, the evidence presented suggests that selection is less substantial than in menu cost models. Chapter 3, ``The Selection Effect and Monetary Non-Neutrality in a Random Menu Cost Model", presents a random menu cost model that nests the Golosov and Lucas (2007) and Calvo (1983) models as extreme cases, as well as intermediate cases, depending on the distribution of menu costs. This model includes idiosyncratic technology shocks and aggregate demand shocks, so it can be applied to price micro data, and to evaluate the degree of monetary non-neutrality implied by different kinds of menu cost distributions. This model can match the empirical patterns presented in Chapter 2. I find that a random menu cost model with a much weaker selection effect (than in existing menu cost models) no longer predicts such a negative relationship between inflation and price change skewness, but still predicts that the frequency of price change rises with inflation, as in the data, and contrary to the Calvo model.

This model also predicts a very high degree of monetary non-neutrality, and the results overall provide evidence in favor of high non-neutrality. Chapter 4, ``The State-Dependent Price Adjustment Hazard Function: Evidence from High Inflation Periods", considers a model-free approach to understanding sticky prices and non-neutrality. The price adjustment hazard function has been used to establish the relationship between individual firms' price setting behavior (micro-level price stickiness) and the response of the aggregate price level to monetary shocks (aggregate stickiness, or monetary non-neutrality), but scant work has been done to estimate the function empirically. We show first that various types of hazard functions (with widely different levels of implied aggregate stickiness) can match the unconditional moments that have been the focus of empirical work on sticky prices (such as the average frequency and size of price changes). However, the relationship between inflation and the shape of the price change distribution over time provides considerable information on the shape of the hazard function.

In particular, we find that in order to match the positive inflation-frequency correlation, and the non-negative inflation-price change skewness correlations, the hazard function has to be asymmetric around zero (price increases are overall more likely than decreases) and relatively flat for small to intermediate values of the desired price gap. The latter feature means that our estimated hazard function implies a large degree of aggregate flexibility.