Amil Petrin

Estimating Production Functions Using Inputs to Control for Unobservables

We introduce a new method for conditioning out serially correlated unobserved shocks to the production technology by building ideas first developed in Olley and Pakes (1996). Olley and Pakes show how to use investment to control for correlation between input levels and the unobserved firm-specific productivity process. We prove that like investment, intermediate inputs (those inputs which are typically subtracted out in a value-added production function) can also solve this simultaneity problem. We highlight three potential advantages to using an intermediate inputs approach relative to investment. Our results indicate that these advantages are empirically important.

A Control Function Approach to Endogeneity in Consumer Choice Models

Endogeneity arises for numerous reasons in models of consumer choice. It leads to inconsistency with standard estimation methods that maintain independence between the models error and the included variables. The authors describe a control function approach for handling endogeneity in choice models. Observed variables and economic theory are used to derive controls for the dependence between the endogenous variable and the demand error. The theory points to the relationships that contain information on the unobserved demand factor, such as the pricing equation and the advertising equation. The authors’ approach is an alternative to Berry, Levinsohn, and Pakess (1995) product-market controls for unobserved quality. The authors apply both methods to examine households’ choices among television options, including basic and premium cable packages, in which unobserved attributes, such as quality of programming, are expected to be correlated with price. Without correcting for endogeneity, aggregate demand is estimated to be upward-sloping, suggesting that omitted attributes are positively correlated with demand. Both the control function method and the product-market controls method produce downward-sloping demand estimates that are similar.

Measuring aggregate productivity growth using plant-level data

We define productivity growth as the change in welfare that arises from additional output holding primary inputs constant. Using this traditional growth-accounting definition, we show that gains may arise because of plant-level technology shocks, and, in imperfectly competitive settings, from the reallocation of inputs across plants with differing markups and/or shadow values of primary inputs. With plant-level data, the alternative and most popular definition of productivity growth looks at the difference in the first moments of the productivity distribution. We show that this definition adds an additional term to the growth-accounting measure, which has been called “reallocation.” We show there is a very weak relationship between the two indexes in almost every 3-digit manufacturing industry in both Chile from 1987-1996 and Colombia from 1981-1991 - 49 in total - primarily because this “reallocation” term is large and volatile. We explore the theoretical reasons for this sharp divergence, in the process uncovering a number of previously unnoticed and unattractive features of the first-moment definition. For example, it is not tethered to any theoretical model, it is sensitive to measured units, and it can report positive productivity growth when welfare has fallen.

Estimating Lost Output from Allocative Inefficiency, with an Application to Chile and Firing Costs

We propose a new measure of allocative efficiency based on unrealized increases in aggregate productivity growth. We show that the difference in the value of the marginal product of an input and its marginal cost at any plantthe plant-input gapis exactly equal to the change in aggregate output that would occur if that plant changed that inputs use by one unit. We show how to estimate this gap using plant-level data for 1982 to 1994 from Chilean manufacturing. We find the gaps for blue- and white-collar labor are quite large in absolute value, and these gaps (unlike for materials and electricity) are increasing over time. The timing of the sharpest increases in the labor gaps suggests that they may be related to increases in severance pay.

Structural Applications of the Discrete Choice Model

A growing body of empirical literature uses structurally-derived economic models to study the nature of competition and to measure explicitly the economic impact of strategic policies. While several approaches have been proposed, the discrete choice demand system has experienced wide usage. The heterogeneous, or “mixed”, logit in particular has been widely applied due to its parsimonious structure and its ability to capture flexibly substitution patterns for a large number of differentiated products.We outline the derivation of the heterogeneous logit demand system. We then present a number of applications of such models to various data sources. Finally, we conclude with a discussion of directions for future research in this area.

Tests for Price Endogeneity in Differentiated Product Models

Abstract We develop simple tests for endogenous prices arising from omitted demand factors in discrete choice models. Our approach only requires one to locate testing proxies that have some correlation with the omitted factors when prices are endogenous. We use the difference between prices and their predicted values given observed demand and supply factors. If prices are exogenous, these proxies should not explain demand given prices and other explanatory variables. We reject exogeneity if these proxies enter significantly in utility as additional explanatory variables. The tests are easy to implement as we show with several Monte Carlos and discuss for three recent demand applications.

Explaining Reallocation's Apparent Negative Contribution to Growth

We explain a puzzle from two recent meta-analyses that cover 25 countries and claim to show that inputs systematically move from higher-value to lower-value activities despite strong aggregate labor productivity growth (ALP). These papers use variants of the Baily, Hulten and Campbell (1992) decomposition of ALP to show that the reallocation covariance term is negative in all but two countries and the reallocation between term is negative in nine countries and weakly positive in most others. We decompose ALP using three micro-level data sets from Chile, Colombia, and Slovenia and show the same puzzle holds. We show that the ALP between term can be decomposed into a term related to reallocation and a term related to the change in the total number of .ms, the latter of which often works to reduce the total between term in our data. We also show these ALP patterns can arise because of heterogeneity in labor and capital, unobserved output prices, or capacity utilization, but controlling for them only marginally helps to explain away the ALP reallocation puzzles in our micro-level data sets. We show that there is no puzzle when one decomposes aggregate productivity growth in the terms of National Accounts, as inputs in the aggregate move from low to high value activities in 36 of our 39 country-year observations. We conclude that there is a fundamental difference in re- allocation measured by the ALP decomposition and that measured by the decomposition of National Accounts growth.

Are We Undercounting Reallocation’s Contribution to Growth?

Reallocation growth occurs when an input moves from a lower marginal product to a higher marginal product activity. Three recent studies use two distinct methodologies to examine the sources of the strong surge in aggregate productivity growth (APG) in India’s manufacturing sector since 1990 following significant economic reforms. They all conclude that APG was primarily driven by within-plant increases in technical efficiency and not between-plant reallocation of inputs. Given the nature of the reforms, where many barriers to input reallocation were removed, this finding has surprised researchers and been dubbed “India’s Mysterious Manufacturing Miracle.” In this paper we show that these findings may be an artifact of the way the studies estimate reallocation. One approach counts all reallocation growth arising from the movement of intermediate inputs as technical efficiency growth. The second approach introduces measurement error into estimated reallocation by using plant-level average products - total factor productivity residuals - as a proxy for marginal products, which could be problematic as economic theory suggests that average products and marginal products are unrelated in equilibrium. Using microdata on manufacturing from 4 countries — the U.S., Chile, Colombia, and Slovenia — we show that both approaches significantly understate the true role of reallocation in economic growth. In the U.S. almost 50% of reallocation growth is due to movements of intermediate inputs, meaning if India is similar to the U.S. then reallocation’s share of total Indian manufacturing APG since 1990 increases from the previous estimate of one-third to almost two-thirds.

Plant-Level Productivity and Imputation of Missing Data in the Census of Manufactures

In the U.S. Census of Manufactures, the Census Bureau imputes missing values using a combination of mean imputation, ratio imputation, and conditional mean imputation. It is wellknown that imputations based on these methods can result in underestimation of variability and potential bias in multivariate inferences. We show that this appears to be the case for the existing imputations in the Census of Manufactures. We then present an alternative strategy for handling the missing data based on multiple imputation. Specifically, we impute missing values via sequences of classification and regression trees, which offer a computationally straightforward and flexible approach for semi-automatic, large-scale multiple imputation. We also present an approach to evaluating these imputations based on posterior predictive checks. We use the multiple imputations, and the imputations currently employed by the Census Bureau, to estimate production function parameters and productivity dispersions. The results suggest that the two approaches provide quite different answers about productivity.