Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems

We provide an asymptotic distribution theory for a class of Generalized Method of Moments estimators that arise in the study of differentiated product markets when the number of observations is associated with the number of products within a given market. We allow for three sources of error: the sampling error in estimating market shares, the simulation error in approximating the shares predicted by the model, and the underlying model error. The limiting distribution of the parameter estimator is normal provided the size of the consumer sample and the number of simulation draws grow at a large enough rate relative to the number of products. We specialise our distribution theory to the Berry, Levinsohn, and Pakes (1995) random coefficient logit model and a pure characteristic model. The required rates differ for these two frequently used demand models. A small Monte Carlo study shows that the difference in asymptotic properties of the two models are reflected in the models' small sample properties. These differences impact directly on the computational burden of the two models.Choice models, Method of moments, Random coefficients, Product differentiation

Aggregate Implications of Firm Heterogeneity: A Nonparametric Analysis of Monopolistic Competition Trade Models

We measure the role of firm heterogeneity in counterfactual predictions of monopolistic competition trade models without parametric restrictions on the distribution of firm fundamentals. We show that two bilateral elasticity functions are sufficient to nonparametrically compute the counterfactual aggregate impact of trade shocks, and recover changes in economic fundamentals from observed data. These functions are identified from two semiparametric gravity equations governing the impact of bilateral trade costs on the extensive and intensive margins of firm-level exports. Applying our methodology, we estimate elasticity functions that imply an impact of trade costs on trade flows that falls when more firms serve a market because of smaller extensive margin responses. Compared to a baseline where elasticities are constant, firm heterogeneity amplifies both the gains from trade in countries with more exporter firms, and the welfare gains of European market integration in 2003-2012

Quantile Regression with Censoring and Endogeneity

In this paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal semiparametrically with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are nonadditive in the unobservables. The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity. For computation, we extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the estimation of the control variable. We give generic regularity conditions for asymptotic normality of the CQIV estimator and for the validity of resampling methods to approximate its asymptotic distribution. We verify these conditions for quantile and distribution regression estimation of the control variable. We illustrate the computation and applicability of the CQIV estimator with numerical examples and an empirical application on estimation of Engel curves for alcohol.Censored, Quantile, Instrumental variable, Censoring, Endogeneity, Engel curve, Alcohol

Quantile regression with censoring and endogeneity

In this paper, we develop a new censored quantile instrumental variable (CQIV)estimator and describe its properties and computation. The CQIV estimator combines Powell(1986) censored quantile regression (CQR) to deal semiparametrically with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are nonadditive in the unobservables. The first stage estimates a nonadditive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a nonadditive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity. For computation, we extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the estimation of the control variable. We give generic regularity conditions for asymptotic normality of the CQIV estimator and for the validity of resampling methods to approximate its asymptotic distribution. We verify these conditions for quantile and distribution regression estimation of the control variable. We illustrate the computation and applicability of the CQIV estimator with numerical examples and an empirical application on estimation of Engel curves for alcohol.

Labor supply models: unobserved heterogeneity, nonparticipation and dynamics

This chapter is concerned with the identification and estimation of models of labor supply. The focus is on the key issues that arise from unobserved heterogeneity, nonparticipation and dynamics. We examine the simple ‘static’ labor supply model with proportional taxes and highlight the problems surrounding nonparticipation and missing wages. The difference in differences approach to estimation and identification is developed within the context of the labour supply model. We also consider the impact of incorporating nonlinear taxation and welfare programme participation. Family labor supply is looked at from botht e unitary and collective persepctives. Finally we consider intertemporal models focusing on the difficulties that arise with participation and heterogeneity

Nonparametric Identification of Differentiated Products Demand Using Micro Data

We examine identification of differentiated products demand when one has “micro data” linking the characteristics and choices of individual consumers. Our model nests standard specifications featuring rich observed and unobserved consumer heterogeneity as well as product/market-level unobservables that introduce the problem of econometric endogeneity. Previous work establishes identification of such models using marketlevel data and instruments for all prices and quantities. Micro data provides a panel structure that facilitates richer demand specifications and reduces requirements on both the number and types of instrumental variables. We address identification of demand in the standard case in which non-price product characteristics are assumed exogenous, but also cover identification of demand elasticities and other key features when these product characteristics are endogenous and not instrumented. We discuss implications of these results for applied work

Using proxy variables to control for unobservables when estimating productivity: A sensitivity analysis

The use of proxy variables to control for unobservables when estimating a production function has become increasingly popular in empirical works in recent years. The present paper aims to contribute to this literature in three important ways. First, we provide a structured review of the different estimators and their underlying assumptions. Second, we compare the results obtained using different estimators for a sample of Spanish manufacturing firms, using definitions and data comparable to those used in most empirical works. In comparing the performance of the different estimators, we rely on various proxy variables, apply different definitions of capital, use alternative moment conditions and allow for different timing assumptions of the inputs. Third, in the empirical analysis we propose a simple (non-graphical) test of the monotonicity assumption between productivity and the proxy variable. Our results suggest that productivity measures are more sensitive to the estimator choice rather than to the choice of proxy variables. Moreover, we find that the monotonicity assumption does not hold for a non-negligible proportion of the observations in our data. Importantly, results of a simple evaluation exercise where we compare productivity distributions of exporters versus non-exporters shows that different estimators yield different results, pointing to the importance of making suitable timing assumptions and choosing the appropriate estimator for the data at hand.Total factor productivity, Semiparametric estimator, Simultaneity, Timing assumptions, Generalized Method of Moments