Fixed Effect Estimation of Large T Panel Data Models

This article reviews recent advances in fixed effect estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where the distribution of the outcome variable conditional on covariates and unobserved effects is specified parametrically, while the distribution of the unobserved effects is left unrestricted. Compared to existing reviews on long panels (Arellano and Hahn 2007; a section in Arellano and Bonhomme 2011) we discuss models with both individual and time effects, split-panel Jackknife bias corrections, unbalanced panels, distribution and quantile effects, and other extensions. Understanding and correcting the incidental parameter bias caused by the estimation of many fixed effects is our main focus, and the unifying theme is that the order of this bias is given by the simple formula p/n for all models discussed, with p the number of estimated parameters and n the total sample size.Comment: 40 pages, 1 tabl

Quantile Models with Endogeneity

In this article, we review quantile models with endogeneity. We focus on models that achieve identification through the use of instrumental variables and discuss conditions under which partial and point identification are obtained. We discuss key conditions, which include monotonicity and full-rank-type conditions, in detail. In providing this review, we update the identification results of Chernozhukov & Hansen (2005). We illustrate the modeling assumptions through economically motivated examples. We also briefly review the literature on estimation and inference

Partial Independence in Nonseparable Models

We analyze identification of nonseparable models under three kinds of exogeneity assumptions weaker than full statistical independence. The first is based on quantile independence. Selection on unobservables drives deviations from full independence. We show that such deviations based on quantile independence require non-monotonic and oscillatory propensity scores. Our second and third approaches are based on a distance-from-independence metric, using either a conditional cdf or a propensity score. Under all three approaches we obtain simple analytical characterizations of identified sets for various parameters of interest. We do this in three models: the exogenous regressor model of Matzkin (2003), the instrumental variable model of Chernozhukov and Hansen (2005), and the binary choice model with nonparametric latent utility of Matzkin (1992)

Instrumental variables estimation of a generalized correlated random coefficients model

We study identification and estimation of the average treatment effect in a correlated random coefficients model that allows for first stage heterogeneity and binary instruments. The model also allows for multiple endogenous variables and interactions between endogenous variables and covariates. Our identification approach is based on averaging the coefficients obtained from a collection of ordinary linear regressions that condition on different realizations of a control function. This identification strategy suggests a transparent and computationally straightforward estimator of a trimmed average treatment effect constructed as the average of kernel-weighted linear regressions. We develop this estimator and establish its $\sqrt{n}$--consistency and asymptotic normality. Monte Carlo simulations show excellent finite-sample performance that is comparable in precision to the standard two-stage least squares estimator. We apply our results to analyze the effect of air pollution on house prices, and find substantial heterogeneity in first stage instrument effects as well as heterogeneity in treatment effects that is consistent with household sorting

Nonparametric Estimates of Demand in the California Health Insurance Exchange

We develop a new nonparametric approach for discrete choice and use it to analyze the demand for health insurance in the California Affordable Care Act marketplace. The model allows for endogenous prices and instrumental variables, while avoiding parametric functional form assumptions about the unobserved components of utility. We use the approach to estimate bounds on the effects of changing premiums or subsidies on coverage choices, consumer surplus, and government spending on subsidies. We find that a $10 decrease in monthly premium subsidies would cause a decline of between 1.8$62 and $74 million, while the savings in yearly subsidy outlays would be between$207 and $602 million. We estimate the demand impacts of linking subsidies to age, finding that shifting subsidies from older to younger buyers would increase average consumer surplus, with potentially large impacts on enrollment. We also estimate the consumer surplus impact of removing the highly-subsidized plans in the Silver metal tier, where we find that a nonparametric model is consistent with a wide range of possibilities. We find that comparable mixed logit models tend to yield price sensitivity estimates toward the lower end of the nonparametric bounds, while producing consumer surplus impacts that can be both higher and lower than the nonparametric bounds depending on the specification of random coefficients

ivcrc: An instrumental-variables estimator for the correlated random-coefficients model

We discuss the ivcrc command, which implements an instrumentalvariables (IV) estimator for the linear correlated random-coefficients model. The correlated random-coefficients model is a natural generalization of the standard linear IV model that allows for endogenous, multivalued treatments and unobserved heterogeneity in treatment effects. The estimator implemented by ivcrc uses recent semiparametric identification results that allow for flexible functional forms and permit instruments that may be binary, discrete, or continuous. The ivcrc command also allows for the estimation of varying-coefficient regressions, which are closely related in structure to the proposed IV estimator. We illustrate the use of ivcrc by estimating the returns to education in the National Longitudinal Survey of Young Men

ivcrc: An instrumental-variables estimator for the correlated random-coefficients model

We discuss the ivcrc command, which implements an instrumentalvariables (IV) estimator for the linear correlated random-coefficients model. The correlated random-coefficients model is a natural generalization of the standard linear IV model that allows for endogenous, multivalued treatments and unobserved heterogeneity in treatment effects. The estimator implemented by ivcrc uses recent semiparametric identification results that allow for flexible functional forms and permit instruments that may be binary, discrete, or continuous. The ivcrc command also allows for the estimation of varying-coefficient regressions, which are closely related in structure to the proposed IV estimator. We illustrate the use of ivcrc by estimating the returns to education in the National Longitudinal Survey of Young Men