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An Extended Class of Instrumental Variables for the Estimation of Causal Effects
 UCSD DEPT. OF ECONOMICS DISCUSSION PAPER
, 1996
"... This paper builds on the structural equations, treatment effect, and machine learning literatures to provide a causal framework that permits the identification and estimation of causal effects from observational studies. We begin by providing a causal interpretation for standard exogenous regresso ..."
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Cited by 32 (13 self)
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This paper builds on the structural equations, treatment effect, and machine learning literatures to provide a causal framework that permits the identification and estimation of causal effects from observational studies. We begin by providing a causal interpretation for standard exogenous regressors and standard “valid” and “relevant” instrumental variables. We then build on this interpretation to characterize extended instrumental variables (EIV) methods, that is methods that make use of variables that need not be valid instruments in the standard sense, but that are nevertheless instrumental in the recovery of causal effects of interest. After examining special cases of single and double EIV methods, we provide necessary and sufficient conditions for the identification of causal effects by means of EIV and provide consistent and asymptotically normal estimators for the effects of interest.
Identification and Estimation of a Nonparametric Panel Data Model with Unobserved Heterogeneity
, 2009
"... This paper considers a nonparametric panel data model with nonadditive unobserved heterogeneity. As in the standard linear panel data model, two types of unobservables are present in the model: individualspecific effects and idiosyncratic disturbances. The individualspecific effects enter the stru ..."
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Cited by 16 (1 self)
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This paper considers a nonparametric panel data model with nonadditive unobserved heterogeneity. As in the standard linear panel data model, two types of unobservables are present in the model: individualspecific effects and idiosyncratic disturbances. The individualspecific effects enter the structural function nonseparably and are allowed to be correlated with the covariates in an arbitrary manner. The idiosyncratic disturbance term is additively separable from the structural function. Nonparametric identification of all the structural elements of the model is established. No parametric distributional or functional form assumptions are needed for identification. The identification result is constructive and only requires panel data with two time periods. Thus, the model permits nonparametric distributional and counterfactual analysis of heterogeneous marginal effects using short panels. The paper also develops a nonparametric estimation procedure and derives its rate of convergence. As a byproduct the rates of convergence for the problem of conditional deconvolution are obtained. The proposed estimator is easy to compute and does not require numeric optimization. A MonteCarlo study indicates that the estimator performs very well in finite sample properties.
How Many Consumers are Rational
, 2009
"... Rationality places strong restrictions on individual consumer behavior. This paper is concerned with assessing the validity of the integrability constraints imposed by standard utility maximization, arising in classical consumer demand analysis. More specifically, we characterize the testable implic ..."
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Cited by 8 (2 self)
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Rationality places strong restrictions on individual consumer behavior. This paper is concerned with assessing the validity of the integrability constraints imposed by standard utility maximization, arising in classical consumer demand analysis. More specifically, we characterize the testable implications of negative semidefiniteness and symmetry of the Slutsky matrix across a heterogeneous population without assuming anything on the functional form of individual preferences. In the same spirit, homogeneity of degree zero is being considered. Our approach employs nonseparable models and is centered around a conditional independence assumption, which is sufficiently general to allow for endogenous regressors. It is the only substantial assumption a researcher has to specify in this model, and has to be evaluated with particular care. Finally, we apply all concepts to British household data: We show that rationality is an acceptable description for large parts of the population, regardless of whether we test on single or composite households.
2012): “Estimating Derivatives in Nonseparable Models with Limited Dependent Variables,”forthcoming in Econometrica
"... We present a simple way to estimate the effects of changes in a vector of observable variables X on a limited dependent variable Y when Y is a general nonseparable function of X and unobservables. We treat models in which Y is censored from above or below or potentially from both. The basic idea is ..."
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Cited by 7 (1 self)
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We present a simple way to estimate the effects of changes in a vector of observable variables X on a limited dependent variable Y when Y is a general nonseparable function of X and unobservables. We treat models in which Y is censored from above or below or potentially from both. The basic idea is to first estimate the derivative of the conditional mean of Y given X at x with respect to x on the uncensored sample without correcting for the effect of changes in x induced on the censored population. We then correct the derivative for the effects of the selection bias. We propose nonparametric and semiparametric estimators for the derivative. As extensions, we discuss the cases of discrete regressors, measurement error Many problems in economics involve dependent variables that are censored in some way. For example, hundreds of empirical studies have used the Tobit and generalized Tobit models to study the effects of a set of independent variables X on a dependent variable Y that is censored at some constant. While great theoretical progress has been made in relaxing
Nonparametric Identification in Nonseparable Panel Data Models with Generalized Fixed Effects
, 2009
"... This paper is concerned with extending the familiar notion of fixed effects to nonlinear setups with infinite dimensional unobservables like preferences. The main result is that a generalized version of differencing identifies local average structural derivatives (LASDs) in very general nonseparable ..."
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Cited by 7 (1 self)
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This paper is concerned with extending the familiar notion of fixed effects to nonlinear setups with infinite dimensional unobservables like preferences. The main result is that a generalized version of differencing identifies local average structural derivatives (LASDs) in very general nonseparable models, while allowing for arbitrary dependence between the persistent unobservables and the regressors of interest even if there are only two time periods. These quantities specialize to well known objects like the slope coefficient in the semiparametric panel data binary choice model with fixed effects. We extend the basic framework to include dynamics in the regressors and time trends, and show how distributional effects as well as average effects are identified. In addition, we show how to handle endogeneity in the transitory component. Finally, we adapt our results to the semiparametric binary choice model with correlated coefficients, and establish that average structural marginal probabilities are identified. We conclude this paper by applying the last result to a real world data example. Using the PSID, we analyze the way in which the lending restrictions for mortgages eased between 2000 and 2004.
FLEXIBLE CORRELATED RANDOM EFFECTS ESTIMATION IN PANEL MODELS WITH UNOBSERVED HETEROGENEITY
, 2007
"... In this paper, we consider identification in a correlated random effects model for panel data. We assume that the likelihood for each individual in the panel is known up to a finite dimensional common parameter and an individual specific parameter. We allow the distribution of unobserved individual ..."
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Cited by 4 (0 self)
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In this paper, we consider identification in a correlated random effects model for panel data. We assume that the likelihood for each individual in the panel is known up to a finite dimensional common parameter and an individual specific parameter. We allow the distribution of unobserved individual specific effects to depend on observed explanatory variables and make no assumptions about the particular functional form of this dependence. This leads to a semiparametric problem where the parameters include a finite dimensional common parameter, θ and an infinite dimensional conditional density, q, that describes the distribution of unobserved individual specific effects. For a given likelihood, we establish restrictions on the space of functions H for the distribution of unobserved heterogeneity under which {θ, q} are identified. We show the model parameters may be consistently estimated by sieve maximum likelihood for a fixed panel length, T. The conditions on H, which include assumptions about the support of explanatory variables and smoothness of q in its arguments, are relatively mild and are similar to those required for nonparametric density estimation.
Comparing Features of Convenient Estimators for Binary Choice Models With Endogenous Regressors
, 2012
"... We discuss the relative advantages and disadvantages of four types of convenient estimators of binary choice models when regressors may be endogenous or mismeasured, or when errors are likely to be heteroskedastic. For example, such models arise when treatment is not randomly assigned and outcomes a ..."
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Cited by 4 (2 self)
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We discuss the relative advantages and disadvantages of four types of convenient estimators of binary choice models when regressors may be endogenous or mismeasured, or when errors are likely to be heteroskedastic. For example, such models arise when treatment is not randomly assigned and outcomes are binary. The estimators we compare are the two stage least squares linear probability model, maximum likelihood estimation, control function estimators, and special regressor methods. We specifically focus on models and associated estimators that are easy to implement. Also, for calculating choice probabilities and regressor marginal effects, we propose the average index function (AIF), which, unlike the average structural function (ASF), is always easy to estimate.
Quantile and Average Effects in Nonseparable Panel Models 1
, 2009
"... 1We thank seminar participants at Stanford and HarvardMIT econometrics workshops, B. Graham, This paper gives identification and estimation results for quantile and average effects in nonseparable panel models, when the distribution of period specific disturbances does not vary over time. Bounds ar ..."
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Cited by 4 (0 self)
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1We thank seminar participants at Stanford and HarvardMIT econometrics workshops, B. Graham, This paper gives identification and estimation results for quantile and average effects in nonseparable panel models, when the distribution of period specific disturbances does not vary over time. Bounds are given for interesting effects with discrete regressors that are strictly exogenous or predetermined. We allow for location and scale time effects and show how monotonicity can be used to shrink the bounds. We derive rates at which the bounds tighten as the number T of This paper gives identification and estimation results for quantile and average effects in nonseparable panel models, when the distribution of period specific disturbances does not vary over time. Bounds are given for interesting effects with discrete regressors that are strictly exogenous or predetermined. We allow for location and scale time effects and show how monotonicity can
2011): “Nonlinear Panel Data Analysis
 Annual Review of Economics
"... Nonlinear panel data models arise naturally in economic applications, yet their analysis is challenging. Here we provide a progress report on some recent advances in the area. We start by reviewing the properties of randomeffects likelihood approaches. We emphasize a link with Bayesian computation ..."
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Cited by 4 (0 self)
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Nonlinear panel data models arise naturally in economic applications, yet their analysis is challenging. Here we provide a progress report on some recent advances in the area. We start by reviewing the properties of randomeffects likelihood approaches. We emphasize a link with Bayesian computation and Markov Chain Monte Carlo, which provides a convenient approach to estimation and inference. Relaxing parametric assumptions on the distribution of individual effects raises serious identification problems. In discrete choice models, common parameters and average marginal effects are generally setidentified. The availability of continuous outcomes, however, provides opportunities for pointidentification. We end the paper by reviewing recent progress on non fixedT approaches. In panel applications where the time dimension is not negligible relative to the size of the crosssection, it makes sense to view the estimation problem as a timeseries finite sample bias. Several perspectives to bias reduction are now available. We review their properties, with a special emphasis on randomeffects methods. JEL codes: C23.
Simple Estimators for Binary Choice Models With Endogenous Regressors
, 2010
"... This paper provides two main contributions to binary choice models with endogenous regressors. First, we propose some variants of special regressor based estimators that are numerically trivial to implement. These estimators provide consistent estimates of binary choice model coef cients when regres ..."
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Cited by 4 (2 self)
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This paper provides two main contributions to binary choice models with endogenous regressors. First, we propose some variants of special regressor based estimators that are numerically trivial to implement. These estimators provide consistent estimates of binary choice model coef cients when regressors (either discretely or continuously distributed) are endogenous, and when the latent errors have heteroskedasticity of unknown form. We also propose an alternative to the average structural function (ASF) measure of tted values for models having a latent index structure that is easier to calculate than ASF. We use this to provide simple estimators for choice probabilities and marginal effects of the regressors. We illustrate these methods with an empirical application to the estimation of migration probabilities within the US.