514 research outputs found
Heterogenous Coefficients, Discrete Instruments, and Identification of Treatment Effects
Multidimensional heterogeneity and endogeneity are important features of a
wide class of econometric models. We consider heterogenous coefficients models
where the outcome is a linear combination of known functions of treatment and
heterogenous coefficients. We use control variables to obtain identification
results for average treatment effects. With discrete instruments in a
triangular model we find that average treatment effects cannot be identified
when the number of support points is less than or equal to the number of
coefficients. A sufficient condition for identification is that the second
moment matrix of the treatment functions given the control is nonsingular with
probability one. We relate this condition to identification of average
treatment effects with multiple treatments.Comment: 15 page
Treatment Effects
This essay discusses the issues of identification and estimation of the average treatment effect and the average effect of treatment on the treated
Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity
This paper investigates identification and inference in a nonparametric structural model with instrumental variables and non-additive errors. We allow for non-additive errors because the unobserved heterogeneity in marginal returns that often motivates concerns about endogeneity of choices requires objective functions that are non-additive in observed and unobserved components. We formulate several independence and monotonicity conditions that are sufficient for identification of a number of objects of interest, including the average conditional response, the average structural function, as well as the full structural response function. For inference we propose a two-step series estimator. The first step consists of estimating the conditional distribution of the endogenous regressor given the instrument. In the second step the estimated conditional distribution function is used as a regressor in a nonlinear control function approach. We establish rates of convergence, asymptotic normality, and give a consistent asymptotic variance estimator.
Automatic Debiased Machine Learning of Causal and Structural Effects
Many causal and structural effects depend on regressions. Examples include
average treatment effects, policy effects, average derivatives, regression
decompositions, economic average equivalent variation, and parameters of
economic structural models. The regressions may be high dimensional. Plugging
machine learners into identifying equations can lead to poor inference due to
bias and/or model selection. This paper gives automatic debiasing for
estimating equations and valid asymptotic inference for the estimators of
effects of interest. The debiasing is automatic in that its construction uses
the identifying equations without the full form of the bias correction and is
performed by machine learning. Novel results include convergence rates for
Lasso and Dantzig learners of the bias correction, primitive conditions for
asymptotic inference for important examples, and general conditions for GMM. A
variety of regression learners and identifying equations are covered. Automatic
debiased machine learning (Auto-DML) is applied to estimating the average
treatment effect on the treated for the NSW job training data and to estimating
demand elasticities from Nielsen scanner data while allowing preferences to be
correlated with prices and income
Constrained Conditional Moment Restriction Models
This paper examines a general class of inferential problems in semiparametric
and nonparametric models defined by conditional moment restrictions. We
construct tests for the hypothesis that at least one element of the identified
set satisfies a conjectured (Banach space) "equality" and/or (a Banach lattice)
"inequality" constraint. Our procedure is applicable to identified and
partially identified models, and is shown to control the level, and under some
conditions the size, asymptotically uniformly in an appropriate class of
distributions. The critical values are obtained by building a strong
approximation to the statistic and then bootstrapping a (conservatively)
relaxed form of the statistic. Sufficient conditions are provided, including
strong approximations using Koltchinskii's coupling.
Leading important special cases encompassed by the framework we study
include: (i) Tests of shape restrictions for infinite dimensional parameters;
(ii) Confidence regions for functionals that impose shape restrictions on the
underlying parameter; (iii) Inference for functionals in semiparametric and
nonparametric models defined by conditional moment (in)equalities; and (iv)
Uniform inference in possibly nonlinear and severely ill-posed problems
Treatment effects (in Russian)
This essay discusses the issues of identification and estimation of the average treatment effect and the average effect of treatment on the treated.
Inference in Linear Regression Models with Many Covariates and Heteroskedasticity
The linear regression model is widely used in empirical work in Economics,
Statistics, and many other disciplines. Researchers often include many
covariates in their linear model specification in an attempt to control for
confounders. We give inference methods that allow for many covariates and
heteroskedasticity. Our results are obtained using high-dimensional
approximations, where the number of included covariates are allowed to grow as
fast as the sample size. We find that all of the usual versions of Eicker-White
heteroskedasticity consistent standard error estimators for linear models are
inconsistent under this asymptotics. We then propose a new heteroskedasticity
consistent standard error formula that is fully automatic and robust to both
(conditional)\ heteroskedasticity of unknown form and the inclusion of possibly
many covariates. We apply our findings to three settings: parametric linear
models with many covariates, linear panel models with many fixed effects, and
semiparametric semi-linear models with many technical regressors. Simulation
evidence consistent with our theoretical results is also provided. The proposed
methods are also illustrated with an empirical application
Alternative Asymptotics and the Partially Linear Model with Many Regressors
Non-standard distributional approximations have received considerable
attention in recent years. They often provide more accurate approximations in
small samples, and theoretical improvements in some cases. This paper shows
that the seemingly unrelated "many instruments asymptotics" and "small
bandwidth asymptotics" share a common structure, where the object determining
the limiting distribution is a V-statistic with a remainder that is an
asymptotically normal degenerate U-statistic. We illustrate how this general
structure can be used to derive new results by obtaining a new asymptotic
distribution of a series estimator of the partially linear model when the
number of terms in the series approximation possibly grows as fast as the
sample size, which we call "many terms asymptotics"
A symptotic Bias for GMM and GEL Estimators with Estimated Nuisance Parameter
This papers studies and compares the asymptotic bias of GMM and generalized empirical likelihood (GEL) estimators in the presence of estimated nuisance parameters. We consider cases in which the nuisance parameter is estimated from independent and identical samples. A simulation experiment is conducted for covariance structure models. Empirical likelihood offers much reduced mean and median bias, root mean squared error and mean absolute error, as compared with two-step GMM and other GEL methods. Both analytical and bootstrap bias-adjusted two-step GMM estima-tors are compared. Analytical bias-adjustment appears to be a serious competitor to bootstrap methods in terms of finite sample bias, root mean squared error and mean absolute error. Finite sample variance seems to be little affected
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