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HIGHDIMENSIONAL METHODS AND INFERENCE ON STRUCTURAL AND TREATMENT EFFECTS
"... The goal of many empirical papers in economics is to provide an estimate of the causal or structural effect of a change in a treatment or policy variable, such as a government intervention or a price, on another economically interesting variable, such as unemployment or amount of a product purchased ..."
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The goal of many empirical papers in economics is to provide an estimate of the causal or structural effect of a change in a treatment or policy variable, such as a government intervention or a price, on another economically interesting variable, such as unemployment or amount of a product purchased. Applied economists attempting to estimate such structural effects face the problems that economically interesting quantities like government policies are rarely randomly assigned and that the available data are often highdimensional. Failure to address either of these issues generally leads to incorrect inference about structural effects, so methodology that is appropriate for estimating and performing inference about these effects when treatment is not randomly assigned and there are many potential control variables provides a useful addition to the tools available to applied economists. It is wellunderstood that naive application of forecasting methods does not yield valid inference about structural effects when treatment variables are not randomly assigned. The lack of random assignment of economic data has led to the adoption of estimation strategies among applied economists such as instrumental variables (IV) methods and conditional on observables estimators for treatment effects, the simplest of which is ordinary least squares (OLS) including
INFERENCE IN HIGH DIMENSIONAL PANEL MODELS WITH AN APPLICATION TO GUN CONTROL
"... Abstract. We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high dimensional setting. The setting allows the number of time varying regressors to be larger than the sample size. To make informative estimation and inference feas ..."
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Abstract. We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high dimensional setting. The setting allows the number of time varying regressors to be larger than the sample size. To make informative estimation and inference feasible, we require that the overall contribution of the time varying variables after eliminating the individual specific heterogeneity can be captured by a relatively small number of the available variables whose identities are unknown. This restriction allows the problem of estimation to proceed as a variable selection problem. Importantly, we treat the individual specific heterogeneity as fixed effects which allows this heterogeneity to be related to the observed time varying variables in an unspecified way and allows that this heterogeneity may be nonzero for all individuals. Within this framework, we provide procedures that give uniformly valid inference over a fixed subset of parameters in the canonical linear fixed effects model and over coefficients on a fixed vector of endogenous variables in panel data instrumental variables models with fixed effects and many instruments. An input to developing the properties of our proposed procedures is the use of a variant of the Lasso estimator that allows for a grouped data structure where data across groups are independent and dependence within groups is unrestricted. We provide formal conditions within this structure under which the proposed Lasso variant selects a sparse model with good approximation properties. We present simulation results in support of the theoretical developments and illustrate the use of the methods in an application aimed at estimating the effect of gun prevalence on crime rates. Key Words: panel data, fixed effects, partially linear model, instrumental variables, high dimensionalsparse regression, inference under imperfect model selection, uniformly valid inference after model selection, clustered standard errors 1.
Treatment effects with many covariates and heteroskedasticity Treatment E¤ects with Many Covariates and Heteroskedasticity
"... Abstract The linear regression model is widely used in empirical work in Economics. Researchers often include many covariates in their linear model speci…cation in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are ..."
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Abstract The linear regression model is widely used in empirical work in Economics. Researchers often include many covariates in their linear model speci…cation in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are obtained using highdimensional approximations, where the number of covariates are allowed to grow as fast as the sample size. We …nd that all of the usual versions of EickerWhite 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 …ndings to three settings: (i) parametric linear models with many covariates, (ii) semiparametric semilinear models with many technical regressors, and (iii) linear panel models with many …xed e¤ects.
A Service of zbw Treatment effects with many covariates and heteroskedasticity Treatment E¤ects with Many Covariates and Heteroskedasticity
"... StandardNutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, ..."
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StandardNutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter OpenContentLizenzen (insbesondere CCLizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Abstract The linear regression model is widely used in empirical work in Economics. Researchers often include many covariates in their linear model speci…cation in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are obtained using highdimensional approximations, where the number of covariates are allowed to grow as fast as the sample size. We …nd that all of the usual versions of EickerWhite 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 …ndings to three settings: (i) parametric linear models with many covariates, (ii) semiparametric semilinear models with many technical regressors, and (iii) linear panel models with many …xed e¤ects.
SHRINKAGE EFFICIENCY BOUNDS
"... We consider estimation of a multivariate normal mean under sum of squared error loss. We construct the e ciency bound (the lowest achievable risk) for minimax shrinkage estimation. This allows us to compare the regret of existing shrinkage estimators. We also construct a new shrinkage estimator whic ..."
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We consider estimation of a multivariate normal mean under sum of squared error loss. We construct the e ciency bound (the lowest achievable risk) for minimax shrinkage estimation. This allows us to compare the regret of existing shrinkage estimators. We also construct a new shrinkage estimator which achieves substantially lower maximum regret than existing estimators.
PROJECTION INFERENCE FOR SETIDENTIFIED SVARS
"... This paper studies the properties of projection inference for setidentified Structural Vector Autoregressions. The objective is to provide a confidence region for the structural impulseresponse function without specifying prior probability distributions for the structural parameters. The proposal ..."
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This paper studies the properties of projection inference for setidentified Structural Vector Autoregressions. The objective is to provide a confidence region for the structural impulseresponse function without specifying prior probability distributions for the structural parameters. The proposal is to project a nominal 1 − α Wald ellipsoid for the model’s reducedform parameters (autoregressive coefficients and the covariance matrix of residuals). The approach can be applied to a general class of models, is computationally feasible, and—under mild assumptions—produces regions with frequentist coverage and Bayesian credibility of at least 1 − α. The projected confidence region covers the parameters of interest more often than necessary. We follow the recent work of Kaido, Molinari, and Stoye (2015) and discuss the extent to which the radius of the Wald ellipsoid can be ‘calibrated’—in theory and in practice—to eliminate projection bias. The main results in this paper are illustrated using the demand/supplymodel for the U.S. labor market in Baumeister and Hamilton (2015).
Uniform inference Model selection Doublyrobust estimator
, 2015
"... Heterogeneous treatment effects ..."
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Can Big Data Solve the Fundamental Problem of Causal Inference?∗
, 2014
"... Science Association that led to this symposium. This paper benefited greatly from discussions with the ..."
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Science Association that led to this symposium. This paper benefited greatly from discussions with the
Bootstrapping KernelBased Semiparametric Estimators
, 2014
"... This paper develops alternative asymptotic results for a large class of twostep semiparametric estimators. The first main result is an asymptotic distribution result for such estimators and differs from those obtained in earlier work on classes of semiparametric twostep estimators by accommodati ..."
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This paper develops alternative asymptotic results for a large class of twostep semiparametric estimators. The first main result is an asymptotic distribution result for such estimators and differs from those obtained in earlier work on classes of semiparametric twostep estimators by accommodating a nonnegligible bias. A noteworthy feature of the assumptions under which the result is obtained is that reliance on a commonly employed stochastic equicontinuity condition is avoided. The second main result shows that the bootstrap provides an automatic method of correcting for the bias even when it is nonnegligible.