In the single-IV model, researchers commonly rely on t-ratio-based inference, even though the lit... more In the single-IV model, researchers commonly rely on t-ratio-based inference, even though the literature has quantified its potentially severe large-sample distortions. Building on Stock and Yogo (2005), we introduce the tF critical value function, leading to a standard error adjustment that is a smooth function of the first-stage F-statistic. For one-quarter of specifications in 61 AER papers, corrected standard errors are at least 49 and 136 percent larger than conventional 2SLS standard errors at the 5-percent and 1percent significance levels, respectively. tF confidence intervals have shorter expected length than those of Anderson and Rubin (1949), whenever both are bounded.
In the single-IV model, researchers commonly rely on t-ratio-based inference, even though the lit... more In the single-IV model, researchers commonly rely on t-ratio-based inference, even though the literature has quantified its potentially severe large-sample distortions. Building on the approach for correcting inference of Stock and Yogo (2005), we introduce the tF critical value function, leading to a minimized standard error adjustment factor that is a smooth function of the first-stage F-statistic. Applying the correction to a sample of 61 AER papers leads to a 25 percent increase in standard errors, on average. tF confidence intervals have shorter expected length than those of Anderson and Rubin (1949), whenever both are bounded intervals. David S. Lee Industrial Relations Section Louis A. Simpson International Bldg. Princeton University Princeton, NJ 08544 and NBER davidlee@princeton.edu Justin McCrary Columbia University Jerome Greene Hall Room 521 435 West 116th Street New York, NY 10027 and NBER jmccrary@law.columbia.edu Marcelo J. Moreira Department of Economics Getulio Varg...
We propose a new approach to the semiparametric analysis of multinomial choice models with fixed ... more We propose a new approach to the semiparametric analysis of multinomial choice models with fixed effects and a group (or panel) structure. A traditional random utility framework is employed, and the key assumption is a group homogeneity condition on the disturbances. This assumption places no restrictions on either the joint distribution of the disturbances across choices or their within group (or across time) correlations. This work follows a substantial nonlinear panel literature
ABSTRACT We examine statistical models, including the workhorse linear instrumental variables mod... more ABSTRACT We examine statistical models, including the workhorse linear instrumental variables model, in which the mapping from the reduced form distribution to the structural parameters of interest is singular. The singularity of this mapping implies certain fundamental restrictions on the finite sample properties of point estimators: they cannot be unbiased, quantile-unbiased, or translation equivariant. The nonexistence of unbiased estimators does not rule out bias reduction of standard estimators, but implies that the bias-variance tradeoff cannot be avoided and needs to be considered carefully. The results can also be extended to weak instrument asymptotics by using the limits of experiments framework.
… Manuscript, Department of Economics, University of …, 2003
Estimation in the Regression Discontinuity Model ∗ Jack Porter Harvard University Department of E... more Estimation in the Regression Discontinuity Model ∗ Jack Porter Harvard University Department of Economics Littauer Center 121 Cambridge, MA 02138 jporter@harvard.edu May 7, 2003 Abstract ... One new estimator is based on Robinson's (1988) partially linear estimator. ...
We consider estimation of bounds determined by multiple features of the data, such as bounds aris... more We consider estimation of bounds determined by multiple features of the data, such as bounds arising from two or more moment inequalities. In such problems, conventional estimators of the boundaries are known to be biased, and test statistics do not have standard limit distributions, at least at certain points in the parameter space. We use a limit of experiments framework to give a characterization of all attainable limit distributions of estimators, when the boundary of interest is identied as the minimum or maximum of a nite number of data features. We nd that certain desirable properties|local asymptotic unbiasedness and regularity|cannot be achieved by any estimator. The problem is closely related to the problem of estimating the minimum of a set of normal means, and examining this simpler problem can suggest alternative procedures that have good risk properties.
We examine challenges to estimation and inference when the objects of interest are nondif-ferenti... more We examine challenges to estimation and inference when the objects of interest are nondif-ferentiable functionals of the underlying data distribution. This situation arises in a number of applications of bounds analysis and moment inequality models, and in recent work on estimating optimal dynamic treatment regimes. Drawing on earlier work relating differentiability to the ex-istence of unbiased and regular estimators, we show that if the target object is not continuously differentiable in the parameters of the data distribution, there exist no locally asymptotically unbiased estimators and no regular estimators. This places strong limits on estimators, bias correction methods, and inference procedures. 1
In the single-IV model, researchers commonly rely on t-ratio-based inference, even though the lit... more In the single-IV model, researchers commonly rely on t-ratio-based inference, even though the literature has quantified its potentially severe large-sample distortions. Building on Stock and Yogo (2005), we introduce the tF critical value function, leading to a standard error adjustment that is a smooth function of the first-stage F-statistic. For one-quarter of specifications in 61 AER papers, corrected standard errors are at least 49 and 136 percent larger than conventional 2SLS standard errors at the 5-percent and 1percent significance levels, respectively. tF confidence intervals have shorter expected length than those of Anderson and Rubin (1949), whenever both are bounded.
In the single-IV model, researchers commonly rely on t-ratio-based inference, even though the lit... more In the single-IV model, researchers commonly rely on t-ratio-based inference, even though the literature has quantified its potentially severe large-sample distortions. Building on the approach for correcting inference of Stock and Yogo (2005), we introduce the tF critical value function, leading to a minimized standard error adjustment factor that is a smooth function of the first-stage F-statistic. Applying the correction to a sample of 61 AER papers leads to a 25 percent increase in standard errors, on average. tF confidence intervals have shorter expected length than those of Anderson and Rubin (1949), whenever both are bounded intervals. David S. Lee Industrial Relations Section Louis A. Simpson International Bldg. Princeton University Princeton, NJ 08544 and NBER davidlee@princeton.edu Justin McCrary Columbia University Jerome Greene Hall Room 521 435 West 116th Street New York, NY 10027 and NBER jmccrary@law.columbia.edu Marcelo J. Moreira Department of Economics Getulio Varg...
We propose a new approach to the semiparametric analysis of multinomial choice models with fixed ... more We propose a new approach to the semiparametric analysis of multinomial choice models with fixed effects and a group (or panel) structure. A traditional random utility framework is employed, and the key assumption is a group homogeneity condition on the disturbances. This assumption places no restrictions on either the joint distribution of the disturbances across choices or their within group (or across time) correlations. This work follows a substantial nonlinear panel literature
ABSTRACT We examine statistical models, including the workhorse linear instrumental variables mod... more ABSTRACT We examine statistical models, including the workhorse linear instrumental variables model, in which the mapping from the reduced form distribution to the structural parameters of interest is singular. The singularity of this mapping implies certain fundamental restrictions on the finite sample properties of point estimators: they cannot be unbiased, quantile-unbiased, or translation equivariant. The nonexistence of unbiased estimators does not rule out bias reduction of standard estimators, but implies that the bias-variance tradeoff cannot be avoided and needs to be considered carefully. The results can also be extended to weak instrument asymptotics by using the limits of experiments framework.
… Manuscript, Department of Economics, University of …, 2003
Estimation in the Regression Discontinuity Model ∗ Jack Porter Harvard University Department of E... more Estimation in the Regression Discontinuity Model ∗ Jack Porter Harvard University Department of Economics Littauer Center 121 Cambridge, MA 02138 jporter@harvard.edu May 7, 2003 Abstract ... One new estimator is based on Robinson's (1988) partially linear estimator. ...
We consider estimation of bounds determined by multiple features of the data, such as bounds aris... more We consider estimation of bounds determined by multiple features of the data, such as bounds arising from two or more moment inequalities. In such problems, conventional estimators of the boundaries are known to be biased, and test statistics do not have standard limit distributions, at least at certain points in the parameter space. We use a limit of experiments framework to give a characterization of all attainable limit distributions of estimators, when the boundary of interest is identied as the minimum or maximum of a nite number of data features. We nd that certain desirable properties|local asymptotic unbiasedness and regularity|cannot be achieved by any estimator. The problem is closely related to the problem of estimating the minimum of a set of normal means, and examining this simpler problem can suggest alternative procedures that have good risk properties.
We examine challenges to estimation and inference when the objects of interest are nondif-ferenti... more We examine challenges to estimation and inference when the objects of interest are nondif-ferentiable functionals of the underlying data distribution. This situation arises in a number of applications of bounds analysis and moment inequality models, and in recent work on estimating optimal dynamic treatment regimes. Drawing on earlier work relating differentiability to the ex-istence of unbiased and regular estimators, we show that if the target object is not continuously differentiable in the parameters of the data distribution, there exist no locally asymptotically unbiased estimators and no regular estimators. This places strong limits on estimators, bias correction methods, and inference procedures. 1
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