Journal of Econometrics最新文献

This paper provides a method to construct simultaneous confidence bands for quantile functions and quantile effects in nonlinear network and panel models with unobserved two-way effects, strictly exogenous covariates, and possibly discrete outcome variables. The method is based upon projection of simultaneous confidence bands for distribution functions constructed from fixed effects distribution regression estimators. These fixed effects estimators are debiased to deal with the incidental parameter problem. Under asymptotic sequences where both dimensions of the data set grow at the same rate, the confidence bands for the quantile functions and effects have correct joint coverage in large samples. An empirical application to gravity models of trade illustrates the applicability of the methods to network data.

We study nonparametric estimation of density functions for undirected dyadic random variables (i.e., random variables defined for all $n\stackrel{def}{\equiv }\left(\frac{N}{2}\right)$ unordered pairs of agents/nodes in a weighted network of order $N$). These random variables satisfy a local dependence property: any random variables in the network that share one or two indices may be dependent, while those sharing no indices in common are independent. In this setting, we show that density functions may be estimated by an application of the kernel estimation method of Rosenblatt (1956) and Parzen (1962). We suggest an estimate of their asymptotic variances inspired by a combination of (i) Newey’s (1994) method of variance estimation for kernel estimators in the “monadic” setting and (ii) a variance estimator for the (estimated) density of a simple network first suggested by Holland and Leinhardt (1976). More unusual are the rates of convergence and asymptotic (normal) distributions of our dyadic density estimates. Specifically, we show that they converge at the same rate as the (unconditional) dyadic sample mean: the square root of the number, $N$, of nodes. This differs from the results for nonparametric estimation of densities and regression functions for monadic data, which generally have a slower rate of convergence than their corresponding sample mean.

Several families of statistical distributions have been used to model financial data. The four-parameter generalized beta of the second kind (GB2) and five-parameter skewed generalized t (SGT) have been fit to return and log-return data, respectively. We introduce the skewed generalized log-t (SGLT) distribution and note that the GB2 and SGLT share such distributions as the asymmetric log-Laplace (ALL), log-Laplace (LL), and log-normal (LN). We then compare the relative performance of the GB2 and SGLT in modeling the distribution of daily, weekly, and monthly stock return data. We find that the GB2 and SGLT perform similarly and that the three-parameter log-t (LT) distribution is quite robust.

We propose a simple data-driven procedure that exploits heterogeneity in the first-stage correlation between an instrument and an endogenous variable to improve the asymptotic mean squared error (MSE) of instrumental variable estimators. We show that the resulting gains in asymptotic MSE can be quite large in settings where there is substantial heterogeneity in the first-stage parameters. We also show that a naive procedure used in some applied work, which consists of selecting the composition of the sample based on the value of the first-stage $t$-statistic, may cause substantial over-rejection of a null hypothesis on a second-stage parameter. We apply the methods to study (1) the return to schooling using the minimum school leaving age as the exogenous instrument and (2) the effect of local economic conditions on voter turnout using energy supply shocks as the source of identification.

This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample distributional approximation in a unified way, allowing for both boundary and interior evaluation points simultaneously. Using this result, we study the asymptotic efficiency of the estimators, and show that a carefully crafted minimum distance implementation based on “redundant” regressors can lead to efficiency gains. Second, we establish uniform linearizations and strong approximations for the estimators, and employ these results to construct valid confidence bands. Third, we develop extensions to weighted distributions with estimated weights and to local $L^2$ estimation. Finally, we illustrate our methods with two applications in program evaluation: counterfactual density testing, and IV specification and heterogeneity density analysis. Companion software packages in Stata and R are available.

When researchers develop new econometric methods it is common practice to compare the performance of the new methods to those of existing methods in Monte Carlo studies. The credibility of such Monte Carlo studies is often limited because of the discretion the researcher has in choosing the Monte Carlo designs reported. To improve the credibility we propose using a class of generative models that has recently been developed in the machine learning literature, termed Generative Adversarial Networks (GANs) which can be used to systematically generate artificial data that closely mimics existing datasets. Thus, in combination with existing real data sets, GANs can be used to limit the degrees of freedom in Monte Carlo study designs for the researcher, making any comparisons more convincing. In addition, if an applied researcher is concerned with the performance of a particular statistical method on a specific data set (beyond its theoretical properties in large samples), she can use such GANs to assess the performance of the proposed method, e.g. the coverage rate of confidence intervals or the bias of the estimator, using simulated data which closely resembles the exact setting of interest. To illustrate these methods we apply Wasserstein GANs (WGANs) to the estimation of average treatment effects. In this example, we find that $\left(i\right)$ there is not a single estimator that outperforms the others in all three settings, so researchers should tailor their analytic approach to a given setting, $\left(ii\right)$ systematic simulation studies can be helpful for selecting among competing methods in this situation, and $\left(iii\right)$ the generated data closely resemble the actual data.

This paper explores the uniformity of inference for parameters of interest in nonlinear econometric models with endogeneity. Here the notion of uniformity arises because the behavior of estimators of parameters of interest is shown to vary with where either they or nuisance parameters lie in the parameter space. As a result, inference becomes nonstandard in a fashion that is loosely analogous to inference complications found in the unit root and weak instruments literature, as well as the models recently studied in Andrews and Cheng (2012), Chen et al. (2014), Han and McCloskey (2019). Our main illustrative example is the standard sample selection model, where the parameter of interest is the intercept term as in Heckman (1990), Andrews and Schafgans (1998) and Lewbel (2007). We show here there is a discontinuity in the limiting distribution for an estimator of this parameter despite it being uniformly consistent. This discontinuity prevents standard inference procedures from being valid, and motivates the development of new methods, for which we establish asymptotic properties. Finite sample properties of the procedure are explored through a simulation study and an empirical illustration using the Mroz (1987) data set as in Newey, Powell, and Walker (1990).

This paper develops the links between overidentification tests, underidentification tests, score tests and the Cragg and Donald (1993, 1997) and Kleibergen and Paap (2006) rank tests in linear instrumental variable (IV) models. For the structural linear model $y=X\beta +u$, with the endogenous explanatory variables partitioned as $X=\left(x_1{X}_2\right)$, this general framework shows that standard underidentification tests are tests for overidentification in an auxiliary linear model, $x_1=X_2\delta +\varepsilon$, estimated by IV estimation methods using the same instruments as for the original model. This simple structure makes it possible to establish valid robust underidentification tests for linear IV models where these have not been proposed or used before, like clustered dynamic panel data models estimated by GMM. The framework also applies to tests for the rank of general parameter matrices. Invariant rank tests are based on the LIML or continuously updated GMM estimators of both structural and first-stage parameters. This insight leads to the proposal of new two-step invariant asymptotically efficient GMM estimators, and a new iterated GMM estimator that, if it converges, converges to the continuously updated GMM estimator.

The control function approach which employs an instrumental variable excluded from the outcome equation is a very common solution to deal with the problem of endogeneity in nonseparable models. Exclusion restrictions, however, are frequently controversial. We first argue that, in a nonparametric triangular structure typical of the control function literature, one can actually test this exclusion restriction provided the instrument satisfies a local irrelevance condition. Second, we investigate identification without such exclusion restrictions, i.e., if the “instrument” that is independent of the unobservables in the outcome equation also directly affects the outcome variable. In particular, we show that identification of average causal effects can be achieved in the two most common special cases of the general nonseparable model: linear random coefficients models and single index models.