Nonparametric IV estimation of local average treatment effects with covariates

In this paper nonparametric instrumental variable estimation of local average treatment effects (LATE) is extended to incorporate covariates. Estimation of LATE is appealing since identification relies on much weaker assumptions than the identification of average treatment effects in other nonparametric instrumental variable models. Including covariates in the estimation of LATE is necessary when the instrumental variable itself is confounded, such that the IV assumptions are valid only conditional on covariates. Previous approaches to handle covariates in the estimation of LATE relied on parametric or semiparametric methods. In this paper, a nonparametric estimator for the estimation of LATE with covariates is suggested that is root-n asymptotically normal and efficient.     

Nonparametric spatial regression under near-epoch dependence

This paper establishes asymptotic normality and uniform consistency with convergence rates of the local linear estimator for spatial near-epoch dependent (NED) processes. The class of the NED spatial processes covers important spatial processes, including nonlinear autoregressive and infinite moving average random fields, which generally do not satisfy mixing conditions. Apart from accommodating a larger class of dependent processes, the proposed asymptotic theory allows for triangular arrays of heterogeneous random fields located on unevenly spaced lattices and sampled over regions of arbitrary configuration. All these features make the results applicable in a wide range of empirical settings.     

Nonparametric trending regression with cross-sectional dependence

Panel data, whose series length T$T$ is large but whose cross-section size N$N$ need not be, are assumed to have common time trend, of unknown form. The model includes additive, unknown, individual-specific components and allows for spatial or other cross-sectional dependence and/or heteroscedasticity. A simple smoothed nonparametric trend estimate is shown to be dominated by an estimate which exploits availability of cross-sectional data. Asymptotically optimal bandwidth choices are justified for both estimates. Feasible optimal bandwidths, and feasible optimal trend estimates, are asymptotically justified, finite sample performance of the latter being examined in a Monte Carlo study. Potential extensions are discussed.     

Endogeneity in quantile regression models: A control function approach

This paper considers a linear triangular simultaneous equations model with conditional quantile restrictions. The paper adjusts for endogeneity by adopting a control function approach and presents a simple two-step estimator that exploits the partially linear structure of the model. The first step consists of estimation of the residuals of the reduced-form equation for the endogenous explanatory variable. The second step is series estimation of the primary equation with the reduced-form residual included nonparametrically as an additional explanatory variable. This paper imposes no functional form restrictions on the stochastic relationship between the reduced-form residual and the disturbance term in the primary equation conditional on observable explanatory variables. The paper presents regularity conditions for consistency and asymptotic normality of the two-step estimator. In addition, the paper provides some discussions on related estimation methods in the literature.     

Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior

We propose a quasi-Bayesian nonparametric approach to estimating the structural relationship φ$\phi$ among endogenous variables when instruments are available. We show that the posterior distribution of φ$\phi$ is inconsistent in the frequentist sense. We interpret this fact as the ill-posedness of the Bayesian inverse problem defined by the relation that characterizes the structural function φ$\phi$. To solve this problem, we construct a regularized posterior distribution, based on a Tikhonov regularization of the inverse of the marginal variance of the sample, which is justified by a penalized projection argument. This regularized posterior distribution is consistent in the frequentist sense and its mean can be interpreted as the mean of the exact posterior distribution resulting from a Gaussian prior distribution with a shrinking covariance operator.     

Measuring correlations of integrated but not cointegrated variables: A semiparametric approach

Many macroeconomic and financial variables are integrated of order one (or I(1)) processes and are correlated with each other but not necessarily cointegrated. In this paper, we propose to use a semiparametric varying coefficient approach to model/capture such correlations. We propose two consistent estimators to study the dependence relationship among some integrated but not cointegrated time series variables. Simulations are used to examine the finite sample performances of the proposed estimators.     

Partial maximum likelihood estimation of spatial probit models

This paper analyzes spatial Probit models for cross sectional dependent data in a binary choice context. Observations are divided by pairwise groups and bivariate normal distributions are specified within each group. Partial maximum likelihood estimators are introduced and they are shown to be consistent and asymptotically normal under some regularity conditions. Consistent covariance matrix estimators are also provided. Estimates of average partial effects can also be obtained once we characterize the conditional distribution of the latent error. Finally, a simulation study shows the advantages of our new estimation procedure in this setting. Our proposed partial maximum likelihood estimators are shown to be more efficient than the generalized method of moments counterparts.     

A family of empirical likelihood functions and estimators for the binary response model

The minimum discrimination information principle is used to identify an appropriate parametric family of probability distributions and the corresponding maximum likelihood estimators for binary response models. Estimators in the family subsume the conventional logit model and form the basis for a set of parametric estimation alternatives with the usual asymptotic properties. Sampling experiments are used to assess finite sample performance.     

On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood

A number of information-theoretic alternatives to GMM have recently been proposed in the literature. For practical use and general interpretation, the main drawback of these alternatives, particularly in the case of conditional moment restrictions, is that they give up the computational and interpretational simplicity of quadratic optimization. The main contribution of this paper is to analyze the informational content of estimating equations within the unified framework of Chi-square distance. Improved inference by control variables, closed form formulae for implied probabilities and information-theoretic interpretations of continuously updated GMM are discussed in the two cases of unconditional and conditional moment restrictions.     

Nonparametric estimation and inference about the overlap of two distributions

This paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques. This quantity has been proposed as a measure of economic polarization between two groups, Anderson (2004) and Anderson et al. (2010). In ecology it has been used to measure the overlap of species. We give the asymptotic distribution theory of our estimator, which in some cases of practical relevance is nonstandard due to a boundary value problem. We also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider. We investigate the finite sample properties of our methods by simulation methods. We give an application to the study of polarization within China in recent years using household survey data from two provinces taken in 1987 and 2001. We find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space.     

Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models

Two classes of semiparametric diffusion models are considered, where either the drift or the diffusion term is parameterized, while the other term is left unspecified. We propose a pseudo-maximum likelihood estimator (PMLE) of the parametric component that maximizes the likelihood with a preliminary estimator of the unspecified term plugged in. It is demonstrated how models and estimators can be used in a two-step specification testing strategy of semiparametric and fully parametric models, and shown that approximate/simulated versions of the PMLE inherit the properties of the actual but infeasible estimator. A simulation study investigates the finite sample performance of the PMLE.     

Testing for non-nested conditional moment restrictions using unconditional empirical likelihood

We propose non-nested hypothesis tests for conditional moment restriction models based on the method of generalized empirical likelihood (GEL). By utilizing the implied GEL probabilities from a sequence of unconditional moment restrictions that contains equivalent information of the conditional moment restrictions, we construct Kolmogorov–Smirnov and Cramér–von Mises type moment encompassing tests. Advantages of our tests over Otsu and Whang’s (2011) tests are: (i) they are free from smoothing parameters, (ii) they can be applied to weakly dependent data, and (iii) they allow non-smooth moment functions. We derive the null distributions, validity of a bootstrap procedure, and local and global power properties of our tests. The simulation results show that our tests have reasonable size and power performance in finite samples.     

Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data

We show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model. Under the approximating model, simple sufficient statistics exist for the subject-specific parameters introduced to capture the unobserved heterogeneity between subjects. The latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors. By conditioning on the sufficient statistics, we derive a pseudo conditional likelihood estimator of the structural parameters of the dynamic logit model, which is simple to compute. Asymptotic properties of this estimator are studied in detail. Simulation results show that the estimator is competitive in terms of efficiency with estimators recently proposed in the econometric literature.     

Adaptive estimation of the dynamics of a discrete time stochastic volatility model

This paper is concerned with the discrete time stochastic volatility model _Yi=exp(_Xi/2)_ηi$Y_i=exp(X_i/2){\eta }_i$, _Xi+1=b(_Xi)+σ(_Xi)_ξi+1$X_{i+1}=b\left(X_i\right)+\sigma \left(X_i\right){\xi }_{i+1}$, where only (_Yi)$\left(Y_i\right)$ is observed. The model is rewritten as a particular hidden model: _Zi=_Xi+_εi$Z_i=X_i+{\epsilon }_i$, _Xi+1=b(_Xi)+σ(_Xi)_ξi+1$X_{i+1}=b\left(X_i\right)+\sigma \left(X_i\right){\xi }_{i+1}$, where (_ξi)$\left({\xi }_i\right)$ and (_εi)$\left({\epsilon }_i\right)$ are independent sequences of i.i.d. noise. Moreover, the sequences (_Xi)$\left(X_i\right)$ and (_εi)$\left({\epsilon }_i\right)$ are independent and the distribution of ε$\epsilon$ is known. Then, our aim is to estimate the functions b$b$ and σ²${\sigma }^2$ when only observations _Z1,…,_Zn$Z_1,\dots ,Z_n$ are available. We propose to estimate bf$bf$ and (b²+σ²)f$(b^2+{\sigma }^2)f$ and study the integrated mean square error of projection estimators of these functions on automatically selected projection spaces. By ratio strategy, estimators of b$b$ and σ²${\sigma }^2$ are then deduced. The mean square risk of the resulting estimators are studied and their rates are discussed. Lastly, simulation experiments are provided: constants in the penalty functions defining the estimators are calibrated and the quality of the estimators is checked on several examples.     

Nonparametric identification and estimation of sample selection models under symmetry

Under a conditional mean restriction Das et al. (2003) considered nonparametric estimation of sample selection models. However, their method can only identify the outcome regression function up to a constant. In this paper we strengthen the conditional mean restriction to a symmetry restriction under which selection biases due to selection on unobservables can be eliminated through proper matching of propensity scores; consequently we are able to identify and obtain consistent estimators for the average treatment effects and the structural regression functions. The results from a simulation study suggest that our estimators perform satisfactorily.     

Nonparametric transfer function models

In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between ‘input’ and ‘output’ time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modeling the correlation in the noise, the transfer function can be estimated more efficiently. The parsimonious ARMA structure improves the estimation efficiency in finite samples. The asymptotic properties of the estimators are investigated. The finite-sample properties are illustrated through simulations and one empirical example.