A locally linear estimation of regression discontinuity

In this paper, we propose a locally linear estimation of a regression discontinuity model. The proposed estimator is applicable to evaluation of the effectiveness of the program treatment, and it improves upon the existing literature by providing not just the treatment effect at discontinuity but also insight of the treatment effect on those near discontinuity. Under some familiar conditions, we establish the consistency and asymptotic normality of the proposed estimator. We also provide an easy to compute consistent covariance matrix.     

SEMINONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION OF CONDITIONAL MOMENT RESTRICTION MODELS*

This article studies estimation of a conditional moment restriction model with the seminonparametric maximum likelihood approach proposed by Gallant and Nychka (Econometrica 55 (March 1987), 363–90). Under some sufficient conditions, we show that the estimator of the finite dimensional parameter θ is asymptotically normally distributed and attains the semiparametric efficiency bound and that the estimator of the density function is consistent under L₂ norm. Some results on the convergence rate of the estimated density function are derived. An easy to compute covariance matrix for the asymptotic covariance of the θ estimator is presented.     

A Tobit-type estimator for the censored Poisson regression model

The Poisson counterpart to the Tobit model is presented. Formulae for the gradient and Hessian of the relevant log-likelihood function are given and incorporated into a Newton-Raphson optimization algorithm. The asymptotic covariance matrix of the estimator is detailed. As an illustration, the NR algorithm is applied to a model of individual shopping behavior.     

Economic benefits of using realized covariance forecasts in risk-based portfolios

This article examines the economic benefit of using the realized covariance matrix forecasts, for constructing the risk-based portfolios. We use the two-scale realized covariance estimator (TSC), the jump robust two-scale realized covariance estimator (RTSC) and the realized bipower covariance estimator (BPC), to forecast the daily realized covariance matrix. Using these covariance matrix forecasts, we implement three risk-based portfolios: the global minimum variance portfolio, the equal risk contribution portfolio and the most diversified portfolio. There is evidence that the portfolio performance improves by using TSC or RTSC estimators as compared to the daily-returns-based estimator. The performance gains are robust to the choice of risk-based portfolio strategy, the degree of investor’s relative risk-aversion, the market conditions and the choice of time intervals.     

Maximum-likelihood estimation of misspecified models

Misspecified models occur frequently in econometric practice. It is therefore important to study the sampling distribution of maximum-likelihood estimators of parameters of misspecified models. This note exhibits the asymptotic covariance matrix of the ML estimator of a misspecified model. It points out that the expression for this matrix given by White is incorrect except for the very special case, rarely occuring in econometrics, that each observation is independent and identically distributed. An illustration using the standard linear regression model is provided.     

Efficient estimation of partially linear varying coefficient models

In this paper, we consider the problem of estimating a semiparametric partially linear varying coefficient model. We derive the semiparametric efficiency bound for the asymptotic variance of the finite-dimensional parameter estimator. We also propose an efficient estimator for estimating the finite-dimensional parameter of the model. Simulation results show substantial efficiency gain of our proposed estimator over a conventional estimator as considered in Ahmad et al. (2005).     

Nonparametric regression estimation with general parametric error covariance: a more efficient two-step estimator

Recently Martins-Filho and Yao (J Multivar Anal 100:309–333, 2009) have proposed a two-step estimator of nonparametric regression function with parametric error covariance and demonstrate that it is more efficient than the usual LLE. In the present paper we demonstrate that MY’s estimator can be further improved. First, we extend MY’s estimator to the multivariate case, and also establish the asymptotic theorem for the slope estimators; second, we propose a more efficient two-step estimator for nonparametric regression function with general parametric error covariance, and develop the corresponding asymptotic theorems. Monte Carlo study shows the relative efficiency loss of MY’s estimator in comparison with our estimator in nonparametric regression with either AR(2) errors or heteroskedastic errors. Finally, in an empirical study we apply the proposed estimator to estimate the public capital productivity to illustrate its performance in a real data setting.     

A THREE‐STEP PROCEDURE FOR ESTIMATING AND TESTING COINTEGRATED ARMAX MODELS*

To deal with a variety of inferential problems on non‐stationary cointegrated time series, this paper proposes a computationally feasible method based on the Whittle likelihood and examines its performance. For the empirical application of our method, the paper investigates three sets of Japanese and US monetary and financial time‐series data. To evaluate the p‐value of the likelihood ratio statistic, we propose an approximation procedure based on the gamma distribution and the accompanying Laguerre expansion for reducing the computational burden. We also provide a numerical procedure for the asymptotic covariance matrix of the Whittle estimator.     

On the Inconsistency of Instrumental Variables Estimators for the Coefficients of Certain Dummy Variables

In this paper we consider the asymptotic properties of the Instrumental Variables (IV) estimator of the parameters in a linear regression model with some random regressors, and other regressors that are dummy variables. The latter have the special property that the number of non-zero values is fixed, and does not increase with the sample size. We prove that the IV estimator of the coefficient vector for the dummy variables is inconsistent, while that for the other regressors is weakly consistent under standard assumptions. However, the usual estimator for the asymptotic covariance matrix of the I.V. estimator for all of the coefficients retains its usual consistency. The t-test statistics for the dummy variable coefficients are still asymptotically standard normal, despite the inconsistency of the associated IV coefficient estimator. These results extend the earlier results of Hendry and Santos (Oxf Bull Econ Stat 67:571–595, 2005), which relate to a fixed-regressor model, in which the dummy variables are non-zero for just a single observation, and OLS estimation is used.

     

Estimation of Structural Nonlinear Errors‐in‐Varibles Models by Simulated Least‐Squares Method

This article proposes a simulation approach to obtain least‐squares or generalized least‐squares estimators of structural nonlinear errors‐in‐variables models. The proposed estimators are computationally attractive because they do not need numerical integration nor huge numbers of simulations per observable. In addition, the asymptotic covariance matrix of the estimator has a simple decomposition that may be used to guide selection of appropriate simulation sizes. The method is also useful for models with missing data or imperfect surrogate covariates, where application of conventional least‐squares and maximum‐likelihood methods is restricted by numerical multidimensional integrations.     

Inter-Industry Wage Differentials in Greece: Evidence from Quantile Regression Analysis

Using a consistent estimator of the covariance matrix of the asymptotic distribution of the quantile regression estimator with intra-cluster correlation of the error terms, the paper investigates whether and to what extent inter-industry wage differentials derive from worker heterogeneity in the form of unobserved quality. To conduct this study, we pioneer in utilizing a unique data set, the European Union Structure of Earnings Survey for Greece, which follows a two-stage random sampling approach of employees clustered within firms. Data refer to 2010 when the first elements of the economic adjustment programme to deal with the chronic deficiencies of the Greek economy and restore sustainable public finances, competitiveness and set the foundation for long-term growth, gained visibility. Results point to high wage dispersion across industries at the mean of the conditional wage distribution, even after controlling for personal and workplace characteristics. However, evidence for the unobserved heterogeneity hypothesis is rather scant. Therefore, there is room for efficiency wage or rent-sharing theories in accounting for a large part of inter-industry wage differentials tentatively implying that firm heterogeneity in the ability to pay matters more than employee unobservable attributes in the wage determination process.     

CONSISTENT ESTIMATION OF A LIMITING COVARIANCE MATRIX

This paper provides a consistent and positive semi-definite estimator of the limiting covariance matrix of a nonlinear instrumental variable estimator for a nonlinear simultaneous equation model with selectivity studied in Sapra (1989).     

The jackknife and heteroskedasticity: Consistent variance estimation for regression models

The weighted jackknife leads to a consistent estimator for the covariance matrix of the least squares estimators of the parameters in a regression model. In this note we show that this estimator has a simple relationship to the White estimator which is widely used in econometrics.     

Forecast of realized covariance matrix based on asymptotic distribution of the LU decomposition with an application for balancing minimum variance portfolio

We derive the asymptotic distribution for the LU decomposition, that is, the Cholesky decomposition, of realized covariance matrix. Distributional properties are combined with an existing generalized heterogeneous autoregressive (GHAR) method for forecasting realized covariance matrix, which will be referred to as a generalized HARQ (GHARQ) method. An out-of-sample forecast comparison of a real data set shows that the proposed GHARQ method outperforms other existing methods in terms of optimizing the variances of portfolios.     

The properties of some covariance matrix estimators in linear models with AR(1) errors

A Monte Carlo study is used to demonstrate how poor some traditional covariance matrix estimators can be in linear models with AR(1) errors. It is also shown that a second-order approximation suggested recently by Ullah et al. (1983) does not lead to a more accurate covariance matrix estimator.     

A comparison of bias approximations for the two-stage least squares (2SLS) estimator

We consider the bias of the two-stage least squares (2SLS) estimator in linear instrumental variable regression with only one endogenous regressor. By using asymptotic expansion techniques, we approximate the 2SLS coefficient estimation bias under various scenarios regarding the number and strength of instruments.     

Hypothesis testing in regression models with AR(1) errors and a lagged dependent variable: Bootstrapping and artificial regression compared

Serially correlated errors in dynamic models render the standard conditional estimator of the covariance matrix inconsistent. A Monte Carlo experiment confirms that the downward bias in the conventional variance estimator also exists in small samples. The results favour a consistent estimator based on an artificial regression (suggested by Davidson and Mackinnon) over bootstrapping the distribution of parameter estimates.     

Hierarchically spatial autoregressive and moving average error model

This paper considers a hierarchically spatial autoregressive and moving average error (HSEARMA) model. This model captures the spatially autoregressive and moving average error correlation, the county-level random effects, and the district-level random effects nested within each county. We propose optimal generalized method of moments (GMM) estimators for the spatial error correlation coefficient and the error components' variances terms, as well as a feasible generalized least squares (FGLS) estimator for the regression parameter vector. Further, we prove consistency of the GMM estimator and establish the asymptotic distribution of the FGLS estimator. A finite-scale Monte Carlo simulation is conducted to demonstrate the good finite sample performances of our GMM-FGLS estimators.     

Heteroskedasticity testing through a comparison of Wald statistics

This paper shows that a test for heteroskedasticity within the context of classical linear regression can be based on the difference between Wald statistics in heteroskedasticity-robust and nonrobust forms. The test is asymptotically distributed under the null hypothesis of homoskedasticity as chi-squared with one degree of freedom. The power of the test is sensitive to the choice of parametric restriction used by the Wald statistics, so the supremum of a range of individual test statistics is proposed. Two versions of a supremum-based test are considered: the first version does not have a known asymptotic null distribution, so the bootstrap is employed to approximate its empirical distribution. The second version has a known asymptotic distribution and, in some cases, is asymptotically pivotal under the null. A simulation study illustrates the use and finite-sample performance of both versions of the test. In this study, the bootstrap is found to provide better size control than asymptotic critical values, namely with heavy-tailed, asymmetric distributions of the covariates. In addition, the use of well-known modifications of the heteroskedasticity consistent covariance matrix estimator of OLS coefficients is also found to benefit the tests’ overall behaviour.     

Trend instrumental variable regression with an application to the US New Keynesian Phillips Curve

When a linear model suffers from endogeneity, a conventional solution is to use external instrumental variables. Sometimes, however, there are either no suitable external IVs or they are of poor quality. This paper constructs an internal instrumental variable from the time trend in the endogenous regressor without using any external IVs. We show that under some mild conditions this new trend IV estimator has desirable asymptotic properties, and also provide a robust Durbin-Wu-Hausman specification test to demonstrate the necessity of the IV method. Monte Carlo simulations show that the estimator and the test have good finite sample performance. In the end, we apply the trend IV estimator to the US New Keynesian Phillips Curve and find that it works as well as the usual external IVs in the literature.