存在遗漏变量时的内生性研究

存在遗漏变量时回归系数的估计是计量经济学的一个重要内容。本文讨论单方程计量经济模型中随机解释变量的内生性,指出了目前的计量经济理论所存在的问题,提出了普通最小二乘估计一致性判别的新方法,并证明了存在遗漏变量情况下的普通最小二乘估计仍是一致估计。     

The endogeneity bias in the relation between cost-of-debt capital and corporate disclosure policy

Abstract

The purpose of this paper is twofold. First, we provide a discussion of the problems associated with endogeneity in empirical accounting research. We emphasize problems arising when endogeneity is caused by (1) unobservable firm-specific factors and (2) omitted variables, and discuss the merits and drawbacks of using panel data techniques to address these causes. Second, we investigate the magnitude of endogeneity bias in Ordinary Least Squares (OLS) regressions of cost-of-debt capital on firm disclosure policy. We document how including a set of variables which theory suggests to be related with both cost-of-debt capital and disclosure and using fixed effects estimation in a panel data-set reduces the endogeneity bias and produces consistent results. This analysis reveals that the effect of disclosure policy on cost-of-debt capital is 200% higher than what is found in OLS estimation. Finally, we provide direct evidence that disclosure is impacted by unobservable firm-specific factors that are also correlated with cost of capital.     

Asymptotic properties of the efficient estimators for cointegrating regression models with serially dependent errors

In this paper, we analytically investigate three efficient estimators for cointegrating regression models: Phillips and Hansen’s [Phillips, P.C.B., Hansen, B.E., 1990. Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies 57, 99–125] fully modified OLS estimator, Park’s [Park, J.Y., 1992. Canonical cointegrating regressions. Econometrica 60, 119–143] canonical cointegrating regression estimator, and Saikkonen’s [Saikkonen, P., 1991. Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7, 1–21] dynamic OLS estimator. We consider the case where the regression errors are moderately serially correlated and the AR coefficient in the regression errors approaches 1 at a rate slower than 1/T$1/T$, where T$T$ represents the sample size. We derive the limiting distributions of the efficient estimators under this system and find that they depend on the approaching rate of the AR coefficient. If the rate is slow enough, efficiency is established for the three estimators; however, if the approaching rate is relatively faster, the estimators will have the same limiting distribution as the OLS estimator. For the intermediate case, the second-order bias of the OLS estimator is partially eliminated by the efficient methods. This result explains why, in finite samples, the effect of the efficient methods diminishes as the serial correlation in the regression errors becomes stronger. We also propose to modify the existing efficient estimators in order to eliminate the second-order bias, which possibly remains in the efficient estimators. Using Monte Carlo simulations, we demonstrate that our modification is effective when the regression errors are moderately serially correlated and the simultaneous correlation is relatively strong.     

A study of estimator densities and performance under misspecification

The exact density functions of the OLS and 2SLS estimators when exogenous variables are wrongly excluded from the equation being estimated, where two endogenous variables appear in the equation of interest, are presented and tabulated. Misspecification does not appear to alter the relative concentrations of OLS and 2SLS — OLS is always more concentrated — but does change the relative biases with the result that under misspecification OLS may indeed be the superior estimation technique. In addition, misspecification can substantially increase the concentration of both estimators, as well as reducing their biases, therebyyielding an apparent improvement in estimator performance.     

Jackknife instrumental variables estimation

Two-stage-least-squares (2SLS) estimates are biased towards the probability limit of OLS estimates. This bias grows with the degree of over-identification and can generate highly misleading results. In this paper we propose two simple alternatives to 2SLS and limited-information-maximum-likelihood (LIML) estimators for models with more instruments than endogenous regressors. These estimators can be interpreted as instrumental variables procedures using an instrument that is independent of disturbances even in finite samples. Independence is achieved by using a ‘leave-one-out’ jackknife-type fitted value in place of the usual first stage equation. The new estimators are first-order equivalent to 2SLS but with finite-sample properties superior, in terms of bias and coverage rate of confidence intervals, compared to those of 2SLS and similar to those of LIML, when there are many instruments. Copyright © 1999 John Wiley & Sons, Ltd.     

Omitted variables,variability of estimated parameters and the appearance of autocorrelated disturbances

This paper shows that in a standard regression model with omitted variables, the OLS formula for the estimated variance matrix of the regression coefficients is more likely to underestimate the appropriate criterion of estimator reliability which is the Mean Square Errors matrix. Using examples of two and three regressor models, we show that overestimation, though possible, occurs in rather special cases. Throughout, our analysis is contrasted with that of Chaudhuri (1977) and clarifies some ambiguities of that paper. Finally, we disagree with Chaudhuri who distinguishes between the corresponding coefficients in the correct and the misspecified models. This distinction is inappropriate and leads to a misplaced criticism of some GLS variants when errors are serially correlated. A first-order Markov process is an inexact representation of serial correlation which is due to omitted regressors.     

Examining bias in estimators of linear rational expectations models under misspecification

Most rational expectations models involve equations in which the dependent variable is a function of its lags and its expected future value. We investigate the asymptotic bias of generalized method of moment (GMM) and maximum likelihood (ML) estimators in such models under misspecification. We consider several misspecifications, and focus more specifically on the case of omitted dynamics in the dependent variable. In a stylized DGP, we derive analytically the asymptotic biases of these estimators. We establish that in many cases of interest the two estimators of the degree of forward-lookingness are asymptotically biased in opposite direction with respect to the true value of the parameter. We also propose a quasi-Hausman test of misspecification based on the difference between the GMM and ML estimators. Using Monte-Carlo simulations, we show that the ordering and direction of the estimators still hold in a more realistic New Keynesian macroeconomic model. In this set-up, misspecification is in general found to be more harmful to GMM than to ML estimators.     

趋势成分引起的虚假回归问题解决方法研究

本文研究了由序列中趋势成分引起的虚假回归问题的解决方法。发现在模型设定式中加入趋势变量,并考虑趋势存在结构突变的情况,再根据残差是否存在自相关进行可行广义最小二乘（FGLS）或普通最小二乘（OLS）估计,可以有效解决趋势成分引起的虚假回归问题。通过理论分析表明,采用本文中的估计方法,所得检验两序列是否为虚假相关的t统计量渐近服从标准正态分布或与标准正态非常接近的分布。Monte Carlo模拟证实了该方法的有效性。最后以Yule(1926)中两高度虚假相关的时间序列为例,佐证文中结论。     

Three Factors to Signal Non‐Response Bias With Applications to Categorical Auxiliary Variables

Non‐response causes bias in survey estimates. The unknown bias can be reduced, for example as in this paper by the use of a calibration estimator built on powerful auxiliary information. Still, some bias will always remain. A bias reduction indicator is proposed and expressed as a product of three factors reflecting familiar statistical ideas. These factors provide a useful perspective on the components that constitute non‐response bias in estimates. To illustrate the indicator, we focus on the important case with information defined by one or more categorical auxiliary variables, each expressed by two or more properties or traits. Together, the auxiliary variables may represent a large number of traits, more or less important for bias reduction. An examination of the three factors of the bias reduction indicator brings the insight that the ultimate auxiliary vector for calibration need not or should not contain all available traits; some are unimportant or detrimental to bias reduction. The question becomes one of selection of traits, not of complete auxiliary variables. Empirical examples are given, and a stepwise procedure for selecting important traits is proposed.     

Methods for multicountry studies of corporate governance: Evidence from the BRIKT countries

We discuss empirical challenges in multicountry studies of the effects of firm-level corporate governance on firm value, focusing on emerging markets. We assess the severe data, “construct validity”, and endogeneity issues in these studies, propose methods to respond to those issues, and apply those methods to a study of five major emerging markets—Brazil, India, Korea, Russia, and Turkey. We develop unique time-series datasets on governance in each country. We address construct validity by building country-specific indices which reflect local norms and institutions. These similar-but-not-identical indices predict firm market value in each country, and when pooled across countries, in firm fixed-effects (FE) and random-effects (RE) regressions. In contrast, a “common index”, which uses the same elements in each country, has no predictive power in FE regressions. For the country-specific and pooled indices, FE and RE coefficients on governance are generally lower than in pooled OLS regressions, and coefficients with extensive covariates are generally lower than with limited covariates. These results confirm the value of using FE or RE with extensive covariates to reduce omitted variable bias. We develop lower bounds on our estimates which reflect potential remaining omitted variable bias.     

Instrumental variable estimation in the presence of many moment conditions

This paper develops shrinkage methods for addressing the “many instruments” problem in the context of instrumental variable estimation. It has been observed that instrumental variable estimators may behave poorly if the number of instruments is large. This problem can be addressed by shrinking the influence of a subset of instrumental variables. The procedure can be understood as a two-step process of shrinking some of the OLS coefficient estimates from the regression of the endogenous variables on the instruments, then using the predicted values of the endogenous variables (based on the shrunk coefficient estimates) as the instruments. The shrinkage parameter is chosen to minimize the asymptotic mean square error. The optimal shrinkage parameter has a closed form, which makes it easy to implement. A Monte Carlo study shows that the shrinkage method works well and performs better in many situations than do existing instrument selection procedures.     

Specification error in multinomial logit models: Analysis of the omitted variable bias

In this article, we analyze the omitted variable bias problem in the multinomial logistic probability model. Sufficient, as well as necessary, conditions under which the omitted variable will not create asymptotically biased coefficient estimates for the included variables are derived. Conditional on the response variable, if the omitted explanatory and the included explanatory variable are independent, the bias will not occur. Bias will occur if the omitted relevant variable is independent with the included explanatory variable. The coefficient of the included variable plays an important role in the direction of the bias.     

Fixed effects estimation of structural parameters and marginal effects in panel probit models

Fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper, I characterize the leading term of a large-T expansion of the bias of the MLE and estimators of average marginal effects in parametric fixed effects panel binary choice models. For probit index coefficients, the former term is proportional to the true value of the coefficients being estimated. This result allows me to derive a lower bound for the bias of the MLE. I then show that the resulting fixed effects estimates of ratios of coefficients and average marginal effects exhibit no bias in the absence of heterogeneity and negligible bias for a wide variety of distributions of regressors and individual effects in the presence of heterogeneity. I subsequently propose new bias-corrected estimators of index coefficients and marginal effects with improved finite sample properties for linear and nonlinear models with predetermined regressors.     

The finite-sample effects of VAR dimensions on OLS bias,OLS variance,and minimum MSE estimators

Vector autoregressions (VARs) are important tools in time series analysis. However, relatively little is known about the finite-sample behaviour of parameter estimators. We address this issue, by investigating ordinary least squares (OLS) estimators given a data generating process that is a purely nonstationary first-order VAR. Specifically, we use Monte Carlo simulation and numerical optimisation to derive response surfaces for OLS bias and variance, in terms of VAR dimensions, given correct specification and several types of over-parameterisation of the model: we include a constant, and a constant and trend, and introduce excess lags. We then examine the correction factors that are required for the least squares estimator to attain the minimum mean squared error (MSE). Our results improve and extend one of the main finite-sample multivariate analytical bias results of Abadir, Hadri and Tzavalis [Abadir, K.M., Hadri, K., Tzavalis, E., 1999. The influence of VAR dimensions on estimator biases. Econometrica 67, 163–181], generalise the univariate variance and MSE findings of Abadir [Abadir, K.M., 1995. Unbiased estimation as a solution to testing for random walks. Economics Letters 47, 263–268] to the multivariate setting, and complement various asymptotic studies.     

Regression analysis with dichotomous regressors and misclassification

We discuss a regression model in which the regressors are dummy variables. The basic idea is that the observation units can be assigned to some well-defined combination of treatments, corresponding to the dummy variables. This assignment can not be done without some error, i.e. misclassification can play a role. This situation is analogous to regression with errors in variables. It is well-known that in these situations identification of the parameters is a prominent problem. We will first show that, in our case, the parameters are not identified by the first two moments but can be identified by the likelihood. Then we analyze two estimators. The first is a moment estimator involving moments up to the third order, and the second is a maximum likelihood estimator calculated with the help of the EM algorithm. Both estimators are evaluated on the basis of a small Monte Carlo experiment.     

Model averaging based on James–Stein estimators

Existing model averaging methods are generally based on ordinary least squares (OLS) estimators. However, it is well known that the James–Stein (JS) estimator dominates the OLS estimator under quadratic loss, provided that the dimension of coefficient is larger than two. Thus, we focus on model averaging based on JS estimators instead of OLS estimators. We develop a weight choice method and prove its asymptotic optimality. A simulation experiment shows promising results for the proposed model average estimator.     

Alternative approximations of the bias and MSE of the IV estimator under weak identification with an application to bias correction

We provide analytical formulae for the asymptotic bias (ABIAS) and mean-squared error (AMSE) of the IV estimator, and obtain approximations thereof based on an asymptotic scheme which essentially requires the expectation of the first stage F-statistic to converge to a finite (possibly small) positive limit as the number of instruments approaches infinity. Our analytical formulae can be viewed as generalizing the bias and MSE results of [Richardson and Wu 1971. A note on the comparison of ordinary and two-stage least squares estimators. Econometrica 39, 973–982] to the case with nonnormal errors and stochastic instruments. Our approximations are shown to compare favorably with approximations due to [Morimune 1983. Approximate distributions of k$k$-class estimators when the degree of overidentifiability is large compared with the sample size. Econometrica 51, 821–841] and [Donald and Newey 2001. Choosing the number of instruments. Econometrica 69, 1161–1191], particularly when the instruments are weak. We also construct consistent estimators for the ABIAS and AMSE, and we use these to further construct a number of bias corrected OLS and IV estimators, the properties of which are examined both analytically and via a series of Monte Carlo experiments.     

Olley and Pakes‐style Production Function Estimators with Firm Fixed Effects

We show that control function estimators (CFEs) of the firm production function, such as Olley–Pakes, may be biased when productivity evolves with a firm‐specific intercept, in which case the correctly specified control function will contain a firm‐specific term, omitted in the standard CFEs. We develop an estimator that is free from this bias by introducing firm fixed effects in the control function. Applying our estimator to the data, we find that it outperforms the existing CFEs in terms of capturing persistent unobserved heterogeneity in firm productivity. Our estimator involves minimal modification to the standard CFE procedures and can be easily implemented using common statistical software.     

Fixed effects instrumental variables estimation in correlated random coefficient panel data models

We provide a set of conditions sufficient for consistency of a general class of fixed effects instrumental variables (FE-IV) estimators in the context of a correlated random coefficient panel data model, where one ignores the presence of individual-specific slopes. We discuss cases where the assumptions are met and violated. Monte Carlo simulations verify that the FE-IV estimator of the population averaged effect performs notably better than other standard estimators, provided a full set of period dummies is included. We also propose a simple test of selection bias in unbalanced panels when we suspect the slopes may vary by individual.