A new class of limited-information estimators for simultaneous equations systems

The TSLS and LIML estimators are evaluated by means of a new class of limited-information estimators, the so-called Ω-class estimators. Under certain assumptions the Ω-class estimator is a maximun-likelihood estimator. These assumptions are superfluous, however, if we view the Ω-class as a class of minimun-distance estimators; all the members are shown to be consistent under general conditions. Besides the TSLS and the LIML estimators some other interesting members are introduced, and it is shown that, under certain conditions, the Ω-class estimators are weighted averages of different TSLS estimators. The use of TSLS in small samples is criticized; an alternative estimator is proposed.     

Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system

In this paper asymptotic expansions are derived for the density functions of the TSLS and LIML estimates of coefficients in a simultaneous equation system when the sample size increases and the effect of the exogenous variables increases along the sample size. These approximations are used to compare the asymptotic moments of the TSLS and LIML estimates and the concentration of probability around the true value of the estimates.     

Finite sample evidence of IV estimators under weak instruments

We present finite sample evidence on different IV estimators available for linear models under weak instruments; explore the application of the bootstrap as a bias reduction technique to attenuate their finite sample bias; and employ three empirical applications to illustrate and provide insights into the relative performance of the estimators in practice. Our evidence indicates that the random‐effects quasi‐maximum likelihood estimator outperforms alternative estimators in terms of median point estimates and coverage rates, followed by the bootstrap bias‐corrected version of LIML and LIML. However, our results also confirm the difficulty of obtaining reliable point estimates in models with weak identification and moderate‐size samples. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Improving the performance of random coefficients demand models: The role of optimal instruments

We shed new light on the performance of Berry, Levinsohn and Pakes’ (1995) GMM estimator of the aggregate random coefficient logit model. Based on an extensive Monte Carlo study, we show that the use of Chamberlain’s (1987) optimal instruments overcomes many problems that have recently been documented with standard, non-optimal instruments. Optimal instruments reduce small sample bias, but they prove even more powerful in increasing the estimator’s efficiency and stability. We consider a wide variety of data-generating processes and an empirical application to the automobile market. We also consider the gains of other recent methodological advances when combined with optimal instruments.     

On finite sample properties of alternative estimators of coefficients in a structural equation with many instruments

We compare four different estimation methods for the coefficients of a linear structural equation with instrumental variables. As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the semi-parametric estimation methods we consider the maximum empirical likelihood (MEL) estimator and the generalized method of moments (GMM) (or the estimating equation) estimator. Tables and figures of the distribution functions of four estimators are given for enough values of the parameters to cover most linear models of interest and we include some heteroscedastic cases and nonlinear cases. We have found that the LIML estimator has good performance in terms of the bounded loss functions and probabilities when the number of instruments is large, that is, the micro-econometric models with “many instruments” in the terminology of recent econometric literature.     

The case against JIVE

We perform an extensive series of Monte Carlo experiments to compare the performance of two variants of the ‘jackknife instrumental variables estimator’, or JIVE, with that of the more familiar 2SLS and LIML estimators. We find no evidence to suggest that JIVE should ever be used. It is always more dispersed than 2SLS, often very much so, and it is almost always inferior to LIML in all respects. Interestingly, JIVE seems to perform particularly badly when the instruments are weak. Copyright © 2006 John Wiley & Sons, Ltd.     

Weak‐instrument robust inference for two‐sample instrumental variables regression

Instrumental variable (IV) methods for regression are well established. More recently, methods have been developed for statistical inference when the instruments are weakly correlated with the endogenous regressor, so that estimators are biased and no longer asymptotically normally distributed. This paper extends such inference to the case where two separate samples are used to implement instrumental variables estimation. We also relax the restrictive assumptions of homoskedastic error structure and equal moments of exogenous covariates across two samples commonly employed in the two‐sample IV literature for strong IV inference. Monte Carlo experiments show good size properties of the proposed tests regardless of the strength of the instruments. We apply the proposed methods to two seminal empirical studies that adopt the two‐sample IV framework.     

Partial rank estimation of duration models with general forms of censoring

In this paper we propose estimators for the regression coefficients in censored duration models which are distribution free, impose no parametric specification on the baseline hazard function, and can accommodate general forms of censoring. The estimators are shown to have desirable asymptotic properties and Monte Carlo simulations demonstrate good finite sample performance. Among the data features the new estimators can accommodate are covariate-dependent censoring, double censoring, and fixed (individual or group specific) effects. We also examine the behavior of the estimator in an empirical illustration.     

The numerical values of some key parameters in econometric models

In the case of two endogenous variables, exogenous predetermined variables, and normally distributed disturbances, the distributions of the Two-Stage Least Squares (TSLS) and Limited Information Maximum Likelihood (LIML) estimators can be compared on the basis of three key parameters: the non-centrality parameter, a standardization of the structural coefficient, and the number of excluded exogenous variables. In this paper the values of these parameters are estimated in eleven structural equations from various actual econometric models. The distribution functions of the normalized TSLS and LIML estimators are given for the first two key parameters set at approximately their trimmed means, and the third at its median.     

Consistent inference in fixed-effects stochastic frontier models

The classical stochastic frontier panel data models provide no mechanism to disentangle individual time invariant unobserved heterogeneity from inefficiency. Greene (2005a, b) proposed the so-called “true” fixed-effects specification that distinguishes these two latent components. However, due to the incidental parameters problem, his maximum likelihood estimator may lead to biased variance estimates. We propose two alternative estimators that achieve consistency for $n\to \infty$ with fixed $T$. Furthermore, we extend the Chen et al. (2014) results providing a feasible estimator when the inefficiency is heteroskedastic and follows a first-order autoregressive process. We investigate the behavior of the proposed estimators through Monte Carlo simulations showing good finite sample properties, especially in small samples. An application to hospitals’ technical efficiency illustrates the usefulness of the new approach.     

Instrumental variable estimation based on grouped data

The paper considers the estimation of the coefficients of a single equation in the presence of dummy intruments. We derive pseudo ML and GMM estimators based on moment restrictions induced either by the structural form or by the reduced form of the model. The performance of the estimators is evaluated for the non-Gaussian case. We allow for heteroscedasticity. The asymptotic distributions are based on parameter sequences where the number of instruments increases at the same rate as the sample size. Relaxing the usual Gaussian assumption is shown to affect the normal asymptotic distributions. As a result also recently suggested new specification tests for the validity of instruments depend on Gaussianity. Monte Carlo simulations confirm the accuracy of the asymptotic approach.     

Complex Reduced Rank Models For Seasonally Cointegrated Time Series

This paper introduces a new representation for seasonally cointegrated variables, namely the complex error correction model, which allows statistical inference to be performed by reduced rank regression. The suggested estimators and tests statistics are asymptotically equivalent to their maximum likelihood counterparts. The small sample properties are evaluated by a Monte Carlo study and an empirical example is presented to illustrate the concepts and methods.     

Estimation and inference in two-stage,semi-parametric models of production processes

Many papers have regressed non-parametric estimates of productive efficiency on environmental variables in two-stage procedures to account for exogenous factors that might affect firms’ performance. None of these have described a coherent data-generating process (DGP). Moreover, conventional approaches to inference employed in these papers are invalid due to complicated, unknown serial correlation among the estimated efficiencies. We first describe a sensible DGP for such models. We propose single and double bootstrap procedures; both permit valid inference, and the double bootstrap procedure improves statistical efficiency in the second-stage regression. We examine the statistical performance of our estimators using Monte Carlo experiments.     

Monte Carlo evidence on the choice between sample selection and two-part models

This Monte Carlo study examines the relative performance of sample selection and two-part models for data with a cluster at zero. The data are drawn from a bivariate normal distribution with a positive correlation. The alternative estimators are examined in terms of means squared error, mean bias and pointwise bias. The sample selection estimators include LIML and FIML. The two-part estimators include a naive (the true specification, omitting the correlation coefficient) and a data-analytic (testimator) variant.In the absence of exclusion restrictions, the two-part models are no worse, and often appreciably better than selection models in terms of mean behavior, but can behave poorly for extreme values of the independent variable. LIML had the worst performance of all four models. Empirically, selection effects are difficult to distinguish from a non-linear (e.g., quadratic) response. With exclusion restrictions, simple selection models were significantly better behaved than a naive two-part model over subranges of the data, but were negligibly better than the data-analytic version.     

Evaluating estimation methods for ordinal data in structural equation modeling

This study examined the performance of two alternative estimation approaches in structural equation modeling for ordinal data under different levels of model misspecification, score skewness, sample size, and model size. Both approaches involve analyzing a polychoric correlation matrix as well as adjusting standard error estimates and model chi-squared, but one estimates model parameters with maximum likelihood and the other with robust weighted least-squared. Relative bias in parameter estimates and standard error estimates, Type I error rate, and empirical power of the model test, where appropriate, were evaluated through Monte Carlo simulations. These alternative approaches generally provided unbiased parameter estimates when the model was correctly specified. They also provided unbiased standard error estimates and adequate Type I error control in general unless sample size was small and the measured variables were moderately skewed. Differences between the methods in convergence problems and the evaluation criteria, especially under small sample and skewed variable conditions, were discussed.     

On Maximum Likelihood Estimation of Dynamic Panel Data Models

We analyse the finite sample properties of maximum likelihood estimators for dynamic panel data models. In particular, we consider transformed maximum likelihood (TML) and random effects maximum likelihood (RML) estimation. We show that TML and RML estimators are solutions to a cubic first‐order condition in the autoregressive parameter. Furthermore, in finite samples both likelihood estimators might lead to a negative estimate of the variance of the individual‐specific effects. We consider different approaches taking into account the non‐negativity restriction for the variance. We show that these approaches may lead to a solution different from the unique global unconstrained maximum. In an extensive Monte Carlo study we find that this issue is non‐negligible for small values of T and that different approaches might lead to different finite sample properties. Furthermore, we find that the Likelihood Ratio statistic provides size control in small samples, albeit with low power due to the flatness of the log‐likelihood function. We illustrate these issues modelling US state level unemployment dynamics.     

Penalized Quantile Regression with Semiparametric Correlated Effects: An Application with Heterogeneous Preferences

This paper proposes new ?₁‐penalized quantile regression estimators for panel data, which explicitly allows for individual heterogeneity associated with covariates. Existing fixed‐effects estimators can potentially suffer from three limitations which are overcome by the proposed approach: (i) incidental parameters bias in nonlinear models with large N and small T ; (ii) lack of efficiency; and (iii) inability to estimate the effects of time‐invariant regressors. We conduct Monte Carlo simulations to assess the small‐sample performance of the new estimators and provide comparisons of new and existing penalized estimators in terms of quadratic loss. We apply the technique to an empirical example of the estimation of consumer preferences for nutrients from a demand model using a large transaction‐level dataset of household food purchases. We show that preferences for nutrients vary across the conditional distribution of expenditure and across genders, and emphasize the importance of fully capturing consumer heterogeneity in demand modeling. Copyright © 2016 John Wiley & Sons, Ltd.     

分整阶数半参数估计的有限样本性质研究

随着对经济和金融时间序列长记忆性的研究,分整阶数估计已成为当前理论研究的焦点问题。以对数周期图回归和局部Whittle方法为代表的半参数分整阶数估计方法在实践中得到广泛应用,但对这两类半参数估计方法的有限样本性质的比较则鲜有涉及,影响了在实践中对估计方法的选择。利用蒙特卡洛模拟方法,在不同数据产生的过程下,这两种半参数估计方法有限样本性质的研究结果表明：在ARFIMA(0, d, 0)过程下,LW类估计量具有较好的小样本性质;在平稳ARFIMA(1, d, 0)过程下,本文建议的QGPH估计量的有限样本性质要优于其他对数周期图估计量;在非平稳过程下,MGPH的偏差最小。     

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.