Full-versus limited-information estimation of a rational-expectations model: Some numerical comparisons

This paper compares numerically the asymptotic distributions of parameter estimates and test statistics associated with two estimation techniques: (a) a limited-information one, which uses instrumental variables to estimate a single equation [Hansen and Singleton (1982)], and (b) a full-information one, which uses a procedure asymptotically equivalent to maximum likelihood to simultaneously estimate multiple equations [Hansen and Sargent (1980)]. The paper compares the two with respect to both (1) asymptotic efficiency under the null hypothesis of no misspecification, and (2) asymptotic bias and power in the presence of certain local alternatives. It is found that (1) full-information standard errors are only moderately smaller than limited-information standard errors, and (2) when the model is misspecified, full-information tests tend to be more powerful, and its parameter estimates tend to be more biased. This suggests that at least in the model considered here, the gains from the use of the less robust and computationally more complex full-information technique are not particularly large.     

The Heckman Correction for Sample Selection and Its Critique

This paper gives a short overview of Monte Carlo studies on the usefulness of Heckman's (1976, 1979) two-step estimator for estimating selection models. Such models occur frequently in empirical work, especially in microeconometrics when estimating wage equations or consumer expenditures.
It is shown that exploratory work to check for collinearity problems is strongly recommended before deciding on which estimator to apply. In the absence of collinearity problems, the full-information maximum likelihood estimator is preferable to the limited-information two-step method of Heckman, although the latter also gives reasonable results. If, however, collinearity problems prevail, subsample OLS (or the Two-Part Model) is the most robust amongst the simple-to-calculate estimators.     

Bayesian measurement of productivity and efficiency in the presence of undesirable outputs: crediting electric utilities for reducing air pollution

Many studies have measured productivity change and efficiency when an undesirable output is a by-product. We flexibly treat the bad as a technology shifter of an input distance function and model a system of nonlinear equations subject to endogeneity. Theory dictates that we impose monotonicity on all inputs, outputs, and the bad. Since a Bayesian full-information likelihood approach can easily be misspecified, we utilize the Kim (J. Econometrics 107 (2002) 175) limited-information likelihood (LIL) derived by minimizing the entropy distance subject to the moment conditions from the Generalized Method of Moments (GMM) estimator. This represents an extension of the Bayesian Method of Moments approach of Zellner and Chen (Macroeconom. Dyn. 5 (2001) 673), Zellner and Tobias (Int. Econom. Rev. 42 (2001) 121), and Zellner (in: Bayesian Analysis in Econometrics and Statistics: The Zellner View and Papers, Edward Elgar, Cheltenham, 1997; J. Econometrics 83 (1998) 185) which uses entropy maximization but does not incorporate a specific likelihood. Using Bayes’ Theorem we combine traditional priors with the LIL, which has a mode at the standard multiple-equation GMM estimator, yielding a limited-information posterior distribution. We generalize the approach of Kim (J. Econometrics 107 (2002) 175) by incorporating an unknown covariance matrix in a Gibbs sampling framework and applying the methodology to nonlinear equations. This allows us to estimate shadow prices, technical efficiency, and productivity change for a panel of electric utilities, yielding results that differ substantially from those obtained using standard GMM.     

Performance of conditional Wald tests in IV regression with weak instruments

We compare the powers of five tests of the coefficient on a single endogenous regressor in instrumental variables regression. Following Moreira [2003, A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048], all tests are implemented using critical values that depend on a statistic which is sufficient under the null hypothesis for the (unknown) concentration parameter, so these conditional tests are asymptotically valid under weak instrument asymptotics. Four of the tests are based on k-class Wald statistics (two-stage least squares, LIML, Fuller's [Some properties of a modification of the limited information estimator. Econometrica 45, 939–953], and bias-adjusted TSLS); the fifth is Moreira's (2003) conditional likelihood ratio (CLR) test. The heretofore unstudied conditional Wald (CW) tests are found to perform poorly, compared to the CLR test: in many cases, the CW tests have almost no power against a wide range of alternatives. Our analysis is facilitated by a new algorithm, presented here, for the computation of the asymptotic conditional p-value of the CLR test.     

Bayesian limited-information analysis of nonlinear simultaneous equations systems

This paper presents a Bayesian limited-information estimation method that can be used to estimate a single nonlinear equation that forms part of a system of simultaneous equations. The method can be looked upon as the Bayesian counterpart of Amemiya's nonlinear limited-information maximum-likelihood estimator as well as a generalization of Drèze's Bayesian limited-information estimator for linear simultaneous equations systems. The method is illustrated by applying it to the problem of estimating a CES-production function which forms part of a complete model of firm behavior.     

Testing for heteroskedasticity and serial correlation in a random effects panel data model

This paper considers a panel data regression model with heteroskedastic as well as serially correlated disturbances, and derives a joint LM test for homoskedasticity and no first order serial correlation. The restricted model is the standard random individual error component model. It also derives a conditional LM test for homoskedasticity given serial correlation, as well as, a conditional LM test for no first order serial correlation given heteroskedasticity, all in the context of a random effects panel data model. Monte Carlo results show that these tests along with their likelihood ratio alternatives have good size and power under various forms of heteroskedasticity including exponential and quadratic functional forms.     

Improved likelihood ratio tests for cointegration rank in the VAR model

We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but as usual the asymptotic results do not require normally distributed innovations. Our tests differ from existing tests in two respects. First, instead of basing our tests on the conditional (with respect to the initial observations) likelihood, we follow the recent unit root literature and base our tests on the full likelihood as in, e.g., Elliott et al. (1996). Second, our tests incorporate a “sign” restriction which generalizes the one-sided unit root test. We show that the asymptotic local power of the proposed tests dominates that of existing cointegration rank tests.     

The nonlinear limited-information maximum- likelihood estimator and the modified nonlinear two-stage least-squares estimator

Several limited-information type estimators of the nonlinear simultaneous equation model are considered and their asymptotic covariance matrices are compared. Amemiya (1974) proposed the general class of nonlinear two-stage least-squares estimators. In this paper, its two specific members are considered and, in addition, the nonlinear limited-information maximum- likelihood estimator and the modified nonlinear two-stage least-squares estimator are proposed. Both are shown to be asymptotically more efficient than the nonlinear two-stage least-squares estimator, and the second has the advantage of being computationally simple.     

Testing conditional symmetry against one-sided alternatives in square contingency tables

For a (k×k) square contingency table with ordered categories, letX(Y) denote the row (column) number. The conditional symmetry model is given byP(X=i, Y=j|X<Y)=P(X=j, Y=i |X>Y), ∀i<j. In this paper, we study the likelihood ratio tests of conditional symmetry in a square contingency table against two particular classes of one-sided alternatives. We obtain the maximum likelihood estimators under each alternative. The asymptotic null distributions of the likelihood ratio statistics are shown to have chi-bar square type distributions. A simulation study is performed by comparing the powers of different tests. The theory developed is illustrated by using the famous eye vision data from Stuart (1953).     

Generalizing weak instrument robust IV statistics towards multiple parameters,unrestricted covariance matrices and identification statistics

We generalize the weak instrument robust score or Lagrange multiplier and likelihood ratio instrumental variables (IV) statistics towards multiple parameters and a general covariance matrix so they can be used in the generalized method of moments (GMM). The GMM extension of Moreira's [2003. A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048] conditional likelihood ratio statistic towards GMM preserves its expression except that it becomes conditional on a statistic that tests the rank of a matrix. We analyze the spurious power decline of Kleibergen's [2002. Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70, 1781–1803, 2005. Testing parameters in GMM without assuming that they are identified. Econometrica 73, 1103–1124] score statistic and show that an independent misspecification pre-test overcomes it. We construct identification statistics that reflect if the confidence sets of the parameters are bounded. A power study and the possible shapes of confidence sets illustrate the analysis.     

Efficient information theoretic inference for conditional moment restrictions

The generalised method of moments estimator may be substantially biased in finite samples, especially so when there are large numbers of unconditional moment conditions. This paper develops a class of first-order equivalent semi-parametric efficient estimators and tests for conditional moment restrictions models based on a local or kernel-weighted version of the Cressie–Read power divergence family of discrepancies. This approach is similar in spirit to the empirical likelihood methods of Kitamura et al. [2004. Empirical likelihood-based inference in conditional moment restrictions models. Econometrica 72, 1667–1714] and Tripathi and Kitamura [2003. Testing conditional moment restrictions. Annals of Statistics 31, 2059–2095]. These efficient local methods avoid the necessity of explicit estimation of the conditional Jacobian and variance matrices of the conditional moment restrictions and provide empirical conditional probabilities for the observations.     

Comparing the accuracy of multivariate density forecasts in selected regions of the copula support

This paper develops a testing framework for comparing the predictive accuracy of competing multivariate density forecasts with different predictive copulas, focusing on specific parts of the copula support. The tests are framed in the context of the Kullback–Leibler Information Criterion, using (out-of-sample) conditional likelihood and censored likelihood in order to focus the evaluation on the region of interest. Monte Carlo simulations document that the resulting test statistics have satisfactory size and power properties for realistic sample sizes. In an empirical application to daily changes of yields on government bonds of the G7 countries we obtain insights into why the Student-t and Clayton mixture copula outperforms the other copulas considered; mixing in the Clayton copula with the t-copula is of particular importance to obtain high forecast accuracy in periods of jointly falling yields.     

Modeling and forecasting short‐term interest rates: The benefits of smooth regimes,macroeconomic variables,and bagging

In this paper we propose a smooth transition tree model for both the conditional mean and variance of the short‐term interest rate process. The estimation of such models is addressed and the asymptotic properties of the quasi‐maximum likelihood estimator are derived. Model specification is also discussed. When the model is applied to the US short‐term interest rate we find: (1) leading indicators for inflation and real activity are the most relevant predictors in characterizing the multiple regimes' structure; (2) the optimal model has three limiting regimes. Moreover, we provide empirical evidence of the power of the model in forecasting the first two conditional moments when it is used in connection with bootstrap aggregation (bagging). Copyright © 2010 John Wiley & Sons, Ltd.     

基于极值分布理论的VaR与ES度量

本文应用极值分布理论对金融收益序列的尾部进行估计,计算收益序列的在险价值VaR和预期不足ES来度量市场风险。通过伪最大似然估计方法估计的GARCH模型对收益数据进行拟合,应用极值理论中的GPD对新息分布的尾部建模,得到了基于尾部估计产生收益序列的VaR和ES值。采用上证指数日对数收益数据为样本,得到了度量条件极值和无条件极值下VaR和ES的结果。实证研究表明:在置信水平很高(如99%)的条件下,采用极值方法度量风险值效果更好。而置信水平在95%下,其他方法和极值方法结合效果会很好。用ES度量风险能够使我们了解不利情况发生时风险的可能情况。     

Testing conditional independence via empirical likelihood

We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother functions. We show that the test statistics are asymptotically normal under the null hypothesis and a sequence of Pitman local alternatives. We also show that the tests possess an asymptotic optimality property in terms of average power. Simulations suggest that the tests are well behaved in finite samples. Applications to some economic and financial time series indicate that our tests reveal some interesting nonlinear causal relations which the traditional linear Granger causality test fails to detect.     

Conditional empirical likelihood estimation and inference for quantile regression models

This paper considers two empirical likelihood-based estimation, inference, and specification testing methods for quantile regression models. First, we apply the method of conditional empirical likelihood (CEL) by Kitamura et al. [2004. Empirical likelihood-based inference in conditional moment restriction models. Econometrica 72, 1667–1714] and Zhang and Gijbels [2003. Sieve empirical likelihood and extensions of the generalized least squares. Scandinavian Journal of Statistics 30, 1–24] to quantile regression models. Second, to avoid practical problems of the CEL method induced by the discontinuity in parameters of CEL, we propose a smoothed counterpart of CEL, called smoothed conditional empirical likelihood (SCEL). We derive asymptotic properties of the CEL and SCEL estimators, parameter hypothesis tests, and model specification tests. Important features are (i) the CEL and SCEL estimators are asymptotically efficient and do not require preliminary weight estimation; (ii) by inverting the CEL and SCEL ratio parameter hypothesis tests, asymptotically valid confidence intervals can be obtained without estimating the asymptotic variances of the estimators; and (iii) in contrast to CEL, the SCEL method can be implemented by some standard Newton-type optimization. Simulation results demonstrate that the SCEL method in particular compares favorably with existing alternatives.     

Testing panel data regression models with spatial error correlation

This paper derives several lagrange multiplier (LM) tests for the panel data regression model with spatial error correlation. These tests draw upon two strands of earlier work. The first is the LM tests for the spatial error correlation model discussed in Anselin (Spatial Econometrics: Methods and Models, Kluwer Academic Publishers, Dordrecht; Rao's score test in spatial econometrics, J. Statist. Plann. Inference 97 (2001) 113) and Anselin et al. (Regional Sci. Urban Econom. 26 (1996) 77), and the second is the LM tests for the error component panel data model discussed in Breusch and Pagan (Rev. Econom. Stud. 47(1980) 239) and Baltagi et al. (J. Econometrics 54 (1992) 95). The idea is to allow for both spatial error correlation as well as random region effects in the panel data regression model and to test for their joint significance. Additionally, this paper derives conditional LM tests, which test for random regional effects given the presence of spatial error correlation. Also, spatial error correlation given the presence of random regional effects. These conditional LM tests are an alternative to the one-directional LM tests that test for random regional effects ignoring the presence of spatial error correlation or the one-directional LM tests for spatial error correlation ignoring the presence of random regional effects. We argue that these joint and conditional LM tests guard against possible misspecification. Extensive Monte Carlo experiments are conducted to study the performance of these LM tests as well as the corresponding likelihood ratio tests.     

Power of Tests for Unit Roots in the Presence of a Linear Trend*

Dickey and Fuller [Econometrica (1981) Vol. 49, pp. 1057–1072] suggested unit‐root tests for an autoregressive model with a linear trend conditional on an initial observation. TPower of tests for unit roots in the presence of a linear trendightly different model with a random initial value in which nuisance parameters can easily be eliminated by an invariant reduction of the model. We show that invariance arguments can also be used when comparing power within a conditional model. In the context of the conditional model, the Dickey–Fuller test is shown to be more stringent than a number of unit‐root tests motivated by models with random initial value. The power of the Dickey–Fuller test can be improved by making assumptions to the initial value. The practitioner therefore has to trade‐off robustness and power, as assumptions about initial values are hard to test, but can give more power.