Spline-based quasi-likelihood estimation of mixed Poisson regression with single-index models

We consider spline-based quasi-likelihood estimation for mixed Poisson regression with single-index models. The unknown smooth function is approximated by B-splines, and a modified Fisher scoring algorithm is employed to compute the estimates. The spline estimate of the nonparametric component is shown to achieve the optimal rate of convergence, and the asymptotic normality of the regression parameter estimates is still valid even if the variance function is misspecified. The semiparametric efficiency of the model can be established if the variance function is correctly specified. The variance of the regression parameter estimates can be consistently estimated by a simple procedure based on the least-squares estimation. The proposed method is evaluated via an extensive Monte Carlo study, and the methodology is illustrated on an air pollution study.     

Statistical inference on regression with spatial dependence

Central limit theorems are developed for instrumental variables estimates of linear and semiparametric partly linear regression models for spatial data. General forms of spatial dependence and heterogeneity in explanatory variables and unobservable disturbances are permitted. We discuss estimation of the variance matrix, including estimates that are robust to disturbance heteroscedasticity and/or dependence. A Monte Carlo study of finite-sample performance is included. In an empirical example, the estimates and robust and non-robust standard errors are computed from Indian regional data, following tests for spatial correlation in disturbances, and nonparametric regression fitting. Some final comments discuss modifications and extensions.     

Small sample properties of maximum likelihood versus generalized method of moments based tests for spatially autocorrelated errors

Many applied researchers have to deal with spatially autocorrelated residuals (SAR). Available tests that identify spatial spillovers as captured by a significant SAR parameter, are either based on maximum likelihood (MLE) or generalized method of moments (GMM) estimates. This paper illustrates the properties of various tests for the null hypothesis of a zero SAR parameter in a comprehensive Monte Carlo study. The main finding is that Wald tests generally perform well regarding both size and power even in small samples. The GMM-based Wald test is correctly sized even for non-normally distributed disturbances and small samples, and it exhibits a similar power as its MLE-based counterpart. Hence, for the applied researcher the GMM Wald test can be recommended, because it is easy to implement.     

Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension

Pseudo maximum likelihood estimates are developed for higher-order spatial autoregressive models with increasingly many parameters, including models with spatial lags in the dependent variables both with and without a linear or nonlinear regression component, and regression models with spatial autoregressive disturbances. Consistency and asymptotic normality of the estimates are established. Monte Carlo experiments examine finite-sample behaviour.     

Testing for autoregressive against moving average errors in the linear regression model

This paper presents a new approach to hypotheses testing problems which are non-nested in the classical sense and which concern the covariance matrix of the disturbance vector of the linear regression model. In particular, the application of the approach to testing for AR(1) disturbances against MA(1) disturbances is explored in some detail. Practical difficulties are discussed and selected upper bounds for the test's five percent significance points are tabulated. The small sample power of four versions of the new test are compared empirically and a clear conclusion is made in regard to the best overall test.     

Gains in efficiency from joint estimation of systems of autoregressive-moving average processes

The paper examines gains in efficiency from joint estimation of systems of ARMA processes where cross-correlation is due to contemporaneous correlation among disturbances. The asymptotic variance of joint estimates is derived and it involves only variances and covariances among purely AR processes corresponding to the AR and MA parts of the constituent processes. Small sample gains are evaluated by Monte Carlo methods. Application of joint estimation to two short-term interest rates is shown to result in more accurate post-sample predictions relative to both univariate models and the FMP econometric model.     

Diagnostics analysis for log‐Birnbaum–Saunders regression models with censored data

This article develops influence diagnostics for log‐Birnbaum–Saunders (LBS) regression models with censored data based on case‐deletion model (CDM). The one‐step approximations of the estimates in CDM are given and case‐deletion measures are obtained. Meanwhile, it is shown that CDM is equivalent to mean shift outlier model (MSOM) in LBS regression models and an outlier test is presented based on MSOM. Furthermore, we discuss a score test for homogeneity of shape parameter in LBS regression models. Two numerical examples are given to illustrate our methodology and the properties of score test statistic are investigated through Monte Carlo simulations under different censoring percentages.     

Logit based parameter estimation in the Rasch model

The similarities between the logistic regression model and the Rasch model (used in psychometric item response theory) are used to derive several methods based on logits that produce parameter estimates for the Rasch model. A result from LeCam and Dzhaparidze is used by which an initial consistent estimate is transformed by one scoring method iteration into an estimate that has the same asymptotic efficiency as the (in this case conditional) maximum likelihood estimate of the item parameters. Indirect evidence about the bias of this CML estimator is produced by studying the (more easily derived) bias of the estimator based on the unweighted logits. Finally, some simple weighted least squares logit-based estimates are presented, and their performance is assessed. On the whole, the computationally simpler logit-based estimates give a fairly good approximation to the CML estimates.     

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.     

Assessing the presence of harmful collinearity and other forms of weak data through a test for signal-to-noise

Data weaknesses (such as collinearity) reduce the quality of least-squares estimates by inflating parameter variances. Standard regression diagnostics and statistical tests of hypothesis are unable to indicate such variance inflation and hence cannot detect data weaknesses. In this paper, then, we consider a different means for determining the presence of weak data based on a test for signal-to-noise in which the size of the parameter variance (noise) is assessed relative to the magnitude of the parameter (signal). This test is combined with other collinearity diagnostics to provide a test for the presence of harmful collinearity and/or short data. The entire procedure is illustrated with an equation from the Michigan Quarterly Econometric Model. Tables of critical values for the test are provided in an appendix.     

A semi-parametric censored regression estimator

This paper introduces a semi-parametric method for estimating regression co underlying parent population of errors in censored. The method is an example of the method of sieves; and it provides simultaneous estimates of the regression coefficients and the density of the underlying parent population.In the very simplest terms, the underlying unknown density is approximated by a spline with mesh size approaching zero with the sample size. The values of the density at the knots are then added to the list of the usual unknown parameters in a censored regression model, e.g., the regression coefficients and scale parameter. A quasi-likelihood function using the approximate spline density is then maximized over all the parameters mentioned above. The method is shown to result in strongly consistent parameter estimates.     

Time aggregation and the distributional shape of unemployment duration

This paper reports empirical evidence on the sensitivity of unemployment duration regression estimates to distributional assumptions and to time aggregation. The results indicate that parameter estimates are robust to distributional assumptions, while estimates of duration dependence are not. Time aggregation does not seem to have drastic effects on the estimates in a simple parametric model like the Weibull, but can produce dramatic changes in the more complicated extended generalized gamma model. Semiparametric models for grouped data produce stable estimates, and perform much better than continuous-time models in terms of significance at high levels of time aggregation.     

Asymptotic theory for nonparametric regression with spatial data

Nonparametric regression with spatial, or spatio-temporal, data is considered. The conditional mean of a dependent variable, given explanatory ones, is a nonparametric function, while the conditional covariance reflects spatial correlation. Conditional heteroscedasticity is also allowed, as well as non-identically distributed observations. Instead of mixing conditions, a (possibly non-stationary) linear process is assumed for disturbances, allowing for long range, as well as short-range, dependence, while decay in dependence in explanatory variables is described using a measure based on the departure of the joint density from the product of marginal densities. A basic triangular array setting is employed, with the aim of covering various patterns of spatial observation. Sufficient conditions are established for consistency and asymptotic normality of kernel regression estimates. When the cross-sectional dependence is sufficiently mild, the asymptotic variance in the central limit theorem is the same as when observations are independent; otherwise, the rate of convergence is slower. We discuss the application of our conditions to spatial autoregressive models, and models defined on a regular lattice.     

Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach

We develop new tests of the capital asset pricing model that take account of and are valid under the assumption that the distribution generating returns is elliptically symmetric; this assumption is necessary and sufficient for the validity of the CAPM. Our test is based on semiparametric efficient estimation procedures for a seemingly unrelated regression model where the multivariate error density is elliptically symmetric, but otherwise unrestricted. The elliptical symmetry assumption allows us to avoid the curse of dimensionality problem that typically arises in multivariate semiparametric estimation procedures, because the multivariate elliptically symmetric density function can be written as a function of a scalar transformation of the observed multivariate data. The elliptically symmetric family includes a number of thick‐tailed distributions and so is potentially relevant in financial applications. Our estimated betas are lower than the OLS estimates, and our parameter estimates are much less consistent with the CAPM restrictions than the corresponding OLS estimates. Copyright © 2002 John Wiley & Sons, Ltd.     

Estimating the LQAC model with I(2) variables

This paper derives a method for estimating and testing the Linear Quadratic Adjustment Cost (LQAC) model when the target variable and some of the forcing variables follow I(2) processes. Based on a forward-looking error-correction formulation of the model it is shown how to obtain strongly consistent estimates of the structural parameters from both a linear and a non-linear cointegrating regression where first-differences of the I(2) variables are included as regressors (multicointegration). Further, based on the estimated parameter values, it is shown how to test and evaluate the LQAC model using a VAR approach. A simple easy interpretable metric for measuring the model fit is suggested. In an empirical application using UK money demand data, the non-linear multicointegrating regression delivers an economically plausible estimate of the adjustment cost parameter. However, the restrictions implied by the exact LQAC model under rational expectations are strongly rejected and the metric for model fit indicates a substantial noise component in the model. Copyright © 1999 John Wiley & Sons, Ltd.     

稳健的HAC法在多元平稳时间序列之间伪回归中的应用

本文在传统HAC法的基础上,将截断参数M设定为样本容量T,并推导新的模型显著性检验Wald*统计量的极限分布。通过比较分析,表明Wald*统计量能大大减少伪回归概率,且新统计量比传统检验统计量更加稳健,但是也发现新的统计量具有一定程度的检验水平扭曲,原因在于截断参数M的设定忽略了AR过程的持久性、MA过程的滞后阶等因素,从而导致Wald*存在检验水平扭曲,说明M的设定不当会产生伪回归和检验水平扭曲现象。     

Bootstrap Co‐integration Rank Testing: The Effect of Bias‐Correcting Parameter Estimates

Bootstrap‐based methods for bias‐correcting the first‐stage parameter estimates used in some recently developed bootstrap implementations of co‐integration rank tests are investigated. The procedure constructs estimates of the bias in the original parameter estimates by using the average bias in the corresponding parameter estimates taken across a large number of auxiliary bootstrap replications. A number of possible implementations of this procedure are discussed and concrete recommendations made on the basis of finite sample performance evaluated by Monte Carlo simulation methods. The results show that bootstrap‐based bias‐correction methods can significantly improve the small sample performance of the bootstrap co‐integration rank tests.     

A new look at the relationship between time-series and structural econometric models

This paper examines the relationship between dynamic structural econometric models (SEM) and time series (TS) models. It extends the work of others by suggesting a reconciliation of SEM and TS models based on classical linear parameter restrictions in regression models rather than on time series methods. The paper demonstrates that in a number of common economic contexts there exist sets of plausible restrictions on the stochastic properties of the disturbances and on the dynamic adjustment processes in a SEM such that familiar structural models take on the form of univariate TS models. Consequently, it is argued that TS models should not be arbitrarily dismissed as being devoid of economic content.     

Testing for structural change in regression quantiles

Most studies in the structural change literature focus solely on the conditional mean, while under various circumstances, structural change in the conditional distribution or in conditional quantiles is of key importance. This paper proposes several tests for structural change in regression quantiles. Two types of statistics are considered, namely, a fluctuation type statistic based on the subgradient and a Wald type statistic, based on comparing parameter estimates obtained from different subsamples. The former requires estimating the model under the null hypothesis, and the latter involves estimation under the alternative hypothesis. The tests proposed can be used to test for structural change occurring in a pre-specified quantile, or across quantiles, which can be viewed as testing for change in the conditional distribution with a linear specification of the conditional quantile function. Both single and multiple structural changes are considered. We derive the limiting distributions under the null hypothesis, and show they are nuisance parameter free and can be easily simulated. A simulation study is conducted to assess the size and power in finite samples.     

Exact inference for the linear model with groupwise heteroscedastic spherical disturbances

Exact nonparametric inference on a single coefficient in a linear regression model, as considered by Bekker (Working Paper, Department of Economics, University of Groningen, 1997), is elaborated for the case of spherically distributed heteroscedastic disturbances. Instead of approximate inference based on feasible weighted least squares, exact inference is formulated based on partial rotational invariance of the distribution of the vector of disturbances. Thus, classical exact inference based on t-statistics is generalized to exact inference that remains valid in a groupwise heteroscedastic context. The approach is applied to a basic two-sample problem, and to the random- and fixed-effects models for panel data.