The minimum error variance rule for non-linear regression models

In this note it is demontrated that Theil's (1961) minimum error variance criterion is asymptotically valid for choosing between non-nested non-linear regression models, as long as one of the models being considered is ‘true’.     

Small sample properties of the two-step and three-step estimators in a heteroscedastic linear regression model and the Bayesian alternative

In this paper, we consider the heteroscedastic linear regression model in which the variance of the disturbance term is assumed to be proportional to one of the regressors raised to an unknown power. We first derive the Bayesian estimator, and compare the mean squared errors of the two-step, three-step and Bayesian estimates by Monte Carlo experiments.     

A note on a posterior approximation in a heteroscedastic model

This paper develops a method of obtaining approximate marginal posteriors for all parameters of interest for a heteroscedastic model. This method improves upon Box and Hill's (1974) method in suggesting a pure Bayesian estimator for a regression coefficient.     

A note on S in a spatially correlated error components regression model for panel data

The ordinary least squares based estimator of the disturbance variance in a panel regression model with spatially correlated error component is shown to be asymptotically unbiased and weakly consistent without any restrictions on the regressor matrix.     

Testing for serial correlation and random effects in a two-way error component regression model

In this paper, we test the existence of serial correlation and random effects in a two-way error component regression model with panel data. Under moment conditions alone, we suggest several easily implemented tests based on the parameter estimators for artificial autoregressions modeled by the differences in residuals. Under the null hypotheses, the tests for serial correlation are two-sided and asymptotically chi-square distributed, whereas those for random effects are one-sided, and are asymptotically standard normally distributed variables. Moreover, these methods can also be used similarly to construct tests for both serial correlation and individual effects jointly, whether or not time effects are present. The proposed tests are able to detect local alternatives that are distinct from the null at the parametric rate. Monte Carlo simulations and real data applications are carried out for purposes of illustration.     

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.     

A vector error correction model of the Singapore stock market

This article examines the long-term equilibrium relationships between the Singapore stock index and selected macroeconomic variables, as well as among stock indices of Singapore, Japan, and the United States. Upon testing appropriate vector error-correction models, we detected that changes in two measures of real economic activities, industrial production and trade, are not integrated of the same order as changes in Singapore's stock market levels. However, changes in Singapore's stock market levels do form a cointegrating relationship with changes in price levels, money supply, short- and long-term interest rates, and exchange rates. While changes in interest and exchange rates contribute significantly to the cointegrating relationship, those in price levels and money supply do not. This suggests that the Singapore stock market is interest and exchanges rate sensitive. Additionally, the article concludes that the Singapore stock market is significantly and positively cointegrated with stock markets of Japan and the United States.     

A generalized panel data switching regression model

This paper considers a generalized panel data model of polychotomous and/or sequential switching which can also accommodate the dependence between unobserved effects and covariates in the model. We showcase our model using an empirical illustration in which we estimate scope economies for the publicly owned electric utilities in the US during the period from 2001 to 2003.     

Inadmissibility of the iterative Stein-rule estimator of the disturbance variance in a linear regression

In this paper, we consider the estimator of the disturbance variance in a linear regression when the Stein-rule estimator is used in place of the OLS estimator (the iterative Stein-rule estimator of the disturbance variance). It is shown that the iterative Stein-rule estimator of the disturbance variance is dominated by the usual estimator of the disturbance variance based on the OLS estimator under the squared error loss criterion, if the number of regressors is greater than or equal to five.     

Test̀ing for heteroscedasticity in a model of seemingly unrelated regression equations with variance components (SUREVC)

In this paper a simple specification of heteroscedasticity in the disturbances of the SUREVC model is assumed and the Lagrangian multiplier test recently proposed by Breusch and Pagan (1979) is applied.     

The derivation of the NPV variance of a risky capital investment project with first-order autoregressive cash flows and autoregressive conditional heteroscedastic variances

In this article, the authors develop a closed-form solution for assessing the capital investment project NPV variance when cash flows obey a first-order autoregressive process. A distinction is established between static and dynamic solutions as the authors focus on the case involving partial positive dependence between cash flows. Under a Markovian process, the NPV solution is stationary in mean but not strictly in variance. Constraining the process to become fully stationary will overestimate the NPV variance. Finally, the authors show that the Markovian NPV variance closed-form solution is robust to the introduction of autoregressive conditional heteroscedastic variances complying with a GARCH(1,1) process; it will, however, have its value increased and consequently the riskiness of the capital investment project.     

A gradual switching regression model with autocorrelated errors

In this note, we set up the gradual switching regression model with autocorrelated errors and show the maximum likelihood estimation procedure. As an empirical example, we examine structural change in the energy demand in Japan at the first oil crisis.     

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.     

Predicting stock realized variance based on an asymmetric robust regression approach

This paper introduces an asymmetric robust weighted least squares (ARLS) approach to improve the forecasting performance of the heterogeneous autoregressive model for realized volatility. The ARLS approach down-weights extreme observations to limit the bad influence of outliers on the estimated parameters. Compared with existing robust regression methods, our model further takes into account the asymmetry of outliers using a class of kernel functions. Out-of-sample results show the ARLS approach can generate more accurate forecasts of the S&P 500 index realized volatility in the statistical and economic senses. The model that considers the asymmetry of outliers gains superior performance among various robust regression competitors. The forecasting improvements also hold in other international stock markets. More importantly, the source of the predictive ability of the ARLS model comes from the less biased and more efficient parameter estimation.     

Finite-maturity stock loans under the constant elasticity of variance model

This article expresses the constant elasticity of variance stock loans pricing formula in terms of the noncentral chi-square distribution. By using the numerical solutions of the integral equation for the early exit boundary, we calculated the valuation of the stock loans. Numerical analysis is carried out to establish explicitly the value of such a loan, as well as the loan amount and the fee for providing such a service.     

A bivariate zero-inflated count data regression model with unrestricted correlation

This paper proposes a computationally simple bivariate zero-inflated count data regression model with an unrestricted correlation pattern. An application to data with excess of zeros on the demand for health services is given.     

A Bayesian note on competing correlation structures in the dynamic linear regression model

A Bayesian posterior odds approach is used to distinguish between different error correlation structures in dynamic linear regression models. Recent classical results are provided with a Bayesian interpretation, and a small empirical example illustrates the approach.     

A modification of the CUSUM test in the linear regression model with lagged dependent variables

We consider testing for structural change in a dynamic linear regression model, and show that the well known CUSUM test, which has been initially devised only for the standard static model, can easily be modified such as to remain asymptotically valid also in this nonstandard situation.     

On Liu estimators for the logit regression model

This paper introduces a shrinkage estimator for the logit model which is a generalization of the estimator proposed by Liu (1993) for the linear regression. This new estimation method is suggested since the mean squared error (MSE) of the commonly used maximum likelihood (ML) method becomes inflated when the explanatory variables of the regression model are highly correlated. Using MSE, the optimal value of the shrinkage parameter is derived and some methods of estimating it are proposed. It is shown by means of Monte Carlo simulations that the estimated MSE and mean absolute error (MAE) are lower for the proposed Liu estimator than those of the ML in the presence of multicollinearity. Finally the benefit of the Lie estimator is shown in an empirical application where different economic factors are used to explain the probability that municipalities have net increase of inhabitants.