Nonlinear regression for unit root models with autoregressive errors

This paper shows that the nonlinear least squares estimator for unit root models has the limiting distribution free of nuisance parameters and is more efficient than the augmented Dickey–Fuller estimator when the sum of coefficients for lagged variables is negative.     

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’.     

Asymptotic inference in regression models with autoregressive errors having roots on the unit circle

An inference procedure is proposed for regression models with stationary regressors and non-stationary autoregressive errors. It is shown that the usual GLS or Cochrane–Orcutt procedure should be done in reverse order by starting the estimation from the error structure.     

Estimating the covariance matrix for regression models with ar(1) errors and lagged dependent variables

We propose a simple procedure, based on an artificial linear regression, for consistently estimating the covariance matrix of the parameter estimates for linear regression models with serially correlated errors and lagged dependent variables.     

The application of transformations to non-linear models

A transmuted model is introduced which allows non-additive error terms and is shown to be an extension of the Box-Cox transformation to intrinsically non-linear equations. Post-transformed models are used to analyze the underlying disturbance term structure with an empirical example presented to illustrate the increased flexibility provided by the transmuted model.     

Hypothesis testing in regression models with AR(1) errors and a lagged dependent variable: Bootstrapping and artificial regression compared

Serially correlated errors in dynamic models render the standard conditional estimator of the covariance matrix inconsistent. A Monte Carlo experiment confirms that the downward bias in the conventional variance estimator also exists in small samples. The results favour a consistent estimator based on an artificial regression (suggested by Davidson and Mackinnon) over bootstrapping the distribution of parameter estimates.     

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.     

On ridge estimators for the negative binomial regression model

The negative binomial (NB) regression model is very popular in applied research when analyzing count data. The commonly used maximum likelihood (ML) estimator is very sensitive to highly intercorrelated explanatory variables. Therefore, a NB ridge regression estimator (NBRR) is proposed as a robust option of estimating the parameters of the NB model in the presence of multicollinearity. To investigate the performance of the NBRR and the traditional ML approach the mean squared error (MSE) is calculated using Monte Carlo simulations. The simulated result indicated that some of the proposed NBRR methods should always be preferred to the ML method.     

Engineering robust instruments for GMM estimation of panel data regression models with errors in variables: a note

Econometricians have long recognized the need to account in some way for measurement errors, specification errors and endogeneity to ensure that the ordinary least squares estimator is consistent. This article introduces a new generalized method of moments estimator that relies on robust instruments to estimate panel data regression models containing errors in variables. We show how this GMM approach can be generalized for the panel data framework using higher moments and cumulants as instruments. The new instruments, engineered for greater robustness, are proposed to tackle the pervasive problem of weak instruments.     

Antithetic variates to estimate the simulation bias in non-linear models

This paper describes a Monte Carlo experiment, which makes use of antithetic variate sampling, to get an accurate estimate of the deterministic simulation bias in the non-linear Klein—Goldberger model. The computational efficiency is more than 500 times greater than in case of simple random sampling.     

Consistency ofs 2 in the linear regression model with correlated errors

We give a simple sufficient condition for consistency of the standard OLS-based estimate of the disturbance variance in the linear regression model with autocorrelated disturbances.Research supported by Deutsche Forschungsgemeinschaft (DFG). We are grateful to B. M. Poetscher for a generous supply of counterexamples.     

Interval regression models with endogenous explanatory variables

We consider the estimation of linear models where the dependent variable is observed by intervals and some continuous regressors may be endogenous. Our approach, an IV version of the technique devised by Stewart (Rev Econ Stud 50(3):737?C753, 1983), is fully parametric and two estimators are proposed: a two-step estimator and a limited-information maximum-likelihood estimator. The results can be summarized as follows: the two-step estimator has an intuitive appeal, and a Monte Carlo experiment suggests that its relative efficiency is rather satisfactory. The limited-information maximum-likelihood estimator, however, is probably simpler to implement and has the advantage of providing a framework in which several testing procedures are more straightforward to perform. The application of two-stage least squares to a proxy of the dependent variable built by taking midpoints, on the other hand, leads to inconsistent estimates; Monte Carlo evidence suggests that the bias arising from the ??midpoint?? technique is much worse than the effect of distributional misspecification. An example application is also included, which uses Australian data on migrants?? remittances; endogeneity effects are substantial and using conventional estimation methods leads to substantially misleading inference.     

Estimation of hedonic price functions via additive nonparametric regression

We model a hedonic price function for housing as an additive nonparametric regression. Estimation is done via a backfitting procedure in combination with a local polynomial estimator. It avoids the pitfalls of an unrestricted nonparametric estimator, such as slow convergence rates and the curse of dimensionality. Bandwidths are chosen using a novel plug in method that minimizes the asymptotic mean average squared error (AMASE) of the regression. We compare our results to alternative parametric models and find evidence of the superiority of our nonparametric model. From an empirical perspective our study is interesting in that the effects on housing prices of a series of environmental characteristics are modeled in the regression. We find these characteristics to be important in the determination of housing prices.First version received: October 2002/Final version received: October 2003We thank B. Baltagi and two anonymous referees for their comments. The authors retain responsibility for any remaining errors.     

On the median regression for SURE models with applications to 3-generation immigrants data in Sweden

In this paper we generalize the median regression method to be applicable to system of regression equations, in particular SURE models. Giving the existence of proper system wise medians of the residuals from different equations, we apply the weighted median regression with the weights obtained from the covariance matrix of the equations obtained from ordinary SURE method. The benefit of this model in our case is that the SURE estimators utilise the information present in the cross regression (or equations) error correlation and hence more efficient than other estimation methods like the OLS method. The Seemingly Unrelated Median Regression Equations (SUMRE) models produce results that are more robust than the usual SURE or single equations OLS estimation when the distributions of the dependent variables are not normally distributed or the data are associated with outliers. Moreover, the results are also more efficient than is the cases of single equations median regressions when the residuals from the different equations are correlated. A theorem is derived and indicates that even if there is no statistically significant correlation between the equations, using SUMRE model instead of SURE models will not damage the estimation of parameters.     

Exact likelihood function for a regression model with MA(1) errors

Balestra (1980) derives analytical expressions for the transformation that can be used to transform a generalized regression problem into a simple regression problem. This note solves this problem using the Kalman filter. It is shown that the exact likelihood function can be obtained very easily.     

Variable selection problem in the censored regression models

In this paper we discuss the variable selection problem for the censored regression models. The Schme-Hahn (1979) estimator for the censored normal model and the Buckley-James (1979) estimator for the non-parametric censored model are discussed. It is shown, through the EM algorithm, that the variable selection problem for these estimators can be converted into a variable selection problem in a standard linear regression model. We show that the expectation of maximum likelihood residuals converges to zero in large samples.     

Conditional mean functions of non-linear models of US output

We compare a number of models of post War US output growth in terms of the degree and pattern of non-linearity they impart to the conditional mean, where we condition on either the previous period's growth rate, or the previous two periods' growth rates. The conditional means are estimated non-parametrically using a nearest-neighbour technique on data simulated from the models. In this way, we condense the complex, dynamic, responses that may be present in to graphical displays of the implied conditional mean. First version received: Feb. 1999/Final version received: June 2001     

The bias of some estimators for panel data models with measurement errors

The paper deals with the (asymptotic) bias in the estimation of regression slope coefficients from panel data observed with error. Unobserved individual and time specific heterogeneity is also assumed. The estimators considered include: the standard ‘within’ and ‘between’ estimators, and estimators based on differences over time. It is shown that in terms of bias, there may be a trade-off between the effect of heterogeneity and of measurement errors. The paper also shows that in situations where the number of observations of each individual is finite (and in practice often small), changes in the correlograms of the measurement error and of the latent exogenous variable may substantially affect the relative bias of the different estimators of the slope coefficient.     

The CUSUM of squares test for the stability of regression models with non-stationary regressors

In this paper, we propose a modified CUSUM of squares test in time series regression models with a non-stationary regressor and show that the limiting distribution of this test is the sup of the absolute value of a Brownian bridge.