Article

On the Estimation of a Linear Time Trend Regression with a One- Way Error Component Model in the Presence of Serially Correlated Errors

08/1998;
Source: RePEc

ABSTRACT In this paper, we study the limiting distributions for the ordinary least squares (OLS), the fixed effects (FE), first difference (FD), and the generalized least squares (GLS) estimators in a linear time trend regression with a one-way error component model in the presence of serially correlated errors. We show that when the error term is I(0), the FE is asymptotically equivalent to GLS. However, when the error term is I(1), the GLS could be less efficient than FD or FE estimators and FD is the most efficient estimator. However, when the intercept is included in the model and the error term is I(0), the OLS, FE, and GLS are asymptotically equivalent. The limiting distribution of the GLS depends on the initial condition significantly when the error term is I(1) and an intercept is included in the regression. Monte Carlo experiments are employed to compare the performance of these estimators in finite samples. The main findings are: (1) the two-steps GLS estimators perform well if the variance component is small and close to zero when autocorrelation coefficient is less than one, (2) the FD estimator dominates the other estimators when autocorrelation coefficient equals to one for all values of variance component and (3) the FE estimator is recommended in practice since it performs pretty well for all values of the autocorrelation coefficient and variance component.

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Keywords

autocorrelation coefficient
 
efficient estimator
 
error term
 
estimators
 
FD estimator
 
FE
 
FE estimator
 
FE estimators
 
finite samples
 
first difference
 
fixed effects
 
limiting distribution
 
limiting distributions
 
linear time trend regression
 
main findings
 
Monte Carlo experiments
 
one-way error component model
 
regression
 
serially correlated errors
 
two-steps GLS estimators