Abstract For the AR(1) model, one implicitly assumes a specific variance on the initial observation, or that the process started a long time ago, to insure homoscedasticity. This paper investigates Anderson and Hsiao's (1982) suggestion of an arbitrary variance on the initial observation of the autoregressive process. This is done in a panel data framework. Regardless of when the AR(1) process started, one can translate this starting date into an ‘effective’ initial variance assumption. This ‘effective’ initial variance can be estimated with panel data and tested for departures from homoscedasticity. The consequences of this departure on various estimators is studied via Monte Carlo experiments. The following estimators are compared: OLS, Iterative Cochrane–Orcutt (ICO), and two maximum likelihood (mle) estimators, one corresponding to the usual stationary assumption denoted by BM [Beach and MacKinnon (1978)] and another mle corresponding to the arbitrary variance assumption on the initial observations. Both mle's can be achieved as iterative GLS – the former using a Prais–Winsten (PW) transformation and the latter using a Generalized PW transformation (GPW). Some of the major findings are the following: BM performs poorly for large departures of the variance of the initial observations from the usual homoscedastic assumption, whereas the mle corresponding to the GPW transformation is robust to various assumptions on the variance of the initial observations. ICO continues to perform poorly relative to estimators that use all time series observations, even though the CO estimator of ϱ performs well compared to that of GPW. The t-statistic which tests the true value of the parameter may be misleading for OLS and BM depending upon the departure of the initial variance from the homoscedastic assumption. However, this t-statistic performs well for the GPW estimator. Finally, the likelihood ratio test which tests the usual homoscedastic assumption on the initial disturbances and a pre-test estimator based on this test perform well in Monte Carlo experiments, and are recommended.
[1]
Marc Nerlove,et al.
Further evidence on the estimation of dynamic economic relations from a time series of cross-sections
,
1971
.
[2]
Asatoshi Maeshiro.
Autoregressive Transformation, Trended Independent Variables and Autocorrelated Disturbance Terms
,
1976
.
[3]
Cheng Hsiao,et al.
Formulation and estimation of dynamic models using panel data
,
1982
.
[4]
Badi H. Baltagi,et al.
A transformation that will circumvent the problem of autocorrelation in an error-component model
,
1991
.
[5]
D. Thornton.
A note on the efficiency of the cochrane-orcutt estimator of the ar(1) regression model
,
1987
.
[6]
Bridger M. Mitchell,et al.
Estimating the Autocorrelated Error Model with Trended Data: Further Results,
,
1980
.
[7]
Trevor Breusch,et al.
Maximum likelihood estimation of random effects models
,
1987
.
[8]
Asatoshi Maeshiro.
On the Retention of the First Observations in Serial Correlation Adjustment of Regression Models
,
1979
.
[9]
Jan Kmenta,et al.
A General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models
,
1974
.
[10]
James G. MacKinnon,et al.
A MAXIMUM LIKELIHOOD PROCEDURE FOR REGRESSION WITH AUTOCORRELATED ERRORS
,
1978
.
[11]
K. R. Kadiyala,et al.
A Transformation Used to Circumvent the Problem of Autocorrelation
,
1968
.
[12]
Cheng Hsiao,et al.
Estimation of Dynamic Models with Error Components
,
1981
.