A comment on 'resolving spurious regressions and serially correlated errors'

In order to diminish size distortions of the t test in a time series linear specification, Agiakloglou (Agiakloglou in Empir Econ, 45(3):1361-1366, 2013) proposed to (1) include the first lag of the dependent variable as a regressor or (2) estimate it using the first differences of the variables. He provided finite-sample evidence to support his proposal. In this paper, we extend the Monte Carlo experiment to different data-generating processes and calculate the asymptotic behavior of the modified specifications. We show that including the lag of the dependent variable as a regressor reduces size distortions when the variables are driftless unit roots, but this approach does not hold under the presence of long memory, nonlinearities, or structural breaks.