Structural breaks with deterministic and stochastic trends

This paper analyzes the consistency, rate of convergence and limiting distributions of parameter estimates in models where the trend function exhibits a slope change at some unknown date and the errors can be either stationary or have a unit root. These estimates are obtained by minimizing the sum of squared residuals in simple regressions involving a constant, a trend, a slope shift regressor and possibly a level shift regressor. Special attention is given to the effects induced by alternative specifications of the slope shift regressor and the inclusion or exclusion of a level shift regressor. Some surprising results are found for which we provide more detailed explanations. We also show via simulations that our asymptotic results provide good approximations in finite samples. We illustrate the issues analyzed applying our results to investigate dates and magnitudes of changes in the growth rates of (log) real per capita GDP series for 10 countries using a historical data set that covers the period 1870–1986.