RESEARCH FIELDS
Econometric Theory, Time Series Econometrics, Financial Econometrics, Empirical Macroeconomics
WORKING PAPERS
Tests for a Broken Trend with Stationary or Integrated Shocks
Abstract: We consider testing for the presence of a structural break in the trend of a univariate time-series where the date of the break is unknown. The tests we propose are robust as to whether the shocks are generated by a stationary or an integrated process. From an empirical standpoint, our robust tests can be quite useful in policy analysis: these tests can easily be employed to evaluate the impact of a one time policy change or a new regulation on a trending variable. Following Harvey et al. (2010), we utilize two different test statistics; one is appropriate for the stationary alternative and the other is for the unit root alternative. Our approach exploits the under-sizing property of each test statistic under the other alternative, and is based on the union of rejections approach proposed by Harvey et al. (2009a). The behavior of the proposed tests is studied through Monte Carlo experiments.The simulation results suggest that our robust tests perform well in small samples, showing good size control and displaying very decent power regardless of the degree of persistence of the data. Finally, as an empirical exercise we consider the convergence issue in U.S. regional incomes and using our tests we have found that there is a slowdown in per-capita income convergence among the U.S. regions at around late 1970s or early 1980s.
Bootstrap Stationarity Test with an Application to Purchasing Power Parity
Abstract: In this paper we propose a bootstrap stationarity test that displays good size control. It is widely known that conventional stationarity tests have significant size distortions in the presence of highly persistent data. There are two main sources of these size distortions in finite samples; i) asymptotic theory fails to deliver a good approximation to the finite sample distributions and ii) the inaccuracy of the long run variance estimation. In this paper, we address these two issues to fix the size distortions. First, we make use of the bootstrap distribution rather than the asymptotic distribution. Second, the estimation of the long run variance is avoided with an appropriate choice of bootstrap test statistic. This choice of the test statistic also leads to higher asymptotic power. The empirical size and power performance of our test is compared with other bootstrap and conventional stationarity tests through Monte-Carlo studies. Simulations demonstrate that our bootstrap test controls size better and has higher power than the competing methods. In an empirical exercise, we employ our bootstrap test to check whether purchasing power parity holds for the countries in our study. We find less evidence against the PPP using our test than the other stationarity tests suggest.
A Powerful Unit Root Test Robust to Initial Condition: An Indirect Inference Based Approach
Abstract: In this paper, we consider the initial condition problem in unit root tests and trend estimation. Majority of the unit root tests are not robust to initial condition and may perform very poorly due to initial displacement. In this paper, we robustify the unit root tests to initial condition by utilizing indirect inference method. Our contribution in this paper is twofold; first we prove that indirect inference method can estimate trend function parameters consistently regardless of the initial displacement. Second, we improve the power of the unit root tests by using the robust indirect inference trend parameter estimates to detrend the data. The simulation results indicate that the power of our robust unit root test is not sensitive to initial condition. The results are useful in empirical testing for the presence of a unit root and for the estimation of the parameters of the trend function that is robust to initial condition.
Econometric Theory, Time Series Econometrics, Financial Econometrics, Empirical Macroeconomics
WORKING PAPERS
Tests for a Broken Trend with Stationary or Integrated Shocks
Abstract: We consider testing for the presence of a structural break in the trend of a univariate time-series where the date of the break is unknown. The tests we propose are robust as to whether the shocks are generated by a stationary or an integrated process. From an empirical standpoint, our robust tests can be quite useful in policy analysis: these tests can easily be employed to evaluate the impact of a one time policy change or a new regulation on a trending variable. Following Harvey et al. (2010), we utilize two different test statistics; one is appropriate for the stationary alternative and the other is for the unit root alternative. Our approach exploits the under-sizing property of each test statistic under the other alternative, and is based on the union of rejections approach proposed by Harvey et al. (2009a). The behavior of the proposed tests is studied through Monte Carlo experiments.The simulation results suggest that our robust tests perform well in small samples, showing good size control and displaying very decent power regardless of the degree of persistence of the data. Finally, as an empirical exercise we consider the convergence issue in U.S. regional incomes and using our tests we have found that there is a slowdown in per-capita income convergence among the U.S. regions at around late 1970s or early 1980s.
Bootstrap Stationarity Test with an Application to Purchasing Power Parity
Abstract: In this paper we propose a bootstrap stationarity test that displays good size control. It is widely known that conventional stationarity tests have significant size distortions in the presence of highly persistent data. There are two main sources of these size distortions in finite samples; i) asymptotic theory fails to deliver a good approximation to the finite sample distributions and ii) the inaccuracy of the long run variance estimation. In this paper, we address these two issues to fix the size distortions. First, we make use of the bootstrap distribution rather than the asymptotic distribution. Second, the estimation of the long run variance is avoided with an appropriate choice of bootstrap test statistic. This choice of the test statistic also leads to higher asymptotic power. The empirical size and power performance of our test is compared with other bootstrap and conventional stationarity tests through Monte-Carlo studies. Simulations demonstrate that our bootstrap test controls size better and has higher power than the competing methods. In an empirical exercise, we employ our bootstrap test to check whether purchasing power parity holds for the countries in our study. We find less evidence against the PPP using our test than the other stationarity tests suggest.
A Powerful Unit Root Test Robust to Initial Condition: An Indirect Inference Based Approach
Abstract: In this paper, we consider the initial condition problem in unit root tests and trend estimation. Majority of the unit root tests are not robust to initial condition and may perform very poorly due to initial displacement. In this paper, we robustify the unit root tests to initial condition by utilizing indirect inference method. Our contribution in this paper is twofold; first we prove that indirect inference method can estimate trend function parameters consistently regardless of the initial displacement. Second, we improve the power of the unit root tests by using the robust indirect inference trend parameter estimates to detrend the data. The simulation results indicate that the power of our robust unit root test is not sensitive to initial condition. The results are useful in empirical testing for the presence of a unit root and for the estimation of the parameters of the trend function that is robust to initial condition.