Smooth structural changes and cointegration analysis in panel data

This dissertation consists of three essays on testing cointegration with structural breaks in time series and panel data. The first study suggests a simple cointegration test with smooth structural changes for the null of no cointegration. The test is based on the Lagrange Multiplier approach, and it can admit serially correlated and heteroskedastic errors, deterministic trends, and smooth structural breaks. The asymptotic distribution of proposed test statistic is derived, and the asymptotic results show that the distribution is free of nuisance parameter dependencies, other than the Fourier frequency. Moreover, the asymptotic analysis reveals that the new test is independent of the number of regressors. To make the testing procedure relatively simple and easy to implement, we use the response surface functions to obtain finite-sample critical values and corresponding p-values. We perform Monte Carlo simulations to evaluate the finite-sample size and power of the suggested test. The simulation results reveal that the proposed test is good size and power properties under different types of structural breaks. The second study proposes new Lagrange Multiplier-based cointegration tests with structural breaks for dependent panels. To take into account unknown multiple structural breaks, we utilize the Fourier approach that can capture unknown multiple structural changes by using small number of frequencies. On the other hand, we use the PANIC approach to consider cross-section dependency. We derive the asymptotic distribution of suggested test statistic and find that the distribution of test statistics only depends on the Fourier frequency and independent of the number of regressors and common factors. The Monte Carlo simulations results reveal that proposed tests are good size and power properties for stationary or non-stationary common factors under the different types of structural breaks. The third study examines the validity of PPP hypothesis for 17 OECD countries by employing our new panel cointegration tests with smooth breaks. The purpose of this study is to show the practical application of the new tests and to compare the results with the panel cointegration test with sharp breaks. The results from our suggested cointegration tests provide evidence in favor of PPP validity which is consistent with theoretical expectations.