Three essays on nonlinear nonstationary econometrics and applied macroeconomics

by 1968- Bae, Youngsoo

My dissertation develops a nonlinear cointegration estimation method and a three-regime threshold unit root test, and applies them to the long-run money demand function estimation and the testing for the purchasing power parity, respectively. In my first essay entitled “A New Nonlinear Cointegration Method” I develop a new nonlinear cointegration estimation method that can be used for the logarithmic function of an I(1) process in a more general time series setting where serial correlation in error terms and temporal dependence between an I(1) process and error terms exit. I propose a new estimator, and establish its asymptotic properties, such as consistency and asymptotic normality. Also for the statistical inference, I propose a fully-modified type technique. My second essay entitled “Money Demand Function Estimation by Nonlinear Cointegration” is an empirical application of the new nonlinear cointegration estimation method developed in the first essay. I estimate three different functional forms of the US and Japanese long-run money demand. Two of them are nonlinear functions of the nominal interest rate that allow for the liquidity trap. Conventionally, the longrun money demand function is estimated by using the linear cointegration methods, such as DOLS and FMOLS. However, using the linear cointegration methods requires different assumptions about the nominal interest rate for different functional forms. ii Meanwhile, nonlinear cointegration method allows us to estimate different functional forms under the one assumption that the nominal interest rate is an I(1) process. For US, the new nonlinear cointegration estimation method results in larger coefficient estimates and produces superior out-of-sample prediction performance than the conventional linear cointegration methods. Among the different functional forms, the nonlinear functional forms outperform the linear functional form in terms of out-ofsample prediction performance. For Japan, the nonlinear functional forms outperform the linear one in terms of out-of-sample prediction performance, however there is no significant difference among different estimation methods. In the final essay of my dissertation entitled “Correlation Robust Threshold Unit Root Tests” I proposes a new three-regime threshold unit root test that is robust against serial correlation in error terms. I use the similar bandwidth-type sequence as in the first essay to eliminate the consequence from discontinuity of the indicator function and general dependence structure in error terms. Since threshold parameters are not identified under the unit root null hypothesis, I consider a test statistic that is obtained by optimizing the t-statistic over the unidentified threshold parameters. In this context, I establish the weak convergence of the test statistic. The limiting distribution of the test statistic does not depend on nuisance parameters. I apply the new test to the real exchange rate of several European countries to test for the purchasing power parity. I find that the new test can reject the unit root null hypothesis more often than the conventional unit root tests, such as ADF and PP tests. iii To my parents and my family iv