This paper investigates the purchasing power parity (PPP) hypothesis using panel data. Under PPP the real exchange rate is stationary around a constant mean. Recent panel data unit root tests are employed to test the PPP proposition where, under the conventional null hypothesis of a unit root, the real exchange rate is not stationary and PPP does not hold. In this case, as the time period t + n approaches infinity, its variance relative to period t will also approach infinity. The usual alternative in unit root tests is stationarity around a constant mean or a linear trend. The paper brings innovation into the PPP and panel unit root testing literature by allowing for possible nonlinear deterministic trends in the alternative hypothesis (as advanced by Cushman (2004)). If the null hypothesis is rejected in favour of the alternative of a non-linear trend, PPP still does not hold, but does at least revert back to a meaningful, stable long-run equilibrium. Given this non-linear trend, the variance of the real exchange rate as t + n approaches infinity, conditional on that trend, remains finite. Overall, evidence for stationarity in exchange rates is found in four out of six panels under consideration, including both support for stationary processes with no trend or a linear trend as well as for processes following a non-linear deterministic trend, in particular at time orders 5 and 6. The rejections are, in fact, most consistent at the nonlinear orders. Given nonlinear trends, PPP as usually defined does not hold, despite the rejection of unit roots. It is also found that stronger evidence for stable long-run equilibria in real exchange rates appears when the German Deutschmark is chosen as a base currency instead of the US Dollar. Finally, it appears that a very recent panel unit root test that takes account of cross-sectional dependencies delivers more consistent and sensible results.

This paper investigates the purchasing power parity (PPP) hypothesis using panel data. Under PPP the real exchange rate is stationary around a constant mean. Recent panel data unit root tests are employed to test the PPP proposition where, under the conventional null hypothesis of a unit root, the real exchange rate is not stationary and PPP does not hold. In this case, as the time period t + n approaches infinity, its variance relative to period t will also approach infinity. The usual alternative in unit root tests is stationarity around a constant mean or a linear trend. The paper brings innovation into the PPP and panel unit root testing literature by allowing for possible nonlinear deterministic trends in the alternative hypothesis (as advanced by Cushman (2004)). If the null hypothesis is rejected in favour of the alternative of a non-linear trend, PPP still does not hold, but does at least revert back to a meaningful, stable long-run equilibrium. Given this non-linear trend, the variance of the real exchange rate as t + n approaches infinity, conditional on that trend, remains finite. Overall, evidence for stationarity in exchange rates is found in four out of six panels under consideration, including both support for stationary processes with no trend or a linear trend as well as for processes following a non-linear deterministic trend, in particular at time orders 5 and 6. The rejections are, in fact, most consistent at the nonlinear orders. Given nonlinear trends, PPP as usually defined does not hold, despite the rejection of unit roots. It is also found that stronger evidence for stable long-run equilibria in real exchange rates appears when the German Deutschmark is chosen as a base currency instead of the US Dollar. Finally, it appears that a very recent panel unit root test that takes account of cross-sectional dependencies delivers more consistent and sensible results.

The studies of exchange rate theory in international finance are divided into several schools. Purchasing Power Parity (PPP) is one important hypothesis in both the Monetary Exchange Rate theory and the main theory in the Open Macroeconomics Model. Although many models are found upon the existence of PPP, but it still has not been proved empirically. That is why it¡¦s important to examine the existence of PPP. In the past, the statistic analyzing processes are all made directly under the models since all variables have been assumed stationary. However, regressing two non-stationary variables may result in Spurious Regression. The Unit Roots Test and Cointegration Test are developed in order to avoid the problem of spurious regression. Therefore, Unit Roots Test and Cointegration Test should be applied to the variables before estimating during regression analyses. Concerning the power deficiency of Unit Roots Test and Cointegration Test, many researches have adopted the combination time-series and cross-section Panel Data Model in order to improve the power and limitation of small samples. The Panel-Unit Root Test and Panel-Cointegration Test have therefore been developed to avoid Spurious Regression. However, Panel-Unit Root Test and Panel-Cointegration Test are applied with long time-series and large cross-section. Nevertheless, obtaining the data has always been the toughest difficulty during empirical researches, let alone the need for long period and large unit data. These Panel Data Models can only be applied to studies for long period, but not to the short periods. In order to avoid these problems; Binder, Hsiao and Pesaran (2004) have developed the Short Panel Vector Autoregressions (sPVAR) Model, a Panel Data Model developed with short time-series and large cross-section. Therefore, this paper will focus on Purchasing Power Parity under the sPVAR Model with the examination of PPP for the 30 countries since the introduction of Euro (1998 to 2004).

Dynamic panel data models are widely used by econometricians to study over time the economics of, for example, people, firms, regions, or countries, by pooling information over the cross-section. Though much of the panel research concerns inference in stationary models, macroeconomic data such as GDP, prices, and interest rates are typically trending over time and require in one way or another a nonstationary analysis. In time series analysis it is well-established how autoregressive unit roots give rise to stochastic trends, implying that random shocks to a dynamic process are persistent rather than transitory. Because the implications of, say, government policy actions are fundamentally different if shocks to the economy are lasting than if they are temporary, there are now a vast number of univariate time series unit root tests available. Similarly, panel unit root tests have been designed to test for the presence of stochastic trends within a panel data set and to what degree they are shared by the panel individuals. Today, growing data certainly offer new possibilities for panel data analysis, but also pose new problems concerning double-indexed limit theory, unobserved heterogeneity, and cross-sectional dependencies. For example, economic shocks, such as technological innovations, are many times global and make national aggregates cross-country dependent and related in international business cycles. Imposing a strong cross-sectional dependence, panel unit root tests often assume that the unobserved panel errors follow a dynamic factor model. The errors will then contain one part which is shared by the panel individuals, a common component, and one part which is individual-specific, an idiosyncratic component. This is appealing from the perspective of economic theory, because unobserved heterogeneity may be driven by global common shocks, which are well captured by dynamic factor models. Yet, only a handful of tests have been derived to test for unit roots in the common and in the idiosyncratic components separately. More importantly, likelihood-based methods, which are commonly used in classical factor analysis, have been ruled out for large dynamic factor models due to the considerable number of parameters. This thesis consists of four papers where we consider the exact factor model, in which the idiosyncratic components are mutually independent, and so any cross-sectional dependence is through the common factors only. Within this framework we derive some likelihood-based tests for common and idiosyncratic unit roots. In doing so we address an important issue for dynamic factor models, because likelihood-based tests, such as the Wald test, the likelihood ratio test, and the Lagrange multiplier test, are well-known to be asymptotically most powerful against local alternatives. Our approach is specific-to-general, meaning that we start with restrictions on the parameter space that allow us to use explicit maximum likelihood estimators. We then proceed with relaxing some of the assumptions, and consider a more general framework requiring numerical maximum likelihood estimation. By simulation we compare size and power of our tests with some established panel unit root tests. The simulations suggest that the likelihood-based tests are locally powerful and in some cases more robust in terms of size. / Solving Macroeconomic Problems Using Non-Stationary Panel Data

The main purpose of this thesis is to explore whether the Balassa-Samuelson hypothesis can effectively explain the long-term change of the real exchange. The recent panel unit root, panel cointegration tests and fully modified OLS are applied to examine the four tested equations that are based on the Balassa-Samuelson hypothesis. 1. Relative differential productivity between traded and non-traded sectors influences price differential in two sectors. 2. We extend the relative productivity in non-traded and traded sectors causing change in non-traded relative price into the two-country model. 3. The appreciation (depreciation) of the real exchange results from the different relative price of the two-country model. 4. The appreciation (depreciation) of the real exchange is caused by the different relative productivity of the two-country model. The data span is from 1971 to 1995, and includes 12 OECD countries. There are three main different points from the existing literatures. 1. We apply some newly developed panel unit root tests to estimate the equations based on Balassa-Samuelson hypothesis. 2. The previous documents only estimated the model of one variable, but the estimation of two variables was rare. In the equation 14 and 15, we examined the two variables in both. 3. In the calculation of the price, owing to the difficulties of collecting data from various sectors, we use a special way to measure the price. Finally, we can observe from the results of the empirical study: when productivity of the domestic sectors differentiates, that is, 1% increase in relative productivity between traded and non-trade sectors causes 0.53% increase in domestic relative prices. When it is taken into the two-country model, the increase of productivity will cause the appreciation of the real exchange rate. This can explain why in the developed countries like the U.S. and Japan, the faster increase in domestic relative productivity causes the appreciation of real exchange rates in the long run.

The main purpose of this thesis is to explore whether the Balassa-Samuelson hypothesis can effectively explain the long-term change of the real exchange. The recent panel unit root, panel cointegration tests and fully modified OLS are applied to examine the four tested equations that are based on the Balassa-Samuelson hypothesis. The data span is from 1985 to 2002, and includes 7 east asian countries. 1. Relative differential productivity between traded and non-traded sectors influences price differential in two sectors. 2. We extend the relative productivity in non-traded and traded sectors causing change in non-traded relative price into the two-country model. 3. The appreciation (depreciation) of the real exchange results from the different relative price of the two-country model. 4. The appreciation (depreciation) of the real exchange is caused by the different relative productivity of the two-country model. Finally, we can observe from the results of the empirical study: when productivity of the domestic sectors differentiates, that is, 1% increase in relative productivity between traded and non-trade sectors causes 0.28% increase in domestic relative prices. When it is taken into the two-country model, the increase of productivity will cause the appreciation of the real exchange rate.

The thesis consists of four papers that address likelihood-based unit root tests for panel data with cross-sectional dependence arising from common factors. In the first three papers, we derive Lagrange multiplier (LM)-type tests for common and idiosyncratic unit roots in the exact factor models based on the likelihood function of the differenced data. Also derived are the asymptotic distributions of these test statistics. The finite sample properties of these tests are compared by simulation with other commonly used unit root tests. The results show that our LM-type tests have better size and local power properties. In the fourth paper, we estimate the spaces spanned by the common factors and the spaces spanned by the idiosyncratic components of the static factor model by using the quasi-maximum likelihood (ML) method and compare it with the widely used method of principal components (PC). Next, by simulation, we compare the size and power properties of established tests for idiosyncratic unit roots, using both the ML and PC methods. Simulation results show that the idiosyncratic unit root tests based on the likelihood-based residuals generally have better size and higher size-adjusted power, especially when the cross-sectional dimension is small and the time series dimension is large.

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The “special treatments” of automobile industry in China, especially in the forms of local protectionism, have been criticized as evidences of domestic market fragmentation for long. Whether these “special treatments” have stunted the integration of a national auto market in China remains a question. This paper seeks to examine the degree of market integration in the automobile markets in China by using tests of cointegration between prices of spatial markets. Several econometric approaches for spatial price analysis, including the ADF unit root test, Maddala-Wu’s Fisher type panel unit root test and more restrictive Dufour-Torres panel unit root test are applied to monthly average retail prices for the main models sold across 36 cities from 1994-2006. Besides the above conventional linear methods, the author also applies the newly developed nonlinear unit root method proposed by Kapetanios et al. (2003). Test results indicate that the nonlinear test support convergence more often than the conventional linear unit root tests. Moreover, they also reveal that price convergence and hence market integration hold for majority of models and markets. The paper also investigates possible explanatory factors in price disparities of auto markets among cities. As the evidence shows, the geographic distance between markets, difference of per capital income, and the existence of local production play important roles in the absolute price differentials as well as the volatility of price differentials among cities.

This thesis is comprised of five papers that all relate to bootstrap methodology in analysis of non-stationary time series. The first paper starts with the fact that the Dickey-Fuller unit root test using asymptotic critical value has bad small sample performance. The small sample correction proposed by Johansen (2004) and bootstrap are two effective methods to improve the performance of the test. In this paper we compare these two methods as well as analyse the effect of bias-adjusting through a simulation study. We consider AR(1) and AR(2) models and both size and power properties are investigated. The second paper studies the asymptotic refinement of the bootstrap cointegration rank test. We expand the test statistic of a simplified VECM model and a Monte Carlo simulation was carried out to verify that the bootstrap test gives asymptotic refinement. The third paper focuses on the number of bootstrap replicates in bootstrap Dickey-Fuller unit root test. Through a simulation study, we find that a small number of bootstrap replicates are sufficient for a precise size, but, with too small number of replicates, we will lose power when the null hypothesis is not true. The fourth and last paper of the thesis concerns unit root test in panel setting focusing on the test proposed by Palm, Smeekes and Urbain (2011). In the fourth paper, we study the robustness of the PSU test with comparison with two representative tests from the second generation panel unit root tests. In the last paper, we generalise the PSU test to the model with deterministic terms. Two different methods are proposed to deal with the deterministic terms, and the asymptotic validity of the bootstrap procedure is theoretically checked. The small sample properties are studied by simulations and the paper is concluded by an empirical example. / <p>Ogiltigt ISBN: 978-91-554-9069-0</p>