THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENTS OF ECONOMICS AND STATISTICS

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1 THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENTS OF ECONOMICS AND STATISTICS COINTEGRATION AND VAR INNOVATION RESPONSE ANALYSIS OF UNEMPLOYMENT, EXCHANGE RATES, AND INTERNATIONAL TRADE GUANHAO FENG SPRING 2012 A thesis submitted in partial fulfillment of the requirements for baccalaureate degrees in Mathematics and Economics with interdisciplinary honors in Economics and Statistics Reviewed and approved* by the following: Herman J. Bierens Professor of Economics Thesis Supervisor James R. Tybout Professor of Economics Honors Adviser Naomi S. Altman Professor of Statistics Honors Adviser * Signatures are on file in the Schreyer Honors College.

2 1 Abstract: The aim of this honors thesis is to examine whether and how fluctuations in exchange rates and international trade affect the unemployment rate in the United States. In particular, on the basis monthly data and cointegrated or regular vector autoregressive (VAR) models I study the response of unemployment to shocks in exchange rates and international trade from the three largest trade partners of the United States (China, Japan and the Euro zone). To distinguish these effects from domestic causes I also include the index of industrial production in these models. The empirical work is to examine whether the time series involved are stationarity or unit root processes, and to conduct cointegration and VAR innovation response analysis. The results show that there is no significant response of unemployment to innovation shocks in the exchange rates. The same applies to innovation shocks in trade, except for trade with Japan and Germany. In particular, the response of unemployment to a unit shock in import from Japan is negative, which is contrary to what one would expect, whereas in a multi-country model the response of unemployment to a unit shock in exports to Germany is positive. i

3 Contents 1 Abstract: i 2 Introduction and Literature Review: 1 3 Data Analysis Data Selection and Sources Unit Root and Stationarity Tests VAR Innovation Response Analysis and Cointegration Stationary VAR Innovation Response Analysis Cointegration Empirical Results Unemployment and Industrial Production Import, Export and Exchange Rate Effects Japan Euro Zone Import and Export Effects Only Japan China Germany Trade Effects Multi-Country Analysis Joint imports Joint exports Conclusion and Future Research 20 7 References 21 ii

4 8 Appendix 22 iii

5 ACKNOWLEDGEMENTS It is my pleasure to thank those people who helped me to finish this thesis. First and foremost, I am heartily grateful to my thesis supervisor Dr. Herman Bierens for his encouragement, supervision and guidance from the beginning to the end. Most definitions and notations of this thesis follow from lecture notes of Professor Bierens, but any errors are mine. I would also like to record my gratitude to thank Dr. David Shapiro, Dr. Naomi Altman and Dr. Neil Wallace for their generous supports and suggestions on my academic work. In addition, I would like to thank Dr. James Tybout and all friends in the Honors Program of Economics for their helpful discussions, comments and advices during this year. Last but not least, I wish to thank my parents, families and friends for being supporting me all the time. iv

6 2 Introduction and Literature Review: In the aftermath of the financial crisis in 2008, high unemployment of about 9% and low growth, stirred up the discontentment of a large number of people. Figure 1: Unemployment rates There have been debates among economists regarding the global trade between developed countries and developing countries and many of them argued that reducing trade barriers lead to job loss (Amornthum, 2004). There were critics that the long-time unfavorable trade balance was one of the main reasons of current depression and high unemployment in the United States. Some analysts argued that American workers lost their jobs to foreign workers and the government should step in and protect the local manufacturing and employment. Most people would agree that, when the country still continued to figure out how to crawl out of the economic despair, workers could definitely be benefited from the recovery of local manufacturing, which was the key engine of local growth and employment. Therefore, an age-old question is how the production and employment of a country are affected by the international competition through global trade. With the increasing participation of developing countries in the global economy in the last three decades, employment and wages of manufacturing workers in the U.S. had been greatly af- 1

7 fected by the abundance of labor from developing countries. These countries encouraged American companies to move their manufacturing factories abroad by providing many preferential policies and abundance of low-waged and skilled labors. According to Forbes, companies from Apple to Ford Motors to Nike to HJ Heinz to Gap were expanding in mainland China to chase the global growth. In 2009, American companies spend $3.6 billion in foreign direct investment in China, up sharply from the $2.9 billion invested in Particularly, the undervaluation of some foreign currencies, for example the Chinese Yuan and Japanese Yen, has been blamed for the out-sourcing of US manufacturing. Undervaluing the currency of a country will lower its import prices and thus increases its competitiveness in the importing market. On one hand, Revenga (1992) empirically showed that changes in import prices have had large and significant effects on both employment and wages. On the other hand, Bergsten and Williamson (2002) emphasized that the over-valued dollar was causing long-term damage by eroding local manufacturing. In theory, real exchange rates adjust to keep every trading partner equally competitive in the market. No country suffers from any persistent trade deficits or enjoys any persistent trade surpluses (Shaikh, 1996). But Bergsten and Williamson (2002) pointed out that China and Japan were two special policy concerns because they had built large accumulations of foreign reserves, which had blocked the yuan and yen from appreciating. The Chinese government has capital controls to prevent the yuan from appreciating and the Japanese have repeatedly engaged in strategic interventions to gain competitive trade advantages. Burgess and Knetter (1996) conducted an international comparison of employment adjustment against exchange rate fluctuations. They estimated models for industry employment dynamics in fourteen industry categories for the G-7 countries. Their study confirmed that a real appreciation of a nation s currency leads to a decline in manufacturing employment, as expected. In addition, Burgess and Knetter (1996) argued that both the elasticity of employment to exchange rates and the speed of employment adjustment to exchange rate shocks were likely to depend primarily on the market structure and the regulations of international trade and the labor market, all of which 2

8 might vary substantially across countries and industries. This paper investigates the innovation response of US employment adjustment to exchange rate and international trade shocks from the three largest trade partners of the United States, China, Japan and the Euro zone, either on the basis of a cointegrated V ector Error C orrection M odel (VECM) if cointegration is present, or on the basis of a nonstructural V ector AutoRegression (VAR).More formal definitions and detailed discussions are included in section 4. In order to determine whether the monthly time series involved are (trend) stationary or unit root (with drift) processes, I have conducted a range of unit root and stationarity tests, since each test has its advantages and disadvantages. I conclude from these tests that almost all the time series in my analysis are unit root processes. Next, I have conducted Johansen s (1991) cointegration analysis to determine possible cointegration relations between these time series. If so, the innovation response analysis has been conducted with the VECM involved. If not, the time series have been differenced to make them stationary, and then the regular Sims (1980) VAR innovation response analysis have been conducted on the differenced time series. In the next section I will discuss the preliminary data analysis, in particular data selection, transformation and unit root tests. Then, in section 4, I proceed with the cointegration and VAR analysis, and in section 5 I make concluding remarks and suggest avenues for future research in this area. The last section is the appendix containing the (raw) data plots and autocorrelation plots of the differenced time series. The latter are used to determine whether to include seasonal dummy variables in the models. 3

9 3 Data Analysis 3.1 Data Selection and Sources The monthly statistics of industrial production, unemployment rate, imports, exports and exchange rates with respect to China, Japan, Germany and the Euro zone have been collected from the following sources: 1. Census Bureau (monthly data of Exports and Imports with China, Japan and Euro zone) 2. Bureau of Labor Statistics (monthly data of unemployment rates) 3. Federal Reserve Bank of S.T. Louis (Industrial Production Index) 4. Federal Reserve Bank of S.T. Louis (monthly data of exchange rates with China, Japan and Euro zone) Initially, I planned to use real GDP instead of industrial production, but GDP data is only available as quarterly data, which would leave me with an insufficient number of observations for my analysis. The Industrial Production Index, an economic indicator released monthly by the Federal Reserve Board, measures real production output, which includes manufacturing, mining, and utilities. As my focus is on the domestic labor market, the Industrial Production Index (IPI) is a reasonable substitute for real GDP. I have chosen imports and exports indicators separately instead of the trade balance because I use the data after logarithmic transformations. The monthly time series started from January of 1997 to September 2011, except for the exchange rate between the euro and the dollar, which started from January of Unit Root and Stationarity Tests Because unit root processes cannot be bounded, and VECM and VAR models assume multivariate normal errors, all positive valued variables in my analysis have been made unbounded by taking 4

10 logs. The unemployment rate U is bounded between zero and 100. Therefore, the unemployment rate U has been transformed by Y = log(u/(100 U)) to make it unbounded. The time series of unemployment rate and Industrial Production Index are seasonally adjusted, but the other time series were not. I have checked the autocorrelation function (ACF) plots of the differences (log) time series involved, and they show obvious seasonal patterns in the import and export data. See the Appendix. Figure 2: CNY/USD Initially I planned to include the exchange rate with China in my analysis, because China is the largest trading partner of the United States. However, the exchange rates between China and the United States were almost constant before 2005, as seen from Figure 2. However, I will get back to China s case when studying models without exchange rates. Consider an AR(p) model in lag operator form: φ p (L)Y t = β 0 + U t, where φ p (L) = 1 β 1 L β 2 L 2 β p L p with L is the lag operator: LY t = Y t 1. 5

11 Given that the errors U t are stationary white noise, a necessary condition for the stationarity of Y t is that all the roots of the polynomial φ p (z) are greater than one in absolute value. In the case that one of the roots of φ p (z) is equal to one, the lag polynomial φ p (L) can be written as φ p (L) = (1 L)ψ p 1 (L), where ψ p 1 (L) is now a lag polynomial of order p 1. Then the AR(p) model becomes an AR(p 1) model in differences: ψ p 1 (L) Y t = β 0 + U t, where Y t = Y t Y t 1. Thus, in the unit root case we need to difference the time series to make it stationary. If the AR(p) model has a unit root, some tests of parameters restrictions may have different null distributions than in the case of a stationary process. For example, to test the null hypothesis that β 1 = 1 in the AR(1) model Y t = β 0 + β 1 Y t 1 + U t using the usual t-test, the null distribution involved is non-normal (Dickey and Fuller, 1979). Therefore, incorrect applications of classical inference may give incorrect results. I subjected the transformed time series to a series of unit root and stationarity tests, namely the Augmented Dickey-Fuller (ADF) test (Dickey and Fuller, 1981), the Phillips-Perron test (Phillips and Perron, 1988), the Breitung s (2002) nonparametric unit root test, the KPSS stationarity test (Kwiatkowski et al., 1992), and the Bierens-Guo stationarity test (Bierens and Guo, 1993). The unit root tests involved test the null hypothesis that the time series Y t has a unit root (with drift) process against the alternative that Y t has a (trend) stationary process, whereas that stationarity tests reverse these hypotheses. The results for the seasonally adjusted data are the following: 1. Y t = log(unemployment rate/(100 - unemployment rate)) H 0 (unit root) was not rejected at the 10% significance level by the ADF test with lag p = 6. (p = 6 was suggested by information criteria.) H 0 (unit root) was not rejected at the 10% significance level by the Phillips-Perron test. H 0 (unit root) was not rejected at neither 5% nor 10% significance levels by Breitung s test. 6

12 H 0 (stationarity) was rejected at the 5% significance level by the KPSS test. H 0 (stationarity) was rejected at the 5% significance level by the Bierens-Guo test. Thus, we conclude that Y t has a unit root process. 2. Y t = log(industrial Production Index) H 0 (unit root with drift) was not rejected at the 10% significance level by the ADF test with lag p = 4. (p = 4 is suggested by Information criteria.) H 0 (unit root with drift) was not rejected at the 10% significance level by the Phillips-Perron test. H 0 (unit root with drift) was not rejected at neither 5% nor 10% significance levels by Breitung s test. H 0 (trend stationarity) was rejected at the 5% significance levels by the KPSS test. H 0 (trend stationarity) was rejected at the 5% significance level by the Bierens-Guo test. Thus, we conclude that Y t has a unit root process with drift. In the presence of seasonal dummy variables the ADF test and Bierens-Guo tests are no longer applicable. A non-seasonal ARIMA(p,r,q) model for a time series Y t takes the form X t = (1 L) r Y t, φ p (L)X t = β 0 + ψ q (L)U t where X t is a stationary ARMA(p,q) process with stationary white noise U t. However, the Phillips-Perron test, Breitung test and the KPSS test are nonparametric tests and can handle ARIMA models. Therefore, these tests remain valid after the seasonal dummy variables are averaged out by a 12 months moving average transformation: MA(Y t ) = m=0 Y t m. Thus, the tests have been conducted on MA(Y t ). If MA(Y t ) is a unit root process, so is Y t, and 7

13 if MA(Y t ) is stationary, so is Y t. The test results are listed below. Note that the variable trade is the sum of import and export. 1. Y t = log(import from Euro zone)) H 0 (unit root with drift) was not rejected at the 10% significance level by the Phillips-Perron test. H 0 (unit root with drift)was not rejected at neither 5% nor 10% significance levels by Breitung s test. H 0 (trend stationarity) was rejected at the 5% significance level by the KPSS test. Conclusion: Y t has a unit root process. 2. Y t = log(export to Euro zone)) H 0 (unit root with drift) was not rejected at the 10% significance level by the Phillips-Perron test. H 0 (unit root with drift) was not rejected at neither 5% nor 10% significance levels by Breitung s test. H 0 (trend stationarity) was not rejected at the 5% significance level but rejected at 10% significance level by the KPSS test. In view of the latter I conclude that Y t has a unit root process with drift. 3. Y t = log(import from Japan)) H 0 (unit root with drift) was not rejected at the 10% significance level by the Phillips-Perron test. H 0 (unit root with drift) was rejected at the 5% significance levels by Breitung s test. H 0 (trend stationarity) was not rejected at neither 5% nor 10% significance levels by the KPSS test. In view of the latter two results my conclusion is that Y t has a trend stationary process. 4. Y t = log(export to Japan)) H 0 (unit root with drift) was not rejected at the 10% significance level by the Phillips-Perron 8

14 test. H 0 (unit root with drift) was rejected at the 5% significance level by Breitung s test. H 0 (trend stationarity) was not rejected at neither 5% nor 10% significance levels by the KPSS test. In view of the latter two results I conclude that Y t has a trend stationary process. 5. Y t = log(eur/usd)) H 0 (unit root) was not rejected at the 10% significance level by the Phillips-Perron test. H 0 (unit root) was not rejected at neither 5% nor 10% significance levels by Breitung s test. H 0 (stationarity) was rejected at the 5% significance level by the KPSS test. Conclusion: Y t has a unit root process. 6. Y t = log(jpy/usd)) H 0 (unit root with drift) was not rejected at the 10% significance level by the Phillips-Perron test. H 0 (unit root) was not rejected at neither 5% nor 10% significance levels by Breitung s test. H 0 (stationarity) was rejected at the 5% significance levels by the KPSS test. Conclusion: Y t is a unit root process. 7. Y t = log(trade with Euro zone)) H 0 (unit root with drift) was not rejected at the 10% significance level by the Phillips-Perron test. H 0 (unit root with drift) was not rejected at neither 5% nor 10% significance levelsby Breitung s test. H 0 (trend stationarity) was not rejected at the 5% significance level but rejected at the 10% significance level by the KPSS test. Despite the latter my conclusion is that Y t is a unit root with drift process. 8. Y t = log(trade with Japan)) H 0 (unit root with drift) was not rejected at the 10% significance level by the Phillips-Perron 9

15 test. H 0 (unit root with drift) was not rejected at neither 5% nor 10% significance levels by Breitung s test. H 0 (trend stationarity) was rejected at the 5% significance level by the KPSS test. Conclusion: Y t is a unit root with drift process. 9. Y t = log(trade with China)) H 0 (unit root with drift) was not rejected at the 10% significance level by the Phillips-Perron test. H 0 (unit root with drift) was not rejected at neither 5% nor 10% significance levels by Breitung s test. H 0 (trend stationarity) was rejected at the 5% significance levels by the KPSS test. Conclusion: Y t is a unit root with drift process. 10. Y t = log(trade with Germany)) H 0 (unit root with drift) was not rejected at the 10% significance level by the Phillips-Perron test. H 0 (unit root with drift) was not rejected at the 5% significant level but rejected at the 10% significance level by Breitung s test. H 0 (trend stationarity) was not rejected at neither 5% nor 10% significance levels by KPSS test. In view of the first two I conclude that Y t is a unit root with drift process. 10

16 4 VAR Innovation Response Analysis and Cointegration 4.1 Stationary VAR Innovation Response Analysis The basic VAR(p) model is: p Y t = η + C s Y t s + U t, s=1 where Y t is a k-variate time series; η is a k-dimensional vector of constants; C s, s = 1, 2, 3,..., p, are k k coefficient matrices; U t is k-variate Gaussian white noise: U t is i.i.d. N k (0, Σ). If the VAR(p) process is stationary then by the Wold decomposition it has an infinite vector moving average, VMA( ), representation: Y t = µ + Γ s U t s, Γ 0 = I k s=1 Moreover, using the Cholesky decomposition Σ = LL, where L is a k k lower-triangular matrix, we can write U t = Le t, where e t = (e 1,t,..., e k,t ) is i.i.d. N k (0, I k ). The components e 1,t,..., e k,t of e t are now the innovations associated to the corresponding components of Y t. It follows now that for m 0, E(Y t+m e t ) = Γ m Le t + µ = Γ m where l i is column i of L. 11 k l i e i,t + µ, i=1

17 The response of Y t+m to a unit shock in the innovation e i,t of component i of Y t is now defined as E(Y t+m e i,t = 1) E(Y t+m ) = Γ m l i. 4.2 Cointegration If all the components of a k-variate time series process Y t are unit root processes, it is possible if there exist one or more linear combinations β Y t that are stationary. This is called cointegration. In this case, and under some regularity conditions, the process Y t can be represented by the following p order vector error correction model, shortly VECM(p): p 1 Y t = π 0 + Π s Y t 1 + αβ Y t p + U t. s=1 Here α and β are k r matrices with linear independent columns, with r k the cointegration rank. If r = 0 then αβ = O, so that the VECM(p) becomes a stationary VAR(p 1) model in the differences Y t, and if r = k then Y t is a stationary VAR(p) process. In the case of cointegration, 1 r < k, we can still use the VECM(p) to conduct innovation response analysis, but in general the innovation responses no longer taper off towards zero, and it is no longer possible to endow the innovation responses with standard errors. Johansen (1991) has proposed two likelihood ratio tests for the cointegration rank r, the lambda-max test and the trace test, under various assumptions about the trend or intercept parameters of the VECM(p) process. The lambda-max test tests the null hypothesis that the cointegration rank is equal to r against the alternative hypothesis that the cointegration rank is greater or equal to r + 1. This test is conducted sequentially for r = 0, 1, 2,..., k 1. The trace test tests the null hypothesis that the cointegration rank is equal to r against the alternative hypothesis that the cointegration rank is k. This test is conducted sequentially in reversed order, for r = k 1, k 2,..., 0. 12

18 5 Empirical Results 5.1 Unemployment and Industrial Production It is obvious that the industrial production index is a major determinant of the unemployment rate. Therefore, all VAR and VECM models below include the unemployment rate and the industrial production index, in the form 1. Y 1,t = log(unemployment rate/(100 - unemployment rate)), 2. Y 2,t = log(industrial Production Index), next to trade and exchange rate variables. Recall that both variables are seasonally adjusted, and that Y 1,t is a unit root without drift process and Y 2,t is a unit root with drift process. To determine whether these two time series are cointegrated, I have conducted Johansen s cointegration tests on the basis of a VECM(p) with a time trend. The reason for the latter is that the two time series veer apart due to the drift in Y 2,t. In particular, the selected option in EasyReg for the deterministic terms in the VECM was intercepts and time trend, without cointegration restrictions on the time trend parameters imposed. The order p was determined on the basis of information criteria. The result was that these two time series are not significantly cointegrated. Consequently, the two variables were differenced to make them stationary, and a VAR(p) was fitted to ( Y 1,t, Y 2,t ). The order p = 4 was chosen on the basis of the Hannan-Quinn information criterion (Hannan and Quinn, 1979). Figure 3 displays the response of Y 1,t+m to a unit shock in the innovation of Y 2,t over a horizon of 18 months: m = 0, 1,..., 18. The dots in this plot represent the one and two times standard error bands. The latter correspond to the 95% confidence intervals. As expected, a positive innovation shock in the growth of industrial production, Y 2,t, has a significant negative effect on the growth of unemployment, for at least 12 months 13

19 Figure 3: Base Model 5.2 Import, Export and Exchange Rate Effects Japan Next to the unemployment and industrial production variables I now include imports exports, the exchange rate with Japan. So, the vector time series Y t involved has the following components: 1. Y 1,t = log(unemployment rate/(100 - unemployment rate)), 2. Y 2,t = log(industrial Production Index), 3. Y 3,t = log(jpy/usd), 4. Y 4,t = log(import from Japan), 5. Y 5,t = log(export to Japan). Recall that the import and export variables are not seasonally adjusted. To determine whether the time series Y 4,t and Y 5,t have seasonally varying drift, I have plotted the autocorrelation functions for Y 4,t and Y 5,t. See the Appendix. Clearly, these ACF plots display seasonal patterns. Thus, in conducting Johansen s cointegration analysis I have selected the option intercepts and seasonally dummies, without cointegration restrictions imposed for the deterministic variables in the VECM(p). The Hannan-Quinn information criterion suggested p = 2. 14

20 The result of the Johansen s test was conclusive: These five variables are cointegrated, with cointegration rank r = 1, and standardized cointegrating vector β = ( , 1, , , ) corresponding to Y t = (Y 1,t,..., Y 5,t ). Thus, β Y t is stationary. The 18-months innovation response plots involved are presented in the figures labeled IRP 1.1, 1.2 and 1.3. Note that export and exchange rate have no effect on unemployment. However, import from Japan has a negative association on unemployment in the US, which is puzzling. We would expect that an increase in imports will lower the domestic production and thus increases the unemployment rate Euro Zone Similar to the case of Japan, the vector time series Y t in the case of the Euro zone has the following components: 1. Y 1,t = log(unemployment rate/(100 - unemployment rate)), 2. Y 2,t = log(industrial Production Index), 3. Y 3,t = log(euro/usd), 4. Y 4,t = log(import from Euro zone), 5. Y 5,t = log(export to Euro zone). Again, I applied the Johansen s cointegration test first, with the same option for the deterministic terms in the VECM as in the case of Japan. It turned out that these five variables are not cointegrated. Therefore, I have fitted a VAR(p) model to Y t.the Hannan-Quinn and Schwarz (1978) information criteria suggest p = 2. 15

21 The 18-months innovation response plots are presented in the figures labeled IRP 1.4, 1.5 and 1.6. Clearly, the import, export and exchange rate with the Euro zone have no significant effect on unemployment in the US. 5.3 Import and Export Effects Only Since the exchange rates with Japan and the Euro zone have no effect on unemployment in the US, I will now change my focus to the possible effect of import and export on unemployment. By removing the exchange rate it is now possible to include China in my analysis. Moreover, I will now select Germany as a representative of Euro zone because then I can use more data for the analysis. The updated data set now starts at January I am expecting a positive innovation response of imports and a negative innovation response of exports on unemployment rates Japan The vector time series Y t involved has the following components: 1. Y 1,t = log(unemployment rate/(100 - unemployment rate)), 2. Y 2,t = log(industrial Production Index), 3. Y 3,t = log(import from Japan), 4. Y 4,t = log(export to Japan). As before, these four time series are cointegrated, with cointegrating rank r = 1 and standardized cointegrating vector β = ( , , 1, ). Thus, β Y t is stationary. The innovation response plots are presented in the figures labeled IRP 2.1 and 2.2. As to be expected, the results are the same as before. 16

22 5.3.2 China The vector time series Y t involved has the following components: 1. Y 1,t = log(unemployment rate/(100 - unemployment rate)), 2. Y 2,t = log(industrial Production Index), 3. Y 3,t = log(import from China), 4. Y 4,t = log(export to China). Johansen s cointegration tests indicate that these time series are not cointegrated. Therefore the innovation response analysis has been conducted via a VAR(p) model for the first differences Y t, with p = 2 suggested by the Hannan-Quinn information criterion. However, the plots of innovation responses in figures labeled IRP 2.3 and 2.4 do not show any significant effect of import and export on unemployment in the US Germany The vector time series Y t involved has the following components: 1. Y 1,t = log(unemployment rate/(100 - unemployment rate)), 2. Y 2,t = log(industrial Production Index), 3. Y 3,t = log(import from Germany), 4. Y 4,t = log(export to Germany). In this case these four variables are cointegrated, with cointegrating rank r = 1 and cointegrating vector β = ( , 1, , ) Therefore, the innovation response analysis is conducted on the basis of a VECM(p), with p = 3 suggested by the Hannan-Quinn information criterion. The innovation response plots in figures IRP 2.5 and 2.6 show no substantial effect of import and export on unemployment. 17

23 5.4 Trade Effects I have also tried to conduct innovation response analysis with the variable trade, which is the sum of imports and exports, instead of imports end exports separately. This trade variable was taken in logs. In neither of the cases for Japan, China and Germany I could find cointegration, so that the innovation response analysis was conducted in the basis of VAR s in differences. The results, presented in the figures labeled 3.1, 3.2 and 3.3, show no significant impact of trade on unemployment. 5.5 Multi-Country Analysis Since so far I didn t get many significant results from the single country cases, I have finally tried the case where the imports from and exports to Japan, China and Germany are jointly included in two vector time series, one for imports and one for exports Joint imports The vector time series Y t involved has the following components: 1. Y 1,t = log(unemployment rate/(100 - unemployment rate)), 2. Y 2,t = log(industrial Production Index), 3. Y 3,t = log(imports from Japan), 4. Y 4,t = log(imports from Germany). 5. Y 5,t = log(imports from China) Johansen s cointegration test showed no cointegration for the vector of these 5 variables, so I used a VAR(p) in differences. The Hannan-Quinn criterion suggested that p = 2. However, the plots of innovation responses in figures IRP 4.1, 4.2 and 4.3 show no significant effects of imports on unemployment. 18

24 5.5.2 Joint exports The vector time series Y t involved has the following components: 1. Y 1,t = log(unemployment rate/(100 - unemployment rate)), 2. Y 2,t = log(industrial Production Index), 3. Y 3,t = log(export to Japan), 4. Y 4,t = log(export to Germany). 5. Y 5,t = log(export to China) The result of Johansen s cointegration analysis is that these time series are cointegrated with one cointegrating vector, β = ( , , , 1, ) The Hannan-Quinn criterion suggested that p = 3 for the VECM(p). In the innovation response plots IRP 4.4, 4.4 and 4.6, the responses of unemployment to unit shocks in exports to Japan and China are negative, as expected. However, in the case of Germany the effect is positive, which constitutes another puzzle. 19

25 6 Conclusion and Future Research Initially, I expected that the overvaluation of the dollar, or the undervaluation of foreign currencies, was one of the main reasons for unemployment in the United States. However, I could not find any significant response of unemployment rates to a unit shock in exchange rates. Thus, I have to conclude that dollar overvaluation is not a significant reason for high unemployment. Next, I changed my focus on the trade part, which is always an important part of domestic production. The case of Japan was interesting because of the positive response of unemployment to a unit shock in the import from Japan, which is contrary to what I expected. However, in the model with several countries, this significance of the innovation response to the imports from Japan disappeared. In fact, the innovation response to imports of any country is insignificant in this model. With respect to the case of exports in the model with several countries, the responses of unemployment were negative to unit shocks in exports to Japan and China as expected, yet positive to a unit shock in exports to Germany, which is interesting for further research. In future research, I will focus on the models with several countries and carry out more empirical analysis. Companies from different countries are competing with American companies with different levels of exports. For example, automobile companies of Japan and Germany are very competitive while imports of China are mainly low level goods. However, if the variables in the VAR model are highly correlated, the effects of multicollinearity might be one of the reasons. The puzzling innovation responses found in this study are interesting topics for further research. 20

26 7 References 1. Amornthum S. (2004): Trade and Unemployment. Retrieved from www2.hawaii.edu/ amornthu/pdf/paper660.pdf 2. Bergsten, C. F. and Williamson, J. (2003): Dollar Overvaluation and the World Economy. Washington: Institute for International Economics 3. Bierens,H.J. and Guo, S. (1993): Testing Stationarity and Trend Stationarity Against the Unit Root Hypothesis. Econometric Reviews 12, Bierens, H. J. (2011): Forecasting, lecture notes for Econ Bierens, H. J. (2011): Model Specification, lecture notes for Econ Bierens, H. J. (2011): Vector auto regressions and innovation response analysis, lecture notes for Econ Bierens, H. J. (2011): The Augmented Dickey-Fuller (ADF) and Phillips-Perron tests, lecture notes for Econ Bierens, H. J. (2011): Cointegration Analysis, lecture notes for Econ Bierens, H. J. (2011): Guided tour on Johansen s cointegration analysis 10. Bierens, H. J. (2011): EasyReg International. hbierens/easyreg.htm 11. Breitung, J. (2002): Nonparametric Tests for Unit Roots and Cointegration. Journal of Econometrics 108, Burgess, S. and Knetter, M. (1998): An international comparison of employment adjustment to exchange rate fluctuations. Review of International Economics, pp Dickey D.A. and Fuller W.A. (1979): Distribution of the estimators for autoregressive times series with a unit root. Journal of the American Statistical Association 74,

27 14. Dickey D.A. and Fuller W.A. (1981): Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49, Epstein, G. and Meredith, R. (2010): U.S. Companies That Invest Big In China. Retrieved from Hannan, E. J., and Quinn, B. G. (1979): The Determination of the Order of an Autoregression. Journal of the Royal Statistical Society, B, 41, Johansen, S. (1991): Estimation and Hypothesis Testing of Cointegrating Vectors in Gaussian Vector Autoregressive Models. Econometrica 59, Krugman, P. R. (1993): What Do Undergrads Need to Know About Trade? American Economic Review, 83(2), pp Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. and Shin, Y. (1992): Testing the Null of Stationarity Against the Alternative of a Unit Root. Journal of Econometrics 54, Phillips, P.C.B. and P.Perron (1988): Testing for a Unit Root in Time Series Regression. Biometrica 75, Revenga, A. (1992): Exporting Jobs? the Impact of Import Competition on Employment and Wages in U.S. Manufacturing. Quarterly Journal of Economics, 107(1), pp Schwarz, G. (1978): Estimating the Dimension of a Model. Annals of Statistics, 6, Shaikh, Anwar (1996): Free trade, unemployment and economic policy. Global Unemployment: Loss of jobs in the 90 s, ME Sharpe, Armonk, New York 24. Sims, C.A. (1980): Macroeconomics and Reality. Econometrica 48, Appendix 22

28 (a) IRP 1.1 (b) IRP 1.2 (c) IRP

29 (d) IRP 1.4 (e) IRP 1.5 (f) IRP

30 (g) IRP 2.1 (h) IRP 2.2 (i) IRP 2.3 (j) IRP

31 (k) IRP 2.5 (l) IRP

32 (m) IRP 3.1 (n) IRP 3.2 (o) IRP

33 (p) IRP 4.1 (q) IRP 4.2 (r) IRP4.3 28

34 (s) IRP 4.4 (t) IRP 4.5 (u) IRP

35 Figure 4: Unemployment Rates and Industrial Production Index Figure 5: JPY/USD 30

36 Figure 6: EUR/USD 31

37 (a) Japan Exports/Imports (b) ACF plot of Japan Exports (c) ACF plot of Japan Imports 32

38 (d) Eurozone Exports/Imports (e) ACF plot of Eurozone Exports (f) ACF plot of Eurozone Imports 33

39 (g) China Exports/Imports (h) ACF plot of China Exports (i) ACF plot of China Imports 34

40 (j) Germany Exports/Imports (k) ACF plot of Germany Exports (l) ACF plot of Germany Imports 35

41 Feng, Guanhao (Gavin) 2220 Plaza Drive, State College, PA Tel: (814) Education Background Pennsylvania State University, University Park, PA 8/2009 5/2012(expected) B.S. in Mathematics, B.S. in Economics, Minor in Statistics Enrolled in Integrated Undergrad and Graduate program of M.S. in Statistics Honors: Honors Program of Economics / Schreyer Honors College / Phi Beta Kappa Zhongshan (Sun Yat-sen) University, Guangzhou, China 9/2007 7/2009 B.S. in Insurance (transferred) Honors: Outstanding Student Scholarship in freshman year Research and Teaching Experiences REU Program of Economics in Summer 2010 and Fall /2010 1/2011 Research Assistant for Prof. David Shapiro, Department of Economics Provide empirical work for three forthcoming papers and future research in Demography and Development collecting and manipulating data; creating and fixing datasets in Excel, STATA and SAS; regression analysis; statistics calculation; reading papers and surveys; preparing abstracts, graphs, tables and presentation files Economics Honors Program: Two course essays in Game Theory and Monetary Theory Senior Honors Thesis: Essay of VAR innovation response analysis on domestic unemployment rate in U.S. Thesis Advisor: Prof. Herman J. Bierens Abstract: The aim of this honors thesis is to examine whether and how fluctuations in exchange rates and international trade affect the unemployment rate in the United States. In particular, on the basis monthly data and cointegrated or regular vector autoregressive (VAR) models I study the response of unemployment to shocks in exchange rates and international trade from the three largest trade partners of the United States (China, Japan and the Euro zone). To distinguish these effects from domestic causes I also include the index of industrial production in these models. The empirical work is to examine whether the time series involved are stationarity or unit root processes, and to conduct cointegration and VAR innovation response analysis. The results show that there is no significant response of unemployment to innovation shocks in the exchange rates. The same applies to innovation shocks in trade, except for trade with Japan and Germany. In particular, the response of unemployment to a unit shock in import from Japan is negative, which is contrary to what one would expect, whereas in a multi-country model the response of unemployment to a unit shock in exports to Germany is positive. Computing Projects Computing Skills: STATA, C++, Matlab, SAS, R, LaTex, Microsoft Office (Word, Excel, PowerPoint) A software of Matrix Calculator in C++ with self-written matrix template class library (Intermediate Programming) Numerical Library for solving linear systems of equations using Matlab (Numerical Analysis I) Application of Numerical Ordinary Differential Equation to Passive Linear Filters (Numerical Analysis II)