Testing purchasing power parity in a multivariate cointegrating framework

This paper examines a bilateral PPP(Purchasing power parity) relationship between Australia and the 11 major trading countries by means of two alternative econometric techniques-a multivariate cointegrating framework and a band-spectral regression. It is acknowledged that there is no strong evidence that classical PPP holds in all cases. However, the generalized version of PPP holds in all cases, and provides a better explanation of the long-run relations between exchange rates and relative prices.The use of different price indices, i.e CPI and WPI,lead to different estimates and hence different policy implications.     

Common trends in prices and exchange rates. Tests of long-run purchasing power parity

The empirical validity of long-run purchasing power parity is investigated using multi-variate cointegration techniques. Both bilateral and multilateral PPP is examined. The data set is monthly and covers almost 22 years (January 1970–August 1991) for four countries — Germany, Japan, the U.S., and Great Britain. While three cointegrating relations are detected among the set of nominal exchange rates and domestic price levels (or equivalently, there exists a reduced number of common stochastic trends) none of these satisfy the linear constraints implied by PPP. We conclude that neither bilateral nor multilateral PPP can be supported by the behavior of the data.     

Long‐Run PPP under the Presence of Near‐to‐Unit Roots: The Case of the British Pound–US Dollar Rate*

Empirical tests typically provide evidence that the British pound–US dollar exchange rate and the relative wholesale price index contain exact unit roots and exhibit cointegration. However, the cointegrating vector is significantly different from [1, ?1], thus raising doubts on the validity of the purchasing power parity (PPP) hypothesis. Following Elliott (1998 ), we show that if the exchange rate and relative price series contain near‐to‐unit roots in the context of a bivariate system, then any inference on the “cointegrating” vector and consequently on PPP, which is based on standard cointegration estimation methods, will be misleading. We then argue that the existing evidence against the PPP hypothesis in the British pound–US dollar market can be attributed to the finite sample bias of the standard cointegration estimators, arising from an endogenous and “nearly” nonstationary regressor. We also show that when robust procedures are employed the evidence favors the PPP hypothesis.     

Imports and exports in 50 countries: Tests of cointegration and structural breaks

This paper provides new evidence on the long-run convergence between imports and exports in 50 countries over the quarterly period 1973:2 to 1998:1. Cointegration analyses are based on the Johansen [Johansen, S. (1995). Likelihood-based inference in cointegrating vector autoregressive models. New York: Oxford University Press.] and the Stock and Watson [J. Am. Stat. Assoc. 83 (1988) 1097.] system approaches. Evidence of stability of the cointegration space is examined using the SupF test developed by Hansen [J. Bus. Econ. Stat. 10 (1992) 321]. Based on the Johansen technique, we find evidence in favor of cointegration in 35 of the 50 countries. In addition, cointegration is confirmed for all countries (except Mexico) using the Stock and Watson test. This finding indicates that macroeconomic policies have been effective in the long-run and suggests that these countries are largely not in violation of their international budget constraint. We find evidence that in most of the countries where the slope coefficient on the export variable is positive, the cointegrating coefficient is also unity. The cointegration space appears stable for most of the countries. Nonetheless, the results suggest that countries in the regions of the Middle East, Latin America, and Europe have cointegrating relations that are more unstable than those in other regions.     

Testing for PPP: Should we use panel methods?

A common finding in the empirical literature on the validity of purchasing power parity (PPP) is that it holds when tested for in panel data, but not in univariate (i.e. country-specific) analysis. The usual explanation for this mismatch is that panel tests for unit roots are more powerful than their univariate counterparts. In this paper we suggest an alternative explanation. Existing panel methods assume that cross-unit cointegrating relationships, that would tie the units of the panel together, are not present. Using simulations, we show that if this important underlying assumption of panel unit root tests is violated, the empirical size of the tests is substantially higher than the nominal level, and the null hypothesis of a unit root is rejected too often even when it is true. More generally, this finding warns against the automatic use of panel methods for testing for unit roots in macroeconomic time series.First version received: November 2001/Final version received : October 2003     

Revisiting the Link Between Stock Prices and Goods Prices in OECD Countries

Fisher hypothesis postulates positive relation between stock return and inflation; however early studies document negative relationship between the two and they conclude that stock cannot be used as a hedge against inflation. In this paper we explore long‐run nonlinear relationship between stock price and goods price. Our sample consists of 19 OECD countries; all or some of these countries have been studied before with the findings of linear cointegration between the stock index and goods price index. Based on unit root tests and linear cointegration test, we apply threshold cointegration tests, Autoregressive Distributed Lag (ARDL) cointegration test and panel VAR method. With all these econometric methods we arrive at heterogeneous findings as follows: two countries have linear cointegration, five countries have threshold cointegration, nine countries do not have any cointegration and finally two countries provide inconclusive results. Estimates of Fisher coefficient provided by linear and nonlinear cointegration methods, which range between 1.27 and 1.86, are consistent with previous studies. Impulse response analysis from panel VAR for countries having no cointegrating relation shows that shock to inflation produces negative response in stock return, which supports findings of earlier studies.     

Revisiting purchasing power parity in G6 countries: an application of smooth time-varying cointegration approach

This study revisits purchasing power parity (PPP) for the G6 countries (i.e., Canada, Italy, Japan, France, Germany, the UK) using smooth time-varying cointegrating approach, proposed by Park and Hahn (Econom Theory 15:664–703, 1999). Using monthly data over the 1971M1–2013M12 period, our empirical results indicate that PPP holds in two out of six countries (i.e., France and Germany).     

Some international evidence on the stability of aggregate import demand function

This paper empirically analyses the stability of the aggregate import demand function for G7 countries. The standard cointegration test and a test developed by Gregory and Hansen are performed. The results of standard cointegration tests suggest that there is no stable cointegrating relation between real import, real GDP and relative import price for all G7 countries. The cointegrating relation is empirically supported for France and Germany if structural change for cointegrating vector is explicitly taken into consideration. The cointegrating relation is empirically rejected for Canada, Italy, Japan, the UK and the USA. Thus, the stimulation of domestic business conditions will not necessarily link the quantity of imports for these five countries.     

Cointegration,dynamic structure,and the validity of purchasing power parity in African countries

The purpose of this paper is to test the validity of the purchasing power parity (PPP) in Africa in the context of a multivariate error-correction model. This approach allows for the consideration of long-run elasticities as well as the dynamics of the short-run adjustment of exchange rates to changes in domestic and foreign prices. Monthly data for fourteen African countries are used, and the period examined is 1973:4 through 2007:7 (i.e., 412 observations). Results from long-run cointegration analysis, short-run error correction models, persistence profile analysis and variance decomposition all confirm the validity of PPP in these moderate-to-high inflation countries, where estimates of half-life deviations from PPP are found to be outside the range suggested by Rogoff (1996).     

Stable cointegrating regressions: Fully-modified estimates for inflation and employment cost indices

This paper investigates the stability of relationships between inflation and changes in employer cost for labor using tests based on the null hypothesis of no cointegration (Gregory and Hansen (1996a)) as well as tests based on the null hypothesis of cointegration (Hansen (1992)). In addition to specifications which include wages or unit labor cost, employment cost indices for compensation and wages are used to eliminate composition bias over the business cycle. Empirical results support stability and fully-modified estimates are obtained using the semiparametric approach of Phillips (1995). In contrast to studies which have found only one-way causality, this paper presents empirical evidence of feedback between inflation and employer cost for labor, consistent with an expectations-adjusted Phillips's Curve. First version received: July 1997/final version received: September 1998     

Long-run relations between private and public sector wages in Sweden

Using a maximum likelihood cointegration approach we find two long-run relationships between central government, local government, and private sector wages in Sweden. This means that there is one common trend for the three sectoral wages. Private sector wages are weakly exogenous for the estimation of the long-run relationships. This suggests that the private sector is the wage leader. Testing linear restrictions on the estimated cointegrating space, we reject stationarity for the three relative wages using likelihood ratio-tests. The hypotheses of homogeneity for the two cointegrating vectors, i.e., that wages do not diverge in the long run, is also rejected.     

Fractional cointegration and the term structure

According to the expectations theory of the term structure of interest rates, the yield spread between long-term and short-term interest rates is an optimal predictor of future changes in short rates over the long-run. Results concerning the empirical validity of this hypothesis are not unanimous. These contradictions may be due to the fact that the traditional concept of cointegration is too restrictive. We refer here to the concept of fractional cointegration introduced by Granger (1986). We study the expectations theory by testing for the existence of a (fractional) cointegration relationship between short-term and long-term interest rates. There is evidence of fractional cointegration between interest rates for the G7 countries, with the exception of Germany.First version received: July 2002 / Final version received: July 2003We thank two anonymous referees for very helpful and detailed comments.     

Purchasing power parity in Brazil: a test for fractional cointegration

The purpose of this paper is to test the validity of the purchasing power parity (PPP) doctrine in Brazil. Historical data for the period 1855–1996 are considered. The period 1855–1990 is also analysed in order to compare the results with those obtained by Zini and Cati (1993) using the conventional cointegration analysis. This article uses fractional cointegration analysis, a flexible methodology which allows for more subtle forms of mean reversion. The tests performed are those of Geweke and Porter-Hudak (1983), and of Hurvich and Ray (1995). The critical values for both tests are generated by simulation because they are non-standard. The empirical results do not support the absolute PPP hypothesis but the relative PPP holds in the long run.     

Estimation of a German money demand system – a long-run analysis

This study presents a multivariate analysis of the stability of long-run relationships between variables that influence the conduct and transmission process of the German monetary policy. The initial VAR comprises the variables real money M3, real GNP, the inflation rate, a long-term and a weighted short-term interest rate. A multivariate approach has been chosen, as this allows for more than one cointegration relationship and to test restrictions on the cointegration space. In contrast to most other studies on German monetary policy, three stable and economically plausible cointegration relationships are obtained simultaneously within the framework of the Johansen procedure: a money demand relationship, a long-run Fisher effect and a long-run relationship between the short- and the long-term interest rate. It is apparent that the structural break of German reunification can be modelled incorporating dummy variables in the model. First version received: October 1996/final version received: July 1997     

A testing of the purchasing power parity hypothesis using a vector autoregressive model

The paper examines the hypothesis of purchasing power parity relations and the hypothesis of interest rates parity relations between the Japanese yen and the US dollar in a four-dimensional VAR (4-VAR) model, using the statistical technique developed by Johansen and Juselius (1992). The paper demonstrates that the so-called symmetry restriction on the PPP relationship holds not in a 3-VAR model but in the 4-VAR model, which indicates that a correct specification of the sampling distribution of data is important. The interest rates parity relation also holds in the 4-VAR model. The one-step prediction based on the ECM representation with such long-run relations outperforms the random walk model. These results are similar to those under the exchange rate control period (January 1974 to December 1980), which support the inclusion of this period in a whole sample period (January 1974 to December 2001).The author is very grateful to the referees and the editor of the journal for their variable and helpful comments. The first draft of the paper was presented at the autumn meeting of Japan Society of Monetary Economics in Oct 1999. The author is thankful to Eiji Ogawa for his helpful comments. The research was supported by Grant-in-Aid 13630104 of the Ministry of Education, Science and Culture of Japan and the Nomura Foundation for Social Science in 2000.First version received: March 2001/Final version received: April 2003     

The Long Run Demand for Broad Money in Australia Subject to Regime Shifts

The goal is to determine if there is a stable Broad Money demand relationship for Australia. Previous studies have not reached a consensus on this important issue, partly because the time series techniques used do not accommodate structural breaks. A standard multivariate cointegration analysis is conducted on monthly data over the period 1976(3) to 1998(4). It reveals some evidence for the presence of cointegration since one cointegrating vector is found. This involves broad money, the spread between interest on broad money and on non-money assets and real GDP. The evidence of cointegration is again present when a structural break is found in the relationship using Gregory and Hansen (GH) methodology. This occurs in 1991 coinciding with a deep recession and policy induced, interest rate reductions. The income elasticity of demand exceeds one, reacts positively to the interest spread and negatively to inflation.     

TESTS OF UNIT ROOTS AND COINTEGRATION HYPOTHESES IN ECONOMETRIC MODELS*

A number of statistical procedures for testing the unit roots hypotheses and the cointegration hypothesis have been proposed by statisticians and econometricians. This paper unifies many of the previous studies on unit roots tests and cointegration tests in the framework of a multivariate regression model and develops some new test statistics. We give a convenient quadratic representation of the limiting distributions of test statistics using stochastic integrals with respect to Brownian motions. The test procedures in this paper include the statistics for testing the unit root, the double unit roots, the seasonal unit roots, and the cointegrating relations for special cases. We also discuss some useful generalizations of unit roots tests and cointegration tests for empirical studies.     

Does exchange-rate volatility depress export flows: The case of LDCs

In the area of international trade, few studies have examined whether increases in exchange-rate volatility depress trade flows of LDCs. The aim of this paper is to investigate empirically the impact of exchange-rate volatility on the export flows of 10 developing countries over the quarterly period 1973–98. The econometric analysis exploits the theory of cointegration, given the obvious nonstationarity of the data. Estimates of the cointegrating relations are obtained using Johansen's multivariate procedure. Evidence of stability of the cointegrating space is examined using Hansen's [1992a] tests. Short-run dynamic modelling is accomplished using the error-correction technique, and the stability test results are obtained using Hansen [1992b] tests. In conformity with theoretical considerations, the results indicate that increases in the exchange-rate volatility exert a significant negative effect upon export demand in both the short-run and the long-run in most of the countries studied. These effects may result in significant reallocation of resources by market participants.     

Long-run purchasing power parity with asymmetric adjustment: Further evidence from nine transition countries

In this study, we applied a threshold cointegration test to investigate the properties of asymmetric adjustment on long-run purchasing power parity (PPP) in nine transition countries between January 1995 and December 2008. Although there was strong evidence of long-run PPP for these nine transition countries (i.e., Bulgaria, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, and Russia), the adjustment mechanism was asymmetric. These results have important policy implications for the nine transition countries included in the study.     

FDIC Coverage on bank failures: Cointegration analysis using annual data, 1942–91

The present study empirically investigates whether in the U.S. federal government-provided deposit insurance, which was intended to prevent runs on banks and to protect depositors of modest means, has acted to induce increased bank failures. This issue has been investigated earlier, but only with regression analysis, and it remains unresolved since results vary sharply from one study to the next. By contrast, the present study uses cointegration techniques to investigate this problem. The cointegration analysis finds strong evidence of a cointegrating relationship between the bank failure rate and the extent of central government-provided deposit insurance, as well as other variables. Maximum eigenvalue and trace test results, along with normalized cointegrating vectors and likelihood ratio test results, are provided for examination.