Showing papers on "Cointegration published in 1994"

Applied Econometric Time Series

Abstract: PREFACE. ABOUT THE AUTHOR. Chapter DIFFERENCE EQUATIONS . 1 Time-Series Models. 2 Difference Equations and Their Solutions. 3 Solution by Iteration. 4 An Alternative Solution Methodology. 5 The Cobweb Model. 6 Solving Homogeneous Difference Equations. 7 Finding Particular Solutions for Deterministic Processes. 8 The Method of Undetermined Coefficients. 9 Lag Operators. Summary and Conclusions. Questions and Exercises. Endnotes. Appendix 1 Imaginary Roots and de Moivre's Theorem. Appendix 2 Characteristic Roots in Higher-Order Equations. Chapter 2 STATIONARY TIME-SERIES MODELS . 1 Stochastic Difference Equation Models. 2 ARMA Models. 3 Stationarity. 4 Stationarity Restrictions for an ARMA(p, q) Model. 5 The Autocorrelation Function. 6 The Partial Autocorrelation Function. 7 Sample Autocorrelations of Stationary Series. 8 Box-Jenkins Model Selection. 9 Properties of Forecasts. 10 A Model of the Interest Rate Spread. 11 Seasonality. 12 Parameter Instability and Structural Change. Summary and Conclusions. Questions and Exercises. Endnotes. Appendix 1 Estimation of an MA(1) Process. Appendix 2 Model Selection Criteria. Chapter 3 MODELING VOLATILITY . 1 Economic Time Series The Stylized Facts. 2 ARCH Processes. 3 ARCH and GARCH Estimates of Inflation. 4 Two Examples of GARCH Models. 5 A GARCH Model of Risk. 6 The ARCH-M Model. 7 Additional Properties of GARCH Processes. 8 Maximum Likelihood Estimation of GARCH Models. 9 Other Models of Conditional Variance. 10 Estimating the NYSE International 100 Index. 11 Multivariate GARCH. Summary and Conclusions. Questions and Exercises. Endnotes. Appendix 1 Multivariate GARCH Models. Chapter 4 MODELS WITH TREND . 1 Deterministic and Stochastic Trends. 2 Removing the Trend. 3 Unit Roots and Regression Residuals. 4 The Monte Carlo Method. 5 Dickey-Fuller Tests. 6 Examples of the ADF Test. 7 Extensions of the Dickey-Fuller Test. 8 Structural Change. 9 Power and the Deterministic Regressors. 10 Tests with More Power. 11 Panel Unit Root Tests. 12 Trends and Univariate Decompositions. Summary and Conclusions. Questions and Exercises. Endnotes. Appendix 1 The Bootstrap. Chapter 5 MULTIEQUATION TIME-SERIES MODELS . 1 Intervention Analysis. 2 Transfer Function Models. 3 Estimating a Transfer Function. 4 Limits to Structural Multivariate Estimation. 5 Introduction to VAR Analysis. 6 Estimation and Identification. 7 The Impulse Response Function. 8 Testing Hypothesis. 9 Example of a Simple VAR Terrorism and Tourism in Spain. 10 Structural VARs. 11 Examples of Structural Decompositions. 12 The Blanchard and Quah Decomposition. 13 Decomposing Real and Nominal Exchange Rate Movements An Example. Summary and Conclusions. Questions and Exercises. Endnotes. Chapter 6 COINTEGRATION AND ERROR-CORRECTION MODELS . 1 Linear Combinations of Integrated Variables. 2 Cointegration and Common Trends. 3 Cointegration and Error Correction. 4 Testing for Cointegration The Engle-Granger Methodology. 5 Illustrating the Engle-Granger Methodology. 6 Cointegration and Purchasing-Power Parity. 7 Characteristic Roots, Rank, and Cointegration. 8 Hypothesis Testing. 9 Illustrating the Johansen Methodology. 10 Error-Correction and ADL Tests. 11 Comparing the Three Methods. Summary and Conclusions. Questions and Exercises. Endnotes. Appendix 1 Characteristic Roots Stability and Rank. Appendix 2 Inference on a Cointegrating Vector. Chapter 7 NONLINEAR TIME-SERIES MODELS . 1 Linear Versus Nonlinear Adjustment. 2 Simple Extensions of the ARMA Model. 3 Regime Switching Models. 4 Testing For Nonlinearity. 5 Estimates of Regime Switching Models. 6 Generalized Impulse Responses and Forecasting. 7 Unit Roots and Nonlinearity. Summary and Conclusions. Questions and Exercises. Endnotes. STATISTICAL TABLES. A. Empirical Cumulative Distributions of the tau. B. Empirical Distribution of PHI . C. Critical Values for the Engle-Granger Cointegration Test. D. Residual Based Cointegration Test with I (1) and I (2) Variables. E. Empirical Distributions of the lambda max and lambda trace Statistics. F. Critical Values for beta 1 = 0 in the Error-correction Model. G. Critical Values for Threshold Unit Roots. REFERENCES. SUBJECT INDEX.

A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration

Abstract: This paper proposes a residual-based test of the null of cointegration using a structural single equation model. It is shown that the limiting distribution of the test statistic for cointegration can be made free of nuisance parameters when the cointegrating relation is efficiently estimated. The limiting distributions are given in terms of a mixture of a Brownian bridge and vector Brownian motion. It is also shown that this test is consistent. Critical values are given for standard, demeaned, and detrended cases. Combining results from our test for cointegration with results from the Phillips-Ouliaris test for no cointegration, we find that there is evidence of cointegration between real consumption and real disposable income over the postwar period.

Cointegration, Fractional Cointegration, and Exchange Rate Dynamics

Abstract: Multivariate tests due to Johansen (1988, 1991) as implemented by Baillie and Bollerslev (1989a) and Diebold, Gardeazabal, and Yilmaz (1994) reveal mixed evidence on whether a group of exchange rates are cointegrated. Further analysis of the deviations from the cointegrating relationship suggests that it possesses long memory and may possibly be well described as a fractionally integrated process. Hence, the influence of shocks to the equilibrium exchange rates may only vanish at very long horizons. IN THE ARTICLE BY Baillie and Bollerslev (1989a), it is argued that seven different nominal spot and forward exchange rates all contain unit roots in their univariate time series representations. At the same time, however, the spot exchange rates appear to be tied together in the long run through a cointegration-type relationship. The latter finding of Baillie and Bollerslev has attracted particular interest and several studies such as those by Hakkio and Rush (1991) and Sephton and Larsen (1991) have already addressed this issue. Using the same data as the Baillie and Bollerslev article, Sephton and Larsen (1991) describe the evidence for the presence of cointegration as being "fragile" and note that mixed conclusions are reached by truncating the Baillie and Bollerslev sample at different points in time. Diebold, Gardeazabal, and Yilmaz (1994) henceforth Diebold et al., provide interesting evidence that application of the Johansen (1988, 1991) tests with and without an intercept will result in different inferences on the Baillie and Bollerslev data set. Furthermore, Diebold et al. carry out an ex ante forecasting experiment and find that the addition of an error correction term to the martingale model, as implied by the standard cointegration paradigm, fails to reduce the prediction mean square error when compared to a simple martingale model. This therefore leads Diebold et al. to conclude that "there exists substantial uncertainty regarding the existence of cointegration relationships among nominal dollar exchange rates." This article provides some additional evidence on the existence of such a long-run relationship among the same seven nominal spot exchange rates. After further analysis it appears that a form of cointegration does exist between the exchange rates, so that they do not drift apart in the long run. We argue that this form of cointegration is

The role of the constant and linear terms in cointegration analysis of nonstationary variables : Cointegrated systems. I

Abstract: The autoregressive model for cointegrated variables is analyzed with respect to the role of the constant and linear terms. Various models for 1(1) variables defined by restrictions on the deterministic terms are discussed, and it is shown that statistical inference can be performed by reduced rank regression. The asymptotic distributions of the test statistics and estimators are found. A similar analysis is given for models for 1(2) variables with a constant term.

The Effects of Additive Outliers on Tests for Unit Roots and Cointegration

Abstract: This article discusses the properties of the univariate Dickey–Fuller test and the Johansen test for the cointegrating rank when there exist additive outlying observations in the time series. We provide analytical as well as numerical evidence that additive outliers may produce spurious stationary. Hence the Dickey–Fuller test will reject a unit root too frequently and the Johansen test will indicate too many cointegrating vectors. The results easily generalize to models with “temporary change” outliers. Through an empirical example we discuss how additive and temporary change outliers can be detected in practice, and we show how dummy variables can be used to remove the influence of such extreme observations.

Testing for unit roots in panel data: are wages on different bargaining levels cointegrated?

Abstract: Theoritical considerations suggest that spillover forces equalize wages for similar jobs Thus, it is expected that firm wages are cointegrated with the corresponding wage rates on an industrial level In this paper we apply various unit root tests to a panel of wage data We show that the familiar techniques can be adopted to this type of data allowing for unobserved heterogeneity and common time effects Our results suggest that firm and industry wages both possess a unit root in the autoregressive representation However, ther is only weak evidence for a cointegration realtionship

Non-Stationary Time Series Analysis and Cointegration

Abstract: This book shows major developments in the econometric analysis of the long run (non-stationary and cointegration) - a field which has developed dramatically over the last twelve years. The papers here describe and evaluate new methods, provide useful overviews, and show detailed implementations helpful to practitioners. Papers include Michael Clements and David Hendry's substantive analysis of economic forecasting, necessarily based around an integral understanding of integration and cointegration. The paper by Fabio Canova, Mary Finn and Adrian Pagan evaluates the real business cycles models using the new techniques. Other topics ocvered include an overview of the different estimators of cointegrating relationships, and a new test of cointegration. Applications are shown finding roots in macroeconomic series, testing the Fisher Hypoethesis, testing money demand functions, to testing for inflationary bubbles. This book provides a good coverage of the depth of this literature showing the importance of an understanding of non-stationarity and cointegration.

Cointegration and market integration: An application to the Indonesian rice market

Abstract: This article suggests improvements in the use of regression analysis to measure spatial market integration. The procedure pioneered by Ravallion is still widespread but is valid only under certain conditions of exogeneity. The alternative offered here is an error‐correction mechanism which makes it possible to test for exogeneity as well as indicating the direction and strength of causality in price formation between markets. The method is illustrated with data on rice prices in different parts of the Indonesian market. The results confirm, among other things, that supply sources are more important than demand sources in driving prices.

Seasonality and cointegration of regional house prices in the UK

Abstract: The data generation process underlying regional house prices in the UK is investigated using new statistical tests. It is found that causal flows tend to be northwards: the South East (rather than Greater London) acts as an exogenous price determinator of the other regions in the south; the Midland regions have a great influence on prices in the north and flows through the East Midlands are characterised by bi-directional causality. These results are largely independent of assumptions made about the data generation process (and tests of these assumptions have low power in any case). There are also similarities between this causality and migration patterns, particularly in the south of England.

On Cointegration and Exchange Rate Dynamics

Abstract: Baillie and Bollerslev (1989) have recently argued that nominal dollar spot exchange rates are cointegrated. Here we examine an immediate implication of their finding, namely, that cointegration implies an error-correction representation yielding forecasts superior to those from a martingale benchmark, in light of a large earlier literature highlighting the predictive superiority of the martingale. In an out-of-sample forecasting exercise, we find the martingale model to be superior. We then perform a battery of improved cointegration tests and find that the evidence for cointegration is much less strong than previously thought, a result consistent with the outcome of the forecasting exercise.

Short-Run versus Long-Run Effects of Devaluation: Error-Correction Modeling and Cointegration

Abstract: After identifying shortcomings associated with most previous studies on the relation between the trade balance and the exchange rate, we reexamine the statistical relation between these two variables by employing the cointegration and error-correction modeling techniques. For most countries considered, we do not find evidence of a long-run relation between the trade balance and the exchange rate. Results from error-correction modeling provide some support for the short-run relation and the J-Curve phenomenon.

A Drunk and Her Dog: An Illustration of Cointegration and Error Correction

Abstract: If there exists a stationary linear combination of nonstationary random variables, the variables combined are said to be cointegrated. A humorous example of a drunk and her dog illustrates...

Unit Roots and Cointegration for the Economist

Abstract: Previous papers by one of the authors, Perman (1989, 1991), have proved popular amongst applied economists seeking an introduction to the new econometrics of unit roots and cointegration. The aim of the present paper is, as before, to provide a comprehensive overview of the field in a manner which minimises the technical knowledge required of the reader and which offers intuitive explanations wherever possible. Other useful surveys, at a slightly higher technical level, include the special issues of the Oxford Bulletin of Economics and Statistics (March 1986, August 1992), Dolado et al. (1990) and Campbell and Perron (1991). In this introduction we motivate the study of unit roots and cointegration, and outline the contents of the rest of the chapter.

Open Access and the Evolution of the U. S. Spot Market for Natural Gas

Abstract: Federal regulations promoting open-access transportation dramatically altered the organizational structure of the U.S. market for natural gas in the 1980s, generally unbundling the merchant and transport functions of interstate pipelines. An empirical analysis of wellhead spot prices is undertaken to examine the effect of open access on the geographic scope of the spot market. Using monthly spot price data from 1984-91, three statistical tests are applied and compared: price correlations, Granger causality, and cointegration. We find that open access integrated the regional wellhead markets into a national competitive market for natural gas. The effects of unbundling on contracts for natural gas are then investigated. Incentives for long-term contracts between pipelines and producers are shown to be effectively removed by the introduction of competitive buying and selling of gas at the wellhead through open access.

Time-series evidence on the sources of trends in wage inequality

Abstract: Changes in wage inequality have long been a concern of labor economists and public policymakers. When the wage premium for college graduates fell during the first half of the 1970's, many researchers blamed the decline on the increase in the relative supply of college graduates. When the college wage premium increased dramatically during the 1980's, researchers offered a variety of explanations, such as skill-biased technological change and the internationalization of the U.S. economy. In this paper, we use time-series analysis to evaluate the most common explanations given for the trends in wage inequality. Using cointegration techniques, we evaluate the link between the trends in the candidate explanatory variables and wage inequality. We show that the only variable that consistently shares the same long-run trend with our wage-inequality series is the durablegoods trade deficit as a percentage of GDP. This variable not only follows the same trend as wage inequality during most of the 1980's, but also for the period from 1949 to 1979. No other single explanation shows the same long-run consistency. I. An Analysis of Trends in Wage Inequality

Cointegration and the US term structure

Abstract: Using the maximum likelihood analysis of cointegration developed by Johansen (1988, 1991), we test the cointegration implications of the expectations hypothesis of the term structure on a sample of US pure discount yields. By using this approach, we are able to analyze systems of more than two interest rates simultaneously, as opposed to most previous studies, which examine interest rates only in pairs. One of the main results is that, for the period 1952–1987, the cointegration implications generally seem to hold.

Cointegration, causality and wagner's law: a test for britain 1870–1913

Abstract: Wagner's law, first proposed in 1883, has been tested on numerous occasions for many countries. The evidence presented to date on the existence of 'the law' has been mixed and interpretation have been hampered by the general neglect of such issues as non-stationary and cointegration. Henrekson (1990) considers the stationarity and cointegration properties of Swedish data, but finds no evidence of Wagner's law. In this study cointegration is taken as a necessary condition for the non-spurious existence of Wagner's law and the testing methodology is applied to British data, 1870-1913. Evidence of co-integration and unidirectional Granger causality is found in the data and support for the law is established. Copyright 1994 by Scottish Economic Society.

Is the budget deficit “too large”?: some further evidence

Abstract: I. INTRODUCTION Since the early 1980s, the U.S. federal government has run unprecedented peacetime deficits. The size of these deficits became a major issue in recent U.S. presidential elections. For example, during the 1992 elections, Ross Perot successfully used his simple charts and tables to convey the notion that the size of the deficit was "too large." Economists look at the deficit issue from a different perspective. Instead of emphasizing the size of the deficit at any particular point in time, they are more concerned with the intertemporal solvency condition, the present value of debt in the long run. This condition focuses on the long-run paths of interest-inclusive expenditures and revenues. Unless these two variables trend together over the long run, the government will have an incentive to default on the debt, losing the confidence of investors. From the standpoint of the intertemporal solvency condition, are recent deficits "too large"? Do they represent boundless growth of government debt? As an empirical proposition, boundless growth of the debt corresponds to non-stationarity of the deficit (or the first-difference of the debt). Recent developments in time-series econometrics have provided ways to examine the intertemporal solvency condition. For example, Hamilton and Flavin [1986] and Trehan and Walsh [1991] apply stationarity tests to the U.S. federal deficit. Similarly, Hakkio and Rush [1991] test for cointegration between interest-inclusive expenditures and revenues, while Bohn [1991] tests for the cointegration of debt, non-interest expenditures and revenues. Hakkio and Rush's results suggest that the deficit is too large for intertemporal solvency, and thus the government has an incentive to default on its debt. They conclude that, over the period 1950 through 1989, interest-inclusive expenditures and revenues are cointegrated, but not one-to-one. This suggests that, although the present discounted value of the debt tends to zero, the undiscounted value of the debt will be unbounded. Moreover, they find that interest-inclusive expenditures are not cointegrated with revenues over the period 1964 to 1989: the government debt appears to drift upward without bound. Overall, Hakkio and Rush's results suggest that the government will have an incentive to default on the debt at some point in the future.(1) We look at the issue from a different point of view. We believe that a discrete break in the fiscal process occurred in the early 1980s as a result of several policy changes, such as the 1981 Economic Recovery and Tax Act, during the first Reagan administration. This Reagan-era change is modeled as a one-time upward shift in the constant component of the deficit. As McCallum [1984] shows, a constant interest-inclusive deficit does not imply boundless growth of government debt and should not provide an incentive to inflate away the debt. As did previous research, we conduct tests for the cointegration of interest-inclusive expenditures and revenues, as well as stationarity tests on the deficit.(2) However, we allow a shift in the intercept term of the cointegration and stationarity tests to capture the break in the fiscal process. Our results show that when the break is included expenditures and revenues are cointegrated with a coefficient not statistically different from unity (i.e., that the deficit is stationary). This contradicts the conclusions of Hakkio and Rush. Of course, the way we choose the break date may be crucial to our analysis. Our initial choice of break date is based on prior information. This is the approach used by Perron [1989], who tests the U.S. GNP with a break chosen using prior information. Christiano [1992] criticizes Perron [1989] on the a priori choice of the break date. He suggests that the break date should be chosen using a formal pre-test procedure. Moreover, any statistical inference that follows must take this pre-test procedure into account. …

Foreign direct investment and exports: a time series approach

Abstract: The impact of the accelerated internationalization of the last decade on the Austrian economy is a controversial issue. Granger's concept of casuality is used to investigate one aspect of the internationalization of production: the realtionship between foreign outward direct investment and exports using aggregate flow data from the Austrian economy. The stationarity of the time series is examined and cointegration tests for the adequacy of the multivariate time series approach are performed. The estimation results suggest significant causality of Austrian foreign outward direct investment and exports in both directions. Impulse response analysis and varience decomposition show a very slow dynamic response of both variables to exogenous shocks of the other. It furthermnore indicates the possiblity of a positive effect of exogeneously increased foreign direct investment on exports and a negative effect of export shocks on foreign direct investment; however, significant long-run effects are not established.

Finite Sample Properties of Likelihood Ratio Tests for Cointegrating Ranks When Linear Trends Are Present

Abstract: This paper investigates the finite sample properties of likelihood ratio tests for 'stochastic cointegration' that have recently been proposed by S. Johansen and P. Perron and J. Y. Campbell. The author transforms the model into a canonical form and conducts a comprehensive simulation study. He finds that the test performance is very sensitive to the value of the stationary root(s) of the process and to the correlation between the innovations that drive the stationary and nonstationary components of the process. Unfortunately, the simulation results suggest that these asymptotic test procedures are not very powerful for sample sizes that are typical for economic time series. Copyright 1994 by MIT Press.

Cointegration and market efficiency in commodities futures markets

Abstract: The hypothesis that futures prices are unbiased predictors of spot prices is a joint hypothesis that markets are efficient and risk premia are absent. Rejection of unbiasedness could be caused by the failure of either premise. Here cointegration techniques are used to test market efficiency while permitting the presence of risk premia. Five commodity markets were tested at the eight and twenty-four week horizon. Results showed that all five were sometimes inefficient but no market was inefficient always. Moreover, rejections of the unbiasedness hypothesis were nearly always caused by market inefficiency rather than the presence of risk premia.

Maximum-Likelihood Estimation of Fractional Cointegration with an Application to U.S. and Canadian Bond Rates

Abstract: We estimate a multivariate ARFIMA model to illustrate a cointegration testing methodology based on joint estimates of the fractional orders of integration of a cointegrating vector and its parent series. Previous cointegration tests relied on a two-step testing procedure and maintained the assumption in the second step that the parent series were known to have a unit root. In our empirical example of fractional cointegration, we illustrate how uncertainty regarding the order of integration of the parent series can be even more important than uncertainty regarding the order of integration of the cointegrating vector when testing for cointegration.

Financial development and economic growth in Singapore: demand-following or supply-leading?

Abstract: Two competing hypotheses regarding financial development and economic growth are empirically investigated, in the context of supply-leading and demand-following finance. The focus is on Singapore as a country which has implemented financial restructuring strategies that, arguably, amount to a ‘supply-leading finance’ experiment. By drawing on some developments in economic theory over the last three decades, hypotheses are formulated within a statistical framework, namely a bivariate vector autoregressive (BVAR) model. A battery of econometric techniques are applied to test for stationarity, cointegration, exogeneity and Granger-causality. The evidence largely supports the supply-leading hypothesis only when broad monetary aggregates and a monetization variable are used as surrogates for financial development. It is concluded that there is a plausible case for those economies which intend to adopt a financial restructuring strategy driven by a supply-leading policy stance that involves enhanced monetizatio...