A Perspective on Unit Root and Cointegration in Applied Macroeconomics

Razzak, Weshah (2003): A Perspective on Unit Root and Cointegration in Applied Macroeconomics. Forthcoming in: The International Journal of Applied Econometrics and Quantitative Studies , Vol. Vol 1, No. Issue (2007)

Abstract

I discuss econometric issues of high relevance to economists in central banks whose job is to interpret the permanency of shocks and provide policy advice to policymakers. Trend, unit root, and persistence are difficult to interpret. There are numerous econometric tests, which vary in their power and usefulness. I provide a set of strategies on dealing with macro time series.

• Item Type: MPRA Paper
• Institution: Department of Labour
• Language: English
• Keywords: Unit root; trend; persistence; cointegration
• Subjects: F - International Economics > F4 - Macroeconomic Aspects of International Trade and Finance; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General

References

Barnhart, S. W., R. McNown and M. S. Wallace, “Non – Informative Tests of the Unbiased Forward Exchange Rate, “Journal of Financial and Quantitative Analysis,” Vol. 34 No.2, June (1999).

Box G E P, and G M Jenkins, Time Series Analysis, Forecasting and Control, Holden Day, San Francisco, (1970).

Cheung, Y W and K S Lai, “Finite-sample Sizes of Johansen’s Likelihood Ratio Tests for Cointegration,” Oxford Bulletin of Economics and Statistics 55, 3 (1993), 313-28.

Christiano, L. and M Eichenbaum, “Unit Roots in Real GNP: Do We Know, and Do We Care?” Carnegie-Rochester Conference Series on Public Policy, Vol. 32 (Spring 1990), 7-62.

Cochrane, J, “Comments,” NBER Macroeconomics Annual 1991,”

Dickey, D A and W Fuller, “Distribution of the Estimators for Autoregressive Time Series with a Unit Root,” Journal of The American Statistical Association (June 1979), 423-31.

Dickey, D A and W Fuller, “The Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root,” Econometrica 49 (July 1981), 1057-72.

Dickey D A and S Pantula, “Determining the Order of Differencing in Autoregressive Processes,” Journal of Business and Economic Statistics, (January 2002) 20(1), 18-24

Elliott, G., “Efficient Tests for a Unit Root when the Initial Observation is Drawn from its Unconditional Distribution,” International Economic Review, Vol. 140, No. 3, (1999), 767-783.

Engle, R and C W J Granger, “Cointegration and Error Correction: Representation, Estimation, and Testing,” Econometrica, vol. 55 (March 1987), 251-76.

Fuller, W, G Farias and S Pantula, “A Comparison of Unit-Root Test Criteria,” Journal of Business and Economic Statistics (October 1994) 12(4), 449-5.

Granger, C W J, “Cointegrated Variables and Error Correcting Models,” WP 83-13, San Diego: University of California, 1983.

Granger, C W J., “Non Linear Relationships Between Extended Memory Series,” Econometrica 63 (1995), 265-280.

Granger, C W J and P Newbold,” Spurious Regressions in Econometrics,” Journal of Econometrics, 2 (1974), 111-20.

Gonzalo, J., “Five Alternative Methods of Estimating Long-Run Equilibrium Relationships,” Journal of Econometrics, Vol.60 issue 1-2, (1994), 203-233.

Guisan, M. Carmen, “A Comparison of Causality Tests Applied to Bilateral Relationship Between Consumption and GDP in the USA and Mexico,” International Journal of Applied Econometrics and Quantitative Studies, Vol. 1, Issue 1, (2004).

Hakkio, C and M Rush, “Cointegration: How Short is the Long Run?” Journal of International Money and Finance (1991), 571-81.

Johansen, S, “Statistical Analysis of Cointegration Vectors,” Journal of Economic Dynamics and Control 12 (1988), 231-54.

Johansen, S and K Juselius, “The Full Information Maximum Likelihood Procedure of Inference on Cointegration with Applications to the Demand for Money,” Oxford Bulletin of Economics and Statistics 52 (May 1990), 169-210.

McCallum, B T, “On ‘Real’ and ‘Sticky-Price’ Theories of the Business Cycle,” Journal of Money, Credit and Banking Vol. 18 (November 1986), 397-414.

McCallum, B T, “Unit Roots in Macroeconomic Time series: Some Critical Issues,” Federal Reserve Bank of Richmond Economic Quarterly, Vol. 79/2 (Spring 1993), 13-43.

Nelson, C R and C Plosser, “Trends and Random Walks in Macroeconomic Time Series,” Journal of Monetary Economics, Vol. 10 (September 1982), 139-62.

Plosser, C and W G Schwert, “Estimation of Noninvertible Moving Average Process: The Case of Overdifferencing,” Journal of Econometrics, Vol. 6 (August 1977), 199-224.

Rudebusch, G, “The Uncertain Unit Root in Real GNP,” American Economic Review, Vol. 83 (March 1993), 264-72.

Perron, P, “Testing for Unit Root in a Time Series with a Changing Mean,” Journal of Business and Economics Statistics, 8 (1990), 153-62.

Perron, P (1989), “The great crash, the oil price shock and the unit root hypothesis,” Econometrica, 57, 1361-1402.

Perron, P, “Trends and random Walks in Macroeconomic Time Series,” Journal of Economic Dynamics and Control 12 (1988), 297-332.

Perron, P,” Further Evidence on Breaking Trend Functions in Macroeconomic Variables,” Journal of Econometrics 80, (1997).

Phillips, P C B, “Laws and Limits of Econometrics,” Economic Journal, Vol. 113, No. 486, (March 2003), c26-c52.

Phillips, P C B and B Hansen, “Statistical Inference in Instrumental Variables Regression with I (1) Processes,” Review of Economic Studies 57, (1990), 99-125.

Phillips, P C B and M. Loretan, “Estimating Long-Run Equilibria”, The Review of Economic Studies 58(3) (1991), 407-436. Phillips, P C B and S Ouliaris, “Asymptotic Properties of Residual Based Tests for Cointegration.” Econometrica 58 (1990), 165–193. Phillips, P C B, “Time Series Regressions with a Unit Root”, Econométrica 55 (1987), 277-301.

Phillips, P C B, “Understanding Spurious Regressions in Econometrics,” Journal of Econometrics, Vol. 33, (1986), 311-40.

Razzak, W, “Monetary policy and forecasting inflation with and without the output gap,” Reserve Bank of New Zealand Discussion Paper 2002/03.

Sims, C A, “Bayesian Skepticism on Unit Root Econometrics,” Journal of Economic Dynamics and Control, Vol. 12, (June/September 1988), 463-74.

Said S and D A Dickey, “Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order,” Biometrika 71 (1984), 599-608.

Stock, J, “Confidence Intervals for the Largest Autoregressive Root in U.S. Macroeconomic Time Series,” Journal of Monetary Economics, Vol. 28, (December 1991), 435-59.

West, K, “On the Interpretation of the Near Random Walk Behaviour in GNP,” American Economic Review, Vol. 78 (march 1988), 202-11.