Hostname: page-component-7dd5485656-g8tfn Total loading time: 0 Render date: 2025-10-29T08:43:28.476Z Has data issue: false hasContentIssue false
  • English
  • Français

NONLINEAR ERROR CORRECTION: THE CASE OF MONEY DEMAND IN THE UNITED KINGDOM (1878–2000)

Published online by Cambridge University Press:  30 January 2004

ALVARO ESCRIBANO
ALVARO ESCRIBANO
Affiliation:
Universidad Carlos III de Madrid, Spain
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper explores single-equation nonlinear error correction (NEC) models with linear and nonlinear cointegrated variables. Within the class of semiparametric NEC models, we use smoothing splines. Within the class of parametric models, we discuss the interesting properties of cubic polynomial NEC models and we show how they can be used to identify unknown threshold points in asymmetric models and to check the stability properties of the long-run equilibrium. A new class of rational polynomial NEC models is also introduced. We found multiple long-run money demand equilibria. The stability observed in the money-demand parameter estimates during more than a century, 1878 to 2000, is remarkable.

Keywords

Money DemandNonlinear Error CorrectionCubic PolynomialsRational PolynomialsSmoothing SplinesNonlinear Cointegration

Information

Type
Research Article
Information
Macroeconomic Dynamics , Volume 8 , Issue 1 , February 2004 , pp. 76 - 116
Copyright
© 2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Arranz M.A. & A. Escribano 2000 Cointegration testing under structural breaks: A robust extended error correction model. Oxford Bulletin of Economics and Statistics 62, 23– 52.Google Scholar
Attfield C.L.F. D. Demery & N.W. Duck 1995 Estimating the UK Demand for Money Function: A Tests of Two Approaches. Discussion paper 95/404, University of Bristol.
Baker G.A. & P. Graves-Morris 1996 Padé approximants. Encyclopedia of Mathematics and Its Applications, 2nd ed. Cambridge, UK: Cambridge University Press.
Banerjee A., J.J. Dolado, D.F. Hendry & G.W. Smith 1986 Exploring equilibrium relationships in econometrics through static models: Some Monte Carlo evidence. Oxford Bulletin of Economics and Statistics 48, 253– 277.Google Scholar
Banerjee A., J.J. Dolado, J.W. Galbraith & D.F. Hendry 1993 Cointegration, Error Correction and the Econometric Analysis of Nonstationary Data. Oxford: Oxford University Press.
Campos J., N. Ericsson & D.F. Hendry 1996 Cointegration tests in the presence of structural breaks. Journal of Econometrics 70, 187– 220.Google Scholar
Davidson J. 1994 Stochastic Limit Theory. New York: Oxford University Press.
Davidson J., D.F. Hendry, F. Srba & S. Yeo 1978 Econometric modelling of the aggregate time-series relationship between consumer's expenditure and income in the United Kingdom. Economic Journal 88, 661– 692.Google Scholar
Dufrénot G. & V. Mignon 2002 Recent Developments in Nonlinear Cointegration with Applications to Macroeconomics and Finance. Boston: Kluwer Academic.
Engle R.F. & C.W.J. Granger 1987 Cointegration and error correction: Representation, estimation and testing. Econometrica 55, 251– 276.Google Scholar
Engle R.F., C.W.J. Granger, J. Rice & A. Weiss 1986 Semiparametric estimates of the relationship between weather and electricity sales. Journal of the American Statistical Association 81, 310– 320.Google Scholar
Ericsson N.R., D.F. Hendry & K.M. Prestwich 1998 The demand for broad money in the United Kingdom, 1878–1993. Scandinavian Journal of Economics 100, 289– 324.Google Scholar
Escribano A. 1985 Non-linear Error-Correction: The Case of Money Demand in the UK (1878–1970). Mimeo, University of California at San Diego.
Escribano A. 1986 Identification & Modelling of Economic Relationships in a Growing Economy, Ch. IV. Ph.D. Dissertation, University of California at San Diego.
Escribano A. 1987 Error-Correction Systems: Nonlinear Adjustments to Linear Long-Run Relationships. Discussion paper 8730, CORE.
Escribano A. 1996 Non-linear Error-Correction: The Case of Money Demand in the UK (1878–1970). Working paper 96-55 (24), Universidad Carlos III de Madrid.
Escribano A. & C.W.J. Granger 1998 Investigating the relationship between gold and silver prices. Journal of Forecasting 17, 81– 107.Google Scholar
Escribano A. & O. Jorda 1999 Improved testing and specification of smooth transition regression models. In P. Rothman (ed.), Nonlinear Time Series Analysis of Economic and Financial Data, 289–320. Boston: Kluwer Academic Press.
Escribano A. & O. Jorda 2001 Testing nonlinearity: Decision rules for selecting between logistic and exponential STAR models. Spanish Economic Review 3, 193– 209.Google Scholar
Escribano A. & S. Mira 1996 Nonlinear Cointegration and Nonlinear Error Correction. Working paper 96-54 (23), Universidad Carlos III de Madrid.
Escribano A. & S. Mira 1997 Nonlinear Error Correction Models. Working paper 97-26 (13), Universidad Carlos III de Madrid.
Escribano A. & S. Mira 2002 Nonlinear error correction models. Journal of Time Series Analysis 23, 509– 522.Google Scholar
Escribano A. & D. Peña 1994 Cointegration and common factors. Journal of Time Series Analysis 15, 577– 586.Google Scholar
Escribano A. & G. Pfann 1998 Nonlinear error correction, asymmetric adjustment and cointegration. Economic Modelling 15, 197– 216.Google Scholar
Feinstein C.H. 1972 National Income, Expenditure and Output of the United Kingdom, 1855–1965. Cambridge: Cambridge University Press.
Friedman M. & A. Schwartz 1982 Monetary Trends in the United States and the United Kingdom: Their Relation to Income, Prices and Interest Rates, 1867–1975. Chicago: University of Chicago Press.
Friedman M. & A. Schwartz 1991 Alternative approaches to analyzing economic data. American Economic Review 81, 39– 49.Google Scholar
Gallant A.R. & H. White 1988 A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models. New York: Basil Blackwell.
Goldfeld S.M. & D.E. Sichel 1990 The demand for money. In B.M. Friedman & F.H. Hahn (eds.), Handbook of Monetary Economics, Vol. 1, Ch. 8, 299– 356. Amsterdam: North-Holland.
Gonzalo J. 1994 Five alternative methods of estimating long-run equilibrium relationships. Journal of Econometrics 60, 203– 233.Google Scholar
Granger C.W.J. 1995 Modelling nonlinear relationships between extended memory variables. Econometrica 63, 265– 279.Google Scholar
Granger C.W.J. & T.H. Lee 1989 Investigation of production, sales and inventory relationships using multicointegration and non-symmetric error correction models. Journal of Applied Econometrics 4, 145– 159.Google Scholar
Granger C.W.J. & T. Teräsvirta 1993 Modelling Nonlinear Economic Relationships. New York: Oxford University Press.
Granger C.W.J., F.C. Huynh, A. Escribano & C. Mustafa 1984 Computer investigation of some nonlinear time series models. In Proceedings of the Conference on Interface Between Statistics and Computing.
Hansen B.E. 1992 Testing for parameter instability in linear models. Journal of Policy Modeling 14, 517– 533.Google Scholar
Härdle W. & O. Linton 1994 Applied nonparametric methods. In Handbook of Econometrics, Vol. IV, Ch. 38, 2297– 2339.Google Scholar
Harris D. & B. Inder 1994 Test of the null hypothesis of cointegration. In C.P. Hargreaves (ed.), Nonstationary Time Series Analysis and Cointegration, 133– 152.Google Scholar
Hendry D.F. 1995 Dynamic Econometrics. Oxford: Oxford University Press.
Hendry D.F. & J.A. Doornik 1996 Empirical Econometric Modelling Using PcGive Professional 9.0 for Windows. London: International Thompson Business Press.
Hendry D.F. & N. Ericsson 1983 Assertion Without Empirical Basis: An Econometric Appraisal of “Monetary Trends in the … United Kingdom” by Milton Friedman and Anna Schwartz in Monetary Trends in the United Kingdom. Paper 22, pp. 45–101 (with additional references), Bank of England Panel of Academic Consultants.
Hendry D.F. & N. Ericsson 1991 An econometric analysis of the UK money demand in “Monetary Trends in the United States and the United Kingdom” by Milton Friedman and Anna Schwartz. American Economic Review 81, 8– 38.Google Scholar
Hendry D.F. & Mizon G.E. 1978 Serial correlation as a convenient simplification, not a nuisance: A comment on a study of the demand for money by the Bank of England. Economic Journal 88, 549– 563.Google Scholar
Hendry D.F. & J.F. Richard 1983 The econometric analysis of economic time series. International Statistical Review 51, 111– 163.Google Scholar
Herrndorf N. 1984 A functional central limit theorem for weakly dependent sequences of random variables. Annals of Probability 12, 141– 153.Google Scholar
Johansen S. 1992 Cointegration in partial systems and the efficiency of single-equation analysis. Journal of Econometrics 52, 389– 402.Google Scholar
Johansen S. 1995 Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford: Oxford University Press.
Judd J.P. & J.L. Scadding 1982 The search for a stable money demand function: A survey of the post-1973 literature. Journal of Economic Literature 20, 993– 1023.Google Scholar
Kwiatkowski D., P.C.B. Phillips, P. Schmidt & Y. Shin 1992 Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics 54, 159– 178.Google Scholar
Laidler D.E.W. 1969 The Demand for Money: Theories and Evidence. Scranton, PA: International Texbook.
Lo A.W. 1991 Long-term memory in stock market prices. Econometrica 59, 1279– 1313.Google Scholar
Longbottom A. & S. Holly 1985 Econometric Methodology and Monetarism: Professor Friedman and Professor Hendry on the Demand for Money. Discussion paper 131, London Business School.
Marmol F., A. Escribano & F. Aparicio 2002 Instrumental variable interpretation of cointegration with inference results for fractional cointegration. Econometric Theory 18, 646– 672.Google Scholar
Phillips A.W. 1954 Stabilization policy in a closed economy. Economic Journal 64, 290– 323.
Phillips A.W. 1957 Stabilization policy and the time-forms of lagged responses. Economic Journal 67, 265– 277.Google Scholar
Phillips P.C.B. 1987 Time series regression with a unit root. Econometrica 55, 277– 301.Google Scholar
Phillips P.C.B. 1991 Optimal inference in cointegrating systems. Econometrica 59, 283– 306.Google Scholar
Phillips P.C.B. & B.E. Hansen 1990 Statistical inference in instrumental variable regression with I(1) Processes. Review of Economic Studies 57, 99– 125.Google Scholar
Phillips P.C.B. & M. Loretan 1991 Estimating long-run economic equilibria. Review of Economidies 59, 407– 436.Google Scholar
Rosenblatt M. 1978 Dependence and asymptotic independence for random processes. In M. Rosenblatt (ed.), Studies in Probability Theory. Washington, D.C.: Mathematical Association of America.
Sargan J.D. 1964 Wages and Prices in the United Kingdom: A Study in Econometric Methodology. In P.E. Hart, G. Mills & J.K. Whitaker (eds), Econometric Analysis for National Economic Planning, Colston Papers, Vol. 16.
Scott A. 1996 Consumption Credit Crunches and Financial Deregulation. Applied Economics Discussion paper 181, University of Oxford.
Shin Y. 1994 A residual based test for the null of cointegration against the alternative of no cointegration. Econometric Theory 10, 91– 115.Google Scholar
Silverman B.W. 1985 Some aspects of the spline smoothing approach to nonparametric regression curve fitting. Journal of the Royal Statistical Society Series B 47, 1– 52.Google Scholar
Stock J.H. 1987 Asymptotic properties of least Squares estimation of cointegrating vectors. Econometrica 55, 1035– 1056.Google Scholar
Teräsvirta T. 1994 Specification, estimation and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association 89, 208– 218.Google Scholar
Teräsvirta T. & A.C. Eliasson 2001 Non-linear error correction and the UK demand for broad money, 1878–1993. Journal of Applied Econometrics 16, 277– 288.Google Scholar
Tong H. 1990 A Dynamic System Approach. Oxford, UK: Oxford University Press.
Tsay R.S. 1986 Non-linearity tests for time series. Biometrica 73, 461– 466.Google Scholar
Wahba G. 1975 Smoothing noisy data with spline functions. Num. Math., 24, 63– 75.Google Scholar
White H. 1984 Asymptotic Theory for Econometricians. Orlando, FL: Academic Press, Inc.
Wooldridge J. & H. White 1988 Some invariance principles and central limit theorems for dependent heterogeneous processes. Econometric Theory 4, 210– 230.Google Scholar