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Testing for and estimating structural breaks and other nonlinearities in a dynamic monetary sector

  • Neil R. Ericsson EMAIL logo
Published/Copyright: May 12, 2016

Abstract

Milton Friedman and Anna Schwartz constructed an important macroeconomic dataset for the United Kingdom that spans 1878–1970. Numerous authors have modeled the demand for broad money on that dataset. Model selection is central to assessing the merits of the resulting empirical models, so the current paper re-evaluates that issue with computer-automated model selection. Some models are robust to the model selection path, as characterized through variations in target size, pre-search testing, fixity of regressors, impulse indicator saturation, representation of the general model, and choice of dependent variable. Model improvement is also feasible, with historically interpretable nonlinearities and structural breaks.

JEL Classification: C52; E41

Acknowledgments

The views in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. The author is grateful to Hildegart Ahumada, Lorena Garegnani, David Hendry, Vivien Hendry, Freja Ingelstam, Jaime Marquez, Bruce Mizrach, Ed Nelson, Phil Rothman, J Seymour, Hal White, and an anonymous referee for helpful comments and discussions. All numerical results were obtained using PcGive Version 14.0B3, Autometrics Version 1.5e, and Ox Professional Version 7.00 in 64-bit OxMetrics Version 7.00: see Doornik and Hendry (2013) and Doornik (2009).

References

Akaike, H. 1973. “Information Theory and an Extension of the Maximum Likelihood Principle.” In Second International Symposium on Information Theory, edited by B. N. Petrov and F. Csaki, 267–281. Budapest: Akademiai Kiado.Search in Google Scholar

Akaike, H. 1981. “Likelihood of a Model and Information Criteria.” Journal of Econometrics 16 (1): 3–14.10.1016/0304-4076(81)90071-3Search in Google Scholar

Akerlof, G. A. 1973. “The Demand for Money: A General-equilibrium Inventory-theoretic Approach.” Review of Economic Studies 40 (1): 115–130.10.2307/2296743Search in Google Scholar

Akerlof, G. A. 1979. “Irving Fisher on His Head: The Consequences of Constant Threshold-target Monitoring of Money Holdings.” Quarterly Journal of Economics 93 (2): 169–187.10.2307/1883190Search in Google Scholar

Akerlof, G. A., and R. D. Milbourne. 1980. “Irving Fisher on His Head II: The Consequences of the Timing of Payments for the Demand for Money.” Quarterly Journal of Economics 95 (1): 145–157.10.2307/1885353Search in Google Scholar

Atkinson, A. C. 1981. “Likelihood Ratios, Posterior Odds and Information Criteria.” Journal of Econometrics 16 (1): 15–20.10.1016/0304-4076(81)90072-5Search in Google Scholar

Attfield, C. L. F., D. Demery, and N. W. Duck. 1995. “Estimating the UK Demand for Money Function: A Test of Two Approaches.” Mimeo, Department of Economics, University of Bristol, Bristol, November.Search in Google Scholar

Bergamelli, M., and G. Urga. 2014. “Detecting Multiple Structural Breaks: Dummy Saturation vs Sequential Bootstrapping. With an Application to the Fisher Relationship for US.” CEA@Cass Working Paper Series No. WP–CEA–03–2014, Cass Business School, London, April.Search in Google Scholar

Bernanke, B. S. 2009. “Reflections on a Year of Crisis.” In Economic Symposium, Jackson Hole, Wyoming, Federal Reserve Bank of Kansas City, Kansas City, Missouri, August 21.Search in Google Scholar

Campos, J., and N. R. Ericsson. 1999. “Constructive Data Mining: Modeling Consumers’ Expenditure in Venezuela.” Econometrics Journal 2 (2): 226–240.10.1111/1368-423X.00029Search in Google Scholar

Campos, J., N. R. Ericsson, and D. F. Hendry. 1990. “An Analogue Model of Phase-Averaging Procedures.” Journal of Econometrics 43 (3): 275–292.10.1016/0304-4076(90)90121-9Search in Google Scholar

Campos, J., N. R. Ericsson, and D. F. Hendry. 2005. “Introduction: General-to-Specific Modelling.” In General-to-Specific Modelling, edited by J. Campos, N. R. Ericsson, and D. F. Hendry, xi–xci. Volume I, Cheltenham: Edward Elgar.Search in Google Scholar

Castle, J. 2005. “Evaluating PcGets and RETINA as Automatic Model Selection Algorithms.” Oxford Bulletin of Economics and Statistics 67 (Supplement): 837–880.10.1111/j.1468-0084.2005.00143.xSearch in Google Scholar

Castle, J. L., and D. F. Hendry. 2010. “A Low-dimension Portmanteau Test for Nonlinearity.” Journal of Econometrics 182 (2): 231–245.10.1016/j.jeconom.2010.01.006Search in Google Scholar

Castle, J. L., J. A. Doornik, and D. F. Hendry. 2012. “Model Selection When There Are Multiple Breaks.” Journal of Econometrics 169 (2): 239–246.10.1016/j.jeconom.2012.01.026Search in Google Scholar

Castle, J. L., X. Qin, and W. R. Reed. 2013. “Using Model Selection Algorithms To Obtain Reliable Coefficient Estimates.” Journal of Economic Surveys 27 (2): 269–296.10.1111/j.1467-6419.2011.00704.xSearch in Google Scholar

Castle, J. L., J. A. Doornik, D. F. Hendry, and F. Pretis. 2015. “Detecting Location Shifts During Model Selection by Step-indicator Saturation.” Econometrics 3 (2): 240–264.10.3390/econometrics3020240Search in Google Scholar

Chow, G. C. 1960. “Tests of Equality Between Sets of Coefficients in Two Linear Regressions.” Econometrica 28 (3): 591–605.10.2307/1910133Search in Google Scholar

Clements, M. P., and D. F. Hendry. 1998. Forecasting Economic Time Series. Cambridge: Cambridge University Press.10.1017/CBO9780511599286Search in Google Scholar

Clements, M. P., and D. F. Hendry. 1999. Forecasting Non-stationary Economic Time Series. Cambridge: MIT Press.10.1017/CBO9780511599286Search in Google Scholar

Cochrane, J. H. 1989. “The Sensitivity of Tests of the Intertemporal Allocation of Consumption to Near-rational Alternatives.” American Economic Review 79 (3): 319–337.10.3386/w2730Search in Google Scholar

Cord, R., and J. D. Hammond. (eds.). 2016. Milton Friedman: Contributions to Economics and Public Policy. Oxford: Oxford University Press.10.1093/acprof:oso/9780198704324.001.0001Search in Google Scholar

Doornik, J. A. 2008. “Encompassing and Automatic Model Selection.” Oxford Bulletin of Economics and Statistics 70 (supplement): 915–925.10.1111/j.1468-0084.2008.00536.xSearch in Google Scholar

Doornik, J. A. 2009. “Autometrics.” Chapter 4 in The Methodology and Practice of Econometrics: A Festschrift in Honour of David F. Hendry, edited by J. L. Castle and N. Shephard, 88–121. Oxford: Oxford University Press.10.1093/acprof:oso/9780199237197.003.0004Search in Google Scholar

Doornik, J. A., and H. Hansen. 2008. “An Omnibus Test for Univariate and Multivariate Normality.” Oxford Bulletin of Economics and Statistics 70 (supplement): 927–939.10.1111/j.1468-0084.2008.00537.xSearch in Google Scholar

Doornik, J. A., and D. F. Hendry. 2013. PcGive 14. London: Timberlake Consultants Press (3 volumes).Search in Google Scholar

Engle, R. F. 1982. “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica 50 (4): 987–1007.10.2307/1912773Search in Google Scholar

Ericsson, N. R. 2011. “Justifying Empirical Macro-econometric Evidence in Practice.” Invited presentation, online conference Communications with Economists: Current and Future Trends commemorating the 25th anniversary of the Journal of Economic Surveys, November.Search in Google Scholar

Ericsson, N. R. 2015. “How Biased Are U.S. Government Forecasts of the Federal Debt?.” International Journal of Forecasting, forthcoming.Search in Google Scholar

Ericsson, N. R. 2016a. “Eliciting GDP Forecasts from the FOMC’s Minutes Around the Financial Crisis.” International Journal of Forecasting 32: in press.10.1016/j.ijforecast.2015.09.007Search in Google Scholar

Ericsson, N. R. 2016b. “Testing for and Estimating Structural Breaks and Other Nonlinearities in a Dynamic Monetary Sector.” International Finance Discussion Paper, Board of Governors of the Federal Reserve System, Washington, DC, forthcoming.Search in Google Scholar

Ericsson, N. R., and S. B. Kamin. 2009. “Constructive Data Mining: Modelling Argentine Broad Money Demand.” Chapter 17 in The Methodology andPractice of Econometrics: A Festschrift in Honour of David F. Hendry, edited by J. L. Castle and N. Shephard, 412–439. Oxford: Oxford University Press.10.1093/acprof:oso/9780199237197.003.0017Search in Google Scholar

Ericsson, N. R., and E. L. Reisman. 2012. “Evaluating a Global Vector Autoregression for Forecasting.” International Advances in Economic Research 18 (3): 247–258.10.1007/s11294-012-9357-0Search in Google Scholar

Ericsson, N. R., D. F. Hendry, and K. M. Prestwich. 1998a. “The Demand for Broad Money in the United Kingdom, 1878–1993.” Scandinavian Journal of Economics 100 (1): 289–324 (with discussion).10.1111/1467-9442.00103Search in Google Scholar

Ericsson, N. R., D. F. Hendry, and K. M. Prestwich. 1998b. “Friedman and Schwartz (1982) Revisited: Assessing Annual and Phase-average Models of Money Demand in the United Kingdom.” Empirical Economics 23 (3): 401–415.10.1007/978-3-662-12539-7_8Search in Google Scholar

Ericsson, N. R., D. F. Hendry, and S. B. Hood. 2016. “Milton Friedman as an Empirical Modeler.” Chapter 6 in Milton Friedman: Contributions to Economics and Public Policy, edited by R. Cord and J. D. Hammond. Oxford: Oxford University Press, 91–142.10.1093/acprof:oso/9780198704324.003.0007Search in Google Scholar

Escribano, A. 1985. “Non-linear Error-correction: The Case of Money Demand in the U.K. (1878–1970).” Mimeo, University of California at San Diego, La Jolla, California, December.Search in Google Scholar

Escribano, A. 2004. “Nonlinear Error Correction: The Case of Money Demand in the United Kingdom (1878–2000).” Macroeconomic Dynamics 8 (1): 76–116.10.1017/S1365100503030013Search in Google Scholar

Flemming, J. S. 1976. Inflation. Oxford: Oxford University Press.Search in Google Scholar

Friedman, M., and A. J. Schwartz. 1963. A Monetary History of the United States, 1867–1960. Princeton: Princeton University Press.Search in Google Scholar

Friedman, M., and A. J. Schwartz. 1970. Monetary Statistics of the United States: Estimates, Sources, Methods. New York: Columbia University Press.Search in Google Scholar

Friedman, M., and A. J. Schwartz. 1982. Monetary Trends in the United States and the UnitedKingdom: Their Relation to Income, Prices, and Interest Rates,1867–1975. Chicago: University of Chicago Press.10.7208/chicago/9780226264257.001.0001Search in Google Scholar

Friedman, M., and A. J. Schwartz. 1991. “Alternative Approaches to Analyzing Economic Data.” American Economic Review 81 (1): 39–49.Search in Google Scholar

Godfrey, L. G. 1978. “Testing for Higher Order Serial Correlation in Regression Equations When the Regressors Include Lagged Dependent Variables.” Econometrica 46 (6): 1303–1310.10.2307/1913830Search in Google Scholar

Hannan, E. J., and B. G. Quinn. 1979. “The Determination of the Order of An Autoregression.” Journal of the Royal Statistical Society, Series B 41 (2): 190–195.10.1111/j.2517-6161.1979.tb01072.xSearch in Google Scholar

Hendry, D. F. 1993. Econometrics: Alchemy or Science? Essays in Econometric Methodology. Oxford: Blackwell Publishers.Search in Google Scholar

Hendry, D. F. 1995. Dynamic Econometrics. Oxford: Oxford University Press.10.1093/0198283164.001.0001Search in Google Scholar

Hendry, D. F. 1999. “An Econometric Analysis of US Food Expenditure, 1931–1989.” Chapter 17 in Methodology and Tacit Knowledge: Two Experiments in Econometrics, edited by J. R. Magnus and M. S. Morgan, 341–361. Chichester: John Wiley and Sons.Search in Google Scholar

Hendry, D. F. 2006. “Robustifying Forecasts from Equilibrium-correction Systems.” Journal of Econometrics 135 (1–2): 399–426.10.1016/j.jeconom.2005.07.029Search in Google Scholar

Hendry, D. F., and N. R. 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, Bank of England Panel of Academic Consultants, Panel Paper No. 22, Bank of England, London, October, 45–101.Search in Google Scholar

Hendry, D. F., and N. R. Ericsson. 1991a. “An Econometric Analysis of U.K. Money Demand in Monetary Trends in the United States and the United Kingdom by Milton Friedman and Anna J. Schwartz.” American Economic Review 81 (1): 8–38.Search in Google Scholar

Hendry, D. F., and N. R. Ericsson. 1991b. “Modeling the Demand for Narrow Money in the United Kingdom and the United States.” European Economic Review 35 (4): 833–881 (with discussion).10.1016/0014-2921(91)90039-LSearch in Google Scholar

Hendry, D. F., and H.-M. Krolzig. 1999. “Improving on ‘Data Mining Reconsidered’ by K. D. Hoover and S. J. Perez.” Econometrics Journal 2 (2): 202–219.10.1111/1368-423X.00027Search in Google Scholar

Hendry, D. F., and H.-M. Krolzig. 2001. Automatic Econometric Model Selection Using PcGets 1.0. London: Timberlake Consultants Press.Search in Google Scholar

Hendry, D. F., and H.-M. Krolzig. 2003. “New Developments in Automatic General-to-Specific Modeling.” Chapter 16 in Econometrics and the Philosophy of Economics: Theory-Data Confrontations in Economics, edited by B. P. Stigum, 379–419. Princeton: Princeton University Press.10.1515/9781400873234-019Search in Google Scholar

Hendry, D. F., and H.-M. Krolzig. 2005. “The Properties of Automatic Gets Modelling.” Economic Journal 115 (502): C32–C61.10.1111/j.0013-0133.2005.00979.xSearch in Google Scholar

Hendry, D. F., and C. Santos. 2010. “An Automatic Test of Super Exogeneity.” Chapter 12 in Volatility and Time Series Econometrics: Essays in Honor of Robert F. Engle, edited by T. Bollerslev, J. R. Russell, and M. W. Watson, 164–193. Oxford: Oxford University Press.10.1093/acprof:oso/9780199549498.003.0009Search in Google Scholar

Hendry, D. F., and F. Pretis. 2013. “Anthropogenic Influences on Atmospheric CO2.” Chapter 12 in Handbook on Energy and Climate Change, edited by R. Fouquet, 287–326. Cheltenham: Edward Elgar.10.4337/9780857933690.00021Search in Google Scholar

Hendry, D. F., and J. A. Doornik. 2014. Empirical Model Discovery and Theory Evaluation: Automatic Selection Methods in Econometrics. Cambridge, Massachusetts: MIT Press.10.7551/mitpress/9780262028356.001.0001Search in Google Scholar

Hendry, D. F., and S. Johansen. 2015. “Model Discovery and Trygve Haavelmo’s Legacy.” Econometric Theory 31 (1): 93–114.10.1017/S0266466614000218Search in Google Scholar

Hendry, D. F., S. Johansen, and C. Santos. 2008. “Automatic Selection of Indicators in a Fully Saturated Regression.” Computational Statistics 23 (2): 317–335, 337–339.10.1007/s00180-008-0112-1Search in Google Scholar

Hoover, K. D., and S. J. Perez. 1999. “Data Mining Reconsidered: Encompassing and the General-to-specific Approach to Specification Search.” Econometrics Journal 2 (2): 167–191 (with discussion).10.1111/1368-423X.00025Search in Google Scholar

Hoover, K. D., and S. J. Perez. 2004. “Truth and Robustness in Cross-country Growth Regressions.” Oxford Bulletin of Economics and Statistics 66 (5): 765–798.10.1111/j.1468-0084.2004.101_1.xSearch in Google Scholar

Hoover, K. D., S. Johansen, and K. Juselius. 2008. “Allowing the Data to Speak Freely: The Macroeconometrics of the Cointegrated Vector Autoregression.” American Economic Review 98 (2): 251–255.10.1257/aer.98.2.251Search in Google Scholar

Hoover, K. D., S. Demiralp, and S. J. Perez. 2009. “Empirical Identification of the Vector Autoregression: The Causes and Effects of US M2.” Chapter 2 in The Methodology and Practice of Econometrics: A Festschrift in Honour of David F. Hendry, edited by J. L. Castle and N. Shephard, 37–58. Oxford: Oxford University Press.10.1093/acprof:oso/9780199237197.003.0002Search in Google Scholar

Huhne, C. 1983. “Monetarism’s Guru ‘Distorts His Evidence’.” The Guardian December 15: 1.Search in Google Scholar

Jarque, C. M., and A. K. Bera. 1980. “Efficient Tests for Normality, Homoscedasticity and Serial Independence of Regression Residuals.” Economics Letters 6 (3): 255–259.10.1016/0165-1765(80)90024-5Search in Google Scholar

Johansen, S., and B. Nielsen. 2009. “An Analysis of the Indicator Saturation Estimator as a Robust Regression Estimator.” Chapter 1 in The Methodology and Practice of Econometrics: A Festschrift in Honour of David F. Hendry, edited by J. L. Castle and N. Shephard, 1–36. Oxford: Oxford University Press.10.1093/acprof:oso/9780199237197.003.0001Search in Google Scholar

Johansen, S., and B. Nielsen. 2013. “Outlier Detection in Regression Using an Iterated One-step Approximation to the Huber-skip Estimator.” Econometrics 1 (1): 53–70.10.3390/econometrics1010053Search in Google Scholar

Johansen, S., and B. Nielsen. 2016. “Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models.” Scandinavian Journal of Statistics, in press.10.1111/sjos.12174Search in Google Scholar

Kohn, D. L. 2009. “Monetary Policy Research and the Financial Crisis: Strengths and Shortcomings.” In Federal Reserve Conference on Key Developments in Monetary Policy, Board of Governors of the Federal Reserve System, Washington, DC, October 9.Search in Google Scholar

Krolzig, H.-M., and D. F. Hendry. 2001. “Computer Automation of General-to-specific Model Selection Procedures.” Journal of Economic Dynamics and Control 25 (6–7): 831–866.10.1016/S0165-1889(00)00058-0Search in Google Scholar

Laidler, D. E. W. 1993. The Demand for Money: Theories, Evidence, and Problems. 4th ed. New York: HarperCollins College Publishers.Search in Google Scholar

Longbottom, A., and S. Holly. 1985. “Econometric Methodology and Monetarism: Professor Friedman and Professor Hendry on the Demand for Money.” Discussion Paper No. 131, London Business School, London, February.Search in Google Scholar

Marczak, M., and T. Proietti. 2016. “Outlier Detection in Structural Time Series Models: The Indicator Saturation Approach.” International Journal of Forecasting 32 (1): 180–202.10.1016/j.ijforecast.2015.04.005Search in Google Scholar

Milbourne, R. (1983) “Optimal Money Holding Under Uncertainty.” International Economic Review 24 (3): 685–698.10.2307/2648794Search in Google Scholar

Miller, M. H., and D. Orr. 1966. “A Model of the Demand for Money by Firms.” Quarterly Journal of Economics 80 (3): 413–435.10.2307/1880728Search in Google Scholar

Nielsen, B., and A. Whitby. 2015. “A Joint Chow Test for Structural Instability.” Econometrics 3 (1): 156–186.10.3390/econometrics3010156Search in Google Scholar

Perez-Amaral, T., G. M. Gallo, and H. White. 2003. “A Flexible Tool for Model Building: The Relevant Transformation of the Inputs Network Approach (RETINA).” Oxford Bulletin of Economics and Statistics 65 (Supplement): 821–838.10.1046/j.0305-9049.2003.00096.xSearch in Google Scholar

Perez-Amaral, T., G. M. Gallo, and H. White. 2005. “A Comparison of Complementary Automatic Modeling Methods: RETINA and PcGets.” Econometric Theory 21 (1): 262–277.10.1017/S0266466605050152Search in Google Scholar

Pretis, F., M. L. Mann, and R. K. Kaufmann. 2015. “Testing Competing Models of the Temperature Hiatus: Assessing the Effects of Conditioning Variables and Temporal Uncertainties Through Sample-wide Break Detection.” Climatic Change 131 (4): 705–718.10.1007/s10584-015-1391-5Search in Google Scholar

Ramsey, J. B. 1969. “Tests for Specification Errors in Classical Linear Least-squares Regression Analysis.” Journal of the Royal Statistical Society, Series B 31 (2): 350–371.10.1111/j.2517-6161.1969.tb00796.xSearch in Google Scholar

Schwarz, G. 1978. “Estimating the Dimension of a Model.” Annals of Statistics 6 (2): 461–464.10.1214/aos/1176344136Search in Google Scholar

Smith, G. W. 1986. “A Dynamic Baumol-Tobin Model of Money Demand.” Review of Economic Studies 53 (3): 465–469.10.2307/2297641Search in Google Scholar

Teräsvirta, T., and A.-C. Eliasson. 2001. “Non-linear Error Correction and the UK Demand for Broad Money, 1878–1993.” Journal of Applied Econometrics 16 (3): 277–288.10.1002/jae.611Search in Google Scholar

White, H. 1980. “A Heteroskedasticity-consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica 48 (4): 817–838.10.2307/1912934Search in Google Scholar

White, H. 2000. “A Reality Check For Data Snooping.” Econometrica 68 (5): 1097–1126.10.1111/1468-0262.00152Search in Google Scholar

Yellen, J. L. 2015. “FOMC Press Conference.” Transcript, Federal Reserve Board, Washington, DC, March 18.Search in Google Scholar

Published Online: 2016-5-12
Published in Print: 2016-9-1

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