Skip to main content Accessibility help


  • Stephen M. Miller (a1), Luis Filipe Martins (a2) and Rangan Gupta (a3)


Money-demand specifications exhibit instability, especially for long spans of data. This paper reconsiders the welfare cost of inflation for the US economy using a flexible time-varying (TV) cointegration methodology to estimate the money-demand function. We find evidence that the TV cointegration estimation provides a better fit of the actual data than a time-invariant estimation and that the throughout unitary income elasticity only exists for the log–log form over the entire sample period. Our estimate of the welfare cost of inflation for a 10% inflation rate lies in the range of 0.025–0.75% of gross domestic product (GDP) and averages 0.27%. In sum, our findings fall well within the ranges of existing studies of the welfare cost of inflation. We find that the welfare cost averages 7.4% higher during expansions than recessions for 10% inflation rate. Finally, the interest elasticity of money demand shows substantial variability over our sample period.


Corresponding author

Address correspondence to: Stephen M. Miller, Department of Economics, University of Nevada, Las Vegas, Las Vegas, Nevada, 89154-6005, USA; e-mail:


Hide All
Adão, B. and Silva, A. C. (2013) Government financing with taxes or inflation. SSRN:
Aiyagari, S. R., Braun, R. A., and Eckstein, Z. (1998) Transaction services, inflation, and welfare. Journal of Political Economy 106, 12741301.10.1086/250047
Andrade, P., Bruneau, C., and Gregoir, S. (2005) Testing for the cointegration rank when some cointegrating directions are changing. Journal of Econometrics 124, 269310.10.1016/j.jeconom.2004.02.003
Bae, Y. and de Jong, R. M. (2007) Money demand function estimation by nonlinear cointegration. Journal of Applied Econometrics 22 (4), 767793.10.1002/jae.915
Bailey, M. (1956) The welfare cost of inflationary finance. Journal of Political Economy 64, 93110.10.1086/257766
Barigozzi, M. and Conti, A. M. (2014) On the stability of Euro Area money demand and its implications for monetary policy. SSRN:
Bierens, H. J. and Martins, L. F. (2010) Time-varying cointegration. Econometric Theory 26, 14531490.10.1017/S0266466609990648
Blake, N. S. and Fomby, T. B. (1997) Threshold cointegration. International Economic Review 38, 627645.10.2307/2527284
Boel, P. and Camera, G. (2011) The welfare cost of inflation in OECD countries. Macroeconomic Dynamics 15 (Suppl. 2), 217251.10.1017/S1365100510000507
Burstein, A. and Hellwig, C. (2008) Welfare costs of inflation in a menu cost model. American Economic Review 98, 438443.10.1257/aer.98.2.438
Cagan, P. (1956) The monetary dynamics of hyperinflation. In Friedman, M. (ed.), Studies in the Quantity Theory of Money, pp. 25117. Chicago: University of Chicago Press.
Calza, A. and Zaghini, A. (2009) Nonlinearities in the dynamics of the Euro Area demand for M1. Macroeconomic Dynamics 13, 119.10.1017/S1365100508070405
Chow, G. C. (1966) On the long-run and short-run demand for money. Journal of Political Economy 74, 111131.10.1086/259130
Cooley, T. F. and Hansen, G. (1989) The inflation tax in a real business cycle. American Economic Review 79, 733744.
Cooley, T. F. and Hansen, G. (1991) The welfare cost of moderate inflations. Journal of Money, Credit and Banking 23, 483503.10.2307/1992683
Craig, B. and Rocheteau, G. (2008) Inflation and welfare: A search approach. Journal of Money, Credit and Banking 40, 89119.10.1111/j.1538-4616.2008.00105.x
Cynamon, B. Z., Dutkowsky, D. H., and Jones, B. E. (2006) Redefining the monetary aggregates: A clean sweep. Eastern Economic Journal 32 (4), 661672.
Cysne, R. P. (2003) Divisaindex, inflation and welfare. Journal of Money, Credit and Banking 35, 221239.10.1353/mcb.2003.0010
Cysne, R. P. (2009) Bailey's measure of welfare costs of inflation as a general equilibrium measure. Journal of Money, Credit and Banking 41, 451459.10.1111/j.1538-4616.2009.00214.x
Cysne, R. P. and Turchick, D. (2010) Welfare costs of inflation when interest-bearing deposits are disregarded: A calculation of the bias. Journal of Economic Dynamics and Control 34, 10151030.10.1016/j.jedc.2010.01.003
de Jong, R.M. (2001) Nonlinear estimation using estimated cointegrating relations. Journal of Econometrics 101, 109122.10.1016/S0304-4076(00)00075-0
Dibooglu, S. and Kenc, T. (2009) Welfare cost of inflation in a stochastic balanced growth model. Economic Modelling 26, 650658.10.1016/j.econmod.2009.01.011
Dickey, D. and Fuller, W. (1981) Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49, 10571072.10.2307/1912517
Dotsey, M. and Ireland, P. N. (1996) The welfare cost of inflation in general equilibrium. Journal of Monetary Economics 37, 2947.10.1016/0304-3932(95)01239-7
Duprey, J. N. (1980) The search for a stable money demand equation. Federal Reserve Bank of Minneapolis Quarterly Review 4 (3), 514.
Elliott, G., Rothenberg, T. J., and Stock, J. H. (1996) Efficient tests for an autoregressive unit root. Econometrica 64, 813836.10.2307/2171846
Engle, R. F. and Granger, C. W. J. (1987) Cointegration and error correction: Representations, estimation and testing. Econometrica 55, 251276.10.2307/1913236
Escribano, A. (2004) Nonlinear error correction: The case of money demand in the United Kingdom (1878–2000). Macroeconomic Dynamics 8, 76116.10.1017/S1365100504030019
Evans, L. and Kenc, T. (2003) Welfare cost of monetary and fiscal policy shocks. Macroeconomic Dynamics 7, 212238.10.1017/S1365100501010343
Feldstein, M. (1997) The costs and benefits of going from low inflation to price stability. In Romer, C. D. and Romer, D. H. (eds.), Reducing Inflation: Motivation and Strategy, pp. 123156. Chicago: The University of Chicago Press.
Feldstein, M. (1999) Capital income taxes and the benefit of price stability'. In Feldstein, M. (ed.), The Costs and Benefits of Price Stability, pp. 946. Chicago and London: The University of Chicago Press.10.7208/chicago/9780226241760.001.0001
Fischer, S. (1981) Towards an understanding of the costs of inflation: II. Carnegie-Rochester Conference Series on Public Policy 15, 541.10.1016/0167-2231(81)90016-6
Friedman, M. (1969) The Optimum Quantity of Money and Other Essays. Chicago: Aldine Publishing Company.
Garcia, G. and Pak, S. (1979) Some clues in the case of the missing money. American Economic Review 69 (2), 330334.
Gillman, M. (1993) The welfare cost of inflation in a cash-in-advance economy with costly credit. Journal of Monetary Economics 31, 97115.10.1016/0304-3932(93)90018-B
Gillman, M. (1995) Comparing partial and general equilibrium estimates of the welfare cost of inflation. Contemporary Economic Policy 13, 6071.10.1111/j.1465-7287.1995.tb00732.x
Goldfeld, S. M. (1976) The case of the missing money. Brookings Papers on Economic Activity 3, 683739.10.2307/2534372
Gomme, P. (1993) Money and growth revisited: Measuring the costs of inflation in an endogenous growth model. Journal of Monetary Economics 32, 5177.10.1016/0304-3932(93)90035-E
Granger, C. W. J. (2008) Non-linear models: Where do we go next–-time varying parameter models? Studies in Nonlinear Dynamics and Econometrics 12, 111.
Granger, C. W. J. and Yoon, G. (2002) Hidden Cointegration. Working paper no. 2002-02, University of California, San Diego.
Gupta, R. and Majumdar, A. (2014) Reconsidering the welfare cost of inflation in the US: A nonparametric estimation of the nonlinear long-run money demand equation using projection pursuit regressions. Empirical Economics 46, 12211240.10.1007/s00181-013-0721-6
Gupta, R. and Uwilingiye, J. (2010) Evaluating the welfare cost of inflation in a monetary endogenous growth general equilibrium model: The case of South Africa. International Business and Economics Research Journal 9, 101112.
Hafer, R. W. and Jansen, D. W. (1991) The demand for money in the United States: Evidence from cointegration tests. Journal of Money, Credit and Banking 23, 155168.10.2307/1992774
Hall, S. G., Psaradakis, Z., and Sola, M. (1997) Cointegration and changes in regime: The Japanese consumption function. Journal of Applied Econometrics 12, 151168.10.1002/(SICI)1099-1255(199703)12:2<151::AID-JAE424>3.0.CO;2-J
Hansen, P. R. (2003) Structural changes in the cointegrated vector autoregressive model. Journal of Econometrics 114, 261295.10.1016/S0304-4076(03)00085-X
Harris, D., McCabe, B., and Leybourne, S. (2002) Stochastic cointegration: Estimation and inference. Journal of Econometrics 111, 363384.10.1016/S0304-4076(02)00111-2
Henriksen, E. and Kydland, F. (2010) Endogenous money, inflation and welfare. Review of Economic Dynamics 13, 470486.10.1016/
Ireland, P. N. (2009) On the welfare cost of inflation and the recent behavior of money demand. American Economic Review 99, 10401052.10.1257/aer.99.3.1040
Jawadi, F. and Sousa, R. M. (2013) Money demand in the euro area, the US and the UK: Assessing the role of nonlinearity. Economic Modelling 32 (C), 507515.10.1016/j.econmod.2013.02.009
Johansen, S. (1988) Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231254.10.1016/0165-1889(88)90041-3
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 15511580.10.2307/2938278
Judd, J. P. and Scadding, J. L. (1982) The search for a stable money demand function. Journal of Economic Literature 20, 9931023.
Juhl, T. and Xiao, Z. (2005) Testing for cointegration using partially linear models. Journal of Econometrics 124, 363394.10.1016/j.jeconom.2004.02.007
Khan, M. S. (1974) The stability of the demand for money function in the United States, 1901-65. Journal of Political Economy 82, 12051220.10.1086/260272
Kumar, S. (2014) The varying interest elasticity and the cost of inflation in India. Applied Economics Letters 21, 497500.10.1080/13504851.2013.870643
Lagos, R. and Wright, R. (2005) A unified framework for monetary theory and policy analysis. Journal of Political Economy 113, 463484.10.1086/429804
Lim, C., Columba, F., Costa, A., Kongsamut, P., Otani, A., Saiyid, M., Wezel, T., and Wu, X. (2011) Macroprudential Policy: What Instruments and How to Use Them? Lessons from Country Experiences. IMF working paper no. 11/238.
Lucas, R. E. Jr. (1981) Discussion of: Stanley Fischer, ‘towards an understanding of the costs of inflation: II.’ Carnegie-Rochester Conference Series on Public Policy 15, 4352.10.1016/0167-2231(81)90017-8
Lucas, R. E. Jr. (1994) The Welfare Costs of Inflation. CEPR working paper no. 394.
Lucas, R. E. Jr. (2000) Inflation and Welfare. Econometrica 68, 247274.10.1111/1468-0262.00109
Lucas, R. Jr. and Nicolini, J. (2013) On the Stability of Money Demand. 2013 Meeting Papers 353, Society for Economic Dynamics.
Lütkepohl, H. (1993) The sources of the U.S. money demand instability. Empirical Economics 18 (4), 729743.10.1007/BF01205418
Martins, L. F. (in press) Bootstrap tests for time varying cointegration. Econometric Reviews.
Meltzer, A. H. (1963) The demand for money: The evidence from the time series. Journal of Political Economy 71, 219246.10.1086/258768
Miller, S. M. (1986) Financial innovation, depository institution deregulation, and the demand for money. Journal of Macroeconomics 8, 279296.10.1016/0164-0704(86)90061-3
Miller, S. M. (1990) Disequilibrium macroeconomics, money as a buffer stock, and the estimation of money demand. Journal of Macroeconomics 12, 563586.10.1016/0164-0704(90)90081-K
Miller, S. M. (1991) Monetary dynamics: An application of cointegration and error-correction modeling. Journal of Money, Credit and Banking 23, 139154.10.2307/1992773
Mogliani, M. and Urga, G. (2015) On the instability of long-run money demand and the welfare cost of inflation in the U.S. Mimeo, Faculty of Finance, Cass Business School.
Nakashima, K. (2009) An extremely-low-interest-rate policy and the shape of the Japanese money demand function. Macroeconomic Dynamics 13, 553579.10.1017/S1365100509080225
Nakashima, K. and Saito, M. (2012) On the comparison of alternative specifications for money demand: The case of extremely low interest rate regimes in Japan. Journal of the Japanese and International Economies 26, 454471.10.1016/j.jjie.2012.04.001
Ng, S. and Perron, P. (2001) Lag length selection and the construction of unit root tests with good size and power. Econometrica 69, 15191554.10.1111/1468-0262.00256
Pakko, M. R. (1998) Shoe-leather costs of inflation and policy credibility. Federal Reserve Bank of St. Louis Review 80, 3750.
Park, J. Y. and Hahn, S. B. (1999) Cointegrating regressions with time varying coefficients. Econometric Theory 15, 664703.10.1017/S0266466699155026
Phillips, P. and Perron, P. (1988) Testing for a unit root in time series regression. Biometrika 75, 335346.10.1093/biomet/75.2.335
Rao, B. B. and Kumar, S. (2011) Is the US demand for money unstable? Applied Financial Economics 21, 12631272.10.1080/09603107.2011.568395
Saikkonen, P. and Choi, I. (2004) Cointegrating smooth transition regressions. Econometric Theory 20, 301340.10.1017/S0266466604202031
Serletis, A. and Shahmoradi, A. (2005) Semi-nonparametric estimates of the demand for money in the United States. Macroeconomic Dynamics 9, 542559.10.1017/S1365100505040307
Serletis, A. and Shahmoradi, A. (2007a) A note on imposing local curvature in generalized Leontief models. Macroeconomic Dynamics 11, 290294.10.1017/S1365100507050298
Serletis, A. and Shahmoradi, A. (2007b) Flexible functional forms, curvature conditions, and the demand for assets. Macroeconomic Dynamics 11, 455486.10.1017/S1365100507060154
Serletis, A. and Yavari, K. (2004) The welfare cost of inflation in Canada and the United States. Economics Letters 84, 199204.10.1016/j.econlet.2004.02.002
Silva, A. C. (2012) Rebalancing frequency and the welfare cost of inflation. American Economic Journal: Macroeconomics 4, 153183.
Tesfatsion, L. and Veitch, J. M. (1990) U.S. money demand instability: A flexible least squares approach. Journal of Economic Dynamics and Control 14, 151173.10.1016/0165-1889(90)90010-E
Vinod, H. R. (1998) Nonparametric estimation of non-linear money demand cointegration equation by projection pursuit methods. In Weisberg, S. (ed.), Computing Science and Statistics, vol. 30, pp. 174183. Fairfax, Virginia: Interface Foundation.
Wang, Y. (2011) The stability of long-run money demand in the United States: A new approach. Economics Letters 111, 6063.10.1016/j.econlet.2011.01.001
Wolters, J. and Lütkepohl, H. (1998) A money demand system for German M3. Empirical Economics 23, 371386.
Wu, Y. and Zhang, J. (1998) Endogenous growth and the welfare costs of inflation: A reconsideration. Journal of Economic Dynamics and Control 22, 465482.10.1016/S0165-1889(97)00067-5
Zuo, H. and Park, S. Y. (2011) Money demand in China and time-varying cointegration. China Economic Review 22, 330343.10.1016/j.chieco.2011.04.001



  • Stephen M. Miller (a1), Luis Filipe Martins (a2) and Rangan Gupta (a3)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.