Another look at long-run money demand

qI am grateful for research assistance from Qiming Chen and Christopher Smith, for suggestionsfrom Pedro DeLima, Martin Eichenbaum, Louis Maccini and an anonymous referee, and for dataand econometric programs from James Stock.

*Correspondence address: Bank of England, Threadneedle Street HO-3, London, EC2R 8AH,UK.

E-mail address: [email protected] (L. Ball).

Journal of Monetary Economics 47 (2001) 31}44

Another look at long-run money demandq

Laurence Ball!,",*!Johns Hopkins University, Baltimore, MD 21218, USA

"Bank of England, Threadneedle Street HO-3, London, EC2R 8AH, UK

Received 15 June 1999; received in revised form 11 January 2000; accepted 23 February 2000

Abstract

This paper investigates the long-run demand for M1 in the postwar United States.Previous studies, based on data ending in the late 1980s, are inconclusive about theparameters of postwar money demand. This paper obtains precise estimates of theseparameters by extending the data through 1996. The income elasticity of money demandis approximately 0.5, and the interest semi-elasticity is approximately !0.05. Theseparameters are signi"cantly smaller in absolute value than the corresponding parametersfor the prewar period. A caveat is that the analysis assumes there is no trend in moneydemand resulting from technological change. ( 2001 Elsevier Science B.V. All rightsreserved.

JEL classixcation: E41

Keywords: Money demand

1. Introduction

This paper investigates the long-run demand for M1 in the postwar UnitedStates. Previous researchers, such as Lucas (1988) and Stock and Watson (1993),

0304-3932/01/$ - see front matter ( 2001 Elsevier Science B.V. All rights reserved.PII: S 0 3 0 4 - 3 9 3 2 ( 0 0 ) 0 0 0 4 3 - X

1Like this paper, Baba et al. (1992) report an income elasticity near 0.5. Their estimate is based ona sample ending in 1988, only a year after Stock and Watson's sample. Baba et al.'s results di!er fromLucas's and Stock and Watson's because of di!erences in econometric methodology. For a critiqueof Baba et al., see Hess et al. (1994).

Fig. 1. Output and the interest rate.

"nd that postwar data are inconclusive about the parameters of money demand.In contrast, this study yields fairly precise estimates. The long-run incomeelasticity of money demand is approximately 0.5, and the interest semi-elasticityis approximately !0.05.

The econometric methods in this paper are similar to the ones in previousstudies. The results are di!erent for a simple reason: the data extend longer.While previous work examines data ending in the late 1980s, this study uses datathrough 1996. It turns out that the data since the late 1980s are very informativeabout money demand.1

Fig. 1 shows why the recent data are important. The "gure plots the log of realoutput and a smoothed series for the interest rate on commercial paper produc-ed with the Kalman "lter. Through the early 1980s, output and the interest ratefollow similar upward trends, and so it is di$cult to separate their e!ects onmoney demand. In other words, there is a collinearity problem. The problem

32 L. Ball / Journal of Monetary Economics 47 (2001) 31}44

2Data on money and interest rates for 1947}1996 are from the Federal Reserve Board and DataResources, Inc. These data are spliced to Stock and Watson's data for 1900}1946. Data on incomeand prices for 1959}1996 are from the Bureau of Economic Analysis, and are spliced to Stock andWatson's data for 1900}1958.

diminishes after the early 1980s, because output continues to trend up butthe interest-rate trend shifts down. The data through 1996 cover moreexperience with independent movements in output and interest rates than dothe data in previous studies, which include only a few years since the early1980s.

In addition to examining the postwar period, this paper considers the behav-ior of money demand over the entire 20th century. A number of authors arguethat long-run money demand is stable over this period (Lucas, 1988; Poole,1988; Stock and Watson, 1993; Christ, 1993). For example, Stock and Watsonconclude that `the evidence [for 1900}1987] is consistent with there beinga single stable long-run demand for money, with an income elasticity near oneand an interest semi-elasticity near !0.10a. This conclusion is valid given thedata used in previous work: the prewar data suggest such a function, and theimprecision of postwar estimates means the function cannot be rejected for thatperiod. When the data are extended through 1996, however, the postwarestimates become precise, and both the income and interest-rate coe$cients aresmaller than the prewar estimates. Thus, the data reject stability across the twoperiods.

Section 2 of this paper presents estimates of long-run money demand. I repli-cate Stock and Watson's study and examine the e!ects of extending the sample.Following Lucas (1988), Section 3 examines the data informally to provideintuition for the results. Section 4 concludes.

2. Money-demand estimates

2.1. The approach

This section estimates the parameters of a canonical money-demandfunction:

m!p"hyy#h

rr#e, (1)

where m, p, and y are the logs of the money stock, the price level, and real outputand r is the level of the nominal interest rate. Following Stock and Watson,money is de"ned as M1, output is NNP, the price level is the NNP de#ator, andthe interest rate is the commercial paper rate. Most of the analysis uses annualdata on these variables.2

L. Ball / Journal of Monetary Economics 47 (2001) 31}44 33

The appropriate estimation technique depends on the time-series behavior ofreal balances, output, and the interest rate. Previous researchers "nd that thesevariables are individually integrated of order one and cointegrated, based onstandard tests such as the Dickey}Fuller and Johansen tests (e.g. Ho!man andRasche, 1991; Stock and Watson, 1993). Extending the data through 1996 doesnot change the results of these tests. I therefore assume cointegration through-out this paper.

There are many estimators of cointegrating relations, and Stock and Watson"nd that postwar money-demand estimates vary widely across them. I thereforeexamine all eight of the techniques used by Stock and Watson. These techniquesare ordinary least-squares, the non-linear least-squares estimator of Baba et al.(1992), Stock and Watson's dynamic OLS and dynamic GLS estimators, theestimators of Phillips (1991) and Phillips and Hansen (1990), and Johansen's(1988) estimator with two and three lags. In addition, I use two versions of thecommercial-paper rate: the raw series, and the series smoothed with the Kalman"lter. All details of the procedures, such as the choices of various lag lengths,follow Stock and Watson.

2.2. Estimates for alternative postwar periods

Table 1 presents money-demand estimates for Stock and Watson's postwarperiod, which is 1946}1987, and for extensions of this period. The extendedperiod is 1946}1996 for some estimators and 1946}1994 for others, whichrequire two leads of the data. The table reports coe$cients and asymptoticstandard errors for the eight estimators (except for OLS and NLLS, for whichstandard errors are unknown).

My results for 1946}1987 are similar to Stock and Watson's results for thatperiod. (Small di!erences are explained by data revisions.) As discussed by Stockand Watson, and also by Ho!man et al. (1995), the income and interest-ratecoe$cients vary widely across estimators. In addition, the standard errorsare usually large. (The standard errors are small for the Phillips andPhillips}Hansen estimators, but Stock and Watson show that these numbersgreatly understate the "nite-sample uncertainty.) Overall, we learn little from thedata; for example, an income coe$cient of one is accepted for several estimators,but so is a coe$cient of zero. Fig. 2A illustrates the uncertainty by plotting 95%con"dence ellipses for various estimators.

The results are quite di!erent when the sample is extended to 1994 or 1996. Inthese cases, the point estimates are clustered near 0.5 for the income coe$cientand !0.05 for the interest-rate coe$cient. As shown in Fig. 2B, the estimatesare fairly precise, and con"dence ellipses bound the coe$cients far from 1.0 and!0.1, the values suggested by Stock and Watson for the 20th century. For theDOLS estimator, for example, the income coe$cient is about eight standarderrors below one and the interest-rate coe$cient is about six standard errors


Tab

le1

Mone

y-dem

and

estim

ates r"

Com

mer

cial

pap

erra

ter"

Smoo

thed

com

mer

cial

pap

erra

te

1946}19

8719

46}19

96!

1946}19

8719

46}19

96!

Est

imat

or

h yh r

h yh r

h yh r

h yh r

SOLS

0.17

96!

0.01

440.

3691

!0.

0320

0.39

13!

0.04

520.

5018

!0.

0599

NL

LS

!0.

4463

0.08

680.

5911

!0.

1484

0.36

95!

0.03

550.

4120

!0.

0460

DO

LS

0.27

32!

0.02

770.

4268

!0.

0449

0.39

72!

0.04

650.

4229

!0.

0492

(0.1

894)

(0.0

230)

(0.0

722)

(0.0

097)

(0.3

150)

(0.0

432)

(0.0

803)

(0.0

119)

DG

LS

0.77

57!

0.01

790.

4469

!0.

0405

0.86

09!

0.09

150.

5166

!0.

0581

(0.3

177)

(0.0

097)

(0.0

628)

(0.0

087)

(0.1

147)

(0.0

141)

(0.0

658)

(0.0

094)

Phill

ips

0.20

92!

0.01

920.

4251

!0.

0435

0.35

84!

0.04

170.

4958

!0.

0590

(0.0

834)

(0.0

098)

(0.0

492)

(0.0

072)

(0.1

460)

(0.0

194)

(0.0

442)

(0.0

072)

Phill

ips}

Han

sen

0.19

13!

0.01

660.

4041

!0.

0401

0.37

96!

0.04

450.

4888

!0.

0593

(0.0

489)

(0.0

055)

(0.0

404)

(0.0

056)

(0.0

964)

(0.0

132)

(0.0

345)

(0.0

058)

Joh.

(2)

2.15

75!

0.29

540.

4386

!0.

0516

!2.

6020

0.38

560.

4248

!0.

0498

(6.5

800)

(0.9

248)

(0.0

666)

(0.0

102)

(6.1

784)

(0.8

918)

(0.0

631)

(0.0

097)

Joh.(3

)!

3.09

860.

4719

0.44

35!

0.04

92!

0.72

270.

1215

0.46

39!

0.05

45(1

3.75

4)(2

.047

2)(0

.050

8)(0

.007

6)(0

.917

0)(0

.136

3)(0

.057

8)(0

.008

9)

!194

6}19

94fo

rD

OL

San

dD

GLS.


Fig. 2. 95% con"dence ellipses for hy

and hr.

3The "nding of an income elasticity below one has a number of implications for monetary policy.For example, it means that the money stock must grow more slowly than output to achieve pricestability. In some models, an elasticity below one also implies that the Friedman rule is not optimal(e.g. Chari et al., 1996).

above !0.1. The s2 statistic for the joint hypothesis that the coe$cients are 1.0and !0.1 is 66.8 (p-value(10~14).3

2.3. Monte Carlo results

Asymptotic con"dence ellipses can greatly overstate the precision of estimatesin "nite samples. I perform Monte Carlo experiments to see how serious this


4 I have also performed Monte Carlo experiments with pseudo-data based on the true data for1900}1994 rather than 1946}1994. The results are similar to the ones reported in the text.

5Lucas argues that one should not assume stable short-run dynamics in testing for stability oflong-run money demand. In his words, `one needs a maintained hypothesis in which one has more,not less, con"dence than one has in the hypothesis being testeda (1988, p. 162).

problem is in my application. I focus on the question of how con"dently one canreject money-demand coe$cients of 1.0 and !0.1. The basic strategy is todetermine how often tests of true hypotheses produce t and s2 statistics of thesizes reported above } in other words, to calculate correct p-values for thesestatistics.

Following Stock and Watson's Monte Carlo experiments, I generate pseudo-data that mimic the dynamics of the true data for 1946}1994. Speci"cally, I setthe long-run money demand coe$cients equal to the DOLS estimates; afterimposing these coe$cients, I estimate the short-run dynamics of real balances,output, and the interest rate with a VECM(2). I generate 49 observations ofpseudo-data by feeding Gaussian errors into the estimated VECM(2). For theseobservations, I calculate t and s2 statistics for the hypotheses that the long-runcoe$cients equal the values used to generate the data, using each of theestimation techniques in Table 1. I replicate this procedure 10,000 times toderive distributions of the t and s2 statistics.4

The results con"rm the rejections of money-demand coe$cients of 1.0 and!0.1. For the DOLS estimator, for example, the t-statistics reported above are7.9 for h

y"1.0 and 5.7 for h

r"!0.1. The Monte Carlo p-values } the fractions

of simulated t-statistics that exceed 7.9 or 5.7 } are 0.001 and 0.02. Thes2 statistic of 66.8 for the joint hypothesis has a Monte Carlo p-value of 0.004.These p-values are orders of magnitude larger than the asymptotic p-values, butthey are small enough to produce strong rejections. The Monte Carlo p-valuesare even smaller for most of the other estimators than for DOLS.

2.4. Prewar vs. postwar estimates

As discussed in the Introduction, several authors argue that long-run moneydemand is stable across broad parts of the 20th century. Lucas, for example,"nds stability across 1900}1957 and 1958}1985, and Stock and Watson "ndstability across 1903}1945 and 1946}1987. Like the postwar parameter esti-mates, these results are sensitive to the endpoint of the data. I document thisusing the stability test that Stock and Watson construct from their DOLSestimator. This procedure tests for the stability of the cointegrating relationunder the assumption of constant short-run dynamics. I also consider a vari-ation in which the parameters describing these dynamics are allowed to shift,which seems appropriate given the well-documented instability of short-runmoney demand.5


Table 2Prewar vs. postwar estimates (DOLS)

1903}1945 1946}1987 1903}1987 1946}1994 1903}1994

r"Commercial paper rateh:

0.8871 0.2732 1.0514 0.4268 1.0531(0.1966) (0.1894) (0.1604) (0.0722) (0.1383)

h3

!0.1060 !0.0277 !0.0916 !0.0449 !0.0910(0.0391) (0.0230) (0.0344) (0.0097) (0.0297)

s2 for subsample stability 1.894 7.157(assumes constant SRdynamics)

(p"0.39) (p"0.03)

s2 for subsample stability 4.019 9.1490(allows di!erent SR dynamics) (p"0.13) (p"0.01)

r"Smoothed commercial paper ratehy

0.8570 0.3972 0.9452 0.4229 0.9512(0.0737) (0.3150) (0.1776) (0.0803) (0.1539)

hr

!0.1340 !0.0465 !0.1208 !0.0492 !0.1195(0.0175) (0.0432) (0.0431) (0.0119) (0.0373)

s2 for subsample stability 0.285 1.637(assumes constant SRdynamics)

(p"0.87) (p"0.44)

s2 for subsample stability 3.489 18.761(allows di!erent SR dynamics) (p"0.18) (p"0.00)

6These results are similar to some of Friedman and Schwartz's money-demand estimates (1982,Section 6.4). Friedman and Schwartz obtain a lower income elasticity with data after 1945 than withdata before 1945, but the estimate for their full sample is close to the pre-1945 estimate (roughly 1.2).Like Lucas and Stock and Watson, Friedman and Schwartz conclude that the income elasticity isconstant over the 20th century. They argue that the post-1945 estimate is unreliable because ofunusual money-demand shocks in the early postwar period.

The "rst three columns of Table 2 contain DOLS estimates of money demandfor 1903}1945, 1946}1987, and 1903}1987, and the associated stability tests. Thecoe$cients on output and the interest rate are close to 1.0 and !0.1 for the "rstsubsample and the combined sample. The estimates for the second subsampleare smaller in absolute value, but they are imprecise, as discussed above.Consequently, there is little evidence that the coe$cients shift: none of thestability tests rejects at the 10% level.6

Once again, the results are very di!erent when the sample is extended to 1994.The parameter estimates for the full sample change only moderately. However,the small and precise estimates for the postwar period produce strong evidence


7The quarterly DOLS regressions use four leads and lags of the data; an AR(4) error was used tocompute the standard errors.

against stability. Under the assumption of constant short-run dynamics, stabil-ity is rejected at the 5% level when the unsmoothed interest rate is used. Whenthe short-run assumption is relaxed, stability is rejected at the 1% level for boththe smoothed and unsmoothed interest rates.

2.5. Quarterly data

As a "nal robustness check, I estimate the postwar money-demand functionusing quarterly rather than annual data. Ho!man et al. examine quarterly datathrough 1990 and, like Lucas and Stock}Watson, they cannot disentangle thee!ects of interest rates and output. Once again, this problem disappears whenthe data are extended. For example, DOLS for 1948 : 2}1995 : 4 produces anincome coe$cient of 0.430 (s.e."0.060) and an interest-rate coe$cient of!0.041 (s.e."0.009). These results, and those for other estimators, are close tothe results for annual data.7

Future research should further investigate the robustness of my results byexamining countries besides the United States. Ho!man et al. estimate moneydemand functions for four other G7 countries and "nd, as for the U.S., thatcollinearity produces inconclusive results in data through 1990. Extending thesamples for these countries might again sharpen the results.

3. Interpretation

3.1. Examining the data

If one has not seen the data, it might be surprising that money-demandestimates change dramatically when the sample is extended by nine years or less.However, Fig. 1 in the introduction shows why the data since 1987 are soimportant. When these years are included, we can compare the pre-1982 period,when interest rates and output trended together, to a substantial post-82 periodwhen they moved in opposite directions. This allows us to disentangle the e!ectsof the two variables on money demand.

We can learn more from Fig. 3, which shows the smoothed interest rate andthe log of the income velocity of money. Through the early 1980s, velocityfollowed an upward trend, which means that money grew less quickly thanincome. By itself, this fact suggests that the income elasticity of money demand isless than one. Lucas, however, o!ers a di!erent interpretation: velocity rosebecause interest rates have strong e!ects on money demand, and interest rates


Fig. 3. Velocity and the interest rate.

rose through the early 1980s. If one imposes a unit income elasticity, an interestsemi-elasticity near !0.1 can explain the velocity trend. Lucas acknowledges,however, that the data can also be explained by a combination of a smallerincome coe$cient and a smaller interest coe$cient.

The data since the early 1980s rule out Lucas's preferred story in favor of theone with lower coe$cients. If the interest-rate coe$cient were large, so risinginterest rates caused the rise in velocity through 1981, the fall in interest ratesafter then should have caused a fall in velocity. In fact, velocity has been roughlytrendless since the early 1980s. By the mid-1990s, interest rates fell to the samelevel as in the late 1960s, but velocity was much higher than in that period. Asthe rise in velocity since the 1960s cannot be explained by interest rates, itimplies an income elasticity below one.

Figs. 4 and 5 make these points a di!erent way. Fig. 4 is a scatterplot (similarto one in Lucas) of the log of velocity against the smoothed interest rate.Through 1987, there is a close linear relation, suggesting a stable money-demand function with a unit income elasticity. The relation breaks downafter 1987, however. Note that 1987 is the last year in Stock and Watson'ssample.

The breakdown in the velocity/interest-rate relation does not imply thatthe money-demand function shifted in 1987. It simply means that a stablefunction must have an income elasticity di!erent from one. In general, themoney-demand function implies a linear relation between the interest rate and


Fig. 4. Velocity and the interest rate.

Fig. 5. Quasi-velocity and the interest rate.

`quasi-velocitya, de"ned as hyy!(m!p). Fig. 5 plots the smoothed interest

rate against quasi-velocity, with hy

set at the DOLS estimate of 0.423. Thisrelation is stable throughout the postwar period.


Table 3Estimates with a time trend (DOLS, 1946}1994)

Restriction None No trend hy"1

hy

!0.0051 0.4268 1.0(0.4575) (0.0722)

hr

!0.0401 !0.0449 !0.0537(0.0105) (0.0097) (0.0110)

Trend 0.0121 0.0 !0.0157(0.0127) (0.0023)

8 If shifts in the transaction technology cause random-walk movements in money demand, thenreal balances are not cointegrated with output and interest rates. In principle, such shifts are ruledout by the common empirical "nding of cointegration. This "nding does not, however, rule outmoney-demand shifts that are well-approximated by a deterministic trend.

3.2. An alternative interpretation

The analysis so far, like the recent literature, rests on the assumption that Eq.(1) is the correct money-demand function } and in particular, the implicitassumption that the function does not include a time trend. It is not clear thatthis restriction is reasonable. For given output and interest rates, money de-mand can change over time if there are changes in the economy's transactiontechnology. And the postwar era has seen a series of changes that allowindividuals to reduce their holdings of M1, such as the creation of near-monies.It is therefore plausible that money demand has trended downward.8

This possibility suggests yet another interpretation of the velocity movementsin Fig. 3. The rise in velocity for given interest rates may re#ect a downwardtrend in money demand rather than an income elasticity below one. In principle,one can test this idea by including a trend in the estimated money-demandfunction. But in practice, a trend is highly collinear with income, so one cannotdisentangle their e!ects. A trend in the transaction technology and a low incomeelasticity are near-observationally-equivalent interpretations of the data.

Table 3 illustrates this problem with several DOLS regressions for 1946}1994.In the "rst column of the table, a time trend is added to the basic money-demandequation, with inconclusive results: neither income nor the trend is signi"cant,because the standard errors are large. The second column repeats a regressionfrom earlier in the paper: it imposes a zero trend to obtain a precise estimate ofthe income coe$cient. The "nal column uses a di!erent identifying assumption:it restricts the income coe$cient to one, and obtains a precisely estimated trendof !1.6% per year. In all speci"cations, the interest-rate coe$cient is close to!0.04 or !0.05.


9Mulligan (1997) compares time-series and cross-sectional estimates of income elasticities.

Is there any way to separate the e!ects of income and technological change?One possibility is to examine cross-sectional variation in money demand, suchas variation across individual "rms and households or across geographic re-gions. If one examines data from a single point in time, it is plausible to assumethat all agents face the same transactions technology. Thus variation in moneyholdings, for example across individuals with di!erent incomes, might pin downthe income elasticity of money demand. Comparing this elasticity to the time-series trend in velocity would determine the money-demand trend arising fromtechnological change.

A number of papers have estimated money-demand functions with cross-sectional data. This literature has not produced a consensus about the incomeelasticity: many studies report elasticities close to one (e.g. Meltzer, 1963; Feige,1964), but recent work reports both higher estimates (e.g. Mulligan and Sala-i-Martin, 1992) and lower estimates. Despite this variation, most reported incomeelasticities exceed this paper's estimate of 0.5: the lowest cross-sectional esti-mates include 0.68 (Mankiw, 1992) and 0.60}0.86 (Radecki and Garver, 1987).Thus the cross-section evidence suggests that my estimates are biased down-ward because of technological change, although the size of the bias is unclear.Future research should try to reconcile the cross-sectional results with eachother and with the time-series evidence.9

4. Conclusion

This paper examines postwar money demand using the same methods asprevious papers, but extends the sample through 1996. This extension has majore!ects on the results. Previous researchers express uncertainty about postwarmoney demand, but suggest an income elasticity near 1.0 and an interestsemi-elasticity near !0.1. My estimates of these parameters are about 0.5 and!0.05. These estimates are signi"cantly smaller in absolute value than thecorresponding estimates for the prewar period.

A caveat is that my estimates depend on the questionable assumption that themoney-demand function does not contain a trend. Future work might relax thisassumption by combining cross-sectional and time-series data.

References

Baba, Y., Hendry, D.F., Starr, R.M., 1992. The demand for M1 in the USA: 1960}1988. Review ofEconomic Studies 59, 25}60.


Chari, V.V., Christiano, L.J., Kehoe, P.J., 1996. Optimality of the Friedman rule in economies withdistorting taxes. Journal of Monetary Economics 37, 203}223.

Christ, C.F., 1993. Assessing applied econometric results. Federal Reserve Bank of St. Louis Review75, 71}94.

Feige, E.L., 1964. The Demand for Liquid Assets: A Temporal Cross-Section Analysis. Prentice-Hall, Englewood Cli!s, NJ.

Freidman, M., Schwartz, A.J., 1982. Monetary Trends in the United States and United Kingdom:Their Relation to Income, Prices and Interest Rates, 1867}1975. University of Chicago Press,Chicago, IL.

Hess, G.D., Jones, C.S., Porter, R.D., 1994. The predictive failure of the Baba, Hendry, and Starrmodel of the demand for M1 in the United States. Federal Reserve Board, Washington, DC.

Ho!man, D., Rasche, R.H., 1991. Long-run income and interest elasticities of money demand in theUnited States. Review of Economics and Statistics 73, 665}674.

Ho!man, D.L., Rasche, R.H., Tieslau, M.A., 1995. The stability of long-run money demand in "veindustrial countries. Journal of Monetary Economics 35, 317}339.

Johansen, S., 1988. Statistical analysis of cointegration vectors. Journal of Economic Dynamics andControl 12, 231}255.

Lucas Jr., R.E., 1988. Money demand in the United States: a quantitative review. Car-negie}Rochester Conference Series on Public Policy 29, 137}168.

Mankiw, N.G., 1992. U.S. money demand: surprising cross-sectional estimates: comment. BrookingsPapers on Economic Activity (2), 330}339.

Meltzer, A.H., 1963. The demand for money: a cross-section study of business "rms. QuarterlyJournal of Economics 77, 405}422.

Mulligan, C.B., 1997. Scale economies, the value of time, and the demand for money: longitudinalevidence from "rms. Journal of Political Economy 105, 1061}1079.

Mulligan, C.B., Sala-i-Martin, X., 1992. U.S. money demand: surprising cross-sectional estimates.Brookings Papers on Economic Activity (2), 285}329.

Phillips, P. C. B., 1991. Spectral regression for cointegrated time series. In: Barnett, W. (Ed.),Nonparametric and Semiparametric Methods in Economics and Statistics. University of Cam-bridge Press, Cambridge.

Phillips, P.C.B., Hansen, B.E., 1990. Statistical inference in instrumental variables regression withI (1) processes. Review of Economic Studies 57, 99}125.

Poole, W., 1988. Monetary policy lessons of recent in#ation and disin#ation. Journal of EconomicPerspectives 2, 73}100.

Radecki, L.J., Garver, C.C., 1987. The household demand for money: estimates from cross-sectionaldata. Federal Reserve Bank of New York Quarterly Review 12, 29}34.

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Documents

Another look at long-run money demand