《货币经济学》课程文献阅读：Money Demand as a Buffer Stock（Miller,1990）

STEPHEN M. MILLER Disequilibrium Macroeconomics, Money as a buffer stock and the Estimation of Money demand ard explanations of the seeming instability of the money demand in the post period usually link to stories about financial innovation and deregulation. I se an alternative hypothesis: Much of the seeming instability occurs because of shifts in monetary policy, either explicit or implicit, in an environment where the Federal Reserve controls a ey stock, My econometric analysis modifies existing methods for estimating markets in disequilibrium and in corporates newly developed cointegration and error-correction modeling. My find ings provide support for the buffer-stock interpretation of the money market 1. Introduction Students of macroeconomic theory are familiar with the recent extensive debate concerning macroeconomic modeling. A part of the debate considers disequilibrium or non-markct clearing macroeco- nomic models(Clower 1965; Patinkin 1965; Leijonhufvud 1968; and Barro and Grossman 1971, 1976), which failed to capture a signif- icant following, at least in the United States. This failure to attract much attention probably stems from the absence of convincing ar- guments for price rigidities One aspect of the disequilibrium macroeconomic literature fo- cuses on money as a buffer stock or shock absorber. Laidler(1984) surveys the theoretical bases for, and empirical analyses of, money as a buffer stock and concludes that "the theoretical basis of the The comments of F.w. Asking, D E w. Laidler, and two anonymous referees are gratefully acknowledged. This research was completed while the author was a Principal Analyst(visiting) at the Congressional Budget Office. The views expressed e mine and do not necessarily reflect those of the Congressional Budget Office ecause of their non-theory of (1079) recant thcir initial cnthu eir usefulness. Howitt(1979) Journal of Macroeconomics, Fall 1990, Vol. 12. No, 4, pp. 563-586 Copyright e 1990 by Louisiana State University Press 01640704/90/$1.50

STEPHEN M. MILLER Uniuersity of Connecticut Storrs, Connecticut Disequilibrium Macroeconomics, Money as a Buffer Stock and the Estimation of Money Demand* Standard explanations of the seeming instability of the money demand in the post- 1973 period usually link to stories about financial innovation and deregulation. I propose an alternative hypothesis: Much of the seeming instability occurs because of shifts in monetary policy, either explicit or implicit, in an environment where the Federal Reserve controls a more “exogenous” money stock. My econometric analysis modifies existing methods for estimating markets in disequilibrium and in￾corporates newly developed cointegration and error-correction modeling. My find￾ings provide support for the buffer-stock interpretation of the money market. 1. Introduction Students of macroeconomic theory are familiar with the recent extensive debate concerning macroeconomic modeling. A part of the debate considers disequilibrium or non-market clearing macroeco￾nomic models (Clower 1965; Patinkin 1965; Leijonhufvud 1968; and Barro and Grossman 1971, 1976), which failed to capture a signif￾icant following, at least in the United States. This failure to attract much attention probably stems from the absence of convincing ar￾guments for price rigidities. r One aspect of the disequilibrium macroeconomic literature fo￾cuses on money as a buffer stock or shock absorber. Laidler (1984) surveys the theoretical bases for, and empirical analyses of, money as a buffer stock and concludes that “the theoretical basis of the *The comments of F.W. Ahking, D.E.W. Laidler, and two anonymous referees are gratefully acknowledged. This research was completed while the author was a Principal Analyst (visiting) at the Congressional Budget Office. The views expressed are mine and do not necessarily reflect those of the Congressional Budget Offrce or its statf. ‘Barr0 (1979) criticizes disequilibrium models because of their “non-theory of price rigidities.” And Barro (1979) and Grossman (1979) recant their initial enthu￾siasm for disequilibrium models, questioning their usefulness. Howitt (1979), in contrast, provides a more sympathetic evaluation. Journal of Macroeconomics, Fall 1990, Vol. 12, No. 4, pp. 563586 563 Copyright 0 1996 by Louisiana State University Press 0164-0704/96/$1.56

Stephen M. Miller buffer stock to monetary analysis is well developed and simple, and it has already withstood a good deal of empirical testing"(32).2 Most econt ric analyses of money demand recognize, at least implicitly, the possibility of disequilibrium. The standard stock (supply) -adjustment model (Chow 1966 and Goldfeld 1973)differ ntiates between short- and long- run demands. But this specifica- tion possesses some peculiarities if the money supply is exogenous (Walters 1965; Starleaf 1970; Artis and Lewis 1976; Laidler 1980 Carr and Darby 1981; Coats 1982; and Andersen 1985 For ex- ample, a change in the money supply requires that the interest rate, real income, and the pi level overshoot their long-run val les in the short run (Starleaf 1970 provides extensive discussion ). Judd and Scadding(1982b)compare supply- and demand-adjustin specifications, concluding that the demand-adjusting models out perform the supply-adjusting models, both for within-sample fit(that is, 1959: i to 1974: i)and for out-of-sample forecasting (that is, 1974: ii Judd and Scadding(1982b)note that even for the best-per forming equation(that is, Coats 1982 ), the out-of-sample simulation encounters the well-known shift in the demand for money in (28). Post-1973 econometric analysis of money de mand also suggests implausibly slow speeds of adjustment udd and Scadding 1982a). The emergence of high levels of autocorrelation and seeming parameter instability in the post-1973 period causes some researchers to search for model misspecifications(for example Gordon 1984 and Rose 1985). A popular explanation states that money lemand shifted down between 1974 and 1976 and again between 1979 and 1981 because of financial innovation (udd and Scadding 1982a). More recently, explanations state that money demand shifted up between 1982 and 1983(Gordon 1984; Hetzel 1984; and Miller 1986)and again between 1985 and 1986(Miller 1989)because of financial deregulation I propose a tentative alternative hypothesis to explain po 1973 events: much of the shifting of money demand reflects shifts in money supply (that is, a shift in monetary policy in the sense of Poole 1975)rather than money demand. Significant decelerations aSome authors(White 1981)question the buffer-stock approach to money,ar- guing that since money is, by definition, the most liquid and flexible asset, a dis- ey market is untenable. Such criticism, by a Examining seven industrial countries, OECD(1984)finds that the adoption of money-stock targeting associates with money demand shifts

Stephen M. Miller buffer stock to monetary analysis is well developed and simple, and it has already withstood a good deal of empirical testing” (32).’ Most econometric analyses of money demand recognize, at least implicitly, the possibility of disequilibrium. The standard stock (supply)-adjustment model (Chow 1966 and Goldfeld 1973) differ￾entiates between short- and long-run demands. But this specifica￾tion possesses some peculiarities if the money supply is exogenous (Walters 1965; Starleaf 1970; Artis and Lewis 1976; Laidler 1980; Carr and Darby 1981; Coats 1982; and Andersen 1985). For ex￾ample, a change in the money supply requires that the interest rate, real income, and the price level overshoot their long-run val￾ues in the short run (Starleaf 1970 provides extensive discussion). Judd and Scadding (1982b) compare supply- and demand-adjusting specifications, concluding that the demand-adjusting models out￾perform the supply-adjusting models, both for within-sample fit (that is, I959:i to I974:ii) and for out-of-sample forecasting (that is, 1974:iii to 1980:iu). Judd and Scadding (198213) note that even for the best-per￾forming equation (that is, Coats 1982), the out-of-sample simulation encounters the “. . . well-known shift in the demand for money in 1975-76 . . .” (28). Post-1973 econometric analysis of money de￾mand also suggests implausibly slow speeds of adjustment (Judd and Scadding 1982a). The emergence of high levels of autocorrelation and seeming parameter instability in the post-1973 period causes some researchers to search for model misspecifications (for example, Gordon 1984 and Rose 1985). A popular explanation states that money demand shifted down between I974 and 1976 and again between 1979 and 1981 because of financial innovation (Judd and Scadding 1982a). More recently, explanations state that money demand shifted up between 1982 and 1983 (Gordon 1984; Hetzel 1984; and Miller 1986) and again between 1985 and 1986 (Miller 1989) because of financial deregulation. I propose a tentative alternative hypothesis to explain post- 1973 events: much of the shifting of money demand reflects shifts in money supply (that is, a shift in monetary policy in the sense of Poole 1975) rather than money demand.3 Significant decelerations ‘Some authors (White 1981) question the buffer-stock approach to money, ar￾guing that since money is, by definition, the most liquid and flexible asset, a dis￾equilibrium in the money market is untenable. Such criticism, by its nature, must question the modeling of the short-run money demand as well. 3Examining seven industrial countries, OECD (19&t) finds that the adoption of money-stock targeting associates with money demand shifts. 564

Disequilibrium Macroeconomics (accelerations)in money-stock growth are incorrectly interpreted as downward (upward)shifts in short-run money demand. If the shifts in money demand noted in the previous paragraph were actually shifts in monetary policy, then my hypothesis suggests contraction ary monetary policy during the first two periods and expansionary policy during the latter two. Moreover, these policy shifts need no have been planned. The first two periods correspond roughly to inflation build-ups after oil- price shocks. If oil-price shocks generate xpected inflation, then a given monetary policy becomes more contractionary (less expansionary)ex post. In addition, the latter two periods correspond to a softening of oil prices and of domestic in flation. In sum, sustained deviations of money-stock growth from its trend generate money-market disequilibria; the demand for money dusts to the new policy regime as the interest rate, real income and the price level change In the next section, I describe the econometric procedures developed for handling market disequilibria and show how these procedures can be modified to address buffer stocks in a macro- economic setting. Inferences concerning the nature of the high au- tocorrelation in post-1973 estimates of money demand emerge from this discussion. I then incorporate relatively new econometric pro- cedures, cointegration and error-correction modeling, before mov ing to my empirical analysis. Section 3 discusses the data and eval uates the estimation results. Finally, Section 4 concludes the paper 2. Methodology Estimating Markets in disequilibrium Expanding on the analysis of Fair and Jaffee(1972), a number of authors estimate markets in disequilibrium( for example, Fair and Kelejian 1974; Maddala and Nelson 1974; Laffont and Garcia 1977 and Quandt and Rosen 1978), usually the mortgage market. The key assumption asserts that, when the market is in disequilibrium the observed quantity reflects the minimum of demand and supply quantities at the given price (that is, the short-side rule). Deter ining whether a demand or supply observation occurs depends on the direction of movement in the market price. If the observed price exceeds the market-clearing level, then the price falls and the observed quantity presumably lies on the demand curve and vice ersa. Estimation of the money market in disequilibrium differs in two important respects. First, the short-side rule breaks down; the

Disequilibrium Macroeconomics (accelerations) in money-stock growth are incorrectly interpreted as downward (upward) shifts in short-run money demand. If the shifts in money demand noted in the previous paragraph were actually shifts in monetary policy, then my hypothesis suggests contraction￾ary monetary policy during the first two periods and expansionary policy during the latter two. Moreover, these policy shifts need not have been planned. The first two periods correspond roughly to inflation build-ups after oil-price shocks. If oil-price shocks generate unexpected inflation, then a given monetary policy becomes more contractionary (less expansionary) ex post. In addition, the latter two periods correspond to a softening of oil prices and of domestic in￾flation. In sum, sustained deviations of money-stock growth from its trend generate money-market disequilibria; the demand for money adjusts to the new policy regime as the interest rate, real income, and the price level change. In the next section, I describe the econometric procedures developed for handling market disequilibria and show how these procedures can be modified to address buffer stocks in a macro￾economic setting. Inferences concerning the nature of the high au￾tocorrelation in post-1973 estimates of money demand emerge from this discussion. I then incorporate relatively new econometric pro￾cedures, cointegration and error-correction modeling, before mov￾ing to my empirical analysis. Section 3 discusses the data and eval￾uates the estimation results. Finally, Section 4 concludes the paper. 2. Methodology Estimating Markets in Disequilibrium Expanding on the analysis of Fair and Jaffee (1972), a number of authors estimate markets in disequilibrium (for example, Fair and Kelejian 1974; Maddala and Nelson 1974; Laffont and Garcia 1977; and Quandt and Rosen 1978), usually the mortgage market. The key assumption asserts that, when the market is in disequilibrium, the observed quantity reflects the minimum of demand and supply quantities at the given price (that is, the short-side rule). Deter￾mining whether a demand or supply observation occurs depends on the direction of movement in the market price. If the observed price exceeds the market-clearing level, then the price falls and the observed quantity presumably lies on the demand curve and vice versa. Estimation of the money market in disequilibrium differs in two important respects. First, the short-side rule breaks down; the

Stephen M. Miller quantity of money observed always falls on the money supply.Sec ond, no unique price of money exists from which market-disequi libria signa Rather, money-market disequilibria generate adjustments of varying degrees and with different timing in the in terest rate, real income, and the price level. If the monetary au- thorities increase the moncy supply, then the cconomy holds too much money. Individuals reduce their holding of money by in creased spending on goods, services, and assets. If asset demands se, then interest rates fall. If goux real income and the price level rise. a consensus exists on the tim ing of these effects; the interest rate adjusts first, followed in order by real income and the price level. As the price level finally ad justs, the interest rate and real income movements attenuate; many argue that in the long run, the price level absorbs all of the ad Justment To illustrate, assume that the demand for money takes the following form In M:=o+ a,In r +aln y, agIn Pt+E, where M is the nominal quantity of money demanded, r is the market interest rate, y is real income, P is the price level, In the natural logarithm operator, and E is a random error. The de- mand is specified in nominal terms and can be written in real terms only if a3 =1. The quantity of money demanded becomes observ able only in equilibrium when it equals the money supply(M) In formulating adjustments to disequilibrium, I develop a modification of the Fair-Jaffee(1972)quantitative method. They as- ume that the market price adjusts to the difference between the quantities demanded and supplied. That is =中(Q-Q;) re is the market price of Q, Qp manded and supplied, D is the first-difference operator, and p is the speed of adjustment. Thus, if o is greater (less)than o, then q rises(falls Osagie and Osayimwese(1981)discuss the ideas of disequilibrium in the money market and how the Fair-Jaifee(1972) technique can be used to estimate the money market. They also discuss the issue of what price to use for identifying disequilibria, but assume incorrectly that the short-side rule operates. Finally, they do not pe

Stephen M. Miller quantity of money observed always falls on the money supply. Sec￾ond, no unique price of money exists from which market-disequi￾libria signals emanate. Rather, money-market disequilibria generate adjustments of varying degrees and with different timing in the in￾terest rate, real income, and the price level. If the monetary au￾thorities increase the money supply, then the economy holds too much money. Individuals reduce their holding of money by in￾creased spending on goods, services, and assets. If asset demands rise, then interest rates fall. If goods and service demands rise, then real income and the price level rise. A consensus exists on the tim￾ing of these effects; the interest rate adjusts first, followed in order by real income and the price level. As the price level finally ad￾justs, the interest rate and real income movements attenuate; many argue that in the long run, the price level absorbs all of the ad￾justment.4 To illustrate, assume that the demand for money takes the following form: ln My = u.,, + cwrln r, + cwzln yt + oaln P, + E, , (1) where MD is the nominal quantity of money demanded, r is the market interest rate, y is real income, P is the price level, In is the natural logarithm operator, and E is a random error. The de￾mand is specified in nominal terms and can be written in real terms only if o3 = 1. The quantity of money demanded becomes observ￾able only in equilibrium when it equals the money supply (MS). In formulating adjustments to disequilibrium, I develop a modification of the Fair-Jaffee (1972) quantitative method. They as￾sume that the market price adjusts to the difference between the quantities demanded and supplied. That is, where q is the market price of Q, QD and Q” are quantities de￾manded and supplied, D is the first-difference operator, and @ is the speed of adjustment. Thus, if Q” is greater (less) than QS, then q rises (falls). 40sagie and Osayimwese (1981) discuss the ideas of disequilibrium in the money market and how the Fair-JaEee (1972) technique can be used to estimate the money market. They also discuss the issue of what price to use for identifying disequilibria, but assume incorrectly that the short-side rule operates. Finally, they do not per￾form any econometric tests. 566

Disequilibrium macroeconomics An additional timing issue must be resolved Laffont and Gar cia(1977) suggest two possibilities D (Q-Q;) Dq=q+-q=中Q-Q;) within the period but does not succeed in clearing the marker Equation(3a)assumes that the price-setting mechanism operate Equation(3b)assumes that Q and Q are determined by the price at the beginning of the period(that is, q )and that the price adjusts over the period in response to this period s excess demand resulting in next periods price (that is, qi+1). My analysis adopts equation Money-market disequilibrium spills into financial and goods markets. Let 8, and 82=(1-81)represent the fractions of the excess supply of money(that is, In M-In M")that spill into the financial and goods markets. Spillovers into financial markets cause djustments in the interest rate, while spillovers into the goods markets cause adjustments in nominal income. Let p, and 2 equal the speeds of adjustment of the interest rate and nominal income to the fraction of the excess supply of money spilling into the fi nancial and goods markets. Thus, the following adjustment equa- tions emerge D In r,=-, 8, (In M:-In M) D In(Py)=2((In MS-In M! Dividing Equations(4)and ( 5)by p, and p2, respectively, and then subtracting Equation(4)from Equation(5)yields In M, In M,--(1/p1)DIn rt +(1/p2)D In(Py),. (6) Since the economy always holds the money stock, the money de- mand is never observed, unless the moncy markct clears. Thu substituting for In M, from Equation(1)produces In MS= Co +a In r +aiN y, +aIn Pr (1/p1)D In r, +(1/p2)D In(Py)+E

Disequilibrium Macroeconomics An additional timing issue must be resolved. Latfont and Gar￾cia (1977) suggest two possibilities. Dqt = qt - qt-1 = @(Qf’ - Q;) > (34 or Dqt = qt+l - qt = WQi’ - Qt”) . W) Equation (3a) assumes that the price-setting mechanism operates within the period but does not succeed in clearing the market. Equation (3b) assumes that Q” and Q” are determined by the price at the beginning of the period (that is, qt) and that the price adjusts over the period in response to this period’s excess demand resulting in next periods price (that is, qt+J. My analysis adopts Equation (W. Money-market disequilibrium spills into financial and goods markets. Let & and a2 = (1 - 6,) represent the fractions of the excess supply of money (that is, In MS - In MD) that spill into the financial and goods markets. Spillovers into financial markets cause adjustments in the interest rate, while spillovers into the goods markets cause adjustments in nominal income. Let aI and a2 equal the speeds of adjustment of the interest rate and nominal income to the fraction of the excess supply of money spilling into the fi￾nancial and goods markets. Thus, the following adjustment equa￾tions emerge. and D ln r, = -@$,(ln Mf - ln My) , (4) D ln(Py), = $(l - S,)(ln Mf - ln MF) . (5) Dividing Equations (4) and (5) by @r and a2, respectively, and then subtracting Equation (4) from Equation (5) yields In Mf - ln Mf = -(l/@JD ln r, + (l/a2)D ln(Py), . (6) Since the economy always holds the money stock, the money de￾mand is never observed, unless the money market clears. Thus, substituting for In MF from Equation (1) produces ln Mf = a0 + alln r, + a&r yt + a,ln P, - (l/al)0 ln r, + (l/@JD ln(Py), + l t . (7) 567

Stephen M. Miller Equation(7)does not separate the effect of the excess supply f money into movements in real income and the price level. Al lowing for these differential effects, Equation(5)becomes Dlny=φ2(1-81nM-hnM) D In P 22(1-8)n MS-In Mp) whereΦ2=Φa1+Φ2,Now, dividing Equations(4,(5a),and⑤5b) byΦ1,Φal,andΦ2;, respectively, and then subtracting twice Equa- tion (4)from the sum of Equations (5a)and (5b) gives In M-In Mt=-(1/1D In T,+(1/2p2 D In y, +(1/2p22)D In P, And finally, substituting from Equation(1)results in In M=ao+aInr,+aIn y, +aaIn P, -(1/p,)D In re +(1/22)Dhy+(1/2a)DhP+∈ Now, first-differencing Equation (1)yields In M,-In Mi-1=a, D In rt-1+ a2D In y,-1 3D In Pt-1+ Et where Equation (3b)defines the adjustments in the interest rate real income, and the price level. Substituting into Equation( 8)from quations(4),(5a), and(5b)generates InMp-In Mp-1=Q(n M,-1-In Mp-1)+eE-1,(9) where =-∝1中181+(221+a32)(1-81) (10) Equation(9)represents, not surprisingly, a demand-adjusting for

Stephen M. Miller Equation (7) does not separate the effect of the excess supply of money into movements in real income and the price level. Al￾lowing for these differential effects, Equation (5) becomes D In qt = cP,,(l - &)(ln Mf - ln Mf) , (54 and D In P, = cP,,(l - S,)(ln Mf - In Mf) , W where apz = a21 + az2. Now, dividing Equations (4), (5a), and (5b) by aI, QS1, and $a, respectively, and then subtracting twice Equa￾tion (4) from the sum of Equations (5a) and (5b) gives In Mf - In MF = -(l/al)0 In r, + (l/2@& In yi + (l/2@.& In P, . And finally, substituting from Equation (1) results in In Mf = a0 + a,ln r, + olJn qt + ol,ln P, - (l/@&I In r, + (1/2@&I In qt + (1/2@.&0 In P, + l , . Now, first-differencing Equation (1) yields lnM:- In ME, = alD In t-,-r + ozD In gt-l + c@ In P,-I + E, - l tel , (64 (74 (8) where Equation (3b) defines the adjustments in the interest rate, real income, and the price level. Substituting into Equation (8) horn Equations (4), (Sa), and (5b) generates In Mf' - ln ME, = LR(ln Mf-, - ln ML,) + E, - Q-~, (9) where n = -a,@16, + (a&!1 + c&&)(1 - 6,) . (10) Equation (9) represents, not surprisingly, a demand-adjusting for- 568

Disequilibrium Macroeconomic he tradition of Starleaf (1970), Artis and Lewis(1976), and Coats(1982). Cordon(1984)states that two major problems face monetary economists-the large coefficients of lagged money and the high autocorrelations in post-1973 samples. Lagged money was originally introduced to account for sluggish portfolio adjustment(Chow 1966) but the post- 1973 coefficients of lagged money suggest implausibly slow speeds of portfolio adjustment. Further, high autocorrelation may indicate model misspecification The existing literature has several things to say about these two issues. Goodfriend(1985)argues that the money market can lear each period and that lagged money does not belong theoret ically in money demand. Measurement errors in the exogenous variables can explain the significance of the coefficient of lagged money and the high autocorrelation. Laidler(1985)and Gordon(1984) argue that money demand regression equations represent semi-re duced-form equations. That is, the parameters of the money de- mand regressions combine the parameters from the money demand and other equations of the macroeconomy offer a competing explanation for these problems hased on Equations(1),(7),(7a), and (9 ). The post-1973 money market ex perienced significant disequilibrium. But the dynamic adjustment is of the demand-, rather than the supply-, adjusting type. Equation (9)shows how my formulation of money-market adjustment con- forms with the demand-adjusting view. Now, a well-behaved (that is, white-noise)error structure in Equation(1) implies a well-be- haved error structure in Equations (7)and(7a)but a moving-at erage error structure with a unit root in Equation(9). If, alterna tively, the partial-adjustment equation possesses a well-behaved error structure,then Equations (1),(7), and(7a) exhibit autocorrelated Equations(7a)and(9) are comparable to Starleaf's (1970, 751-52) Equations (3.4)and (3.5)after several adjustments. First, Starleaf assumes that the adjustment quation(that is, [3. 4]does not involve a random error. Equation( 9)includes a gn. seco mand for money and the demand-adjustment equation are in real terms. Thus, the price terms appearing in Equation(7a)disappear in Starleaf's specification. Thir Starleaf assumes that this periods demand for money adjusts to the differe tween this period's money supply and last period's money demand. Equation (9) has last periods money supply instead of this period s. Starleaf's adjustment eq tion results when Equation (3a) is adopted rather than Equation(3b)as the dis equilihrium adjustment specification. Finally, to derive Starleaf s quation(3.5)from Equation (7a), assume that n2=a 1=a2p2i

Disequilibrium Macroeconomics mulation in the tradition of Starleaf (1970), Artis and Lewis (1976), and Coats (1982).’ Gordon (1984) states that two major problems face monetary economists-the large coefficients of lagged money and the high autocorrelations in post-1978 samples. Lagged money was originally introduced to account for sluggish portfolio adjustment (Chow 1966); but the post-1973 coefficients of lagged money suggest implausibly slow speeds of portfolio adjustment. Further, high autocorrelation may indicate model misspecification. The existing literature has several things to say about these two issues. Goodfriend (1985) argues that the money market can clear each period and that lagged money does not belong theoret￾ically in money demand. Measurement errors in the exogenous variables can explain the significance of the coefficient of lagged money and the high autocorrelation. Laidler (1985) and Gordon (1984) argue that money demand regression equations represent semi-re￾duced-form equations. That is, the parameters of the money de￾mand regressions combine the parameters from the money demand and other equations of the macroeconomy. I offer a competing explanation for these problems based on Equations (l), (7), (7a), and (9). The post-1973 money market ex￾perienced significant disequilibrium. But the dynamic adjustment is of the demand-, rather than the supply-, adjusting type. Equation (9) shows how my formulation of money-market adjustment con￾forms with the demand-adjusting view. Now, a well-behaved (that is, white-noise) error structure in Equation (1) implies a well-be￾haved error structure in Equations (7) and (7a) but a moving-av￾erage error structure with a unit root in Equation (9). If, alterna￾tively, the partial-adjustment equation possesses a well-behaved error structure, then Equations (l), (7), and (7a) exhibit autocorrelated ‘Equations (7a) and (9) are comparable to Starleaf’s (1970, 751-52) Equations (3.4) and (3.5) after several adjustments. First, Starleaf assumes that the adjustment equation (that is, [3.4]) does not involve a random error. Equation (9) includes a random error due to different model design. Second, Starleaf assumes that the de￾mand for money and the demand-adjustment equation are in real terms. Thus, the price terms appearing in Equation (7a) disappear in Starleaf’s specification. Third, Starleaf assumes that this periods demand for money adjusts to the difference be￾tween this periods money supply and last period’s money demand. Equation (9) has last periods money supply instead of this periods. Starleaf’s adjustment equa￾tion results when Equation (3a) is adopted rather than Equation (3b) as the dis￾equilibrium adjustment specifkation. Finally, to derive Starleaf’s Equation (3.5) from Equation (7a), assume that n = a,@, = up&I. 569

Stephen M. Miller error structures with unit roots. In sum. a well-behaved demand- djusting partial-adjustment model of the money market implies an autoregressive crror structure with a unit root for estimated moncy demand equations, potentially explaining the high autocorrelation in the post-1973 money demand regressions Estimation of Equations (7)and (7a)present several econo- metric problems. First, the equations contain right-side endogenous variables. The rates of change in the interest rate nominal and real income, and the price level, since they are based on Equation(3b), follow, in a timing sense, the other variables in the equations, it cluding the left-hand-side money stock. Thus, two-stage estimation appears appropriate, assuming that the rate of change variables are endogenous. But, such an approach implies an exogenous left-hand side variable. Cointegration and error-correction modeling, consid ered in the next section, provide a possible solution to these prob. ems Cointegration and Error-Correction Econometric method precedes econometric practice, some- times with a substantial lead. Fo or exam ple, the possibility of spu us co-movement between variables has been acknowledged for a long time(for example, Jevons 1884, 3), with Yule(1926)conduct ing the first formal analysis(Hendry 1986 provides more details) Nonetheless. econometricians continued to use standard time-series regressions with little concern for whether the relationships were sUch a dichotomy does not occur with the supply-adjusting model, where the error structures of the partial-adjustment and estimating equations are identical Gordon(1984, 414)introduces the error term into the partial-adjustment, rather han the demand, equation with little effect, since the final error structure of the stimating equation is unaffected. Such is not the case for the demand-adjusting EStimation also assumes constant parameters, inviting the Lucas(1976)criti- cism. The speeds of adjustment( that is,中,中;,φa,andφ2y) are especially open to this criticism, since they measure how the interest rate, nominal and real in (1985)makes this point as it applies to the estimation of standard post-1973 money demand functions. In addition, exogenous oil-price shocks cause temporary pertur- bations in the price- level adjustment process. For example, as the price level larger(smaller)changes in D In P than are indicated by previ equilibria. As a consequence, the estimates of and aa are biased (downward) during the time when the oil-price shock is being transmitted to the domestic price level

Stephen M. Miller error structures with unit roots. In sum, a well-behaved demand￾adjusting partial-adjustment model of the money market implies an autoregressive error structure with a unit root for estimated money demand equations, potentially explaining the high autocorrelation in the post-1973 money demand regressions.‘j Estimation of Equations (7) and (7a) present several econo￾metric problems. First, the equations contain right-side endogenous variables. The rates of change in the interest rate, nominal and real income, and the price level, since they are based on Equation (3b), follow, in a timing sense, the other variables in the equations, in￾cluding the left-hand-side money stock. Thus, two-stage estimation appears appropriate, assuming that the rate of change variables are endogenous. But, such an approach implies an exogenous left-hand￾side variable. Cointegration and error-correction modeling, consid￾ered in the next section, provide a possible solution to these prob￾lems.7 Cointegration and Error-Correction Econometric method precedes econometric practice, some￾times with a substantial lead. For example, the possibility of spu￾rious co-movement between variables has been acknowledged for a long time (for example, Jevons 1884, 3), with Yule (1926) conduct￾ing the first formal analysis (Hendry 1986 provides more details). Nonetheless, econometricians continued to use standard time-series regressions with little concern for whether the relationships were real or spurious. Spurious regression can occur when the regression ‘Such a dichotomy does not occur with the supply-adjusting model, where the error structures of the partial-adjustment and estimating equations are identical. Gordon (1984, 414) introduces the error term into the partial-adjustment, rather than the demand, equation with little effect, since the final error structure of the estimating equation is unatfected. Such is not the case for the demand-adjusting framework. ‘Estimation also assumes constant parameters, inviting the Lucas (1976) criti￾cism. The speeds of adjustment (that is, a,, $, Q2,, and a,,) are especially open to this criticism, since they measure how the interest rate, nominal and real in￾come, and the price level respond to disequilibria in the money market. Laidler (1985) makes this point as it applies to the estimation of standard post-1973 money demand functions. In addition, exogenous oil-price shocks cause temporary pertur￾bations in the price-level adjustment process. For example, as the price level rises in response to previous excess supplies of money, oil-price increases (decreases) cause larger (smaller) changes in D In P than are indicated by previous money￾market disequilibria. As a consequence, the estimates of Qz and @a are biased upward (downward) during the time when the oil-price shock is being transmitted to the domestic price level. 570

Disequilibrium Macroeconomics adjusted coefficient of determination(R)exceeds the Durbin-Wat son statistic(Granger and Newbold 1974 and Plosser and Schwert Cointegration analysis addresses the spurious regression prob lem, attempting to identify conditions for which regression rela ionships are not spurious(Eugle and Granger 1987; Granger 1986; and Hendry 1986). When two time-series variables are cointegrated, their secular trends move subject to an equilibrium constraint, and the cyclical components of the series conform to a dynamic speci- fication in the class of error-correction models The problem of spurious regression emerges because most economic time series exhibit non-stationary tendencies. Thus, the high R may reflect correlated trends rather than underlying eco- mic relationships; the low Durbin-Watson statistic may indicate non-stationary residuals. One specification check for spurious regression involves first-differenced regressions. That specification check probably produces stationary residuals. The question emerges as to whether relationships found in regressions on levels remain under the first-differenced specification. But, first-differencing re- moves the low-frequency (long-run)information. Cointegration and error-correction modeling reintroduces the low-frequency informa tion into first-differenced regressions in a statistically acceptable way Consider two time-series x, and y, that are non-stationary in their levels but stationary in their first differences. The series are cointegrated when a factor B exists, such that z, y, -Bx, is sta tionary. If it does exist, then the cointegration factor must be unique in the two-variable case, since altering it to(B+ 8) introduces an additional term(-Sxt), which is non-stationary by definition. Since the temporal characteristics of zt and its components are so differ- ent, a special relationship exists between cointegrated variables. To it,y, and Bx, must exhibit low-frequency(long-run)components that cancel, producing a stationary series zr. The long- run(equilib- rium)relationship may emerge from economic theory, where z measures short-term deviations from the trend (equilibrium) rela In sum, cointegration and error-correction modeling is a two- step procedure. The first step estimates the cointegration equation which captures the long- run(trend)relationships, if any, between the variables of interest. The errors from the cointegration regres sion are then used in the second step to estimate the error-correc- tion model, which captures the short-run (cyclical)relationships among the variable

Disequilibrium Macroeconomics adjusted coefficient of determination (R’) exceeds the Durbin-Wat￾son statistic (Granger and Newbold 1974 and Plosser and Schwert 1978). Cointegration analysis addresses the spurious regression prob￾lem, attempting to identify conditions for which regression rela￾tionships are not spurious (Engle and Granger 1987; Granger 1986; and Hendry 1986). When two time-series variables are cointegrated, their secular trends move subject to an equilibrium constraint, and the cyclical components of the series conform to a dynamic speci￾fication in the class of error-correction models. The problem of spurious regression emerges because most economic time series exhibit non-stationary tendencies. Thus, the high R2 may reflect correlated trends rather than underlying eco￾nomic relationships; the low Durbin-Watson statistic may indicate non-stationary residuals. One specification check for spurious regression involves first-differenced regressions. That specification check probably produces stationary residuals. The question emerges as to whether relationships found in regressions on levels remain under the first-differenced specification. But, first-differencing re￾moves the low-frequency (long-run) information. Cointegration and error-correction modeling reintroduces the low-frequency informa￾tion into first-ditlerenced regressions in a statistically acceptable way. Consider two time-series xt and yt that are non-stationary in their levels but stationary in their first differences. The series are cointegrated when a factor B exists, such that z, = yt - Bx, is sta￾tionary. If it does exist, then the cointegration factor must be unique in the two-variable case, since altering it to (B + 6) introduces an additional term (-6x,), which is non-stationary by definition. Since the temporal characteristics of z, and its components are so differ￾ent, a special relationship exists between cointegrated variables. To wit, yt and Bx, must exhibit low-frequency (long-run) components that cancel, producing a stationary series zt. The long-run (equilib￾rium) relationship may emerge from economic theory, where zt measures short-term deviations from the trend (equilibrium) rela￾tionship. In sum, cointegration and error-correction modeling is a two￾step procedure. The first step estimates the cointegration equation, which captures the long-run (trend) relationships, if any, between the variables of interest. The errors from the cointegration regres￾sion are then used in the second step to estimate the error-correc￾tion model, which captures the short-run (cyclical) relationships among the variables. 571

Stephen M. Miller This discussion applies directly to the present problem timating money demand, since the buffer-stock view implie the money market exhibits short -run departures from long-run equilibrium. Equation(1), therefore, represents the long-run(equi librium)money demand, where each variable refers to the trend of the long-run relationship with observed time-series, where the re- siduals measure the short-run deviations from long-run equilibrium Second, modification of the Fair- Jaffee quantitative procedure for estimating markets in disequilibrium suggests that the rates of hange in the interest rate, nominal and real Income. a nd the price level depend on short-run deviations from long-run equilibrium. That is, the residuals from the cointegration regression can be used to estimate directly Equations (4),(5),(5a), and (5b), solving one of the previously mentioned econometric problems Third, the cointegration regression uses simple ordinary least squares, where all variables are potentially endogenous. The error correction model emerges as a restricted vector autoregression. As seen below the estimation of Equations(4),(5),(5a), and (5b )are contained within the class of error-correction models, although with further restrictions 3. Empirical Analysis Considerable debate surrounds the choice of variables to use in the money demand function. Questions arise about the mone- tary aggregate, the interest rate, and the scale variable. I examine three alternatives for the monetary aggregate Ml, MIA, and M2 wo alternatives for the interest rate, the four-to-six-month com- mercial-paper rate (re) and the dividend-to-price ratio (ra); and one alternative for the scale variable, nominal gross national product Y Hendry (1980) and Motley(1988)employ error-correction models, uncon- strained by cointegration equations, to study money demand. Trehan(198 bines cointegration equations with error-correction models to examine Wes oney demand, but does not link the analysis to the estimation of emarket The data are from the Federal Reserve Board Qr data base. Precise definitions of variables are in the 1959 i to 1987: iD. All statistical analysis is performed with the aid of RATS, version 2.03, October9,1956

Stephen M. Miller This discussion applies directly to the present problem of es￾timating money demand, since the buffer-stock view implies that the money market exhibits short-run departures from long-run equilibrium.’ Equation (l), therefore, represents the long-run (equi￾librium) money demand, where each variable refers to the trend of the observed series. Cointegration analysis allows the estimation of the long-run relationship with observed time-series, where the re￾siduals measure the short-run deviations from long-run equilibrium. Second, modification of the Fair-Jalfee quantitative procedure for estimating markets in disequilibrium suggests that the rates of change in the interest rate, nominal and real income, and the price level depend on short-run deviations li-om long-run equilibrium. That is, the residuals from the cointegration regression can be used to estimate directly Equations (4), (5), (5a), and (5b), solving one of the previously mentioned econometric problems. Third, the cointegration regression uses simple ordinary least squares, where all variables are potentially endogenous. The error￾correction model emerges as a restricted vector autoregression. As seen below, the estimation of Equations (4), (5), (5a), and (5b) are contained within the class of error-correction models, although with further restrictions. 3. Empirical Analysis Considerable debate surrounds the choice of variables to use in the money demand function.’ Questions arise about the mone￾tary aggregate, the interest rate, and the scale variable. I examine three alternatives for the monetary aggregate, Ml, MIA, and M2; two alternatives for the interest rate, the four-to-six-month com￾mercial-paper rate (rc) and the dividend-to-price ratio (l;i); and one alternative for the scale variable, nominal gross national product (Y), ‘Hendry (1980) and Motley (1988) employ error-correction models, uncon￾strained by cointegration equations, to study money demand. Trehan (1988) com￾bines cointegration equations with error-correction models to examine West Ger￾man money demand, but does not link the analysis to the estimation of markets in disequilibrium. ‘The data are from the Federal Reserve Board Quarterly Econometric Model data base. Precise definitions of variables are in the Appendix. The sample covers 1959:i to 1987:iu. All statistical analysis is performed with the aid of BATS, version 2.03, October 9, 1986. 572