Anticipated monetary and fiscal policy effects on output

CHIEN-HSUN CHEN Chung-Hua Znstitution for Economic Research

FRANK G. STEINDL Oklahoma State Uniuersity

Anticipated Monetary and Fiscal Policy Effects on Output*

This paper is a test of the LSW proposition. In a Sargent and Wallace model, two different formal money supply mechanisms are incorporated. One is based on the government budget restraint and the other on the Fed’s reaction function. Neither is a pure feedback mechanism. The stochastic process of output is a function of the interaction of the monetary and fiscal policy parameters with the models’ disturbances. Thus, the question of the LSW proposition comes down to an empirical issue. The models are then estimated by 3SLS. The results are not incompatible with the policy ineffectiveness proposition.

1. Introduction In the last decade, an interesting mutation has occurred.

Keynesians and monetarists, adversaries in a decades-long policy debate, now find themselves allied against the New Classicists. Ev- idently, it is not only politics that makes strange bedfellows.

One of the principal results associated with the New Classi- cists is the policy ineffectiveness proposition. Though first estab- lished in Lucas’s formidable, demanding, uncompromising “Expec- tations and the Neutrality of Money” (1972), its importance was enhanced in the Sargent and Wallace paper (1975); hence, the ac- ronym LSW as a synonym for policy ineffectiveness.

A number of theoretical models followed, some having the LSW proposition [McCallum and Whitaker (1979); McCallum (1980)], others not [Fischer (1979)]. Empirical support for the LSW proposition was first offered by Barro in his influential work (1977, 1978). His strat- egy was to decompose the observed money supply into anticipated and unanticipated components. The anticipated component was estimated by imputing to the Fed various money supply “motives”- reaction function responses. No formal money supply mechanism

*An earlier version was read and useful comments received at our departmental Macroeconomics Workshop and the 1986 Midwest Economics Association meeting in Chicago. The final version was written while the second author was visiting at the Volkswirtschaftliches Institut, the University of Munich. We are especially gratefU1 to the referee for providing most useful, penetrating comments.

Journal of Macroeconomics, Spring 1987, Vol. 9, No. 2, pp. 255-274 255 Copyright 0 1987 by Louisiana State University Press 0x4-0704/87/$1.50

Chien-Hsun Chen and Frank G. Steindl

was used. Barro’s empirical procedure was adopted by a large number of subsequent investigators [such as Attfield and Duck (1983) and Canarella and Garston (1983)], who found support for the LSW proposition. Among those who rejected it on empirical grounds were Mishkin (1982), Driscoll et al. (1983), and Demery (1984).

In this paper, the Sargent-Wallace model due to McCallum (1980) and McCallum and Whitaker (1979) is the basis for 3SLS estimates addressing the LSW proposition. The distinguishing char- acteristic of this paper is that a formal money supply mechanism is incorporated in the model. In models concerned with the LSW proposition, the typical monetary mechanism consists simply of a function that underscores that monetary policy has a systematic component. The determinants of the systematic component are generally left unspecified, other than their composing a feedback mechanism that incorporates previous money and income.

In the present paper, two different formal money mechanisms are used. One money supply mechanism is based on the government budget restraint. The other derives from the Feds reaction function. In each of these money mechanisms, the behavior of the money stock depends in part on the behavior of several endogenous variables. For each of the two, the model is solved analytically. The LSW proposition may or may not hold, depending on the stochastic process of output behavior. The fact that the money supply function is not simply a feedback mechanism but, rather, a function of several endogenous variables is the reason why the policy ineffectiveness proposition may not hold. The reduced form solution for output is a complex function of the interaction of the monetary and fiscal policy parameters with the model’s disturbances. Thus, the question of the LSW proposition comes down to an empirical issue. The models are then estimated by 3SLS, quarterly and annually, for 1954i-831iu.

2. The Model The basic model follows McCailum and Whitaker’s (1979) ex-

position of the Sargent and Wallace (1975) framework. It consists of IS and LM relationships and a Lucas Supply function. The IS relation is augmented to take account of the fiscal policy variables.

IS: In Yt = b, + bi[ln i, - Et-l (In P,+l - In P,)]

+ b, In G, - b, In T, - (b, - b3) In P, + i.~r~ ;

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Monetary and Fiscal Policy Effects

b, < 0 ; b2, b, > 0 ; 0)

LM: lnM,=cO+cllny,+czlni,+lnP,+~,,,;

c2 < 0 < Cl ; (2)

AS: ln y, = Q, + q(ln P, - E,-, In P,) + a2 In yt-r + ~~~ ;

al>O; O<a,<l; (3)

where:

yt = real current output; P, = current price level; i, = nominal interest rate;

G, = nominal government expenditure; Tt = nominal taxes; and

M, = nominal money stock;

and E,-lX,+j is the mathematical expectation of X,, (j = 0, 1, . . .) given the equations and information as of t - 1. The pit (i = 1, 2, 3) are random disturbance terms with zero means and constant vari- antes .

In order to complete the model, it is necessary to specify the government policy action equations. Assume that real government expenditure is a function of the lagged value of real output and its own lagged value; the former represents the historical upward trend of expenditure and the latter is autogressive [McCallum and Whitaker (1979), p. 1741. This can be expressed as

In G, = go + g,(ln G,-, - ln P,-I)

+ g, In yt-l + In P, + Elt ;

g1, is2 ’ 0 . (4)

The eit(i = 1, . . . , 4) have zero means and constant variances. Personal and corporate income taxes are the two major revenue sources for the federal government. The tax law permits carry- back to adjust losses in previous years. Real tax revenue can, therefore, be taken as a function of current and lagged real income; the

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logarithmic version of the tax equation is, therefore,

In T, = to + tl In gt + t2 In Ytml + In P, + Ezt ;

0 < t1, t2 < 1 . (5)

To the basic model, (l)-(5), a money supply rule is added. Two different rules are employed. The first derives from the government budget restraint. The other is based on the Feds reaction function. These are Equations (6) and (7), respectively. The model with (6) is called model A and the one with (7) is model B.

The Money Supply Mechanism As indicated earlier, the monetary mechanism is usually writ-

ten in terms of the intuitively appealing but ad hoc feedback form in which there is a systematic component-generally the previous period’s income and money stock-and possibly a random (that is, nonsystematic) component.

mt = ~0 + wkl + p2Yt-1 + Et. (6’)

This, for example, is the mechanism in Sargent and Wallace (1975), McCallum and Whitaker (1979), and McCallum (1980). Neither of the money mechanisms in this paper takes the above form; each is more complex.

One way to formulate the behavior of the monetary authorities is to derive it from the government budget restraint. The restraint underscores the interdependence of monetary and fiscal policy [Christ (1968)]. The restraint is:

G, = T, + AB, + AH,, (6”)

where AB is the change in the net government debt and AH is the change in the monetary base. Equation (6”) can be written in terms of H, which can then be substituted into the M = mH money supply framework. The logarithmic version of the money mechanism is:

In M, = ho + h, In G, + h2 In T, + h3 In B,

+ h, In B,-l + h5 In Hfwl + •3~ ;

hl, h3, h4, h5 > 0 ; h, < 0 . (6)

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Equation (6) together with (l)-(5) constitute model A, the budget restraint money mechanism model.

The model with the reaction function monetary rule (model B) also has (l)-(5). Th e money supply mechanism (7) derives from a Barro-type (1977) reaction function. The price and unemployment U, variables reflect the policy goals of price level stability and high employment. For fiscal policy purposes, the unemployment rate is positively related to current T/P and negatively to current G/P. Substituting this policy function relation into the reaction function gives the following money supply mechanism.’

In M, = fo + fi In M,-, + fi In M,-, + f3 In P, + f4 In Ptel

+ f5 In G, + f6 In Tt + f, In U,-i + eqt ;

(7)

The model with the money supply reaction mechanism thus consists of equations (I)-(5) and (7).

3. Theoretical Implications and Econometric Issues Model with Government Budget Restraint Monetary Mechanism

In this section, each of the two models is solved for the equilibrium yt. In each case, both the monetary and fiscal policy parameters affect the equilibrium.

In Equation (2), write In i, in terms of the other variables. Substitute into (l), thereby eliminating i,. This gives:

- [h + c&h - @I In P,

- blc2E,-1 (In P,,, - In P,) + b,c, In G,

- Jw2 ln Tt + ~2~1~ - bZtl . 03)

Each of the two models can now be solved. For model A-the

‘The setup of the mechanism is an elaboration of Barre (1977) and his Fed reaction function approach. Details of this derivation are available from the authors.

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Chien-Hwn Chen and Frank G. Steindl

budget restraint money supply mechanism-substitute (4), (S), and (6) into (8). This gives:

In it = PO + Pdn G,-, - In Pt.-J + p2 In ytel

+ P3 In Pt + P&-din Pt+l - In PJ

-I- p5 In B, + p6 In B,-, + p7 In H,-, + egt ; (9)

where:

PO = O/A)[c&o - b lco + 0, + go@+, + bzcz) + tohhz- b,s)l; A = blcl + c2 - tl(blh2 - b,c2);

PI = UlANgdhh + h41; P2 = WAkdWl + bzcz) + tdbhz - bdl; Ps = WWdh, + h, - 1); P4 = (l/N--W; P5 = W~~@dd Pe = WWJd; I% = WAh)(hM; and l 5t = WANC~CLU - h/+zt + bleat + W, + b2c&lt + (b,h, -

b&2tl.

Of particular interest are p3 and et5 because they also appear in the basic result of the analysis-the reduced form solution for output, Equation (12), below. Each has as one of its components the systematic monetary policy parameters h, and h2, and the fiscal parameter tl. Notice also that E(cst) = 0, since the expected values of the p.s and ES comprising it are zero. Substituting (9) into (3) gives the equation for the price level.

ln Pt = Ma1 - P31 [PO - a0 + Pdln G-I - In Pt-J

+ 032 - ad ln ~~-1 + P&l b Pt+l - ln PJ

+ p5 In B, + p6 In II-I + p7 In H,-,

+ aJLl ln P, + •5~ - PA. (10)

Take the expectation E,-, of (10) and subtract from (10); this gives

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ln Pt - Et-l ln Pt = [l/h - PJI(G - PA . (11)

As can be readily verified, the partial derivatives of (11) with respect to the monetary policy parameters hl and h, in (6) and the tax parameter tl in (5), which are encapsulated in R3 and l gt, are not in general equal to zero.

The behavior of output can be obtained by substituting the price-level forecast error (11) into (3). The stochastic process of output is governed by

ln Yt = a, + a2 ln Y~-~ + Ma1 - PJI (ah - P3t.d . (12)

Recall from (9) that pa and l gt are functions of the monetary and fiscal policy parameters. Specifically, each encapsulates the hl, h, systematic monetary policy parameters and the tl marginal tax rate. McCallum and Whitaker (1979, p. 177) have the latter in their equivalent of our Equation (12); they do not have any monetary policy parameter from their monetary (feedback) mechanism of type (6’). Their argument as to why the tax parameter appears in the reduced form output equation and the monetary policy parameters do not is that

the efficacy of built-in stabilization [that is, the marginal tax rate tl], as contrasted with the impotence of activist counter- cyclical efforts, results essentially from the fact that tax liabil- ities are automatically generated in the tatonnement at [time] t, even though no one yet knows the aggregative magnitudes [of yt, P,, and iJ. . . . [Clentralized control policies must nec- essarily be of the feedback type that relates current actions to past values of aggregative endogenous variables. (1979, p. 179)

In the present model, the government budget restraint monetary mechanism has both current expenditures and taxes affecting the money stock; that is, the money supply is a function in part of several (current) endogenous variables. Reference to Equation (6) shows that h, is the (positive) effect of an increase in current expenditures on the money stock and h2 is the (negative) effect of current taxes on it. That is, the policy ineffectiveness proposition is dependent upon the monetary mechanism being of the feedback type.2

‘Notice that the government expenditures function (4) is a feedback mechanism, whereas the tax function (5) depends on current income. Hence, “activist counter- cyclical” expenditure policy has no effect.

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The behavior of real output is thus influenced not only by a,,, al, a, and p3t, but also by R3 and l gt. In (12), E(ln yt) = a0 + al In ytml. Hence R3 and l st do not affect the “average” behavior of real output. Rather, they affect the variance of output.3 That is, the distribution of yt is not independent of the monetary policy parameters hl, h, and the marginal tax rate tl. Economic policy therefore has a systematic effect on real output. The empirical issue, then, is to determine the quantitative significance of the policy variables. This issue is addressed in Section 4.

Model with Reaction Function Monetary Mechanism When the money supply mechanism is as given for the re-

action function approach (7), the analysis proceeds in the same manner that gave (11) and (12), except that (7) is now substituted for (6). The solution procedure is identical to that used to obtain equations (11) and (12). Substitute (4), (5) and (7) into (8). This gives an expression for In yt analogous to (9). When this latter equation is substituted into (3), an expression for in P, analogous to (10) is obtained. Taking the expectation E,-, of this and then subtracting it from the In P, equation gives

ln P, - C-1 ln Pt = [l/b1 - PS)l kk - 1.4 (13)

where

+ blf5 + bzcz + b& - hczl ;

A’ = [blcl + cr. - tl(blf6 - b3cZ)] ; and

/3; and ES, are analogous to R3 and E 5t in that they are functions of

3The effects and interpretation of policy appearing in the disturbance term for the output equation were first noted by McCallum and Whitaker. Equation (12) may be considered a straightforward extension of their basic result (1979, p. 177). The fact that the (unconditional) variance of qt is affected by the marginal tax rate is stressed.


the monetary and fiscal policy parameters. B; is written in terms of the f3, f5 and fs money supply parameters and E& in terms of f5 and fG. Both B; and E;, are also functions of the tl tax parameter. Sim- ilarly, real current output yt is obtained by substituting (13) into (3), thereby giving an expression identical to (I2), except that B; is substituted for B3 and E;, for egt. The stochastic process for output is

ln Yt = a0 + a2 ln ~~-1 + W(al - P~)l(wL - P&J . (14)

Both the expectation error (13) and output (14) depend on the parameters B; and & and these are functions of the monetary and fiscal policy parameters.

In a manner analogous to the discussion of Equation (12), the monetary policy parameters f3, f5 and f6, representing the endogenous variables in the money mechanism (7), are present in (14) and for the same reason: they represent automatically generated effects of several endogenous variables on the current periods stock of money, though no one currently knows their (approximate current periods) quantitative values. Thus, the distribution of yt is influenced by the f3, f5 and f6 monetary policy parameters, and the marginal tax rate tl fiscal parameter.

In (14) as in (12), E(ln yJ = a, + aI In ytel. Thus, here again economic policy does not affect the “average” level of real output. Rather, it affects its variance. Consequently, macroeconomic policy can affect the price expectation error and thereby aflect real output.

The output Equation, (14)-as in the case of the output expression for the budget restraint money mechanism model (12)- is influenced not only by the variances of the model’s disturbances but also by the policy parameters. As in the discussion of (12), since the expected value of (14) is equal to the first two terms on the right-hand side, economic policy affects the variability of output and not its “average” level.

Thus, the LSW proposition does not hold as a theoretical matter in either the reaction function money mechanism, model B, or the previous government budget restraint money mechanism, model A. Whether the parameters encapsulating the policy parameters are empirically significant is the question to which we now turn.

Anticipated and Unanticipated Effects In what has gone previously, it has not been necessary to dis-

tinguish carefully between what is “anticipated” and what is “un-

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anticipated’ policy. The problem now is to implement empirically that distinction. Following Barro (1977, 1978), a model is estimated in which monetary and fiscal policy is included. The unanticipated values of the policy variables are the calculated residuals. The fitted values are taken as the anticipated values.

A “reduced form” output equation based on (12) [and (14)], in which anticipated and unanticipated policy variables are present, is then estimated. The output equation is thus written in terms of anticipated and unanticipated policy variables. Policy variables whose parameters appear in (12) and (14) are incorporated in the output equation. Those variables whose parameters do not-that is, those for which the policy ineffectiveness proposition holds-are not included. The one policy variable that does not appear in (12) and (14) is government expenditure. Hence, anticipated government expenditure does not appear in the output equation. The estimated output equation thus derives from the theoretical model.

Since the question of lags is essentially an empirical one, the output equation is estimated for various lags. The general form of the “reduced form” output equation is:

In yt = CQ + o1 In ytml + A(L + B(L)AM + C(L)UG

+ D(L)UT + E(L)UM + E, ;

where:

(15)

AT = anticipated taxes; AM = anticipated money supply; UC = unanticipated government expenditures; UT = unanticipated taxes;

UM = unanticipated money supply;

and L is a lag polynomial. In Equation (15), as indicated above, anticipated government expenditure, AC, does not appear. The reason for this is that in both (12) and (14), no parameter capturing such expenditure appears. Unanticipated government expenditure, UG, does appear in order to determine whether changes in it aifect real output.

The models which are estimated are, first, Equations (4), (5), (6), (15), and (16). Second, (7) is used instead of (6) and the other equations are the same. Equation (16) follows Barro (1978) in that the price level is estimated from the demand for real balances. The

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particular expression is

In Pt = In M, - y. - y1 In yt - y2 In i, - kt ;

Yl=-0, Yz<O. (16)

Three-stage least squares is applied to estimate the anticipated and unanticipated components of the policy variables. This method takes into account all a priori restrictions inherent in the specification. The endogenous variables are G, T, M, and P in the models formed by excluding (15). For estimating (15), the fitted values of the endogenous variables of the 3SLS estimates of (4), (5), (16), and (6) or (7), d P d g e en in on model A or B, are taken as the anticipated monetary and fiscal variables. The residuals are taken as the unanticipated policy variables. Because each of the structural equations is over-identified, 3SLS is consistent and asymptotically more efficient than 2SLS.

For testing the policy ineffectiveness proposition, output equation, (15), is estimated by OLS. This procedure yields consistent estimates of the model’s parameters [Mishkin (1982), p. 411.

Annual and quarterly data for 19541 through 1983iv are used. The data are discussed in the Appendix.

4. Empirical Results In Table 1, the estimates of the output equation, (15), are

reported. The annual and quarterly real output results for the budget restraint money mechanism specification are (1.1) and (1.2), respectively. The last two equations in the table are the annual and quarterly estimates for the reaction function money mechanism specification. The annual and quarterly 3SLS estimates of (4)-(6), and (16)-the budget restraint model-are in Table 2, while the following table has the annual and quarterly 3SLS estimates of (4), (5), (7), and (16)-th e reaction function specification. It is from the 3SLS estimates that the anticipated and unanticipated variables of Table 1 are calculated.

In each of the four output equations in Table 1, there is never a case where an anticipated policy variable is statistically significant.4 On the other hand, in each equation there is always at least

‘The particular lags appearing in the output equations in Table 1 were selected on the basis of appropriate economic sign and statistical significance, subject to the restriction that each variable in (15) had to appear in each equation. No variable for which L = 2, . . . , 5 was significant at the 5% level.

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TABLE 1. Anticipated and Unanticipated Polictl Effect on Output

A. Budget Restraint Money Mechanism

Annual (1.1) In yt = -0.132 + 1.056 In ytwl - 0.009 In AT,-,

(-0.640) (19.255)* (-1.666)

- 0.033 In AM, + 0.311 In UG,-, (-0.964) (3.418)*

- 0.015 In UT,-, + 0.616 In UM, (-0.188) (1.980)**

II2 = 0.995 SE = 0.020 D.W. = 1.879

Quarterly (1.2) In yt = 0.005 + 1.002 In yt-l - 0.004 In AT,

(0.056) (56.211)* (-0.557)

+ 0.002 In AMtdl + 0.063 In UT,-, (1.063) (2.202)**

- 0.075 In UT,-, + 0.057 In UM, (-2.841)* (0.754)

R2 = 0.999 SE = 0.011 D.W. = 1.570

B. Reaction Function Money Mechanism

Annual (1.3) In yt = 0.052 + 1.002 In yt-l - 0.012 In AT,

(0.357) (41.053)* (-1.537)

+ 0.005 In AM,-, + 0.307 In UC,-, (0.895) (2.012)**

- 0.043 In UT,-, + 0.243 In UM, (-0.460) (0.661)

R2 = 0.994 SE = 0.022 D.W. = 1.680

Quarterly (1.4) In yt = 0.039 + 0.994 In yt-l - 0.002 In AT,-,

(1.047) (155.204)* (-0.569)

+ 0.004 In AM, + 0.040 In UG,-, (1.293) (0.783)

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TABLE 1. Anticipated and Unanticipated Policy Effect on Output fcont’d)

- 0.079 In UT,-, - 0.004 In UM, (-2.801)* (-0.075)

R2 = 0.999 SE = 0.011 D.W. = 1.542

NOTE: t-statistics are in parentheses. *Indicates significance at 1% level. **Indicates significance at 5% level.

TABLE 2. Model A Equations Estimates

(2.1)

(2.2)

(2.3)

(2.4)

A. Annual

In G, = -2.936 + 0.647 (In G,-, - In P,-,) (-3.323)* (5.490)*

+ 0.469 In ytdl+ 0.996 In Pt (3.502)* (19.819)*

I22 = 0.998 SE = 0.031

In Tt = -6.821 + 0.717 In yt + 0.321 In yt-l (-16.581)* (1.856)** (0.786)

+ 1.067 In Pt (13.590)*

R2 = 0.994 SE = 0.126

In M, = 1.378 + 0.187 In G, + 0.062 In Tt (15.058)* (3.441)* (1.066)

+ 0.125 In I?,+ 0.094 In B,-1 + 0.317 In Html (1.031) (0.776) (6.080)*

R2 = 0.998 SE = 0.017

In P, = 0.852 + 1.112 In M, - 0.333 In yt (3.137)* (25.737)* (-5.043)*

+ 0.028 In i, (1.667)

ET2 = 0.995 SE = 0.029

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Chien-Hmn Chen and Frank G. Steindl

(2.5)

(2.6)

(2.7)

cw

B. Quarterly

In G, = -1.038 + 0.874 (In G,-, - In Ptml) (-3.617)* (22.625)*

+ 0.161 In yt...l + 1.006 In Pt (3.784)* (63.355)*

R2 = 0.999 SE = 0.020

In Tt = -7.120 + 0.585 In yt + 0.538 In ytml (56.036)* (2.172)* (1.980)*

+ 1.003 In Pt (41.848)*

R2 = 0.997 SE = 0.036

In M, = 1.338 + 0.06 In G, + 0.159 In Tt (34.818)* (2.049) (5.161)*

+ 0.379 In B, - 0.146 In B,-, (2.687)* (-1.040)

+ 0.339 In H,-, (14.067)*

ii2 = 0.998 SE = 0.015

In P, = 0.950 + 1.129 In M, - 0.362 In yt (6.457)* (51. ill)* (-10.255)*

+ 0.036 In i, (4.043)*

R2 = 0.994 SE = 0.030

NOTE: t-statistics are in parentheses. *Indicates significance at 1% level. **Indicates signiikance at 5% level.

one correctly signed significant unanticipated policy variable. Usu- ally, it is unanticipated (lagged) government expenditures, as in (l.l),

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(1.2), and (1.3). Unanticipated (lagged) taxes are significant in two cases-(1.2) and (1.4)-and unanticipated money is significant only in (1.1). The policy ineffectiveness proposition thus appears to be supported empirically. Though, theoretically, the models allow for anticipated policy to have an effect, the empirical estimates indicate that anticipated policy has no effect on real output. Only unanticipated fiscal and monetary policies have an effect, though the estimates permit neither a ranking of fiscal relative to monetary policy nor are they sufficiently robust regarding the dominant (unanticipated) policy instrument. The estimates in the table indicate that in two different money supply regimes, with both annual and quarterly data, anticipated policy has no effect on real output.

The absence of serial correlation is particularly important in rational expectations models. Since the Box-Pierce (1970) Q-statistic is a cumulative serial correlation test that is not influenced by the presence of lagged dependent variables, it is the appropriate test for serial correlation. The calculated values of the Box-Pierce Q (with 24 degrees of freedom) for Equations (l.l)-(1.4) are 21.09, 27.40, 22.83, and 26.37, respectively. Each of these is less than the 1% significance level critical value of 43. Thus, the Box-Pierce test indicates the absence of serial correlation, hence, exploitable information, in the output equations.’

The 3SLS estimates of Model A-the budget restraint money mechanism model-are reported in Table 2. The estimates for annual data are in the top half and those with quarterly data are in the lower half. The equations are the empirical counterparts to (4), (5), (6), and (16). Th e estimates for both the annual and quarterly data are quite satisfactory for the individual equations.

Table 3 reports estimates for the reaction function money supply model-model B. The annual and quarterly estimates are the empirical counterparts of Equations (4), (5), (7), and (16). As in the previous model, the data fit the model quite well.

The money supply mechanism is given in (3.3) and (3.7). Of the ultimate goals of policy, only the current and previous price levels, P, and P,-l, are significant. The unemployment rate is not. These contrast with Barro’s (1977, p. 104) empirical reaction function results, which had a significant lagged unemployment rate but did not contain the price level.

%opies of the Box-Pierce statistics are available from the authors.

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Zhien-Hsun Chen and Frank G. Steindl

rABLE 3. Model B Equation Estimates

A. Annual

13.1) In G, = -2.025 + 0.731 (In G,-l - In Ptpl) (-2.204)** (6.126)*

+ 0.311 In yt-l+ 1.024 In P, (3.241)* (21.506)”

R2 = 0.999 SE = 0.030

13.2) h Tt = -6.902 + 0.455 In yt + 0.611 In yt-, (-15.355)* (1.091) (1.368)

+ 1.044 lnP, (12.691)”

R2 = 0.996 SE = 0.053

:3.3) In M, = -0.435 + 1.857 In M,-, - 0.467 In M,-, (-0.914) (3.362)* (-0.742)

- (-g;)** In Pt+ 0.853 In I’,-1

(1.733)**

+ 0.143 In G, - 0.134 In T, (1.048) (-0.847)

- 0.008 In U,-, (-0.038)

R2 = 0.998 SE = 0.015

:3.4) lnP, = 1.082 + 1.162 In M, - 0.402 In yt (3.359)* (26.583)* (-5.476)*

+ 0.016 In i, (0.705)

R2 = 0.995 SE = 0.026

B. Quarterly

13.5) In G, = 0.840 + 0.893 (In G,-, - In P,-I) (-2.903)* (23.194)*

+ 0.127 In ytel + 1.011 In Pt (2.952)* (66.650)*

R2 = 0.999 SE = 0.019


TABLE 3. Model B Equation Estimates (cont’d)

(3.6) In Tt ,r 7.118 + 0.339 In gt + 0.788 In ytel (-55.166)* (1.158) (2.674)*

+ 0.997 In P, (41.703)*

ET2 = 0.998 SE = 0.075

(3.7) In M, = 0.205 + 0.993 ln M,-, + 0.180 In M,-, (-1.911)** (5.857)* (0.894)

- 2.534 In P, + 2.357 In P,-l (-2.588)* (2.524)*

- 0.033 In G, + 0.056 In T, (-0.715) (1.027)

+ 0.007 In V,-, (0.623)

R2 = 0.997 SE = 0.011

(3.8) In P, = 0.974 + 1.128 In M, - 0.365 ln yt (5.781)* (49.897)* (-9.353)*

+ 0.037 In i, (3.517)*

R2 = 0.994 SE = 0.030

NOTE: t-statistics are in parentheses. *Indicates significance at 1% level. **Indicates significance at 5% level.

5. Conclusions The LSW proposition has certainly not lacked for interest. This

paper offers a model bearing on it. The distinguishing feature is that two explicit money supply mechanisms are formally incorporated as monetary “rules.” A fiscal sector is also present.

Upon solving the model, the behavior of real output is seen to depend on some of the monetary and fiscal parameters. No government expenditure parameter is involved-only the marginal tax rate. The model therefore does not preclude policy ineffectiveness. The money supply functions have as arguments several endogenous variables; that is, they are not simply feedback mechanisms. This

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is the reason why the model does not preclude policy ineffectiveness. The issue then becomes an empirical one,

The model is estimated by 3SLS. These estimates are used as the basis for calculating the anticipated values of the policy variables, with the residuals being the unanticipated values. These are then employed in a generalized output equation. The model is estimated both annually and quarterly for each money supply specification.

The most important finding is that anticipated monetary and fiscal variables are never significant in any of the formulations. Also, in each formulation, at least one unanticipated policy variable is significant, with the monetary policy variable significant in only one case.

Though the models developed in this paper allow for anticipated policy to have an effect on real output, the empirical estimates lend support to the policy ineffectiveness proposition. They constitute a bit more evidence in favor of the LSW proposition that real output is affected only when economic agents are surprised.

Received: July 1985 Final version: October 1986

References Attfield, C.L.F., and N.W. Duck. “The Influence of Unanticipated

Money Growth on Real Output: Some Cross-Country Esti- mates.” Journal of Money, Credit and Banking 15 (November 1983): 442-54.

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Budget Restraint.” Journal of Political Economy 76 (January/ February 1968): 53-67.

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Appendix The money supply (M) is defined as old Ml (1954-1958) and

new Ml (1959-1983), seasonally adjusted. The rate of nominal interest (i) is the commercial paper (three-month) rate. The stock of high-powered money (H) is currency held by the nonbank public and commercial bank reserves. These are taken from Banking and Monetary Statistics 1941-1970, Annual Statistical Digest 1970-1979, 1980, 1981, and from various issues of the Federal Reserve Bulletin.

The price level (P) is the GNP implicit price deflator, 1972 = 100. Real output (y) is GNP in 1972 dollars. Federal government expenditures (G) include government purchases and transfer pay- ments, and T is federal government nominal tax receipts. These are obtained from various issues of the Surwey of Current Business.

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The unemployment rate (U) is taken from Labor Force Sta- tistics Derived from the Current Population Survey: A Data Book, and from various issues of the Monthly Labor Review.

The federal government’s outstanding debt exclusive of agency and Federal Reserve holdings (B) is taken from various issues of the Treasury Bulletin.

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Anticipated monetary and fiscal policy effects on output

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