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A comparison of some basic monetary policy regimes for open economies
Carnegie-Rochester Conference Series on Public Policy 39 (1993) 319-327 North-Holland
A comparison of some basic monetary policy regimes for open economies A comment Robert H. Rasche Michigan State University, East Lansing, MI 48823
The Henderson-McKibbin (1993) study analyzes models of two large countries which produce goods that are imperfect substitutes (apples and oranges). The two countries are interrelated by trade in commodities and by interest-rate arbitrage as private agents construct portfolios that include bonds issued in both countries. It is impossible to give full and appropriate recognition to the amount of work that is involved in the construction of these analyses. There are three models x three sources of shocks x two types of shocks (symmetric and asymmetric) x four policy rules xn variants of each policy rule (from full instrument adjustment (FIA) to varying degrees of partial instrument adjustment (PIA)). G iven the range of the analysis, I will not give much attention to the discussion of the specific results which is the subject of the many tables and charts accompanying the paper, but rather concentrate on the structure of the models and the analysis. The authors should be commended for their ambitious undertaking. As presented, the analysis requires a considerable amount of care to fully grasp exactly what is going on. Nevertheless, there are a number of ways in which things could be clarified. functions First, equations (8) in Table 1 are defined as excess-demand has been applied. In a paper for goods (page 227), where log-linearization with 77 equations, I would forgive the authors if they added a couple more equations showing the explicit derivation of equations (8) in order to show the reader that foreign country demands for domestic output are properly measured in domestic output units and that there is no problem of adding apples and oranges in these equations. The only information that I can find 0167-2231/93/$06.00
0 1993 - Elsevier Science Publishers
B.V.
All rights reserved.
to suggest that this measurement of 6 in footnote 8. Second,
equations
is done correctly
is implicit in the definition
(24) and (29) in the sums and differences
models of
Table 4 are referred to in the text as “Aggregate-Demand Schedules.” I find this a confusing and misleading use of standard terminology even with the explanation provided in footnote 23. Conventional use locus by solving (24) and (25), or a yd - pd locus by to eliminate i, and id, respectively.’ What is called an schedule here is the conventional textbook IS schedule rather than y - (; - p) space. Third, equations (28) and (33) require equation addition to the derivation stated in the text.
is to obtain a ya - p, solving (29) and (30) “Aggregate-Demand” plotted in y -p space
(16),
w = w* = w in
Fourth, with the exception of the parameters of the policy rules, which are varied under the partial instrument adjustment investigation, there is no analysis of the sensitivity of the results of the analysis to choice of parameter values. All of this can be determined immediately for the “contractshypothesis” model from the results in Appendix A; all that is necessary is to compute the elasticities of the various reduced-form coefficients with respect to the parameters of the model and evaluate them at the chosen parameter values. This would provide the reader with some indication of those parameters for which the choice of a particular value may significantly affect the conclusions reported. Since the Phillips Curve model is completely log linear, the explicit reduced form for this model is also easily computed and the corresponding sensitivity analysis performed. The MSG2 model is presumably so large and nonlinear that such sensitivity analysis is a monumental undertaking. Unfortunately this leaves the outside observer with no way to verify independently if the MSG2 model is a credible representation of real world economic processes. As Zellner [1992] has noted: “Many large econometric and other models on the scene involve hundreds of nonlinear stochastic difference equations. It is not clear whether these models have one or many roots and the dynamics of these black-box monstrosities are not well understood” (p. 4). I n a previous draft of this study, the authors presented some initial analysis using their “workhorse model,” supplemented by an overlapping wage contract (Taylor) hypothesis. In the published version this analysis has been abandoned in favor of simulations of the MSG2 model. In my judgment this change in research strategy represents an unfortunate rejection
of Zellner’s
“keep it sophisticatedly
simple” dictum.
‘The notation used here is that of Henderson and McKibbon (1993). The variables are defined in Table I. Starred variables refer to the foreign economy. Variables subscripted with an s measure
the world economy
(the sum of the domestic
Variables subscripted with a d measure the differential differences between domestic and foreign measures).
320
impact
and foreign
variables).
on the two economies
(the
Fifth,
in the models all information
ately. This is critical temporary
to the construction
is assumed
to be available
of the policy rules.
in a model such as the “contracts
hypothesis,”
immedi-
If the shocks are
where there are no
distributed lag effects, then the appropriate response to lagged information is no response, since lagged information is uninformative about the size of the shocks that will hit the economy in the current period or in future periods. Sixth,
there appears
to be some inconsistency
between
the results
from
the contracts hypothesis presented in Tables 7-9 and the corresponding information in Figures 3, 5, 6, 8, and 9. The text states that the information plotted in the figures is the undiscounted sum of square deviations of the variable from the baselines. The contracts hypothesis is a static model, (see reduced forms in Appendix A), so deviations in response to temporary shocks are just the impact effects, which for full instrument adjustment (FIA) are reported in Tables 7-9. Thus for full adjustment, the values indicated in the figures should be just the squares of the corresponding values in the tables. In many cases there are major discrepancies (e.g., inflation with symmetric money demand shock (-1.26)2 [Table 71 < 2.8 [Figure 31) which are not explained. More substantive issues involve the structure of the various models. The contracts and Phillips Curve models are identical in all respects except one nominal wage determination, as indicated in equations (A) - (D) of my Table I. Equations (E) of that table indicate clearly that the “contracts hypothesis” model is just a g-equation static exogenous money wage-rate model of two large open economies. We can call this what we want, but it must be recognized that it is observationally equivalent to a textbook exogenous money-wage-rate Keynesian model. The results derived here are the direct extension (with the generalization to include the labor-demand functions and the aggregate-production
functions)
of the Poole [1970] model.
It should be noted that consumer prices (q) do not appear in Table I (I have substituted them out). In fact, the only role for consumer prices is to cause the LM curve in both economies to shift with changes in the real exchange rate, since real interest rates are defined in terms of consumer prices (q), not domestic output prices (p). This is important since it implies that consumer prices play no role in the impact of symmetric shocks on the world (summed) economy for any of the three models. Sum equations (B) in Table I and the real exchange rate drop out of the “world LM” equation, so the behavior of the world economy would be the same if we define real interest rates in terms of domestic output prices (p) and consumer prices never appeared in the models. Only the distributional effects between economies of symmetric shocks are affected by the inclusion of consumer prices in the structure of these models. The real exchange
rate also drops out of the summed 321
equations
(C) in
Table I, the “world IS” equation, so it has no influence on the behavior of the (closed) world economy. Thus, with the exception of the generalization to include supply shocks, the analysis of the “contracts-hypothesis” model under sums is the Poole [1970] analysis. A second structural
feature
of the two models is the specification
of the
money-demand functions. The assumed parameter values restrict the moneydemand functions to be velocity functions ($ = 1.0) which are extremely interest inelastic. The latter conclusion follows from the semi-log specification
(2nV = Xi) where X = 8 (Appendix B) and the definition of real interest rates as r = i -Ain&, where Q is the appropriate consumer price index. The latter definition implies that r and i are JU& measured in percentages (i.e., nominal rates of five percent are measured as .05). Hence the elasticity of velocity with respect to nominal interest rates evaluated at a five-percent nominal rate is Xi = 8 * .05 = .04. Whether this is reasonable or not presumably depends on whether you view these as very short-run (say monthly) models or longerrun (say annual) models. If the models are supposed to be very short-run, it seems hard to justify the equilibrium specifications in (B) and (C). The money-wage-rate adjustment mechanisms of the Phillips Curve models seem consistent with a longer-run time interval. Such a measurement interval would seem to require a much higher estimate of the interest elasticity of velocity (Poole [1988]; Hoffman and Rasche [1991]) for a narrowly defined monetary
aggregate.
The structure of the Phillips Curve model requires some explanation of the expectations mechanism that is assumed. Equation (38) (Table 10) has no inflation or price expectations terms, only actual prices one period ahead. Since equation (38) is derived by summing equations (13), the Phillips Curve models are being solved either under perfect foresight or rational expectations assumptions. If the shocks are truly understood to be one-time and temporary, E,[pt+i] is exactly pt+i (for confirmation see p. 245). The question is what produces the gradual adjustment to the steady state in this model (Figures 10, 13,27, and 28), since with one-time temporary shocks and either perfect foresight or rational expectations and no dynamic structure on the demand side of the economy, many models would imply an immediate return to a steady-state equilibrium after the temporary shock disappears. The answer is found by examining the inflation-output trade-off relations implicit in the supply side of this model (the alternative to equations (E) in Table I) in Table II. Note that in equation (10) the rate of wage inflation from t to t+ l(wt+r Wt) depends upon employment during t(nt). Substituting (2) and (1) into (10) gives (B) in Table II, a relationship between domestic output price inflation, expected inflation, and current and lagged output. The authors assume that the coefficient on lagged output, (1 - e/(1 - (Y)}, is > 0, even 322
though they note that stability term be < 1. They justify alternating
adjustment
requires only that the absolute
their restriction
value of this
on the grounds
that it rules out
paths (it is not clear why alternating
paths should be
ruled out, since additional dynamic structure in the demand side of the model would likely convert the negative root of this first-order system into stable but complex roots in a higher order system). The restriction that { 1 - 8/( lo)} > 0 is sufficient, but not necessary to rule out alternating adjustment paths. The experiments reported are constructed under the assumption that cr = .7 and 0 = .2. An estimate of .7 for the output elasticity of labor input in a Cobb-Douglas production function (a) seems an appropriate choice based on a large number of studies, at least for U.S. data. The assumption that the slope of the short-run Phillips Curve, 8, equals .2 is more problematic. In particular, if 8 were chosen at .3 (given cr = .7), then the first-order difference equation in n, (equation 43) is degenerate, the necessary condition for nonalternating paths is satisfied, and n,,t+l depends only on (z,,l+i z,,~). Thus with these parameter values the model produces an immediate adjustment to a steady state similar to the adjustment in the “contractshypothesis” model after an unexpected transitory shock. The complete Phillips Curve model specified by equations (A) - (D) in Table I and (B) in Table II is clearly a dynamic linear model in the shocks and the endogenous variables. It is straightforward to construct the final form(s) of such models (the impulse-response functions to use VAR jargon) that are analogous to the reduced forms of the static models in Appendix B. Once such final forms are constructed, sensitivity analysis to model parameter variation is an exercise in partial differentiation. In my judgment, such sensitivity analyses are much more revealing than the “simulation analyses” reported in the text and accompanying
charts.
It is not clear why the authors have concentrated exclusively on the effect of various policy rules on temporary or transitory shocks. My reading of the statistical analyses of macroeconomic time series over the past 15 years and the development of macroeconomic theory during the same period is that permanent shocks are an important feature in the models and a characteristic of the data-generating process. The implications of the various policy rules under such conditions are ignored in this analysis. Given this limitation on the scope of the analysis, there may be reason to be skeptical of the authors’ broad general conclusion that in the results presented here “additional support [is] provided for the increasingly widely shared view that the price level is determinate under fairly general conditions when the interest rate is the instrument of monetary policy” (page 268). Beyond the structure of the models, there are questions about the nature of the policy rules. In the “contracts-hypothesis” model, the interest-rate exogenous (II) rule is clearly a fixed exchange-rate regime. This follows since 323
under II (; - i*) = 0. But in this model e+n = 0 from (16), so from (5) e=(;i*) = 0 (see also footnote 2 and Table 5-7). At the other extreme, the money-stock exogenous (MM) rule is a type of “flexible exchange-rate” regime, since the nominal money stock in each economy is insulated from all shocks, both foreign and domestic. However, the nominal income (YY) and inflation-real-output (CC) re g imes are probably closer to what is vaguely characterized as a “floating-rate regime,” since under these rules the interest rate in each economy is adjusted only in response to movements in domestic prices and output, regardless of what is happening in the foreign economy. However, this raises the question of whether the latter regimes are really independent policy rules. Consider equations (7) and (14) under the assumption that the income elasticity of the demand for real balances (6) equals 1.0. These reduce to (; - 2) = p[ ml - Xit - ut] and (i* - i*) = p[m; - X$ - v;], If l = s* = 0 under (14) (which since P, = *p, + yt = 0 under (14). is not clear from Table 3), then it = {p/(1 - A)}m, - {l/(1 - X)}v, and i; = {p/(1 - A)}mr - {l/(1 - x)}vt which are stochastic variants of (13) with a partial instrument adjustment (PIA) coefficient of {p/(1 - X)) = 5p since A = 8. In the analysis of z and 21 shocks, vt is identically zero, so in these cases the YY regime is just a MM - PIA regime with a particular partial-adjustment coefficient. The authors continually refer to one policy rule being better or worse than another in terms of a single variable. The criterion is the undiscounted sum of squared deviations of the variable from its baseline value (see Figures 3, 5-6,8-g, 11-12, 14-20,22-26). Th is objective function penalizes all deviations from baseline and does not allow for offsets. This certainly does not reflect contemporary political discussion in the United States where, for example, increases in employment are regarded as positive and decreases negative. Presumably a general objective function would take the form: CxCWij6tKjt i
j
t
where i indexes countries, j the observed variables that are the policy goals, and t the elapsed time since the shock. wij is the weight assigned to the jth policy goal in the ifh country,
6 < 1 the discount
factor,
and I&
a function
of the observed deviations from baseline. The problem is that the choice of wij is arbitrary. We have no information on whether the authors’ ranking of policies is robust to reasonable alternatives to their particular choice of wij and functional form (squared) of xjt.
324
Table I (Contract-Hypothesis
Model)
Solve (1) for nt and substitute into (2): -(l - o)& + ap; - 2; = (w; - w) - (Y)Y~+ apt - zt = (tot -w)
(A)
-(l
(‘9
Substitute (3) and (16) into (6) and then into (7): mt = pt + hit - X[rt - pt - 74 + ut m; = p; + 4~; - X[P; - p; + yzr] + U;
(C)
Prom (8): 7cY; - P - (I- 7)dYf - 7vrt (1 - YklYt + 7CYf -[I-(l - 7)vr; - 6rt + u; = 0 -(l - 7)vrr - 7vr; + 6tt + ut = 0
(D)
Solve (4) for et and substitute into (5) it = i; - tt + P: - Pt
(E)
wt = w
Prom (17): w; = w
9 Equations: Endogenous: yt,pt,rt,Zt,wt,Y~,P;,rf,w; Exogenous: mt,m~,w,xt,vt,ut,x;,vf,u; Y, Y*
n, n’ x,x* w,w* P,P4
Q,Q’
Definitions of Variables real exchange-rate consumer z outputs e nominal exchange rate ($/ROECD) employments nominal interest rates i, i’ productivity shocks real interest rates r, r’ nominal wages money-demand shocks v, v’ output prices u, u* goods-demand shocks consumer price levels (CPIs)
325
Table II Phillips Curve Model
(10)
%+1 - wt = ant + pt+lIt - pt
(*)
Pt+l - Pt = (1 - a)nt+l
Solve (2) for wt and substitute
Solve (1) for rzt and substitute (B)
Pt+1 - Pt = e%t+1
into (10)
- [(I - a) - d]nt + [Pt+lp - Pt] + [Zt+l - xt]
-
(+x1
into (4) -
326
(&)lYt
+ lpt+1jt
- pt] + &+I
- $[l - B]zt
References Hoffman, D. and Rasche, R.H., (1991).
Long-Run
Income and Interest Elas-
ticities of Money Demand in the U.S., Review of Economics 78: 665-674.
and Statistics,
Poole, W., (1970). Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model, Quarterly Journal of Economics, 84: 197-216. Poole, W., (1988). M onetary Policy Lessons of Recent Inflation and Disinflation, Economic Perspectives, Summer, 2: 73-100. Zellner, A., (1992). Statistics, Science and Public American Statistical Association, 87: l-6.
327
Policy,
Journal
of the
A comparison of some basic monetary policy regimes for open economies A comment Robert H. Rasche Michigan State University, East Lansing, MI 48823
The Henderson-McKibbin (1993) study analyzes models of two large countries which produce goods that are imperfect substitutes (apples and oranges). The two countries are interrelated by trade in commodities and by interest-rate arbitrage as private agents construct portfolios that include bonds issued in both countries. It is impossible to give full and appropriate recognition to the amount of work that is involved in the construction of these analyses. There are three models x three sources of shocks x two types of shocks (symmetric and asymmetric) x four policy rules xn variants of each policy rule (from full instrument adjustment (FIA) to varying degrees of partial instrument adjustment (PIA)). G iven the range of the analysis, I will not give much attention to the discussion of the specific results which is the subject of the many tables and charts accompanying the paper, but rather concentrate on the structure of the models and the analysis. The authors should be commended for their ambitious undertaking. As presented, the analysis requires a considerable amount of care to fully grasp exactly what is going on. Nevertheless, there are a number of ways in which things could be clarified. functions First, equations (8) in Table 1 are defined as excess-demand has been applied. In a paper for goods (page 227), where log-linearization with 77 equations, I would forgive the authors if they added a couple more equations showing the explicit derivation of equations (8) in order to show the reader that foreign country demands for domestic output are properly measured in domestic output units and that there is no problem of adding apples and oranges in these equations. The only information that I can find 0167-2231/93/$06.00
0 1993 - Elsevier Science Publishers
B.V.
All rights reserved.
to suggest that this measurement of 6 in footnote 8. Second,
equations
is done correctly
is implicit in the definition
(24) and (29) in the sums and differences
models of
Table 4 are referred to in the text as “Aggregate-Demand Schedules.” I find this a confusing and misleading use of standard terminology even with the explanation provided in footnote 23. Conventional use locus by solving (24) and (25), or a yd - pd locus by to eliminate i, and id, respectively.’ What is called an schedule here is the conventional textbook IS schedule rather than y - (; - p) space. Third, equations (28) and (33) require equation addition to the derivation stated in the text.
is to obtain a ya - p, solving (29) and (30) “Aggregate-Demand” plotted in y -p space
(16),
w = w* = w in
Fourth, with the exception of the parameters of the policy rules, which are varied under the partial instrument adjustment investigation, there is no analysis of the sensitivity of the results of the analysis to choice of parameter values. All of this can be determined immediately for the “contractshypothesis” model from the results in Appendix A; all that is necessary is to compute the elasticities of the various reduced-form coefficients with respect to the parameters of the model and evaluate them at the chosen parameter values. This would provide the reader with some indication of those parameters for which the choice of a particular value may significantly affect the conclusions reported. Since the Phillips Curve model is completely log linear, the explicit reduced form for this model is also easily computed and the corresponding sensitivity analysis performed. The MSG2 model is presumably so large and nonlinear that such sensitivity analysis is a monumental undertaking. Unfortunately this leaves the outside observer with no way to verify independently if the MSG2 model is a credible representation of real world economic processes. As Zellner [1992] has noted: “Many large econometric and other models on the scene involve hundreds of nonlinear stochastic difference equations. It is not clear whether these models have one or many roots and the dynamics of these black-box monstrosities are not well understood” (p. 4). I n a previous draft of this study, the authors presented some initial analysis using their “workhorse model,” supplemented by an overlapping wage contract (Taylor) hypothesis. In the published version this analysis has been abandoned in favor of simulations of the MSG2 model. In my judgment this change in research strategy represents an unfortunate rejection
of Zellner’s
“keep it sophisticatedly
simple” dictum.
‘The notation used here is that of Henderson and McKibbon (1993). The variables are defined in Table I. Starred variables refer to the foreign economy. Variables subscripted with an s measure
the world economy
(the sum of the domestic
Variables subscripted with a d measure the differential differences between domestic and foreign measures).
320
impact
and foreign
variables).
on the two economies
(the
Fifth,
in the models all information
ately. This is critical temporary
to the construction
is assumed
to be available
of the policy rules.
in a model such as the “contracts
hypothesis,”
immedi-
If the shocks are
where there are no
distributed lag effects, then the appropriate response to lagged information is no response, since lagged information is uninformative about the size of the shocks that will hit the economy in the current period or in future periods. Sixth,
there appears
to be some inconsistency
between
the results
from
the contracts hypothesis presented in Tables 7-9 and the corresponding information in Figures 3, 5, 6, 8, and 9. The text states that the information plotted in the figures is the undiscounted sum of square deviations of the variable from the baselines. The contracts hypothesis is a static model, (see reduced forms in Appendix A), so deviations in response to temporary shocks are just the impact effects, which for full instrument adjustment (FIA) are reported in Tables 7-9. Thus for full adjustment, the values indicated in the figures should be just the squares of the corresponding values in the tables. In many cases there are major discrepancies (e.g., inflation with symmetric money demand shock (-1.26)2 [Table 71 < 2.8 [Figure 31) which are not explained. More substantive issues involve the structure of the various models. The contracts and Phillips Curve models are identical in all respects except one nominal wage determination, as indicated in equations (A) - (D) of my Table I. Equations (E) of that table indicate clearly that the “contracts hypothesis” model is just a g-equation static exogenous money wage-rate model of two large open economies. We can call this what we want, but it must be recognized that it is observationally equivalent to a textbook exogenous money-wage-rate Keynesian model. The results derived here are the direct extension (with the generalization to include the labor-demand functions and the aggregate-production
functions)
of the Poole [1970] model.
It should be noted that consumer prices (q) do not appear in Table I (I have substituted them out). In fact, the only role for consumer prices is to cause the LM curve in both economies to shift with changes in the real exchange rate, since real interest rates are defined in terms of consumer prices (q), not domestic output prices (p). This is important since it implies that consumer prices play no role in the impact of symmetric shocks on the world (summed) economy for any of the three models. Sum equations (B) in Table I and the real exchange rate drop out of the “world LM” equation, so the behavior of the world economy would be the same if we define real interest rates in terms of domestic output prices (p) and consumer prices never appeared in the models. Only the distributional effects between economies of symmetric shocks are affected by the inclusion of consumer prices in the structure of these models. The real exchange
rate also drops out of the summed 321
equations
(C) in
Table I, the “world IS” equation, so it has no influence on the behavior of the (closed) world economy. Thus, with the exception of the generalization to include supply shocks, the analysis of the “contracts-hypothesis” model under sums is the Poole [1970] analysis. A second structural
feature
of the two models is the specification
of the
money-demand functions. The assumed parameter values restrict the moneydemand functions to be velocity functions ($ = 1.0) which are extremely interest inelastic. The latter conclusion follows from the semi-log specification
(2nV = Xi) where X = 8 (Appendix B) and the definition of real interest rates as r = i -Ain&, where Q is the appropriate consumer price index. The latter definition implies that r and i are JU& measured in percentages (i.e., nominal rates of five percent are measured as .05). Hence the elasticity of velocity with respect to nominal interest rates evaluated at a five-percent nominal rate is Xi = 8 * .05 = .04. Whether this is reasonable or not presumably depends on whether you view these as very short-run (say monthly) models or longerrun (say annual) models. If the models are supposed to be very short-run, it seems hard to justify the equilibrium specifications in (B) and (C). The money-wage-rate adjustment mechanisms of the Phillips Curve models seem consistent with a longer-run time interval. Such a measurement interval would seem to require a much higher estimate of the interest elasticity of velocity (Poole [1988]; Hoffman and Rasche [1991]) for a narrowly defined monetary
aggregate.
The structure of the Phillips Curve model requires some explanation of the expectations mechanism that is assumed. Equation (38) (Table 10) has no inflation or price expectations terms, only actual prices one period ahead. Since equation (38) is derived by summing equations (13), the Phillips Curve models are being solved either under perfect foresight or rational expectations assumptions. If the shocks are truly understood to be one-time and temporary, E,[pt+i] is exactly pt+i (for confirmation see p. 245). The question is what produces the gradual adjustment to the steady state in this model (Figures 10, 13,27, and 28), since with one-time temporary shocks and either perfect foresight or rational expectations and no dynamic structure on the demand side of the economy, many models would imply an immediate return to a steady-state equilibrium after the temporary shock disappears. The answer is found by examining the inflation-output trade-off relations implicit in the supply side of this model (the alternative to equations (E) in Table I) in Table II. Note that in equation (10) the rate of wage inflation from t to t+ l(wt+r Wt) depends upon employment during t(nt). Substituting (2) and (1) into (10) gives (B) in Table II, a relationship between domestic output price inflation, expected inflation, and current and lagged output. The authors assume that the coefficient on lagged output, (1 - e/(1 - (Y)}, is > 0, even 322
though they note that stability term be < 1. They justify alternating
adjustment
requires only that the absolute
their restriction
value of this
on the grounds
that it rules out
paths (it is not clear why alternating
paths should be
ruled out, since additional dynamic structure in the demand side of the model would likely convert the negative root of this first-order system into stable but complex roots in a higher order system). The restriction that { 1 - 8/( lo)} > 0 is sufficient, but not necessary to rule out alternating adjustment paths. The experiments reported are constructed under the assumption that cr = .7 and 0 = .2. An estimate of .7 for the output elasticity of labor input in a Cobb-Douglas production function (a) seems an appropriate choice based on a large number of studies, at least for U.S. data. The assumption that the slope of the short-run Phillips Curve, 8, equals .2 is more problematic. In particular, if 8 were chosen at .3 (given cr = .7), then the first-order difference equation in n, (equation 43) is degenerate, the necessary condition for nonalternating paths is satisfied, and n,,t+l depends only on (z,,l+i z,,~). Thus with these parameter values the model produces an immediate adjustment to a steady state similar to the adjustment in the “contractshypothesis” model after an unexpected transitory shock. The complete Phillips Curve model specified by equations (A) - (D) in Table I and (B) in Table II is clearly a dynamic linear model in the shocks and the endogenous variables. It is straightforward to construct the final form(s) of such models (the impulse-response functions to use VAR jargon) that are analogous to the reduced forms of the static models in Appendix B. Once such final forms are constructed, sensitivity analysis to model parameter variation is an exercise in partial differentiation. In my judgment, such sensitivity analyses are much more revealing than the “simulation analyses” reported in the text and accompanying
charts.
It is not clear why the authors have concentrated exclusively on the effect of various policy rules on temporary or transitory shocks. My reading of the statistical analyses of macroeconomic time series over the past 15 years and the development of macroeconomic theory during the same period is that permanent shocks are an important feature in the models and a characteristic of the data-generating process. The implications of the various policy rules under such conditions are ignored in this analysis. Given this limitation on the scope of the analysis, there may be reason to be skeptical of the authors’ broad general conclusion that in the results presented here “additional support [is] provided for the increasingly widely shared view that the price level is determinate under fairly general conditions when the interest rate is the instrument of monetary policy” (page 268). Beyond the structure of the models, there are questions about the nature of the policy rules. In the “contracts-hypothesis” model, the interest-rate exogenous (II) rule is clearly a fixed exchange-rate regime. This follows since 323
under II (; - i*) = 0. But in this model e+n = 0 from (16), so from (5) e=(;i*) = 0 (see also footnote 2 and Table 5-7). At the other extreme, the money-stock exogenous (MM) rule is a type of “flexible exchange-rate” regime, since the nominal money stock in each economy is insulated from all shocks, both foreign and domestic. However, the nominal income (YY) and inflation-real-output (CC) re g imes are probably closer to what is vaguely characterized as a “floating-rate regime,” since under these rules the interest rate in each economy is adjusted only in response to movements in domestic prices and output, regardless of what is happening in the foreign economy. However, this raises the question of whether the latter regimes are really independent policy rules. Consider equations (7) and (14) under the assumption that the income elasticity of the demand for real balances (6) equals 1.0. These reduce to (; - 2) = p[ ml - Xit - ut] and (i* - i*) = p[m; - X$ - v;], If l = s* = 0 under (14) (which since P, = *p, + yt = 0 under (14). is not clear from Table 3), then it = {p/(1 - A)}m, - {l/(1 - X)}v, and i; = {p/(1 - A)}mr - {l/(1 - x)}vt which are stochastic variants of (13) with a partial instrument adjustment (PIA) coefficient of {p/(1 - X)) = 5p since A = 8. In the analysis of z and 21 shocks, vt is identically zero, so in these cases the YY regime is just a MM - PIA regime with a particular partial-adjustment coefficient. The authors continually refer to one policy rule being better or worse than another in terms of a single variable. The criterion is the undiscounted sum of squared deviations of the variable from its baseline value (see Figures 3, 5-6,8-g, 11-12, 14-20,22-26). Th is objective function penalizes all deviations from baseline and does not allow for offsets. This certainly does not reflect contemporary political discussion in the United States where, for example, increases in employment are regarded as positive and decreases negative. Presumably a general objective function would take the form: CxCWij6tKjt i
j
t
where i indexes countries, j the observed variables that are the policy goals, and t the elapsed time since the shock. wij is the weight assigned to the jth policy goal in the ifh country,
6 < 1 the discount
factor,
and I&
a function
of the observed deviations from baseline. The problem is that the choice of wij is arbitrary. We have no information on whether the authors’ ranking of policies is robust to reasonable alternatives to their particular choice of wij and functional form (squared) of xjt.
324
Table I (Contract-Hypothesis
Model)
Solve (1) for nt and substitute into (2): -(l - o)& + ap; - 2; = (w; - w) - (Y)Y~+ apt - zt = (tot -w)
(A)
-(l
(‘9
Substitute (3) and (16) into (6) and then into (7): mt = pt + hit - X[rt - pt - 74 + ut m; = p; + 4~; - X[P; - p; + yzr] + U;
(C)
Prom (8): 7cY; - P - (I- 7)dYf - 7vrt (1 - YklYt + 7CYf -[I-(l - 7)vr; - 6rt + u; = 0 -(l - 7)vrr - 7vr; + 6tt + ut = 0
(D)
Solve (4) for et and substitute into (5) it = i; - tt + P: - Pt
(E)
wt = w
Prom (17): w; = w
9 Equations: Endogenous: yt,pt,rt,Zt,wt,Y~,P;,rf,w; Exogenous: mt,m~,w,xt,vt,ut,x;,vf,u; Y, Y*
n, n’ x,x* w,w* P,P4
Q,Q’
Definitions of Variables real exchange-rate consumer z outputs e nominal exchange rate ($/ROECD) employments nominal interest rates i, i’ productivity shocks real interest rates r, r’ nominal wages money-demand shocks v, v’ output prices u, u* goods-demand shocks consumer price levels (CPIs)
325
Table II Phillips Curve Model
(10)
%+1 - wt = ant + pt+lIt - pt
(*)
Pt+l - Pt = (1 - a)nt+l
Solve (2) for wt and substitute
Solve (1) for rzt and substitute (B)
Pt+1 - Pt = e%t+1
into (10)
- [(I - a) - d]nt + [Pt+lp - Pt] + [Zt+l - xt]
-
(+x1
into (4) -
326
(&)lYt
+ lpt+1jt
- pt] + &+I
- $[l - B]zt
References Hoffman, D. and Rasche, R.H., (1991).
Long-Run
Income and Interest Elas-
ticities of Money Demand in the U.S., Review of Economics 78: 665-674.
and Statistics,
Poole, W., (1970). Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model, Quarterly Journal of Economics, 84: 197-216. Poole, W., (1988). M onetary Policy Lessons of Recent Inflation and Disinflation, Economic Perspectives, Summer, 2: 73-100. Zellner, A., (1992). Statistics, Science and Public American Statistical Association, 87: l-6.
327
Policy,
Journal
of the