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The policy evaluation problem and the demand for money
99
Economics Letters 16 (1984) 99-103 North-Holland
THE POLICY EVALUATION PROBLEM THE DEMAND FOR MONEY Meir
KOHN
Dartmouth
and
Joyce M. MANCHESTER
AND
*
College, Hanover, NH 03755, USA
Received 9 January 1984
This paper applies the Lucas policy evaluation proposition to the money demand function. We find some support for the hypothesis that the decrease in serial correlation of interest rates since the Fed policy change in 1979 has resulted in an increase in the estimated elasticity of money demand.
1. Introduction The policy evaluation proposition, first enunciated by Lucas (1981), states that observed aggregate empirical relationships are unlikely to be invariant to changes in policy regime. Much work has been done to examine the validity of this proposition as it relates to the Phillips curve. The purpose of the current paper is to examine its validity with respect to another important empirical relationship - the ‘money demand function’. The money demand function is a prime candidate for such an examination for three reasons. First, expectations are clearly important. A speculative element, dependent on expected changes in the rate of interest, played an important role both in the original formulation as stated by Keynes (1936) and, more recently, in the formulation suggested by Friedman (1970). Second, it is hard to claim that the estimated equation is ‘structural’ in the sense of Lucas: problems of identifying supply and demand and of deriving a precise specification from individual optimization behavior are frequently commented upon. 1 Third, a
* We would like to thank Colin Campbell for helpful comments on an earlier draft. 1 See, e.g., Cooley and Leroy (1981). 01651765/84/$3.00
0 1984, Elsevier Science Publishers B.V. (North-Holland)
100
M. Kahn, J.M.
Manchester
/ Policy
eualuatronand
money
demand
change in policy regime in October, 1979 provides us with a handy opportunity to test for a shift in the equation.
2. Theory A simple theoretical justification for the postulated shift would run as follows. * Money demand consists of a transactions demand, dependent on the level of economic activity, and a speculative demand, dependent on the expected change in the rate of interest. This could be written m, = ayt + P@,+,
(1)
- i,),
where m, is the level of real balances, y, a measure of income, i, the current market rate and (Ei,,, - i,) the ‘rationally’ expected change in the current market rate. 3 The first term on the right-hand side represents the transactions demand, the second term the speculative demand. The conditionally expected rate of interest may be written Ei
t+1
=
y.
+
xi,,
(2)
where y. may contain other time-t variables. Substituting (2) in (l), we obtain 4 m, = ayI + Pvo - PC1 - yi)i,. From eq. (3) we see that the observed interest elasticity of the ‘demand for money’ will be inversely related to the degree of serial correlation in interest rates. While the exact nature of the change in policy regime in October, 1979 is open to debate, 5 it does seem clear that greater weight has been given to stabilizing the rate of growth of monetary aggregates and less to stabilizing rates of interest. In terms of the very simple model presented here, the expected result would be a decrease in the serial correlation of interest rates and a resulting increase in the interest elasticity of the estimated money demand equation. ’ See Walsh (1983) 3 The ‘rational
4 See,e.g.,Judd
for a more thorough
expectation’
and Scadding
’ See Poole (1982)
treatment.
is the conditional (1982)
for an expanded
expected
or Duprey discussion.
(1980).
value given information
at time
t.
M. Kahn, J.M. Manchester
/ Policy evaluation and money demand
101
3. Estimation
We need to establish first that, whatever the nature of the change in policy in October, 1979, there has been a major increase in volatility of interest rates. We estimated the autoregressive equation
for the subperiods from 1960.1 through 1979.111 and from 1979.IV through 1983.11. Using the three-month Treasury bill rate, the serial correlation coefficient yi fell from 0.99 to 0.65, and the standard error of regression increased from 0.59 to 2.1. (For the ten-year Treasury bond rate, serial correlation fell from 1.0 to 0.71, and the standard error of regression rose from 0.28 to 1.1.) Testing for the expected increase in the interest elasticity of the empirical money demand equation is made much harder by the well known difficulties of estimating this equation at all. Cooley and Leroy (1981, p. 543) have gone so far as to suggest that ‘the negative interest elasticity of money demand reported in the literature represents prior beliefs much more than sample information’. We make no claim to solving this general problem of specification and estimation. Indeed, the ‘non-structurality’ of the equation is an important reason for our testing for a shift in the interest elasticity in response to a change in policy regime: if the estimated elasticity represented consumer tastes alone, there would be no reason to expect any such shift. We propose, therefore, to test fairly standard specifications of the money demand equation, with some variation to indicate the robustness of our results. Our basic specification - the ‘Goldfeld equation’ - is the one seen most frequently in the money demand literature (perhaps because it yields the interest elasticity most in accordance with prior expectations). We use quarterly data from 1960.1 through 1983.11 and break the sample after the third quarter of 1979. Ml divided by the GNP deflator is used as the dependent variable and the three-month T-bill rate as the interest rate. 6
6 Our specification
differs
only in its omission
There has been no variation inclusion superfluous.
Estimation
the reported
All equations
equation.
sive procedure, The numbers
where p represents in parentheses
of the rate payable
in this rate in the post-October
on savings
deposits.
1979 period, thus making its
for the earlier period yielded no major deviations were estimated
the estimated
below the estimated
according
from
to a first-order
autoregres-
value of the serial correlation
coefficient.
parameter
values are t-statistics.
102
M. Kahn, J.M. Manchester / Policy evaluation and money demand
1960.1-1979.111 ln(MI/P)
p = 0.50,
= -0.18 +0.97[ln(MZ/P)]_, ( - 0.7) (22.0) .SSR = 0.0023,
R2 = 0.97,
+O.O291n(GNP/P) (2.6) DW=
1.95.
-O.OlSlni,,,. (- 3.4) (5)
(5 .O) 1979.IV-1983.11 ln(MI/P)
p=
-0.36, (-1.4)
= -0.63 +0.80[ln(MI/P)]_, ( - 0.9) (5.5) SSR = 0.0022,
z2 = 0.97,
+0.341n(GNP/P) (1.2) DW=
2.43.
-O.O501ni,,,. (- 3.3) (6)
Note that the estimated interest elasticity is almost three times larger for the second period. The difference in estimated coefficients turns out to be just significant at the 5% level. ’ To test for the robustness of these results we reestimated using a variety of different specifications. In general we found weak confirmation that the interest elasticity had indeed increased. Imposing a unitary income elasticity in the equation makes the rise in interest elasticity more pronounced. ’ In addition, we tested a nominal MI specification that yielded a small but insignificant increase in the interest elasticity. This was also true of the results for various specifications for M2. The interest elasticity using real A42 deflated by real GNP and the rate on long-term Treasury bonds showed a ten-fold increase over the two subperiods, but neither coefficient was statistically significant. To test whether the shift in elasticity after 1979:111 was ‘special’ or merely the reflection of a generally unstable equation, we estimated the equation with twelve different breakpoints from 1963.IV to 1978.IV using fifteen quarters of data both before and after the breakpoint. We found a large increase in interest elasticities from the early 1960’s to the middle of
’ The t-value is 1.99 with 86 d.f. * From - O.OOlS(- 0.3) to - 0.0531( - 4.6). The t-value for the difference is 4.1 with 88 d.f.
M. Kahn, J.M. Manchester
/ Policy evaluation and money demand
103
the decade, a sharp decline in both the magnitude and significance of the interest elasticity from the late 1960’s through the late 1970’s, and then the sharp
increase
explanation
in the elasticity
for the large elasticities
as reported during
above.
No satisfactory
the mid-1960’s
although the hypothesis presented here does account increase during the post-October 1979 period.
is apparent,
for the observed
4. Conclusion We have found some support for the hypothesis that the interest elasticity has increased since the change in Fed operating procedures using a variety of money demand specifications. While the validity of the theory underlying money demand is acknowledged to be shaky, we wished to test the historical relationship between money and interest rates as a non-structural aggregate empirical relationship. In the standard ‘Goldfeld equation’ the estimated interest elasticity increased in magnitude in the fifteen quarters following October of 1979 as compared to the seventy-nine quarters prior to the policy change. This elasticity shift provides
further support
ships are sensitive
for the notion
to changes
that aggregate
empirical
relation-
in policy.
References Cooley, Thomas F. and Stephen F. Leroy, 1981, Identification and estimation of money demand, American Economic Review 71, Dec., 825-844. Duprey, James N., 1980, The search for a stable money demand function, Federal Reserve Bank of Minneapolis Quarterly Review, Summer, 5-14. Friedman, Milton, 1970, A theoretical framework for monetary analysis, Journal of Political Economy 78, March/April, 193-238. Goldfeld, Stephen M., 1976, The case of the missing money, Brookings Papers on Economic Activity 3, 683-730. Judd, John P. and John L. &adding, 1982, The search for a stable money demand function, Journal of Economic Literature XX, Sept., 993-1023. Keynes, John Maynard, 1936, The general theory of employment, interest, and money (Macmillan, London). Lucas, Robert E., Jr., 1981, Some international evidence on output-inflation tradeoffs, in: Studies in business-cycle theory (The MIT Press, Cambridge, MA) 131-145. Poole, William, 1982, Federal reserve operating procedures: A survey and evaluation of the historical record since October 1979, Journal of Money, Credit and Banking 14, part 2, Nov., 575-596. Walsh, Carl E., Interest rate volatility and monetary policy, Mimeo. (Princeton University, Princeton, NJ).
Economics Letters 16 (1984) 99-103 North-Holland
THE POLICY EVALUATION PROBLEM THE DEMAND FOR MONEY Meir
KOHN
Dartmouth
and
Joyce M. MANCHESTER
AND
*
College, Hanover, NH 03755, USA
Received 9 January 1984
This paper applies the Lucas policy evaluation proposition to the money demand function. We find some support for the hypothesis that the decrease in serial correlation of interest rates since the Fed policy change in 1979 has resulted in an increase in the estimated elasticity of money demand.
1. Introduction The policy evaluation proposition, first enunciated by Lucas (1981), states that observed aggregate empirical relationships are unlikely to be invariant to changes in policy regime. Much work has been done to examine the validity of this proposition as it relates to the Phillips curve. The purpose of the current paper is to examine its validity with respect to another important empirical relationship - the ‘money demand function’. The money demand function is a prime candidate for such an examination for three reasons. First, expectations are clearly important. A speculative element, dependent on expected changes in the rate of interest, played an important role both in the original formulation as stated by Keynes (1936) and, more recently, in the formulation suggested by Friedman (1970). Second, it is hard to claim that the estimated equation is ‘structural’ in the sense of Lucas: problems of identifying supply and demand and of deriving a precise specification from individual optimization behavior are frequently commented upon. 1 Third, a
* We would like to thank Colin Campbell for helpful comments on an earlier draft. 1 See, e.g., Cooley and Leroy (1981). 01651765/84/$3.00
0 1984, Elsevier Science Publishers B.V. (North-Holland)
100
M. Kahn, J.M.
Manchester
/ Policy
eualuatronand
money
demand
change in policy regime in October, 1979 provides us with a handy opportunity to test for a shift in the equation.
2. Theory A simple theoretical justification for the postulated shift would run as follows. * Money demand consists of a transactions demand, dependent on the level of economic activity, and a speculative demand, dependent on the expected change in the rate of interest. This could be written m, = ayt + P@,+,
(1)
- i,),
where m, is the level of real balances, y, a measure of income, i, the current market rate and (Ei,,, - i,) the ‘rationally’ expected change in the current market rate. 3 The first term on the right-hand side represents the transactions demand, the second term the speculative demand. The conditionally expected rate of interest may be written Ei
t+1
=
y.
+
xi,,
(2)
where y. may contain other time-t variables. Substituting (2) in (l), we obtain 4 m, = ayI + Pvo - PC1 - yi)i,. From eq. (3) we see that the observed interest elasticity of the ‘demand for money’ will be inversely related to the degree of serial correlation in interest rates. While the exact nature of the change in policy regime in October, 1979 is open to debate, 5 it does seem clear that greater weight has been given to stabilizing the rate of growth of monetary aggregates and less to stabilizing rates of interest. In terms of the very simple model presented here, the expected result would be a decrease in the serial correlation of interest rates and a resulting increase in the interest elasticity of the estimated money demand equation. ’ See Walsh (1983) 3 The ‘rational
4 See,e.g.,Judd
for a more thorough
expectation’
and Scadding
’ See Poole (1982)
treatment.
is the conditional (1982)
for an expanded
expected
or Duprey discussion.
(1980).
value given information
at time
t.
M. Kahn, J.M. Manchester
/ Policy evaluation and money demand
101
3. Estimation
We need to establish first that, whatever the nature of the change in policy in October, 1979, there has been a major increase in volatility of interest rates. We estimated the autoregressive equation
for the subperiods from 1960.1 through 1979.111 and from 1979.IV through 1983.11. Using the three-month Treasury bill rate, the serial correlation coefficient yi fell from 0.99 to 0.65, and the standard error of regression increased from 0.59 to 2.1. (For the ten-year Treasury bond rate, serial correlation fell from 1.0 to 0.71, and the standard error of regression rose from 0.28 to 1.1.) Testing for the expected increase in the interest elasticity of the empirical money demand equation is made much harder by the well known difficulties of estimating this equation at all. Cooley and Leroy (1981, p. 543) have gone so far as to suggest that ‘the negative interest elasticity of money demand reported in the literature represents prior beliefs much more than sample information’. We make no claim to solving this general problem of specification and estimation. Indeed, the ‘non-structurality’ of the equation is an important reason for our testing for a shift in the interest elasticity in response to a change in policy regime: if the estimated elasticity represented consumer tastes alone, there would be no reason to expect any such shift. We propose, therefore, to test fairly standard specifications of the money demand equation, with some variation to indicate the robustness of our results. Our basic specification - the ‘Goldfeld equation’ - is the one seen most frequently in the money demand literature (perhaps because it yields the interest elasticity most in accordance with prior expectations). We use quarterly data from 1960.1 through 1983.11 and break the sample after the third quarter of 1979. Ml divided by the GNP deflator is used as the dependent variable and the three-month T-bill rate as the interest rate. 6
6 Our specification
differs
only in its omission
There has been no variation inclusion superfluous.
Estimation
the reported
All equations
equation.
sive procedure, The numbers
where p represents in parentheses
of the rate payable
in this rate in the post-October
on savings
deposits.
1979 period, thus making its
for the earlier period yielded no major deviations were estimated
the estimated
below the estimated
according
from
to a first-order
autoregres-
value of the serial correlation
coefficient.
parameter
values are t-statistics.
102
M. Kahn, J.M. Manchester / Policy evaluation and money demand
1960.1-1979.111 ln(MI/P)
p = 0.50,
= -0.18 +0.97[ln(MZ/P)]_, ( - 0.7) (22.0) .SSR = 0.0023,
R2 = 0.97,
+O.O291n(GNP/P) (2.6) DW=
1.95.
-O.OlSlni,,,. (- 3.4) (5)
(5 .O) 1979.IV-1983.11 ln(MI/P)
p=
-0.36, (-1.4)
= -0.63 +0.80[ln(MI/P)]_, ( - 0.9) (5.5) SSR = 0.0022,
z2 = 0.97,
+0.341n(GNP/P) (1.2) DW=
2.43.
-O.O501ni,,,. (- 3.3) (6)
Note that the estimated interest elasticity is almost three times larger for the second period. The difference in estimated coefficients turns out to be just significant at the 5% level. ’ To test for the robustness of these results we reestimated using a variety of different specifications. In general we found weak confirmation that the interest elasticity had indeed increased. Imposing a unitary income elasticity in the equation makes the rise in interest elasticity more pronounced. ’ In addition, we tested a nominal MI specification that yielded a small but insignificant increase in the interest elasticity. This was also true of the results for various specifications for M2. The interest elasticity using real A42 deflated by real GNP and the rate on long-term Treasury bonds showed a ten-fold increase over the two subperiods, but neither coefficient was statistically significant. To test whether the shift in elasticity after 1979:111 was ‘special’ or merely the reflection of a generally unstable equation, we estimated the equation with twelve different breakpoints from 1963.IV to 1978.IV using fifteen quarters of data both before and after the breakpoint. We found a large increase in interest elasticities from the early 1960’s to the middle of
’ The t-value is 1.99 with 86 d.f. * From - O.OOlS(- 0.3) to - 0.0531( - 4.6). The t-value for the difference is 4.1 with 88 d.f.
M. Kahn, J.M. Manchester
/ Policy evaluation and money demand
103
the decade, a sharp decline in both the magnitude and significance of the interest elasticity from the late 1960’s through the late 1970’s, and then the sharp
increase
explanation
in the elasticity
for the large elasticities
as reported during
above.
No satisfactory
the mid-1960’s
although the hypothesis presented here does account increase during the post-October 1979 period.
is apparent,
for the observed
4. Conclusion We have found some support for the hypothesis that the interest elasticity has increased since the change in Fed operating procedures using a variety of money demand specifications. While the validity of the theory underlying money demand is acknowledged to be shaky, we wished to test the historical relationship between money and interest rates as a non-structural aggregate empirical relationship. In the standard ‘Goldfeld equation’ the estimated interest elasticity increased in magnitude in the fifteen quarters following October of 1979 as compared to the seventy-nine quarters prior to the policy change. This elasticity shift provides
further support
ships are sensitive
for the notion
to changes
that aggregate
empirical
relation-
in policy.
References Cooley, Thomas F. and Stephen F. Leroy, 1981, Identification and estimation of money demand, American Economic Review 71, Dec., 825-844. Duprey, James N., 1980, The search for a stable money demand function, Federal Reserve Bank of Minneapolis Quarterly Review, Summer, 5-14. Friedman, Milton, 1970, A theoretical framework for monetary analysis, Journal of Political Economy 78, March/April, 193-238. Goldfeld, Stephen M., 1976, The case of the missing money, Brookings Papers on Economic Activity 3, 683-730. Judd, John P. and John L. &adding, 1982, The search for a stable money demand function, Journal of Economic Literature XX, Sept., 993-1023. Keynes, John Maynard, 1936, The general theory of employment, interest, and money (Macmillan, London). Lucas, Robert E., Jr., 1981, Some international evidence on output-inflation tradeoffs, in: Studies in business-cycle theory (The MIT Press, Cambridge, MA) 131-145. Poole, William, 1982, Federal reserve operating procedures: A survey and evaluation of the historical record since October 1979, Journal of Money, Credit and Banking 14, part 2, Nov., 575-596. Walsh, Carl E., Interest rate volatility and monetary policy, Mimeo. (Princeton University, Princeton, NJ).