the monetary approach to exchange rate …
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Journal of International Economics 18 (1985) I-16. North-Holland
THE MONETARY APPROACH TO EXCHANGE RATE DETERMINATION UNDER RATIONAL EXPECTATIONS
The dollar-deutschmark rate
Wing T. WOO* Economic Studies Program, The Brookings Institution, Washington, Dc\.@O36, USA
Received August 1983, revised version received March 1984
This paper reformulates the monetary approach after ascertaining that a money demand function with a partial adjustment mechanism had more empirical support than a money demand function which assumed instantaneous stock adjustment. The resulting exchange rate equation is estimated by two rational expectations techniques. The parameter estimates are reasonable, and are robust to the estimation technique used, to dilferent specifications of the driving processes, and to changes in the estimation period. The structural model outperforms the random walk model and its own unconstrained equivalent, a pure time series equation, in out- of-sample forecasts.
1. Introduction
This paper begins from the work of Goldfeld (1973) on the short-run money demand function. We suspect that the inability of four recent studies [Frankel (1980), Dornbusch (1981), Hartley (1981), Woo (1981)] to find empirical support for the monetary approach to exchange rate determination may be due to an inappropriate specification of the money demand function.’ Section 2 of this paper reviews several studies of money demand function which incorporated partial adjustment behavior. Section 3 derives the exchange rate equation, and section 4 estimates this exchange rate equation in three ways and finds that the same results were obtained in each case. Section 5 compares the out-of-sample forecasts of our exchange rate equation, the random walk model and the unconstrained version of our exchange rate equation. The monetary exchange rate equation has a smaller
*I thank Jeffrey Sachs, Benjamin Friedman and Hendrik Houthakker for comments on an earlier draft, and Mark Watson and Thomas Sargent for econometric guidance. The referee’s and co-editor’s comments were very helpful in revising this paper. I alone am responsible for the remaining errors. Opinions expressed here are solely those of the author and should not be attributed to any other person affiliated with the Brookings Institution. I am grateful to the Sloan Foundation, National Bureau of Economic Research and Data Resources, Inc. for computation support, and to Anita Whitlock for the superb typing job.
‘In the. case of Dornbusch and Frankel papers, an additional reason may be the use of inappropriate estimation techniques. Hartley’ and Woo used rational expectations estimation techniques.
0022-1996/85/$3.30 @ 1985, Elsevier Science Publishers B.V. (North-Holland)
2 W?Y Woo, Exchange rate determination
RMSE and MAE than the random walk model which Meese and Rogoff (1983) have shown to perform at least as well as a group of structural models. A summary of the main findings is presented in section 6.
2. The form of the money demand function
Since Goldfeld’s (1973) seminal paper on the U.S. short-run money demand function, we know that a lagged money term is needed in the specification to capture the partial adjustment in money holdings. Boughton (1981) has recently shown that Goldfeld’s specification holds for Canada, France, West Germany, the United Kingdom and Japan as well. The specified form is z =f(r, y) + az- i, where z is real balances and a < 1. Frenkel (1978) and Dornbusch (1981) considered the empirical importance of a monetary partial adjustment mechanism in their exchange rate equations and did not find support for it. On the other hand, Bilson (1978a, 1978b, 1979) found that it was vital to obtaining strong support for the monetary model. It should be noted, however, that none of the exchange rate equations in Bilson’s studies could be derived from a money demand function with partial adjustment in real balance holdings. Bilson defended the irrelevance of formally deriving an exchange rate equation from an explicit money demand function by claiming that ‘the particular form of the money demand function cannot be specified on theoretical grounds; it depends upon the particular relative price that is under study’ [Bilson (1979)]‘.
This pragmatic stance on a flexible translation from theoretical structure to empirical estimation may be legitimate in many circumstances. But in a case like ours, where agents are assumed to be rational, the theoretical motivation imposes strict conditions on every aspect of the empirical equation, e.g. the error term has to be explicitly motivated and not to be treated as an inconvenience or as an afterthought. Identification of plausible money demand parameters from an exchange rate equation is a prerequiste for the validity of the monetary approach. In Woo (1982) we found that money demand functions which assumed instantaneous stock equilibrium had no empirical basis in the monthly data for Germany and the United States. On the other hand, the Goldfeld specification gave statistically significant coefficient estimates which were in line with those from previous studies [summarized in Laidler (1977)]. Moreover, we found the Goldfeld specification to be stable over the period of our study, 1974:3 to 1981:10.3
‘Hodrick’s (1979) comments on Bilson’s (1979) study anticipated some of the points made in this paper.
30f particular concern here are the studies of Enxler, Johnson and Paulus (1976), Goldfeld (1976) and Boughton (1981) which indicated that there was a shift in the U.S. short-run money demand function in the 1970s. This means that the monetary exchange rate equation will not be indentiCed even if it were true. This apparent instability, however, is controversial; see Heller and Kahn (1979) and Friedman and Schwartz (1982). Even if a money demand function shift did
WT. Woo, Exchange rate determination 3
The results suggest to us that a fair testing of the monetary approach ought to be based on an empirically valid specification of the money demand function.
3. Deriving the exchange rate equation
On the basis of work in Woo (1982), we assume that the monthly money demand functions of the United States and Germany have the same interest rate semi-elasticity and the same partial adjustment coefficient. Hence we get:
-P(r,-r:)--CL(PI-l-P~-l)+(ar--*), (1)
where an asterisk denotes U.S., 4, p > 0, 0 <a < 1, and m, p, y are in logs. We interpret the term a, to be either technological innovation or portfolio disturbance, which is seen by the agent but not the econometrician. The hallmark of the monetary approach are the following two assumptions about the speed of arbitrage in goods markets and the nature of risk behavior in financial markets:
purchasing power parity, pI = p: + e,, (2)
uncovered interest parity, P, = r: + E(e, + 1 -e, 1 Cl,), (3)
where e is the log of the exchange rate. Substituting (2) and (3) into (I), and after some manipulation we get:
where
R=(l, -a, -4, +4*),
z: = (M,, M, - 12 Y,, Y3,
M,=m,-mm:,
EtW, + I) =EW, + l/Q,), i20,
(4)
occur, it may have taken place before the period we are studying. Hafer and Hein (1982) working with quarterly data reported: ‘The evidence.. . points to the existence of a significant, once-and-for-all downward level shift in the relationship in 11/1974.’ Only our lirst observation is before this date.
W7I Woo, Exchange rate determination
&,=a,-a:,
w,= -&, when E, is white noise,
w,= -p(i;-p)’ when E, = p E, - r + u,, u, is white noise.
Eq. (4), like the usual monetary exchange rate equation, emphasizes the notion that the current value of the exchange rate depends on expected future relative money supply and relative income level. It differs from the usual monetary equation in that a lagged exchange rate is included, and this lagged term comes from the sluggish adjustment in real balance holdings. The coefficient of this lagged exchange rate is not a free parameter but is an exact nonlinear function of a and p.
4. Estimation
It may appear that estimation is relatively straightforward because (4) can be rewritten as:
Y+- P a 1 1 e,=-l+p 1-l-p ~,(e,.,)+l+pel-~+l+B~~~-l+pE~. (5)
Since uncovered interest parity is assumed, the log of the observed forward rate at time t is identical to the unobserved E,(e, +,). Replacing E,(e,+,) in (5) with the forward rate, we can then estimate (5) by OLS. This straightforward method is unfortunately incorrect.
Direct estimation of (5) by OLS is incorrect because we had assumed in our theoretical motivation that agents (but not econometricians) observe E,, making E, E Q,. This means that E,(e, + r) is correlated with E, and when there is contemporaneous correlation between the regressor and the error term OLS estimation is inconsistent.4
4Bilson (1979) was aware of this point, and he suggested that ‘it is likely that movements in the exogenous variables dominate the determination of the forward premium so that the elTect of the bias is small’. A consistent single equation estimation procedure is given in McCallum (1979), it is, however, less elhcient than the techniques used here.
WT. Woo, Exchange rate determination 5
We estimate the relationship embodied in (5) by two techniques which we call the exogenous technique and the endogenous technique.5 Both tech- niques may look formally similar but they are very different in motivation.6
4.1. Estimation using the exogenous technique
We assume the forcing variables, Z,, to be characterized by ‘a vector, covariance stationary, linearly indeterministic stochastic process’ [I thank Hansen and Sargent (1981) for this delightful phrase]:
Z,=AZ,-,+u, (6)
where A=A,+A,L+A2L2+A3L3+ . . . and E(u,) =O, and E(u,u,) =0 for s # t. Then the exchange rate equation takes the form:’
e,=cn+c,e,_,+DZ,_,+u,, (7)
where D=D,+D,LfD2L2+d,L3= . . . . To ensure that the stationarity assumption is fulfilled, the usual practice is
to prefilter the entire data set in some way. We adopt the method in Sargent (1978b): we. regress each variable ‘on a constant, trend, and trend squared terms, and use the residuals as the data. The general form of the system to be estimated is:
Y,=CbiM,-i+Cb,+iy,-i+~bzn+iy,*_i+u,G,
y:=~CiM,-i +CC,+i Yt-i +zC2n+i Y;“-i +$“3 (8)
The cross-equation constraints implied by the joint assumption of rational expectations and monetary approach are:*
~Gbj-~“Scj-&d7bi+di3c~+di+I)+ l+P+JiiT+Qd +g
2 I i Ui =
(1 +PdJ ,
for i=1,2,3,4,5,7;8,9,10,11,13,14,15,16; wheren=6; (9) 5The choice of the terms ‘exogenous’ and ‘endogenous’ here is inspired by Sargent (1978a)
who, to our knowledge, was the first to use these two techniques together but was too modest to bequest a name on them.
6Woo (1982) discusses the differences in motivation in greater detail. ‘See Woo (1982) for derivation. sThe number of lags for M, y and y* are assumed to be six, six and five, respectively.
WT Woo, Exchange rate determination
g1=ff, g,=O, for i>l;
~Gbj-~USCj-(d,bj+d13Cj)+ l+p+Jmd
2 i Oj =
(1 +M) ,
for j = 6,12,17.
Sims (1980) pointed out that the usual likelihood ratio test statistic has a bias against the null hypothesis and suggested the use of a modified form of the statistic; we will report both the usual and the modilied form of the chi- square statistic.
Part 1 of table 1 shows the results of the Full Information Maximum Likelihood (FIML) estimation. We find that:
(1) The restrictions in (9) cannot be rejected. (2) All the money demand parameters have the expected signs and are of
plausible magnitudes. The average call money rate over the period of estimation for the United States and Germany were 0.094 and 0.062, respectively; the long-run short-term interest elasticity, (p/(1 -a))*rnvB, is hence between 0.399 and 0.607. Laidler (1977) estimated the U.S. long-run short-term interest elasticity to be between 0.17 to 0.20 and the U.S. long-run long-term interest elasticity to be between 0.5 and 0.8. Since our money demand specification does not include a long rate, this may be why our short rate of interest elasticity is between the two ranges of values.
(3) ,l, is less than unity and 1, to be greater than unity, a finding which is reassuring.
In the money demand studies reviewed in section 2, correction for tirst- order serial correlating was necessary in every case. Part 2 of table 1 reports the re-estimation of the preceding exchange rate equation with serial correlation correction. The results are almost the same as in part 1, showing that the parameter estimates are stable for small changes in specification. The estimated 1, and A2 again ‘have the expected magnitudes. The observed autocorrelation of the combined money demand function is not found in the exchange rate equation.
4.2. Estimation using the endogenous technique
The endogenous technique does not need to first derive an exchange rate equation as we did in section 3. We start by formulating a totally general representation of all the processes that we are interested in. We represent (Z,, et) by:
Z,=AZ,-,+Be,_,+u,, (10)
e,=c,+CZ,-,+4e,-,+u,, (11)
W!T Woo, Exchange rate determination
Table 1 Testing the amended monetary approach: The exogenous technique (estimation
period 1974:3 to 1981:lO). Part 1: No correction for serial correlation
x2(14) = 17.0, Modified x2(14) = 13.766,
Coefficient
Marginal significance = 0.256 Marginal significance = 0.467 SD. t-statistic
PO 1.2964 0.5935 2.1844 $“, 0.5924 0.3466 0.2851 0.408 1 1.2156 1.4518
Ii
1:
0.7991 0.7996 0.0875 0.2876 9.1380 2.7787
2.1716 2.0844 1.0447
Part 2: Correction of tirst-order serial correlation
x2( 14) = 16.44, Modilied x2( 14) = 13.268,
Marginal significance = 0.287 Marginal significance=0.506
Coellicient S.D. t-statistic
ti 1.2223 0.438 2.789 Z”S 0.4713 0.2867 0.325 0.232 1.234 1.449
a 0.8570 0.213 4.032
z -0.1211 0.8294 0.111 0.195 - 2
0.622 7.502 1.8869 1.459 1.293
where A, B, C, D are lag operators of the form X=X0 + X1L+X,L2 + . . . and (u,, u,) are white noises and are orthogonal to all positive lags of 2, and e,. Note that (11) is not derivable from (5) and (lo), unlike (7) which is derived from (5) and (6). Eqs. (10) and (11) should be interpreted as optimal forecasts of 2, and e, upon the information set sZ,- r =(Z, -r,. . . ,Zt-“, e,- r,. . . , e,-,). The cross-equation constraints imposed by eq. (5) on eqs. (10) and (11) are:’
a,-4Gbi-4 “SCi-P(d~bi+d,,ci+di+~)+(l+P-~dl~)di+ki I-
(1 +W 2
fori=1,2,3,4,5,7,8,9,10,13,14,15,16,18,19,20;
kI=a, k18= -a all other ki’S=O;
a =9Gbj-4 “SCi-P(d,bi+d,,Ci)+(1+B-Bd,8)di j
(1 + WA ,
j=6,12,17,21.
‘The number of lags assumed for M, y, y* and e are six, six, live and four, respectively. Coetlkients a, 6, c and d refer to the M, y, y* and e equations, respectively, similar to eq. (8).
a WT Woo, Exchange rate determination
Part 1 of table 2 reports the results of the estimation using the endogenous method. The parameter estimates are in every case within two standard deviations from those in table 1. The troubling part of the results in table 2 is that LY is geater than 1, implying that the postulated partial adjustment mechanism may be questionable even though u is insignificantly different from 0.8. We decided to use a Monte Carlo method to study the value of IX estimated by the endogenous method as we have need to use rolling estimation for the out-of-sample forecasting exercise in section 5. We used a shortened version of the VAR (described in section 5) and estimated the constrained VAR over different sample periods. The estimated values of CI are reported in part 2. Since u is always less than unity and insignificantly different from 0.8, we suspect that the value of u in part 1 is at the upper end of a distribution whose expected value is less than unity.
Table 2 Testing the amended monetary approach: Endogenous technique.
Part 1: 197413 to 1981:lO
~2(17)=21.54, Moditied x2(17)= 16.565,
CoeNicient
Marginal significance = 0.203 Marginal significance =0.484 SD. t-statistic
2.1983 1.6130 1.3628 0.0948 0.5246 0.1808 0.3312 0.4157 0.7968
a 1.0804 0.1681 6.4263
Part 2: Estimated values of a by the endogenous method from the reduced VAR
Period of estimation a S.D. t-statistic
19742 to 1980~2 0.9556 0.125 7.643 1974~2 to 1980:3 0.9594 0.120 7.986 19742 to 1980:4 0.9610 0.109 8.778 19742 to 1980:5 0.9480 0.126 7.519 19742 to 1980:6 0.9558 0.110 8.652 19742 to 1980:7 0.9404 0.125 7.496 197412 to 1980~8 0.9434 0.119 7.927 19742 to 198019 0.9419 0.109 8.614 19742 to 1980~10 0.9426 0.109 8.614 1974~2 to 1980~11 0.9427 0.109 8.654 19742 to 1980~12 0.9437 0.108 a.719 19742 to 1981:l 0.9255 0.115 8.068 19742 to 1981:2 0.9239 0.112 8.263 1974~2 to 1981:3 0.9242 0.108 8.560 19742 to 1981:4 0.9208 0.118 7.817 197412 to 1981:s 0.9323 0.114 8.210 197412 to 1981:6 0.9262 0.110 8.421 19742 to 1981:7 0.9324 0.111 8.376 19742 to 1981:8 0.9298 0.105 8.820 19742 to 1981:9 0.923 1 0.107 8.665 1974:2 to 1981:lO 0.9227 0.103 8.944
MT Woo, Exchange rate determination 9
To check the robustness of the results reported in tables 1 and 2, we reduced the number of lags in the driving process and the VAR (as in section 5) an re-estimated the model over the same period (see table 3). In every case the restrictions implied by rational expectations cannot be rejected by the modified likelihood ratio test. The less satisfactory coefficient estimates from the endogenous technique may be because the reduction in the number of lags has given us inadequate representation of the (Z,,e,) processes.
In work not reported here, we found that our estimation results are robust to all the periods of estimation in part 2 of table 2, and that the 2, process [i.e. eq. (6)] and the VAR [i.e. eqs. (10) and (1 l)] are stable across subperiods. The latter finding is pertinent in light of the Lucas critique.
Table 3 Parameter estimates of the reduced model: 19743 to 1981:10.
Exogenous method
Coeff. t-stat.
Exogenous method with autocorrelation correction
Coe& t-stat.
Endogenous method
CoelY. t-stat.
a P Chi-square Marginal significance Modified chi-square Marginal significance
1.3160 2.2799 0.6226 1.7206 0.3662 1.5504 0.7880 2.7960
x2( 10) = 10.34 0.411
x2(10)=8.82 0.549
1.2295 2.9539 0.4834 1.6032 0.2961 1.5194 0.8533 4.0401
-0.1347 -0.8312 x2( 10) = 10.22
0.421 x*(10)=8.69
0.562
0.4719 0.6590 0.4107 1.1074 0.1749 0.8946 0.9246 9.0298
x2( 11) = 20.68 0.037
x2( 11) = 17.25 0.101
5. Out-of-sample forecasting
We performed twb sets of out-of-sample forecast comparisons. The first set was inspired by a recent paper of Meese and Rogoff (1983) who compared the out-of-sample ‘static’ simulation forecasts of several structural models against a random walk model. lo The results were startling: the random walk model was superior. This rightly establishes the random wa1.k model as a benchmark with which to compare structural models.”
We used the last twenty observations in our sample, 1980:3 to 1981:10, for the out-of-samplk forecast comparison with random walk model. To ensure adequate degrees of freedom in the estimations using the smaller sample, we moved the period of estimation back by one period, and reduced the number
loSee footnote 12. “We found our filtered exchange rate series to be best characterized by a random walk
process (results omitted here). The RMSE and MAE reported here are independent of our filtering method. We only have to add the same deterministic component to all the series in order to arrive at the ‘original’ level.
10 bVT Woo, Exchange rate determination
of lags for M from six to five, for yG from six to four and for yus from live to four. In using the endogenous method we decreased the number of lagged exchange rates from four to two. As our structural equation has at least one lagged exchange rate on the right-hand side, static simulation would bias the results in our favor. We did a partial dynamic simulation and a full dynamic stimulation to compare the forecasts of our model with those of the random walk model. In partial dynamic simulation only values of exchange rate generated by the simulation are used on the right-hand-side, while realized values of the other right-hand-side variables are used.12 In full dynamic simulation, all values of the right-hand-side variables are generated by the simulation. We used rolling estimation to generate out-of-sample two-, three- four-, six- and twelve-month ahead forecasts.
The results of the two dynamic simulations are almost identical, see tables 4 and 5. The structural model outperforms the random walk model in every case under the mean-absolute-error (MAE) criteria. Only in the full dynamic simulation is there one instance where the random walk model is better by the root-mean-squared-error (RMSE) criteria. It seems fair to say that our structural model gives smaller MAE and RMSE than the random walk model in out-of-sample forecasts of the dollar-mark rate over the period covered by this study. It must be emphasized that our results in no way overturn the findings of Meese and Rogoff. Their study is much more comprehensive, as it covers three bilateral exchange rates and an effective exchange rate.
In the second set of out-of-sample forecast comparisons, we used the forecasts of the unconstrained versions of our structural model. This is because we expect a true model to outforecast its unconstrained equivalent, i.e. a pure time series equation, for all time horizons if the sample size is large. The structural model is the better predictor for horizons of less than six months ahead. After that, the unconstrained time series equation is superior, see tables 4 and 5. This inconsistent performance indicates either that the model is false or that the sample size for the long forecast horizon is too small to permit valid comparisons:The error statistics for the two-step ahead forecasts were computed from nineteen observations, while those of the twelve-step ahead forecasts were from only nine observations. We think that the inconsistent performance is due to the second reason.
To see this, note that our structural model differs from the unconstrained time series equation only in parameters and not in the right-hand-side variables. The results in tables 4 and 5 are due to two differences: different parameters and different values for the same set of right-hand-side variables. To isolate the difference in forecast performance due only to the cross- equation restrictions, we subjected the two equations to static simulation.
% the terminology used here, the Meese-RogoK’ simulations are partially dynamic because their structural models have serially correlated errors.
Table
4
Out-o
f-sam
ple
parti
al dy
nam
ic sim
ulat
ion.
2:
. . Y
2-m
onth
3-
mon
th
Cmon
th
6-m
onth
1Z
mon
th
4 .-
RMSE
M
AE
RMSE
M
AE
RMSE
M
AE
RMSE
M
AE
RMSE
M
AE
B xb
Rand
om w
alk
0.05
85
0.04
94
0.07
66
0.06
69
0.09
55
0.08
16
0.13
54
0.12
21
0.25
54
0.24
43
%
Stru
ctur
al
equa
tion
estim
ated
by:
E 2
Exog
enou
s te
chniq
ue
0.05
33
0.03
94
0.06
79
0.04
68
0.07
91
0.05
55
0.09
41
0.07
27
0.12
34
0.10
85
Exog
enou
s te
chniq
ue w
ith
a 0 au
toco
rrelat
ion
corre
ctio
n 0.
0527
0.
0401
0.
0670
0.
0489
0.
0785
0.
0572
0.
0960
0.
0767
0.
1301
0.
1178
R-
En
doge
nous
te
chniq
ue
0.05
00
0.03
81
0.06
27
0.04
74
0.07
20
0.05
33
0.08
53
0.06
92
0.11
34
0.10
20
E 3 Un
cons
train
ed
vers
ion
of e
quat
ion
estim
ated
by:
=.
Ex
ogen
ous
tech
nique
0.
0543
0.
0432
0.
0682
0.
0510
0.
0813
0.
0628
0.
0953
0.
0761
0.
1133
0.
0998
s P
Exog
enou
s te
chniq
ue
with
s
auto
corre
lation
co
rrect
ion
0.05
32
0.04
14
0.06
77
0.05
16
0.08
08
0.06
16
0.09
69
0.07
75
0.11
73
0.10
47
Endo
geou
s te
chniq
ue
0.05
26
0.04
14
0.06
77
0.05
17
0.08
13
0.06
16
0.09
96
0.08
01
0.12
08
0.10
89
t
Table
5
Out-o
f-sam
ple
full
dyna
mic
simul
atio
n.
2-mo
nth
3-m
onth
Cm
onth
6-
mon
th
12-m
onth
RMSE
M
AE
RMSE
M
AE
RMSE
M
AE
RMSE
M
AE
RMSE
M
AE
Rand
om
walk
0.05
85
0.04
94
0.07
66
0.06
69
0.09
55
0.08
16
0.13
54
0.12
21
0.25
54
0.24
43
Stru
ctur
al
equa
tion
estim
ated
by:
Ex
oaen
ous
tech
niaue
0.
0573
0.
0422
0.
0770
0.
0554
0.
0922
0.
0705
0.
1137
0.
0907
0.
1408
0.
1361
Ex
ogen
ous
tech
nique
wi
th
auto
corre
lation
co
rrect
ion
0.05
66
0.04
28
0.07
58
0.05
62
0.09
09
0.06
96
0.11
33
0.09
21
0.14
86
0.14
46
Endo
geno
us
tech
nique
0.
0550
0.
0417
0.
0741
0.
0543
0.
0903
0.
0691
0.
1166
0.
0969
0.
1589
0.
1532
Un
cons
train
ed
vers
ion
of e
quat
ion
estim
ated
by:
Ex
ogen
ous
tech
nique
0.
0566
0.
0447
0.
0785
0.
0591
0.
0957
0.
0751
0.
1189
0.
0926
0.
1220
0.
1132
Ex
ogen
ous
tech
nique
wi
th
auto
corre
lation
co
rrect
ion
0.05
56
0.04
30
0.07
74
0.05
86
0.09
34
0.07
32
0.11
07
0.08
58
0.12
36
0.11
57
Endo
geno
us
tech
nique
0.
0546
0.
0427
0.
0763
0.
0576
0.
0917
0.
0707
0.
1093
0.
0859
0.
1341
0.
1243
WIT Woo, Exchange rate determination 13
The out-of-sample forecasts of the constrained equation are better than those of the unconstrained equation for all horizons, see table 6.
6. Conclusion
In this paper we have used the existing empirical literature on the short- run money demand function to reformulate the monetary approach. We have provided what we deem to be reasonable evidence in support of the reformulated monetary approach.
We satisfied all the usual statistical requirements: (1) The null hypothesis that the cross-equation constraints implied by the
reformulated monetary approach are true cannot be rejected. (2) The elasticity estimates from the constrained FIML estimation are in
general agreement with those from the OLS estimation of the monthly money demand functions reported in Woo (1982). The same parameter from the two different estimation techniques agree on the degree of statistical significance in every case. All the parameter estimates have the correct signs and are of plausible magnitudes.
(3) The FIML results are stable across changes in the specification of the model.
It appears that the monetary model is still alive. This is somewhat surprising since there exists quite’ convincing evidence that two of its building blocks - purchasing power parity and interest rate parity - are not true [see Frenkel (1980) and Cumby and Obstfeld (1982)]. Presumably, the best defense for the reformulated monetary approach in the face of these contradictory findings is to appeal to a positive methodology argument. And if so, the better prediction of the structural model over its unconstrained time series equivalent lends additional support to the monetary model.
Description of data
e: Exchange rate, DM per US& end of period figures. Series are from January 1982 IFS tape.
G. Y * German industrial production index (1975 = loo), period average, seasonally adjusted. Series 66c from January 1982 IFS tape. The value for February 1981 was not available; we used the average of the January and March figures for it.
US. Y * U.S. industrial production index (1975 = loo), period average, season- ally adjusted. Series 66c from January 1982 IFS tape.
mG: Adjusted German Ml, billions of DM, end of period, seasonally adjusted. Series 34b from January 1982 IFS tape.
mUS: Adjusted US Ml A, currency plus demand deposits plus travellers checks, billions of dollars, average of daily figures, seasonally adjusted.
Table
6
Out-o
f-sam
ple
stat
ic sim
ulat
ion.
l-mon
th
2-m
onth
3-
mon
th
Cmon
th
Fore
cast
hor
izon
RMSE
M
AE
RMSE
M
AE
RMSE
M
AE
RMSE
M
AE
Stru
ctur
al
equa
tion
estim
ated
by:
Ex
ogen
ous
tech
nique
0.
0412
0.
0297
Ex
ogen
ous
tech
nique
with
au
toco
rrelat
ion
corre
ctio
n 0.
0423
0.
0315
En
doge
nous
te
chniq
ue
0.04
03
0.03
00
Unco
nstra
ined
ve
rsio
n of
equ
ation
es
timat
ed b
y:
Exog
enou
s te
chniq
ue
0.04
24
0.03
21
Exog
enou
s te
chniq
ue w
ith
auto
corre
lation
co
rrect
ion
0.04
31
0.03
28
Endo
geno
us
tech
niue
0.04
34
0.03
30
0.03
63
0.02
66
0.03
51
0.02
56
0.03
57
0.02
57
0.03
69
0.02
81
0.03
72
0.02
78
0.03
80
0.02
80
0.03
50
0.02
59
0.03
43
0.02
54
0.03
49
0.02
55
o.o4
oo
0.03
04
0.03
80
0.02
90
0.03
90
0.03
08
0.03
94
0.03
08
0.03
98
0.03
06
0.04
07
0.03
18
0.03
89
0.03
07
0.03
93
0.03
07
0.04
01
0.03
82
6-m
onth
1Z
mon
th
2 RM
SE
MAE
RM
SE
MAE
3 ? h
0.03
73
0.02
75
0.04
43
0.03
26
z z 0.
0401
0.
0309
0.
0478
0.
0383
4
0.03
60
0.02
67
0.04
11
0.03
14
2 l-2
4.
0.04
07
0.03
30
0.04
55
0.03
85
z 9.
0.04
27
0.03
42
0.04
92
0.04
08
3 0.
0420
0.
0341
0.
0491
0.
0409
E.
9
PG:
pus.
rG:
ps.
WT. Woo, Exchange rate determination 15
FRS Statistical Release H.6 and the Federal Reserve Bulletin. (Month- ly data for Series 34b is incomplete on IFS tape.) Wholesale prices: Industrial Index (1975 = loo), period average. Series 63 from January 1982 IFS tape. Wholesale price index (1975= loo), period average. Series 63 from January 1982 IFS tape. Call money rate, period average. Series 60b from January 1982 IFS tape. Federal Funds rate, period average. Series 60b from January 1982 IFS tape.
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16 WT. Woo, Exchange rate determination
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