Silviase/jgov_v1.4_full_ann huggingface dataset:
3.6 Different Specifications for the Money Demand Function for the Philippines

We found out that the interest rate variable in the money demand function was entirely insignificant for the Philippines. Two interpretations may be possible: first, the yields of TB may not be relevant interest rate variable for the money demand function, so we may seek alternative measures of the interest rates for this economy. However, at this moment only the discount rate, lending rate, and deposit rate are available for this country. Among these yields, TB rate still seems to be the more appropriate interest rate variables. Second, as mentioned in the introduction of this chapter, other factors, such as substitution between money and real capital, foreign currency, and foreign bonds may be relevant for this economy.

Okuda (1991) estimated the money demand function for the Philippine economy using annual data. He estimated money demand function, using both M1 and quasi-money, explicitly taking into account of considerations mentioned above; he incorporated actual inflation rate and nominal yields of U.S. treasury bills in the money demand function.

However, we constructed the expected inflation rates, calculated by the AR model for the inflation rate process. This expected inflation rates were taken to be a relevant variable for the consideration of the substitution between money and the real assets. $ ^{23} $ Furthermore, to capture the substitution between domestic money and foreign currency, the expected rate of change of the exchange rate is formulated, using the estimated AR model for the exchange rate process. Finally, the expected rates of return for U.S. TB, that is the yield of U.S. TB plus the expected appreciation in the foreign currency, were constructed to incorporate capital mobility. With these new variables, the money demand function was re-estimated and the estimated results are shown in Table 3.7. $ ^{24} $

According to these results, it turned out that only expected inflation rate was significant at the 5% level. This result is robust with the inclusion of the other variables, as shown in the table. Though our reestimation does not reveal statistical significance of the foreign variables in the money demand function, Cuddington (1983) also reports
### TABLE 3. 7: MONEY DEMAND FUNCTION FOR PHILIPPINE

COUNTRY	PERIOD	CONSTANT	GNP	M/P(-1)	EINF	EER	EUSTB	$ \rho $	$ \overline{R}^{2} $	DW
PHILIPPINE	1981:II - 1990:I
-.265	.322	.888	-.006	-.475	.998	1.978
(-.400)	(3.038)	(12.611)	(-2.461)	(-2.851)
.201	.334	.843	-.002	-.373	.997	1.939
(.267)	(2.472)	(10.378)	(-.677)	(-2.137)
.185	.322	.836	-.002	-.373	.997	1.930
(.245)	(2.848)	(10.603)	(-.728)	(-2.132)
-.517	.379	.884	-.008	.005	-.533	.999	1.996
(-.785)	(3.369)	(12.984)	(-2.728)	(1.216)	(-2.728)
-.438	.336	.895	-.007	.003	-.517	.999	1.995
(-.664)	(3.234)	(13.029)	(-2.612)	(.002)	(-3.138)

Notes: GNP=real GNP, INT=interest rate, M/P(-1)=lagged value of real money balance.

EINF=expected inflation rate, EER=expected rate of change of exchange rate.

EUSTB=expected rate of return of TB of the United States.

$ \overline{R}^{2} $ =adjusted $ R^{2} $ , DW=Durbin-Watson statistics.

Numbers in the parentheses indicate t values.
that inclusion of foreign assets produced rather disappointing results for U.K., Canada, U.S. and Germany; he only found slight evidence of capital mobility for U.S. and currency substitution for Germany.

However, whether this reflects substitution between money and real assets can still be questioned. The possible correlation between the expected rate of inflation and the expected rate of change for the exchange rate may simply explain the result. Furthermore, even if this result is convincing, then a more serious problem with the conduct of the monetary policy now comes in. It is easy to see that the transmission mechanism for the money supply in this result, is different from that of traditional money demand function. In any event, since our time series models used in this section are rather naive, our finding is not final.

### 3.7 LAG STRUCTURE OF MONEY DEMAND FUNCTION

So far in this chapter, the specification of the money demand function was justified by the partial adjustment hypothesis. However, this hypothesis has been criticized on many grounds. For example, the adjustment mechanism implicit in equation $ (3.6) $ will yield continuous under or over-prediction of short-run money demand over long-run money demand. $ ^{25} $ It is conceivable for speed of adjustment coefficient dependent on economic variables such as levels and/or variability of income and interest rate. Moreover, the symmetrical assumption in the cost function $ (3.2) $ can be questioned. It may be much more costly to be below the long run equilibrium position. Furthermore, compared with the cost function for the investment, the cost function in this context might lack solid microeconomic foundation. Though this framework incorporates divergence of the short-run money balances from the long-run equilibrium position, the disequilibrium adjustment in interdependent asset markets are ignored and so on. $ ^{26} $

It is well-known that the lag structure in the money demand function, such as (3.6), can be justified by the adaptive expectation mechanism as well. Let us briefly review the argument. Suppose that the long run money demand is determined by,

$$ \mathbf{M}_{\mathrm{t}}=\boldsymbol{\eta}_{\mathrm{y}}\mathbf{Y}_{\mathrm{t}}^{\mathrm{e}}-\boldsymbol{\eta}_{\mathrm{r}}\mathbf{r}_{\mathrm{t}} $$

That is, the long-run money demand is determined by the expected income, $ Y_{t}^{e} $ , and
nominal interest rate (regarding interest rate, no adaptive expectation mechanism is assumed here). Concerning the expectation formation, the adaptive expectation formation,

$$ \mathrm{Y}_{\mathrm{t}}^{\mathrm{e}}-\mathrm{Y}_{\mathrm{t}-1}^{\mathrm{e}}=\theta\mathrm{~(Y_{t}-Y_{t-1}^{\mathrm{e}})} $$

is assumed. Substituting $ (3.9) $ into $ (3.8) $ results in,

$$ \mathbf{M}_{\mathrm{t}}=\boldsymbol{\eta}_{\mathrm{y}}\boldsymbol{\theta}\mathrm{Y}_{\mathrm{t}}-\boldsymbol{\eta}_{\mathrm{r}}\mathbf{r}_{\mathrm{t}}+(1-\boldsymbol{\theta})\mathbf{r}_{\mathrm{t}-1}+(1-\boldsymbol{\theta})\mathbf{M}_{\mathrm{t}-1} $$

Unlike the case of the partial adjustment case, the lagged value of the interest rate enters the money demand equation in this specification of the adaptive expectation hypothesis. $ ^{27} $ Though, the adaptive expectation hypothesis is only optimal in somewhat restrictive circumstances, we rather focus its relationship with partial adjustment hypothesis.

It is well-known that including lagged value of the dependent variables in the money function greatly enhances the empirical tractability of the actual data. If equation $ (3.10) $ is a true money demand function, then the money demand function in the form of $ (3.6) $ would “work” well and vice versa. $ ^{28} $ The lag structure of the money demand function is loosely defended on the grounds of either the partial adjustment mechanism or the adaptive expectation hypothesis mentioned above. It is fair to say that the relationship between these two mechanism are not seriously focused. However, we cannot exclude the possibilities of coexistence of those two mechanism apri-ori. If coexistence happens to be the case, then the estimated money demand function based on solely one mechanism will surely have biased estimates. However, we rather take this largely ignored “mere” theoretical possibility in detail here because coexistence of two mechanism may shed the some new insight for the instability of the money demand function as well. It is in our interest to examine the possibility of co-existence of these mechanisms in detail for the four countries of our study.

In any case, combining these two hypotheses together consists of a system of
equations,

$$ \mathbf{M}_{\mathrm{t}}^{*}=\boldsymbol{\eta}_{\mathrm{y}}\mathbf{Y}_{\mathrm{t}}^{\mathrm{e}}-\boldsymbol{\eta}_{\mathrm{r}}\mathbf{r}_{\mathrm{t}} $$

$$ \mathrm{Y}_{\mathrm{t}}^{\mathrm{e}}-\mathrm{Y}_{\mathrm{t}-1}^{\mathrm{e}}=\theta\mathrm{~(Y_{t}-Y_{t-1}^{\mathrm{e}})} $$

$$ \mathbf{M}_{\mathbf{t}}-\mathbf{M}_{\mathbf{t}-1}=\gamma\left(\mathbf{M}_{\mathbf{t}}^{*}-\mathbf{M}_{\mathbf{t}-1}\right) $$

Substituting (3.12) and (3.13) into (3.11) results in a final nonlinear equation to estimate,

$$ \mathbf{M}_{\mathbf{t}}=\gamma\boldsymbol{\eta}_{\mathrm{y}}\theta\mathbf{Y}_{\mathbf{t}}-\gamma\boldsymbol{\eta}_{\mathbf{r}}(1-\theta)\mathbf{r}_{\mathbf{t}-1}+(2-\gamma-\theta)\mathbf{M}_{\mathbf{t}-1}-(1-\theta)(1-\gamma)\mathbf{M}_{\mathbf{t}-2} $$

This issue was first focused by Feige (1967). Equation (3.14) is interesting in the following senses; first if the true money demand function is indeed (3.14), then the popular reduced form money demand function,

$$ \mathbf{M}_{\mathbf{t}}=\boldsymbol{\delta}_{1}+\boldsymbol{\delta}_{2}\mathbf{Y}_{\mathbf{t}}+\boldsymbol{\delta}_{3}\mathbf{r}_{\mathbf{t}}+\boldsymbol{\delta}_{4}\mathbf{M}_{\mathbf{t}-1} $$

will have biased estimates. Moreover, the instability of the money demand function in the form of (3.15) could be related with the omitted variables, $ r_{t-1} $ and $ M_{t-2} $ . Second, the stability of the reduced form money demand function based on (3.14),

$$ \mathbf{M_{t}}=\boldsymbol{\delta}_{1}+\boldsymbol{\delta}_{2}\mathbf{Y_{t}}+\boldsymbol{\delta}_{3}\mathbf{r_{t}}+\boldsymbol{\delta}_{4}\mathbf{M_{t-1}}+\boldsymbol{\delta}_{5}\mathbf{M_{t-1}}+\boldsymbol{\delta}_{6}\mathbf{M_{t-2}} $$

can be analyzed in terms of the underlying parameters; long-run equilibrium coefficients of the money demand function, $ \eta_{y} $ , $ \eta_{r} $ , a short-run partial adjustment parameter $ \gamma $ and an expectation adjustment parameter $ \theta $ . In the context of the rational expectations hypothesis, it can be argued that the instability of the conventional form of the money demand function might be caused by the changes in the adaptive expectation coefficient, $ \theta $ , and/or changes in the speed of adjustment, $ \gamma $ , with other “structural” parameters being unchanged. Since this phenomenon is obviously related to the well-known Lucas critique, it is quite interesting to see if the mere theoretical possibility should be dismissed empirically. Since demand function (3.16) is due to changes in $ \eta_{y} $ , $ \eta_{r} $ or changes in $ \gamma $ and/or $ \theta $ , joint estimation of the income expectation generating equation and the money demand function, if fully implemented, may provide some insights on the stability issue. $ ^{[29]} $ Cuthbertson and Taylor (1990)
indeed estimated such a model, in spirit, for the U.S. data under the hypothesis of the rational expectation and the multi-period cost function. They examined the hypothesis that shifts in expectations formation function caused the instability of the money demand function, not the changes of the underlying long-run money demand function and the results seem to be promising. $ ^{30} $

In any event, since equation (3.14) is an over-identified equation, Feige estimated this equation for U.S. annual data from 1915-1963, using constrained nonlinear two-stage estimation procedure. He found the results, $ \gamma=1.091 $ , $ \theta=0.239 $ for M2. Hence instantaneous adjustment is concluded. However, Laidler and Parkin (1970) found two local maxima by searching over the values of $ \theta $ and $ \gamma $ in the range $ (0,1) $ for U.K. quarterly data. One maxima was with large value of $ \theta $ and small value of $ \gamma $ and the other was an opposite combination. They were in favor of short adjustment lags. Mayer and Neri (1975) also adopted searching method and found out both mechanism were operative for the annual U.S. data from 1897 to 1960. Furthermore, using maximum likelihood estimation method, Thornton (1982) also found out that both mechanism were operative, using U.S. quarterly data from 1952:2 to 1972:4. He revealed that inclusion of adaptive expectation, did increase, otherwise implausibly slow, adjustment of speed. In any event, as a first step, we also adopt the searching method to examine this equation in line with them.

The value of $ \gamma $ , the coefficient of partial adjustment is assumed to be 0.1, 0.2, ..... 0.9. Given those values, equation (3.14) is estimated by non-linear estimation method. Estimated results that maximized the log likelihood function were shown in Table 3.8. $ ^{31} $

For Japan, the adaptive expectation mechanism is not instantaneous for both periods. As in the standard analysis, the speed of adjustment is considerably slow. Interest rate elasticities are excessively high. Adaptive expectation coefficients are relatively high in the first period for Korea. However, the speed of adjustment is

structure revealed by, say, “error correction” models. See Cuthbertson and Taylor (1992) on this.
### TABLE 3.8 : MONEY DEMAND FUNCTION REVISITED

COUNTRY	PERIOD	LON RUN INCOME ELASTICITY	LOHG RUN INTEREST RATE ELASTICITY	COEFFICIENT OF EXECTAION ADJUSTMENT	COEFFICIENT OF PARTIAL ADJUSTMENT	ρ	R²	DW
JAPAN	1962:II-1973:I	1.036 (.017)	.532 (.104)	.688 (.104)	.1	.118	.998	2.484
JAPAN	1973:III-1990:I	1.043 (.008)	.535 (.076)	.720 (.1000)	.1	.13	.998	1.551
KOREA	1973:IV-1979:IV	1.064 (.076)	.249 (.204)	.881 (.162)	.5	.276	.963	2.283
KOREA	1980:II-1990:I	1.084 (.018)	.308 (.127)	.825 (.116)	.2	.231	.996	1.286
INDONESIA	1977:II-1983:IV	.862 (.094)	.123 (.219)	.604 (.153)	.1	.161	.986	1.723
INDONESIA	1983:II-1990:I	1.043 (.008)	.536 (.076)	.720 (.100)	.1	.282	.982	2.248

Notes: Numbers in the parentheses indicate standard error.
surprisingly high for this period. $ ^{32} $ For the second period, the results are similar to those of Japan. Nonetheless, interest rate elasticity is considerably lower. Basically the results for the Indonesian case echo with other results; both mechanism are at work for both periods.

On the whole, adaptive expectation mechanism and partial adjustment mechanism are simultaneously operative for most of the cases. Multiple local maxima were not found here. Moreover, it is worth noticing that the income elasticity of the long-run money demand function in this formulation is invariably close to one, excepting for the first period for Indonesia. Compared with the calculated long-run income elasticity in Table 3.1, these figures deserve attention. Especially long-run income elasticities for the Indonesian economy became smaller than half of the standard analyses. Those results seem to be in favor of a research agenda on the instability of the money demand function from this new perspective. $ ^{33} $

These results are tentative, however, besides the issue of the unit root and cointegration, $ ^{34} $ the specification of the money demand function may still demand further thorough inquiry.

### 3.8 Concluding Remarks

In this chapter, we investigated the most important macroeconomic function in the conduct of the monetary policy, the money demand function.

We found simple partial adjustment model a la Goldfeld to be reasonably solid in terms of sign conditions, significance of the estimated coefficients, except for the Philippines. The puzzling results for the Philippines could be due to the inappropriate choice of the interest rate variable or the different monetary transmission mechanism prevailing in the economy. Though we found the result in line with the second possibility, this awaits further investigation.

Furthermore, we examined the instability issue of the money demand function within a given sample period. We used a sequence of Chow test to take into account of the conceivable multiple break points. According to the calculated test statistics, this
issue of the instability of the money demand function is most serious for Japan. For the other countries, though a slight possibility for the possible single break point within a given sample period was found in the several results, this instability problem need not be taken too seriously. However, the suggested possibility of the co-existence of the partial adjustment mechanism and adaptive expectation mechanism may require further efforts.
### Chapter 4. Results of the Monetary Policies of Four Asian Countries - VAR Analysis

### 4.1 Introduction

In this chapter, we applied the Vector Autoregressive Model (VAR Model) to examine the effects of the monetary policy of the four Asian countries concerned. The advantage of applying the VAR Model is that we can examine the results of economic activities without constructing large-scale econometric models. Thus we will be able to obtain a base for comparative study by using identical model structures with similar data sets.

The VAR model is advocated by Sim's celebrated study of 1972 and 1980. He challenged the conventional econometric methodology by criticizing its use of "incredible" identification restriction. He then claimed that unrestricted vector autoregressions (VAR) can provide better instruments for understanding interrelationships between important macroeconomic variables, such as money, interest rate, prices, and output.

Since the VAR model, variance-decomposition, and impulse response function are all well-known and widely practiced in many studies, let us briefly review the basic methodology. Starting from the vector autoregressive representation,

$$ \mathrm{X}_{\mathrm{t}}=\mathrm{b}(\mathrm{L})\mathrm{X}_{\mathrm{t}}+\mathrm{e}_{\mathrm{t}} $$

where $ x_{t} $ is a stationary stochastic process and L is the lag operator. However, most VAR analyses are based on vector moving average representation due to the Wald decomposition theorem,

$$ \mathbf{X}_{\mathrm{t}}=\mathbf{n}_{\mathrm{t}}+\mathbf{a}(\mathbf{L})\mathbf{e}_{\mathrm{t}} $$

$$ \begin{aligned}\mathrm{E}(\mathbf{e}_{\mathrm{t}})&=0\\\mathrm{E}(\mathbf{e}_{\mathrm{t}}\mathbf{e}_{\mathrm{t}-\mathrm{k}})&=\mathrm{W},\quad\left|\mathbf{k}\right|>0\\&=\mathrm{~0},\quad\left|\mathbf{k}\right|=0\end{aligned} $$

$$ \mathbf{e}\mathbf{r}=(\dot{\mathbf{g}},\dot{\mathbf{i}},\dot{\mathbf{p}}\dot{\mathbf{c}},\dot{\mathbf{p}}\dot{\mathbf{w}},\Delta\mathbf{R},\dot{\mathbf{e}}\dot{\mathbf{x}},\mathbf{Z}\mathbf{B}\mathbf{P}) $$

where $ n_{t} $ is assumed as perfectly predictable. The vectors of errors are the forecast error of the autoregression given information available at t-1 if the roots of a(Z) lie outside the unit circle. To obtain impulse response function and variance decomposition normalization is necessary. To examine cumulative quantitative response of an element of $ x_{t} $ to an unpredicted innovation of some component of $ e_{t} $ , components of $ e_{t} $ must be orthogonal.
However, matrix W is not always likely to be diagonal. Hence artificial division of the covariance of the residuals enables the errors to be orthogonal. The usual convention is some particular ordering of the residuals, and then variance decomposition of the k-step-ahead forecast error is the proportion of the total variance of one component of $ x_{t} $ caused by shocks to the moving average representation of another variable. $ ^{1} $

In our study, we must note that there are difficulties in obtaining the economic interpretation by the results of our VAR model. Data we applied in our VAR Models are the difference between current and previous periods of each variable, except interest rate, to avoid non-stationary feature by the existence of the unit root. $ ^{2} $ However, because we applied the difference model, we faced the difficulty of interpreting the economic meanings directly by observing the sign of the coefficients of the estimated equation of VAR Model and the adjustment process depicted by impulse response function. Particularly, the variance decomposition applied in this chapter is based on the Cholesky decomposition, as in the traditional approach applied in Sims (1972). There exists a weak point of the traditional VAR approach that results depend very much on the ordering of the variables in the model. Another weak point of this analysis is that the structure of the model cannot be determined, and to overcome this difficulties we must apply Structural VAR Model which has been recently developed, but this issue is left for the future study.

Using the VAR Model, we will investigate monetary policies of Japan, Korea, Indonesia, and the Philippines. Variables we chose were: real GNP, wholesale price index, M2, and the level of interest rate (basically money market rate). The aim of this study is to determine whether money is an endogenous variable or exogenous variable. If one variable can be identified as exogenous variable from the variance decomposition analysis, we defined this variable as an operational variable, which is a “policy variable.” If money or interest rate can be defined as “policy variable,” and they have effect on other variables, we interpreted that “fine tuning” type of macroeconomic monetary policy was implemented. From this analysis, the equation on money can be assumed to be “money supply function.” However, by applying VAR approach based on Cholesky decomposition as mentioned above, and using difference of the data on the independent variables makes the sign of the estimated
equation ambiguous. This means that we cannot precisely identify whether the estimated results are money demand or money supply function.

In applying variance decomposition, contribution of percentage of forecasting errors in the second and twentieth periods are shown in the attached Tables 4-1 to 4-12. $ ^{3} $ We will basically consider the percentage contribution in the twentieth period in picturing the causality between the variables in Figures 4-1 to 4-12. In this study, as well as in the other studies, there is no clear criteria for measuring the strength of the innovation of one variable to the other variables by using variance decomposition. In this study, we pick up the contribution of variance decomposition exceeding 10% level as the existence of “causality,” as has been done in many previous studies.

We divided the estimation period into two parts, coinciding with the estimation period of the reaction function and money demand function but slight differences appeared due to the seasonal adjustment of the data set. The division of the period was made by the difference of the exchange rate regime in the cases of Japan and Korea. The estimation period of Indonesia is divided by the constraints in the continuity of the data set.

### 4.2 Japan $ ^{4} $

(1) Period I: From 1962 Q3 to 1973 Q1 (Fixed exchange rate regime)

The percentage of variance decomposition of forecasting error is shown in Table 4-1. On the innovation of the interest rate, 75% of the shock was caused by the innovation itself, while the contribution of the money supply and real GDP growth accounted for 14% and 13% respectively. Innovations of money supply have an effect on their own variables by 92%, a result which suggests the strong exogenous feature of the money supply. That the money supply does not have strong impact on inflation is shown by the 9% contribution of innovation to the forecasting error. Inflation can be considered as an independent variable. Contribution of the interest rate innovation of real GNP growth is 11%.

The results of variance decomposition indicate that interest rate had strong effect on