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Appendix

Sources and Definitions of Variables Used in Regressions

(All values are in billions of pesos; all constant price variables are in terms of 1980 prices; and all indices take 1980 = 1.0.)

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References

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  • Kim, Inchul,Exchange Market Pressure in Korea: An Application of the Girton-Roper Monetary Model,Journal of Money. Credit and Banking, Vol. 17, No. 2 (May 1985), pp. 258263.

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  • Toyoda, Toshihisa,Use of the Chow Test Under Heteroscedasticity,Econometrica, Vol. 42, No. 3 (May 1974), pp. 60108.

1/

The authors would like to thank David Burton, Peter Isard, Mohsin Khan, and Donald J. Mathieson for helpful comments on an earlier draft of the paper. Thanks are also due to Kellet Hannah for providing exceptionally capable research assistance.

2/

Separate reserve requirements are imposed for deposits with a maturity of above and below 730 days. At end-1988, the required reserve ratios on deposits with a maturity below 730 days (the bulk of deposits) was 21 percent and the reserve ratio for longer-term deposits was 5 percent. The Central Bank pays a relatively low interest rate (currently 4 percent) on banks’ reserve deposits, so the high reserve requirements represent a fairly significant implicit tax on financial intermediation.

3/

Banks issued a variety of interest-bearing securities to their depositors during the 1970s, partly in an effort to avoid interest rate ceilings on deposits; however, these deposit substitutes were also subject to interest-rate ceilings during 1976-81.

4/

If, for example, the interest rate rises from 2 percent to 3 percent, the log of the rate rises from -3.91 to -3.51, which is a change of 0.40. But when the interest rate rises from 10 percent to 11 percent, the log of the rate rises from -2.30 to -2.21, which is only a change of 0.09. There is little reason to expect that a 1 percentage point rise in the interest rate would have four times the effect on the log of desired money holdings when the change is from a base of 2 percent than when it is from a base of 10 percent (see Fair (1983)).

5/

All rates of return included in the estimating equations are for assets with a maturity period of one quarter. This avoids any potential within-period capital gains or losses owing to changes in interest rates. Thus, apart from taxation and risk of default, the expected return on these assets should be equal to their yield.

6/

This may be because the estimated parameter for the lagged dependent variable in the estimating equation already reflects much of the information on the extent to which inflationary expectation are determined by past inflation rates.

7/
One objection to this specification is that it implicitly assumes that any change in the real value of nominal money balances due to changing prices leads to an immediate adjustment. An alternative specification, suggested by Goldfeld (1976), defines the adjustment process in terms of nominal money stocks: the right hand side of equation (3) becomes δ[log(Mtd)log(Mt1)] and so the lagged term in equation (4) becomes (1-δ) log (Mt-1/Pt). A third alternative, used by Laidler (1982), stipulates that, for the economy as a whole, it is prices and not money balances that adjust to equate the desired and actual money stock. Thus,
(5)log(Pt)log(Pt1)=δ[log(Mt)log(MtdPt).Pt1]

In this case, the lagged term in equation (4) would become (1-δ) log (Mt/Pt-1).

Although these alternative specifications of the stock adjustment process are derived from quite distinct theoretical hypotheses, it may prove difficult to distinguish between them in practice. One reason for this is that estimation of lags involving a price index can be blurred because the price of goods covered by the index are actually sampled on different dates during any reporting period and may also be based on list prices that lag behind actual prices. In the event, estimates of demand for money functions using the three different lagged terms showed little variation. Estimates using the form of equation (4) are reported in this paper, but none of the substantive conclusions would appear to be affected with one of the alternative functional forms.

8/

The demand for money using the estimation technique developed by Hatanaka has been examined for the United States by Laumas and Spencer (1980) and Allen and Hafer (1983).

9/

Although econometric theory indicates that the expected value of estimated coefficients is the true coefficient in well-specified equations that have serial correlation, the coefficient estimates could deviate substantially from their true values, and the standard errors, which are understated, will suggest much better fits than is, in fact, the case. Lieberman (1980) showed that many of the coefficient estimates of the money demand functions for the United States are affected radically when the equations are re-estimated adjusting for serial correlation.

10/

In the approach based on the work of Hendry (see, for example, Hendry (1986), Hendry, Pagan, and Sargan (1984), and Hendry and Richard (1982)), the existence of serial correlation is typically taken to be evidence of model misspecification. Consequently, a more general class of autoregressive distributed-lag equations, in principle allowing for multiple lagged values of both the dependent and independent variables, is estimated. The resultant equation is sequentially simplified (“tested down”) by dropping insignificant higher-order lags. Although general distributed lag models resolve many of the shortcomings of the simple partial adjustment models, such as incomplete dynamic specification and real balances are not constrained to adjust with the same geometric distributed lag to each independent variable, the partial adjustment mechanism has often served as the workhorse to capture the underlying dynamics in money demand equations (see Goldfeld and Sichel (1987)).

11/
The recursive residual based on forward forecast errors is defined as
uft=et/(1+xt(Xt1Xt1)1xt)1/2,
where et is the prediction error for period t, XT = (x1, x2, …, xT)’ is a (T × K) matrix of observations on the K explanatory variables, and Xt-1 contains only the first t-1 rows of XT. For a set of time series observations, there will be a (T-K) vector of these recursive residuals, uf = (ufK+1, ufK+2, …ufT). By running the same procedure backwards, another vector of recursive residuals, ub = (ubT-K-1, ubT-K-2, … ub), is generated. The forward versions of the cumulative sum series (cuf) and the cumulative sum of squares (cusqf) are defined as:
cuf(t)=(1/σ^)Σtufi,whereσ^=(ΣT(ufiuf)2/(TK1))1/2andcusqf(t)=Σtufi2/ΣTufi2.

Confidence limits can be placed around a line representing constant increments in the recursive residuals, and a movement of the actual sum of the residuals outside these limits leads to rejection of the null hypothesis of stability.

12/

The impact of allowing ρ to vary over the range of -0.9 to 0.9, to study the sensitivity of the conclusions to different values of ρ, was minimal. The main conclusions of the recursive residuals analysis are the same independently of ρ. For almost all of the parameter values of ρ, the cusums test support the hypothesis of stability, whereas the cusums of squares test provide evidence of a structural break.

13/

In the Quandt likelihood ratio test, the sample is divided into two segments (1…r) and (r+1…T). The null hypothesis, H0, is that the regression coefficients and the variance of the error term are constant over the two segments, while the alternative hypothesis, H1, is that they come from two separate models. For each observation, r, from r = T-k-1, the log10 maximum likelihood ratio is calculated: λr=log10(maximum likelihood of the observations givenH0maximum likelihood of the observations givenH1)

This statistic is computed, moving throughout the entire sample, and the point of discontinuity is diagnosed as the value of r at which λr attains its minimum. Because several regimes may exist, interest will also focus on local minima. The shortcoming of this approach is that since the distribution of λr under the null hypothesis is unknown, it does not lend itself to exact significance testing. However, once the relevant subperiods have been chosen, one may use the Chow test to obtain an F-statistic for whether the subsamples are drawn from different populations.

14/

Strictly speaking, the levels of significance of the F statistics used in the Chow test are only accurate if the variances of the error terms are equal for the two sub-periods. However, heteroscedasticity does not appear large and one of the sub-periods has a relatively large number of observations (40). Toyoda (1974) has shown that the Chow test is well-behaved under such conditions. There is an additional complication in the application of the Chow test since the equations are adjusted for serial correlation. However, if the serial correlation coefficients from the different regimes are reasonably close, the test results can be viewed as reliable. It should also be noted that one observation will be common to both subsamples because of the presence of the lagged dependent variable, which raises the question of the statistical independence of the sums of squares.

15/

The exchange market pressure model has been applied to several developing countries. The applications include Connolly and Da Silveira’s (1979) study for Brazil, Modeste’s (1981) study for Argentina, and Kim’s (1985) study for Korea.

16/

As was mentioned earlier, the principal aggregate used to measure the stance of monetary policy in the Philippines is base money, defined as reserve money plus bank holdings of reserve eligible securities plus reserve deficiencies. Two sets of estimation were done for the exchange market pressure model, using different measures for the exchange rate and foreign price level variable. One set used the U.S. dollar per Philippine peso rate and the U.S. consumer price index, whereas the other set used the nominal effective exchange rate and the industrial country consumer price index. Since the results did not differ in any significant way, only those using the U.S. dollar per Philippine peso and the U.S. consumer price index are reported.

17/

The simpler ratio e^/r^ was not used because it is discontinuous for values of r^=0.

18/

The standard deviation of r^ for the period Q1 1973-Q3 1984 was 0.140 and for the period Q4 1984 - Q4 1988 it was 0.138; and the standard deviation of ê for the two subperiods was 0.039 and 0.042, respectively.

Monetary Policy in the Philippines During Periods of Financial Crisis and Changes in Exchange Rate Regime: Targets, Instruments, and the Stability of Money Demand
Author: International Monetary Fund