Back Matter

### APPENDIX I

In this appendix we provide some detail concerning the empirical tests conducted in Section II of the main text.

#### 1. Time series properties of the data series

In order to test for the presence of unit roots in the time series representation of each data series, the following regressions were estimated:

$\begin{array}{cc}{\begin{array}{c}\mathrm{\Delta }\text{x}\end{array}}_{\text{t}}=-{\phi }_{1}{\text{x}}_{\text{t}-1}+{\text{u}}_{\text{t}}& \left(A1\right)\end{array}$
$\begin{array}{cc}{\mathrm{\Delta }}^{2}{\text{x}}_{2}\text{ =}\text{ }-{\phi }_{2}\mathrm{\Delta }{\text{x}}_{\text{t}-1}\text{ +}{\text{ v}}_{t}& \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\text{A2}\right)\end{array}$
$\text{x}\text{ =}\text{ }\left\{{\text{P}}^{S},\text{ P,}\text{ }{\text{s}}^{\text{ij}},\text{ q,}{\text{ e}}^{\text{ij}}\right\}$

If Φ1 is not significantly different from zero and Φ2 is, a unit root is present in the level of x but not in its first difference. In other words, x is integrated of order 1. Using the appropriate critical values for the test (i.e., those presented in Dickey and Fuller) it was found, not surprisingly perhaps, that for all variables and for all countries it was not possible to reject the presence of one unit root in each series. 35/

#### 2. Causality tests

In order to test for the existence of lead-lag relationships across countries, Granger-causality tests were carried out on both real and nominal stock prices. 36/ Specifically, the following relationships were estimated

$\begin{array}{cc}\mathrm{\Delta }{\ell \text{nP}}_{\text{t}}^{\text{si}}\text{ =}\text{ }{\alpha }_{0}\text{ +}\text{ }\underset{\text{k=1}}{\overset{6}{\mathrm{\Sigma }}}\text{ }{\alpha }_{\text{k}}\text{ }\mathrm{\Delta }{\ell \text{nP}}_{\text{t}-\text{k}}^{\text{si}}\text{ +}\text{ }\underset{\text{}\text{k=0}}{\overset{6}{\mathrm{\Sigma }}}\text{ }{\beta }_{\text{k}}\mathrm{\Delta }\ell {\text{nP}}_{\text{t}-\text{k}}^{\text{sj}}\text{ +}\text{ }\underset{\text{}\text{k=1}}{\overset{6}{\mathrm{\Sigma }}}\text{ }{\gamma }_{\text{k}}\mathrm{\Delta }{\ell \text{ns}}_{\text{t}-\text{k}}^{\text{ij}}\text{ +}{\text{ u}}_{\text{t}}^{\text{j}}& \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\text{A3}\right)\end{array}$

and

$\begin{array}{cc}\mathrm{\Delta }{\ell \text{nq}}_{\text{t}}^{\text{i}}\text{ =}\text{ }{\alpha }_{0}\text{ +}\text{ }\underset{\text{k=1}}{\overset{6}{\mathrm{\Sigma }}}\text{ }{\alpha }_{\text{k}}\text{ }\mathrm{\Delta }{\ell \text{nq}}_{\text{t}-\text{k}}^{\text{i}}\text{ +}\text{ }\underset{\text{k=0}}{\overset{6}{\mathrm{\Sigma }}}\text{ }{\beta }_{\text{k}}\text{ }\mathrm{\Delta }{\ell \text{nq}}_{\text{t}-\text{k}}^{\text{j}}\text{ +}{\text{ v}}_{\text{t}}^{\text{j}}& \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\text{A4}\right)\end{array}$

and the joint significance of the lagged values of the independent variable was examined using conventional F-tests. The results are presented in Tables I and II respectively.

Table I.

Tests for Granger-Causality Based on $\mathrm{\Delta }ln{\text{P}}_{\text{t}}^{\text{si}}\text{ =}\text{ }{\alpha }_{0}\text{ +}\text{ }\underset{\text{k=1}}{\overset{6}{\mathrm{\Sigma }}}\text{ }{\alpha }_{\text{k}}\text{ }\mathrm{\Delta }ln{\text{P}}_{\text{t-k}}^{\text{si}}\text{ }{\beta }_{\text{k}}\text{ }\mathrm{\Delta }ln{\text{P}}_{\text{t-k}}^{\text{sj}}\text{ +}\text{ }\underset{\text{k=1}}{\overset{6}{\mathrm{\Sigma }}}\text{ }{\gamma }_{\text{k}}\text{ }\mathrm{\Delta }ln{\text{S}}_{\text{t-k}}^{\text{ij}}\text{ +}{\text{ u}}_{\text{t}}$

Note: USA=>i corresponds to the hypothesis that lagged values of qUSA are significant in the regression equation for qi. i=>USA corresponds to the hypothesis that lagged values of qi are significant in the regression equation for qUSA. USA<=>i corresponds to the hypothesis that the contemporaneous value of qUSAis signifiant in the qi equation. Numbers refer to marginal significance levels, An * indicates a marginal significance level <.01. A lack of number indicates a marginal significance level >.10.
Table II.

Tests for Granger-Causality Based on $\mathrm{\Delta }ln{\text{q}}_{\text{t}}^{\text{i}}\text{ =}\text{ }{\alpha }_{0}\text{ +}\text{ }\underset{\text{k=1}}{\overset{6}{\mathrm{\Sigma }}}\text{ }{\alpha }_{\text{k}}\text{ }\mathrm{\Delta }ln{\text{q}}_{\text{t-k}}^{\text{i}}\text{ +}\text{ }\underset{\text{k=0}}{\overset{6}{\mathrm{\Sigma }}}\text{ }{\beta }_{\text{k}}\text{ }\mathrm{\Delta }ln{\text{q}}_{\text{t-k}}^{\text{j}}\text{ +}{\text{ u}}_{\text{k}}$

Note: USA=>i corresponds to the hypothesis that lagged values of qUSA are significant in the regression equation for qi. i=>USA corresponds to the hypothesis that lagged values of qi are significant in the regression equation for qUSA. USA<=>i corresponds to the hypothesis that the contemporaneous value of qUSA is signifiant in the qi equation. Numbers refer to marginal significance levels, An * indicates a marginal significance level <.01. A lack of number indicates a marginal significance level >.10.

## References

• Adler, M. and B. Dumas, “International Portfolio Choice and Corporate Finance: A Synthesis,” Journal of Finance, Vol. 38, No. 3 (June 1983), pp. 92584.

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• Andresen, S., “Integrated Equity Markets and International Business Cycles,” (unpublished PhD dissertation, Graduate Institute of International Studies, Geneva, Switzerland, 1988).

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• Aoki, M., Dynamic Analysis of Open Economies. (Academic Press: New York (1981).

• Bhandari, Jagdeep S., Exchange Rate Determination and Adjustment, (Praeger: New York, 1982).

• Bhandari, Jagdeep S., Robert P. Flood and Jocelyn P. Horne, “Evolution of Exchange Rate Regimes,” (Forthcoming, Staff Papers, International Monetary Fund, 1989).

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• Cutler, D., J. Poterba, and L. Summers, “What Moves Stock Prices?”, NBER Working Paper No. 2538 (Cambridge, Massachusetts: National Bureau of Economic Research, March 1988).

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• Engle, R.F., and C.W.J. Granger, “Co-Integration and Error Correction: Representation, Estimation and Testing,” Econometrica, Vol. 55, (1987), pp. 25176.

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• Friedman, M., “Money and Stock Prices,” Journal of Political Economy, Vol. 96, No. 2, (April 1988), pp. 22145.

• Gavin, M., “The Stock Market and Exchange Rate DynamicsInternational Finance Discussion Paper, No. 278, Board of Governors of the Federal Reserve System (1986).

• Crossref
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• International Monetary Fund, World Economic Outlook, 1988.

• Murphy, R., “Stock Prices, Real Exchange Rates, and Optimal Capital Accumulation,” International Monetary Fund Working Paper, WP/88/31, (Washington: 1988).

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• Schwert, G.W., “Why Does Stock Market Volatility Change over Time?Working Paper No. 2798, National Bureau of Economic Research, (1988).

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• Turnovsky, S.J., “Monetary and Fiscal. Policy under Perfect Foresight: A Symmetric Two-Country Analysis,” Economica, Vol. 53 (1986), pp. 139157.

The authors are grateful to Morris Goldstein and Mohsin Khan, as well as to participants of the Research Department seminar for helpful comments on an earlier draft of this paper. This paper was begun while Hans Genberg was a consultant with the Research Department.

Indeed, interest parity conditions are central to the transmission mechanisms in the majority of recent open economy macroeconomic models.

Theoretical work incorporating stock market effects in open economy macroeconomic models includes Gavin (1986) and Murphy (1988). The finance literature has of course been concerned with linkages between national stock markets in studies of the benefits of international portfolio diversification. See, for example, the comprehensive survey by Adler and Dumas (1983), which also contains references of empirical evidence on correlation between returns in various markets. Andresen (1988) presents evidence suggesting that common international factors can explain a significant portion of the variation in national stock price indexes and, furthermore, that the same international factors are leading indicators of national business cycles. See also Schwert (1988) for an empirical investigation of stock market volatility.

Real stock prices are defined as the nominal price deflated by the domestic price of goods.

Canada, France, the Federal Republic of Germany, Italy, Japan, the United Kingdom, and the United States. Data sources were DRI for all stock price indices and IFS for all other series.

See the Appendix for details.

In co-integration tests, equation (2) is interpreted as the long-run relationship between the variables provided that the residual in the equation is stationary, and is referred to as the co-integration regression.

In the first of these, the point estimate of the coefficient β2 was –.47 as opposed to the theoretical value of +1 under the null hypothesis of PPP.

Given the non-stationarity of the residual in the regression one must be careful in drawing formal inferences from the estimated coefficients.

Specifically, the number of cases increased from two pairs of countries to four (three) based on the ADF (DF) statistic and a 10% significance level. When the real exchange rate is included in the co-integration regression (see Table 3a), the number increases to six if the ADF statistic is used, but stays at three according to DF. It is interesting to note that co-integration could be rejected in all but one case when one of the two countries was the United States.

At a popular level it is frequently said that a real depreciation of the domestic currency is “good” for domestic economic activity. According to this argument depreciations ought to be associated with increases in domestic stock prices relative to foreign.

Alternatively, one could run regressions over various sub-periods to test for stability of the relationship.

The model to be described below can be viewed either as a two-country extension of Gavin (1986), or as a elaboration of existing two-country models such as Bhandari (1982) or Turnovsky (1986), suitably amended to incorporate stock markets in each country.

The reason for this is that we do not model differences in risk characteristics between stocks issued in different countries. This in turn implies that given certain conditions the arbitrage relationships which must hold between real and financial assets in the model are unaffected by permitting trade in equity shares. One condition under which this is so is that the share of domestic stocks in the domestic portfolio is equal to the share of domestic goods in the domestic general price index.

In addition, D > 0 is the usual stability condition which is also assumed satisfied.

These price indices are exact if the underlying utility function is Cobb-Douglas in nature.

These equations represent arbitrage relationships between bonds and stocks in each economy.

An additional dynamic equation involving s would ordinarily have been involved had we imposed perfect foresight directly instead of utilizing the expectational scheme described in (6)..

The averages-differences technique can also be utilized if parameters are not country-wise identical; however, additional approximations are involved in this case. See Aoki (1981) for details.

It is straightforward however, to incorporate ongoing inflation in the steady state.

It may be shown that the average level of stock prices increases following an increase in domestic money, while the effect upon the difference level is unclear, i.e.,

$\begin{array}{c}\left({\text{d}\text{q}}_{\mathrm{ο}}^{\text{a}}/\text{dm}\right) = -\frac{\zeta \left(1-{\text{d}}_{1}\right)}{{2\gamma \text{d}}_{2}} > 0;\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left({\text{d}\text{q}}_{\mathrm{ο}}^{\text{d}}/\text{dm}\right)=-\frac{\left(\lambda +{\text{a}}_{11}\right)}{{\text{a}}_{12}}\end{array} \gtrless 0$

Along the perfect foresight path, the stable root is given by λ < 0.

In fact, numerical simulations indicate that for a wide variety of parameter magnitudes, nominal exchange rate undershooting rather than overshooting occurs.

This is because of the decline in the nominal interest rate coupled with an increase in rate of expected (and actual) inflation (p).

Notice also that q < 0, since q must return to its predisturbance level along a first-order path.

Notice also that with δ = 1 (i.e., if the national price level were used in place of the price index), there are no dynamic effects upon the exchange rate following fiscal expansion, i.e., (ds°/dg)=(ds/dg).

Two conflicting effects upon domestic output are observed. First, domestic fiscal expansion directly stimulates domestic income while the resulting real appreciation exerts a depressive effect; see equation (1).

There are three channels of effect upon y*; specifically, the increase in the domestic income and real appreciation both of which serve to increase y* (see equation (2)); however, a decline in foreign stock prices works in the opposite direction.

These magnitudes are roughly similar to those in Gavin (1986) and several other studies and are in broad conformity with empirical data for the G-7 countries.

Note that C2 = (elasticity of consumption)/(q), while the elasticity of consumption with respect to q is given by the product of the elasticity of consumption with respect to wealth and the elasticity of wealth with respect to q. This product is assumed to be .15. Given q = 6.25, the value of C2 = .024 follows.

It is of course possible that the tests carried out are not sensitive enough to discriminate between the possibility of complete lack of long-run relationships and a high degree of persistence.

If the common movement in stock prices is the result of ‘transmission’ of purely country-specific shocks, the weak and unstable relationships between these movements and exchange rate changes can occur if the shocks alternate between countries.

See World Economic Outlook, 1983, Appendix B, Table 5.

Andresen (1988) contains an informal but suggestive discussion of an international q-theory of investment.

Appropriately modified, the method used in Bhandari, Flood, and Horne (1989) seems to be a good candidate.

To economize on space, details of the results are not presented here. They may be obtained from the authors.

It has been suggested to us that the more general VAR technique, which can accommodate more than two countries at a time, would have been preferable to the bilateral Granger tests. Given the results we have obtained, we feel confident that estimated VAR systems would show that most of the inter-country correlation between stock prices is contemporaneous.

1/

Recall that q = q* = qa and qd = 0.

Exchange Rate Movements and International Interdependence of Stock Markets
Author: International Monetary Fund