Identifying long-run relationships between the exchange rate, interest rates and stock prices

ABSTRACT

This study investigates the long-run relationship between the exchange rate, interest rate, stock prices and output. The results demonstrate that a single restricted relationship is accepted when a structural break is incorporated into the cointegrating vector. Compared with the hypothesis tests on the single restricted relationship, the hypothetical structure comprising multiple relationships in the cointegrating vector is generally accepted in most countries, confirming the interaction between the relationships in the system. Our findings regarding the real exchange rate and stock price differentials appear to contradict the uncovered equity returns parity condition, whereas the relationship between the real exchange rate and interest rate differentials is consistent with the flexible price approach.

KEYWORDS:

• Exchange rates
• stock price
• interest rate
• cointegration
• uncovered equity parity

JEL CLASSIFICATION:

• E44
• F31
• G15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ For example,$y_t=y_t-y_t^{\ast }$. The variable denoted by the asterisk represents the foreign counterpart of the domestic variable and the US is the assumed foreign country.

² Contrary to UEP, we employed $R_t=R_t-R_t^{\ast }$ rather than $R_t=R_t^{\ast }-R_t$ to maintain consistency with the other variables. Therefore, we expect a positive sign on the coefficient on the relative stock return.

³ The reason for choosing the G7 countries is that they account for approximately 30% of global GDP and 40% of international trade in 2020, while the Asian countries have a high reliance on capital inflows and have close economic linkages with the US. We believe this selection should provide invaluable insights into the determination of the exchange rate.

⁴ The sample period may be different in some countries due to the availability of data.

⁵ The stock index includes: Canada (S&P/TSX composite), France (CAC40), Germany (DAX), Italy (FTSE MIB), Japan (Nikkei 225), Korea (KOSPI), Thailand (SET), United Kingdom (FTSE100) and United States (S&P 500).

⁶ The nominal exchange rate, based on unit labour costs, is employed for France, Italy, and Germany.

⁷ Following Hoffmann and MacDonald (2009), we constructed an estimate of the expected inflation rate by implementing the moving window procedure, beginning with a univariate autoregressive estimation of the inflation rate with four lags, and utilizing the data from the past 5 years (60 observations), as well as the in-sample period data, to predict the one-step-ahead (month) inflation rate.

⁸ Zhou, (2001) indicates that increasing the data frequency may yield considerable power gain and less size distortion.

⁹ Knowing the stationarity of the variables in the system could be of interest in the current context. Using Perron’s (1988) testing procedure, the Philip-Perron and ADF tests results show that all variables are non-stationary in levels and stationary in first-differences. However, a limitation of the conventional unit root tests is that the results, in the presence of structural change, may potentially bias towards the non-rejection of the unit root.

¹⁰ We preferred the Johansen trace test to the Johansen MaxEigenvalue test because its superior performance has been proven (Lutkepohl et al., 2001).

¹¹ Many studies (e.g. Hansen and Juselius, 1995) report that the choice of the deterministic component of a model exerts significant implications on the asymptotic distribution of the cointegration tests.

¹² Notably, the homogeneity constraint for European countries (France, Germany, and Italy) would be ${\beta }_i=-{\beta }_{\mathit{i}+1}$. This is because the real effective exchange rate is used for the European countries. An increase (decrease) in the real effective exchange rate indicated that the economy was losing (gaining) competitiveness compared with its trading partners. It can also be considered as currency appreciation (depreciation).

¹³ The symbol (*) is used to represent no restriction.

¹⁴ The estimated coefficients represent the cases where the hypothesis tests were accepted at the≤10% significance level in Table 4b.

¹⁵ We also performed two sets of tests that a zero restriction was imposed on the shift dummy for $H_3\left(1\right)\mathit{to}{H}_3\left(3\right);$ and for $H_4\left(1\right),$ respectively. To save space, the results of these tests are not included in this paper. We can provide them upon request.

¹⁶ The corresponding speed of adjustments are reported in Appendix 1.

¹⁷ Please refer to Fama and French (1988) and Poterba and Summers (1988).

¹⁸ We are grateful to an anonymous referee for making this point.