Re-examining the real interest rate parity hypothesis (RIPH) using panel unit root tests with asymmetry and cross-section dependence

Abstract

This paper investigates the validity of the real interest rate parity hypothesis (RIPH) using a panel unit root approach. For this purpose, first we estimate the possible nonlinear data-generating processes of the real interest rate differential series and using these estimates determine which panel unit root test is better for analyzing the RIPH. To this end, smooth transition autoregressive and threshold autoregressive (TAR) models are estimated for two different panels of countries: G7 and post-Soviet transition economies. The results show that the data displays both strong asymmetry and high transition speed. Therefore, secondly, we propose a new panel unit root test where the alternative is stationary with asymmetric TAR adjustment, and provide their empirical power properties. Finally, we demonstrate that our newly proposed test is able to provide conclusive evidence in favor of the RIPH in contrast to the other panel unit root tests considered.

Appendix

Consider the following PTAR(1) model:

$$ \Delta y_{it} = \alpha_{i} + \rho_{i1} I_{it} y_{i,t - 1} + \rho_{i2} \left( {1 - I_{it} } \right)y_{i,t - 1} + \eta_{it} $$

(11)

$$ I_{it} = \left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{if}}\quad y_{i,t - 1} \ge \tau } \hfill \\ 0 \hfill & {{\text{if}}\quad y_{i,t - 1} < \tau } \hfill \\ \end{array} } \right. $$

where $\tau$ denotes the threshold variable. We have set this variable to zero as in Enders and Granger (1998) and obtained the critical values tabulated in Tables 8 and 9. If $\rho_{i1} = \rho_{i2} = 0$ in Eq. (11) then $y_{it}$ contains a unit root, while if $\rho_{i1} = \rho_{i2} < 0$, $y_{it}$ is a stationary TAR process with symmetric adjustment, and if $\rho_{i1} < 0,\,\,\rho_{i2} < 0$ and $\rho_{i1} \ne \rho_{i2}$, $y_{it}$ is a stationary TAR process displaying asymmetric adjustment. We propose testing for whether $y_{it}$ contains a unit root using the F-statistic for testing $\rho_{i1} = \rho_{i2} = 0$ in (11), and/or the most significant of the t-statistics from those for testing $\rho_{i1} = 0$ and $\rho_{i2} = 0$. In a panel framework, for the model given in (11), the relevant $F$ and t-statistic will be referred to as $\bar{F}_{1p,\alpha }$ and $\bar{t}_{1p,\alpha }$. The test statistics are computed through taking the average of individual EG statistics across the whole panel. Also we have generated the critical values for the PMTAR unit root test, but they are very similar to the values reported in Tables 8 and 9. Hence, we do not tabulate them here, but they are available upon request.^{32 , 33}

$$ I_{it} = \left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{if}}\quad \Delta y_{i,t - 1} \ge \tau } \hfill \\ 0 \hfill & {{\text{if}}\quad \Delta y_{i,t - 1} < \tau } \hfill \\ \end{array} } \right. $$

(12)

The threshold values, which are obtained taking the average of the series, can be denoted as follows:

$$ I_{it} = \left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{if}}\quad \Delta y_{i,t - 1} \ge a} \hfill \\ 0 \hfill & {{\text{if}}\quad \Delta y_{i,t - 1} < a} \hfill \\ \end{array} } \right. $$

(13)

where a denotes the average of the series.

Table 8 Exact critical values of $\bar{t}_{1p,\alpha }$ statistics

Table 9 Exact critical values of $\bar{F}_{1p,\alpha }$ statistics