IV. DOLLARIZATION AND PRICE DYNAMICS
4. Relative Price Level Divergence in the Long Run
4.2. Long-Run Relative Price Level Movements
The implication of the Balassa-Samuelson hypothesis is that, because higher productivity growth leads to both an appreciating real exchange rate and better standards of living, countries with higher levels of per-capita income must have higher average price levels. To formally test this implication, the following regression model is estimated:
t i t i i i t
i y
q', =µ +δ ', +ε, (4.20)
Variables q′i,t and y′i,t were defined in section 2, with equations (4.2) and (4.3) as the common-currency relative price level and relative real per-capita GDP level between country i and the U.S. at time t, respectively, both calculated with data from the PWT.
Equation (4.20) can also be interpreted as an estimation of the relationship presented by equation (4.18) with relative real per-capita GDP, or relative income, being used as a proxy for relative productivity between country i and the U.S. (i.e. for the term ai,T - aT*.) According to this relationship, coefficient µi is expected to be roughly zero, and δi to be positive and between zero and 1 because it would be estimating θi from equation (4.18).
The estimation of equation (4.20) is first done using period-specific, cross-section averages of the variables after assuming a common intercept and slope coefficient across countries (that is, with µi = µ and δi = δ for all i.) Through a cross-section analysis it is
possible to determine whether Panama’s price level relative to that of the U.S. is higher than expected for the average Latin American country after controlling for the Balassa- Samuelson income effect. With Panama’s being dollarized for a long time, higher economic integration with the U.S. may have contributed to it having a price level that is higher than expected for its income level. The analysis, thus, consists of doing cross- section estimations of equation (4.20) for different time periods and evaluating the influence of Panama’s observation on the estimation.
To evaluate the influence of Panama’s observation on the cross-section estimations of equation (4.20), four regression diagnostic criteria found in Belsley, Kuh, and Welsch (1980) are used.89 They are: the studentized residual, rstudent (an adjusted z-score); a measure of the change in the determinant of the covariance matrix of the estimates, covratio; a measure of the change in the predicted value of the observation, dffits; and a measure of the change in each estimated coefficient, dfbeta. The criteria are calculated by comparing the estimation results when Panama’s observation is excluded with those when it is included. The observation would be too influential if the absolute values of the criteria are above certain size-adjusted upper limits. The upper limit for rstudent is 2, for covratio is 1+3p/n, for dffits is 2 p/n , and for each dfbeta is 2/ n; where p is the number of parameters estimated (in this case 2: the intercept and the relative income coefficient), and n is the sample size (in this case 13 countries.)
To examine the robustness of the results obtained through the cross-section estimations of equation (4.20), the relationship between relative price and relative income is also investigated using time-series regressions for the sub-periods 1950-1971 and
1972-2000. Considering the short length of the series available, the results of this analysis have to be regarded as tentative. First, equation (4.20) is estimated individually for each country using the Ordinary Least Squares (OLS) method, and the residual series obtained from these regressions are tested for stationarity using the usual unit-root ADF test. If for a given country, the residuals are found to be stationary, the series q′i,t and y′i,t can be considered cointegrated, i.e. not drifting too far apart from each other in the long-run.90 According to Johnson (1990), Engle and Granger (1987), and Stock (1987), if q′i,t and y′i,t
are cointegrated, the OLS estimation of equation (4.20) gives consistent estimates of the coefficients. However, according to Banerjee et al. (1986) and Stock (1987), the coefficients will be biased in small samples, particularly if the fit of the model is poor.
This is obviously a problem with the available series that is ignored in this study.
Second, under the assumption of cointegration, a simple Error Correction Model (ECM) suggested by Engle and Granger (1987) is estimated. The purpose of this estimation is mainly to corroborate the existence of cointegration between q′i,t and y′i,t by confirming that the coefficient of the lagged Error Correction term is negative and statistically significant. Each country has its own Error Correction term which is the residual series obtained above through the estimation of equation (4.20) for each country individually. The ECM estimation consists of regressing the first difference of the relative price series, ∆q′i,t, on a constant, the first difference of the relative income series,
∆y′i,t, and the one-period lagged OLS residual, Ui,t-1.91 To deal with the low power of the tests due to the short length of the series, the ECM is estimated with the 13 countries as a
90 See Ramanathan (1998, p. 540) for the details about testing for cointegration using the ADF test.
91 This two-step estimation method for an ECM is shown to be consistent and efficient by Engle and Granger (1987). Still these are asymptotic properties which may not hold in small samples. See also Johnson (1990).
panel. The estimation is done, first assuming common intercept and slope coefficients across countries, and then relaxing this assumption. The country-specific results may be used to get an idea of the nature of the short-term relationship between the relative price and income variables for each country. To control for possible cross-country heteroscedasticity and contemporaneous correlations, the estimation uses the Seemingly Unrelated Regression (SUR) method.