III. DOLLARIZATION AND PRICE DYNAMICS
4. Price Integration in Ecuador under Dollarization
4.2. Price Integration Analysis
The analysis assumes that Quito and the other cities were initially sharing the same inflation rate. Then, after a transition period around the start of dollarization during which
inflation rates are allowed to diverge, the other cities and Quito return to a new steady state under dollarization, again sharing the same inflation rate. The initial and final inflation rates need not be the same.63 This process implies that there may have been a statistically significant shift in the mean relative prices of the cities with respect to Quito after the adoption of dollarization. In addition, the spread of the commodity relative prices could have changed.
The main result for this analysis is obtained using a pre-post t test. According to section 2, for each city the relative prices of commodities would be distributed around a city-specific mean, qi,t, with standard deviation si,t. This approach consists of testing for a change in the average levels of qi,t and si,t from before to after the start of dollarization.
Taking into account that the series may have been more volatile around the time dollarization was adopted, the test considers a transition period. The “Before”
dollarization period is chosen to be from January 1997 to December 1998, and the
“After” the start of dollarization period from July 2001 to April 2003. The test is a
“matched-samples” test to control for city-specific fixed effects. As a robustness check, the non-parametric Wilcoxon Signed Rank test is also used.
The next step is to analyze the implications of the results for convergence in relative prices, if any, across the cities. For absolute convergence, there should be a negative relationship between the change in the relative price level after dollarization and its level before dollarization. The approach is borrowed from the income convergence literature64, and consists of estimating the following regression:
i Before i
i q
q =α+β +ε
∆ , (3.9)
63 In fact, average annual inflation for 1997-1998 is over 30%, while for 2002-2003 is only around 8%.
where qi,Before is the average qi,t for the “Before” period, and ∆qi is the difference between
qi,After and qi,Before, where qi,After is the average qi,t for the “After” period, all for city i.
Under absolute convergence, coefficient α is common for all cities and depends on parameters of the process of convergence, particularly on the new steady state.
Coefficient β is expected to be negative and statistically significant. It has to be noted that, because there are only 11 cities other than Quito, the tests will likely have low statistical power. Convergence is also analyzed within each city for the commodity prices. For that purpose, equation (3.9) is estimated for each city separately replacing the city subscript i with the subscript j for the commodity, with j = 1, 2,…, 223.
The final step of the analysis consists of some robustness checks. The first is a variation of the pre-post test to include time variability in the estimations. For that, the following regressions are estimated for each city, i, individually:
t i t i i i t
i D
q, =α0 +α1 , +ε, (3.10)
t i t i i i t
i D
s, =β0 +β1 , +υ, (3.11)
where Di,t is a dummy variable that takes on the value 1 for t ≥ January 2000, and zero otherwise. The intercepts capture the average level of the series before dollarization, and the coefficients of the dummy variable capture any change in this mean after the start of dollarization. Coefficient tests use Newey-West HAC standard errors and covariances to account for possible heteroscedasticity and autocorrelation of unknown form in the error terms.65 For the time series analysis, the full period from January 1997 to April 2003 is used.
65 See Newey and West (1987).
The time series analysis can be extended by using an approximation to equation (3.10) under the assumption that the relative price, qi,t follows a first-order autoregressive process with a break in mean. For this, the following equation is estimated for each city i individually:
t i t i i t i i i t
i D q
q, =α0 +α1 , +ρ ,−1+ε, (3.12)
where coefficient ρi gives the persistence of the process, and the intercept and the coefficient of the dollarization dummy can be used to calculate the means of the relative- price series process before and after the start of dollarization as α0i /(1-ρi) and (α0i + α1i)/(1-ρi), respectively, for each city i. Still, a statistically significant dummy variable coefficient would indicate a shift in mean after the start of dollarization. An advantage of this method is that the estimation of the before and after mean relative-price levels can be done without the prices actually reaching the steady states. Another advantage is that it allows an estimation of persistence. A disadvantage is that the parametric assumption for the time series may be too restrictive.
The last robustness check consists of a panel-regression analysis in an effort to use at simultaneously both the time and cross-section variability in the relative price data. Two different specifications are used, each estimated for each city i individually as a panel of 223 commodity relative price series in length of 76 months (January 1997 to April 2003.) The first model is the panel version of equation (3.10):
t j i t j i i j i t j
i D
q,, =α0, +α1 , , +ε, , (3.13)
which is estimated ignoring any serial correlation in the series, and assuming common dummy coefficients but different intercepts across commodities. The second specification
(3.13) plus the assumption that the autoregressive coefficient is common across commodities:
t j i t j i i t j i i j i t j
i D q
q,, =α0, +α1 ,, +ρ , ,−1+ε, , (3.14)
Because of the presence of the lagged dependent variable as a regressor, equation (3.14) has to be estimated as a dynamic panel.