A recursive cointegration test using the Kalman filter and its application to fiscal equilibrium in the Dominican Republic

Abstract

This letter puts forward a recursive version of the Engle and Granger cointegration test, using the Kalman filter, for the analysis of fiscal equilibrium in the Dominican Republic. The method employs a time-varying-coefficient augmented Dickey and Fuller test and finds that government income and spending display movements both toward and away from equilibrium that can be associated to various policy reforms and shocks to the economy.

Acknowledgements

The author thanks José R. Sánchez-Fung and several members of the Economics Department at the Ministry of Finance of the Dominican Republic for their helpful advice and useful comments. All remaining errors are the authors.

Notes

This technique could be also applied to alternative stationarity test such as Phillips and Perron (1988), Kwiatkowski et al. (1992), and Perron and Ng (1996), among others.

A weaker condition suggests that fiscal equilibrium would be feasible when 0<β ≤ 1 (see Hakkio and Rush, 1991). In this special case, government spending, on average, would grow slower that income.

If only the cointegration requirement is met, the government is said to be in a potential position to achieve intertemporal fiscal equilibrium. If cointegration is not satisfied, however, no equilibrium is present in the fiscal apparatus.

The critical surface of standard unit root tests is used provided that the recursive TVC and the fixed coefficient model are asymptotically equivalent.

It is usually suggested that taxes and spending should be measured in terms of foregone private consumption, in which case the use of a CPI deflator is appropriate. The data set is drawn from the IMF International Financial Statistics (IFS).

Debt services include both the internal as well as the external burden, and tax revenues include grants and other subsidies to the government.

Hereafter, significance at the 95% and 99% levels are denoted by * and ** respectively. Standard errors are inside parentheses. In order of appearance, N is the number of observations adjusted for end points, R ² corresponds to its sample adjusted version, σ is the standard error of the regression, DW is the Durbin–Watson statistic and ADF corresponds to the test presented by Equation 2.

The test is marginally significant at the 90% level. The ADF test includes constant, no trend and 3 lags differences. The optimal lag length, choice of intercept and trend, were selected according to the Akaike and Schwarz information criteria (see Grasa, 1989). Critical values are from Davidson and MacKinnon (1993) Table 20.2.

A failure of cointegration implies that a necessary condition for fiscal equilibrium is violated, and that that the meaningfulness of the parameters become irrelevant.

Following Hatemi-J (2002), a recursive TVC version of Equation 4 was also tested. The results, not shown and available upon request, reproduced the asymptotic parameter estimates, residuals and TVC-ADF conclusions.

The error bands are calculated using the TVC-ADF test to the one-step-ahead error bands of the residuals.

See Young et al. (1999) for a comprehensive overview of the social, political and economic events in the DR during the 1990s, and Coutts et al. (1986) for the different episodes characterizing the DR during 1966 through 1986.