SERIE RESEARCH mEmORBnDH ARMAX MODEL SPECIFICATION TESTING, WITH AN APPLICATION TO UNEMPLOYMENT IN THE NETHERLANDS fay

In this paper we present a new model specification test for ARMAX models. The null hypothesis that the ARMAX model represents the conditional expectation of the dependent variable given the entire past of the economie time series process under review is tested against the alternative hypothesis that the null is false. The test involved is a consistent Standard nortnal test, as under the null hypothesis the test statistic is asymptotically N(0,1) distributed, whereas under the alternative that the null is false and under the hypothesis of strict stationarity of the data generating process the absolute value of the test statistic converges in probability to infinity. This test is applied to testing the rational expectations-natural rate (RE-NR) hypothesis for the Netherlands according to the approach of Sargent (1976), on the basis of monthly data and the ARMAX framework. As for the result, it appears that unemployment in the Netherlands is caused, in the sense of Granger (1969), by the money interest rate and unemployment itself. According to Sargent the RE-NR hypothesis therefore has to be rejected. This empirical result can be explained by Baumol's (1959) sales revenue maximization hypothesis, augmented with the hypothesis of a flexible labor effort rate. *) This paper has been presented at the 1986 CAMP Econometrics conference and at econometrics siminars at the University of California, San Diego, the University of Minnesota, Queen's University, the University of Western Ontario and the University of Toronto. In particular I acknowledge the comments of Robert Engle, Joop Hartog, Tammo Oegema, Teo-Perez, Benedict M.Pötscher, Chistopher A.Sims and two referees. April 1986