The method of generalized estimating equations(GEE) is widely used in the analysis of a correlated dataset that consists of repeatedly observed responses within subjects. The GEE uses a quasi-likelihood equations to find the parameter estimates without assuming a specific distribution for the correlated responses. In this paper we study the importance of specifying the working correlation structure appropriately in fitting GEE for correlated counts data. We investigate the empirical coverages of confidence intervals for the regression coefficients according to four kinds of working correlations where one structure should be specified by the users. The confidence intervals are computed based on the asymptotic normality and the sandwich variance estimator.