STATA does not provide the value for the Durban Watson for the case of cross sectional data, thus there is no direct way to determine the presence of autocorrelation. So following syntax can be used after the OLS regression to generate the Durban Watson Statistic.
predict resid, resid
generate lresid = resid[_n-1]
generate devsq = (resid – lresid)^2
generate ressq = resid * resid
tabstat ressq devsq, statistics( sum )
here divide the displayed value of devsq with ressq it will provide the value of DW, it ranges from 0 to 4. The more it is nearer to 2 the more chances that there is not autocorrelation.
Since it is a cross sectional data, so presence of autocorrelation means that there is some quality that exists in the error term that is inter-related across the cross sections. In other words it means there are some important variables missing.