In this paper we consider the default risk models with multi-period stochastic covariates，incorporating the dynamics of macroeconomic，firm-specific and industry-specific covariates which were used to characterize the credit contagion between industries． We propose maximum likelihood estimators for parameters of default risk intensities，and then show the maximum likelihood estimator for term structure of conditional corporate default probabilities． Meanwhile，it is easy to construct the significant test for credit contagion effect in multi-period corporate default risk models by the maximum likelihood estimators． Finally，simulation studies are conducted to compare the performance of the working independence estimator to that of the weighted marginal likelihood estimator．