<p>In this paper, we develop pretest and shrinkage estimators for integer-valued autoregressive (INAR) models of order one with covariates when it is conjectured that some regressors are insignificant. Model parameters are estimated within a quasi-likelihood framework. We show that shrinkage estimators have significantly higher relative efficiency than non-shrinkage estimators. A Monte Carlo simulation experiment is conducted for different combinations of insignificant predictors and the performance of each estimator is evaluated in terms of the simulated mean squared error. Our study shows that pretest and shrinkage estimators outperform unrestricted estimators in terms of mean squared error when the number of insignificant predictors in the model is relatively large. The benefit of our method is illustrated by a regression model for a precipitation count time series dataset.</p>