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In this paper we propose a sparse indirect inference estimator. In order to achieve sparse estimation of the parameters, we add the Smoothly clipped absolute deviation $\ell_1$--penalty of Fan and Li (2001) into the indirect inference objective function introduced by Gouri{\'e}roux et al (1993). We extend the asymptotic theory and we show that the sparse--Indirect Inference estimator enjoys the oracle properties under mild regularity conditions. The method is applied to estimate the parameters of large dimensional Seemingly unrelated non-Gaussian regression models