Often‎, ‎in high dimensional problems‎, ‎where the number of variables is large the number of observations‎, ‎penalized estimators based on shrinkage methods have better efficiency than the OLS estimator from the prediction error viewpoint‎. In these estimators‎, ‎the tuning or shrinkage parameter plays a deterministic role in variable selection‎. ‎The bridge estimator is an estimator which simplifies to ridge or LASSO estimators varying the tuning parameter‎. ‎In these paper‎, ‎the shrinkage bridge estimator is derived under a linear constraint on regression coefficients and its consistency is proved‎. ‎Furthermore‎, ‎its efficiency is evaluated in a simulation study and a real example‎.