This paper applies new panel estimation techniques to the estimation of the elasticity of private production with respect to public capital in a regional setup. We use the widely applied production function approach and regional data from Finland in the period of 1975-2004. In contrast to many previous studies about the productivity of public capital, we focus especially on panel estimation techniques. We show that the results from commonly applied fixed effects OLS are probably biased and sensitive to change of an estimator. To get more reliable results, we use the panel DOLS and panel DSUR estimators. According to results, public capital seems to have had a positive impact on private production.