| In this dissertation I have researched into three different fields of econometrics: the use of prior information modelled as stochastic restrictions, the methodology of indirect inference (I.I.) and the econometric estimation of the capital stock.; Related with the first issue, first I have found that under some technical assumptions on the variance of the stochastic restrictions (more natural in a finite sample context), the nonlinear least squares under stochastic restrictions (SR) estimator is asymptotically more efficient than the nonlinear least squares (NLS) estimator, as found when normal errors are assumed in finite samples. This result is stated in the opposite direction of the standard asymptotic theory result about the relevance of the prior information, and recovers the importance of prior information in nonlinear contexts. Second, I show that the suggested approximated distribution of the SR estimator is a better approximation to the true one than the one suggested when the stochastic restrictions are not taken into account, i.e., the NLS distribution.; In the second research field, I define a new estimation method that comes up when the stochastic restriction approach is extended to the I.I. methodology. In this context, I show the following results. First, I provide the definition and the distribution of the new estimator called Indirect Inference under Stochastic Restrictions (IISR). Second, I show that the IISR estimation is asymptotically more efficient than the I.I. estimation in which is based, and hence approximated terms for finite samples. Finally, I suggest a test for the validity of the stochastic restrictions used in the estimation.; The third research field is related with the econometric estimation of the physical capital stock of an economy. First, I suggest two methods to estimate a variable rate of depreciation, what is not an easy task in standard econometric packages. This method allows estimating an endogenous rate of depreciation by NLS or ML together with the parameters of a production function. The effectiveness of the methods proposed is shown by mean of the empirical estimation of the rate of depreciation of the capital stock of several economies of the EU, which leads to depreciation rates around 5%. Once the estimation problem of a variable rate of depreciation is solved, I develop new methods to estimate an endogenous and stochastic rate of depreciation. The estimation of the parameters needs to be solved by mean of simulated based estimation methods, since stochastic parameters are considered. Finally the problem is solved when prior information on the rate of depreciation is feasible. Given the properties of the model, IISR method is suitable to solve the estimation problem, which is shown in several Monte Carlo exercises. |
