We document the results of two straightforward Monte Carlo exercises to illustrate the
reliability of the
respy package. We use the first parameterization from Keane and
Wolpin (1994) and simulate a sample of 1,000 agents. Then we run two estimations with
alternative starting values. We use the root-mean squared error (RMSE) of the simulated
choice probabilities to assess the estimator’s overall reliability. We use the NEWUOA
algorithm with its default tuning parameters and allow for a maximum of 3,000
evaluations of the criterion function.
… starting at true values¶
Initially we start at the true parameter values. While taking a total of 1,491 steps, the actual effect on the parameter values and the criterion function is negligible. The RMSE remains literally unchanged at zero.
… starting with myopic agents¶
Again we start from the true parameters of the reward functions, but now estimate a static (\(\delta = 0\)) model first. We then use the estimation results as starting values for the subsequent estimation of a correctly specified dynamic model (\(\delta = 0.95\)). For the static estimation, we start with a RMSE of about 0.44 which, after 950 steps, is cut to 0.25. Most of this discrepancy is driven by the relatively low school enrollments as there is no investment motive for the myopic agents.
We then set up the estimation of the dynamic model. Initially, the RMSE is about 0.23 but is quickly reduced to only 0.01 after 1,453 steps of the optimizer.
Overall the results are encouraging. However, doubts about the correctness of our implementation always remain. So, if you are struggling with a particularly poor performance in your application, please do not hesitate to let us know so we can help with the investigation.