Maximum likelihood estimation in a Gompertzian stochastic model for salaries

Abstract

This thesis discusses the parameter estimation of a homogeneous stochastic Gompertz diffusion model. This study can be divided into three main parts. In the first part we give an introduction to stochastic calculus. This will give us important theoretical results which will be used in the remaining sections. In the second part we derive the transition probability density function from the corresponding stochastic differential equation and Kolmogorov equation. With this density function in hand, in the third and final part we discuss the maximum likelihood method for estimating parameters. First we apply this methodology on simulated data with known parameters. The estimates obtained are then compared with those used in the simulation. Finally we apply this method to our data, which is the average salary per worker per year for the period 1970 till 2008.