For instance, taking a person who finds a job with a high salary this year, it will be easier for her to find a job with a high salary next year because the fact that she has a high-wage job this year will be a very positive signal for the potential employers.
The essence of this type of dynamic effect is the state dependence of the outcome.
The "unobservable effects" here refers to the factor which partially determines the outcome of individual but cannot be observed in the data.
For instance, the ability of a person is very important in job-hunting, but it is not observable for researchers.
Expectation Maximum (EM) algorithm is usually a good solution for this computation issue.
[3] Based on the consistent point estimates from MLE, Average Partial Effect (APE)[4] can be calculated correspondingly.
In this type of model, economists have a special interest in ρ, which is used to characterize the state dependence.
For example, yi,t can be a woman's choice whether to work or not, zit includes the i-th individual's age, education level, number of children, and other factors.
ci can be some individual specific characteristic which cannot be observed by economists.
There are several MLE-based approaches to estimate δ and ρ consistently.
The simplest way is to treat yi,0 as non-stochastic and assume ci is independent with zi.
Treating yi,0 as non-stochastic implicitly assumes the independence of yi,0 on zi.
An improvement on the approach above is to assume a density of yi,0 conditional on (ci, zi) and conditional likelihood P(yi,t , yi,t-1 , … , yt,1,yi,0 | ci, zi) can be obtained.
Based on the estimates for (δ, ρ) and the corresponding variance, values of the coefficients can be tested[9] and the average partial effect can be calculated.