2. Interpreting fixed effects estimation Suppose a panel data set consisting of 54 firms, over the years 1987, 1988, and 1989, is collected in order to study the influence of a job training program on worker productivity in manufacturing firms. No firm received a job training program grant prior to 1988. In this case, worker productivity at a firm is measured by the scrap rate, which is the number of items per 100 that must be scrapped due to defects. Therefore, a lower scrap rate indicates higher worker productivity, and a higher scrap rate indicates lower worker productivity. Consider the following unobserved effects model (which is then transformed into a fixed effects model): log(scrapit)=1d88t+2d89t+3grantit+4grantit-1+ai+uit where scrapit = scrap rate at firm i in year t d88t = 1 if the year is 1988, and = 0 otherwise d89t = 1 if the year is 1989, and = 0 otherwise grantit = 1 if firm i received a training grant in year t , and = 0 otherwise grantit-1 = 1 if firm i received a training grant in the previous year t1 , and = 0 otherwise ai = unobserved, time-constant effect uit = idiosyncratic error Suppose the within transformation