Unobserved effects versus idiosyncratic errors
Suppose you have two years' worth of panel data on wages and work experience of adults; however, the data set has no further information on the characteristics of the individuals in the data set. Specifically, you have cross-sectional wage and work experience data on individuals in 2006, and cross-sectional data on those same individuals in 2012. You plan to use the following fixed effects model to analyze the effects of work experience on wages:
log (wage it ) = βo + 80 yr10, + B1 experit + ai + uit
where
wage it = yearly wage of individual i at time t, in dollars
yrl0, =1 in the year 2010 (t = 2), and =0 otherwise (t = 1)
exper = years of work experience of individual i, at time t
ai = unobserved (time-invariant) effect
uit = idiosyncratic error
Two other factors that can influence wage, which you have not controlled for in your model, are height and industry of employment.
Use the following table to indicate which term in the fixed effects model captures the effect of height, which term captures the effect of industry of employment, and which term captures the effect of work experience.
ai uit β1
Work experience
Height
Industry of employment

The "idiosyncratic error" (uit) describes the unobserved factors that impact the dependent variable. For example, industry of employment, and this factor vary from one-time period to the next.

The unobserved (time-invariant) effect (ai) refers to the height of the industry of employment, which does not vary over time.

Finally, work experience is depicted by β1, which is a factor that changes with time.