"Fixed effect" regression


Fortran must die
I am trying to figure out what the author means by this. I have not seen this terminology used before.

The basic statistical model framework under WIOA is the fixed effect model specified as follows (Sutter [7]): Consider the linear model for our data observations grouped into states j = 1, ..., j, for each quarterly time period t = 1, ..., t: yjt = aj + βxjt + ε jt; ε ijt ~ N(0, σ y 2 ). (3) The effect of x on y, denoted β, is the primary quantity of interest. After accounting for the effect of x, there is still additional variation in the overall level of y across units. The unit effect aj captures the additional variation by which predictions of y ... in unit j must be adjusted upward or downward, given only observations of x. The interpretation of aj is that it represents un-measurable or omitted factors that affect y, beyond those included in x. If these factors were measurable and of interest, they could be included as additional explanatory variables in the matrix x, eliminating the variation captured by a j . However, these variables are not practicably measurable and must be captured by modeling aj . The fixed effects model is a linear regression of y on x along with a series of dummy variables that account for unit-to unit variation in the outcome variable. The coefficients, aˆ j , computed for each unit are estimates of the true unit effects aj . The mean unit effect is estimated by μ a and σa 2 denotes how much the unit effects vary around μ a. The fixed effects model will produce unbiased estimates of β but those estimates can be subject to high sample to-sample variability.

Part of the problem is we are suggesting variables we feel are left out of the model and their response is that all such effects are inherently part of the fixed effect. Almost like an intercept although I don't think that is what they mean. The overall impact of individual states is shown in large part by this fixed effect.