randomcoefficients

Random coefficients refer to parameters in a statistical model that are not fixed but are instead treated as random variables themselves. This means that instead of assuming a single, constant value for a coefficient, we allow it to vary according to some probability distribution. This approach is commonly used in econometrics, particularly in panel data analysis, and in other fields where heterogeneity across units or time is expected.

The primary motivation for using random coefficients is to account for unobserved heterogeneity. For example, in a study examining the relationship between education and income, the return to education might not be the same for everyone. Some individuals might benefit more from additional schooling than others due to unobserved factors like innate ability, motivation, or quality of education. A random coefficients model can capture this variability by allowing the coefficient on education to differ across individuals, with these individual-specific coefficients drawn from a common distribution.

When estimating a random coefficients model, the goal is not only to estimate the mean of the distribution of the coefficients but also to estimate the variance or other parameters that characterize this distribution. This provides more insight into the extent of heterogeneity present in the data. Compared to fixed effects models, which allow coefficients to vary but treat them as unknown constants to be estimated, random coefficients models assume a specific distributional form for these varying coefficients and estimate the parameters of that distribution. This can lead to more efficient estimation, especially when the number of units or time periods is large relative to the number of predictors. However, the validity of the inference relies on the correctness of the assumed distribution for the random coefficients.