Working Paper: NBER ID: w18252
Authors: Edward C. Norton
Abstract: Although independent unobserved heterogeneity--variables that affect the dependent variable but are independent from the other explanatory variables of interest--do not affect the point estimates or marginal effects in least squares regression, they do affect point estimates in nonlinear models such as logit and probit models. In these nonlinear models, independent unobserved heterogeneity changes the arbitrary normalization of the coefficients through the error variance. Therefore, any statistics derived from the estimated coefficients change when additional, seemingly irrelevant, variables are added to the model. Odds ratios must be interpreted as conditional on the data and model. There is no one odds ratio; each odds ratio estimated in a multivariate model is conditional on the data and model in a way that makes comparisons with other results difficult or impossible. This paper provides new Monte Carlo and graphical insights into why this is true, and new understanding of how to interpret fixed effects models, including case control studies. Marginal effects are largely unaffected by unobserved heterogeneity in both linear regression and nonlinear models, including logit and probit and their multinomial and ordered extensions.
Keywords: No keywords provided
JEL Codes: C25; I19
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Independent unobserved heterogeneity does not affect point estimates in least squares regression (C20) | Independent unobserved heterogeneity affects point estimates in nonlinear models such as logit and probit models (C21) |
| Normalization of coefficients through the error variance changes when additional irrelevant variables are included (C51) | Odds ratios must be interpreted conditionally on the model specification (C25) |
| Odds ratios must be interpreted conditionally on the model specification (C25) | Each odds ratio is dependent on the specific data and model used (C29) |
| Odds ratios must be interpreted conditionally on the model specification (C25) | Complicates comparisons across different studies and models (C52) |
| Independent unobserved heterogeneity influences the interpretation of results across different modeling approaches (C21) | Interpretation of odds ratios is significantly more complex than previously understood (C25) |
| Independent unobserved heterogeneity influences the interpretation of results across different modeling approaches (C21) | Makes it challenging to generalize findings (C90) |
| Researchers should be cautious in reporting odds ratios without clearly stating the conditioning factors (C90) | Can lead to misinterpretation and misunderstanding of the results (C83) |
| Results from Monte Carlo simulations illustrate that the estimated coefficients in probit and logit models increase when independent variables are added (C35) | In contrast to linear models where coefficients remain unchanged (C51) |