Statalist:
I am running the following Probit model on pooled panel data:
\[ P(y_{it} = 1 \vert x_{it}) = \Phi(b_0 + \delta_t + b_1 \varepsilon_t \times x_{it} + b_2 x_{it}) \] The RHS includes two terms: (i) an interaction term between the individual-specific, binary variable x and a variable epsilon that is common across all observations in each time period, i.e., a macro variable; and (ii) time fixed-effects, denoted delta. Suppose I want to estimate exactly this specification, with x = 0 as base value. Then Stata correctly returns the coefficient b2 which indicates a level shift if x = 1. However, the interaction effect b1 captures the additional elasticity of y w.r.t. to x if x = 0, i.e., the wrong base level. Here is a cooked-up example:
Note that as long as I allow for the level of varepsilon to enter the model, the base categories are correct (obviously, I cannot have time fixed-effects in this case).
Any hints would be greatly appreciated!
Thanks,
Peter
I am running the following Probit model on pooled panel data:
\[ P(y_{it} = 1 \vert x_{it}) = \Phi(b_0 + \delta_t + b_1 \varepsilon_t \times x_{it} + b_2 x_{it}) \] The RHS includes two terms: (i) an interaction term between the individual-specific, binary variable x and a variable epsilon that is common across all observations in each time period, i.e., a macro variable; and (ii) time fixed-effects, denoted delta. Suppose I want to estimate exactly this specification, with x = 0 as base value. Then Stata correctly returns the coefficient b2 which indicates a level shift if x = 1. However, the interaction effect b1 captures the additional elasticity of y w.r.t. to x if x = 0, i.e., the wrong base level. Here is a cooked-up example:
Code:
webuse union, clear * generate variable common across all observations in a given year gen vareps = rnormal() by year, sort: replace vareps = vareps[1] drop if grade<4 * model with both level terms and interaction probit union c.vareps##ib0.black, coeflegend -------------------------------------------------------------------------------- union | Coef. Legend ---------------+---------------------------------------------------------------- vareps | .0253084 _b[vareps] 1.black | .2894273 _b[1.black] | black#c.vareps | 1 | -.0096174 _b[1.black#c.vareps] | _cons | -.8508753 _b[_cons] -------------------------------------------------------------------------------- * model with level of black and interaction with vareps plus year fixed-effects probit union ib0.black c.vareps#ib0.black i.year, coeflegend -------------------------------------------------------------------------------- union | Coef. Legend ---------------+---------------------------------------------------------------- 1.black | .2884075 _b[1.black] | black#c.vareps | 0 | .0112105 _b[0b.black#c.vareps] 1 | 0 _b[1o.black#co.vareps] | _cons | -.8902326 _b[_cons] --------------------------------------------------------------------------------
Any hints would be greatly appreciated!
Thanks,
Peter
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