Negative predictions of wage

[Facundo Duran]

Hello everyone!
I am working with a panel data model, which contains information on workers from 1996 to 2021. As there are periods where workers stop working, to correct the selection bias I am using the Heckman correction, more precisely the one suggested by wooldridge .

For this I am doing it manually since the xtheckmanfe command does not work with my data.
First, I compute the inverse of the mills ratio by running 312 probits of the selection equation, which are the monthly periods from 1996 to 2021.
Then once I have the inverse of the mills ratio I enter it in my regression as follows

reg wb_tot edad tenure medad mtenure mdesempleo T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14 T15 T16 T17 T18 T19 T20 T21 T22 T23 T24 T25 T26 T27 T28 T29 T30 T31 T32 T33 T34 T35 T36 T37 T38 T39 T40 T41 T42 T43 T44 T45 T46 T47 T48 T49 T50 T51 T52 T53 T54 T55 T56 T57 T58 T59 T60 T61 T62 T63 T64 T65 T66 T67 T68 T69 T70 T71 T72 T73 T74 T75 T76 T77 T78 T79 T80 T81 T82 T83 T84 T85 T86 T87 T88 T89 T90 T91 T92 T93 T94 T95 T96 T97 T98 T99 T100 T101 T102 T103 T104 T105 T106 T107 T108 T109 T110 T111 T112 T113 T114 T115 T116 T117 T118 T119 T120 T121 T122 T123 T124 T125 T126 T127 T128 T129 T130 T131 T132 T133 T134 T135 T136 T137 T138 T139 T140 T141 T142 T143 T144 T145 T146 T147 T148 T149 T150 T151 T152 T153 T154 T155 T156 T157 T158 T159 T160 T161 T162 T163 T164 T165 T166 T167 T168 T169 T170 T171 T172 T173 T174 T175 T176 T177 T178 T179 T180 T181 T182 T183 T184 T185 T186 T187 T188 T189 T190 T191 T192 T193 T194 T195 T196 T197 T198 T199 T200 T201 T202 T203 T204 T205 T206 T207 T208 T209 T210 T211 T212 T213 T214 T215 T216 T217 T218 T219 T220 T221 T222 T223 T224 T225 T226 T227 T228 T229 T230 T231 T232 T233 T234 T235 T236 T237 T238 T239 T240 T241 T242 T243 T244 T245 T246 T247 T248 T249 T250 T251 T252 T253 T254 T255 T256 T257 T258 T259 T260 T261 T262 T263 T264 T265 T266 T267 T268 T269 T270 T271 T272 T273 T274 T275 T276 T277 T278 T279 T280 T281 T282 T283 T284 T285 T286 T287 T288 T289 T290 T291 T292 T293 T294 T295 T296 T297 T298 T299 T300 T301 T302 T303 T304 T305 T306 T307 T308 T309 T310 T311 T312 ano#c.lambda2

where wb_tot is the salary, edad is the age of the worker in each period, tenure is the worker's experience, mtenure and mdesempleo are the averages of experience and unemployment, then there is a dummy for each period and lambda2 is the inverse of the mills ratio.
The problem I have is that when I run the regression and predict the salary, it generates negative values for some observations. How can I correct the model so that it is limited to only positive values?

[George Ford]

how are you predicting?

[Facundo Duran]

how are you predicting?

predict yhat, xb

[George Ford]

run it without lamba2 to see if that's the source.

[George Ford]

You've probably got a scale effect (wide ranges on the X's). Are you using logs?

I'm not surprised you'd get a few negatives. The model is predicting the mean. truncreg might help.

[Facundo Duran]

run it without lamba2 to see if that's the source.

Thank you for the answer!
I did it without lambda2 but there are still negative values
I do not use logarithm because I want to predict the wage to compare it with the observed one and to later make forecasting for the future values.
But why would it be negative if the model predicts the mean and the observed salaries are positive?

[FernandoRios]

Hi Facundo
The answer is simple, Its a linear model . Linear models have the limitation of being terrible at predictions of Limited dependent variables.
We usually cover this in econometrics for the Linear Probability case, but it is present in other models as well.
A LRM may sometimes predict negative (unrealistic) values because its imposing a linear relationship to the data.
F

[George Ford]

logs may help.

predict yhat, xb
replace yhat = (exp(yhat)*exp((`e(rmse)'^2)/2))

[Clyde Schechter]

And when thinking of predicting a log transformed variables, consider -poisson, vce(robust)-.

[Facundo Duran]

logs may help.

predict yhat, xb
replace yhat = (exp(yhat)*exp((`e(rmse)'^2)/2))

Thank you for the answer!
Please can you explain to me what the code does? Because when I run it it replaces all the values with missing

[Facundo Duran]

And when thinking of predicting a log transformed variables, consider -poisson, vce(robust)-.

Thanks for the reply!
If I understood correctly, the idea would be to use the logarithm of the salary and instead of doing a linear regression, do a poisson, something like that?

 
 poisson log_wb_tot edad tenure medad mtenure mdesempleo T1 T2 T3 T4 T5 T6 T7 ... T312 ano#c.lambda2, vce(robust)

Then can I apply the exponential to the results to have the salary again?

[Facundo Duran]

Hi Facundo
The answer is simple, Its a linear model . Linear models have the limitation of being terrible at predictions of Limited dependent variables.
We usually cover this in econometrics for the Linear Probability case, but it is present in other models as well.
A LRM may sometimes predict negative (unrealistic) values because its imposing a linear relationship to the data.
F

Thanks for your answer!
What would you suggest?
I am seeing that the negative values of the predicted salary correspond when the individual is not working.

[Jeff Wooldridge]

Facundo: This is almost always done using log wage or salary. That's what I would recommend. Usually, prediction is not the point of estimating a wage equation and accounting for selection. If you're interested in predicting wb_tot after estimating the model for log(wb_tot), I can make some suggestions. For now, I assume you are concerned about the logical inconsistency of negative fitted values.

BTW, fitting 312 different probits is the most flexible approach but might not be necessary. You could estimate a pooled probit with time dummies and the controls entered flexibly. If you have large N, you can get away with one for each time period.

[Jeff Wooldridge]

Just to check: You should be setting wb_tot to missing, not zero, when the individual isn't working.

[Facundo Duran]

Facundo: This is almost always done using log wage or salary. That's what I would recommend. Usually, prediction is not the point of estimating a wage equation and accounting for selection. If you're interested in predicting wb_tot after estimating the model for log(wb_tot), I can make some suggestions. For now, I assume you are concerned about the logical inconsistency of negative fitted values.

BTW, fitting 312 different probits is the most flexible approach but might not be necessary. You could estimate a pooled probit with time dummies and the controls entered flexibly. If you have large N, you can get away with one for each time period.

Dr Wooldrige thank you for your answer!
Yes, my idea would be to be able to make salary predictions, to compare it with the observed salary and also to be able to make future predictions, and thus be able to complete the observed window. The latter is because I am working on seeing the redistributive effect of the pension system throughout life, the data panel is 26 years old, the idea would be to be able to complete the observations through predictions.
So you recommend that I use log(wb_tot) ?
Yes, wb_tot is missing when individual isn´t working