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I run an OLS multiple regression model estimating expected chance of getting a job at a company $X$ for different subgroups.

${gets~job}_i = \hat{\alpha} + \hat{\beta_1}\cdot talent_i + \hat{\beta_2}\cdot woman_i + \hat{\beta}3 \cdot talent_i \cdot woman_i + \hat{\epsilon}_i$.

$E[gets~job|woman = 0, talent = 0] = \alpha $
$E[gets~job|woman = 0, talent = 1] = \alpha + \beta_1 $
$E[gets~job|woman = 1, talent = 0] = \alpha + \beta_2 $
$E[gets~job|woman = 1, talent = 1] = \alpha + \beta_1 + \beta_2 + \beta_3 $

My question: How do I, by hand and (quickly) in R, test the hypothesis $\beta_1 + \beta_3 = 0$ in words something like "does talent matter for women?".

Dummy data for R:

n = 1e4
set.seed(6)
df <- data.frame(gets.job = sample(0:1, size = n, replace = TRUE),
                 talent   = sample(0:1, size = n, replace = TRUE),
                 woman    = sample(0:1, size = n, replace = TRUE))

ols.m <- lm(gets.job ~ talent*woman, data = df)
snoram
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1 Answers1

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I think this is a standard problem. You might want to look for instance,

Fitting models in R where coefficients are subject to linear restriction(s)

Community
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F. Tusell
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    This is being automatically flagged as low quality, probably because it is so short. At present it is more of a comment than an answer by our standards. Can you expand on it? You can also turn it into a comment. – gung - Reinstate Monica Sep 13 '16 at 12:17
  • Sorry. I thought that an internal link (to a Cross Validated page) would be of a guaranteed persistency and hence acceptable. – F. Tusell Sep 14 '16 at 04:40