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My regression model is this:

R2 <- lm(lnwage ~ educ + exper + hrswk + educ*exper + educ2 + exper2)

and I want to estimate: $\frac{\partial ln(wage)}{\partial educ}$ and $\frac{\partial ln(wage)}{\partial exper}$

Is there any way I can do this with R?

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  • $\begingroup$ oh and educ2 and exper2 each refer to the quadratic model! $\endgroup$
    – Ethan
    Commented May 17, 2016 at 2:18
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    $\begingroup$ Do you know how to take derivatives of quadratic functions? $\endgroup$
    – Glen_b
    Commented May 17, 2016 at 5:40

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I hope I'm not misunderstanding you, but can't you just calculate them from the estimated coefficients? $\frac{d lnwage}{d educ} (educ,exper,hrswk)$ Will just equal the coefficient on $educ$ plus $exper$ times the coefficient on $(educ*exper)$ plus 2 times the coefficient on $(educ^2)$ for instance.

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You can do it on R but you'll have to write the code yourself (there's no explicit method for the lm class that will do it for you) If your model is $Y:=\beta_0+\beta_1a+\beta_2b+\beta_3ab+\beta_4a^2+\beta_5b^2+\epsilon$, then:

$\frac{\delta Y}{\delta a} = \beta_1 + b\beta_3 +2a\beta_4$

R will provide the $\beta_k$ coefficients with coefficients(R2), returning a numeric. But be careful, as coefficients(R2)[1] is the intercept, coefficients(R2)[2] is $\beta_1$ and so on!

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Maybe this is what you're looking for, Ryacas lets you do a little algebra:

##### set your algebraic symbols
intercept = Ryacas::ysym("intercept")
educ = Ryacas::ysym("educ")
exper = Ryacas::ysym("exper")
hrswk = Ryacas::ysym("hrswk")
Coefeduc = Ryacas::ysym("Coefeduc")
Coefexper = Ryacas::ysym("Coefexper")
Coefhrswk = Ryacas::ysym("Coefhrswk")
Coefeduc2 = Ryacas::ysym("Coefeduc2")
Coefexper2 = Ryacas::ysym("Coefexper2")
Coefeducexper = Ryacas::ysym("Coefeducexper")

##### give the function (that equals lnwage)
f = intercept + Coefeduc*educ + Coefexper*exper + Coefhrswk*hrswk + Coefeducexper*educ*exper + Coefeduc2*educ^2 + Coefexper2*exper^2
f
# y: intercept+Coefeduc*educ+Coefexper*exper+Coefhrswk*hrswk+Coefeducexper*educ*exper+Coefeduc2*educ^2+Coefexper2*exper^2

##### find the derivatives of your functions with respect to your two variables
g_educ = deriv(f, "educ")
g_exper = deriv(f, "exper")

g_educ
# y: Coefeduc+Coefeducexper*exper+2*Coefeduc2*educ

g_exper
# y: Coefexper+Coefeducexper*educ+2*Coefexper2*exper
```
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