Dear list members,
I am interested in the effect of x on y and have reason to assume that it is non-linear. Therefore I started by creating dummies x1, x2 and x3 for x being above its 25th, 50th and 75th percentile and regressing y on x1, x2 and x3. I found positive coefficients on x1 and x2, but a negative one on x3, suggesting that the marginal effect of x on y does indeed become smaller again for the highest x.
However, critics rightly made the point that these coefficients are likely to suffer from omitted variable bias. Luckily I found a good instrument z for x, so that I can estimate -ivreg y (x=z)-. However, I am unsure whether I can now still cut x into a set of dummies and investigate whether the effect is nonlinear. In principle I could as well cut z into z1, z2 and z3 for the 25th, 50th and 75th percentile and instrument x1 with z1, x2 with z2 and x3 with z3. But I am not sure whether this would really be valid or whether there is any good reference for doing so. Would anyone happen to know more here?
Thank you so much and kind regards,
PM
I am interested in the effect of x on y and have reason to assume that it is non-linear. Therefore I started by creating dummies x1, x2 and x3 for x being above its 25th, 50th and 75th percentile and regressing y on x1, x2 and x3. I found positive coefficients on x1 and x2, but a negative one on x3, suggesting that the marginal effect of x on y does indeed become smaller again for the highest x.
However, critics rightly made the point that these coefficients are likely to suffer from omitted variable bias. Luckily I found a good instrument z for x, so that I can estimate -ivreg y (x=z)-. However, I am unsure whether I can now still cut x into a set of dummies and investigate whether the effect is nonlinear. In principle I could as well cut z into z1, z2 and z3 for the 25th, 50th and 75th percentile and instrument x1 with z1, x2 with z2 and x3 with z3. But I am not sure whether this would really be valid or whether there is any good reference for doing so. Would anyone happen to know more here?
Thank you so much and kind regards,
PM
