Hello,
This is sort of a continuation of the discussion here: https://www.statalist.org/forums/for...ally-very-high
Prof. Wooldridge kindly got me on the right track on interpreting margins dydx for the linear model with square terms. Now, I have a more conceptual followup question. I thought that this better be in a different thread as the topic is quite different from the original thread above.
Say have my model as :
ln(y) = b0 + b1 x + b2 x^2 + b3 z1 + b4 z2 + e
I estimated and have coefficients for it, it does exhibit the inverted U behavior. Please note that x is a variable between 0 and 1, and the inflection point is well within the range.
Now, if I evaluate ln(y1) = ln(y) evaluated at x=x1 and ln(y2) = ln(y) evaluated at x=x2, then
ln(y2) - ln(y1) = -b1 x1 - b2 x1^2 + b1 x2 + b2 x2^2
Taking exponents on both sides and simplifying:
y2/y1 = Exp(-b1 x1 - b2 x1^2 + b1 x2 + b2 x2^2)
So, if I now substitute b1, b2 coefficients and select two points x1 and x2 (x2>x1, and both are smaller than the inflection point) in the RHS, can I then interpret that as the ratio between y2/y1?
Say, that the ratio is evaluated as 1.4, then can I state that moving x from x1 to x2, yields a 40% increase in y?
From my experiments with predicted values, this does work out. But I am concerned that I am just playing around with point estimates and making some grave errors on not considering standard errors.
This is sort of a continuation of the discussion here: https://www.statalist.org/forums/for...ally-very-high
Prof. Wooldridge kindly got me on the right track on interpreting margins dydx for the linear model with square terms. Now, I have a more conceptual followup question. I thought that this better be in a different thread as the topic is quite different from the original thread above.
Say have my model as :
ln(y) = b0 + b1 x + b2 x^2 + b3 z1 + b4 z2 + e
I estimated and have coefficients for it, it does exhibit the inverted U behavior. Please note that x is a variable between 0 and 1, and the inflection point is well within the range.
Now, if I evaluate ln(y1) = ln(y) evaluated at x=x1 and ln(y2) = ln(y) evaluated at x=x2, then
ln(y2) - ln(y1) = -b1 x1 - b2 x1^2 + b1 x2 + b2 x2^2
Taking exponents on both sides and simplifying:
y2/y1 = Exp(-b1 x1 - b2 x1^2 + b1 x2 + b2 x2^2)
So, if I now substitute b1, b2 coefficients and select two points x1 and x2 (x2>x1, and both are smaller than the inflection point) in the RHS, can I then interpret that as the ratio between y2/y1?
Say, that the ratio is evaluated as 1.4, then can I state that moving x from x1 to x2, yields a 40% increase in y?
From my experiments with predicted values, this does work out. But I am concerned that I am just playing around with point estimates and making some grave errors on not considering standard errors.
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