I am estimating a learning curve model: Y = bX^-.4
I would like to graph the marginal effect of X on Y with a confidence interval across the range of X.
As I understand it, the marginal effect = -.4bX^-1.4
I am not sure, however, how estimate a standard errors for the effect. Following/extending the material in Brambor, Clark, and Golder (2006), it appears that the formula would be:
gen conse2=sqrt(varb*(-.4*-.4)*(X^-2.8))
However, this formula ensures that the standard error can only decrease as X increases, which seems odd to me.
Is this formula for the standard error correct? Any thoughts?
I would like to graph the marginal effect of X on Y with a confidence interval across the range of X.
As I understand it, the marginal effect = -.4bX^-1.4
I am not sure, however, how estimate a standard errors for the effect. Following/extending the material in Brambor, Clark, and Golder (2006), it appears that the formula would be:
gen conse2=sqrt(varb*(-.4*-.4)*(X^-2.8))
However, this formula ensures that the standard error can only decrease as X increases, which seems odd to me.
Is this formula for the standard error correct? Any thoughts?