Hi all,

Upon visual inspection of my data, I noticed that my continuous variable, csh_sh, increased and decreased with age. Using a bar chart comparing mean values across age categories, I observed a cubic function.

I therefore used the following commands which confirmed this:

Code:
regress csh_sh c.age##c.age##c.age
margins, at(age = (18(7)90))
marginsplot
Array




I now have my regression model as csh_sh = b0 + b1age +b2age^2 + b3age^3 excluding control variables for simplification purposes. The results from OLS estimation is as follows:

Code:
regress csh_sh c.age##c.age##c.age
---------------------------------------------------------------------------------
cashshare | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------------------+----------------------------------------------------------------
age | -.0256759 .0049533 -5.18 0.000 -.035386 -.0159658
|
c.age#c.age | .0005023 .0001001 5.02 0.000 .0003062 .0006985
|
c.age#c.age#c.age | -3.11e-06 6.42e-07 -4.84 0.000 -4.37e-06 -1.85e-06
|
_cons | .6778854 .0771562 8.79 0.000 .5266348 .8291361


With regard to the interpretation of coefficients (in bold), can any provide any recommendations? I know that interpreting these coefficients is a lot more complex than interpreting linear relationships.

When I include my control variables, all three coefficients are no longer statistically insignificant. In this case, I would argue no significant relationship is present. However, I would be useful to understand what the size of of the coefficients actually mean/imply.

Any advice/recommendation on this would be really appreciated. Thanks!