st: Test between two non-nested models

[Jacob Hansen <jacobmoller@gmail.com>]

Dear fellow Statalist users

I would like to know if there is a way I can formally test which of
two competing models is best? The one is linear and the other is
non-linear, i.e. i use OLS for one and nonlinear least squares for the
other. I have two models because I am testing two different
"competing" economic theories.

Short intraduction:
I am trying to test if I can reject that people discount exponentially
or hyperbolically. I am doing this based on intra-monthly consumption.
I have information on peoples consumption and when their pay-day is.

In my estimation I use individual-specific fixed effects on the NLLS
and individual AND time
fixed effects for OLS. The reason I only use individual-specific on 1
is lack of computational power.

I find that both beta from NLLS and delta from OLS are highly
significant. But, R-squared is much greater in NLLS than in OLS (0.18 vs
0.7).

Does anyone have an idea to how I can test/argue for for which model
is better? Other than just R-squared.

In the article I am using he jointly estimated the two by including
t*log(delta) in 1). He then test if beta=1 and delta<=1 against beta<1
and delta=1. Is this the right way to go about it?

Article: "Heterogeneity in Intra-Monthly Consumption Patterns,
Self-Control, and Savings at Retirement 2009" see page 178 for his
short comments on the joint estimation.

Any help is greatly appreciated.

Jacob Hansen

(I use Stata 12.1 and have Windows 8)
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