Interpreting 2SLS results

[nonsi nkomo]

Hi All

I know this is a bit of a simple question but I keep confusing myself. I have run a 2SLS regression with self-reported health (excellent, very good, good, fair and poor) as the dependent variable. The coefficient of exercise is -0.951. Exercise is measured in 3 categories, inactive, moderately active and highly active. Am I correct in saying that an individual that exercises has poorer health, relative to those that are inactive?

Kind Regards
Nonsi Nkomo

[William Lisowski]

You don't tell us how self-reported health is coded. And on reflection, you don't tell us how exercise is coded, either.

[nonsi nkomo]

My apologies. Self reported health is coded as follows: 1-excellent 2-very good 3-good 4-fair 5-poor and exercise is coded 1 (0 days of exercise per week) 2 (1-4 days) 3 (5 - 7 days).

[William Lisowski]

We can say, given your model and the 2SLS coefficient estimates, that increasing exercise results in a larger value for the exercise variable. Taking this together with the negative estimated coefficient means you will have a smaller predicted value for the self-reported health variable. But the self-reported health variable is coded backwards (1 is better than 2, etc.), so a smaller predicted value of the variable corresponds to better self-reported health.

I would not say that "an individual that exercises has better health, relative to those that are inactive". Stating that requires a belief that the model and its coefficient estimates accurately reflect reality. I have my doubts, largely due to treating categorical variables as continuous.

That's my opinion, in the second paragraph. The statement in the first paragraph, though, is my attempt at a factual statement.

[nonsi nkomo]

Hi William

I am slightly confused. So essentially, less exercise (smaller values of exercise) corresponds to better health. Hence, more days of exercise per week corresponds to poorer health?

Kind Regards
Nonsi Nkomo

[William Lisowski]

I did not make myself clear in post #4.

What you write in post #1 and repeat in post #5 is incorrect.

more days of exercise per week corresponds to poorer health

Let us say that Y is self-reported health coded 1 (excellent) to 5 (poor) and X is exercise coded 1 (no exercise) to 3 (most exercise).

Then your 2SLS results tell you

Y(X) = -0.95 * X + <other things>

where the <other things> do not depend on X.

So if X = 0

Y = -0.95 * 0 + <other things>

and if X = 1

Y = -0.95 * 1 + <other things>

So changing X by +1 changes Y by -0.95.

Now look at your coding for Y - self-reported health. Smaller values of Y mean better health, not poorer health.