# Testing for equality of estimated coefficients between two models

#### naelwing

##### New Member
Good morning,

I need an information as I'm estimating two models by OLS :

- The first one estimates a standard linear model Y = a + B.X + epsilon
This gives me the estimation of a coefficient (beta) for the variable X with a certain estimated standard deviation S0

- The second one splits the variable X and the constant into a positive part and a negative part with the help of a dummy variable D, which is equal to 1 when X is positive and 0 when X is negative :
Y = a_pos*D + a_neg*(1-D) + b_pos*D*X + b_neg*(1-D)*X + e

Therefore this second model would check for a possible assymetry effect in beta.

With it, I obtain estimates for the constants, and two coefficients beta_pos and beta_neg with standard deviations S1 and S2 ( and both are different to eachother and to S0)

My problem here is, I would like to compare the two estimates I get from the second model to the one I got from the first model to check if beta_pos and beta_neg are together equivalent to the beta from the first model or if there's an assymetry effect.

I suppose that I am supposed to use some sort of t (or F?)-test for mean comparison using the value of the estimated coefficients and standard deviations, but I'm not so sure how to proceed since I'm comparing 2 estimates to only one.

Could someone tell me which test would check for this? Thanks for your help.

#### hlsmith

##### Omega Contributor
You can compare them. I don't run much linear regression, so I don't recall the actual calculations. Though you can use some type of test based on RSS values between models if I recall. Yeah, likely f-test related.

Sorry I am not more helpful. If they were nested models you could use a log likelihood test.