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An authority has decided to legislate on stricter rules regarding amortization. The previous legislation stated that a mortgage loan has to be amortized down to a degree of at least 75% of the price that you bought the property for within 15 years. The new legislation states that a mortgage loan has to be amortized down to a degree of at least 70% of the price that you bought the property for within 15 years. The new legislation also states that all banks has to do an individual recommendation of amortization for all customers.

How can I do if I want to compare the mean monthly amortization before and after the legislation? Of course the mean should be at least 5% higher due to the stricter rules, but it is the effect of the individual recommendation that is of interest. Is there a way to estimate whether people amortize more on top of the minimum amortization compared to before and at the same time control for the effect that the extra 5% has on the mean?

I know about fixed-effects in regression analysis, is there anything like it in t-test?

I have tried to be as specific as I can but english is not my native toungue. If any questions emerge, I will try to explain what I want to do better.

Regards, Filip

Filip
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I don't know of a named 'fixed-effect t-test', but regression can be viewed as a generalization of a t-test. Therefor, you can just set up a fixed-effects regression model where you have an intercept term, and one independent variable called say, vector $\mathbf{x}$, and your dependent variable vector $\mathbf{y}$, the monthly amortization. If $\mathbf{y}_{i}$ is a a amortization value from before legislation, set $\mathbf{x}_{i} = 0$. If $\mathbf{y}_{i}$ is the value after legislation, set $\mathbf{x}_{i} = 1$. This is called a dummy variable encoding. Then solve your regression model

$$\mathbf{y}_{i} = 1\beta_{0} + \mathbf{x}_{i} \beta_{1} + \alpha + \epsilon_{i}$$

and do hypothesis testing on $\beta_{1}$. You can read more about variable encoding here.

The important point is that a regression model can be made equivalent to ANOVA can be made equivalent to a t-test by variable encoding (and your distributional assumptions).

Much more detailed answers on CrossValidated here.

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bill_e
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  • I see. Would it be a valid assumption to use log terms here, since it is reasonable to think that it was "easier" to amortize on top of the minimum before legislation? – Filip Feb 20 '15 at 07:27
  • I dunno what amortization is, but you can do whatever kinds of variable transforms you want. – bill_e Feb 20 '15 at 21:33