Threshold for independent variables and bootstrap technique

[Mina Sami]

I am running the following regression:

Size=constant+ beta (Interest rate)

The objective is to find whether the level of interest rate is linear on Size (firm size).

When I had a look on boostrap technique in stata, I type the command:

sqreg Size interest_rate , q(.25 .50 .75)

The main problem is that bootstrap provides quantiles to the Y (Size) not the X (interest rate)
There is any bootstrap technique that provides quantiles for the X (intreset rate) and not the Y?



Notes:
1. The objective is to find threshold point from which the effect of interest rate will not be significant.

2. I did this manually for different cutoff points for interest rate 10%, 20%,....
But I need to do it formally


Best,
Mina

[Clyde Schechter]

I don't understand what you're trying to do here. You have a linear equation: Size constant + beta*interest rate. So under this model the effect of interest rate on size is just beta, regardless of the value of interest rate. If you believe that the effect of interest rate on size varies with size, then you need some kind of non-linear model. Not being involved in finance/economics, I have no advice to offer as to just what non-linear model is appropriate for this kind of problem, but it is mathematically clear that linear models will not do what you are asking of them.

You are correct that -sqreg- estimates quantiles of the dependent variables. That's what it's meant to do.

Assuming you settle on a suitable non-linear model for Size as a function of interest rate, the way to determine the effect of interest rate on size at various quantiles (for illustration, the 25th 50th and 75th) of interest rate would be:

run the non-linear regression model
margins, dydx(interest_rate) at((p25) interest_rate) at ((p50) interest_rate) at((p75) interest_rate)

Note: Not tested. Beware of typos, unbalanced or misplaced parentheses, etc.

[River Huang]

I guess that you are interested in estimating a threshold regression, rather than a quantile regression here. Please visit https://www.ssc.wisc.edu/~bhansen/progs/progs_threshold.html , and in particular, the paper "Sample splitting and threshold estimation." Econometrica, (2000)".