A coefficient which is a ratio of two regression coefficients


I'm trying to replicate an econometric approach from an article. The author starts by running a Seemingly Unrelated Regression (SUR) based on a system of two equations.

So, I proceeded this way:

X1 <- dta$V1

X2 <-  dta$V2

Y1 <-  dta$V3

Y2 <-  dta$V4

Y <- cbind(Y1, Y2)

eq1 <- X1 ~ Y

eq2 <- X2 ~ Y

system <- list(eq1 = eq1, eq2 = eq2)


sur <- systemfit(system, method = "SUR", data = dta)

So far, no problems.

Take Wife's BMI and Wife's Education as X1 and X2, respectively. The picture shows (this is from the author) the estimated coefficients and their standard errors under parentheses.

If you look at the last row of the regression's output, you'll notice that each value is precisely the ratio of the coefficients above and, most important, each ratio is expressed as a coefficient. This is what I need to do: to present a coefficient as a ratio of those two coefficients already estimated. This is important because I need the standard error of the ratio of the coefficients to estimate the statistic for the Wald's test. My purpose is to run a Wald's test using the two ratios. I've tried the linearhypothesis for the test but it didn't work.

restrictions <- "(eq1_Y1/eq1_Y2) - (eq2_Y1/eq2_Y2)"
linearhypothesis(sur, restrictions, data =dta)

Could anybody help me on this?

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