Thanks a lot, Scott. Just two follow-up questions.
1) If my dependent variable is net worth (say the var name is "wealth"),
do I simply use log(wealth+sqrt(wealth^wealth+1)) as the dependent
variable in regression?
2) How to interpret the coefficients for control variables (eg. gender,
edu, logged wages)? Same as the log transformation?
Ying
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First, as Roger noted, there was a typo in my reply. The function should be
IHS = log(z + sqrt(z^2 + 1))
1. Yes, but more generally, the ihs fuctions is ln(theta*z + sqrt((theta^2 * z^2
+ 1))/theta; where theta is scale parameter that could be estimated.
2. If z is large relative to 1/theta, the ihs function approximates log(z) for positive values and -log(z) for negative values. The graph looks like:
clear
set obs 800
egen z = fill(-20 -19.95)
gen ihs_z = ln(z + sqrt(z^2 +1))
twoway line ihs z, xline(0) yscale(noline) yline(0) xscale(noline)
The marginal effects of wealth with respect to a change in x would be:
ihs(wealth) = ln(wealth + sqrt(wealth^2 +1)) = b_0 + b_1*x + e
d(w)/d(x) = d(ihs(w))/d(x) * d(w)/d(ihs(w)) where the first term is the estimated coefficient on x (b_1) and the second term is sqrt(w^2 +1).
Hope this helps,
Scott
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