# Thread: OLS Regression after Logit Transformation: Interpreting the Coefficients

1. ## OLS Regression after Logit Transformation: Interpreting the Coefficients

Hi all,

I'm currently doing an empirical project in econometrics. I examine the effect of globalisation and some other control variables on poverty, doing OLS cross section given a sample of 74 countries (OECD and highly industrialized countries are excluded).

Now I have quite a problem in understanding how to interpret the coefficients of a standard OLS regression ("regress" in stata) if the dependant variable is not the initial variable of interest but its logit transformation. That is:

My variable of interest is the poverty headcount ratio by the Worldbank, i.e. the percentage share of the population of a country that lives with less than 3.10\$ a day. If I'm right, I cannot simply do OLS with an dependant variable being share or percentage since it is by nature restricted to lie between 0 and 1 (or 0 and 100). Therefore, I did a logit transformation which - if I'm right - allows me to do a standard linear regression afterwards.

If p being the percentage share of population who live with less than 3.10§ as explained above, I get: logit( p ) = log( p / 100-p ). My then runs with the logit-transformed p as the dependant variable.

I now do not understand how to interpret the results and how to do standard ceteris paribus analysis. I attached the output in stata after doing one example regression with the Globalisation-Index ( - "Glob", reaching from 0 to 100 - and health expenditures per capita in dollars as regressors.
The coefficients are significant and have the expected signs assumed by theory. That is, if globalisation increases, poverty is expected to decrease. Same with health expenditures.

However, in the end I'm interested in the effect on poverty not in the effect on the log-odds of poverty.
So given my output in stata, it tells me that by a 1 percent increase in globalisation the dependant variable, that is the logit of the poverty headcount ratio, decreases by .098. But how does poverty itself change, so how does a 1 percent increase in globalisation change the share of people living under 3.10 dollar?

I would be very grateful for any help. I do see the close relationship to a logistic regression and also I read a bit of fractional regression models which both seem to relate to my problem. However, as undergraduate student I'm new to regression analysis and we never studied anything other than standard OLS cross section, time series issues and panel data on rudimentary level.

Much thanks and best regards
Markst

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