When reading a paper for my research I had difficulties understanding the transformation of regression coefficients to standardized values. From a table in the paper I get the following numbers:

OLS regression table (t-statistics in parentheses)

            Log ODA alldonors
Openness     0.383 (2.57)
Friend Japan 0.153 (4.0)

Table 4 Alesina and Dollar

In the text the authors write the following:

"The values of the coefficients are very instructive. Ceteris paribus a country that is relatively open (1 standard deviation above the mean) receives 20 per cent more aid. […] a country that voted relatively often with Japan in the UN receives 172 per cent more aid."

My main question is: how do the authors arrive at the numbers in the text, given the numbers in the table?

It has to do with standardizing the variable (in that way the unit of measurement is standard deviations), but I can't manage to obtain the correct values myself. On forums I encountered several formulas:

Standardizing a coefficient (standardized value is the coefficient minus its mean divided by its standard deviation)


Standardizing a variable (standardized value is the value of the coefficient times its own standard deviation, divided by the standard deviation of the y-variable)


So secondly I would like to ask: which of the formulas applies in this case?


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