I am reading a paper (Stockhammer, Onaran and Ederer, 2011) which estimates the effects of GDP, profits and the interest rate on investment in an ECM form. I am quoting the relevant part of it:

The investment function estimated is of the general form $I = f (Y, R,$ $i)$. [...] The investment function was estimated in an ECM form with the restriction that in the long run the investment share in GDP is stable, that is, the long-run coefficient of output on investment is unity. The investment function includes the profits and the real long-term interest rate. After experimentation with the lag structure of the differenced variables, a structure with one lag for the short run effects was adopted. [...] The long-run elasticity of profits is 0.15 and is statistically significant only at the 10% level

A table with the results is attached to this message. The coefficients of first differences should be the short-run coefficients, while the last three should be in the cointegration equation and therefore be the long-run effects. What I would like to understand is: the specification is in a log-log form (at least, that is what I understand from the table, since the specification is not reported). The value of the coefficient of profits (R) turns out to be 0.03. It should be an elasticity itself, because of the log-log (alleged) specification. Then, why do the authors write that the LR elasticity of profits is 0.15?

P.S. Sorry for all those "should be"'s, but the paper is very "parsimonious" in explanations.


Remember that OLS is linear on parameters. This is, regression estimates the parameters of each regressor in the following equation:

$$ \Delta ln I = \beta_{1}\Delta lnY + \beta_{2}\Delta lnY(-1) + \beta_{3}\Delta lnR + \beta_{4}\Delta lnR(-1) + \beta_{5}\frac{lnI(-1)}{Y(-1)} + \beta_{6}lnR(-1) + \beta_{7}i(-1) + \epsilon $$

However, the ECM has parameters within the long-run component (the long run relationship, or cointegration vector) and outside of it (the adjustment speed of long run deviations). Thus, using the parameters in the equation above, the ECM is:

$$ \Delta ln I = \beta_{1}\Delta lnY + \beta_{2}\Delta lnY(-1) + \beta_{3}\Delta lnR + \beta_{4}\Delta lnR(-1) + \beta_{5}\left(\frac{lnI(-1)}{Y(-1)} - \frac{-\beta_{6}}{\beta_{5}}lnR(-1) - \frac{-\beta_{7}}{\beta_{5}}i(-1)\right) + \epsilon $$

The long run relationship is the one inside the parenthesis. Therefore, the long run elasticity of the interest rate is $\dfrac{-\beta_{6}}{\beta_{5}}=\dfrac{0.030}{0.210}\approx0.15$.


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