Estimation of direct and indirect effects ( transmission mechanisms) in stata

[gashts]

I am undertaking a research project on the determinants of Microfinance Institutional Sustainability using the Huasman and Taylor Instrumental variable technique on a panel data set. I suspect the dependent variable say 'Y' is directly affected by a variable X. And the variable X intern could have an indirect effect on Y through its effect on a variable Z. The variable Z has also a direct effect on Y. Under this scenario, I first estimated Y on Z, X and other control variables to get their partial effects. Later, I tried to single-out the indirect effect of X on Y through Z by the following procedure:
First: I regressed Z on X and other control variables, then I generated a new data series for Z by multiplying each data points of X and its coefficient estimates and assigning zero values for the rest of the variables included in the estimation of Z. Finally, I plugged the estimated Z values (Z estimated= cX+0(other variables)) in the original model where Y is the dependent variable, along with other control variables. However, I am not sure if I am doing the right thing. I also considered to interact Z and X in the initial model but I suspected this could not make sense in defining the causality between X and Z.I then considered the Frisch-Waugh orthogonalization but couldn't manage to get the command in stata.

Thus, I resorted to presenting the issue to this forum so that I could get advice on how to deal, particularly in stata, to single out direct and indirect effects of explanatory variables. In short, the question is on how to deal with transmission mechanisms from one variable to a series of other variables before reaching the target dependent variable. Could you please help me out with this? I hope I am making sense.

[Dick Campbell]

If your outcome variable is continuous you may be able to get what you want via the Stata SEM command. See the documentation for estat teffect in the SEM manual. That command computes estimates of indirect effects and their standard errors. However, you mention two complicating issues -- panel data and instrumental variables. SEM can handle instrumental variables and, depending on design, it may be able to handle the panel data. If your endogenous variables are not continuous you need Stata's gsem command, but teffects is not available there. You would need to tell us more about your data structure and variables to get better advice.

[gashts]

Thanks a lot Professor Richard T. Campbell!!

Since I received you reply, I have been intensively reading about the options you suggested. Finally, I found gsem command relevant to my problem. Operational Self-Sufficiency ( which is a proxy for Microfinance Institutions financial viability) is the outcome variable. Some of the explanatory variables are: Operating expense per loan portfolio, average loan size per loan client, number of loan clients, proportion of women from the total borrowers and other control variables. The reason why I wanted estimating the direct and indirect effects is because I suspected three of the above explanatory variables could also have indirect affects on the outcome variable( operational self-sufficiency) through their direct effect on the other explanatory variable ( operating expense per loan portfolio). Now, with the gsem command, I regressed operational self-sufficiency on operational expense per loan portfolio, average loan per client, number of borrowers, proportion of women borrowers and other determinants.And in the second path, I regressed operational expense per loan portfolio on average loan per client, number of borrowers, proportion of women borrowers ,and its other determinants. It seems to me that the estimation is ok now but if you think there exists further issues I should be taking care off in due course, please do so and I remain grateful!!

Thanks a lot!!

Gashaw