Is it correct to use a predicted value as an explanatory variable?

[Ngozi ADELEYE]

Dear all,

I use Stata13 although this is not a software-related question but on empirical approach.

I want to seek the opinion of experts if it is econometric-ally correct to use a predicted value as an EXPLANATORY VARIABLE in another regression in order to test a hypothesis.

I have a time series data from 1980 to 2015 using the ARDL framework. My hypothesis is that credit growth (an outcome of a financial reform) is a predictor of income inequality and in order to test this, I need to first analyse the impact of interest rate (the reform variable) on credit growth after which I test the impact of credit growth on income inequality - in order to establish a nexus.

Using the Gini index as the measure of income inequality, and domestic credit as proxy for credit growth, I formulate 2 equations:

First equation: credit = intercept + interest rate + per capita income + broad money + u

Second equation: gini = credit_hat + per capita income + education + age dependency + u

My questions are: is my 2nd equation appropriate, with:
1) credit_hat as an explanatory variable?
2) the inclusion of "per capita income" as an explanatory variable in the Gini equation having used it in the credit equation?

What questions/criticisms are likely to emanate from reviewers as regards using this approach? Suggestions and comments will be much appreciated.

Thanks!

[Daniel Feenberg]

It looks like you are trying to invent Two-Stage Least Squares, but not getting quite right. TSLS is explained in all econometrics textbooks. A very accessible explanation is in "Mastering Metrics" by Joshua D. Angrist, Jörn-Steffen Pischke but I think that is all about cross-sections and you might have trouble applying those insights to a time-series problem. Nevertheless, that is where I would start as a beginner as most textbooks make no effort to provide intuition for the methods they describe.