# How to correct for generated regressor bias?

Dear Stack Exchange heroes,

For my thesis I am writing a paper on the financial crisis. In my model, I use two regressions, which look like this:

$$CONF = α + β_1 DEF_t + β_2 DIV_t + β_3 INF_t + β_4 IP_t + β_5 CONS_t + β_6 TBILL_t + β_7 URATE_t + β_8 NBER_t + β_9 DEF_{t-1} + β_{10} DIV_{t-1} + β_{11} INF_{t-1} + β_{12} IP_{t-1} + β_{13} CONS_{t-1} + β_{14} TBILL_{t-1} + β_{15} URATE_{t-1} + β_{16} NBER_{ t-1} + ε_t$$

Where $CONF$ is confidence index data and the rest are macroeconomic variables.

$$ΔS_t = α_1 + λΔε_{t-1} + η_t$$

Where $S$ is a stock price index and $Δε$ uses the residuals from the previous equation.

I use Eviews to run these equations and it works fine, but apparently I need to correct for the fact that $Δε$ is a generated regressor. The Pagan (1984) paper is often referred to for this, but after attempting to read it I'm still clueless on what to adjust in my covariance matrix to fix for this bias.

Is there any program that can do this for me, or someone who can explain this in easy steps? Any help is appreciated :)

## 1 Answer

The paper I usually see referred to is Murphy and Topel (1985). Hardin (2002) re-iterated their algebra and demonstrated how a sandwhich estimator can be constructed elegantly using Stata. How easy (or difficult) it is to re-program in Eviews is beyond me.

• The guys at my local statistics department tell me they've never had to use this directly, but they say using the "Heteroskedasticity consistent coefficient covariance" (White) option will automatically fix this for me. Is this true? – Alexander Wolff Jun 5 '12 at 14:33
• I don't know the details of how it is implemented in Eviews, but I doubt that this would suffice. You might be able to cast it as a system of equations and estimate it simultaneously, but if you estimate it equation by equation, you have to do something about it. Have you read the papers to see why? – StasK Jun 9 '12 at 14:55
• There's also Hole (2006), which simplifies the procedure in Hardin (2002). Link: stata-journal.com/article.html?article=st0114 – Dimitriy V. Masterov Feb 11 '13 at 21:06
• Dimitriy, I remember I had issues with that "simplification". Can't recall off the top of my head, but it was something like her proposal was only working in a very limited range of situations. So I prefer to stick to the original Hardin's work. – StasK Feb 11 '13 at 22:45
• thanks for the reference. Do you know where the Hardin (2002) code can be found and downloaded? That would help A LOT! Thanks – user46568 Jun 2 '14 at 16:46