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I am trying to get my head around how I can perform a GMM regression to replicate Fama and French's three factor asset pricing model. I have 25 portfolios (ie 25 observations for Rit) and the model is specified as:
Rit = ai + bi(MRP) + ciSMB + diHML + ei

I want to run this model where there are 4N sample moment equations
1) Mean regression error term is zero
2) E(MRP,e) = 0
3) E(SMB,e) = 0
4) E(HML,e) = 0

ie for 2-4 I need to define that the regression error term is orthogonal to each regressor. I have having particular difficulty defining the error term in EViews, which I think is required in order to write the systems I have specified (1-4 above). Help on the programming would be greatly appreciated!

Not quite sure I follow this exactly...

At first pass it looks like really you're just saying that you want to do least-squares. The moment conditions that the regressors are orthogonal to the residual is really just the same thing as saying you want all the regressors to be instruments, which is the same thing as saying you want to do least squares (you can verify this by creating a gmm equation, entering in mrp smb and hml as regressors and as instruments, then comparing the answers against simple least squares with the same regressors).

Of course in least squares the mean of the residuals is equal to zero.



At second pass I got a bit confused by your notation. Do you actually have a panel set of data? Do you have both cross-sections (portfolios) and time dimensions (observations for each portfolio through time). Thus Rit is actually return of portfolio i in time t? If so then shouldn't something on the right hand side of your equation also have a time element?

You are correct, I made an error in specifying my model as the variables on the RHS do vary across time, such that:
Rit = a +biMRPt + ciSMBt + diHMLt + eit

I believe I would like to set up my test to allow for direct estimation of the mean premia for the four risk factors:
MRPt = λ mrp,t + emrp,t

SMBt = λ smb,t + esmb,t

HMLt = λ hml,t + ehml,t