Growth regressions over 3-year periods; regressors in average or year values? Say that I want to estimate a growth regression basically similar to the Augmented Solow Model one, except my dependent variable is not Y/L, but it's the average GDP growth over a 3-year period. As my independent variables, I'd take GDP at the beginning of the period and then average values of savings rate, human capital, etc... over the period. However, I've seen it done taking savings rate and such values for the last year of the period. So, it turns out something lie:

Avg Growth 2010-2012 = GDP 2010 + Sav Rate 2012 + Hum K 2012 etc...

When I estimate it, the coefficients are correct and significant, however I cannot understand if it's right. I'd understand taking all independent variables in first year values, or taking the rates as averages over the period, but I can't see why it would be correct to base the growth of the period over the last year's value.

Can somebody shed some light on this please? Could it just be a mistake?
I have never seen any "serious" (i.e. peer-reviewed) study defining independent variables as the end of the period under consideration (if you could provide some link to the ones you are referring to, it would be helpful). Normally, they are used as the average over the period or at the initial year. For instance, in the big field of finance and growth, that is the common approach. Thorsten Beck - among the most renown researchers in this field - says it himself (bottom half of page 2). There are many examples of this in other fields too. For instance, when estimating inequality on growth (top of page 282), or the famous paper by Xala-i-Martin, where he run 4 million growth regressions. Look in page 7 and 8, in sections "Data" and "Choosing the Fixed Variables".

Now, why not to use final period variables? Because of reverse causality concerns. An economy which grows fast over a given period might end up with a higher savings rate and human capital level at the end of the period. As such, the order of causality is in fact the opposite at the one your equation is assuming (even though the sign coming from estimations might be the same!), leading to endogeneity and therefore to inconsistent estimates. 

Even the use of average period variables is subject to some controversy. As Xala-i-Martin puts it in the aforementioned paper (page 8):


  I reluctantly use some variables of this sort (the average savings or investment rate and the DeLong and Summers measures of equipment and non-equipment investment are examples in this category). The reason for being reluctant to the inclusion of such variables is that these may be “more endogenous” than the variables measured at the beginning of the period. 


To conclude, using end of period variables is a very risky practice, and in my view very hard to justify theoretically and empirically. Even more, it seems unnecessary. Why not use beginning of period? Or average?