Xtabond2: Using the nolevel command when one variable is already differenced AND divided by a value from last period.

[Ross Mckenzie]

Hey all,

I am currently using xtabond2 for my small T large N panel data estimation.

My variables look something like this:

Group	Time	lnY	X	A	B
1	1	2.3	.	20	590
1	2	2.7	.0012	27	598
1	3	2.6	.0192	39	643
1	4	2.7	.016	50	630
2	1	1.7	.	80	1055
2	2	1.8	-.003	83	1062
2	3	1.9	.007	91	1092
2	4	2	.005	97	1136
3	1	2.1	.	10	235
3	2	2.3	.016	14	243
3	3	2.2	.004	15	249
3	4	2.1	-.015	11	255

Where Y is my dependent variable and X is my independent variable. I construct X by:

X_t=(A_t-A_t-1)/(A_t-1+B_t-1)

I want to run the xtabond2 command using Differenced GMM such that:

xtabond2 Yt Xt i.time, iv(Xt i.time) nolevel

The issue however is that I do not want Xt to be first differenced in this regression, only my dependent(and some controls which I have left out for simplicity).

I am unsure how to do this due to the denominator of my dependent variable being lags already.

To my knowledge just running

xtabond2 d.Yt Xt i.time, iv(Xt i.time)

Does not obtain the same results as I tried it with a variable more simply defined as: Xt=(A_t/N_t)- (A_t-1-B_t-1)

Thanks for any comments that may help with this,

Ross

[Sebastian Kripfganz]

It seems that you are mixing up the modeling and the estimation stage. Difference-GMM is just an estimation method. Your question really is whether in your model the level of Xt should affect the level of Yt or whether the level of Xt should affect the first difference of Yt. This comes along with the assumption that in the first case there are unobserved unit-specific effects in the level of Yt, while in the second case there are unobserved unit-specific effects in the first difference of Yt (i.e. the growth rate of Yt if Yt is measured in logs).

In the first case, specify

xtabond2 Yt Xt i.time, iv(Xt i.time) nolevel

In the second case, specify

xtabond2 D.Yt Xt i.time, iv(Xt i.time) nolevel

The coefficients are interpreted for the model as specified, even if it is estimated in first differences.

[Ross Mckenzie]

Hey Sebastian,

Thank you for your response!

For my model, I care about how the level of At/At+Bt effects Yt. However, due to unobserved group effects I want to estimate using first differences. When I estimate using the change in At/At+Bt my estimations make sense(the way I check this is that my normal ols with time fixed effects estimated with the reg command has a very similar coefficient to using xtabond2 to do OLS).

However having At+Bt as part of the regression can cause a negative bias, so one solution in the literature is to instead estimate with the denominator being lagged as A_t-1+B_t-1 which is what I am now trying to do(and trying both of the codes above I found I do not get similar results to the normal regression command for ols.).

So my issue is, by using the nolevel option in my estimation, I am first differencing the whole equation so instead of having the change in At, it is the change of d.At which is not what I would like to do.

Perhaps my method for checking if I have the correct estimation equation by comparing it to a standard ols regression is wrong?

Please let me know if this makes sense or if I have misunderstood what you are saying.

Thanks,

Ross

[Sebastian Kripfganz]

OLS estimation is for a model where it is assumed that there are no unobserved "fixed effects". Difference GMM estimation is for a model where it is assumed that there are unobserved fixed effects that can be removed by first differencing. Because of these different assumptions, you should not expect to obtain similar results with the two estimation methods (unless there is indeed no endogeneity problem in levels due to the unobserved effects).