Help with system GMM and xtabond2

[Bharat Di]

Hi,

I have a panel data with 58 countries over the period 1970-2014. I am trying to check whether human capital plays any role in productivity growth and reducing the distance from the technological frontier. I am using the following empirical specification:
gTFP_it = b₀ + b₁ logHC_it + b2 DTF_it + b3 (logHC*DTF)_it + b4 X_it + c_i + t_t + e_it

where gTFP = growth in Total Factor Productivity; HC = human capital; X = control variables (which includes Trade Openness, FDI, Inflation, Financial Development); c_i = unobserved country-specific fixed effects; t = unobserved individual invariant time effects; e_it = stochastic error term. b₁, b₂, and b₃ are parameters to be estimated.

The above equation is estimated using system GMM estimator. The system GMM estimator allows for the use of internal instruments (lagged differences and lagged levels) and external instruments. Apart from the internal instruments, I plan to use life expectancy and polity as external instruments.

I am using the following code:
xtabond2 gTFP logHC DTF logHC*DTF TO FDI Inflation Fin_dev i.Year, gmm(logHC DTF logHC*DTF, lag(2 3) collapse) iv(TO FDI Inflation Fin_dev i.Year life_exp polity) small orthogonal twostep robust


Am I writing the code correctly? Also, I don't know whether I am using the external instrument correctly or not.

Please advice.

Thank you,
Bharat

[Sebastian Kripfganz]

I strongly advise against using the iv() option without referring to a specific equation with suboption equation(). You can find a discussion of this issue with particular emphasis on time dummies in the following two Statalist topics:

• System GMM - Time dummies
• XTSEQREG: new Stata command for sequential / two-stage (GMM) estimation of linear panel models

Yet, the arguments therein generally apply also to variables other than time dummies.

[Bharat Di]

Dear Dr. Kripfganz,

Thank you for your reply. I was also wondering if you could please tell me whether I have used the two external instruments (life_exp and polity) correctly or not.

Thank you,
Bharat

[Sebastian Kripfganz]

Apart from my previous comment: Yes, provided that you are assuming that all those internal and external instrument that you have put into the iv() option are uncorrelated with the unobserved country-specific effects (that are in this case, strictly speaking, no longer "fixed effects").

[Bharat Di]

Thank you for your reply. I have another question.

The following is the reference paper for my research: Jakob, M., Islam, R., Ang, J., 2010. "Catching up to the technology frontier: the dichotomy between innovation and imitation". The Canadian Journal of Economics, Vol 43(4), pp. 1389-1411.

In this paper, the authors have used the following empirical specification:
gTFP_it = b_0i + b₁ log(rd)_it + b2 ln(A^max_t-1/A_i,t-1) + b₃ [rd_it* ln(A^max_t-1/A_i,t-1)] + b₄ C_it + e_it

where gTFP_it = growth rate in Total Factor Productivity; rd = Research & Development; A^max_t-1/A_i,t-1 = Distance from the Frontier; C_it = vector of control variables (which includes Trade Openness, FDI inflows, Financial development, distance from the equator, and Inflation); e_it = stochastic error term.

The authors use constant, time and country dummies. They also use 2nd and 3rd lags of the explanatory variables as instruments for the differenced equation and 1st differences of the explanatory variables are taken as instruments for the level equation. They also consider three external instruments (which includes patent protection, effective executive, and effectiveness of legislature) for rd, and the interaction between rd, and the distance to the frontier.

After reading the paper I am interpreting the Stata code will be the following:

xtabond2 gTFP log(rd) log(l.DTF) rd*log(l.DTF) TO FDI Fin_dev Equator Infl timedum countrydum, gmm(log(rd), lag(2 3) collapse) gmm(log(l.DTF), lag(1 2) collapse) gmm(rd*log(l.DTF), lag(2 3) collapse) iv(TO FDI Fin_dev Equator Infl timedum countrydum patent executive legislature, eq(level)) small robust

Am I interpreting it correctly? Any suggestion will help me understand the paper better.

Thanks,
Bharat

[Bharat Di]

Dear Dr. Kripfganz,

If could please help me with my last post.

Thank you,
Bharat