Discussion on Dynamic Panel Analysis used One-Step System GMM (xtabond2)

[Khampaserd Manysay]

Dear Stata expert, econometrician, and researcher,

This is Manysay Khampaserd, a master student in Economics at Yamaguchi University, Japan. Previously, I kept this discussion privately. Thank you very much Sebastian Kripfganz for your kind remind and recommendation. Hopefully, I am now posting it publicly.

Currently, I am doing a research on Fiscal Decentralization (FD) and Economic Growth in Lao PDR. Here are the brief information for the discussion:


Method: dynamic panel analysis, One-Step System GMM, xtabond2 technique in STATA BE 17.0

Model: Dependent variable is Economic growth (lnGDPK) and explanatory variables: Tax Revenue Decentralization (FDTax), Capital Expenditure Decentralization (FDCAP); control variables: Three-build Policy (SamSang) - dummy, Poverty Ratio (PR), and Regional Inflation Rate (RIA)

Data: Panel data at provincial level in Lao PDR, 17 provinces, from 2010-2019 (10 years)

Model Specification: lnGDPK = l.lnGDPK + FDTax + FDCAP + SamSang + PR + RIA + error terms

One year lagged economic growth (l.lnGDPK) is treated as an endogenous variable and internal instrument; instrument variables use two types: (1) variables from the model (FDTax FDCAP SamSang RIA), (2) variables from outside the model [log of provincial population (lnPOP), household electricity access ratio (HEAR), log of total provincial number of tourists ( lnTTOUR)]. Note: PR is not put as one of instrument variables.

Command in STATA:

Model 1 (Include all FD variables without collapse and robust options): xtabond2 lnGDPK l.lnGDPK FDTax FDCAP SamSang PR RIA, gmmstyle(l.lnGDPK) ivstyle(FDTax FDCAP SamSang lnPOP RIA HEAR lnTTOUR) nodiffsargan small

Model 2 (Run with all FD variables with collapse and robust options): xtabond2 lnGDPK l.lnGDPK FDTax FDCAP SamSang PR RIA, gmmstyle(l.lnGDPK, collapse) ivstyle(FDTax FDCAP SamSang lnPOP RIA HEAR lnTTOUR) nodiffsargan small robust

Model 3a (Run with each FD variable with collapse and robust options): xtabond2 lnGDPK l.lnGDPK FDTax SamSang PR RIA, gmmstyle(l.lnGDPK, collapse) ivstyle(FDTax SamSang lnPOP RIA HEAR lnTTOUR) nodiffsargan small

Model 3b (Run with each FD variable with collapse and robust options): xtabond2 lnGDPK l.lnGDPK FDCAP SamSang PR RIA, gmmstyle(l.lnGDPK, collapse) ivstyle(FDCAP SamSang lnPOP RIA HEAR lnTTOUR) nodiffsargan small

GMM estimator is quite new to me. I have been trying to learn and read related materials, but I have not understood it well. Therefore, I would like to have some points to discuss with you as follows:

1. I found in some papers used GMM approach and did the unit-root test while others did not. Therefore, I am confused. Does GMM estimator need to do the Unit-root test before starting the regressions?

2. Instrument variables, I do not include all independent variables as instruments. I just pick some of them and include the outside variables (as seen in Model 3a and Model 3b). I would like to make sure that am I doing correctly towards instrument variables? and is there any technique to check whether selected instruments are uncorrelated with the error terms?

3. Due to containing large number of instruments, the collapse option is employ to reduce instruments. Regarding this, is it widely acceptable to reduce the instruments by using the collapse option?

4. Can GMM estimator, especially One-Step System GMM, be allowed and valid for the long-run estimation?

5. Are they any additional tests to do in order to check the correction of the model, apart from AR (1), (2) tests and Hansen test?

I have attached the results from STATA below. I look forward to hearing and receiving comments and recommendations from all of you.


Best regards,

Manysay Khampaserd

[Sebastian Kripfganz]

1. The GMM estimator for dynamic panel models is usually applicable in a situation where you have many cross-sectional units and few time periods. In this case, there is no need for unit root testing because the estimator's properties are largely determined by the cross-sectional dimension.

2. Instruments should be sufficiently strong and valid. Not including strong and valid instruments may lead to a loss of efficiency and in the worst case even to underidentification of the model coefficients. It is not possible to check whether all instruments are uncorrelated with the error term. You can only check for the validity of the overidentifying restrictions (losely speaking, the validity of any additional instruments once you have included as many valid instruments [which is an untestable assumption] as regressors).

3. Yes. An alternative is curtailing, i.e. to restrict the maximum lag order for GMM-style instruments.

4. I do not understand what you mean by "long-run estimation". The one-step estimator is generally inefficient compared to the two-step estimator. However, given that you only have 17 cross-sectional units, estimating an optimal weighting matrix with a two-step estimator is very likely to lead to unreliable results. On a related note, the Hansen test is only consistent after two-step estimation and therefore again unreliable given the small number of provinces.

5. You could also check for possible underidentification problems. Please see my 2019 London Stata Conference presentation for more information:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

[Khampaserd Manysay]

Dear Sebastian Kripfganz,

Thank you very much for your comments.

I would like to reiterate the question No 4 that typically GMM approach is designed for estimating the short-run effect/ coefficient. Apparently, referring to the attached file, I first ran the regressions (short-run effect). Then I did the estimation for computing the long-run coefficient. Is it (GMM) allowed to run the regression for estimating the long-run coefficient?

I look forward to hearing from you.

Best regards,

Manysay Khampaserd

[Sebastian Kripfganz]

Yes, you can compute the long-run estimates in the usual way. It does not matter which estimator you use for the short-run coefficients.