Omitted period dummies in GMM xtabond

[paola rozas]

This paper contains a short panel data set with 69 cross-sectional countries and 5 periods length covering the years 1990-2015. The time period consideration is similar to the one utilized on Forbes (2000) paper, using five-year panels to avoid any short run disturbances due to business cycles and shock-related influences. I am using GMM since I have a lagged dependent variable (income) and I have read papers about it which recommend using it. I have been struggling with the regiondummies and the period dummies to estimate the regression. I created the region dummy with the output below:

tabulate region1, gen(regiondummy)

Region dummy | Freq. Percent Cum.
--------------------------------+-----------------------------------
Asia | 70 20.29 20.29
Europe | 55 15.94 36.23
Latin America and the Caribbean | 95 27.54 63.77
Middle East and North Africa | 30 8.70 72.46
North America | 15 4.35 76.81
Oceania | 15 4.35 81.16
Sub-Saharan Africa | 65 18.84 100.00
--------------------------------+-----------------------------------
Total | 345 100.00
and the period dummy:
tabulate Period, gen(Perioddummy)

Period | Freq. Percent Cum.
------------+-----------------------------------
1 | 69 20.00 20.00
2 | 69 20.00 40.00
3 | 69 20.00 60.00
4 | 69 20.00 80.00
5 | 69 20.00 100.00
------------+-----------------------------------
Total | 345 100.00

when I ran the regression with both dummies, they drop Period 1 and 2 and I am not sure why this happens. I know it drops the regions as well because they do not change in time? I would appreciate any help.

. xtabond Growth GDP GINI EDUCATION PPPI regiondummy* Perioddummy*, lags(1) artests(2)
note: regiondummy1 dropped from div() because of collinearity
note: regiondummy2 dropped from div() because of collinearity
note: regiondummy3 dropped from div() because of collinearity
note: regiondummy4 dropped from div() because of collinearity
note: regiondummy5 dropped from div() because of collinearity
note: regiondummy6 dropped from div() because of collinearity
note: regiondummy7 dropped from div() because of collinearity
note: Perioddummy1 dropped from div() because of collinearity
note: regiondummy6 dropped because of collinearity
note: Perioddummy1 dropped because of collinearity
note: Perioddummy2 dropped because of collinearity

Arellano-Bond dynamic panel-data estimation Number of obs = 146
Group variable: country1 Number of groups = 55
Time variable: Period
Obs per group:
min = 1
avg = 2.654545
max = 3

Number of instruments = 14 Wald chi2(8) = 87.55
Prob > chi2 = 0.0000
One-step results
------------------------------------------------------------------------------
Growth | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Growth |
L1. | -.0359517 .0837034 -0.43 0.668 -.2000072 .1281039
|
GDP | -5.23e-06 6.66e-07 -7.86 0.000 -6.54e-06 -3.93e-06
GINI | -.0000231 .0005334 -0.04 0.965 -.0010685 .0010223
EDUCATION | -.0399015 .0157948 -2.53 0.012 -.0708587 -.0089443
PPPI | -.012411 .0121955 -1.02 0.309 -.0363136 .0114917
regiondummy1 | 0 (omitted)
regiondummy2 | 0 (omitted)
regiondummy3 | 0 (omitted)
regiondummy4 | 0 (omitted)
regiondummy5 | 0 (omitted)
regiondummy7 | 0 (omitted)
Perioddummy3 | .014034 .0036619 3.83 0.000 .0068568 .0212111
Perioddummy4 | .0256401 .0045572 5.63 0.000 .0167082 .0345721
Perioddummy5 | .0297034 .0055404 5.36 0.000 .0188445 .0405623
_cons | .1252553 .0258666 4.84 0.000 .0745576 .175953
------------------------------------------------------------------------------
Instruments for differenced equation
GMM-type: L(2/.).Growth
Standard: D.GDP D.GINI D.EDUCATION D.PPPI D.Perioddummy2
D.Perioddummy3 D.Perioddummy4 D.Perioddummy5

[Sebastian Kripfganz]

One time dummy is dropped because the lagged dependent variable shortens the estimation sample. The dropping of the second time dummy is a known bug in xtabond; see point 3 in the following post:
https://www.statalist.org/forums/for...mm#post1576543

[paola rozas]

One time dummy is dropped because the lagged dependent variable shortens the estimation sample. The dropping of the second time dummy is a known bug in xtabond; see point 3 in the following post:
https://www.statalist.org/forums/for...mm#post1576543

Thank you Sebastian. I am having problems using xtabond2. My initial regression is
Growth_it= GDP_i,t-1+GINI_i,t-1+EDUCATION_i,t-1+PPPI_i,t-1+countrydummies_i+perioddummies_t+u_it

xtset country1 Period
panel variable: country1 (unbalanced)
time variable: Period, 1 to 5
delta: 1 unit

There are 69 countries and 5 periods of five years each from 1990-2015.

I was reading Forbes(2000) paper and Casselli (1996) and wanted to use xtabond2 to assess the dynamic panel data problem. The problem is that I do not understand how to use this code or how many lags to use if my T=5.
https://www.aeaweb.org/articles?id=10.1257/aer.90.4.869
That is Forbes paper.
Could you guide me on how the coding should be.
xtabond2 Growth L.Growth GDP GINI PPPI EDUCATION Perioddummy* countrydummy*, gmm(?),iv(?)

That is how far I got, I have never used GMM so my knowledge on this estimator is limited. I would appreciate your help.

[David Roodman]

Toward the bottom of https://www.cgdev.org/publication/no...king-paper-125, you should find links to data and code from my best reproduction of Forbes.

[paola rozas]

Toward the bottom of https://www.cgdev.org/publication/no...king-paper-125, you should find links to data and code from my best reproduction of Forbes.

Thanks David, what is the difference between these 4 regressions you made?

* Best reproduction of Forbes preferred regression, her Table 3, regression 4
xtabond2 growth L.(gini lgdp syrm syrf pi) _Iper*, iv(_Iper*) gmm(L.(syrm syrf pi gini lgdp)) two small nol robust
* Same, but collapse instruments
xtabond2 growth L.(gini lgdp syrm syrf pi) _Iper*, iv(_Iper*) gmm(L.(syrm syrf pi gini lgdp), c) two small nol robust
* Same, but limit lag depth to 1 instead
xtabond2 growth L.(gini lgdp syrm syrf pi) _Iper*, iv(_Iper*) gmm(L.(syrm syrf pi gini lgdp), lag(1 1)) two small nol robust
* Collapse instruments and limit lag depth
xtabond2 growth L.(gini lgdp syrm syrf pi) _Iper*, iv(_Iper*) gmm(L.(syrm syrf pi gini lgdp), lag(1 1) c) two small nol robust


and if there are 7 periods, why does the regression drops period 6 and 1? leaving only 5? I thought it was only gonna drop period 1.
Additionally the sargan test looks like all of them are significant at 0.05 how do you interpret that??? Thought it had to be more to fail to reject the null.
Thank you

[paola rozas]

Toward the bottom of https://www.cgdev.org/publication/no...king-paper-125, you should find links to data and code from my best reproduction of Forbes.

ADDITIONALLY , i am working with data 1990-2015 ... where did you take the data for the quintiles???

[David Roodman]

The various regressions are discussed in the paper.
I got the quintile data from the same source as Forbes, the Deininger & Squire (1996) data set. Looks like it's at https://microdata.worldbank.org/index.php/catalog/1790.

[paola rozas]

The various regressions are discussed in the paper.
I got the quintile data from the same source as Forbes, the Deininger & Squire (1996) data set. Looks like it's at https://microdata.worldbank.org/index.php/catalog/1790.

When i apply it to my data, the same happens, period 4 and 1 are dropped from the estimation. (there are 5 periods) What does this mean? Doesnt period 4 need to be included?
Also most of my data is not significant, could it be a reason for that?
Tha Sargan test is rejecting the null at 0.002 ? Then, does it mean my instruments are not valid?

Thanks

[paola rozas]

One time dummy is dropped because the lagged dependent variable shortens the estimation sample. The dropping of the second time dummy is a known bug in xtabond; see point 3 in the following post:
https://www.statalist.org/forums/for...mm#post1576543

When reproducing this code to explain the growth relationship, it drops both period 1 and period 4 dummies, and the sargan test seems to reject the null. What can I improve in the coding to avoid period 4 to be dropped and how should I interpret the results as most of them are not significant which is worrying me.

xtabond2 l.Growth L.(GINI logGDP EDUCATION PPPI) _IPer*, iv(_IPer*) gmm(L.(EDUCATIO
> N PPPI GINI logGDP)) two small nol robust
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed,
> perm.
_IPeriod_4 dropped due to collinearity
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix for two-step estim
> ation.
Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step difference GMM
------------------------------------------------------------------------------
Group variable: country1 Number of obs = 139
Time variable : Period Number of groups = 51
Number of instruments = 27 Obs per group: min = 0
F(0, 51) = . avg = 2.73
Prob > F = . max = 3
------------------------------------------------------------------------------
| Corrected
L.Growth | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
GINI |
L1. | -.0004038 .001774 -0.23 0.821 -.0039652 .0031575
|
logGDP |
L1. | -.0144806 .0576446 -0.25 0.803 -.1302069 .1012456
|
EDUCATION |
L1. | .0658534 .0283553 2.32 0.024 .0089278 .122779
|
PPPI |
L1. | -.0310512 .026564 -1.17 0.248 -.0843807 .0222783
|
_IPeriod_2 | .0099311 .013796 0.72 0.475 -.0177655 .0376278
_IPeriod_3 | .0065741 .0084682 0.78 0.441 -.0104266 .0235748
_IPeriod_5 | .0006271 .0080175 0.08 0.938 -.0154687 .0167229
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(_IPeriod_2 _IPeriod_3 _IPeriod_4 _IPeriod_5)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/4).(L.EDUCATION L.PPPI L.GINI L.logGDP)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.30 Pr > z = 0.022
Arellano-Bond test for AR(2) in first differences: z = 0.04 Pr > z = 0.970
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(20) = 37.41 Prob > chi2 = 0.010
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(20) = 25.23 Prob > chi2 = 0.193
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
iv(_IPeriod_2 _IPeriod_3 _IPeriod_4 _IPeriod_5)
Hansen test excluding group: chi2(17) = 21.38 Prob > chi2 = 0.210
Difference (null H = exogenous): chi2(3) = 3.85 Prob > chi2 = 0.279