Time dummies in XTABOND2

[Sreekar Vanapalli]

Hello,

I am running a one step difference GMM dynamic panel model on stata using xtabond2.

I am trying to predict the change in advances given by bank by using bank-specific and macro economic independent variables.

I use the following code:

xtabond2 adv_ratio l1.adv_ratio log_ta npa_ratio roa gdp rir inflation i.year, gmm(l.adv_ratio, collapse) iv(l1.log_ta l1.npa_ratio l1.roa l1.depratio l1.gdp l1.rir l.inflation i.year) noleveleq nodiffsargan robust orthogonal small

When I use this code 2 of my macroeconomic variables are omitted due to collinearity. However, when I remove the year dummy as independent variable it gives my results which make sense. I wanted to know if it is feasible to remove year dummy as independent variable but use it as my instrumental variable.

My code which makes sense:

xtabond2 adv_ratio l1.adv_ratio log_ta npa_ratio roa gdp rir inflation, gmm(l.adv_ratio, collapse) iv(l1.log_ta l1.npa_ratio l1.roa l1.depratio l1.gdp l1.rir l.inflation i.year) noleveleq nodiffsargan robust orthogonal small

Thanks

[Sebastian Kripfganz]

If the inclusion of year dummies lead to the omission of some of your macroeconomic variables (likely because they are constant across banks), then this means that the effects of these macroeconomic variables are not identified. If year effects are present, which is likely to be the case, and you remove the year dummies, you end up with an omitted-variables bias. You do not need to include those macroeconomic variables just for the sake of controlling for them. The time dummies already take care of that.

[Sreekar Vanapalli]

Dear Sebastian Kripfganz,

Thank you for responding.
Macroeconomic variables are actually not control variables. I need them in them model.

I decided on removing time dummy as my independent variable but I still want to use it as my IV in the model because it gives me better results when it comes to Hansen test and AR correlation tests.

I wanted to know if that is feasible.

Thanks,
Sreekar

[Fei Wang]

IVs are the variables that are correlated with endogenous variables but unrelated with error terms. Year dummies are very likely to be correlated with error terms and cannot be valid IVs. If you hope to maintain the coefficients of macroeconomic variables, you may at least control for year trends (linear or higher order trends).

[Sreekar Vanapalli]

Hello Fei,

When I run regression without the year dummy as my IV the are tests show that there is correlation. Below are the results with year dummy as IV and without.

My IV set is stronger when I run the code with year dummy as IV.

Without Year dummy as IV:

Dynamic panel-data estimation, one-step difference GMM

Group variable: bank_panel Number of obs = 544
Time variable : year Number of groups = 39
Number of instruments = 18 Obs per group: min = 13
F(0, 39) = . avg = 13.95
Prob > F = . max = 14

Robust
adv_ratio Coefficient std. err. t P>t [95% conf. interval]

adv_ratio
L1. -.0503807 .1719643 -0.29 0.771 -.3982114 .29745

log_ta 3.640959 1.015664 3.58 0.001 1.586584 5.695334
npa_ratio -.9829383 .1398598 -7.03 0.000 -1.265831 -.7000452
roa -4.116902 .8325872 -4.94 0.000 -5.800969 -2.432835
gdp .0141944 .1000714 0.14 0.888 -.1882191 .2166079
rir .2037556 .1321143 1.54 0.131 -.0634707 .4709819
inflation -.3154633 .1238663 -2.55 0.015 -.5660066 -.06492

Instruments for orthogonal deviations equation
Standard
FOD.(L.log_ta L.npa_ratio L.roa L.depratio)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/15).L.adv_ratio collapsed

Arellano-Bond test for AR(1) in first differences: z = -0.93 Pr > z = 0.351
Arellano-Bond test for AR(2) in first differences: z = -2.34 Pr > z = 0.019

Sargan test of overid. restrictions: chi2(11) = 19.84 Prob > chi2 = 0.048
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(11) = 18.81 Prob > chi2 = 0.065
(Robust, but weakened by many instruments.)


With Year dummy as IV

Dynamic panel-data estimation, one-step difference GMM

Group variable: bank_panel Number of obs = 544
Time variable : year Number of groups = 39
Number of instruments = 32 Obs per group: min = 13
F(0, 39) = . avg = 13.95
Prob > F = . max = 14

Robust
adv_ratio Coefficient std. err. t P>t [95% conf. interval]

adv_ratio
L1. .4083228 .0767891 5.32 0.000 .2530022 .5636435

log_ta 1.797379 .40948 4.39 0.000 .9691279 2.625631
npa_ratio -.5030997 .1459645 -3.45 0.001 -.7983408 -.2078587
roa -1.534085 .9262613 -1.66 0.106 -3.407626 .339455
gdp -.0582709 .0729579 -0.80 0.429 -.2058423 .0893004
rir .1420015 .1286228 1.10 0.276 -.1181627 .4021656
inflation -.2375281 .0914302 -2.60 0.013 -.4224632 -.0525931

Instruments for orthogonal deviations equation
Standard
FOD.(L.log_ta L.npa_ratio L.roa L.depratio 2005b.year 2006.year 2007.year
2008.year 2009.year 2010.year 2011.year 2012.year 2013.year 2014.year
2015.year 2016.year 2017.year 2018.year 2019.year 2020.year)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/15).L.adv_ratio collapsed

Arellano-Bond test for AR(1) in first differences: z = -3.55 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = 1.59 Pr > z = 0.112

Sargan test of overid. restrictions: chi2(25) = 66.84 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(25) = 33.92 Prob > chi2 = 0.110
(Robust, but weakened by many instruments.)

[Fei Wang]

I stick to my suggestion in #4: year dummies cannot be valid IVs, and you may include year trends as covariates. One should not make decisions on model specification according to whether the estimates are significant or not.

[Marco Astori]

I'm using xtabond2 and I'd like to insert time dummies: I tried with i.year (where year is the name of my time variable of my panel) but I got this error

. xtabond2 LSECI L.LSECI LRR1 LP LSFI1 i.year, gmm(L.LSECI, lag(1 3)) iv(LRR1 LP LSFI1 i.year)
factor-variable operators not allowed
r(101);

[Sebastian Kripfganz]

You may not be using the latest version of xtabond2. Please update the package and see if the problem persists.

[Marco Astori]

You may not be using the latest version of xtabond2. Please update the package and see if the problem persists.

Ok, I think I used an old package, quite sure was st0159. Is it possibile that I obtained wrong results respect to the package xtabond2?

[Sebastian Kripfganz]

In the latest xtabond2 version, some bugs have been fixed which may have led to incorrect results in previous versions.

[Marco Astori]

Thank you Sebastian Kripfganz

[Marco Astori]

Sebastian Kripfganz about year dummies how do they have to be treated? If they're considered as exogenous, the estimator gives zeros after the transformation, in the first difference equation, then the same dummies as instruments for the level equation? I feel a bit confused

[Sebastian Kripfganz]

I am not sure what you mean by the following?

[USER="1674"]the estimator gives zeros after the transformation, in the first difference equation

The time dummies should not drop out in first differences.

If you are estimating the model by system GMM, it is sufficient to include time dummies as instruments for the level model only, i.e. iv(i.year, eq(level)).

[Marco Astori]

I am not sure what you mean by the following?The time dummies should not drop out in first differences.

Maybe it was my mistake: in first differences with year dummies we have \[
year_{t}-year_{t-1}=0
\]
when we use values related to t and t-1? This for 1 if the value belongs to t and 1 if belongs to t-1.

[Sebastian Kripfganz]

For the current year \(t\):
\[year_t - year_{t-1} = 1\]

For the previous year \(t-1\):
\[year_t - year_{t-1} = -1\]