Dear all,
I am working on Stata 13.0 with panel data and my linear model has two regressors (x1 and x2 below) which are both endogenous because of reverse causality. The analysis is based on a fixed effects model (hence the reason of -fe- in the code).
I chose to use the command -xtivreg- for panel data to apply an instrumental variable technique, with one IV (iv1 and iv2 below) per each regressor - I have done some research on the topic and it seems to be both possible and sensible, but if you have comments on this point, please feel free to offer your suggestions.
My code, where x1, x2 are the endogenous variables and regressors; y independent variable; iv1 and iv2 respectively the instruments for the regressor x1 and regressor x2; c1, c2, c3, c4 the control variables; is:
The thing I do not understand is why, in the last table, Stata says that I instrumented -x1 and x2 (correct) with c1 c2 c3 c4 iv1 iv2 (too many! the instruments are only iv1 and iv2). So maybe I am doing something wrong on the syntax side; but after following the help document and searching for an answer, I am still clueless. Besides, I found a very limited number of models with two regressors which are both instrumented.
Don't bother looking at the numerical results - they are temporary.
Thank you in advance for your precious help!
I am working on Stata 13.0 with panel data and my linear model has two regressors (x1 and x2 below) which are both endogenous because of reverse causality. The analysis is based on a fixed effects model (hence the reason of -fe- in the code).
I chose to use the command -xtivreg- for panel data to apply an instrumental variable technique, with one IV (iv1 and iv2 below) per each regressor - I have done some research on the topic and it seems to be both possible and sensible, but if you have comments on this point, please feel free to offer your suggestions.
My code, where x1, x2 are the endogenous variables and regressors; y independent variable; iv1 and iv2 respectively the instruments for the regressor x1 and regressor x2; c1, c2, c3, c4 the control variables; is:
Code:
.
. xtset
panel variable: CountryMark (strongly balanced)
time variable: Year, 2000 to 2014
delta: 1 year
. xtivreg y c1 c2 c3 c4 c5 c6 (x1 x2 = iv1 iv2), fe first
First-stage within regression
Fixed-effects (within) regression Number of obs = 83
Group variable: CountryMark Number of groups = 16
R-sq: within = 0.8263 Obs per group: min = 1
between = 0.6704 avg = 5.2
overall = 0.4224 max = 8
F(7,60) = 40.77
corr(u_i, Xb) = -0.9921 Prob > F = 0.0000
-------------------------------------------------------------------------------------------
x1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
c1 | 3.991628 2.179243 1.83 0.072 -.3675069 8.350764
c2 | 1.512567 1.751205 0.86 0.391 -1.990365 5.015499
c3 | -9.588328 1.767561 -5.42 0.000 -13.12398 -6.05268
c4 | -4.564994 2.565139 -1.78 0.080 -9.696035 .566048
iv1 | 33.40758 9.801486 3.41 0.001 13.80169 53.01347
iv2 | .0842356 .3823848 0.22 0.826 -.6806478 .849119
_cons | 405.9367 99.26616 4.09 0.000 207.3748 604.4986
--------------------------+----------------------------------------------------------------
sigma_u | 230.14575
sigma_e | 13.768958
rho | .99643348 (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------
F test that all u_i=0: F(15, 60) = 13.24 Prob > F = 0.0000
First-stage within regression
Fixed-effects (within) regression Number of obs = 83
Group variable: CountryMark Number of groups = 16
R-sq: within = 0.3931 Obs per group: min = 1
between = 0.0089 avg = 5.2
overall = 0.0067 max = 8
F(7,60) = 5.55
corr(u_i, Xb) = -0.2638 Prob > F = 0.0001
-------------------------------------------------------------------------------------------
x2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
c1 | .8159419 .2826313 2.89 0.005 .2505951 1.381289
c2 | .1652445 .285271 0.58 0.565 -.4053825 .7358715
c3 | -1.200964 .413994 -2.90 0.005 -2.029075 -.3728521
c4 | .0002438 .0001594 1.53 0.131 -.0000749 .0005626
iv1 | 33.40758 9.801486 3.41 0.001 13.80169 53.01347
iv2 | -.0036747 .061714 -0.06 0.953 -.1271211 .1197717
_cons | 5.465016 16.02081 0.34 0.734 -26.58137 37.5114
--------------------------+----------------------------------------------------------------
sigma_u | 13.100655
sigma_e | 2.2222059
rho | .97203189 (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------
F test that all u_i=0: F(15, 60) = 56.09 Prob > F = 0.0000
Fixed-effects (within) IV regression Number of obs = 83
Group variable: CountryMark Number of groups = 16
R-sq: within = . Obs per group: min = 1
between = 0.5223 avg = 5.2
overall = 0.6442 max = 8
Wald chi2(7) = 308.66
corr(u_i, Xb) = -0.9891 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------------
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
x1 | -13.34982 95.60653 -0.14 0.889 -200.7352 174.0355
x2 | 259.4363 2165.715 0.12 0.905 -3985.286 4504.159
c1 | -96.37982 979.8331 -0.10 0.922 -2016.817 1824.058
c2 | -171.2541 1636.062 -0.10 0.917 -3377.877 3035.369
c3 | -203.7811 1278.566 -0.16 0.873 -2709.725 2302.163
c4 | 249.9043 2121.014 0.12 0.906 -3907.208 4407.016
_cons | 6319.568 29518.49 0.21 0.830 -51535.61 64174.75
--------------------------+----------------------------------------------------------------
sigma_u | 5729.8217
sigma_e | 575.43353
rho | .99001496 (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------
F test that all u_i=0: F(15,60) = 2.47 Prob > F = 0.0070
-------------------------------------------------------------------------------------------
Instrumented: x1 x2
Instruments: c1 c2 c3 c4 iv1 iv2
-------------------------------------------------------------------------------------------
The thing I do not understand is why, in the last table, Stata says that I instrumented -x1 and x2 (correct) with c1 c2 c3 c4 iv1 iv2 (too many! the instruments are only iv1 and iv2). So maybe I am doing something wrong on the syntax side; but after following the help document and searching for an answer, I am still clueless. Besides, I found a very limited number of models with two regressors which are both instrumented.
Don't bother looking at the numerical results - they are temporary.
Thank you in advance for your precious help!
Comment