Hi Everyone,
I have an unbalanced panel of hospitals. I am trying to examine the impact of telehealth on hospital rating. When I run an xtivreg model
xtivreg H_HSP_RATING_9_10 H_COMP_2_A_P newNetwrkMem logLicensedBeds CMI2 logAdmissions logTotOutpatVis PhysAndNursTot forprofit (OF1bTelehealthhistorical = Totalfacil RV ) , fe
Fixed-effects (within) IV regression Number of obs = 6058
Group variable: AHAID Number of groups = 2310
R-sq: within = . Obs per group: min = 1
between = 0.1717 avg = 2.6
overall = 0.1576 max = 4
Wald chi2(9) = 2.62e+06
corr(u_i, Xb) = -0.0273 Prob > chi2 = 0.0000
------------------------------------------------------------------------------------------
H_HSP_RATING_9_10 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
OF1bTelehealthhistorical | 1.927841 .5520274 3.49 0.000 .8458873 3.009795
H_COMP_2_A_P | .655708 .0310748 21.10 0.000 .5948024 .7166135
newNetwrkMem | .2702723 .2780665 0.97 0.331 -.274728 .8152727
logLicensedBeds | .3527704 .7032932 0.50 0.616 -1.025659 1.7312
CMI2 | .8622487 1.199664 0.72 0.472 -1.48905 3.213547
logAdmissions | .0148941 .5895468 0.03 0.980 -1.140596 1.170385
logTotOutpatVis | .1035788 .2985862 0.35 0.729 -.4816395 .6887971
PhysAndNursTot | -.0008241 .0006443 -1.28 0.201 -.002087 .0004387
forprofit | 2.486796 .9016759 2.76 0.006 .7195435 4.254048
_cons | 6.959503 6.667382 1.04 0.297 -6.108325 20.02733
-------------------------+----------------------------------------------------------------
sigma_u | 7.0374608
sigma_e | 3.395186
rho | .81119256 (fraction of variance due to u_i)
------------------------------------------------------------------------------------------
F test that all u_i=0: F(2309,3739) = 5.65 Prob > F = 0.0000
------------------------------------------------------------------------------------------
Instrumented: OF1bTelehealthhistorical
Instruments: H_COMP_2_A_P newNetwrkMem logLicensedBeds CMI2 logAdmissions
logTotOutpatVis PhysAndNursTot forprofit Totalfacilityexpensesexcludin RV
------------------------------------------------------------------------------------------
.
I then ran a similar model to get the first stage results from xtivreg2
xtivreg2 H_HSP_RATING_9_10 H_COMP_2_A_P newNetwrkMem logLicensedBeds CMI2 logAdmissions logTotOutpatVis PhysAndNursTot forprofit (OF1bTelehealthhistorical = Totalfacil RV ) , fe robust first small
FIXED EFFECTS ESTIMATION
------------------------
Number of groups = 1660 Obs per group: min = 2
avg = 3.3
max = 4
First-stage regressions
-----------------------
Unable to display all first-stage regressions.
There may be insufficient room to store results using -estimates store-,
or names of endogenous regressors may be too long to store the results.
Try dropping one or more estimation results using -estimates drop-,
using the -savefprefix- option, or using shorter variable names.
Summary results for first-stage regressions
-------------------------------------------
(Underid) (Weak id)
Variable | F( 2, 3738) P-val | SW Chi-sq( 2) P-val | SW F( 2, 3738)
OF1bTeleheal | 10.93 0.0000 | 21.91 0.0000 | 10.93
NB: first-stage test statistics heteroskedasticity-robust
Stock-Yogo weak ID F test critical values for single endogenous regressor:
10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for i.i.d. errors only.
Underidentification test
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic Chi-sq(2)=18.73 P-val=0.0001
Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic 13.70
Kleibergen-Paap Wald rk F statistic 10.93
Stock-Yogo weak ID test critical values for K1=1 and L1=2:
10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
Anderson-Rubin Wald test F(2,3738)= 10.19 P-val=0.0000
Anderson-Rubin Wald test Chi-sq(2)= 20.43 P-val=0.0000
Stock-Wright LM S statistic Chi-sq(2)= 22.17 P-val=0.0000
NB: Underidentification, weak identification and weak-identification-robust
test statistics heteroskedasticity-robust
Number of observations N = 5408
Number of regressors K = 9
Number of endogenous regressors K1 = 1
Number of instruments L = 10
Number of excluded instruments L1 = 2
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity
Number of obs = 5408
F( 9, 3739) = 27.59
Prob > F = 0.0000
Total (centered) SS = 31581.08333 Centered R2 = -0.3648
Total (uncentered) SS = 31581.08333 Uncentered R2 = -0.3648
Residual SS = 43100.52916 Root MSE = 3.395
------------------------------------------------------------------------------------------
| Robust
H_HSP_RATING_9_10 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
OF1bTelehealthhistorical | 1.927841 .7168633 2.69 0.007 .5223598 3.333322
H_COMP_2_A_P | .655708 .0490046 13.38 0.000 .5596297 .7517862
newNetwrkMem | .2702723 .2737156 0.99 0.324 -.2663741 .8069188
logLicensedBeds | .3527704 .7312045 0.48 0.630 -1.080828 1.786369
CMI2 | .8622487 1.439348 0.60 0.549 -1.959734 3.684232
logAdmissions | .0148941 .8592885 0.02 0.986 -1.669826 1.699614
logTotOutpatVis | .1035788 .3254017 0.32 0.750 -.5344033 .741561
PhysAndNursTot | -.0008241 .0005658 -1.46 0.145 -.0019335 .0002852
forprofit | 2.486796 1.083747 2.29 0.022 .3620025 4.611589
------------------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 18.734
Chi-sq(2) P-val = 0.0001
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 13.699
(Kleibergen-Paap rk Wald F statistic): 10.926
Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 3.845
Chi-sq(1) P-val = 0.0499
------------------------------------------------------------------------------
Instrumented: OF1bTelehealthhistorical
Included instruments: H_COMP_2_A_P newNetwrkMem logLicensedBeds CMI2
logAdmissions logTotOutpatVis PhysAndNursTot forprofit
Excluded instruments: Totalfacilityexpensesexcludin RV
------------------------------------------------------------------------------
The coefficients are the same, but the number of groups is 1660, vastly differing from 2310 above. The total observations are also obviously different. My question is, what is the number of hospitals? Is 1660 or 2310 the right number to report? Further, the number of observations are different too (N*T), but how can the coefficients end up being the same?
I have an unbalanced panel of hospitals. I am trying to examine the impact of telehealth on hospital rating. When I run an xtivreg model
xtivreg H_HSP_RATING_9_10 H_COMP_2_A_P newNetwrkMem logLicensedBeds CMI2 logAdmissions logTotOutpatVis PhysAndNursTot forprofit (OF1bTelehealthhistorical = Totalfacil RV ) , fe
Fixed-effects (within) IV regression Number of obs = 6058
Group variable: AHAID Number of groups = 2310
R-sq: within = . Obs per group: min = 1
between = 0.1717 avg = 2.6
overall = 0.1576 max = 4
Wald chi2(9) = 2.62e+06
corr(u_i, Xb) = -0.0273 Prob > chi2 = 0.0000
------------------------------------------------------------------------------------------
H_HSP_RATING_9_10 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
OF1bTelehealthhistorical | 1.927841 .5520274 3.49 0.000 .8458873 3.009795
H_COMP_2_A_P | .655708 .0310748 21.10 0.000 .5948024 .7166135
newNetwrkMem | .2702723 .2780665 0.97 0.331 -.274728 .8152727
logLicensedBeds | .3527704 .7032932 0.50 0.616 -1.025659 1.7312
CMI2 | .8622487 1.199664 0.72 0.472 -1.48905 3.213547
logAdmissions | .0148941 .5895468 0.03 0.980 -1.140596 1.170385
logTotOutpatVis | .1035788 .2985862 0.35 0.729 -.4816395 .6887971
PhysAndNursTot | -.0008241 .0006443 -1.28 0.201 -.002087 .0004387
forprofit | 2.486796 .9016759 2.76 0.006 .7195435 4.254048
_cons | 6.959503 6.667382 1.04 0.297 -6.108325 20.02733
-------------------------+----------------------------------------------------------------
sigma_u | 7.0374608
sigma_e | 3.395186
rho | .81119256 (fraction of variance due to u_i)
------------------------------------------------------------------------------------------
F test that all u_i=0: F(2309,3739) = 5.65 Prob > F = 0.0000
------------------------------------------------------------------------------------------
Instrumented: OF1bTelehealthhistorical
Instruments: H_COMP_2_A_P newNetwrkMem logLicensedBeds CMI2 logAdmissions
logTotOutpatVis PhysAndNursTot forprofit Totalfacilityexpensesexcludin RV
------------------------------------------------------------------------------------------
.
I then ran a similar model to get the first stage results from xtivreg2
xtivreg2 H_HSP_RATING_9_10 H_COMP_2_A_P newNetwrkMem logLicensedBeds CMI2 logAdmissions logTotOutpatVis PhysAndNursTot forprofit (OF1bTelehealthhistorical = Totalfacil RV ) , fe robust first small
FIXED EFFECTS ESTIMATION
------------------------
Number of groups = 1660 Obs per group: min = 2
avg = 3.3
max = 4
First-stage regressions
-----------------------
Unable to display all first-stage regressions.
There may be insufficient room to store results using -estimates store-,
or names of endogenous regressors may be too long to store the results.
Try dropping one or more estimation results using -estimates drop-,
using the -savefprefix- option, or using shorter variable names.
Summary results for first-stage regressions
-------------------------------------------
(Underid) (Weak id)
Variable | F( 2, 3738) P-val | SW Chi-sq( 2) P-val | SW F( 2, 3738)
OF1bTeleheal | 10.93 0.0000 | 21.91 0.0000 | 10.93
NB: first-stage test statistics heteroskedasticity-robust
Stock-Yogo weak ID F test critical values for single endogenous regressor:
10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for i.i.d. errors only.
Underidentification test
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic Chi-sq(2)=18.73 P-val=0.0001
Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic 13.70
Kleibergen-Paap Wald rk F statistic 10.93
Stock-Yogo weak ID test critical values for K1=1 and L1=2:
10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
Anderson-Rubin Wald test F(2,3738)= 10.19 P-val=0.0000
Anderson-Rubin Wald test Chi-sq(2)= 20.43 P-val=0.0000
Stock-Wright LM S statistic Chi-sq(2)= 22.17 P-val=0.0000
NB: Underidentification, weak identification and weak-identification-robust
test statistics heteroskedasticity-robust
Number of observations N = 5408
Number of regressors K = 9
Number of endogenous regressors K1 = 1
Number of instruments L = 10
Number of excluded instruments L1 = 2
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity
Number of obs = 5408
F( 9, 3739) = 27.59
Prob > F = 0.0000
Total (centered) SS = 31581.08333 Centered R2 = -0.3648
Total (uncentered) SS = 31581.08333 Uncentered R2 = -0.3648
Residual SS = 43100.52916 Root MSE = 3.395
------------------------------------------------------------------------------------------
| Robust
H_HSP_RATING_9_10 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
OF1bTelehealthhistorical | 1.927841 .7168633 2.69 0.007 .5223598 3.333322
H_COMP_2_A_P | .655708 .0490046 13.38 0.000 .5596297 .7517862
newNetwrkMem | .2702723 .2737156 0.99 0.324 -.2663741 .8069188
logLicensedBeds | .3527704 .7312045 0.48 0.630 -1.080828 1.786369
CMI2 | .8622487 1.439348 0.60 0.549 -1.959734 3.684232
logAdmissions | .0148941 .8592885 0.02 0.986 -1.669826 1.699614
logTotOutpatVis | .1035788 .3254017 0.32 0.750 -.5344033 .741561
PhysAndNursTot | -.0008241 .0005658 -1.46 0.145 -.0019335 .0002852
forprofit | 2.486796 1.083747 2.29 0.022 .3620025 4.611589
------------------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 18.734
Chi-sq(2) P-val = 0.0001
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 13.699
(Kleibergen-Paap rk Wald F statistic): 10.926
Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93
15% maximal IV size 11.59
20% maximal IV size 8.75
25% maximal IV size 7.25
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 3.845
Chi-sq(1) P-val = 0.0499
------------------------------------------------------------------------------
Instrumented: OF1bTelehealthhistorical
Included instruments: H_COMP_2_A_P newNetwrkMem logLicensedBeds CMI2
logAdmissions logTotOutpatVis PhysAndNursTot forprofit
Excluded instruments: Totalfacilityexpensesexcludin RV
------------------------------------------------------------------------------
The coefficients are the same, but the number of groups is 1660, vastly differing from 2310 above. The total observations are also obviously different. My question is, what is the number of hospitals? Is 1660 or 2310 the right number to report? Further, the number of observations are different too (N*T), but how can the coefficients end up being the same?
Comment