Hello everybody,
I am trying to estimate the impact of vote preferences (var: prop_repdem2020) on the daily COVID-19 vaccination rate (var: series_complete_pop_pct) at the US county level. To do so, I want to implement an IV regression with fixed effects where moral value data (var: values_communal_shrink) are used as an instrument for vote preferences. However, since both prop_repdem2020 and values_communal_shrink are time-invariant, I have to make them interact with dummies for months (var: mdate) in order to estimate their coefficient. Here is the model that I would estimate:
My questions are:
1) Is it correct, from an econometric point of view, to include the interaction between a continuous and categorical variable (time unit) as an instrument for an endogenous regressor?
2) If so, how should I interpret the coefficient for the variable prop_repdem_mdate (since I have multiplied prop_repdem2020 with categorical values) ?
Here is the regression output and a sample of the data:
I am trying to estimate the impact of vote preferences (var: prop_repdem2020) on the daily COVID-19 vaccination rate (var: series_complete_pop_pct) at the US county level. To do so, I want to implement an IV regression with fixed effects where moral value data (var: values_communal_shrink) are used as an instrument for vote preferences. However, since both prop_repdem2020 and values_communal_shrink are time-invariant, I have to make them interact with dummies for months (var: mdate) in order to estimate their coefficient. Here is the model that I would estimate:
Code:
gen prop_repdem_mdate = prop_repdem2020*mdate gen relative_comm_mdate = relative_comm*mdate xtivreg2 series_complete_pop_pct L1.(total_cases_rate total_deaths_rate sqtotal_cases_rate) /// (prop_repdem_mdate = values_communal_mdate), fe
1) Is it correct, from an econometric point of view, to include the interaction between a continuous and categorical variable (time unit) as an instrument for an endogenous regressor?
2) If so, how should I interpret the coefficient for the variable prop_repdem_mdate (since I have multiplied prop_repdem2020 with categorical values) ?
Here is the regression output and a sample of the data:
Code:
Number of obs = 929663
F( 4,927408) = 3.4e+05
Prob > F = 0.0000
Total (centered) SS = 313676707.5 Centered R2 = 0.5493
Total (uncentered) SS = 313676707.5 Uncentered R2 = 0.5493
Residual SS = 141363511.1 Root MSE = 12.35
------------------------------------------------------------------------------------
series_complete_~t | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------------+----------------------------------------------------------------
prop_repdem_mdate | -.7309044 .0140289 -52.10 0.000 -.7584006 -.7034081
|
total_cases_rate |
L1. | .9149285 .0030804 297.02 0.000 .9088911 .9209659
|
total_deaths_rate |
L1. | 7.404845 .1172504 63.15 0.000 7.175039 7.634652
|
sqtotal_cases_rate |
L1. | -.0017409 5.63e-06 -309.05 0.000 -.0017519 -.0017298
------------------------------------------------------------------------------------
Underidentification test (Anderson canon. corr. LM statistic): 1.6e+04
Chi-sq(1) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 1.6e+04
Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
Source: Stock-Yogo (2005). Reproduced by permission.
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments): 0.000
(equation exactly identified)
------------------------------------------------------------------------------
Instrumented: prop_repdem_mdate
Included instruments: L.total_cases_rate L.total_deaths_rate
L.sqtotal_cases_rate
Excluded instruments: values_communal_mdate
------------------------------------------------------------------------------
Code:
* Example generated by -dataex-. For more info, type help dataex clear input str26 county int(date mdate) float(series_complete_pop_pct prop_repdem2020 prop_repdem_mdate values_communal_shrink values_communal_mdate) "Autauga" 22672 744 42.3 2.64 1964.16 .95 706.8 "Autauga" 22673 744 42.4 2.64 1964.16 .95 706.8 "Autauga" 22674 744 42.4 2.64 1964.16 .95 706.8 "Autauga" 22675 744 42.4 2.64 1964.16 .95 706.8 "Autauga" 22676 744 42.5 2.64 1964.16 .95 706.8 "Baldwin" 22263 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22264 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22265 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22266 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22267 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22268 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22269 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22270 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22271 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22272 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22273 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22274 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22275 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22276 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22277 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22278 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22279 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22280 731 0 3.4 2485.4 -.11 -80.41 "Baldwin" 22281 732 0 3.4 2488.8 -.11 -80.52 "Baldwin" 22282 732 0 3.4 2488.8 -.11 -80.52 "Baldwin" 22283 732 0 3.4 2488.8 -.11 -80.52 "Baldwin" 22284 732 0 3.4 2488.8 -.11 -80.52 "Baldwin" 22285 732 0 3.4 2488.8 -.11 -80.52 "Baldwin" 22286 732 0 3.4 2488.8 -.11 -80.52 "Baldwin" 22287 732 .1 3.4 2488.8 -.11 -80.52 "Baldwin" 22288 732 .1 3.4 2488.8 -.11 -80.52 end format %td date format %tm mdate
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