Table 3.

Transmission equation (IV) for different underlying epidemiological data generating processes.

	(1)	(2)	(3)	(4)	(5)	(6)
Mean days of..
Infectiousness	Fixed	5	4	7	5	5
Latency	duration	1	1	1	2	3
Panel a: transmission
$\Delta Infectiou{s}_{ot}$	1.17***	1.208***	1.171***	1.273***	1.226***	1.247***
	(0.062)	(0.0458)	(0.0430)	(0.0514)	(0.0511)	(0.0555)
Observations	81,594	81,594	81,594	81,594	81,594	81,594
State-day FE	Yes	Yes	Yes	Yes	Yes	Yes
Kleibergen Paap F	252	113.3	129.1	97.04	103.9	96.38
Hansen J	3.15	4.410	4.433	4.357	4.403	4.392
p-value	0.116	0.0357	0.0352	0.0369	0.0359	0.0361
Panel b: conditioned on density
$\Delta Infectiou{s}_{ot}$	0.88***	0.711***	0.645***	0.825***	0.723***	0.748***
	(0.055)	(0.178)	(0.174)	(0.190)	(0.193)	(0.207)
$\Delta Infectiou{s}_{ot}$ x log density	0.043***	0.0706***	0.0751***	0.0636**	0.0714***	0.0705**
	(0.0051)	(0.0247)	(0.0243)	(0.0266)	(0.0270)	(0.0291)
Log density	−0.67*	−0.562*	−0.470*	−0.672**	−0.594*	−0.624*
	(0.37)	(0.296)	(0.278)	(0.323)	(0.319)	(0.338)
Observations	81,594	81,594	81,594	81,594	81,594	81,594
State-day FE	Yes	Yes	Yes	Yes	Yes	Yes
Kleibergen Paap F	44.2	10.74	11.68	9.599	10.11	9.569
Hansen J	2.87	4.280	4.286	4.255	4.292	4.296
p-value	0.24	0.118	0.117	0.119	0.117	0.117

Notes. ***$p$ $<$ 0.01, **$p$ $<$ 0.05, *$p$ $<$ 0.1. Estimated in first differences. Twoway (county and day) clustered standard errors in parentheses. In column 1, the dependent variable is the number of new cases detected at the county-day level and$\Delta Infectiou{s}_{ot}$is the 6-day lagged 5-day average number of infected measured within the county. In columns 2–6, the dependent variable is the daily number of county infections implied by the SEIR model based on observed detections. $\Delta Infectiou{s}_{ot}$is the pool of infectious as constructed according to the SEIR model. The durations of latency and infectiousness translate to SEIR parameters as$1/\sigma$and$1/\left(\gamma +\delta \right)$respectively.