We can now perform the first stage regression of the determinants of fertility at US census tract level by using tract-level house price indices. The corresponding index construction is described here. It’s a new index published by the FHFA, going back 40 years, repeat sales method, at tract level and up.

FHFA Index Availability

For spatial availability see figure 1 in the paper. Each census tract starts their first year in the panel at a value of 100.

Merging with Census / ACS data

we can merge this by tract identifier and year to the FHFA index.

Plots at MSA level

## INFO [2022-04-05 11:15:01] running first stages for year 2010

In the raw data, larger cities have lower kids per adult.

Regressions

including distance reduces the impact of prices. If we don’t control for distance, a 1% increase in the house price index is associated with a -0.16% reduction in kids per adult. The average time series sd of the hpi series is about 35: so a one sd increase in the HPI goes together with a 5.6% reduction in kids per adult.

## Warning: In version 0.8.0 of the `modelsummary` package, the default significance markers produced by the `stars=TRUE` argument were changed to be consistent with R's defaults.
## This warning is displayed once per session.
Dependent Variable: log(kids_per_adult)
log(hpi) −0.091*** −0.053* −0.125*** −0.161***
(0.023) (0.024) (0.016) (0.017)
log(dist_CZ_pop) 0.096*** 0.086***
(0.010) (0.010)
pct_ed_lt_HS 0.349** 0.368***
(0.129) (0.109)
log(faminc) 0.315*** 0.329***
(0.014) (0.014)
Num.Obs. 50875 50875 50875 50875
R2 0.055 0.091 0.165 0.137
Std.Errors by: CZ by: CZ by: CZ by: CZ
FE: CZ X X X X
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001

here we use the HPI appreciation over the last 10 years (variable cumapp10) in a census tract rather than the level of the HPI. the estimated impact is thus \(\beta_1 \times 40 \times 100\) where 40 is the median 10-year appreciation in 2010. That means that the median house price index appreciation over 2000-2010 is associated with a \(-0.008 \times 40 \times 100 = 32\%\) reduction in kids per adult.

Dependent Variable: log(kids_per_adult)
cumapp10 −0.009*** −0.008*** −0.008*** −0.008***
(0.001) (0.001) (0.000) (0.001)
log(dist_CZ_pop) 0.078*** 0.076***
(0.010) (0.011)
pct_ed_lt_HS 0.461*** 0.497***
(0.137) (0.116)
log(faminc) 0.325*** 0.330***
(0.014) (0.014)
Num.Obs. 43001 43001 43001 43001
R2 0.122 0.148 0.231 0.207
Std.Errors by: CZ by: CZ by: CZ by: CZ
FE: CZ X X X X
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001

here is the plot for those house price appreciations.