FF Variable Checks

Separated Timing and Underlying Risk

The following models separate the timing of Flood Factor information release from the underlying level of flood risk. Property fixed effects absorb time-invariant parcel characteristics, while year fixed effects control for broader market conditions.

Binary High Flood Factor Models

The binary specifications estimate whether properties with high Flood Factor scores experienced differential price changes after Flood Factor information became publicly available. The specification using i(event, high_ff_score, ref = FALSE) keeps the identified post-release contrast while avoiding the time-invariant main effect that is absorbed by property fixed effects.

Event == TRUE for all sales that occurred after First Street released its flood risk data.

high_ff_score == TRUE for properties that had a flood factor score of 5 or higher

High FF × Post High FF × Post, identified term only
high_ff_scoreTRUE -0.517
(15358.633)
eventTRUE 0.058*** 0.058***
(0.006) (0.006)
high_ff_scoreTRUE × eventTRUE -0.106***
(0.011)
i(factor_var = event, var = high_ff_score, ref = FALSE) -0.106***
(0.011)
Num.Obs. 666566 666566
R2 0.859 0.859
R2 Within 0.002 0.002
Std.Errors by: pin10 by: pin10
FE: pin X X
FE: sale_year X X

After Flood Factor information became available, high-risk properties sold for roughly 10.6% less relative to lower-risk properties, net of property fixed effects and overall market time effects.

Ordinal Flood Factor Models

The ordinal specifications estimate separate post-release effects for each Flood Factor score category. These models are useful for identifying whether the price response is concentrated among higher Flood Factor scores rather than changing linearly across the full scale.

Ordinal Ordinal × Triad Change Type × Ordinal × Event × Triad Change Type × Ordinal × Event
eventTRUE 0.061*** 0.015* 0.015* 0.060***
(0.006) (0.008) (0.008) (0.006)
ff_score_ord2 × eventTRUE 0.023 0.013 0.012 0.022
(0.040) (0.061) (0.061) (0.041)
ff_score_ord3 × eventTRUE -0.028 -0.030 -0.031 -0.030
(0.020) (0.027) (0.027) (0.020)
ff_score_ord4 × eventTRUE -0.015 -0.036 -0.033 -0.020
(0.019) (0.027) (0.027) (0.020)
ff_score_ord5 × eventTRUE -0.073** -0.095** -0.095** -0.080**
(0.027) (0.033) (0.033) (0.028)
ff_score_ord6 × eventTRUE -0.118*** -0.144*** -0.123*** -0.108***
(0.015) (0.017) (0.018) (0.015)
ff_score_ord7 × eventTRUE -0.068** -0.101*** -0.101*** -0.082***
(0.022) (0.027) (0.028) (0.024)
ff_score_ord8 × eventTRUE -0.163*** -0.154*** -0.154*** -0.181***
(0.021) (0.020) (0.020) (0.019)
ff_score_ord9 × eventTRUE -0.126*** -0.163*** -0.164*** -0.144***
(0.018) (0.016) (0.016) (0.018)
ff_score_ord10 × eventTRUE -0.071+ -0.217*** -0.222*** -0.114*
(0.038) (0.041) (0.041) (0.045)
eventTRUE × TriadNorth -0.020* -0.021**
(0.008) (0.008)
eventTRUE × TriadSouth 0.181*** 0.180***
(0.008) (0.008)
ff_score_ord2 × eventTRUE × TriadNorth -0.025 -0.029
(0.067) (0.066)
ff_score_ord3 × eventTRUE × TriadNorth -0.027 -0.038
(0.038) (0.039)
ff_score_ord4 × eventTRUE × TriadNorth 0.061+ 0.038
(0.033) (0.032)
ff_score_ord5 × eventTRUE × TriadNorth 0.065+ 0.055
(0.038) (0.040)
ff_score_ord6 × eventTRUE × TriadNorth 0.158*** 0.126***
(0.025) (0.027)
ff_score_ord7 × eventTRUE × TriadNorth 0.187*** 0.201***
(0.040) (0.044)
ff_score_ord8 × eventTRUE × TriadNorth 0.123** 0.126**
(0.044) (0.047)
ff_score_ord9 × eventTRUE × TriadNorth 0.229*** 0.217***
(0.047) (0.057)
ff_score_ord10 × eventTRUE × TriadNorth 0.236*** 0.147*
(0.056) (0.064)
ff_score_ord2 × eventTRUE × TriadSouth 0.064 0.070
(0.067) (0.067)
ff_score_ord3 × eventTRUE × TriadSouth 0.087** 0.094**
(0.032) (0.032)
ff_score_ord4 × eventTRUE × TriadSouth 0.072* 0.071*
(0.031) (0.031)
ff_score_ord5 × eventTRUE × TriadSouth 0.141*** 0.131**
(0.042) (0.043)
ff_score_ord6 × eventTRUE × TriadSouth 0.150*** 0.127***
(0.022) (0.024)
ff_score_ord7 × eventTRUE × TriadSouth 0.040 -0.001
(0.052) (0.059)
ff_score_ord8 × eventTRUE × TriadSouth 0.093 -0.032
(0.078) (0.117)
ff_score_ord9 × eventTRUE × TriadSouth 0.222*** 0.245***
(0.044) (0.053)
ff_score_ord10 × eventTRUE × TriadSouth 0.123* 0.147*
(0.060) (0.060)
change_typeAlways SFHA × eventTRUE -0.373*** 0.015
(0.069) (0.072)
change_typeAlways SFHA × ff_score_ord2 × eventTRUE -0.130 0.073
(0.102) (0.109)
change_typeAlways SFHA × ff_score_ord3 × eventTRUE -0.132 0.074
(0.088) (0.082)
change_typeAlways SFHA × ff_score_ord4 × eventTRUE -0.150* 0.057
(0.074) (0.100)
change_typeAlways SFHA × ff_score_ord6 × eventTRUE 0.111 -0.116
(0.074) (0.087)
change_typeAlways SFHA × ff_score_ord7 × eventTRUE 0.368*** 0.114
(0.079) (0.090)
change_typeAlways SFHA × ff_score_ord8 × eventTRUE 0.214 0.328***
(0.141) (0.098)
change_typeAlways SFHA × ff_score_ord9 × eventTRUE 0.397*** 0.206*
(0.089) (0.091)
change_typeAlways SFHA × ff_score_ord10 × eventTRUE 0.616*** 0.113
(0.108) (0.091)
change_typeAlways SFHA × eventTRUE × TriadNorth 0.478***
(0.082)
change_typeAlways SFHA × eventTRUE × TriadSouth 0.397***
(0.088)
change_typeAlways SFHA × ff_score_ord2 × eventTRUE × TriadNorth 0.189
(0.184)
change_typeAlways SFHA × ff_score_ord3 × eventTRUE × TriadNorth 0.183+
(0.109)
change_typeAlways SFHA × ff_score_ord4 × eventTRUE × TriadNorth 0.167
(0.107)
change_typeAlways SFHA × ff_score_ord6 × eventTRUE × TriadNorth -0.124
(0.093)
change_typeAlways SFHA × ff_score_ord7 × eventTRUE × TriadNorth -0.553***
(0.110)
change_typeAlways SFHA × ff_score_ord8 × eventTRUE × TriadNorth -0.329+
(0.175)
change_typeAlways SFHA × ff_score_ord9 × eventTRUE × TriadNorth -0.437***
(0.123)
change_typeAlways SFHA × ff_score_ord10 × eventTRUE × TriadNorth -0.567***
(0.129)
change_typeAlways SFHA × ff_score_ord4 × eventTRUE × TriadSouth 0.105
(0.117)
change_typeAlways SFHA × ff_score_ord6 × eventTRUE × TriadSouth -0.121
(0.098)
change_typeAlways SFHA × ff_score_ord7 × eventTRUE × TriadSouth -0.230*
(0.117)
change_typeAlways SFHA × ff_score_ord9 × eventTRUE × TriadSouth -0.486***
(0.130)
change_typeAlways SFHA × ff_score_ord10 × eventTRUE × TriadSouth -0.710***
(0.159)
Num.Obs. 666364 666364 666364 666364
R2 0.859 0.861 0.861 0.859
R2 Within 0.002 0.012 0.013 0.002
Std.Errors by: pin10 by: pin10 by: pin10 by: pin10
FE: pin X X X X
FE: sale_year X X X X

The ordinal marginal effects are the clearest way to communicate the nonlinear pattern. Lower Flood Factor scores generally show smaller estimated price responses, while higher scores show larger negative post-release effects.

The following marginal effects summarize the estimated post-release price change for each Flood Factor score across Cook County regions.

Triad ff_score_ord estimate std.error conf.low conf.high pct_change pct_low pct_high p.value
City 1 0.01 0.01 0.00 0.03 1.49 0.00 2.99 0.05
City 2 0.03 0.06 -0.09 0.15 2.81 -8.65 15.71 0.65
City 3 -0.02 0.03 -0.07 0.04 -1.52 -6.48 3.71 0.56
City 4 -0.02 0.03 -0.07 0.03 -2.15 -6.96 2.90 0.40
City 5 -0.08 0.03 -0.14 -0.02 -7.69 -13.41 -1.60 0.01
City 6 -0.13 0.02 -0.16 -0.10 -12.08 -14.71 -9.38 0.00
City 7 -0.09 0.03 -0.14 -0.03 -8.27 -12.89 -3.41 0.00
City 8 -0.14 0.02 -0.18 -0.10 -12.96 -16.23 -9.57 0.00
City 9 -0.15 0.02 -0.18 -0.12 -13.81 -16.36 -11.17 0.00
City 10 -0.20 0.04 -0.28 -0.12 -18.35 -24.68 -11.50 0.00
North 1 -0.00 0.01 -0.02 0.01 -0.48 -1.79 0.84 0.47
North 2 -0.02 0.03 -0.07 0.04 -1.69 -6.96 3.88 0.54
North 3 -0.06 0.03 -0.11 -0.01 -5.97 -10.66 -1.03 0.02
North 4 0.02 0.02 -0.02 0.06 1.99 -1.97 6.10 0.33
North 5 -0.03 0.02 -0.07 0.00 -3.40 -6.95 0.30 0.07
North 6 0.01 0.02 -0.03 0.05 0.96 -2.65 4.71 0.61
North 7 0.08 0.03 0.02 0.14 8.49 2.17 15.20 0.01
North 8 -0.04 0.04 -0.11 0.04 -3.51 -10.64 4.18 0.36
North 9 0.06 0.04 -0.03 0.15 6.22 -2.61 15.86 0.17
North 10 0.01 0.04 -0.06 0.09 1.37 -5.88 9.18 0.72
South 1 0.20 0.01 0.18 0.21 21.64 20.00 23.31 0.00
South 2 0.27 0.03 0.22 0.33 31.41 24.43 38.78 0.00
South 3 0.25 0.02 0.22 0.29 28.74 24.52 33.10 0.00
South 4 0.23 0.02 0.20 0.27 26.07 21.84 30.45 0.00
South 5 0.24 0.03 0.19 0.29 27.40 21.21 33.92 0.00
South 6 0.20 0.02 0.17 0.23 22.47 18.85 26.21 0.00
South 7 0.14 0.04 0.05 0.22 14.45 4.81 24.98 0.00
South 8 0.14 0.08 -0.01 0.28 14.49 -1.17 32.64 0.07
South 9 0.25 0.04 0.17 0.34 28.97 18.90 39.91 0.00
South 10 0.10 0.04 0.02 0.19 10.72 1.69 20.56 0.02

These models are more saturated and should usually be treated as appendix or robustness material. They are useful for checking whether Flood Factor effects differ depending on FEMA floodplain status, but the number of interaction cells makes direct coefficient interpretation difficult.

change_type Triad ff_score_ord estimate std.error conf.low conf.high pct_change pct_low pct_high p.value
Never SFHA City 1 0.02 0.01 0.00 0.03 1.52 0.03 3.03 0.05
Never SFHA City 2 0.03 0.06 -0.09 0.15 2.79 -8.67 15.68 0.65
Never SFHA City 3 -0.02 0.03 -0.07 0.04 -1.54 -6.50 3.69 0.56
Never SFHA City 4 -0.02 0.03 -0.07 0.03 -1.78 -6.63 3.31 0.49
Never SFHA City 5 -0.08 0.03 -0.14 -0.02 -7.71 -13.42 -1.62 0.01
Never SFHA City 6 -0.11 0.02 -0.14 -0.08 -10.19 -13.01 -7.27 0.00
Never SFHA City 7 -0.09 0.03 -0.14 -0.03 -8.26 -13.14 -3.11 0.00
Never SFHA City 8 -0.14 0.02 -0.18 -0.10 -12.98 -16.25 -9.59 0.00
Never SFHA City 9 -0.15 0.02 -0.18 -0.12 -13.86 -16.45 -11.19 0.00
Never SFHA City 10 -0.21 0.04 -0.29 -0.13 -18.69 -24.90 -11.97 0.00
Never SFHA North 1 -0.01 0.01 -0.02 0.01 -0.63 -1.93 0.69 0.35
Never SFHA North 2 -0.02 0.03 -0.08 0.03 -2.24 -7.33 3.12 0.41
Never SFHA North 3 -0.07 0.03 -0.13 -0.02 -7.19 -12.00 -2.12 0.01
Never SFHA North 4 -0.00 0.02 -0.04 0.04 -0.19 -3.86 3.62 0.92
Never SFHA North 5 -0.05 0.02 -0.09 -0.00 -4.53 -8.53 -0.36 0.03
Never SFHA North 6 -0.00 0.02 -0.04 0.04 -0.34 -4.22 3.71 0.87
Never SFHA North 7 0.09 0.03 0.03 0.16 9.77 2.67 17.37 0.01
Never SFHA North 8 -0.03 0.04 -0.12 0.05 -3.40 -11.23 5.11 0.42
Never SFHA North 9 0.05 0.06 -0.06 0.15 4.69 -6.06 16.68 0.41
Never SFHA North 10 -0.08 0.05 -0.18 0.02 -7.77 -16.33 1.67 0.10
Never SFHA South 1 0.20 0.01 0.18 0.21 21.60 19.95 23.26 0.00
Never SFHA South 2 0.28 0.03 0.22 0.33 32.10 24.87 39.76 0.00
Never SFHA South 3 0.26 0.02 0.23 0.29 29.60 25.40 33.95 0.00
Never SFHA South 4 0.23 0.02 0.20 0.27 26.35 22.20 30.65 0.00
Never SFHA South 5 0.23 0.03 0.18 0.28 26.02 19.50 32.91 0.00
Never SFHA South 6 0.20 0.02 0.17 0.23 22.14 18.16 26.26 0.00
Never SFHA South 7 0.09 0.05 -0.01 0.20 9.71 -1.03 21.62 0.08
Never SFHA South 8 0.01 0.12 -0.22 0.24 0.99 -19.53 26.74 0.93
Never SFHA South 9 0.28 0.05 0.18 0.38 31.87 19.35 45.70 0.00
Never SFHA South 10 0.12 0.04 0.03 0.21 12.83 3.47 23.03 0.01
Always SFHA City 1 -0.36 0.07 -0.49 -0.22 -30.09 -38.91 -20.00 0.00
Always SFHA City 4 -0.54 0.01 -0.55 -0.53 -41.77 -42.50 -41.04 0.00
Always SFHA City 6 -0.37 0.02 -0.41 -0.33 -30.88 -33.45 -28.21 0.00
Always SFHA City 7 -0.09 0.03 -0.14 -0.04 -8.70 -13.49 -3.65 0.00
Always SFHA City 9 -0.13 0.05 -0.23 -0.02 -11.82 -20.68 -1.96 0.02
Always SFHA City 10 0.04 0.07 -0.11 0.18 3.66 -10.05 19.46 0.62
Always SFHA North 1 0.10 0.04 0.01 0.19 10.40 1.17 20.48 0.03
Always SFHA North 2 0.14 0.14 -0.14 0.42 15.12 -13.27 52.81 0.33
Always SFHA North 3 0.08 0.04 0.00 0.16 8.57 0.33 17.48 0.04
Always SFHA North 4 0.12 0.06 0.00 0.24 12.84 0.28 26.97 0.04
Always SFHA North 5 0.00 0.04 -0.07 0.08 0.35 -7.08 8.37 0.93
Always SFHA North 6 0.09 0.03 0.03 0.15 9.28 2.91 16.03 0.00
Always SFHA North 7 0.01 0.05 -0.09 0.12 1.35 -8.76 12.59 0.80
Always SFHA North 8 -0.04 0.08 -0.21 0.12 -4.38 -18.81 12.61 0.59
Always SFHA North 9 0.11 0.05 0.02 0.20 11.69 1.84 22.49 0.02
Always SFHA North 10 0.07 0.03 0.02 0.13 7.62 1.91 13.65 0.01
Always SFHA South 1 0.22 0.06 0.11 0.33 24.59 11.82 38.81 0.00
Always SFHA South 2 0.17 0.08 0.01 0.33 18.81 1.39 39.22 0.03
Always SFHA South 3 0.15 0.07 0.02 0.28 16.39 2.12 32.65 0.02
Always SFHA South 4 0.21 0.07 0.07 0.35 23.75 7.56 42.38 0.00
Always SFHA South 5 0.34 0.07 0.21 0.47 40.85 23.58 60.52 0.00
Always SFHA South 6 0.21 0.03 0.16 0.27 23.95 16.80 31.52 0.00
Always SFHA South 7 0.26 0.04 0.17 0.34 29.07 18.80 40.22 0.00
Always SFHA South 8 0.25 0.06 0.13 0.36 28.11 14.14 43.80 0.00
Always SFHA South 9 0.21 0.06 0.10 0.33 23.57 10.12 38.68 0.00
Always SFHA South 10 0.05 0.09 -0.13 0.23 5.20 -12.45 26.41 0.59

The following table identifies coefficients omitted from interpretation due to extremely large standard errors or lack of identification under the fixed-effects structure. Large standard errors typically indicate that a coefficient is not identified within the property fixed-effects framework because the underlying variable does not vary within parcels over time, or because certain interaction combinations contain extremely sparse observations.

Continuous Flood Factor Models

The continuous specifications estimate the marginal price effect associated with a one-point increase in Flood Factor score after public release of the information.

Continuous Continuous × Triad Change Type × Continuous × Event × Triad Change Type × Continuous × Event
eventTRUE 0.080*** 0.041*** 0.039*** 0.081***
(0.007) (0.009) (0.009) (0.007)
env_flood_fs_factor × eventTRUE -0.018*** -0.024*** -0.022*** -0.019***
(0.002) (0.002) (0.002) (0.002)
eventTRUE × TriadNorth -0.051*** -0.047***
(0.010) (0.010)
eventTRUE × TriadSouth 0.157*** 0.158***
(0.010) (0.010)
env_flood_fs_factor × eventTRUE × TriadNorth 0.027*** 0.021***
(0.003) (0.004)
env_flood_fs_factor × eventTRUE × TriadSouth 0.026*** 0.024***
(0.003) (0.003)
change_typeAlways SFHA × eventTRUE -0.511*** -0.003
(0.052) (0.059)
change_typeChanges SFHA × eventTRUE -0.099 0.024
(0.062) (0.062)
change_typeAlways SFHA × env_flood_fs_factor × eventTRUE 0.043*** 0.002
(0.010) (0.011)
change_typeChanges SFHA × env_flood_fs_factor × eventTRUE 0.033 0.054**
(0.021) (0.021)
change_typeAlways SFHA × eventTRUE × TriadNorth 0.622***
(0.065)
change_typeAlways SFHA × eventTRUE × TriadSouth 0.539***
(0.073)
change_typeAlways SFHA × env_flood_fs_factor × eventTRUE × TriadNorth -0.046***
(0.012)
change_typeAlways SFHA × env_flood_fs_factor × eventTRUE × TriadSouth -0.047***
(0.013)
Num.Obs. 666564 666564 666564 666564
R2 0.859 0.861 0.861 0.859
R2 Within 0.002 0.012 0.013 0.002
Std.Errors by: pin10 by: pin10 by: pin10 by: pin10
FE: pin X X X X
FE: sale_year X X X X

The following marginal effects estimate the post-release association between a one-point increase in Flood Factor score and sale price across Cook County regions.

Triad estimate std.error conf.low conf.high pct_change pct_low pct_high p.value
City -0.02 0.00 -0.03 -0.02 -2.42 -2.89 -1.94 0.00
North 0.00 0.00 -0.00 0.01 0.25 -0.18 0.69 0.25
South 0.00 0.00 -0.00 0.01 0.19 -0.22 0.60 0.38

The continuous marginal effects summarize how strongly prices changed with each additional Flood Factor point after information release. This is usually the most compact way to present regional heterogeneity in the continuous specification.

These models are more saturated and should usually be treated as appendix or robustness material. They are useful for checking whether Flood Factor effects differ depending on FEMA floodplain status, but the number of interaction cells makes direct coefficient interpretation difficult.

change_type Triad estimate std.error conf.low conf.high pct_change pct_low pct_high p.value
Never SFHA City -0.02 0.00 -0.03 -0.02 -2.18 -2.66 -1.70 0.00
Never SFHA North -0.00 0.00 -0.01 0.00 -0.08 -0.58 0.43 0.76
Never SFHA South 0.00 0.00 -0.00 0.01 0.18 -0.28 0.65 0.45
Always SFHA City -0.43 8411.74 -16487.15 16486.28 -35.21 -100.00 1.00
Always SFHA North -0.46 8411.59 -16486.87 16485.95 -36.81 -100.00 1.00
Always SFHA South -0.39 10585.78 -20748.14 20747.35 -32.60 -100.00 1.00
Changes SFHA South 0.03 1.16 -2.24 2.31 3.53 -89.36 906.93 0.98

The following table identifies coefficients omitted from interpretation due to extremely large standard errors or lack of identification under the fixed-effects structure. Large standard errors typically indicate that a coefficient is not identified within the property fixed-effects framework because the underlying variable does not vary within parcels over time, or because certain interaction combinations contain extremely sparse observations.