Preliminary Summary of MSA to City Matches

  • Our cities cover 307 MSAs (in 2017)

  • The Chicago Metro Area covers 55 cities

  • 17 metro areas cover more than 10 cities

  • 143 metro areas cover only one city

## # A tibble: 217 × 2
##    msa_name                                    n
##    <chr>                                   <int>
##  1 Dallas-Fort Worth-Arlington, TX            15
##  2 Los Angeles-Long Beach-Anaheim, CA         14
##  3 Boston-Cambridge-Newton, MA-NH             13
##  4 Minneapolis-St. Paul-Bloomington, MN-WI    10
##  5 Charlotte-Concord-Gastonia, NC-SC           7
##  6 Detroit-Warren-Dearborn, MI                 7
##  7 Milwaukee-Waukesha-West Allis, WI           7
##  8 New York-Newark-Jersey City, NY-NJ-PA       7
##  9 Cleveland-Elyria, OH                        6
## 10 Houston-The Woodlands-Sugar Land, TX        6
## # … with 207 more rows

City-Level and Year Fixed Effects Log Level Time Series

Note: Intercepts are not shown

regression term est se p_val
Police Salaries
log_police_salaries vs union_localpol log_housing_index 0.172 0.015 0.000
log_police_salaries vs union_localpol union_localpol:log_housing_index 0.000 0.017 0.996
Police Employment
log_police_pc vs union_localpol log_housing_index -0.146 0.046 0.002
log_police_pc vs union_localpol union_localpol:log_housing_index 0.112 0.052 0.031

Metro-Level Panel Data Regressions (No Instrument)

Log Panel Data with MSA * Single Year Fixed Effects

Including 12 MSAs that cross states (returns non-collinear estimates for union bargaining)

Specifications:

  • Fixed Effects: MSA * Single Year

  • Clusters: MSA

  • Error Type: Linear Group Fixed Effects

regression term est se p_val
Police Salaries
Includes Union Local Pol (no interaction)
log_police_salaries vs log_housing_index + union_localpol log_housing_index -0.016 0.069 0.815
log_police_salaries vs log_housing_index + union_localpol union_localpol 0.060 0.007 0.000
log_police_salaries vs log_housing_index + union_localpol log_hh_income 0.274 0.046 0.000
log_police_salaries vs log_housing_index + union_localpol log_tot_crime 0.016 0.003 0.000
Includes Union Local Pol (interaction w/ HPI)
log_police_salaries vs log_housing_index*union_localpol log_housing_index 0.219 0.051 0.000
log_police_salaries vs log_housing_index*union_localpol union_localpol 0.777 0.174 0.000
log_police_salaries vs log_housing_index*union_localpol log_hh_income 0.262 0.044 0.000
log_police_salaries vs log_housing_index*union_localpol log_tot_crime 0.017 0.003 0.000
log_police_salaries vs log_housing_index*union_localpol log_housing_index:union_localpol -0.337 0.082 0.000
Includes Right to Work (interaction w/ HPI(
log_police_salaries vs log_housing_index*right_to_work log_housing_index -0.315 0.066 0.000
log_police_salaries vs log_housing_index*right_to_work right_to_workYes -0.789 0.126 0.000
log_police_salaries vs log_housing_index*right_to_work log_hh_income 0.288 0.079 0.000
log_police_salaries vs log_housing_index*right_to_work log_tot_crime 0.016 0.004 0.000
log_police_salaries vs log_housing_index*right_to_work log_housing_index:right_to_workYes 0.361 0.060 0.000
Police Employment per Capita
Includes Union Local Pol (no interaction)
log_police_pc vs log_housing_index + union_localpol log_housing_index 0.415 0.272 0.129
log_police_pc vs log_housing_index + union_localpol union_localpol -0.207 0.033 0.000
log_police_pc vs log_housing_index + union_localpol log_hh_income -0.600 0.174 0.001
log_police_pc vs log_housing_index + union_localpol log_tot_crime 0.044 0.012 0.000
Includes Union Local Pol (interaction w/ HPI)
log_police_pc vs log_housing_index*union_localpol log_housing_index -0.339 0.242 0.162
log_police_pc vs log_housing_index*union_localpol union_localpol -2.509 0.891 0.005
log_police_pc vs log_housing_index*union_localpol log_hh_income -0.560 0.175 0.002
log_police_pc vs log_housing_index*union_localpol log_tot_crime 0.043 0.012 0.000
log_police_pc vs log_housing_index*union_localpol log_housing_index:union_localpol 1.083 0.426 0.012
Includes Right to Work (interaction w/ HPI)
log_police_pc vs log_housing_index*right_to_work log_housing_index 0.917 0.312 0.004
log_police_pc vs log_housing_index*right_to_work right_to_workYes 2.697 0.547 0.000
log_police_pc vs log_housing_index*right_to_work log_hh_income -1.067 0.162 0.000
log_police_pc vs log_housing_index*right_to_work log_tot_crime 0.022 0.011 0.055
log_police_pc vs log_housing_index*right_to_work log_housing_index:right_to_workYes -1.276 0.265 0.000

Excluding 12 MSAs that cross states (returns non-collinear estimates for union bargaining)

MSA Clusters and Linear Group Fixed Effects

Specifications:

  • Fixed Effects: MSA * Single Year

  • Clusters: MSA

  • Error Type: Linear Group Fixed Effects

regression term est se p_val
Police Salaries
log_police_salaries vs log_housing_index log_housing_index -0.203 0.200 0.312
log_police_salaries vs log_housing_index log_hh_income 0.209 0.041 0.000
log_police_salaries vs log_housing_index log_tot_crime 0.017 0.004 0.000
Police Employment per Capita
log_police_pc vs log_housing_index log_housing_index 1.181 0.565 0.038
log_police_pc vs log_housing_index log_hh_income -0.670 0.247 0.007
log_police_pc vs log_housing_index log_tot_crime 0.043 0.015 0.003

No SE Cluster, Still MSA by Year Fixed Effects

regression term est se p_val
Police Salaries
log_police_salaries vs log_housing_index log_housing_index -0.203 0.058 0
log_police_salaries vs log_housing_index log_hh_income 0.209 0.015 0
log_police_salaries vs log_housing_index log_tot_crime 0.017 0.001 0
Police Employment per Capita
log_police_pc vs log_housing_index log_housing_index 1.181 0.253 0
log_police_pc vs log_housing_index log_hh_income -0.670 0.065 0
log_police_pc vs log_housing_index log_tot_crime 0.043 0.006 0

Log Panel Data with MSA * Five Year Fixed Effects

Including 12 MSAs that cross states (returns non-collinear estimates for union bargaining)

Specifications:

  • Fixed Effects: MSA * Five Year

  • Clusters: MSA

  • Error Type: Linear Group Fixed Effects

regression term est se p_val
Police Salaries
Includes Union Local Pol (no interaction)
log_police_salaries vs log_housing_index + union_localpol log_housing_index -0.011 0.049 0.824
log_police_salaries vs log_housing_index + union_localpol union_localpol 0.060 0.007 0.000
log_police_salaries vs log_housing_index + union_localpol log_hh_income 0.269 0.046 0.000
log_police_salaries vs log_housing_index + union_localpol log_tot_crime 0.016 0.003 0.000
Includes Union Local Pol (interaction w/ HPI)
log_police_salaries vs log_housing_index*union_localpol log_housing_index 0.213 0.049 0.000
log_police_salaries vs log_housing_index*union_localpol union_localpol 0.686 0.140 0.000
log_police_salaries vs log_housing_index*union_localpol log_hh_income 0.256 0.044 0.000
log_police_salaries vs log_housing_index*union_localpol log_tot_crime 0.016 0.003 0.000
log_police_salaries vs log_housing_index*union_localpol log_housing_index:union_localpol -0.294 0.065 0.000
Includes Right to Work (interaction w/ HPI)
log_police_salaries vs log_housing_index*right_to_work log_housing_index -0.060 0.148 0.686
log_police_salaries vs log_housing_index*right_to_work right_to_workYes -0.198 0.243 0.417
log_police_salaries vs log_housing_index*right_to_work log_hh_income 0.279 0.075 0.000
log_police_salaries vs log_housing_index*right_to_work log_tot_crime 0.016 0.004 0.000
log_police_salaries vs log_housing_index*right_to_work log_housing_index:right_to_workYes 0.084 0.115 0.463
Police Employment per Capita
Includes Union Local Pol (no interaction)
log_police_pc vs log_housing_index + union_localpol log_housing_index 0.265 0.153 0.084
log_police_pc vs log_housing_index + union_localpol union_localpol -0.209 0.032 0.000
log_police_pc vs log_housing_index + union_localpol log_hh_income -0.576 0.163 0.000
log_police_pc vs log_housing_index + union_localpol log_tot_crime 0.042 0.012 0.001
Includes Union Local Pol (interaction w/ HPI)
log_police_pc vs log_housing_index*union_localpol log_housing_index -0.393 0.215 0.069
log_police_pc vs log_housing_index*union_localpol union_localpol -2.048 0.537 0.000
log_police_pc vs log_housing_index*union_localpol log_hh_income -0.538 0.165 0.001
log_police_pc vs log_housing_index*union_localpol log_tot_crime 0.042 0.012 0.000
log_police_pc vs log_housing_index*union_localpol log_housing_index:union_localpol 0.865 0.255 0.001
Includes Right to Work (interaction w/ HPI)
log_police_pc vs log_housing_index*right_to_work log_housing_index -0.054 0.352 0.879
log_police_pc vs log_housing_index*right_to_work right_to_workYes 0.292 0.915 0.750
log_police_pc vs log_housing_index*right_to_work log_hh_income -1.035 0.155 0.000
log_police_pc vs log_housing_index*right_to_work log_tot_crime 0.020 0.011 0.065
log_police_pc vs log_housing_index*right_to_work log_housing_index:right_to_workYes -0.137 0.430 0.751

Excluding 12 MSAs that cross states (returns non-collinear estimates for union bargaining)

MSA Clusters and Linear Group Fixed Effects

Specifications:

  • Fixed Effects: MSA * Single Year

  • Clusters: MSA

  • Error Type: Linear Group Fixed Effects

regression term est se p_val
Police Salaries
log_police_salaries vs log_housing_index log_housing_index -0.058 0.092 0.531
log_police_salaries vs log_housing_index log_hh_income 0.200 0.040 0.000
log_police_salaries vs log_housing_index log_tot_crime 0.016 0.004 0.000
Police Employment per Capita
log_police_pc vs log_housing_index log_housing_index 0.376 0.237 0.114
log_police_pc vs log_housing_index log_hh_income -0.619 0.230 0.008
log_police_pc vs log_housing_index log_tot_crime 0.046 0.014 0.002

No SE Cluster, Still MSA by Year Fixed Effects

regression term est se p_val
Police Salaries
log_police_salaries vs log_housing_index log_housing_index -0.058 0.028 0.035
log_police_salaries vs log_housing_index log_hh_income 0.200 0.012 0.000
log_police_salaries vs log_housing_index log_tot_crime 0.016 0.001 0.000
Police Employment per Capita
log_police_pc vs log_housing_index log_housing_index 0.376 0.111 0.001
log_police_pc vs log_housing_index log_hh_income -0.619 0.048 0.000
log_police_pc vs log_housing_index log_tot_crime 0.046 0.004 0.000

Pct Change / Long Difference Regressions (No Instrument)

MSA Fixed Effects and MSA-Clustered Standard Errors

## 
## Call:
## lm_robust(formula = pct_change_police_salaries ~ pct_change_hpi + 
##     union_localpol + pct_change_hh_income + pct_change_crime, 
##     data = model_pct_change, clusters = msa_name, fixed_effects = ~msa_name)
## 
## Standard error type:  CR2 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper
## pct_change_hpi        -0.0862     0.1173  -0.734   0.5593  -0.7815   0.6091
## union_localpol        -0.0826     0.0635  -1.299   0.4161  -0.8721   0.7070
## pct_change_hh_income   0.1845     0.1016   1.816   0.0898  -0.0324   0.4013
## pct_change_crime      -0.0199     0.0318  -0.625   0.5594  -0.1016   0.0618
##                         DF
## pct_change_hpi        1.52
## union_localpol        1.01
## pct_change_hh_income 14.73
## pct_change_crime      5.00
## 
## Multiple R-squared:  0.652 , Adjusted R-squared:  0.227
## Multiple R-squared (proj. model):  0.0259 ,  Adjusted R-squared (proj. model):  -1.17 
## F-statistic (proj. model): 1.05 on 4 and 204 DF,  p-value: 0.384
regression term est se p_val
Police Salaries
Includes Union Local Pol (no interaction)
pct_change_police_salaries vs pct_change_hpi + union_localpol pct_change_hpi -0.086 0.117 0.559
pct_change_police_salaries vs pct_change_hpi + union_localpol union_localpol -0.083 0.064 0.416
pct_change_police_salaries vs pct_change_hpi + union_localpol pct_change_hh_income 0.184 0.102 0.090
pct_change_police_salaries vs pct_change_hpi + union_localpol pct_change_crime -0.020 0.032 0.559
Includes Union Local Pol (interaction w/ HPI)
pct_change_police_salaries vs pct_change_hpi*union_localpol pct_change_hpi 0.253 0.273 0.391
pct_change_police_salaries vs pct_change_hpi*union_localpol union_localpol 0.127 0.161 0.504
pct_change_police_salaries vs pct_change_hpi*union_localpol pct_change_hh_income 0.182 0.099 0.086
pct_change_police_salaries vs pct_change_hpi*union_localpol pct_change_crime -0.027 0.030 0.403
pct_change_police_salaries vs pct_change_hpi*union_localpol pct_change_hpi:union_localpol -0.365 0.279 0.239
Includes Right to Work (interaction w/ HPI(
pct_change_police_salaries vs pct_change_hpi*right_to_work pct_change_hpi NA NA NA
pct_change_police_salaries vs pct_change_hpi*right_to_work right_to_workYes 0.049 0.080 0.560
pct_change_police_salaries vs pct_change_hpi*right_to_work pct_change_hh_income 0.118 0.114 0.332
pct_change_police_salaries vs pct_change_hpi*right_to_work pct_change_crime 0.002 0.034 0.947
pct_change_police_salaries vs pct_change_hpi*right_to_work pct_change_hpi:right_to_workYes 0.236 0.258 0.388
Police Employment per Capita
Includes Union Local Pol (no interaction)
pct_change_police_employment vs pct_change_hpi + union_localpol pct_change_hpi -0.033 0.072 0.706
pct_change_police_employment vs pct_change_hpi + union_localpol union_localpol -0.323 0.124 0.231
pct_change_police_employment vs pct_change_hpi + union_localpol pct_change_hh_income 0.206 0.107 0.074
pct_change_police_employment vs pct_change_hpi + union_localpol pct_change_crime 0.173 0.065 0.046
Includes Union Local Pol (interaction w/ HPI)
pct_change_police_employment vs pct_change_hpi*union_localpol pct_change_hpi -0.208 0.291 0.504
pct_change_police_employment vs pct_change_hpi*union_localpol union_localpol -0.431 0.190 0.138
pct_change_police_employment vs pct_change_hpi*union_localpol pct_change_hh_income 0.207 0.107 0.071
pct_change_police_employment vs pct_change_hpi*union_localpol pct_change_crime 0.177 0.063 0.034
pct_change_police_employment vs pct_change_hpi*union_localpol pct_change_hpi:union_localpol 0.188 0.290 0.541
Includes Right to Work (interaction w/ HPI)
pct_change_police_employment vs pct_change_hpi*right_to_work pct_change_hpi NA NA NA
pct_change_police_employment vs pct_change_hpi*right_to_work right_to_workYes 0.117 0.120 0.360
pct_change_police_employment vs pct_change_hpi*right_to_work pct_change_hh_income 0.350 0.146 0.042
pct_change_police_employment vs pct_change_hpi*right_to_work pct_change_crime 0.148 0.059 0.104
pct_change_police_employment vs pct_change_hpi*right_to_work pct_change_hpi:right_to_workYes -0.266 0.383 0.509

MSA Fixed Effects and No Clustered Standard Errors

## 
## Call:
## lm_robust(formula = pct_change_police_salaries ~ pct_change_hpi + 
##     union_localpol + pct_change_hh_income + pct_change_crime, 
##     data = model_pct_change, fixed_effects = ~msa_name)
## 
## Standard error type:  HC2 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper  DF
## pct_change_hpi        -0.0862     0.1551  -0.555   0.5793 -0.39239   0.2201 170
## union_localpol        -0.0826     0.1129  -0.732   0.4654 -0.30534   0.1402 170
## pct_change_hh_income   0.1845     0.0903   2.044   0.0425  0.00628   0.3627 170
## pct_change_crime      -0.0199     0.0313  -0.635   0.5266 -0.08167   0.0419 170
## 
## Multiple R-squared:  0.652 , Adjusted R-squared:  0.227
## Multiple R-squared (proj. model):  0.0259 ,  Adjusted R-squared (proj. model):  -1.17 
## F-statistic (proj. model): 1.15 on 4 and 170 DF,  p-value: 0.336
regression term est se p_val
Police Salaries
Includes Union Local Pol (no interaction)
pct_change_police_salaries vs pct_change_hpi + union_localpol pct_change_hpi -0.086 0.155 0.579
pct_change_police_salaries vs pct_change_hpi + union_localpol union_localpol -0.083 0.113 0.465
pct_change_police_salaries vs pct_change_hpi + union_localpol pct_change_hh_income 0.184 0.090 0.043
pct_change_police_salaries vs pct_change_hpi + union_localpol pct_change_crime -0.020 0.031 0.527
Includes Union Local Pol (interaction w/ HPI)
pct_change_police_salaries vs pct_change_hpi*union_localpol pct_change_hpi 0.253 0.265 0.340
pct_change_police_salaries vs pct_change_hpi*union_localpol union_localpol 0.127 0.204 0.534
pct_change_police_salaries vs pct_change_hpi*union_localpol pct_change_hh_income 0.182 0.089 0.043
pct_change_police_salaries vs pct_change_hpi*union_localpol pct_change_crime -0.027 0.030 0.372
pct_change_police_salaries vs pct_change_hpi*union_localpol pct_change_hpi:union_localpol -0.365 0.287 0.205
Includes Right to Work (interaction w/ HPI(
pct_change_police_salaries vs pct_change_hpi*right_to_work pct_change_hpi NA NA NA
pct_change_police_salaries vs pct_change_hpi*right_to_work right_to_workYes 0.049 0.077 0.530
pct_change_police_salaries vs pct_change_hpi*right_to_work pct_change_hh_income 0.118 0.121 0.335
pct_change_police_salaries vs pct_change_hpi*right_to_work pct_change_crime 0.002 0.031 0.936
pct_change_police_salaries vs pct_change_hpi*right_to_work pct_change_hpi:right_to_workYes 0.236 0.246 0.341
Police Employment per Capita
Includes Union Local Pol (no interaction)
pct_change_police_employment vs pct_change_hpi + union_localpol pct_change_hpi -0.033 0.080 0.682
pct_change_police_employment vs pct_change_hpi + union_localpol union_localpol -0.323 0.185 0.082
pct_change_police_employment vs pct_change_hpi + union_localpol pct_change_hh_income 0.206 0.104 0.049
pct_change_police_employment vs pct_change_hpi + union_localpol pct_change_crime 0.173 0.063 0.007
Includes Union Local Pol (interaction w/ HPI)
pct_change_police_employment vs pct_change_hpi*union_localpol pct_change_hpi -0.208 0.265 0.434
pct_change_police_employment vs pct_change_hpi*union_localpol union_localpol -0.431 0.251 0.088
pct_change_police_employment vs pct_change_hpi*union_localpol pct_change_hh_income 0.207 0.104 0.048
pct_change_police_employment vs pct_change_hpi*union_localpol pct_change_crime 0.177 0.062 0.005
pct_change_police_employment vs pct_change_hpi*union_localpol pct_change_hpi:union_localpol 0.188 0.269 0.487
Includes Right to Work (interaction w/ HPI)
pct_change_police_employment vs pct_change_hpi*right_to_work pct_change_hpi NA NA NA
pct_change_police_employment vs pct_change_hpi*right_to_work right_to_workYes 0.117 0.100 0.247
pct_change_police_employment vs pct_change_hpi*right_to_work pct_change_hh_income 0.350 0.172 0.045
pct_change_police_employment vs pct_change_hpi*right_to_work pct_change_crime 0.148 0.058 0.012
pct_change_police_employment vs pct_change_hpi*right_to_work pct_change_hpi:right_to_workYes -0.266 0.320 0.409