California Regressions

OLS

## 
## ========================================================================================
##                                             Dependent variable:                         
##                     --------------------------------------------------------------------
##                        pay_police      empl_police        pay_fire         empl_fire    
##                           (1)              (2)               (3)              (4)       
## ----------------------------------------------------------------------------------------
## city_hpi_norm            0.940            0.002            -7.250            -0.001     
##                         (1.950)          (0.002)           (6.630)          (0.002)     
##                                                                                         
## ----------------------------------------------------------------------------------------
## Year FE                    X                X                 X                X        
## City FE                    X                X                 X                X        
## Observations              789              789               390              390       
## R2                       0.942            0.999             0.885            0.996      
## Adjusted R2              0.926            0.998             0.848            0.994      
## Residual Std. Error 6.820 (df = 614) 0.022 (df = 614) 12.600 (df = 295) 0.015 (df = 295)
## ========================================================================================
## Note:                                                        *p<0.1; **p<0.05; ***p<0.01
## 
## =================================================================================================
##                                                      Dependent variable:                         
##                              --------------------------------------------------------------------
##                                 pay_police      empl_police        pay_fire         empl_fire    
##                                    (1)              (2)               (3)              (4)       
## -------------------------------------------------------------------------------------------------
## city_hpi_norm                     8.350            -0.036           17.800           -0.205**    
##                                  (28.400)         (0.096)          (80.300)          (0.094)     
##                                                                                                  
## city_lpop_2012                                                                                   
##                                  (0.000)          (0.000)           (0.000)          (0.000)     
##                                                                                                  
## city_hpi_norm:city_lpop_2012      -1.530           0.008            -5.040           0.041**     
##                                  (5.860)          (0.020)          (16.500)          (0.019)     
##                                                                                                  
## -------------------------------------------------------------------------------------------------
## Year FE                             X                X                 X                X        
## City FE                             X                X                 X                X        
## Observations                       789              789               390              390       
## R2                                0.942            0.999             0.885            0.996      
## Adjusted R2                       0.925            0.998             0.848            0.994      
## Residual Std. Error          6.820 (df = 613) 0.022 (df = 613) 12.700 (df = 294) 0.015 (df = 294)
## =================================================================================================
## Note:                                                                 *p<0.1; **p<0.05; ***p<0.01
## 
## =================================================================================================
##                                                      Dependent variable:                         
##                              --------------------------------------------------------------------
##                                 pay_police      empl_police        pay_fire         empl_fire    
##                                    (1)              (2)               (3)              (4)       
## -------------------------------------------------------------------------------------------------
## city_hpi_norm                    -43.800          0.211**           -94.100           0.082      
##                                  (91.300)         (0.098)          (209.000)         (0.123)     
##                                                                                                  
## city_linc_2012                                                                                   
##                                  (0.000)          (0.000)           (0.000)          (0.000)     
##                                                                                                  
## city_hpi_norm:city_linc_2012      9.260           -0.043**          18.000            -0.017     
##                                  (18.900)         (0.020)          (42.400)          (0.025)     
##                                                                                                  
## -------------------------------------------------------------------------------------------------
## Year FE                             X                X                 X                X        
## City FE                             X                X                 X                X        
## Observations                       789              789               390              390       
## R2                                0.942            0.999             0.885            0.996      
## Adjusted R2                       0.926            0.998             0.848            0.994      
## Residual Std. Error          6.820 (df = 613) 0.022 (df = 613) 12.700 (df = 294) 0.015 (df = 294)
## =================================================================================================
## Note:                                                                 *p<0.1; **p<0.05; ***p<0.01

2SLS: Instrumenting city_hpi_norm ~ county_loo_hpi_norm + county_loo_hpi_norm:city_lpop_2012 + county_loo_hpi_norm:city_linc_2012

With City FE

First Stage

## 
## ==============================================
##                                     Model 1   
## ----------------------------------------------
## county_loo_hpi_norm                   9.11 ***
##                                      (1.24)   
## city_lpop_2012                                
##                                               
## city_linc_2012                                
##                                               
## county_loo_hpi_norm:city_lpop_2012    0.59 ***
##                                      (0.06)   
## county_loo_hpi_norm:city_linc_2012   -2.34 ***
##                                      (0.23)   
## ----------------------------------------------
## R^2                                   0.78    
## Adj. R^2                              0.72    
## Num. obs.                           798       
## F statistic (Full model)             12.28    
## F (full model): p-value               0.00    
## ==============================================
## *** p < 0.001; ** p < 0.01; * p < 0.05

Second Stage

## 
## =========================================================================================
##                                              Dependent variable:                         
##                      --------------------------------------------------------------------
##                         pay_police      empl_police        pay_fire         empl_fire    
##                            (1)              (2)               (3)              (4)       
## -----------------------------------------------------------------------------------------
## city_lpop_2012                                                                           
##                                                                                          
##                                                                                          
## city_linc_2012                                                                           
##                                                                                          
##                                                                                          
## `city_hpi_norm(fit)`      1.810            0.011            -5.790            0.004      
##                          (3.120)          (0.010)           (6.190)          (0.008)     
##                                                                                          
## -----------------------------------------------------------------------------------------
## Year FE                     X                X                 X                X        
## City FE                     X                X                 X                X        
## Observations               789              789               390              390       
## R2                        0.942            0.999             0.885            0.996      
## Adjusted R2               0.926            0.998             0.848            0.994      
## Residual Std. Error  6.820 (df = 614) 0.022 (df = 614) 12.600 (df = 295) 0.015 (df = 295)
## =========================================================================================
## Note:                                                         *p<0.1; **p<0.05; ***p<0.01

National Regressions

OLS

## 
## ===========================================================================================
##                                               Dependent variable:                          
##                     -----------------------------------------------------------------------
##                        pay_police        empl_police        pay_fire          empl_fire    
##                            (1)               (2)               (3)               (4)       
## -------------------------------------------------------------------------------------------
## city_hpi_norm             1.730             0.053           3.670***           0.054*      
##                          (1.330)           (0.037)           (1.310)           (0.028)     
##                                                                                            
## -------------------------------------------------------------------------------------------
## Year FE                     X                 X                 X                 X        
## City FE                     X                 X                 X                 X        
## Observations              3,606             3,606             3,578             3,578      
## R2                        0.866             0.999             0.897             0.998      
## Adjusted R2               0.843             0.999             0.880             0.998      
## Residual Std. Error 8.550 (df = 3075) 0.268 (df = 3075) 9.000 (df = 3051) 0.113 (df = 3051)
## ===========================================================================================
## Note:                                                           *p<0.1; **p<0.05; ***p<0.01
## 
## ====================================================================================================
##                                                        Dependent variable:                          
##                              -----------------------------------------------------------------------
##                                 pay_police        empl_police        pay_fire          empl_fire    
##                                     (1)               (2)               (3)               (4)       
## ----------------------------------------------------------------------------------------------------
## city_hpi_norm                     16.400            -0.537*           11.700           -0.870**     
##                                  (13.400)           (0.283)          (12.600)           (0.414)     
##                                                                                                     
## city_lpop_2012                                                                                      
##                                   (0.000)           (0.000)           (0.000)           (0.000)     
##                                                                                                     
## city_hpi_norm:city_lpop_2012      -2.710            0.109*            -1.480            0.171**     
##                                   (2.640)           (0.057)           (2.480)           (0.078)     
##                                                                                                     
## ----------------------------------------------------------------------------------------------------
## Year FE                              X                 X                 X                 X        
## City FE                              X                 X                 X                 X        
## Observations                       3,606             3,606             3,578             3,578      
## R2                                 0.867             0.999             0.898             0.999      
## Adjusted R2                        0.844             0.999             0.880             0.998      
## Residual Std. Error          8.510 (df = 3074) 0.266 (df = 3074) 8.990 (df = 3050) 0.100 (df = 3050)
## ====================================================================================================
## Note:                                                                    *p<0.1; **p<0.05; ***p<0.01
## 
## ====================================================================================================
##                                                        Dependent variable:                          
##                              -----------------------------------------------------------------------
##                                 pay_police        empl_police        pay_fire          empl_fire    
##                                     (1)               (2)               (3)               (4)       
## ----------------------------------------------------------------------------------------------------
## city_hpi_norm                     45.600            -0.038           -64.000**          -0.049      
##                                  (66.000)           (0.212)          (30.300)           (0.145)     
##                                                                                                     
## city_linc_2012                                                                                      
##                                   (0.000)           (0.000)           (0.000)           (0.000)     
##                                                                                                     
## city_hpi_norm:city_linc_2012      -9.220             0.019           14.200**            0.022      
##                                  (13.900)           (0.040)           (6.420)           (0.032)     
##                                                                                                     
## ----------------------------------------------------------------------------------------------------
## Year FE                              X                 X                 X                 X        
## City FE                              X                 X                 X                 X        
## Observations                       3,606             3,606             3,578             3,578      
## R2                                 0.866             0.999             0.898             0.998      
## Adjusted R2                        0.843             0.999             0.881             0.998      
## Residual Std. Error          8.530 (df = 3074) 0.268 (df = 3074) 8.960 (df = 3050) 0.113 (df = 3050)
## ====================================================================================================
## Note:                                                                    *p<0.1; **p<0.05; ***p<0.01

2SLS: Instrumenting city_hpi_norm ~ county_loo_hpi_norm + county_loo_hpi_norm:city_lpop_2012 + county_loo_hpi_norm:city_linc_2012

With City FE

First Stage

## 
## ===============================================
##                                     Model 1    
## -----------------------------------------------
## county_loo_hpi_norm                   -2.97 ***
##                                       (0.42)   
## city_lpop_2012                                 
##                                                
## city_linc_2012                                 
##                                                
## county_loo_hpi_norm:city_lpop_2012     0.10 ***
##                                       (0.02)   
## county_loo_hpi_norm:city_linc_2012     0.67 ***
##                                       (0.09)   
## -----------------------------------------------
## R^2                                    0.85    
## Adj. R^2                               0.83    
## Num. obs.                           3485       
## F statistic (Full model)              32.98    
## F (full model): p-value                0.00    
## ===============================================
## *** p < 0.001; ** p < 0.01; * p < 0.05

Second Stage

## 
## ============================================================================================
##                                                Dependent variable:                          
##                      -----------------------------------------------------------------------
##                         pay_police        empl_police        pay_fire          empl_fire    
##                             (1)               (2)               (3)               (4)       
## --------------------------------------------------------------------------------------------
## city_lpop_2012                                                                              
##                                                                                             
##                                                                                             
## city_linc_2012                                                                              
##                                                                                             
##                                                                                             
## `city_hpi_norm(fit)`     4.470***            0.008           7.960***          0.047***     
##                           (0.920)           (0.017)           (0.986)           (0.007)     
##                                                                                             
## --------------------------------------------------------------------------------------------
## year FE                      X                 X                 X                 X        
## City FE                      X                 X                 X                 X        
## Observations               3,473             3,473             3,445             3,445      
## R2                         0.873             0.999             0.901             0.998      
## Adjusted R2                0.851             0.998             0.883             0.998      
## Residual Std. Error  8.240 (df = 2962) 0.151 (df = 2962) 8.790 (df = 2938) 0.063 (df = 2938)
## ============================================================================================
## Note:                                                            *p<0.1; **p<0.05; ***p<0.01