All: Year FE and City Clustered SE

## 
## ====================================================================
##                                Model 1  Model 2   Model 3  Model 4  
## --------------------------------------------------------------------
## county_loo_hpi                  -2.54     -7.34     0.86      1.81  
##                                 (1.52)    (4.84)   (1.19)    (4.21) 
## city_lpop_2012                 -38.61              89.38            
##                                (86.80)            (74.21)           
## county_loo_hpi:city_lpop_2012    0.27               0.01            
##                                 (0.31)             (0.25)           
## city_linc_2012                            16.56             633.62 *
##                                         (319.17)           (278.40) 
## county_loo_hpi:city_linc_2012              1.25              -0.24  
##                                           (1.00)             (0.88) 
## --------------------------------------------------------------------
## Num. obs.                      615       615      615       615     
## R^2 (full model)                 0.69      0.72     0.46      0.51  
## R^2 (proj model)                 0.08      0.14     0.43      0.48  
## Adj. R^2 (full model)            0.67      0.70     0.45      0.51  
## Adj. R^2 (proj model)            0.01      0.08     0.42      0.48  
## F statistic (full model)        30.97     34.35    57.83     70.74  
## F (full model): p-value          0.00      0.00     0.00      0.00  
## F statistic (proj model)         6.14      6.11    20.68     34.05  
## F (proj model): p-value          0.00      0.00     0.00      0.00  
## Num. groups: county             34        34                        
## Num. groups: Year                7         7        7         7     
## ====================================================================
## *** p < 0.001; ** p < 0.01; * p < 0.05
## 
## ========================================================================
##                                               Model 1       Model 2     
## ------------------------------------------------------------------------
## county_loo_hpi                                   82.45 ***     72.80 ***
##                                                 (19.40)       (17.93)   
## city_lpop_2012                                 6357.93 **    2914.85    
##                                               (2001.67)     (1822.32)   
## city_linc_2012                                 6141.63 **    3149.69    
##                                               (1959.20)     (1692.24)   
## county_loo_hpi:city_lpop_2012                   -19.65 ***    -16.14 ***
##                                                  (4.26)        (4.20)   
## county_loo_hpi:city_linc_2012                   -17.73 ***    -15.07 ***
##                                                  (4.10)        (3.73)   
## city_lpop_2012:city_linc_2012                 -1350.56 **    -598.04    
##                                                (429.73)      (388.68)   
## county_loo_hpi:city_lpop_2012:city_linc_2012      4.19 ***      3.37 ***
##                                                  (0.90)        (0.88)   
## ------------------------------------------------------------------------
## Num. obs.                                       615           615       
## R^2 (full model)                                  0.77          0.58    
## R^2 (proj model)                                  0.30          0.55    
## Adj. R^2 (full model)                             0.75          0.57    
## Adj. R^2 (proj model)                             0.24          0.54    
## F statistic (full model)                         40.72         63.51    
## F (full model): p-value                           0.00          0.00    
## F statistic (proj model)                          8.69         22.69    
## F (proj model): p-value                           0.00          0.00    
## Num. groups: county                              34                     
## Num. groups: Year                                 7             7       
## ========================================================================
## *** p < 0.001; ** p < 0.01; * p < 0.05

County FE: No, Year FE: Yes, City-Clustered SE: Yes

## 
## ====================================
##                           Model 1   
## ------------------------------------
## county_loo_hpi              0.91 ***
##                            (0.15)   
## ------------------------------------
## Num. obs.                 615       
## R^2 (full model)            0.42    
## R^2 (proj model)            0.39    
## Adj. R^2 (full model)       0.42    
## Adj. R^2 (proj model)       0.38    
## F statistic (full model)   63.75    
## F (full model): p-value     0.00    
## F statistic (proj model)   37.40    
## F (proj model): p-value     0.00    
## Num. groups: Year           7       
## ====================================
## *** p < 0.001; ** p < 0.01; * p < 0.05