Timing: - CARES Act funds should have been received between July - November 2020 [https://dof.ca.gov/budget/covid-19-information/coronavirus-relief-fund-allocations-for-cities-and-counties/]

Distribution of Pct Change in Outlays

Seems like there are some pretty far right outliers

Regressions w/ Outlays % Change 2020-2021 as outcome

X = Log Allocation, < 200% Change

## 
## Call:
## lm(formula = outlays_chng_20_21 ~ log_allocation, data = combined %>% 
##     filter(outlays_chng_20_21 < 2 & outlays_chng_20_21 > -2))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.84816 -0.07705 -0.01547  0.04885  1.66170 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)
## (Intercept)    -0.016336   0.030186  -0.541    0.588
## log_allocation  0.003566   0.002265   1.574    0.116
## 
## Residual standard error: 0.2178 on 1946 degrees of freedom
## Multiple R-squared:  0.001272,   Adjusted R-squared:  0.0007587 
## F-statistic: 2.478 on 1 and 1946 DF,  p-value: 0.1156

X = Log Allocation per Pop, < 200% Change

## 
## Call:
## lm(formula = outlays_chng_20_21 ~ log_allocation_per_pop, data = combined %>% 
##     filter(outlays_chng_20_21 < 2 & outlays_chng_20_21 > -2))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.84928 -0.07719 -0.01993  0.05212  1.66546 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            0.029923   0.005429   5.512 4.02e-08 ***
## log_allocation_per_pop 0.286543   1.036171   0.277    0.782    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2179 on 1946 degrees of freedom
## Multiple R-squared:  3.93e-05,   Adjusted R-squared:  -0.0004746 
## F-statistic: 0.07647 on 1 and 1946 DF,  p-value: 0.7822

X = Log Allocation per Pop, < 500% Change

## 
## Call:
## lm(formula = outlays_chng_20_21 ~ log_allocation_per_pop, data = combined %>% 
##     filter(outlays_chng_20_21 < 5 & outlays_chng_20_21 > -2))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.8538 -0.0807 -0.0235  0.0489  3.6965 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            0.032682   0.006022   5.427 6.45e-08 ***
## log_allocation_per_pop 0.823921   1.148588   0.717    0.473    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2418 on 1949 degrees of freedom
## Multiple R-squared:  0.0002639,  Adjusted R-squared:  -0.000249 
## F-statistic: 0.5146 on 1 and 1949 DF,  p-value: 0.4733

Regressions w/ Outlays % Change 2020-2022 as outcome

X = Log Allocation, < 200% Change

## 
## Call:
## lm(formula = outlays_chng_20_22 ~ log_allocation, data = combined %>% 
##     filter(outlays_chng_20_22 < 2 & outlays_chng_20_22 > -2))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.94134 -0.12439 -0.03571  0.07766  1.84838 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)
## (Intercept)    0.038844   0.038907   0.998    0.318
## log_allocation 0.003576   0.002918   1.225    0.221
## 
## Residual standard error: 0.279 on 1933 degrees of freedom
## Multiple R-squared:  0.000776,   Adjusted R-squared:  0.0002591 
## F-statistic: 1.501 on 1 and 1933 DF,  p-value: 0.2206

X = Log Allocation per Pop, < 200% Change

## 
## Call:
## lm(formula = outlays_chng_20_22 ~ log_allocation_per_pop, data = combined %>% 
##     filter(outlays_chng_20_22 < 2 & outlays_chng_20_22 > -2))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.93959 -0.12755 -0.03604  0.08071  1.85512 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            0.084334   0.006974  12.093   <2e-16 ***
## log_allocation_per_pop 0.708332   1.330865   0.532    0.595    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2791 on 1933 degrees of freedom
## Multiple R-squared:  0.0001465,  Adjusted R-squared:  -0.0003707 
## F-statistic: 0.2833 on 1 and 1933 DF,  p-value: 0.5946

X = Log Allocation per Pop, < 500% Change

## 
## Call:
## lm(formula = outlays_chng_20_22 ~ log_allocation_per_pop, data = combined %>% 
##     filter(outlays_chng_20_22 < 5 & outlays_chng_20_22 > -2))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.9620 -0.1458 -0.0564  0.0604  3.6834 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            0.106715   0.009466  11.274   <2e-16 ***
## log_allocation_per_pop 0.806718   1.810865   0.445    0.656    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.38 on 1948 degrees of freedom
## Multiple R-squared:  0.0001019,  Adjusted R-squared:  -0.0004114 
## F-statistic: 0.1985 on 1 and 1948 DF,  p-value: 0.656

Regressions w/ Police Exp % Change 2020-2022 as outcome

X = Log Allocation, < 200% Change

## 
## Call:
## lm(formula = police_exp_chng_20_22 ~ log_allocation, data = combined %>% 
##     filter(police_exp_chng_20_22 < 2 & police_exp_chng_20_22 > 
##         -2))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.05427 -0.08742 -0.02988  0.03890  1.78111 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)   
## (Intercept)     0.1020319  0.0351781   2.900  0.00377 **
## log_allocation -0.0007556  0.0026409  -0.286  0.77482   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.254 on 1941 degrees of freedom
## Multiple R-squared:  4.217e-05,  Adjusted R-squared:  -0.000473 
## F-statistic: 0.08186 on 1 and 1941 DF,  p-value: 0.7748

X = Log Allocation per Pop, < 200% Change

## 
## Call:
## lm(formula = police_exp_chng_20_22 ~ log_allocation_per_pop, 
##     data = combined %>% filter(police_exp_chng_20_22 < 2 & police_exp_chng_20_22 > 
##         -2))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.05498 -0.08688 -0.03028  0.03956  1.78062 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             0.09386    0.00634  14.803   <2e-16 ***
## log_allocation_per_pop -0.79784    1.20123  -0.664    0.507    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.254 on 1941 degrees of freedom
## Multiple R-squared:  0.0002272,  Adjusted R-squared:  -0.0002879 
## F-statistic: 0.4411 on 1 and 1941 DF,  p-value: 0.5067

X = Log Allocation per Pop, < 500% Change

## 
## Call:
## lm(formula = police_exp_chng_20_22 ~ log_allocation_per_pop, 
##     data = combined %>% filter(police_exp_chng_20_22 < 5 & police_exp_chng_20_22 > 
##         -2))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.06034 -0.09243 -0.03515  0.03629  2.77249 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             0.099702   0.006943  14.361   <2e-16 ***
## log_allocation_per_pop -1.099615   1.316623  -0.835    0.404    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2784 on 1945 degrees of freedom
## Multiple R-squared:  0.0003585,  Adjusted R-squared:  -0.0001555 
## F-statistic: 0.6975 on 1 and 1945 DF,  p-value: 0.4037