Import Dataset

cf_data_clean_new <- read.csv("cf_data_clean_new.csv")

Codebook

Unit of analysis: County level
Variable transformation: Z-score and Centered variables at their means

  • CT_A: Total contribution per $1,000 assets
  • DAF_A: Total DAFs per $1,000 assets
  • median_1000: Median Household income
  • sk_index: Social capital index
  • bachelor: % bachelor’s degree holders
  • capital_z_C: Centered capital index (median income, social capital, education)
  • capital_z_C^2: A squared term of centered capital index
  • Gini: Gini index
  • GiniC: Centered Gini index
  • GiniC^2: A squared term of centered Gini index
  • all_AT: Total assets
  • all_AT_C: Centered total assets
  • age_avg: Averaged organizational age
  • age_avgC: Centered averaged organizational age
  • Urbanity: Urbanity (1-9 : urban-rural)
  • UrbanityC: Centered urbanity
  • pop_100000: Total population (per 100,000)
  • pop_100000C: Centered total population (per 100,000)

Negative Binomial Regression Models

Models 1-2: Baseline models with individual variables

summary(c_CT_m <- glm.nb(CT_A ~ median_1000 + sk_index + bachelor + Gini + all_AT +
                         age_avg + Urbanity + pop_100000, data = cf_data_clean_new))
## 
## Call:
## glm.nb(formula = CT_A ~ median_1000 + sk_index + bachelor + Gini + 
##     all_AT + age_avg + Urbanity + pop_100000, data = cf_data_clean_new, 
##     init.theta = 1.570558108, link = log)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -3.841  -0.874  -0.391   0.144  18.435  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  3.17e+00   3.40e-01    9.32  < 2e-16 ***
## median_1000  1.03e-02   2.49e-03    4.14  3.4e-05 ***
## sk_index     6.33e-02   2.37e-02    2.68  0.00747 ** 
## bachelor     4.56e-04   3.00e-03    0.15  0.87913    
## Gini         4.44e-02   6.85e-03    6.48  9.0e-11 ***
## all_AT      -4.42e-10   1.30e-10   -3.38  0.00071 ***
## age_avg     -1.76e-02   1.35e-03  -13.07  < 2e-16 ***
## Urbanity    -3.42e-02   8.77e-03   -3.90  9.4e-05 ***
## pop_100000   8.80e-03   5.85e-03    1.50  0.13244    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(1.57) family taken to be 1)
## 
##     Null deviance: 2776.1  on 2176  degrees of freedom
## Residual deviance: 2392.8  on 2168  degrees of freedom
##   (92 observations deleted due to missingness)
## AIC: 25733
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  1.5706 
##           Std. Err.:  0.0441 
## 
##  2 x log-likelihood:  -25713.0730
summary(c_DAF_m <- glm.nb(DAF_A ~ median_1000 + sk_index + bachelor + Gini + all_AT + age_avg +
               Urbanity + pop_100000, data = cf_data_clean_new))
## 
## Call:
## glm.nb(formula = DAF_A ~ median_1000 + sk_index + bachelor + 
##     Gini + all_AT + age_avg + Urbanity + pop_100000, data = cf_data_clean_new, 
##     init.theta = 0.8020071701, link = log)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -3.294  -0.749  -0.148   0.302   8.662  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  4.39e+00   4.74e-01    9.26  < 2e-16 ***
## median_1000  5.76e-03   3.47e-03    1.66  0.09721 .  
## sk_index    -2.51e-01   3.30e-02   -7.63  2.4e-14 ***
## bachelor     1.52e-02   4.18e-03    3.65  0.00026 ***
## Gini         2.51e-02   9.54e-03    2.63  0.00866 ** 
## all_AT      -1.20e-10   1.81e-10   -0.66  0.50976    
## age_avg     -8.97e-03   1.88e-03   -4.78  1.7e-06 ***
## Urbanity    -2.68e-02   1.22e-02   -2.19  0.02837 *  
## pop_100000   3.37e-04   8.15e-03    0.04  0.96708    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(0.802) family taken to be 1)
## 
##     Null deviance: 2950.0  on 2176  degrees of freedom
## Residual deviance: 2633.4  on 2168  degrees of freedom
##   (92 observations deleted due to missingness)
## AIC: 29110
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  0.8020 
##           Std. Err.:  0.0228 
## 
##  2 x log-likelihood:  -29089.5480

Models 3-4: Baseline models with capital index

summary(c_CT_Z_C <- glm.nb(CT_A ~ capital_z_C + GiniC + all_AT_C + age_avgC +
               UrbanityC + pop_100000C, data = cf_data_clean_new))
## 
## Call:
## glm.nb(formula = CT_A ~ capital_z_C + GiniC + all_AT_C + age_avgC + 
##     UrbanityC + pop_100000C, data = cf_data_clean_new, init.theta = 1.567662604, 
##     link = log)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -3.830  -0.870  -0.397   0.146  18.419  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  4.95e+00   1.72e-02  287.27  < 2e-16 ***
## capital_z_C  6.39e-02   7.90e-03    8.09  6.0e-16 ***
## GiniC        3.66e-02   5.46e-03    6.71  2.0e-11 ***
## all_AT_C    -4.25e-10   1.30e-10   -3.26   0.0011 ** 
## age_avgC    -1.77e-02   1.35e-03  -13.11  < 2e-16 ***
## UrbanityC   -3.52e-02   7.18e-03   -4.90  9.6e-07 ***
## pop_100000C  8.59e-03   5.76e-03    1.49   0.1358    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(1.57) family taken to be 1)
## 
##     Null deviance: 2771.1  on 2176  degrees of freedom
## Residual deviance: 2393.1  on 2170  degrees of freedom
##   (92 observations deleted due to missingness)
## AIC: 25734
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  1.5677 
##           Std. Err.:  0.0441 
## 
##  2 x log-likelihood:  -25717.7690
summary(c_DAF_Z_C <- glm.nb(DAF_A ~ capital_z_C + GiniC + all_AT_C + age_avgC +
               UrbanityC + pop_100000C, data = cf_data_clean_new,
               control = glm.control(maxit = 1000)))
## 
## Call:
## glm.nb(formula = DAF_A ~ capital_z_C + GiniC + all_AT_C + age_avgC + 
##     UrbanityC + pop_100000C, data = cf_data_clean_new, control = glm.control(maxit = 1000), 
##     init.theta = 0.7811732932, link = log)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -3.404  -0.797  -0.150   0.286  10.031  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  5.70e+00   2.43e-02  234.52  < 2e-16 ***
## capital_z_C  5.88e-03   1.11e-02    0.53  0.59745    
## GiniC        5.51e-02   7.71e-03    7.15  8.5e-13 ***
## all_AT_C    -1.98e-10   1.84e-10   -1.08  0.28159    
## age_avgC    -9.57e-03   1.90e-03   -5.04  4.7e-07 ***
## UrbanityC   -7.76e-02   1.01e-02   -7.66  1.9e-14 ***
## pop_100000C  2.76e-02   8.13e-03    3.40  0.00068 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(0.781) family taken to be 1)
## 
##     Null deviance: 2879.5  on 2176  degrees of freedom
## Residual deviance: 2636.0  on 2170  degrees of freedom
##   (92 observations deleted due to missingness)
## AIC: 29171
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  0.7812 
##           Std. Err.:  0.0221 
## 
##  2 x log-likelihood:  -29155.3220

Models 5-6: Capital index models with squared terms

summary(c_CT_Z_C_sq <- glm.nb(CT_A ~ capital_z_C + GiniC + I(capital_z_C^2) + I(GiniC^2) +
                                all_AT_C + age_avgC + UrbanityC + pop_100000C, 
                              data = cf_data_clean_new))
## 
## Call:
## glm.nb(formula = CT_A ~ capital_z_C + GiniC + I(capital_z_C^2) + 
##     I(GiniC^2) + all_AT_C + age_avgC + UrbanityC + pop_100000C, 
##     data = cf_data_clean_new, init.theta = 1.576651791, link = log)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -3.890  -0.876  -0.404   0.150  18.514  
## 
## Coefficients:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept)       4.89e+00   2.20e-02  222.48  < 2e-16 ***
## capital_z_C       5.32e-02   8.60e-03    6.19  5.9e-10 ***
## GiniC             2.74e-02   5.84e-03    4.70  2.6e-06 ***
## I(capital_z_C^2)  6.41e-03   1.89e-03    3.39  0.00069 ***
## I(GiniC^2)        2.01e-03   8.87e-04    2.27  0.02304 *  
## all_AT_C         -4.46e-10   1.30e-10   -3.42  0.00062 ***
## age_avgC         -1.69e-02   1.35e-03  -12.54  < 2e-16 ***
## UrbanityC        -3.38e-02   7.19e-03   -4.70  2.6e-06 ***
## pop_100000C       9.33e-03   5.75e-03    1.62  0.10487    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(1.58) family taken to be 1)
## 
##     Null deviance: 2786.7  on 2176  degrees of freedom
## Residual deviance: 2391.9  on 2168  degrees of freedom
##   (92 observations deleted due to missingness)
## AIC: 25723
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  1.5767 
##           Std. Err.:  0.0443 
## 
##  2 x log-likelihood:  -25703.1300
summary(c_DAF_Z_C_sq <- glm.nb(DAF_A ~ capital_z_C + GiniC + I(capital_z_C^2) + I(GiniC^2) +
                                all_AT_C + age_avgC + UrbanityC + pop_100000C, 
                              data = cf_data_clean_new))
## 
## Call:
## glm.nb(formula = DAF_A ~ capital_z_C + GiniC + I(capital_z_C^2) + 
##     I(GiniC^2) + all_AT_C + age_avgC + UrbanityC + pop_100000C, 
##     data = cf_data_clean_new, init.theta = 0.789131465, link = log)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -3.379  -0.789  -0.144   0.279   9.500  
## 
## Coefficients:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept)       5.59e+00   3.10e-02  180.59  < 2e-16 ***
## capital_z_C      -2.12e-02   1.21e-02   -1.75   0.0800 .  
## GiniC             4.13e-02   8.22e-03    5.03  5.0e-07 ***
## I(capital_z_C^2)  1.27e-02   2.66e-03    4.79  1.7e-06 ***
## I(GiniC^2)        2.97e-03   1.25e-03    2.38   0.0174 *  
## all_AT_C         -2.30e-10   1.83e-10   -1.26   0.2082    
## age_avgC         -8.60e-03   1.90e-03   -4.54  5.8e-06 ***
## UrbanityC        -7.62e-02   1.01e-02   -7.53  5.0e-14 ***
## pop_100000C       2.48e-02   8.10e-03    3.06   0.0022 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Negative Binomial(0.789) family taken to be 1)
## 
##     Null deviance: 2906.5  on 2176  degrees of freedom
## Residual deviance: 2635.0  on 2168  degrees of freedom
##   (92 observations deleted due to missingness)
## AIC: 29150
## 
## Number of Fisher Scoring iterations: 1
## 
## 
##               Theta:  0.7891 
##           Std. Err.:  0.0223 
## 
##  2 x log-likelihood:  -29129.9110

Adjusted standard errors

or1a <- exp(c_CT_m$coefficients)
var.diag1 = diag(sandwich::vcovCL(c_CT_m, cluster = ~ state, type = "HC1"))
or.se1a = sqrt(or1a^2 * var.diag1)

or1d <- exp(c_DAF_m$coefficients)
var.diag1d = diag(sandwich::vcovCL(c_DAF_m, cluster = ~ state, type = "HC1"))
or.se1d = sqrt(or1d^2 * var.diag1d)

or3a <- exp(c_CT_Z_C$coefficients)
var.diag3a = diag(sandwich::vcovCL(c_CT_Z_C, cluster = ~ state, type = "HC1"))
or.se3a = sqrt(or3a^2 * var.diag3a)

or3d <- exp(c_DAF_Z_C$coefficients)
var.diag3d = diag(sandwich::vcovCL(c_DAF_Z_C, cluster = ~ state, type = "HC1"))
or.se3d = sqrt(or3d^2 * var.diag3d)

or6a <- exp(c_CT_Z_C_sq$coefficients)
var.diag6a = diag(sandwich::vcovCL(c_CT_Z_C_sq, cluster = ~ state, type = "HC1"))
or.se6a = sqrt(or6a^2 * var.diag6a)

or6d <- exp(c_DAF_Z_C_sq$coefficients)
var.diag6d = diag(sandwich::vcovCL(c_DAF_Z_C_sq, cluster = ~ state, type = "HC1"))
or.se6d = sqrt(or6d^2 * var.diag6d)

Regression Table

Negative Binomial Regression Results for Community Philanthropy
Dependent variable:
CT_A DAF_A CT_A DAF_A CT_A DAF_A
Contributions (baseline) DAF (baseline) Contributions (index) DAFs (index) Contributions (squared) DAFs (squared)
(1) (2) (3) (4) (5) (6)
median_1000 1.01*** 1.01+
(0.01) (0.01)
sk_index 1.07** 0.78***
(0.16) (0.06)
bachelor 1.00 1.02***
(0.01) (0.01)
Gini 1.05*** 1.03**
(0.02) (0.02)
all_AT 1.00*** 1.00
(0.00) (0.00)
age_avg 0.98*** 0.99***
(0.01) (0.005)
Urbanity 0.97*** 0.97*
(0.05) (0.02)
pop_100000 1.01 1.00
(0.01) (0.01)
capital_z_C 1.07*** 1.01 1.05*** 0.98+
(0.03) (0.05) (0.03) (0.04)
GiniC 1.04*** 1.06*** 1.03*** 1.04***
(0.02) (0.03) (0.02) (0.02)
I(capital_z_C2) 1.01*** 1.01***
(0.004) (0.003)
I(GiniC2) 1.00* 1.00*
(0.002) (0.002)
all_AT_C 1.00** 1.00 1.00*** 1.00
(0.00) (0.00) (0.00) (0.00)
age_avgC 0.98*** 0.99*** 0.98*** 0.99***
(0.01) (0.01) (0.01) (0.005)
UrbanityC 0.97*** 0.93*** 0.97*** 0.93***
(0.03) (0.02) (0.03) (0.02)
pop_100000C 1.01 1.03*** 1.01 1.03**
(0.01) (0.01) (0.01) (0.01)
Constant 23.80*** 80.60*** 142.00*** 300.00*** 133.00*** 268.00***
(29.60) (117.00) (9.50) (23.70) (9.35) (21.90)
Observations 2,177 2,177 2,177 2,177 2,177 2,177
Log Likelihood -12,858.00 -14,546.00 -12,860.00 -14,579.00 -12,853.00 -14,566.00
theta 1.57*** (0.04) 0.80*** (0.02) 1.57*** (0.04) 0.78*** (0.02) 1.58*** (0.04) 0.79*** (0.02)
Akaike Inf. Crit. 25,733.00 29,110.00 25,734.00 29,171.00 25,723.00 29,150.00
Note: (+ p<0.1; * p<0.05; ** p<0.01; *** p<0.001); Exponentiated coefficients (Incidence Rate Ratio) reported; Cluster-Robust standard errors in parentheses