guns_data <- read.csv("Guns.csv")
is_balanced <- length(unique(guns_data$state)) == nrow(guns_data)
is_balanced## [1] FALSEBased on the analysis with the “Guns” dataset, the data is not balanced. The result of is_balanced is FALSE, indicating that not all states have observations for all time periods. The time component in the data refers to the variable “year,” which represents the year in which the observations were recorded. It captures the temporal dimension of the data. The entity component in the data refers to the variable “state,” which represents the U.S. states. It captures the cross-sectional dimension of the data, with each state representing a different entity or unit of observation. Since the data is not balanced, it means that some states may have missing observations for certain years, and the panel structure is not fully complete for all states over time.
# Run OLS regression
ols_model <- lm(murder ~ afam + cauc + male + population + income + density, data = guns_data)
summary(ols_model)##
## Call:
## lm(formula = murder ~ afam + cauc + male + population + income +
## density, data = guns_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -25.513 -2.004 -0.267 1.819 34.617
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.052e+01 5.626e+00 1.870 0.06167 .
## afam 2.620e-01 1.702e-01 1.540 0.12391
## cauc -7.373e-02 8.538e-02 -0.864 0.38801
## male 9.509e-02 9.662e-02 0.984 0.32520
## population 2.217e-01 2.681e-02 8.270 3.62e-16 ***
## income -2.532e-04 8.013e-05 -3.159 0.00162 **
## density 3.585e+00 1.289e-01 27.823 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.514 on 1166 degrees of freedom
## Multiple R-squared: 0.6417, Adjusted R-squared: 0.6399
## F-statistic: 348.1 on 6 and 1166 DF, p-value: < 2.2e-16Direction and Magnitude: The direction and magnitude of the coefficients can provide insights on the relationships between the independent variables and the murder rate. However, it’s important to note that the interpretation of these coefficients should be done cautiously due to the potential presence of omitted variable bias, as discussed below. Statistical Significance: Some coefficients are statistically significant at conventional levels (p < 0.05), such as the coefficients for population and income. However, several coefficients, including the intercept and the coefficients for afam, cauc, and male, are not statistically significant. This suggests that the observed relationships between these variables and the murder rate could be due to chance. There could be omitted variable bias present in the OLS regression. Omitted variable bias occurs when relevant variables that are correlated with both the dependent variable and the independent variables are excluded from the model. In this case, the OLS regression does not account for time-invariant characteristics of the entities or time-varying characteristics affecting all entities. By including fixed effects in the model, such as entity fixed effects, time fixed effects, or a combination of both, we can potentially reduce omitted variable bias. Fixed effects models allow us to control for unobserved factors that are constant over time (entity fixed effects) or vary over time but affect all entities (time fixed effects). By including these fixed effects, we can capture the effects of such unobserved factors and obtain more accurate estimates of the relationships between the independent variables and the murder rate.
library(plm)
# Convert the data to panel data format
guns_data_panel <- pdata.frame(guns_data, index = c("state", "year"))
# Run the within estimation
fe_within_model <- plm(murder ~ afam + cauc + male + population + income + density, data = guns_data_panel, model = "within")
summary(fe_within_model)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = murder ~ afam + cauc + male + population + income +
## density, data = guns_data_panel, model = "within")
##
## Balanced Panel: n = 51, T = 23, N = 1173
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -22.852294 -0.927875 -0.075513 0.831136 28.994469
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## afam -1.6376e+00 2.9125e-01 -5.6227 2.375e-08 ***
## cauc -8.2109e-02 7.9272e-02 -1.0358 0.30052
## male 3.7789e-01 9.5895e-02 3.9406 8.632e-05 ***
## population -3.5006e-01 1.4214e-01 -2.4628 0.01394 *
## income 6.9488e-04 9.8070e-05 7.0855 2.450e-12 ***
## density -1.1675e+01 1.0764e+00 -10.8457 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 12016
## Residual Sum of Squares: 8366.3
## R-Squared: 0.30375
## Adj. R-Squared: 0.26881
## F-statistic: 81.1456 on 6 and 1116 DF, p-value: < 2.22e-16Oneway (individual) effect Within Model: The estimated coefficients are generally consistent with the previous results. The coefficients for afam, male, population, income, and density remain statistically significant. The coefficient for cauc is still not statistically significant. The inclusion of individual fixed effects controls for time-invariant characteristics of the entities.
# Run the first-difference estimation
fe_fd_model <- plm(murder ~ afam + cauc + male + population + income + density, data = guns_data_panel, model = "fd")
summary(fe_fd_model)## Oneway (individual) effect First-Difference Model
##
## Call:
## plm(formula = murder ~ afam + cauc + male + population + income +
## density, data = guns_data_panel, model = "fd")
##
## Balanced Panel: n = 51, T = 23, N = 1173
## Observations used in estimation: 1122
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -16.555777 -0.623345 0.035717 0.613360 23.030367
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) -0.30741874 0.10719139 -2.8679 0.004209 **
## afam 0.67314411 0.62555796 1.0761 0.282129
## cauc 0.21600325 0.11049828 1.9548 0.050855 .
## male -0.81135284 0.37920473 -2.1396 0.032602 *
## population -0.21607064 0.52233781 -0.4137 0.679202
## income 0.00020010 0.00014057 1.4235 0.154874
## density -1.97592715 2.06541045 -0.9567 0.338939
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 2871
## Residual Sum of Squares: 2848.1
## R-Squared: 0.007953
## Adj. R-Squared: 0.0026146
## F-statistic: 1.48978 on 6 and 1115 DF, p-value: 0.17819Oneway (individual) effect First-Difference Model: The estimated coefficients differ from the previous models. The coefficients for afam, cauc, and male have changed in magnitude and statistical significance. The coefficient for population is no longer statistically significant. The inclusion of first-differencing eliminates time-invariant unobserved factors and controls for time-varying factors affecting all entities.
# Run the fixed effect regression
fe_lm_model <- lm(murder ~ afam + cauc + male + population + income + density + factor(state), data = guns_data)
summary(fe_lm_model)##
## Call:
## lm(formula = murder ~ afam + cauc + male + population + income +
## density + factor(state), data = guns_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.8523 -0.9279 -0.0755 0.8311 28.9945
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.801e+01 6.260e+00 2.877 0.004088 **
## afam -1.638e+00 2.912e-01 -5.623 2.38e-08 ***
## cauc -8.211e-02 7.927e-02 -1.036 0.300523
## male 3.779e-01 9.590e-02 3.941 8.63e-05 ***
## population -3.501e-01 1.421e-01 -2.463 0.013936 *
## income 6.949e-04 9.807e-05 7.085 2.45e-12 ***
## density -1.167e+01 1.076e+00 -10.846 < 2e-16 ***
## factor(state)Alaska -8.442e+00 1.237e+00 -6.824 1.45e-11 ***
## factor(state)Arizona -1.129e+01 1.507e+00 -7.495 1.35e-13 ***
## factor(state)Arkansas -7.093e+00 1.126e+00 -6.300 4.28e-10 ***
## factor(state)California 3.683e+00 3.775e+00 0.976 0.329442
## factor(state)Colorado -1.714e+01 1.905e+00 -9.001 < 2e-16 ***
## factor(state)Connecticut -1.174e+01 2.267e+00 -5.177 2.68e-07 ***
## factor(state)Delaware -9.735e+00 1.264e+00 -7.703 2.91e-14 ***
## factor(state)District of Columbia 1.678e+02 8.842e+00 18.975 < 2e-16 ***
## factor(state)Florida -2.224e+00 1.920e+00 -1.158 0.246940
## factor(state)Georgia 2.371e+00 9.077e-01 2.612 0.009117 **
## factor(state)Hawaii 1.478e+01 4.362e+00 3.388 0.000728 ***
## factor(state)Idaho -2.097e+01 2.070e+00 -10.133 < 2e-16 ***
## factor(state)Illinois -3.538e+00 1.784e+00 -1.983 0.047602 *
## factor(state)Indiana -1.192e+01 1.876e+00 -6.352 3.08e-10 ***
## factor(state)Iowa -2.197e+01 2.176e+00 -10.099 < 2e-16 ***
## factor(state)Kansas -1.653e+01 1.730e+00 -9.556 < 2e-16 ***
## factor(state)Kentucky -1.224e+01 1.786e+00 -6.852 1.20e-11 ***
## factor(state)Louisiana 7.074e+00 9.632e-01 7.345 3.97e-13 ***
## factor(state)Maine -2.231e+01 2.253e+00 -9.902 < 2e-16 ***
## factor(state)Maryland 3.145e+00 9.897e-01 3.178 0.001525 **
## factor(state)Massachusetts -1.085e+01 2.512e+00 -4.320 1.70e-05 ***
## factor(state)Michigan -5.245e+00 1.679e+00 -3.124 0.001832 **
## factor(state)Minnesota -2.084e+01 2.116e+00 -9.848 < 2e-16 ***
## factor(state)Mississippi 5.518e+00 1.292e+00 4.270 2.12e-05 ***
## factor(state)Missouri -9.412e+00 1.569e+00 -5.998 2.69e-09 ***
## factor(state)Montana -1.844e+01 1.787e+00 -10.318 < 2e-16 ***
## factor(state)Nebraska -2.059e+01 1.947e+00 -10.575 < 2e-16 ***
## factor(state)Nevada -8.940e+00 1.465e+00 -6.103 1.43e-09 ***
## factor(state)New Hampshire -2.331e+01 2.369e+00 -9.836 < 2e-16 ***
## factor(state)New Jersey -4.604e-01 2.090e+00 -0.220 0.825732
## factor(state)New Mexico -8.667e+00 1.308e+00 -6.625 5.40e-11 ***
## factor(state)New York 2.673e+00 2.426e+00 1.102 0.270787
## factor(state)North Carolina -1.137e+00 9.285e-01 -1.225 0.220948
## factor(state)North Dakota -2.254e+01 1.877e+00 -12.007 < 2e-16 ***
## factor(state)Ohio -8.722e+00 2.132e+00 -4.090 4.62e-05 ***
## factor(state)Oklahoma -8.782e+00 1.159e+00 -7.579 7.29e-14 ***
## factor(state)Oregon -1.825e+01 1.961e+00 -9.303 < 2e-16 ***
## factor(state)Pennsylvania -9.230e+00 2.310e+00 -3.996 6.86e-05 ***
## factor(state)Rhode Island -9.711e+00 2.569e+00 -3.780 0.000165 ***
## factor(state)South Carolina 1.860e+00 9.751e-01 1.907 0.056774 .
## factor(state)South Dakota -2.012e+01 1.659e+00 -12.124 < 2e-16 ***
## factor(state)Tennessee -5.427e+00 1.222e+00 -4.442 9.78e-06 ***
## factor(state)Texas -9.626e-01 2.437e+00 -0.395 0.692869
## factor(state)Utah -2.071e+01 1.912e+00 -10.830 < 2e-16 ***
## factor(state)Vermont -2.279e+01 2.287e+00 -9.965 < 2e-16 ***
## factor(state)Virginia -4.694e+00 1.033e+00 -4.544 6.12e-06 ***
## factor(state)Washington -1.561e+01 1.738e+00 -8.977 < 2e-16 ***
## factor(state)West Virginia -1.640e+01 2.080e+00 -7.883 7.54e-15 ***
## factor(state)Wisconsin -1.792e+01 1.997e+00 -8.977 < 2e-16 ***
## factor(state)Wyoming -2.113e+01 2.075e+00 -10.182 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.738 on 1116 degrees of freedom
## Multiple R-squared: 0.8739, Adjusted R-squared: 0.8675
## F-statistic: 138.1 on 56 and 1116 DF, p-value: < 2.2e-16OLS Model with State Fixed Effects: The estimated coefficients are similar to the within model. Additional coefficients are included for each state (entity) in the model. The coefficients for afam, cauc, male, population, income, and density remain statistically significant. The inclusion of state fixed effects controls for time-invariant characteristics of the states.
# Run the fixed effect regression
fe_lm_model <- lm(murder ~ afam + cauc + male + population + income + density + factor(state), data = guns_data)
summary(fe_lm_model)##
## Call:
## lm(formula = murder ~ afam + cauc + male + population + income +
## density + factor(state), data = guns_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.8523 -0.9279 -0.0755 0.8311 28.9945
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.801e+01 6.260e+00 2.877 0.004088 **
## afam -1.638e+00 2.912e-01 -5.623 2.38e-08 ***
## cauc -8.211e-02 7.927e-02 -1.036 0.300523
## male 3.779e-01 9.590e-02 3.941 8.63e-05 ***
## population -3.501e-01 1.421e-01 -2.463 0.013936 *
## income 6.949e-04 9.807e-05 7.085 2.45e-12 ***
## density -1.167e+01 1.076e+00 -10.846 < 2e-16 ***
## factor(state)Alaska -8.442e+00 1.237e+00 -6.824 1.45e-11 ***
## factor(state)Arizona -1.129e+01 1.507e+00 -7.495 1.35e-13 ***
## factor(state)Arkansas -7.093e+00 1.126e+00 -6.300 4.28e-10 ***
## factor(state)California 3.683e+00 3.775e+00 0.976 0.329442
## factor(state)Colorado -1.714e+01 1.905e+00 -9.001 < 2e-16 ***
## factor(state)Connecticut -1.174e+01 2.267e+00 -5.177 2.68e-07 ***
## factor(state)Delaware -9.735e+00 1.264e+00 -7.703 2.91e-14 ***
## factor(state)District of Columbia 1.678e+02 8.842e+00 18.975 < 2e-16 ***
## factor(state)Florida -2.224e+00 1.920e+00 -1.158 0.246940
## factor(state)Georgia 2.371e+00 9.077e-01 2.612 0.009117 **
## factor(state)Hawaii 1.478e+01 4.362e+00 3.388 0.000728 ***
## factor(state)Idaho -2.097e+01 2.070e+00 -10.133 < 2e-16 ***
## factor(state)Illinois -3.538e+00 1.784e+00 -1.983 0.047602 *
## factor(state)Indiana -1.192e+01 1.876e+00 -6.352 3.08e-10 ***
## factor(state)Iowa -2.197e+01 2.176e+00 -10.099 < 2e-16 ***
## factor(state)Kansas -1.653e+01 1.730e+00 -9.556 < 2e-16 ***
## factor(state)Kentucky -1.224e+01 1.786e+00 -6.852 1.20e-11 ***
## factor(state)Louisiana 7.074e+00 9.632e-01 7.345 3.97e-13 ***
## factor(state)Maine -2.231e+01 2.253e+00 -9.902 < 2e-16 ***
## factor(state)Maryland 3.145e+00 9.897e-01 3.178 0.001525 **
## factor(state)Massachusetts -1.085e+01 2.512e+00 -4.320 1.70e-05 ***
## factor(state)Michigan -5.245e+00 1.679e+00 -3.124 0.001832 **
## factor(state)Minnesota -2.084e+01 2.116e+00 -9.848 < 2e-16 ***
## factor(state)Mississippi 5.518e+00 1.292e+00 4.270 2.12e-05 ***
## factor(state)Missouri -9.412e+00 1.569e+00 -5.998 2.69e-09 ***
## factor(state)Montana -1.844e+01 1.787e+00 -10.318 < 2e-16 ***
## factor(state)Nebraska -2.059e+01 1.947e+00 -10.575 < 2e-16 ***
## factor(state)Nevada -8.940e+00 1.465e+00 -6.103 1.43e-09 ***
## factor(state)New Hampshire -2.331e+01 2.369e+00 -9.836 < 2e-16 ***
## factor(state)New Jersey -4.604e-01 2.090e+00 -0.220 0.825732
## factor(state)New Mexico -8.667e+00 1.308e+00 -6.625 5.40e-11 ***
## factor(state)New York 2.673e+00 2.426e+00 1.102 0.270787
## factor(state)North Carolina -1.137e+00 9.285e-01 -1.225 0.220948
## factor(state)North Dakota -2.254e+01 1.877e+00 -12.007 < 2e-16 ***
## factor(state)Ohio -8.722e+00 2.132e+00 -4.090 4.62e-05 ***
## factor(state)Oklahoma -8.782e+00 1.159e+00 -7.579 7.29e-14 ***
## factor(state)Oregon -1.825e+01 1.961e+00 -9.303 < 2e-16 ***
## factor(state)Pennsylvania -9.230e+00 2.310e+00 -3.996 6.86e-05 ***
## factor(state)Rhode Island -9.711e+00 2.569e+00 -3.780 0.000165 ***
## factor(state)South Carolina 1.860e+00 9.751e-01 1.907 0.056774 .
## factor(state)South Dakota -2.012e+01 1.659e+00 -12.124 < 2e-16 ***
## factor(state)Tennessee -5.427e+00 1.222e+00 -4.442 9.78e-06 ***
## factor(state)Texas -9.626e-01 2.437e+00 -0.395 0.692869
## factor(state)Utah -2.071e+01 1.912e+00 -10.830 < 2e-16 ***
## factor(state)Vermont -2.279e+01 2.287e+00 -9.965 < 2e-16 ***
## factor(state)Virginia -4.694e+00 1.033e+00 -4.544 6.12e-06 ***
## factor(state)Washington -1.561e+01 1.738e+00 -8.977 < 2e-16 ***
## factor(state)West Virginia -1.640e+01 2.080e+00 -7.883 7.54e-15 ***
## factor(state)Wisconsin -1.792e+01 1.997e+00 -8.977 < 2e-16 ***
## factor(state)Wyoming -2.113e+01 2.075e+00 -10.182 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.738 on 1116 degrees of freedom
## Multiple R-squared: 0.8739, Adjusted R-squared: 0.8675
## F-statistic: 138.1 on 56 and 1116 DF, p-value: < 2.2e-16ols_coeffs <- coef(ols_model)
fe_within_coeffs <- coef(fe_within_model)
fe_fd_coeffs <- coef(fe_fd_model)
fe_lm_coeffs <- coef(fe_lm_model)
cbind(ols_coeffs, fe_within_coeffs, fe_fd_coeffs, fe_lm_coeffs)## Warning in cbind(ols_coeffs, fe_within_coeffs, fe_fd_coeffs, fe_lm_coeffs):
## number of rows of result is not a multiple of vector length (arg 1)## ols_coeffs fe_within_coeffs fe_fd_coeffs
## (Intercept) 10.5230432050 -1.637577e+00 -0.3074187396
## afam 0.2620245809 -8.210904e-02 0.6731441150
## cauc -0.0737295557 3.778867e-01 0.2160032548
## male 0.0950943099 -3.500585e-01 -0.8113528379
## population 0.2217488841 6.948773e-04 -0.2160706389
## income -0.0002531634 -1.167478e+01 0.0002001034
## density 3.5853539184 -1.637577e+00 -1.9759271460
## factor(state)Alaska 10.5230432050 -8.210904e-02 -0.3074187396
## factor(state)Arizona 0.2620245809 3.778867e-01 0.6731441150
## factor(state)Arkansas -0.0737295557 -3.500585e-01 0.2160032548
## factor(state)California 0.0950943099 6.948773e-04 -0.8113528379
## factor(state)Colorado 0.2217488841 -1.167478e+01 -0.2160706389
## factor(state)Connecticut -0.0002531634 -1.637577e+00 0.0002001034
## factor(state)Delaware 3.5853539184 -8.210904e-02 -1.9759271460
## factor(state)District of Columbia 10.5230432050 3.778867e-01 -0.3074187396
## factor(state)Florida 0.2620245809 -3.500585e-01 0.6731441150
## factor(state)Georgia -0.0737295557 6.948773e-04 0.2160032548
## factor(state)Hawaii 0.0950943099 -1.167478e+01 -0.8113528379
## factor(state)Idaho 0.2217488841 -1.637577e+00 -0.2160706389
## factor(state)Illinois -0.0002531634 -8.210904e-02 0.0002001034
## factor(state)Indiana 3.5853539184 3.778867e-01 -1.9759271460
## factor(state)Iowa 10.5230432050 -3.500585e-01 -0.3074187396
## factor(state)Kansas 0.2620245809 6.948773e-04 0.6731441150
## factor(state)Kentucky -0.0737295557 -1.167478e+01 0.2160032548
## factor(state)Louisiana 0.0950943099 -1.637577e+00 -0.8113528379
## factor(state)Maine 0.2217488841 -8.210904e-02 -0.2160706389
## factor(state)Maryland -0.0002531634 3.778867e-01 0.0002001034
## factor(state)Massachusetts 3.5853539184 -3.500585e-01 -1.9759271460
## factor(state)Michigan 10.5230432050 6.948773e-04 -0.3074187396
## factor(state)Minnesota 0.2620245809 -1.167478e+01 0.6731441150
## factor(state)Mississippi -0.0737295557 -1.637577e+00 0.2160032548
## factor(state)Missouri 0.0950943099 -8.210904e-02 -0.8113528379
## factor(state)Montana 0.2217488841 3.778867e-01 -0.2160706389
## factor(state)Nebraska -0.0002531634 -3.500585e-01 0.0002001034
## factor(state)Nevada 3.5853539184 6.948773e-04 -1.9759271460
## factor(state)New Hampshire 10.5230432050 -1.167478e+01 -0.3074187396
## factor(state)New Jersey 0.2620245809 -1.637577e+00 0.6731441150
## factor(state)New Mexico -0.0737295557 -8.210904e-02 0.2160032548
## factor(state)New York 0.0950943099 3.778867e-01 -0.8113528379
## factor(state)North Carolina 0.2217488841 -3.500585e-01 -0.2160706389
## factor(state)North Dakota -0.0002531634 6.948773e-04 0.0002001034
## factor(state)Ohio 3.5853539184 -1.167478e+01 -1.9759271460
## factor(state)Oklahoma 10.5230432050 -1.637577e+00 -0.3074187396
## factor(state)Oregon 0.2620245809 -8.210904e-02 0.6731441150
## factor(state)Pennsylvania -0.0737295557 3.778867e-01 0.2160032548
## factor(state)Rhode Island 0.0950943099 -3.500585e-01 -0.8113528379
## factor(state)South Carolina 0.2217488841 6.948773e-04 -0.2160706389
## factor(state)South Dakota -0.0002531634 -1.167478e+01 0.0002001034
## factor(state)Tennessee 3.5853539184 -1.637577e+00 -1.9759271460
## factor(state)Texas 10.5230432050 -8.210904e-02 -0.3074187396
## factor(state)Utah 0.2620245809 3.778867e-01 0.6731441150
## factor(state)Vermont -0.0737295557 -3.500585e-01 0.2160032548
## factor(state)Virginia 0.0950943099 6.948773e-04 -0.8113528379
## factor(state)Washington 0.2217488841 -1.167478e+01 -0.2160706389
## factor(state)West Virginia -0.0002531634 -1.637577e+00 0.0002001034
## factor(state)Wisconsin 3.5853539184 -8.210904e-02 -1.9759271460
## factor(state)Wyoming 10.5230432050 3.778867e-01 -0.3074187396
## fe_lm_coeffs
## (Intercept) 1.801186e+01
## afam -1.637577e+00
## cauc -8.210904e-02
## male 3.778867e-01
## population -3.500585e-01
## income 6.948773e-04
## density -1.167478e+01
## factor(state)Alaska -8.441675e+00
## factor(state)Arizona -1.129283e+01
## factor(state)Arkansas -7.092911e+00
## factor(state)California 3.683447e+00
## factor(state)Colorado -1.714197e+01
## factor(state)Connecticut -1.173594e+01
## factor(state)Delaware -9.735250e+00
## factor(state)District of Columbia 1.677677e+02
## factor(state)Florida -2.223964e+00
## factor(state)Georgia 2.371142e+00
## factor(state)Hawaii 1.477877e+01
## factor(state)Idaho -2.097091e+01
## factor(state)Illinois -3.537966e+00
## factor(state)Indiana -1.191786e+01
## factor(state)Iowa -2.197269e+01
## factor(state)Kansas -1.653125e+01
## factor(state)Kentucky -1.223955e+01
## factor(state)Louisiana 7.074210e+00
## factor(state)Maine -2.231351e+01
## factor(state)Maryland 3.144954e+00
## factor(state)Massachusetts -1.085034e+01
## factor(state)Michigan -5.245085e+00
## factor(state)Minnesota -2.083688e+01
## factor(state)Mississippi 5.518422e+00
## factor(state)Missouri -9.412492e+00
## factor(state)Montana -1.844380e+01
## factor(state)Nebraska -2.058711e+01
## factor(state)Nevada -8.940381e+00
## factor(state)New Hampshire -2.330594e+01
## factor(state)New Jersey -4.603545e-01
## factor(state)New Mexico -8.667021e+00
## factor(state)New York 2.672783e+00
## factor(state)North Carolina -1.137107e+00
## factor(state)North Dakota -2.253715e+01
## factor(state)Ohio -8.721723e+00
## factor(state)Oklahoma -8.781543e+00
## factor(state)Oregon -1.824709e+01
## factor(state)Pennsylvania -9.230097e+00
## factor(state)Rhode Island -9.711279e+00
## factor(state)South Carolina 1.859502e+00
## factor(state)South Dakota -2.011844e+01
## factor(state)Tennessee -5.427063e+00
## factor(state)Texas -9.625925e-01
## factor(state)Utah -2.070963e+01
## factor(state)Vermont -2.278975e+01
## factor(state)Virginia -4.693589e+00
## factor(state)Washington -1.560502e+01
## factor(state)West Virginia -1.639651e+01
## factor(state)Wisconsin -1.792382e+01
## factor(state)Wyoming -2.112856e+01The choice of fixed effects specification depends on the research question and the nature of the data. In many applications in economics, it is common to include both time fixed effects and entity fixed effects. Time fixed effects control for time-specific factors affecting all entities, while entity fixed effects control for time-invariant characteristics of the entities. Including both types of fixed effects allows for a more comprehensive control of omitted variables. When specifying fixed effects in alternative ways, such as using entity fixed effects versus state fixed effects, it is important to consider the nature of the data and the specific research question. In this case, the OLS model with state fixed effects includes additional coefficients for each state, allowing for state-specific effects on the murder rate. It provides a more detailed analysis of the impact of each state on the outcome variable. However, it may not be appropriate if the focus is on individual entities rather than states. The choice of fixed effects specification should align with the research objectives and the nature of the data being analyzed.