Accidents = β0 + β1 * Taxes
see output
| Dependent variable: | |
| accidents | |
| Constant | 1,359.74*** |
| (262.70) | |
| taxes | 760.12 |
| (494.49) | |
| Note: | p<0.1; p<0.05; p<0.01 |
No, the Pooled OLS model suggests that beer taxes do not have a statistically significant effect on reducing car accidents, as indicated by the non-significant coefficient for taxes.
The coefficient represents the estimated average increase in car accidents associated with a one-unit increase in beer taxes. However, this effect is not statistically significant, which means we cannot conclude that beer taxes have a significant effect on car accidents. This is the average effect of beer taxes on car accidents across states, not within states.
Accidents_it = β1 * Taxes_it + α_i
The pooled OLS model assumes that the relationship between the independent variable(s) and the dependent variable is constant across all groups. In contrast, the fixed effect model allows for group-specific effects by including additional terms (fixed effects) in the model.
This question is incredibly confusing as written.
See the output.
| Dependent variable: | ||
| Car Accidents | ||
| FE with Intercept | FE without Intercept | |
| (1) | (2) | |
| Constant - State 1 | 2,090.57*** | |
| (8.64) | ||
| Taxes | -31.37** | -31.37** |
| (13.76) | (13.76) | |
| State 1 | 2,090.57*** | |
| (8.64) | ||
| State 2 | 6.42 | 2,096.99*** |
| (5.94) | (8.52) | |
| State 3 | -2.80 | 2,087.77*** |
| (5.95) | (8.29) | |
| State 4 | -1,159.82*** | 930.75*** |
| (6.05) | (7.64) | |
| State 5 | 9.66 | 2,100.24*** |
| (5.94) | (8.72) | |
| State 6 | -607.00*** | 1,483.57*** |
| (5.95) | (8.42) | |
| State 7 | -495.99*** | 1,594.58*** |
| (6.06) | (7.63) | |
| Note: | p<0.1; p<0.05; p<0.01 | |
Beer taxes have a statistically significant effect on reducing car accidents in both models. An increase in beer taxes is associated with a decrease in car accidents.
The effect represents the within-state effect. This means that the model measures the relationship, controlling for unobserved, time-invariant factors that differ by state. The taxes coefficient (-31.37) is statistically significant and suggests a one-unit increase in beer taxes is associated with a decrease of 31.37 car accidents within a state.
This question is incredibly confusing. It doesn’t specify which
models are needed or which order is 1 or 2. If the plm()
model was used above, there is no apples:apples comparison to be had
here. I’m also assuming that model_1 is with and model_2 is
without.
Answer: The State 1 intercept is 2,090.57 and is significant. It represents the average number of car accidents in State 1, when taxes are equal to zero.
| Dependent variable: | ||
| Car Accidents | ||
| FE with Intercept | FE without Intercept | |
| (1) | (2) | |
| Constant - State 1 | 2,090.57*** | |
| (8.64) | ||
| Taxes | -31.37** | -31.37** |
| (13.76) | (13.76) | |
| State 1 | 2,090.57*** | |
| (8.64) | ||
| State 2 | 6.42 | 2,096.99*** |
| (5.94) | (8.52) | |
| State 3 | -2.80 | 2,087.77*** |
| (5.95) | (8.29) | |
| State 4 | -1,159.82*** | 930.75*** |
| (6.05) | (7.64) | |
| State 5 | 9.66 | 2,100.24*** |
| (5.94) | (8.72) | |
| State 6 | -607.00*** | 1,483.57*** |
| (5.95) | (8.42) | |
| State 7 | -495.99*** | 1,594.58*** |
| (6.06) | (7.63) | |
| Note: | p<0.1; p<0.05; p<0.01 | |
The value is -1,159.82 and is significant. This coefficient represents the difference in the average number of car accidents between State 4 and State 1. State 4 has 1,159.82 fewer car accidents on average compared to State 1.
The value is 930.75 and is significant. This coefficient represents the average number of car accidents in State 4 when taxes are equal to zero.
In model 1, there is no significant difference in the average number of car accidents between State 3 and State 1. However, model 2 suggests the average number car accidents in State 3 is significantly different from zero.
Both State geographical location (north, south, east… )
and State form of government are time-invariant factors
(meaning they remain constant for each state over time), so
Annual unemployment rates would be the variable I would
suggest. Higher unemployment rates might lead to less disposable income
for drinking; however, higher unemployment rates could lead to higher
rates of despair, which might increase rates over time.
This would be the best choice because it adds additional explanatory power to the model and controls for confounders that affect the relationship between accidents and taxes.
# state means
data_demeaned <-
data %>%
group_by(state) %>%
mutate(mean_taxes = mean(taxes), taxes_demeaned = taxes - mean_taxes,
mean_accidents = mean(accidents), accidents_demeaned = accidents - mean_accidents) %>%
ungroup()| Dependent variable: | |
| De-meaned Car Accidents | |
| De-meaned Taxes | -0.00 |
| (1.48) | |
| taxes_demeaned | -31.37** |
| (12.85) | |
| Note: | p<0.1; p<0.05; p<0.01 |
While the coefficients are the same, the standard errors differ slightly (13.76 vs. 12.85).
The similarity is expected because de-meaning the data is equivalent to running a fixed effect model. Both methods control for unobserved time-invariant variables of each state.
I’m unsure why the standard errors are different, but it could be due to how the calculations are performed.