In-class Exercise 3

library(dplyr)
library(wooldridge)
data("vote1")

(i)

• The effect of expendB on voteA is \(\beta_3+\beta_4expendA\)
• The effect of expendA on voteA is \(\beta_2+\beta_4expendB\)
• The sign of \(\beta_4\) is not immediately obvious and would depend on the dynamics between the two candidates’ spending behavior.

(ii)

model <- lm(voteA ~ prtystrA + expendA + expendB + expendA*expendB, data = vote1)
summary(model)

## 
## Call:
## lm(formula = voteA ~ prtystrA + expendA + expendB + expendA * 
##     expendB, data = vote1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -28.9999  -8.7632  -0.1726   8.2310  29.7325 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3.212e+01  4.591e+00   6.995 5.99e-11 ***
## prtystrA         3.419e-01  8.799e-02   3.886 0.000146 ***
## expendA          3.828e-02  4.960e-03   7.718 1.00e-12 ***
## expendB         -3.172e-02  4.588e-03  -6.915 9.32e-11 ***
## expendA:expendB -6.629e-06  7.186e-06  -0.923 0.357584    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.13 on 168 degrees of freedom
## Multiple R-squared:  0.5708, Adjusted R-squared:  0.5606 
## F-statistic: 55.86 on 4 and 168 DF,  p-value: < 2.2e-16

The p-value indicates that the interaction term is statistically insignificant.

(iii)

mean(vote1$expendA)

## [1] 310.611

The average expenditure of candidate A in the sample is $310,611.

beta3 <- model$coefficients[4]  
beta4 <- model$coefficients[5]
expendA <- 300

partial_effect_expendB <- beta3 + beta4 * expendA
effect_100k_expendB <- partial_effect_expendB * 100

effect_100k_expendB

##   expendB 
## -3.371269

• For every additional $100,000 spent by candidate B, the predicted percentage of votes for candidate A (voteA) is expected to decrease by 3.37 percentage points, holding the spending of candidate A (expendA) fixed at $300,000.

• Given the size of the effect and the residual error, this change might be large enough to impact the election outcome, especially if the candidates are close in vote share. However, it’s essential to compare this to typical variations in the election data to understand the practical significance fully.

(iv)

beta2 <- model$coefficients[3]  
beta4 <- model$coefficients[5]
expendB <- 100

partial_effect_expendA <- beta2 + beta4 * expendB
effect_100k_expendA <- partial_effect_expendA * 100

effect_100k_expendA

##  expendA 
## 3.761799

• The estimated effect of an additional $100,000 spent by candidate A on their vote share voteA, holding expendB fixed at $100,000, is approximately 0.0376 percentage points.

• This result makes sense in the context of the model.

(v)

It does make sense to replace the interaction term with \(\text{shareA}\) if you’re focusing on the effect of presidential support on congressional vote share. However, holding \(\text{expendA}\) and \(\text{expendB}\) fixed while changing \(\text{shareA}\) may not fully capture the dynamics, since campaign spending is often influenced by factors like voter support. This approach isolates the effect of \(\text{shareA}\), but could miss the interaction between spending and support.

(vi)

model_shareA <- lm(voteA ~ prtystrA + expendA + expendB + shareA, data = vote1)
beta3 <- coef(model_shareA)["expendB"]
partial_effect_expendB <- beta3

partial_effect_expendB

##    expendB 
## 0.00426694

The positive partial effect of expendB on voteA is somewhat unusual in the context of a typical election model, where higher spending by one candidate generally reduces the vote share of the opposing candidate. However, in this case, it suggests that the spending by candidate B may have a positive or neutral effect on candidate A’s vote share, possibly due to other dynamics captured by the model