chp6

Load Required Libraries and Data

library(wooldridge)

# Load the VOTE1 dataset
data("vote1")

(i) Partial Effects and Expected Signs

This part requires interpreting coefficients after estimating the model.

(ii) Estimate the Model with Interaction Term

# Estimate the model with interaction between expendA and expendB
model <- lm(voteA ~ prtystrA + expendA + expendB + I(expendA * expendB), data = vote1)

# Display the summary to report results and check if the interaction term is significant
summary(model)

## 
## Call:
## lm(formula = voteA ~ prtystrA + expendA + expendB + I(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 ***
## I(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

(iii) Average of expendA and Estimated Effect of Additional Spending by Candidate B

# Calculate the average of expendA
avg_expendA <- mean(vote1$expendA, na.rm = TRUE)
avg_expendA

## [1] 310.611

# Set expendA at 300 and estimate the effect of an additional $100,000 on expendB
expendA_val <- 300
expendB_val <- 100  # Assuming an additional $100,000 means expendB + 100
new_data <- data.frame(prtystrA = mean(vote1$prtystrA, na.rm = TRUE),
                       expendA = expendA_val,
                       expendB = expendB_val,
                       expendA_expendB = expendA_val * expendB_val)

# Predict voteA with new values
predicted_effect <- predict(model, new_data)
predicted_effect

##        1 
## 57.24437

(iv) Fix expendB at 100 and Estimate the Effect of Change in expendA

# Fix expendB at 100, and check effect of expendA increasing by 100
expendB_fixed <- 100
expendA_change <- 100

# Predict with expendA + 100
new_data_expendA <- data.frame(prtystrA = mean(vote1$prtystrA, na.rm = TRUE),
                               expendA = expendA_val + expendA_change,
                               expendB = expendB_fixed,
                               expendA_expendB = (expendA_val + expendA_change) * expendB_fixed)

# Predict with expendA unchanged
new_data_original <- data.frame(prtystrA = mean(vote1$prtystrA, na.rm = TRUE),
                                expendA = expendA_val,
                                expendB = expendB_fixed,
                                expendA_expendB = expendA_val * expendB_fixed)

# Calculate difference in predictions
predicted_diff <- predict(model, new_data_expendA) - predict(model, new_data_original)
predicted_diff

##        1 
## 3.761799

(v) Replace Interaction with Share and Estimate Model

The variable shareA (the percentage share of total campaign expenditures by Candidate A) needs to be created, as it is not in the dataset.

# Create the shareA variable
vote1$shareA <- vote1$expendA / (vote1$expendA + vote1$expendB)

# Estimate the new model without interaction
model_share <- lm(voteA ~ prtystrA + shareA, data = vote1)

# Display summary
summary(model_share)

## 
## Call:
## lm(formula = voteA ~ prtystrA + shareA, data = vote1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -17.7258  -3.7460  -0.0886   3.0517  30.7756 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 19.85013    2.41558   8.218 5.08e-14 ***
## prtystrA     0.15320    0.04962   3.087  0.00236 ** 
## shareA      45.08931    1.47955  30.475  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.231 on 170 degrees of freedom
## Multiple R-squared:  0.8638, Adjusted R-squared:  0.8622 
## F-statistic:   539 on 2 and 170 DF,  p-value: < 2.2e-16

(vi) Partial Effect Calculation (Requires Calculus)

This involves calculating the partial derivative of voteA with respect to expendB given specific values.

# Define expendA = 300 and expendB = 0 for calculation
expendA_val <- 300
expendB_val <- 0

# Calculate the partial effect (derivative with respect to expendB)
partial_effect <- coef(model)["expendB"] + coef(model)["I(expendA * expendB)"] * expendA_val
partial_effect

##     expendB 
## -0.03371269