In this classwork, we’ll replicate parts of a chapter of Political Psychology, Presidential Approval and Gas Prices: Sociotropic or Pocketbook Influence? (Laurel Harbridge, Jon A. Krosnick, Jeffrey M. Wooldridge, 2016). Take a look at it here.
In this chapter, authors estimated a dynamic model of the presidential approval rate of George W. Bush, who was the US president from 2001 to 2009. During that time, 9/11 happened, there was a snafu about whether Iraq might have weapons of mass destruction, and in 2003 we invaded Iraq.
Public approval is important because it helps determine the ability of the president to push their agenda effectively in Congress and get bills passed. A high public approval rating is also a strong signal that the president’s party will win subsequent elections (although shockingly, this was not the case in last week’s midterm elections!).
Many people in politics are interested in modeling and understanding the variables that affect the public approval rating of the president. Events like 9/11 and the invasion of Iraq had clear, large effects on that approval rating. What we’re interested in though is the question of whether gas prices seem to effect the presidential approval rating. People’s perceptions of the health of the economy as a whole effects the approval rating, but it doesn’t seem to follow that higher or lower gas prices necessarily indicates a better or worse economy.
But high gas prices are bad for consumers, and a 2008 Gallup poll found that most Americans believe that the president can take steps to reduce the price of gas (even though fluctuations in the price of gas usually occur because of events far beyond the control of the president). As you’ll find in this classwork, during George Bush’s presidency, as gas prices were increasing, Bush’s approval rating kept falling, and Wooldridge et. al. were ready to call the relationship causal.
This research question is interesting nowadays because recently we’ve seen incredibly high gas prices and incredibly low approval ratings for President Biden. I’ll outline some extra credit you can do at the end of this assignment to explore more recent data.
We’ll use a dataset published with the Wooldridge econometrics
textbook called approval. To read about the variables, go
here.
approve is the presidential approval rating, measured in
percentage points (0 to 100), and rgasprice is the real gas
price, measured in cents. Authors took the US city average retail price
of unleaded regular gasoline and adjusted the prices for general
inflation by dividing them by a CPI using 1982-194 as a baseline.
You’ll need to install the package ‘wooldridge’:
# install.packages("wooldridge")library(tidyverse)
library(wooldridge)
data('approval') # This line of code adds the dataset "approval" to your environment
# These lines of code make it into a tibble:
approval <- as_tibble(approval) %>%
select(time = id, month, year, approve, rgasprice, sep11 = X11.Sep, iraqinvade)approve time seriesPlot approve on the y-axis against time on
the x-axis. Can you see where September 11th happened and where the
invasion of Iraq happened? Draw vertical lines to mark those dates. Did
the approval rating of the president seem to rise or fall because of
these events?
Use rgasprice. Draw two geom_line()’s: one
for approve against time, and another for
rgasprice against time. Overall, does it seem
like as gas prices increase, Bush’s approval rating decreases?
\(approval_t = \beta_0 + \beta_1 rgasprice_t + u_t\)
In the workbook we learned that in models without lagged dependent variables on the right hand side, the consequences of autocorrelation are just that conventional standard errors are incorrect. But here, autocorrelation in \(u_t\) is a little more concerning because it indicates that we seem to have omitted important variables that are autocorrelated over time, which may bias our estimate for the effect of gas prices on the presidential approval rate.
Take the static model from the previous question, calculate the residuals, and plot time on the x-axis and the residuals on the y-axis. Can you visually see that large residuals seem to follow other large residuals, and small residuals seem to follow other small residuals? Or, do the residuals seem to be following a path? If so, this is autocorrelation.
Implement the Breusch-Godfrey test yourself. You don’t need to make
this one a function, but you can check your work by running
lmtest::bgtest(). Make sure to install the package ‘lmtest’
first and read the help docs to figure out how to use
bgtest().
For this question, you can either use your own implementation or
lmtest::bgtest(). Try up to 5 lags.
approve?Remember, if you add a lag of the dependent variable to the right hand side, it’s more important than ever to check for autocorrelation in \(u_t\) because if there is still autocorrelation, that means estimates are biased and inconsistent.
Model: \(approve_t = \beta_0 + \beta_1 rgasprice_t + \beta_2 approve_{t-1} + u_t\)
Instead of having approve on the left, the model has the
first difference of approve on the left. Then on the right
is rgasprice and one lag of approve.
\((approve_t - approve_{t - 1}) = \beta_0 + \beta_1 rgasprice_t + \beta_2 approve_{t - 1} + u_t\)
Check for autocorrelation of \(u_t\) using the Breusch-Godfrey test (your
own implementation or lmtest::bgtest)
Estimate the model and interpret coefficients. Wooldridge et al. reported, after including a couple more variables, that they found a 10 cent increase in gas prices caused a .6 percentage point decrease in the approval rating of the president. Do you find something similar?
2 more questions:
Justify why Wooldridge et al might have wanted to use the first
difference of approve as the dependent variable instead of
using approve.
Wooldridge et al found a negative coefficient on \(approve_{t-1}\) and made a comment that it showed that the approval rate tends to “regress to the mean”. What does that mean?