The purpose of this in-class lab is to use R to practice estimating time series regression models with standard errors corrected for heteroskedasticity and serial correlation (HAC). To get credit, upload your .R script to the appropriate place on Canvas.

## For starters

First, install the pdfetch, tsibble, sandwich, and COVID19 packages. pdfetch stands for “Public Data Fetch” and is a slick way of downloading statistics on stock prices, GDP, inflation, unemployment, etc. tsibble is a package useful for working with time series data. It is the “tibble” for time series data. sandwich is helpful for obtaining HAC standard errors. COVID19 pulls up-to-date data on COVID-19 cases, deaths, etc.

Open up a new R script (named ICL10_XYZ.R, where XYZ are your initials) and add the usual “preamble” to the top:

# Add names of group members HERE
library(tidyverse)
library(wooldridge)
library(modelsummary)
library(broom)
library(car)
library(magrittr)
library(lmtest)
# new packages installed today:
library(pdfetch)
library(sandwich)
library(tsibble)
library(COVID19)

We’re going to use data on US COVID-19 cases, deaths and other information.

df <- covid19(c("US"))
df.ts <- as_tsibble(df, key=id, index=date)

Now it will be easy to include lags of various variables into our regression models.

## Plot time series data

Let’s have a look at the data on new daily cases and deaths:

df.ts %<>% mutate(new_deaths = difference(deaths),    # data comes in cumulative format
new_tests  = difference(tests),     # "difference" converts it to
new_cases  = difference(confirmed)) # "new cases" etc.

# plots
ggplot(df.ts, aes(date, new_cases)) + geom_line()
## Warning: Removed 1 row(s) containing missing values (geom_path).
ggplot(df.ts, aes(date, new_deaths)) + geom_line()
## Warning: Removed 1 row(s) containing missing values (geom_path).
# plots with 7-day rolling average
ggplot(df.ts, aes(date, new_cases)) + geom_line(aes(y=rollmean(new_cases, 7, na.pad=TRUE)))
## Warning: Removed 7 row(s) containing missing values (geom_path).
ggplot(df.ts, aes(date, new_deaths)) + geom_line(aes(y=rollmean(new_deaths, 7, na.pad=TRUE)))
## Warning: Removed 7 row(s) containing missing values (geom_path).

## Determinants of US COVID-19 cases

Now let’s estimate the following regression model: $\log(new\_cases_{t}) = \beta_0 + \beta_1 gath_t + \beta_2 gath_{t-7} + \beta_3 gath_{t-14} + \beta_4 \log(new\_cases_{t-7}) + u_t$ where $$new\_cases$$ is the number of new COVID cases, and $$gath$$ is a variable taking on values 0–4 representing severity of gatherings restricitons.

df.ts %<>% mutate(log.new.cases = log(new_cases),
log.new.cases = replace(log.new.cases,new_cases==0,NA_real_)) # since log(0) = -Inf
## Warning in log(new_cases): NaNs produced
est <- lm(log.new.cases ~ gatherings_restrictions + lag(gatherings_restrictions,7) +
lag(gatherings_restrictions,14) + lag(log.new.cases,7), data=df.ts)
1. Are any of these variables significant determinants of new COVID cases? If so, which ones?

## Correcting for Serial Correlation

Now let’s compute HAC (Heteroskedasticity and Autocorrelation Consistent) standard errors. To do so, we’ll use the vcov option in the modelsummary() function along with the NeweyWest function from the sandwich package.

modelsummary(est) # re-display baseline results
modelsummary(est, vcov=sandwich::NeweyWest(est))

or, putting them side-by-side:

modelsummary(list(est,est),
vcov=list("iid",sandwich::NeweyWest(est))
)
1. How does your interpretation of the the effect of gathering restrictions change after using the Newey-West standard errors?

## Oklahoma COVID cases

df.ok <- covid19(c("US"),level=2) %>%
df.ts.ok <- as_tsibble(df.ok, key=id, index=date)
df.ts.ok %<>% mutate(new_deaths = difference(deaths),
new_tests  = difference(tests),
new_cases  = difference(confirmed))
ggplot(df.ts.ok, aes(date, new_cases)) + geom_line(aes(y=rollmean(new_cases, 7, na.pad=TRUE)))
## Warning: Removed 12 row(s) containing missing values (geom_path).
ggplot(df.ts.ok, aes(date, new_deaths)) + geom_line(aes(y=rollmean(new_deaths, 7, na.pad=TRUE)))
## Warning: Removed 12 row(s) containing missing values (geom_path).
df.ts.ok %<>% mutate(log.new.cases = log(new_cases),
log.new.cases = replace(log.new.cases,new_cases==0,NA_real_)) # since log(0) = -Inf
est.ok <- lm(log.new.cases ~ gatherings_restrictions + lag(gatherings_restrictions,7) +
lag(gatherings_restrictions,14) + lag(log.new.cases,7), data=df.ts.ok)

With HAC standard errors:

modelsummary(list(est.ok,est.ok),
vcov=list("iid",sandwich::NeweyWest(est.ok)))

## Traditional macroeconomic model of interest rates and inflation

We can also use data on US macroeconomic indicators. The wooldridge data set is called intdef.

df.ts <- as_tsibble(intdef, key=NULL, index=year)

Now it will be easy to include lags of various variables into our regression models.

## Plot time series data

Let’s have a look at the inflation rate for the US over the period 1948–2003:

ggplot(df.ts, aes(year, inf)) + geom_line()

## Determinants of the interest rate

Now let’s estimate the following regression model: $i3_{t} = \beta_0 + \beta_1 inf_t + \beta_2 inf_{t-1} + \beta_3 inf_{t-2} + \beta_4 def_{t} + u_t$ where $$i3$$ is the 3-month Treasury Bill interest rate, $$inf$$ is the inflation rate (as measured by the CPI), and $$def$$ is the budget deficit as a percentage of GDP.

est <- lm(i3 ~ inf + lag(inf,1) + lag(inf,2) + def, data=df.ts)
modelsummary(list(est,est), vcov=list("iid",sandwich::NeweyWest(est)))