lab10noCovid.Rmd

---
title: "In-Class Lab 10"
author: "ECON 4223 (Prof. Tyler Ransom, U of Oklahoma)"
date: "October 1, 2020"
output:
  html_document:
    df_print: paged
  pdf_document: default
  word_document: default
bibliography: biblio.bib
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, results = 'hide', fig.keep = 'none')
```

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`, and `sandwich` 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.

Open up a new R script (named `ICL10_XYZ.R`, where `XYZ` are your initials) and add the usual "preamble" to the top:
```{r message=FALSE, warning=FALSE, paged.print=FALSE}
# Add names of group members HERE
library(tidyverse)
library(wooldridge)
library(broom)
library(car)
library(pdfetch)
library(magrittr)
library(lmtest)
library(sandwich)
library(tsibble)
```

### Load the data
We're going to use data on US macroeconomic indicators. The `wooldridge` data set is called `intdef`.

```{r}
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:
```{r}
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.

```{r}
est <- lm(i3 ~ inf + lag(inf,1) + lag(inf,2) + def, data=df.ts)
```

1. Are any of these variables significant determinants of the interest rate? 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 `NeweyWest` option in the `coeftest()` function of the `lmtest` package.[^2]

```{r}
coeftest(est) # re-display baseline results
coeftest(est, vcov=NeweyWest)
```

2. How does your interpretation of the interest rate model change, using the Newey-West standard errors?

### Another way to correct for serial correlation
Another way to get rid of serial correlation is to *difference* the data. In this case, we will estimate the following regression:
\[
\Delta i3_{t} = \beta_0 + \beta_1 \Delta inf_t + \beta_2 \Delta inf_{t-1} + \beta_4 \Delta def_{t} + u_t
\]
where $\Delta x_{t} = x_{t}-x_{t-1}$ for any variable $x_{t}$. Aside from addressing serial correlation, the differenced model also accounts for people's interest rate expectations.

```{r}
est <- lm(difference(i3) ~ difference(inf) + lag(difference(inf),1) + lag(difference(inf),2) + difference(def), data=df.ts)
```

3. Compute the Newey-West SEs on the difference model. Are they much different from the baseline model?

4. What do you conclude about the effect of inflation on the *change in* the interest rate?

[^1]: You may need to install the `sandwich` package.
[^2]: `NeweyWest` comes from the `sandwich` package.