Impulse Response Functions

I bought a copy of Ed Leamer's book Macroeconomic Patterns and Stories after hearing him speaking about it on EconTalk. Actually, Professor Leamer is probably my favourite guest on EconTalk, so purchasing his book was a no-brainer for me. If you've heard of him before it's probably due to his famous paper Let's Take the Con Out of Econometrics. He is also well known for advocating "extreme bounds analysis", which, in basic terms, involves finding a possible range of values for an estimate and investigating the fragility of the model by seeing if the value of the estimate is sensitive to small changes in model specification.

The example of EBA given in Let's Take the Con Out of Econometrics is to do with the effect of capital punishment on the murder rate. Using a number of regressions, with different, but somewhat similar specifications, Leamer shows that at one end of the spectrum, the estimate is negative, but at the other end, the estimate is positive!

In his book, Macroeconomic Patterns and Stories, Professor Leamer talks about four key macro variables in detail; namely, Growth, Unemployment, Inflation, and Interest Rates. In this post, I want to focus on these four variables and in particular to the topic of Chapter 6 of the book which is Extrapolative Forecasting.

In Chapter 6, a table is shown and it contains regression results. There are four separate regressions and each of them are autoregressive. Growth is modeled as an AR(2) process, so too is the unemployment rate and 3-month treasuries, while inflation is modeled as an AR(4) process. Admittedly, Professor Leamer says that a more careful data analysis could be done on the data, but the results from these regressions still permit us to get an insight into the dynamic nature of the four variables.

In R, I've estimated how each of the four variables respond to a one unit shock. I've plotted the results in the Figure 1 below. A similar graph appears on page x in Leamer's book and this gives me confidence that the code I wrote in R is correct.

Figure 1

To explain the dynamic behaviour of each of the four variables in response to a shock, Leamer introduces two concepts to the reader: persistence and momentum.