VARs: Interpreting Voodoo

Vector auto regressions spent the last 20 years helping provide a method to the madness that is macroeconomics

Macroeconomics was once described to me as voodoo. Nobody can agree on how it works. Every time the Fed raises or lowers rates, we still argue over the fallout. But that doesn't mean we know nothing. Time and technology have given us to tools to help define the relationships between macro variables.

Enter vector auto-regressions (VAR). Auto regression means modeling a thing on its past behavior. Economics usually predicts Y only on X and X's past values. Auto regression means we now take into account Y's past behavior in predicting its future.

VARs can tell us three things;

a) do past values of x help predict y,

b) what might happen to future values of y if we change x 1%

c) what might happen if we had a monetary regime change.

First, we need to ask, why look at interest rates at all? Because they make stuff move. Here I use the federal funds rate, the rate banks lend to each other overnight. It's important because it impacts consumer loans and credit cards. The funds rate is also a good predictor of GDP and other macro variables. In time series analysis, when one variable is helpful in predicting another, it's called Granger causality. Rates Granger cause our income (GDP), how much we buy (consumption), and how many of us looking for jobs can find one (unemployment). Now that we have a good predictor in rates, we need to know how many past value to include if we're to then make a forecast.

My VAR evalauted 12 different models that included one through 12 past values of both variables. The model that performed the best included 4 previous quarters of data. Turns out, rates from last year still impact us today! Now that we have our model we can make predictions. Below, I made forecasts for 2020-2023 using data up to 2019, then compared my predictions to their actual values as a visual accuracy test. The black dots are the actual values while the blue lines are my predictions.

We outperformed my models! Obviously other VAR models are better than mine, but the Federal Reserve used a souped-up Bayesian VAR model that had similar findings.

The second purpose of VARs is to determine the elasticity of one time series to another. Impulse response functions (IRF) tackle this problem. IRFs predict the future path of income given a 1% change in rates. My IRFs evaluate one off events, which throws their predictions into questions the next time interest rates move. However, they've still proved useful in determining the consequences of infrastructure investment on the broader economy, and how the government's money multiplier behaves in good times and in bad.

Macroeconomics is voodoo for the million other things that can cause GDP, unemployment, and consumption that aren't in my model. That being said, theory has stood up pretty well. David Hume justified his causal model over 200 years ago and it's still considered the best framework (you guessed it, contested). You can view Hume's model of the economy of page 9 of Causality in Macroeconomics. Still, VARs have a lot to teach us. Namely, that policy making is inherently a long-term game and should be approached with foresight in mind.