Let the Data Speak: Sims and the Vector Autoregression

In the 1970s, macroeconomic forecasting was done by enormous models. Hundreds of equations, thousands of parameters, whole rooms of economists maintaining them. Each equation encoded a theory: this is how consumption responds to income, this is how investment responds to interest rates, and so on.

To make such a system solvable, you had to make assumptions. Lots of them. You had to declare that variable X does not appear in equation 47, that variable Y is "exogenous" and gets determined outside the model, and so on, hundreds of times over. Without those exclusions, the whole thing is mathematically unidentifiable and you cannot estimate anything.

In 1980, Christopher Sims looked at those assumptions and used a word that became famous in the profession. He called them "incredible." Not wrong, exactly. Incredible: as in, nobody actually believes them. And he proposed replacing the entire apparatus with something almost shockingly simple.

The problem: the theory was doing the work, not the data

Here is the uncomfortable core of Sims's argument. When a macro model tells you that a monetary shock raises output, where did that answer come from?

Partly from the data. But mostly from the exclusion restrictions: the hundreds of assumptions the modeller made about which variables cannot influence which other variables. Change those assumptions, and the answer changes. And those assumptions were rarely derived from anything solid. They were chosen because they made the model tractable, or because they matched a theoretical fashion, or because the previous generation had chosen them.

So the "empirical" findings of macroeconomics were, in an important sense, assumptions in disguise. The model was not learning from data. The model was telling you what you had already told it, dressed up in the authority of a regression.

Sims's complaint was not that economists had bad theories. It was that they were smuggling those theories into the estimation stage, and then presenting the output as evidence.

The key idea via analogy: stop deciding who is allowed to talk

Imagine a dinner party where you are trying to work out who influences whom. The old approach was to declare in advance that Alice never listens to Bob, Carol only listens to Dave, and Erin talks to nobody. Then you watch the conversation and, unsurprisingly, you conclude exactly what you assumed.

Sims's approach: let everyone potentially talk to everyone. Do not exclude anybody. Just write down, for each person, a rule that says "what this person says today depends on what everyone at the table said yesterday, and the day before, and the day before that."

That is a vector autoregression. Take your handful of macro variables (output, prices, money, interest rates). Regress each one on the recent past of all of them, including itself. No exclusions. No exogeneity assumptions. No theory about who influences whom. Just a symmetric, agnostic description of how the system evolves.

The word "vector" just means you are handling several series at once. "Autoregression" means each is explained by the past. That is genuinely all it is: a small system of regressions, treating every variable as equal.

What you actually do with it

A VAR by itself is a black box of coefficients that nobody can read. Sims's second contribution was showing what to ask it. Two questions, both of which became standard.

The first is the impulse response function. You ask: suppose an unexpected shock hits the interest rate today. Trace out, period by period, what happens to output, to prices, to everything else, over the following months and years. The VAR can simulate this, and the resulting picture, a set of little response curves over time, is enormously more informative to a human than a table of coefficients. It answers the question people actually care about: if this thing moves, what happens next, and for how long?

The second is variance decomposition. You ask: of all the wobble in output over the next two years, how much of it traces back to shocks in output itself, how much to monetary shocks, how much to price shocks? This tells you which forces actually drive the system, rather than which ones a theorist thought should.

Why it mattered

• It became the default tool of empirical macroeconomics. VARs are now the standard workhorse. Central banks run them. Every macro paper that claims to measure the effect of a policy shock is, somewhere, running one. Sims shared the Nobel Prize in 2011 largely for this.
• It was a genuine methodological revolution. The idea that you should minimise the theoretical assumptions you impose before looking at the data, and let the data describe the dynamics, propagated far beyond macroeconomics.
• It is directly useful in quant finance. Any time you have several interrelated series (a set of yields, a set of currency pairs, order flow and price, volatility and returns) and want to know how a shock in one propagates through the others, you are in VAR territory. The impulse response is a natural way to think about how long a signal's effect persists.
• It reframed forecasting. A VAR, being atheoretical, often forecasts better than a carefully theorised structural model, precisely because it is not being dragged around by assumptions the world does not respect.

The honest limitations

The irony of the VAR literature is beautiful and worth appreciating.

• The assumptions came back. Sims wanted to abolish incredible restrictions. But the moment you want an impulse response, you have to answer a question the VAR cannot answer for itself: when interest rates and output both move unexpectedly in the same month, which one shocked which? The data is symmetric and silent on this. To break the tie, you must impose an identifying assumption. Sims's original choice, a simple ordering of variables, is itself an assumption about causal timing, and is no more "credible" than what it replaced. The entire subsequent literature on structural VARs is one long argument about how to make this choice, which means the problem Sims set out to escape was merely relocated, not solved.
• They eat degrees of freedom alive. With four variables and four lags, you are estimating sixteen coefficients per equation. Add a fifth variable and it balloons. Macro data arrives quarterly, so you might have 150 observations. The model quickly has more parameters than the data can support, which is why practical VARs are kept small and why Bayesian shrinkage methods became popular.
• Being atheoretical is a cost as well as a benefit. A VAR can describe how the system has behaved. It has much less to say about how it would behave under a policy regime that has never been tried, which is often the exact question policymakers need answered. This is the Lucas critique, and VARs do not escape it.
• It assumes the relationships are stable. A VAR fitted across a period containing a regime change is fitting an average of two different worlds and describing neither.

The one-line takeaway

Sims argued that macroeconomics was mistaking its own assumptions for evidence, and proposed the vector autoregression as a humbler alternative: let every variable depend on the past of every other variable, impose almost nothing, and ask the data what a shock actually does, a revolution that succeeded so completely that its central unsolved problem, how to tell which shock came first, is still being argued about today.