VAR vs WTF!?

Vector auto regressions (VARs) are supposed to tell us how the economy would respond over time if hit by a shock, by looking at past patterns of responses to shocks. A "shock" means "a deviation of one of the variables in the VAR from the level that was forecast by the VAR". And "shocks" include policy shocks.

1. Suppose at its next meeting the Bank of Canada increased the overnight rate from 0.75% to 1.50%. And suppose this was a totally unexpected move. And suppose a computer glitch meant that the Bank's statement explaining why it had done this was never published. How would markets react to the shock?

2. Now ask exactly the same question, but suppose the Bank of Canada instead reduced the overnight rate from 0.75% to 0.00%. How would markets react to the shock?

A VAR would give exactly opposite answers to those two questions. If you take the answer to the first question, reverse all the signs, you would get the answer to the second question. (That's only strictly true for a linear model.)

I think the answers to the two questions would be pretty much the same. The immediate response would be: "WTF!?".

If the Bank of Canada had private information, it would be much easier for markets to interpret the Bank's surprising action. It would still be a surprise, that they could not have forecast, but it would not lead to a "WTF!?" response. In the first example markets would assume that the Bank's private information revealed that aggregate demand was stronger than the public forecast. In the second example markets would assume that aggregate demand was weaker than the public forecast. And so you would get opposite answers to the first and second questions.

But notice that what we observe would be the effect of two shocks, not one. The first shock is the revelation of the Bank's private information; the second shock is the Bank's response to that private information. We would observe only the sum of the effects of those two shocks. And that second shock isn't really a shock. The market is inferring the Bank's private information by assuming that the Bank is responding to the private information according to what the market believes is the Bank's response function. The Bank's response is the forecast response, conditional on the inferred private information. For example, if the market assumed the Bank was responding correctly to its private information, to keep future inflation anchored at the 2% target, the VAR would tell us that monetary policy "shocks" have zero effect on expected inflation.

Now the Bank of Canada does not really have any private information. (An academic economist who joined the Bank for a year tells an amusing story about his asking for the secret data when he first arrived, and being told there wasn't any.) The only private information the Bank has are its own interpretations of the public data.

We saw a (very small) WTF?! moment recently when the Bank unexpectedly cut the overnight rate from 1.00% to 0.75%. (Some bond traders seemed upset that the Bank did not announce in advance it was going to cut, which strikes me as strange, because if the Bank had announced the cut one month prior to the actual cut, then bond traders would presumably have been equally upset one month previously because the Bank did not announce that it was going to announce that it was going to cut.) But it is unlikely that markets interpret the Bank's unexpected actions as a sign that the Bank has abandoned its 2% inflation target. More likely they figure that the Bank's interpretation of the public data must be different from what they expected the Bank's interpretation to be.

So if the Bank unexpectedly cuts the overnight rate, how that affects market expectations of future inflation depends on: how the market revises its beliefs about how the Bank interprets the data; and how the market revises its own beliefs about how to interpret the data. For example, if the market thinks the Bank is better than the market at interpreting the data, and so revises its own interpretation accordingly, the VAR would tell us that monetary policy "shocks" have zero effect on expected inflation.

The market (presumably) wants to know how the Bank interprets the data, both because the Bank's interpretation may be right, and because, even if the Bank's interpretation is wrong, knowing how the Bank interprets the data helps the market forecast the Bank's future actions. And the Bank (definitely) wants to know how the market interprets the data, both because the market's interpretation may be right, and because, even if the market's interpretation is wrong, knowing how the market interprets the data helps the Bank forecast the market's future actions. The Bank of Canada looks at market expectations of inflation (for example) when it decides whether to raise or lower the overnight rate. An increase in expected inflation, even if it's a purely irrational increase, will require the Bank to raise the overnight rate to prevent actual inflation rising above target. The Bank does not just do things, it does things for a reason, and the effects of what it does depends on what it says about those reasons, and whether market participants believe what it says about those reasons.

Imagine the exact same increase in the overnight rate with 4 different explanations:

a) "Our new model shows the economy is much stronger than our old model says it was."

b) "We decided to increase the inflation target from 2% to 3%, figured expected inflation would rise very quickly to the new target, and didn't want real interest rates to drop too much."

c) "We've turned Swedish, and decided to raise the overnight rate to reduce asset prices, even if it means inflation drops below the 2% target temporarily."

d) "The person responsible has been fired, and normal monetary policy will resume shortly."

We are not going to get the same response across all 4 cases.

Then there's a whole other question about VARs that I have blogged about before. The market has information; the Bank has information; and the econometrician doing the VAR has information. And in nearly all cases (unless the econometrician is using final revised data which differs from real time data, which raises a whole other question) the econometrician has less information than the market and the Bank. Because he would run out of degrees of freedom unless he drew the line somewhere on what data to include in the VAR. So what looks like a monetary "shock" in the VAR might simply be the monetary policy response to a variable that is missing from the VAR. It's like if the Bank of Canada sometimes flips a coin to decide whether to raise or lower the overnight rate, and the econometrician knows for sure that the flip of the coin does not affect the economy except via its effect on what the Bank of Canada does, because the econometrician knows for sure he has already included all the variables that matter in his VAR. That's how randomised experiments are supposed to work. But that's not (I hope) how the Bank of Canada works.

A VAR study of the effects of monetary policy "shocks" is trying to answer a question we hope we never have to ask, and to which the only sensible answer is "WTF!? Why the hell did the Bank do that?"

[This post is a long riff off Jeff's excellent comment on Scott Sumner's very good post.]

Comments

[Scott Sumner]

WTF! How can there be no comments to this excellent post? I have my own pathetic effort here:

http://www.themoneyillusion.com/?p=29304

[marcus nunes]

Nick, As they say, garbage in, garbage out. Economists have become enamoured with "tools" and "sophisticated techniques". What has gone missing after the "tool/technique revolution" is reasoning!

[James in London]

As someone in the markets, this is an excellent description of how I see many "financial markets" economists spending their days. They are more psychologists, or even psychiatrists, than economists. What did Fischer say? What did Fisher just say? What will Yellen say? How could they think that? Was Draghi really stuck in the lift to that press conference or was the German opposition to ECB QE almost scuppering it? Or is he cracking up under the pressure of the job? What did the Atlanta Fed Nowcast just do in response to the latest data releases? How bad was the weather in the U.S. on average, this Winter? What does the Fed think about it? What will they think about it?

[Nick Rowe]

Scott: thanks! You are asking deeper and harder questions, about free will and what monetary policy means. I've ducked those questions here. But I think this whole thing is somehow related to your "never reason from a price change" thing. What caused the price/Bank of Canada's overnight rate target to change?

I too was wondering why no comments. I thought that maybe people objected to my bad language? Mark Thoma didn't link to it, though I can't complain, because Mark links to more of my posts than always really deserve it, though I thought this post was more deserving than some of my others.

marcus: I think that VARs are probably telling us something useful, and I'm glad people are doing them. But I think we need to think about what exactly it is they are telling us.

James: I'm very pleased to hear you say that. It was what I suspected, but I don't have the first-hand knowledge that you do.

[Kenneth Duda]

I love this post, Nick. Beautiful illustration of the central nature of expectations in monetary policy. I especially love your example of the four different stories the bank could tell around an unexpected rate hike (economy looks strong, or we raised our inflation target, or we are going Swedish, or it was just a mistake that we'll fix shortly), because it is so obvious how the market response would be night-and-day different depending on which explanation accompanied the exact same rate hike, which in turn illustrates the uselessness of studying the effects of rate hikes. Never reason from an interest rate change...

-Ken

Kenneth Duda
Menlo Park, CA

[Scott Sumner]

Nick, I doubt anyone objected to the language, perhaps the VAR topic is not well understood outside academia. Heck, I'm in academia and only have a limited understanding of it.

My biggest frustration is that I can't get any real pushback from the mainstream on my policy "stance" crusade. Everyone seems to think I'm crazy for thinking money wasn't easy in 2008-09, but no one gives me a reason why.

[Nick Rowe]

Thanks Ken!

Scott: I have a limited understanding of VAR too. But don't tell anyone.

I keep waiting for some real pushback from the VAR people, but I don't get any. So I suspect these problems are either ones they know about, but don't want to advertise, or else didn't know about, and don't want to advertise that either. Or maybe they haven't read this, or simply can't be bothered.

[JKH]

The Bank of Canada is constrained in that it changes rates discontinuously with respect to both magnitude and timing (like all central banks I think) – it generally moves in “chunks” of 25 basis points and it generally moves at scheduled meetings. It seems obvious that the Bank’s recent move had a lot to do with the anticipated effect of lower oil prices. I would guess that in moving it thought it was minimizing the negative consequences of being wrong in whatever decision it made. The risk of not moving was the risk of negative data coming out rapidly over the subsequent 6 weeks, with the Bank being perceived as being behind the curve. And given the relatively short distance to the zero bound, it made sense to use the first part of that distance as effectively as possible, rather than risk being squeezed by the necessity of making a bigger move at a later date. There’s only so much room to work with – and that’s a precious scarce resource in Canada’s case. Whereas the risk in moving is only the risk of an eventual tightening cycle starting a bit sooner than otherwise might be the case. It was an insurance policy whose cost was far less that the worst outcome of not taking out insurance.

I don’t know how all that fits into a VAR model, but I would think the reality of those discontinuities in the process – in rates and timing – should be important. The path of rates would look a lot different if the Bank was able to change rates by as little as a basis point and change them every day.

[Nick Rowe]

JKH: that sounds to me like a sensible defence of the Bank's decision. (Personally, I was unsure at the time whether the Bank should stay at 1.00% or cut to 0.75%, and only marginally voted for 1.00%)

If the econometrician did not include oil price in the VAR, the cut to 0.75% would look like more of a "shock" than it was.

[K]

Re; a central bank's access to private information or "secret data", some banks do have it. For example, the Reserve Bank of Australia conducts a monthly business survey that is not published, which includes confidential information passed on by local companies. It also has access to the bank regulator's unpublished survey of lending standards. The bank also has very deep pockets in buying private-sector data and so has a more complete picture of the housing and commodities market than any single investor or private bank.

[Nick Rowe]

K: Interesting. I didn't know that. The Bank of Canada publishes its quarterly business and loan officer surveys.