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I'm a little confused about this. It seems like you are saying at first that monetary policy is not deterministic and the saying that if it is deterministic, it will have no shocks. The latter point is true by construction of course, but then isn't M(t)=bX(t)+e(t) not the correct model? (Or, more precisely, if you had the correct bX(t) and e(t)=0 for all t--meaining, M(t) is determinate--you would estimate e(t) to be zero for all t and when you tried to run the regression, you would get everything fitting perfectly and the effect of monetary shocks would not exist because there would be none--neither in reality, nor in your model. Do in other words the model would be accurate and not lead us into any particular confusion....?

It seems to be that there must either actually BE some shocks, like the board of governors rolls 2 ten-sided dice to determine policy, in which case it is not terminate, or the model has to be wrong, (something is in the true X(t) that is not in the model) in order to get any errors in the model at all. Of course, the first case seems like a stretch and in the latter case, since we don't know what is causing the shocks, it may be a stretch to call them "monetary shocks" but if by "monetary shock" we simply mean "whatever affects monetary policy which is not in the model, then there's nothing crazy going on is there? (Maybe I'm missing the point, I'm not an econometrician.)

Mike: (I'm not an econometrician either!)

The deterministic case is just the limiting extreme, that shows more clearly how wrong it is to define "monetary shocks" in that way. But the same point remains true even in the more general indeterministic case.

But if it IS indeterministic, then there are some actual shocks and if there are actual shocks and your model is right (yes, a heroic assumption) then what you estimate is actually the effect of the shocks. Right?

For what it's worth, I'm willing to believe that monetary policy is close to deterministic and the things people generally capture when they try to model the shocks are mostly, in fact, errors in their models (I'm not well versed in the empirical research on this). But I don't see this as a fundamental econometric flaw, just a poorly fit model.

Mike: No. You are missing the whole point of this post (which may be my fault, for not being clear enough). It's about what we mean by "monetary shocks".

Well, I had a feeling I might be missing it. What do we mean exactly? Do you have a definition of "monetary shock" in mind that is independent of a statistical model or are you basically saying there's no such thing?

(For the record, I'm not sure I TOTALLY missed it, this was sorta my question to begin with.)

'And so "monetary shocks" would explain 0% of anything, because there weren't any. 100% of macroeconomic fluctuations were caused by other, non-monetary shocks.'

When we look back at at a period macroeconomic fluctuations, how will we be able to tell what was down to the wrong monetary policy reaction function and what caused by other, non-monetary shocks?

Mike: A "monetary shock" should be defined as "any shock caused by the central bank not following the best monetary policy" (i.e "doing something daft").

And we know (at least we think we know) that setting M(t) or i(t) or whatever by tossing a coin (which is what the e(t) represents) is *one* daft thing that central banks might do. But it is certainly not the *only* daft thing that central banks can do. There are lots of deterministic things that are daft too.

Something like that is the theoretically correct definition of "monetary shock". Trouble is, as MF notes, it's not at all easy to know what was daft, because we don't know what is the best monetary policy reaction function. Except in a macroeconomic model that we have built ourselves. But when we see the same sorts of symptoms in the real world that we know we would observe if the Central bank did something obviously daft (like tossing a coin), then we figure that those symptoms are also caused by the central bank doing something daft, though less obviously daft.

Yep, macro is hard.

Long term listener, first time caller :)

I am with Mike. Nick you've said that "estimate of the monetary policy reaction function is correct." To me it says that bX(t) is true monetary policy. So any deviations of M(t) from bX(t) are monetary shocks (unexpected deviations from true and correct policy bX(t)).

What caused the Great Depression again?

I think there's two different effects at play.

The first effect is what the econometrician measures: the departure of the money supply from it 'should' be, given a presumed monetary reaction function b(X). This isn't meaningless in the real world, because central bankers would generally agree that their actual reactions differ from their ideal reactions. For example, central bankers have to make decisions based on first reports of GDP/inflation, whereas these variables are routinely significantly revised.

Additionally, central bankers try to define policy in terms of hidden 'root' variables like de-noised inflation rates, but since the universe is causal we don't have proper central moving averages for current variables: bankers have to look at old data.

This means that, for a well-intentioned central bank that does not deviate from its known policies, we can model the money supply as M(t) = b(X(t)) + (b(X'(t))-b(X(t))), linearizing as M = b·X + b·(X'-X). That second term comprises your e(t), and it's both estimatable and meaningful.

However, you're also quite right to say that it's not particularly relevant. The central bank's opinion of the current state of the economy is reasonably close to the truth, it's just that it's possibly chosen the wrong reaction function. That might be following inflation as the 'dog that didn't bark', or by pursuing deliberately slow responses to demand shocks.

OK. Clearly I haven't written this post clearly enough.

Here's what "M=bX+e" *might* mean. The CB does M=bX, and then flips a coin at the last minute to either add or subtract \$1 billion.

Excellent. Very good way of explaining it--wish I'd thought of it.

Nick, what you are really saying is that policy doesn't have to be unpredictable to be bad. Policy "shocks" in the econometrician's sense are policy that was not predicted. There is a tendencency in the profession to think that anticipated monetary policy can't have bad effects, and that's what you're really disagreeing with.

@Jeff: I think you've hit on something there.

Monetary policy since the financial crisis can be generally explained by a single prevailing philosophy, that if central banks "do nothing," inflation tends to increase over time. That means that any monetary stimulus (relative to "doing nothing") will be of a short term, transitory nature in response to an unforeseen event, whereas monetary tightening might have to be deep and persistent to "break the back" of inflation.

That is, central banks learned too-narrow of a lesson from the 1970s. They stand vigilant to re-enact the Volcker recession, whereas economic commentators have to invent entirely new language to describe persistently tight money and/or weak demand.

Part of the problem might be that we have plenty of dramatic anecdotes about hyperinflation, but the economy itself isn't symmetric: a 'deflationary spiral' doesn't look like a hyperinflation with the signs reversed. Our closest anecdote is the Great Depression, but even identifying what monetary policy was over that period is unintuitive, hence books like Sumner's.

As a result, we see central banks facing some very real and fundamental policy differences. They don't even agree on what dramatic easing would look like, so we're left with the very odd idea that central banks can lose credibility in raising inflation. When talking about reducing inflation, we now equate 'credibility' with 'nerve': central banks can lower inflation but might not be willing to do it. As Nick Rowe has pointed out before, this wasn't a consensus opinion in the 1970s.

@Nick Rowe:

I wish that central banks would do that coin-flipping thing. Then, we'd have widespread agreement that policy as-implemented diverged from ideal policy, so we'd have consistent natural experiments about whether the underlying modeling of "ideal" policy was in error.

Scott: thanks!

Jeff: yes. Though I think we need to distinguish between "unforecastable" and "unexplainable/toincoss". The latter is a subset of the former.

Majro: We may have natural experiments which come close to a cointoss.

The macro fluctuations caused by the cointoss "monetary shocks" put a lower bound on the macro fluctuations caused by bad monetary policy (since we are pretty sure that cointosses are bad, but not the only way monetary policy can be bad).

Nick,

"Monetary shocks mean the central bank chose the wrong monetary policy reaction function."

No such thing as positive shocks? Suppose the central bank goes on a coin flipping binge for a while and then switches back to something more sensible. Is this not a positive shock?

Also,

Central Bank reaction function to economy:
M(t) = b * X(t-1) + e(t) : X(t-1) is always backward looking data

Economy reaction function to central bank:
X(t) = c * M(t-1) + f(t) : M(t-1) is always backward looking data

To stabilize X(t), it is not enough for the central bank to just set b at some predictable value because of real worlds shocks ( f(t) ).

@Frank Restly:

> No such thing as positive shocks? Suppose the central bank goes on a coin flipping binge for a while and then switches back to something more sensible. Is this not a positive shock?

In that case, you alleviate the stochastically bad part of monetary policy, but you can preserve a deterministically bad component. Consider driving a car "straight" with shaky hands versus driving a car with steady hands and incorrect wheel alignment; the former will swerve all over the road but tend to go straight, while the latter will consistently veer off to one side.

> To stabilize X(t), it is not enough for the central bank to just set b at some predictable value because of real worlds shocks ( f(t) ).

That's remarkably untrue. Linear control systems can stabilize systems with backward-looking data, even in the presence of physical shocks, imperfect measurement, or incomplete modeling. Remember that 'b*' in this model is a matrix-vector product, not a scalar multiplication, and it corresponds to the entire monetary policy reaction function.

The Taylor Rule is one example of a simple, linear monetary reaction function, corresponding approximately to a PD Controller (no integral term; derivative modeled by Y-Y* rather than lagged inflation differences).

Majromax,

I don't think the linear control system is a good example because there are two sides (central bank and economy) both reacting to each other's movements. It is more akin to one person handling the accelerator / brake and another handling the steering wheel - both trying to get a car to a point in the distance in the quickest amount of time.

Over time (with no shocks), there will become a stable relationship between b and c. In fact if we set e(t) = 0, f(t) = 0, and b = 1/c, then the equations above reduce to:

X(t) = c * M(t-1) = 1/b * M(t-1) = 1/b * b * X(t-2) = X(t-2) : We have stabilized X(t) through time (assuming no shocks).

The problem is we don't know if the central bank is setting it's b equal to 1/c or if the economy is setting it's c equal to 1/b. So we introduce shocks ( f(t) for real shocks, e(t) for monetary shocks ) and say the central bank is setting it's b equal to 1/c and introducing monetary policy shocks ( e(t) ) to try to offset real world shocks ( f(t) ).

As a continuation:

Central Bank reaction function to economy:
M(t) = b * X(t-1) + e(t) : X(t-1) is always backward looking data

Economy reaction function to central bank:
X(t) = c * M(t-1) + f(t) : M(t-1) is always backward looking data

b = 1/c

X(t) = c * [ 1/c * X(t-2) + e(t) ] + f(t)
X(t) = X(t-2) + c * e(t) + f(t)

For stable X(t) : X(t) = X(t-2)
e(t) = -f(t) / c

Foreigners' decide they don't like your country and won't buy your goods no more. CB doesn't change anything. That's a monetary shock?

Notsneaky: "CB doesn't change anything."

Does that mean: doesn't change: price of gold, exchange rate, interest rate, money base, M1, inflation, NGDP, or what?

There are 1001 different meanings of "doing nothing". The very same shock will have very different consequences depending on which of those things the CB holds constant.

"A "monetary shock" should be defined as "any shock caused by the central bank not following the best monetary policy" (i.e "doing something daft")."

"Here's what "M=bX+e" *might* mean. The CB does M=bX, and then flips a coin at the last minute to either add or subtract \$1 billion."

Isn't the latter, coin flipping "e", something "daft"? But then "e" is a monetary shock by the former, isn't it?

I have tried to get it, maybe it makes sense but somehow I think the post mixes up the role of "b" and "e" in a confusion way.

In an econometric model "b" and "e" are always tangled. The "e" captures effects from the miss-spefied models, meaning e.g. too few or wrong explanatory variables ("b").

I think this is also confusing:

"Any deterministic monetary policy will have zero "monetary shocks","

vs

"Monetary shocks mean the central bank chose the wrong monetary policy reaction function."

What if the central bank had an deterministic but wrong monetary policy reaction function?"

Jussi: those are two different definitions of "monetary shocks"

The first one is the standard one. The second one is the one I prefer. This whole post is about my saying the standard definition is a bad one.

"Any deterministic monetary policy will have zero monetary shocks."
"Monetary shocks mean the central bank chose the wrong monetary policy reaction function."

Just my opinion, but they are both bad definitions. Perhaps this instead:

A monetary shock is a change in monetary policy stance in reaction to events outside the direct influence of both the monetary authority / central bank and market participants that utilize that central bank's preferred medium of exchange.

Meaning even deterministic monetary policy will have shocks - yes the central bank has a predetermined plan for dealing with an asteroid strike, but because an asteroid strike is a shockingly unexpected event, so too is the central bank's response to that event. And whether that central bank's response is ultimately proven right or wrong makes little difference in how shocking it was / will be.

Isn't this actually a discussion about the definition of the Central Bank's job? If I understood Nick's original post correctly, the implication is that the CB's job is something like "manage the money supply/interest rate so that the economy - which is always changing - runs smoothly over time" (whatever "smoothly" means to you...). And a corollary might be: "just because the speed of change in the economy might sometimes be greater than at other times (e.g., crises), it doesn't absolve the CB from reacting to it and managing it".

In the original example about gold, the fact that the CB failed to react to the discovery of new mines or the jewelry fashion trends means that they were doing a really bad job, and hence caused a monetary shock (the economy stopped running smoothly because of too much or too little money, which the CB did not manage). The failure to change behaviour as needed is just as much a failure, in this reading, as changing behaviour unnecessarily (like flipping a coin). If you don't define the job of the CB this way, then the idea of a monetary shock becomes meaningless. Say, if you define the job as just "setting expectations about money supply", then of course there can be no such thing as a monetary shock, only economic shocks.

Am I oversimplifying this, or missing the point?

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