Archive for the Category Monetary Theory


Playing with toy models

Back in 2002, Bennett McCallum did a really nice survey piece on contemporary monetary economics.  The best parts are his insights into some of the controversial issues, but I’d like to focus on something else (in the equations I changed the style a bit—I can’t do subscripts and deltas).  Here’s McCallum, with adjustments:

A striking feature of the typical models in the NBER and Riksbank conferences is that they include no money demand equations or sectors. That none is necessary can be understood by reference to the following simple three-equation system.

yt = α0 + α1Et(yt+1) + α2(Rt − Et(dpt+1)) + α3(gt − Et(gt+1)) + vt (1)
dpt = Et(dpt+1) + α4(yt − ynt) + ut                                           (2)
Rt = µ0 + µ1(dpt − dp∗) + µ2(yt − ynt) + et                               (3)

Here equations (1)–(3) represent an expectational IS equation, a price adjustment relationship, and a Taylor-style monetary policy rule, respectively. The basic variables are yt = log of output, pt = log of price level, and Rt = nominal one-period interest rate, so dpt represents inflation, Rt − Et(dpt+1) is the real interest rate, and yt − ynt ≡ ˜yt is the fractional output gap (output relative to its capacity or natural rate value, whose log is ynt). Also, gt represents the log of government purchases, which for present purposes we take to be exogenous. In this system, Et denotes the expectations operator conditional on information available at time t, so Et(pt+1) is the rational expectation formed at t of pt+1, the inflation rate one period in the future.

(In the original dpt was “delta” pt.  I also corrected a typo in equation 2.)

Now let’s do something similar in the MM model.  In equation 3 we will replace R in the previous model with NGDP futures prices (NGDPF), which is the instrument of monetary policy.  (It’s not really the instrument, the base is.  But then the fed funds rate is also not really the instrument, the base is. Both NGDPF and R are financial market variables that are observable and controllable in real time.)  The NGDP futures price equals the target value, plus a systematic error (SE).  The systematic error is the predictable part of the central bank’s policy failure.

In equation 2, actual NGDP reflects both the predicted value (previous NGDPF), and an unforecastable error term (et.)  The employment gap in equation 1, more specifically the gap between actual hours worked and the natural rate of hours worked, is alpha times the NGDP gap. Alpha is probably roughly one.  The hours worked gap is thus roughly equal to the difference between actual and target NGDP growth.  Between mid-2008 and mid-2009, NGDP fell about 8% below trend, and hours worked also fell about 8% below trend

(Ht – Hnt) = α(NGDPt – NGDPTt)      (1)

NGDPt = NGDPFt-1 + et                      (2)

NGDPFt-1 = NGDPTt + SEt-1            (3)

And all this boils down to:

(Ht – Hnt) = α(SEt-1 + et)                    (1)

Where the monetary policymaker determines SEt-1.

If they do NGDP futures targeting, then SE = 0.  Let’s use an inflation targeting analogy.  The ECB is targeting inflation at 1.9%, and last time I checked the 5-year inflation forecast in the German TIPS market was about -0.1%.  So in the eurozone SEt-1 is roughly negative 2%.  If the ECB pegged CPI futures prices at 1.9% inflation, then the SE would rise from negative 2% to zero.  Actual eurozone inflation would be 1.9% plus et.  Under NGDP futures targeting, SE is equal to zero and the hours worked gap is a random walk.

Of course this oversimplifies everything (but then so does the 3 equation model described by McCallum.)  Hours worked would actually depend on Wage/NGDP, or even better Wage/(NGDP/person). Further refinement would include shocks to labor’s share of national income.  Nominal wages depend on expected future NGDP, but are also very sticky, adjusting slowly when pushed away from the desired Wage/NGDP ratio.  That would all have to be modeled.

The NGDPF market could be modeled as follows.  Define the ratio of next period’s NGDP and the current monetary base as “quasi-velocity” (QV.):

Mt*QVt = NGDPt+1

Then create a futures market in QV, and tell traders that the base will be set at such a level that the base times equilibrium QV (in the futures market) is equal to target NGDP (NGDPT.) That replaces the Taylor rule. And by using a velocity futures market, you avoid the circularity problem discussed by Bernanke and Woodford (1997). QV is obviously a function of the nominal interest rate. (This is based on a 2006 Economic Inquiry paper I did with Aaron Jackson.)

There is nothing at all like the IS relationship, as equation 2 is simply an application of the EMH (plus the assumption that the NGDP futures price is an unbiased forecast of future NGDP.) The hours worked gap is the closest thing to a Phillips Curve.  If you want output gaps, you can derive them from the hours gap equation using a variant of Okun’s Law.  Once you have real output, you can also derive the price level, as NGDP is already determined.  But why would you want those things?  The hours gap equation measures the business cycle, and NGDP is superior to the price level as a proxy for the welfare costs of inflation.  And if it’s long run economic growth you are interested in, then why mess around with monetary models?

I see several differences between the standard approach and my toy model:

1.  I use NGDP futures prices, which is not subject to the ambiguity associated with nominal interest rates.  NeoFisherites will not misinterpret my policy equation.  And it’s more efficient, as it cuts out the middleman and uses open market operations to directly target NGDP futures, which is what you care about.

2.  My “Phillips Curve” uses NGDP and not inflation (the switch from unemployment to hours is not so important.)  Inflation is problematic, because it might reflect either demand or supply shocks. So the standard model needs to account for supply shocks.  NGDP is better, as it only reflects demand shocks, which are what drive any Phillips Curve relationship.  It simplifies things.

This is just a toy model; perhaps someone else can create a real model along market monetarist lines.  As a blogger this is the approach I like best.  As director of the Mercatus Monetary Policy Program, I want the model that the rest of the profession finds most convincing.  I imagine that would be something more along the lines of a Nick Rowe model.

Cash and the zero lower bound

Let’s review the (alleged) zero bound problem.  The nominal interest rate falls to zero.  The Fed injects base money, and banks choose to hold it as excess reserves.  The Fed could try to force banks to lend it out with negative interest on reserves (IOR), but in that case deposit rates would go slightly negative and the public would pull the money out and hold it as cash.  The existence of cash creates an effective zero lower bound on nominal interest rates, or perhaps a lower bound of a few basis points negative, as there are costs of holding cash.

Many Keynesians think that this in some way makes monetary stimulus ineffective.  This is wrong, but let’s put that issue aside and consider another issue—does eliminating cash solve the zero bound problem, at least from the perspective of monetary policy ineffectiveness?  And the answer is clearly yes.  If you eliminate cash then the medium of account is 100 percent bank reserves.  If the Fed charges a negative 6 percent rate on bank reserves then the demand for bank reserves would plunge much lower, and AD would soar much higher. What happens to market interest rates in that scenario?  I’m not sure, but it doesn’t matter.  Eliminate cash and you definitely eliminate the zero bound problem on the policy rate.  The Fed can again use interest rates (IOR) as their policy lever.

Tyler Cowen links to a John Cochrane post that discusses the Keynesian argument for eliminating currency.  I agree with Cochrane that eliminating cash is a really bad idea, for standard libertarian reasons.  But Cochrane misses the point when he argues that people can still earn zero rates of return on other assets, such as stamps, gift cards and prepaid taxes, even if cash were eliminated.  Stamps,  gift cards and prepaid taxes are not the medium of account, only cash and bank reserves count.  If you eliminate cash and charge a strongly negative rare of bank reserves, the hot potato effect kicks in with a vengeance. Monetary policy is all about changes in the supply and demand for the medium of account.

Ironically, despite the fact that Cochrane teaches at the University of Chicago, he uses a strongly interest-rate oriented approach to monetary economics.  Milton Friedman used to insist that Keynesians kept making basic mistakes by assuming that monetary policy could be thought of in terms of market interest rates. Friedman was right, focusing on interest rates causes nothing but confusion.  (And recall the neo-Fisherian debate, which also got on the wrong track by assuming that changes in fed funds interest rates were “monetary policy.”)

PS.  I’m skipping over the dubious assumption that investors would be able to park trillions of dollars in zero interest gift cards in a negative IOR scenario.  My point is that even if they could, it would not prevent negative IOR from solving the zero bound “problem,” which of course all market monetarists already know is not actually a problem.

My macro toolkit

I’ve begun reading a very interesting book by the brilliant Steven Landsburg, entitled The Big Questions.  I find that we share a taste for contrarian opinions.  Of course Steven is much more skilled at defending his views.  Here’s something that caught my eye:

I sometimes hear economists defend the unrealism of their models thusly: “Economics is an infant science. Today our models are unrealistic; a decade from now, they’ll be a little so, in a decade from then little less. Eventually we’ll have realistic models that make accurate predictions.”

That, I think, is pure poppycock. Our predictions are not, and never will be, based on models; they’re based on informal reasoning. We study models because they own our reasoning skills. We can figure out what happens in these models and thereby develop a good intuitive feeling for what sorts of reasoning are likely to be productive.

In this we are no different from, say, physicists.

. . .

When economists can’t do is tell you what interest rates will be eighteen months from now. Neither can the physicists. You could, I suppose, point to that as a failure of modern physics. After all, interest rates are determined by physical processes in the brains of bond traders; isn’t that the stuff of physics? The answer, of course, is that physical (or economic) models are not designed to make precise predictions of complicated phenomena outside the laboratory.  They are designed to hone the intuition.

Great stuff.  I used to complain that physicists were horrible at predicting earthquakes, or the weather next month.  Steven has the courage of his convictions, and finds even deeper flaws.  :)

So I decided to sit down and try to make a list of my money/macro toolkit.  Here’s what I came up with off the top of my head:

1.  The hot potato effect (AKA Quantity Theory of Money.)

2.  The interest elasticity of money demand

3.  Value of money = 1/P (or 1/NGDP, or 1/forex prices)

4.  Money neutrality

5.   The liquidity effect

6.  The income effect

7.  The price level effect

8.  The Fisher effect

9.  Money superneutrality

10.  The Natural Rate Hypothesis (Exp. augmented Phillips Curve.)

11.  Sticky wages and prices.

12.  Nominal debt contracts

13.  Non-indexed capital income taxes

14.  Money illusion

15.   Purchasing power parity

16.   Interest parity theorem

17.   current account deficit =  capital account surplus

18.   Consumption smoothing

19.   Okun’s law

20.   Wage tax =  consumption tax =  universal 401(k)

21.   Exchange-rate overshooting

22.   Balassa-Samuelson effect

23.   Optimum quantity of money

24.   Efficient markets hypothesis

25.   Arbitrage

26.   Asset purchases =  asset sales

27.   Ricardian equivalence

28.   Crowding out

29.   Monetary offset of fiscal policy

30.   Policy impotence under fixed rates

31.    Temporary versus permanent monetary injections

32.   Downward-sloping labor demand schedule

33.   Expectations hypothesis of the term structure

34.   Liquidity premium hypothesis of the term structure

35.   Laffer curve effect

36.   Solow growth model

37.   CAPM

38.   Tax equivalence: consumer and producer taxes

39.  Tax equivalence: import and export taxes

40.   Export subsidies neutralize import taxes

41.   Zero bound on nominal interest rates

42.  Wicksellian equilibrium interest rate

43.  Identification problem

44.  Lucas critique

45.  Rational expectations

46.  AS/AD model

47.  Policy credibility

(I’m sure there are dozens I’ve forgotten)

Some of these tools are based on more basic tools.  Thus Dornbusch’s overshooting model relies on the QTM, PPP, liquidity effect, price level effect, ratex, and IPT.

Some economists are really good at zeroing in the the proper tool to employ in a given situation. Paul Krugman is perhaps the best in the macro blogosphere. Among academics, Bennett McCallum is excellent.  Keep in mind that this is just one skill among many.  Thus about 90% of the time I would agree with John Cochrane on policy issues more than with Paul Krugman, and yet on methodological issues I’m far closer to Krugman.  I tend to think the profession overrates the importance of things like micro foundations and general equilibrium, although for certain problems a GE model is appropriate.

Regarding Landsburg’s opening remarks about progress in economics, I can’t help thinking of Milton Friedman’s claim (made in the 1970s) that in the past 200 years macroeconomics had merely gone one derivative beyond Hume.  Today I can proudly say we are ahead of Hume in three areas, monetary superneutrality (the extra derivative), rational expectations, and the EMH.  The latter two also represent advances over Friedman.  Unfortunately, on the liquidity trap the profession still lags behind John Locke.  (Yes, Landsburg’s point was slightly different.)

Over at Econlog I repeat the Landsburg quotation, and apply it to a specific example.

PS.  David Beckworth has recently been showing off his artistic skills.  I’m honored to be portrayed here and here.

Update:  In this op ed, John Cochrane shows off one of his best skills, brutally skewering Keynesianism.

Inflationistas and liquidity trappers

For six years Paul Krugman has been engaged in an intellectual war against the forces of evil on the right.  Those who claim that monetary stimulus would lead to high inflation.  Over that same period I’ve been engaged in a three-way struggle; market monetarism against the forces of misguidedness on both the left and the right.  (Unlike Krugman I believe my opponents are well intentioned.) Monetary stimulus won’t lead to high inflation, and it’s not ineffective.  For once I’m the sensible moderate.  Now the battle continues—and this time it’s Krugman’s post that needs correcting:

Switzerland has never paid interest on reserves — and lately it has taken to doing the opposite, charging banks 0.25 percent for the privilege of parking their money at the central bank. So has the Swiss National Bank’s huge increase in the monetary base, which dwarfs what the Fed has done, produced inflation?

Well, look at the included chart. Monetary base up by a factor of eight. Money supply up by much less, because banks didn’t lend the funds out. And consumer prices flat, indeed flirting with deflation.

This is all exactly what a basic liquidity trap model — the one I laid out in 1998 — predicted. So the inflationistas are finally going to concede their mistake, right?

As I’ve noted before, the 1998 model doesn’t say monetary policy is ineffective, indeed soon after it was published he was using the model to argue against fiscal stimulus and in favor of monetary stimulus in Japan.

In 2010 the Swiss franc had become too strong for comfort, and the Swiss National Bank was buying up lots of foreign assets to hold down its value.  By then Krugman had become very skeptical of the effectiveness of monetary stimulus at zero rates:

Oh, and about the exchange rate: there’s this persistent delusion that central banks can easily prevent their currencies from appreciating. As a corrective, look at Switzerland, where the central bank has intervened on a truly massive scale in an attempt to keep the franc from rising against the euro — and failed:

Later I pointed out that even that claim was wrong, but at least it was plausible. Beginning in September 2011, however, the claim was no longer even plausible, as the SNB depreciated the franc sharply and then pegged its value to the euro.  As I’ve argued many times, there is much in Krugman’s monetary analysis that is correct, and even ahead of his critics.  But there is one fatal flaw, shared by many of my commenters.  Krugman assumes that if a central bank has done X purchases of assets, and failed to hit its nominal target, then it would have to do more than X to hit its target.  But in the Alice in Wonderland world of monetary economics, it’s exactly the opposite; the more ambitious your target, the less you have to do.  And that’s equally true of exchange rate targets and NGDP targets.  Among the developed countries, Australia had the most ambitious NGDP target in this century, and its central bank has had to do the least to hit it.

In 2012 Evan Soltas provided evidence that as soon as the SNB started pegging the exchange rate, they didn’t need to buy anywhere near as many foreign assets to hold down the value of the SF.

Its credibility is so powerful, in fact, that the SNB has stopped having to buy up foreign currencies with new swiss franc, which it did in earnest to prove its commitment in 2011, increasing its foreign exchange reserves by 177 billion from July to September. It hasn’t had to defend at all the value of its currency against appreciation since September, despite what should be enormous pressures. (See here and here for the data.) That is truly remarkable, when you zoom out for the macroeconomic big picture.

That is the power of credible monetary promises. And we can do the same thing with the price level path, of course, managing correctly the striking strength of market expectations. All it takes is the appropriate use of the expectational channel; re-establish 5 percent annual NGDP growth as did the SNB for its currency, and then the market will do the rest for you.

I found some monetary base data that is quite interesting.  From January to September 2011 the Swiss monetary base soared from 79b SF to 253b SF.  That’s Zimbabwean money printing, and it shows why Krugman is so contemptuous of the inflationistas.  Switzerland got essentially zero inflation.  But then something interesting happened; after the currency was depreciated and pegged at 1.2 SF/euro, the base actually fell to 215b by May 2012.  Once investors stopped thinking the SF was going to move ever higher, they no longer had a strong incentive to speculate in that asset. It became easier to defend the currency.

Alas, there was one more attack in mid-2012, as eurozone investors worried about a collapse in the euro.  Naturally, in that environment the SF would be attractive at even a zero expected rate of return.  The base rose again to 349b SF in September 2012, at which point growth slowed sharply (it’s 376b today.)  More importantly, the 1.2 SF/euro peg held.  Krugman was wrong, currency depreciation is not difficult if it is followed up with a level targeting regime.

With the recent collapse of the Russian economy, the SNB imposed a negative 0.25% interest rate on reserves.  So I suppose you could call that a “problem,” that is, if having the rest of the world be willing to pay you to accept their loans is considered problem.  Personally, I can think of lots of other European countries that would be happy to trade places with Switzerland.  Starting with Greece, and ending with . . . let’s face it, except for Norway wouldn’t any of them rather be in Switzerland’s shoes right now?

The recent success of the SNB and the BOJ in their attempts to depreciate their currencies is pretty conclusive evidence that the liquidity trappers are wrong.  Yet Paul Krugman continues to trumpet his successes against the inflationistas, which quite frankly is like shooting ducks in a barrel, and ignore the monetary theory that is superior to both the crude quantity theory and crude liquidity trap Keynesianism. The only macro theory capable of explaining all of the major stylized facts of the past 6 years.

The theory that didn’t even have a label until Lars Christensen named it in 2010.

Krugman on the limits of monetary policy

Here’s Paul Krugman, in his pessimistic mood:

You might think that it’s a fundamental insight that doubling the money supply will eventually double the price level, but what the models actually say is that doubling the current money supply and all future money supplies will double prices. If the short-term interest rate is currently zero, changing the current money supply without changing future supplies — and hence raising expected inflation — matters not at all.

And as a result, monetary traction is far from obvious. Central banks can change the monetary base now, but can they commit not to undo the expansion in the future, when inflation rises? Not obviously — and certainly “credibly promising to be irresponsible”, to not undo expansion in the face of future inflation, is a much harder thing to achieve than simply acting when the economy is depressed.

Just to be clear, Krugman is not saying the central bank must promise a specific future money supply on a specific date, he’s saying the expected future money supply must be large enough to produce a specific expected future inflation rate (or price level.)

There are several possible solutions to the credibility problem.  One that both Michael Woodford and I have discussed is level targeting.  Suppose the central bank always falls short of its price level or NGDP target by 1%, due to a lack of credibility.  You might argue that this describes the current situation in Japan, for instance.  If the central bank has a level target, that shortfall only has significant macroeconomic effects in the very first year.  After that the level of the target variable continues to fall 1% below target, but the growth rate of the aggregate (which is what really matters) is always on target (after the first year.)

A second solution is to adjust the monetary base as needed to peg the price of CPI futures, or NGDP futures.  That will keep expected future growth in the nominal aggregate right on target.  If that seems “to good to be true,” it’s because it exposes the fact that worry about “liquidity traps” is actually worry about something else—the size of the central bank balance sheet.  But in the long run the central bank balance sheet will be smaller with a more expansionary policy, and perhaps (as the Swiss central bank showed a few years ago) even in the short run. If the central bank balance sheet is too big for comfort when you are hitting your target for expected future inflation, or expected future NGDP growth, then raise the Price level/NGDP target path or lower the rate of interest on reserves.

In my view this is where Krugman goes off course.  He assumes that if the central bank has done a lot, and has still fallen short, it would have had to do even more to succeed—bleeding into fiscal policy. In fact, just the opposite is true.  The central banks that succeed are those (like the Reserve Bank of Australia) that do the least. That’s because faster NGDP growth leads to a much lower desired ratio of base money to GDP, and hence smaller central bank balance sheets.

Krugman continues:

Just to be clear, I have supported QE in both Britain and the US, on the grounds that (a) central bank purchases of longer-term and riskier assets may help and can’t hurt, and (b) given political paralysis in the US and the dominance of bad macroeconomic thinking in the UK, it’s all we’ve got. But the view I used to hold before 1998 — that central banks can always cause inflation if they really want to — just doesn’t hold up, theoretically or empirically.

I seem to recall that Krugman was quite pessimistic about the ability of the BOJ to succeed in producing inflation, at least a few years ago.  But when they raised their inflation target to 2%, they did succeed in moving from deflation to mild inflation (albeit still short of the 2% goal.)  The good news is that we now know that the Japanese government can sharply depreciate the yen anytime it wishes to (something else that Krugman had originally doubted.)  That means the BOJ can inflate–it’s just a matter of how committed they are to make it happen.  In a sense this is also Krugman’s view (when he’s in the more optimistic mood), and he’d undoubtedly argue that the political push from Abe helped the BOJ.  In the past Krugman seemed to think fiscal stimulus was an easier sell politically.  That may be true in a few cases, but in Japan monetary stimulus has turned out to be the easiest part of the three-part reform project.  And monetary policy doesn’t have to worry about fiscal offset, in the way that fiscal policy must worry about monetary offset.

On the other hand, my recent Econlog post on the ECB shows an almost Krugmanian level of pessimism.  I just don’t see the institutional resolve at the ECB to raise inflation up to their 1.9% target. Europe badly needs to rethink everything they are doing, from the ground up.

HT: Ken Duda