# Why is the 30-year forward yen at about 50 to the dollar?

Nick Rowe likes to teach PPP with a thought experiment, asking students to imagine how they might guess an exchange rate between the dollar and a foreign currency.  Thus if you went to Japan and noticed that most prices seem to be about 100 times higher than in the US, you might guess that 100 yen equals one dollar.  Of course PPP often does not hold true, but it’s still probably the best first guess for the exchange rate, if you had absolutely nothing else to go on.

In that case, it is more useful to think of the exchange rate being caused by the Japanese price level being 100 times higher than in the US?  Or should we think about the price level difference being caused by the exchange rate?  Is this even a meaningful question?

I like to think about the two price levels as being in some sense more fundamental, as I could imagine a case with no contract between the two countries.  Then once contact is made by Commodore Perry, the exchange rate conforms to the pre-existing price levels.  But you can also imagine a new country being settled by England, and choosing to use the dollar rather than the pound.  In that case the two price levels would be determined by the choice of the exchange rate.  The adoption of the euro is an obvious recent example, which caused Italian prices to plummet dramatically.

In a recent comment section I’ve discussed the fact that the 30-year forward dollar trades at roughly 50 yen (actually 49.332).  Is that exchange rate caused by the interest rate differential, or is the interest rate differential caused by the forward exchange rate?  People in the financial markets may focus on interest rate differentials as the primary factor, as the 30-year forward exchange rate is not very liquid and seems to be roughly 50Y/\$ merely to prevent easy arbitrage opportunities, given the interest rate differential.

[I tried to see if interest parity held, but I don’t know the interest rate on 30-year zero coupon bonds.  So I took the yields on actual 30-year bonds as a proxy.  The US 30-year bond yields 3.17% and the Japanese bond yields 0.747%.  The differential is 2.423%.  Then I took 1.02423, and raised it to the 30th power, which equals 2.0508.  Then I took the actual exchange rate of 106.17, and divided by 2.0508, and got 51.77 as the implied 30-year forward yen. Is that right?]

In my view, it makes more sense to think of the expected 30-year forward exchange rate of 50 as the fundamental factor, and the interest rate differential as contingent on that expected future exchange rate.  Conversely, consider what would happen if we were to start with the interest rate differential as fundamental.  Then thinking in terms of interest rates, what would the BOJ have to do to prevent the yen from getting so strong in 30 years?  Obviously they need to make monetary policy more expansionary.  That’s how you weaken a currency.  But how do you do that in terms of the interest rate differential?  Obviously you need to get rid of the interest rate differential if you want the yen to be worth roughly 106 out in the year 2048.  But how do you get rid of the interest rate differential, while making monetary policy much more expansionary?

Let’s assume the BOJ cannot do anything about the level of interest rates in the US.  If they want the yen to be worth 106Y/\$ in the year 2048, they need to get Japanese interest rates up to 3.17% on 30-year Japanese government bonds.  Even more daunting, they must do so with a highly expansionary monetary policy.  (Cochrane and Williamson are smiling at this point.)

So how do you do that?  Normally, a decision to raise interest rates is treated by the financial markets as a tight money policy, which causes the currency to appreciate.  So the BOJ needs to get interest rates up to 3.17% on 30-year bonds, and keep the exchange rate close to 106Y/\$.  So how do they do that?  The simplest solution is to go back to Bretton Woods, and peg the yen to the dollar at 106.  If credible, that will cause Japanese 30-year bond yields to rise to 3.17%, and after 30 years the exchange rate will still be 106.  Because of PPP, Japan’s inflation rate over the next 30 years probably won’t be much different from the US inflation rate.  More importantly, the current expected inflation rate will rise to roughly 2%, just as in the US.

The fact that investors now expect the yen to be trading at about 50Y/\$ in 2048 tells you just how far away from success the BOJ remains.  This is why I say that any talk of exiting from monetary stimulus is crazy.  Monetary policy in Japan remains extremely tight, expected to produce very low inflation over the next 30 years.  They need more than tinkering; they need a dramatic regime change.  I don’t advocate a fixed exchange rate system, but that’s one example of a radical regime change that would “work”.  A better option might be level targeting, combined with a “do whatever it takes” approach to monetary policy implementation.  I.e. buy as many assets as needed to get prices or NGDP rising along the desired level targeting path.

We don’t have that regime today, which makes the 30-year forward yen a useful proxy for policy credibility.  Only when the 30-year forward yen rises far above the current level of 50 can the BOJ start relaxing.  The BOJ has had some success in boosting prices and NGDP, but very little success in convincing the markets that this policy will continue in the very long run.  It seems like markets believe that once Abe is gone the BOJ will revert to its old habits.

PS.  If the regime change is credible they won’t have to buy very many assets.

# Is Mexico now targeting the forecast?

Commenter HL directed me to this slide from a presentation by the Mexican central bank:

HL suggested that this meant the Bank of Mexico is now “targeting the forecast”.  It does sort of suggest that policy is being adopted, but it’s hard for me to be sure.  Any comments would be welcome.

Let’s recall the mistakes made by the Fed in 2008:

1. Too much weight on inflation, too little on NGDP growth.

2. Growth rate targeting rather than level targeting.

3.  Failure to target the forecast (as well as too little reliance on market forecasts.)

4.  Failure to do “whatever it takes”.

That seems like a lot, but fixing some of these problems makes the other issues much less of a problem.  Addressing problem #2 alone, or #4 alone, would have gone a long way toward making the 2007-09 recession much less “Great”.

When combined with David Beckworth’s recent post on level targeting, I’m becoming more optimistic about global trends in monetary policy.

John Taylor has been pressing the Fed to move toward a more rules-based approach.  I think Taylor is right on the big issue, although I don’t share his preference for using interest rates as a policy instrument.

I’ve always believed that the first step toward a rules-based approach is to clearly spell out the goal of monetary policy.  That should be an issue on which everyone on the FOMC agrees, once a decision has been made and voted on.  Unfortunately, the Fed has not done this.  The Fed’s policy goals are still shrouded in mystery.

The simplest solution would be for the Fed to set a univariate policy goal, say 2% PCE inflation or 4% NGDP growth.  Then spell out whether they favor growth rate targeting or level targeting.  Instead the Fed has chosen a dual target of 2% PCE inflation and unemployment close to the natural rate.  But what does that actually mean?  In order to make the goal clear, we need enough information to figure out whether previous policy was to expansionary or too contractionary.  Right now we lack that information.  Over the past 12 months, the unemployment rate has fallen to a level below the Fed estimate of the natural rate, while inflation has undershot their target.  So was the policy instrument setting 12 months ago too expansionary or too contractionary?  I don’t know, which is precisely the problem.

The Fed often objects that explicit policy rules are too simplistic, and that they need to take many data points into account, as the economy is quite complex.  OK, but that doesn’t excuse the lack of an explicit target, it just makes the target a bit more complicated.  So let’s discuss what a plausible Fed target might look like.

1.  For inflation, the Fed might worry about the distorting effects of oil price shocks.  In that case, they can use core PCE inflation, setting the target at two percent.

2.  The labor market is even more complicated.  The Fed might want to take account of both the standard U-3 unemployment rate, as well as the more comprehensive U-6.  Some would even add in the prime age labor force participation rate (PALFPR).  Here’s how a labor market indicator might look with those three variables:

Labor slack = U3 + 0.5*U6 + 0.1*(100% – PALFPR)

At the moment, U3 unemployment is 4.1% and U6 unemployment is 8.2%.  U6 is also roughly twice as volatile as U3.  The coefficient of 0.5 on the U6 rate is intended to give the two measures roughly equal weight.  The labor force participation rate is 81.8%, so 100% minus that rate is 18.2%.  I gave this variable a lower weight, because it’s partly cyclical and partly structural.  Monetary policy can only address cyclical changes.

Using these weights, my current measure of labor market slack is 4.1% + 0.5*8.2% + 0.1*18.2% = 10.02%

For simplicity, let’s suppose the Fed sets a target of 2% inflation and 10.0% labor market slack, using this formula.  (They could adjust that figure over time, as research on labor markets gave the Fed a better feel for the “natural rate” of labor market slack.)  Then the Fed would also want to create a set of “indifference curves”, each of which illustrates a set of outcomes that are equally suboptimal.  Unless I’m mistaken, that map would look like a target:

While I lack Jasper Johns’ skill as an artist, I think you get the point.  Interestingly, some conservatives get why inflation above 2% is bad, but are confused as to why below 2% inflation is a problem.  Some liberals get why high labor market slack is a problem, but don’t see why a tight labor market is a problem.  But if the Fed is serious about its targets, it should treat overshoots and undershoots of each variable as both being undesirable.  I.e., 3% unemployment is bad because it leads to future instability in the economy.  That doesn’t mean the indifference curves must be perfect circles, but they should at be least vaguely circular.

Of course I do not favor this dual variable policy goal; I favor something like 4% NGDP growth targeting, level targeting.  That looks like a point on a line, and is far easier to explain.  But even a complex target like inflation and labor market slack can be turned into a mathematical formula, which makes it possible to evaluate the effectiveness of Fed policy.

This is all the first step towards a Taylor-like policy rule.  The next step is to spell out an instrument rule.  You need to explain how and why you adjust the policy instrument.  If the instrument is the fed funds rate, Taylor would recommend something like the “Taylor Rule”, although he’s indicated that under his proposal the Fed would be free to choose its own rule, and even deviate on occasion if they spelled out why to Congress.  (Presumably he is thinking of extreme events, like the 2008 financial crisis.)  I’d use the monetary base as my instrument (it has no zero bound problem) and my rule would adjust the base according to trading in the NGDP futures market.  Whatever it takes.

PS.  Contrary to what you often read, Congress’s dual mandate does not require the Fed to adopt a complex dual variable policy goal.  NGDP targeting is 100% consistent with the Fed’s dual mandate, as it implicitly address both employment and inflation.  NGDP growth is inflation plus RGDP growth, and the latter variable is highly correlated with employment at cyclical frequencies.

PPS. After I drew up the graph, I realized that the horizontal axis should be called labor slack, not labor utilization.

# Are hawks and doves simply confused?

I say yes.

Commenter BC tried to explain why it might be rational for some people to be hawks and others end up being doves:

I think of the dove and hawk designations as denoting the bias or errors that one makes in implementing discretionary policy. Doves tend to underestimate the likelihood that low inflation is “transitory” and overestimate the likelihood that high inflation is transitory and thus tend to overestimate the amount of stimulus needed when inflation is low and underestimate the amount of contractionary policy needed when inflation is high. Vice versa for hawks. One can also think in terms of expected future inflation, which is unobservable. Doves’ inflation expectations are persistently lower than hawks’ expectations. Thus, under the same current conditions, doves tend to advocate more stimulus than hawks.

While I concede this explanation might be true, I believe it quite unlikely.  If the dispute were merely a technical disagreement about how to forecast inflation, then hawkishness and dovishness would be 100% uncorrelated with political ideology.  But that’s clearly not the case.  Being hawkish is strongly correlated with being right of center, and dovishness is correlated with being left of center.  That tells me that hawks and doves are simply confused.

Elsewhere I’ve argued that in a world of 2% inflation targets it no longer makes any sense to be a hawk or a dove.  At one time those two terms did have a coherent meaning; hawks preferred a lower inflation rate than doves.  There was no inflation target at that time.  So in 1976, hawks and doves might have disagreed about setting the fed funds target at 7%, even as they agreed that this setting would likely lead to 6.2% inflation.  I believe these two groups continue to exist because they wrongly think we still live in a world where this disagreement has meaning.

We can have a world were the inflation rate is always exactly 2%.  Or we can have a policy that tries to push inflation above 2% during some periods and below 2% during other periods (my preference).  Hawkishness and dovishness have absolutely no role to play in either of those worlds.  Some doves seem to think it’s always possible to have an inflation rate that’s higher than expected, that is, policy can be consistently “expansionary”.  Some hawks wrongly believe the opposite outcome is possible.  They are simply confused.

Hawks were right that policy was too expansionary during the Great Inflation.  But they were wrong about policy during the Great Recession.  It’s wrong to be a hawk for the simple reason that it’s wrong to always favor a more contractionary policy.  That’s like always favoring turning the steering wheel in one direction.

Doves were right that policy was too tight during the Great Recession, but they are in danger of overstaying their welcome and continuing to advocate monetary stimulus at all times.  It makes no sense to always favor an expansionary policy, as we now know that expansionary policies are stimulative only to the extent to which policy is more expansionary than expected.

People should not be either hawks or doves; they should favor easier or tighter money based on whether AD is too low or too high to hit the central bank’s target.

That does not mean we can’t have ideological debates about the proper target of monetary policy.  We can and should have those debates.  (I favor NGDPLT, at roughly 4%).  But if three of the four people in the car have voted to go to Las Vegas, the fact that the driver prefers Taos is completely irrelevant.  The driver needs to steer the car towards Las Vegas.  (The driver can demand the four go see Penn and Teller instead of Britney Spears, as compensation for losing out on Taos.)

# Cowen and Smith on monopoly and stimulus

In a recent Bloomberg debate, there was an interesting exchange.  First, Tyler Cowen:

But Noah, I have a question for you. You’ve written several columns about how the American economy is becoming more monopolistic. If true (and it is not exactly my view), that implies output could be much higher with current resources, even at full employment. A boost in demand could spur firms to produce more, rather than restricting output so much. So are you now a fan of these Trumpian deficits? They may not be your preferred form of deficit spending, but do you see them still as a net positive?

Then Noah Smith:

As you say, monopoly power could potentially increase the case for stimulus in bad times.

Actually, that’s not what Tyler said, nor is what Tyler said true.  (Now everyone will be annoyed at me.)

One of the fundamental principles of modern macro is that demand-side stimulus cannot solve real problems.  It can overcome problems such as high unemployment caused by sticky wages and prices combined with inadequate spending, but that’s all it can do.  Inefficiencies associated with monopoly are a real problem, and cannot be solved by printing money.  There are actually a number of issues here that need to be disentangled, some of which are quite subtle.

1.   Monopoly is a microeconomic problem, not a macroeconomic problem.  Thus it’s quite possible to have low unemployment rates and high levels of monopolization.  Indeed, I’d argue that’s true in America right now.  Employment in the monopolistic sector is indeed lower than we’d like, but the result of this is not unemployment, it’s workers being employed in the less efficient competitive sector of the economy.  This is important, because the mechanism by which demand stimulus creates growth is by encouraging more employment (not moving workers between sectors).  But we are already at full employment.

2.  Suppose I’m wrong, and monopolization causes the natural rate of unemployment to be higher than otherwise. Say America’s natural unemployment rate rises to French levels, due to monopolization.  Is Tyler correct in that case?  No, demand stimulus is still not called for even if monopolization causes the natural rate of unemployment to be higher than otherwise.  That’s because when you are at the natural rate, demand stimulus basically tricks workers and firms into producing more output than they’d like, by pushing up nominal spending in the face of sticky wages and prices.

So doesn’t that make us better off?  In the short run yes, but only at the cost of being worse off in the long run.  When prices are sticky, demand stimulus can reduce a monopoly’s real price, which is its price relative to NGDP.  But once the monopoly catches on to the higher NGDP, it will raise the real price again.  That might not sound so bad, but it leads to cyclical instability.  Ditto for wage stickiness.  Demand stimulus will give monopolies an incentive to hire more workers, as long as nominal wages are sticky.  That will indeed make the economy more efficient for a short time (this may have been Tyler’s intuition), but at a cost of future instability.

This is why we have independent central banks.  Because our economy is riddled with inefficient policies such as minimum wage laws and taxes on labor, our natural rate of output is suboptimal.  Demand stimulus tricks us into producing more, and we move closer to the optimal position for the economy.  But it’s not sustainable. It’s a sugar rush.  Minimum wages eventually get increased with NGDP, and workers renegotiate contracts.  In the short run, the stimulus really does make us better off as a country (with or without monopoly), but it overheats the economy and leads to a painful recession in future years.  Once mainstream monetarist and New Keynesian economists understood this problem, they decided the best we could do was to keep the economy close to the natural rate of unemployment, and then advocated setting up independent central banks that would be immune from pressure by a corrupt future president that might have a big ego and a short attention span.  (Hmmm . . . . )

Unless I’m mistaken, there is nothing particularly controversial about this post.  Think about a standard NK model, which produces an optimal policy of 2% inflation.  How would the existence of monopoly change the optimal policy?  Make it more expansionary?  But what does that even mean?  In the standard model, money is neutral in the long run.  Going to 3% inflation doesn’t have any long run benefit.  I suppose you could advocate steadily rising inflation, ending up in hyperinflation, but that won’t work if there are any welfare costs of inflation.  In fact, the optimal policy under a NK model is no more expansionary with monopoly than without.

Now I suppose there might be models where the optimal policy is more countercyclical if there is monopoly, and this seems to be what Noah is hinting at.  But that doesn’t help Tyler’s argument, as in that case policy should actually be more contractionary when unemployment is 4.1%.  And I’m not even sure that claim is true; do NK models imply that more weight should be put on output, and lesson inflation, when the economy is more monopolistic? Are there any models that do so?

PS.  Tyler might argue that the monopoly argument was not his view, just the implication of Keynesian models with which he does not agree.  But I’m saying even that’s not true.  The argument he makes is not even an implication of any sound Keynesian model that I’m aware of.

PPS.  I have a new post criticizing proposals to “experiment” with a hot economy, over at Econlog.