Friday, April 3, 2015

Bernanke and Low Real Interest Rates

As you probably know, Ben Bernanke has a series of blog posts on why we have low interest rates. My two main points are: (i) Bernanke may be missing what is most important about the phenomenon of low real interest rates; (ii) He's giving Larry Summers way too much credit.

Bernanke starts by making a very useful point, which is that conventional macroeconomic theory tells us that monetary policy can affect real rates of interest only in the short run. A couple of implications of this are: (i) Leaving aside any effects of quantitative easing (QE), there has been no change in U.S. monetary policy since late 2008, so any nonneutralities of money dissipated long ago. For example, if the Fed had, in late 2008, gone to a fed funds rate range of 1.0%-1.25% instead of 0-0.25%, and stuck with that, real economic activity in April 2015 in the United States under that alternative policy would not be significantly different from what it actually is now. (ii) If you are looking for reasons why the real rate of interest is currently low, you shouldn't be blaming the Fed.

So where does Bernanke look for solutions to the low-real-interest-rate puzzle? He first contemplates Larry Summers's "secular stagnation hypothesis." I discussed secular stagnation in this blog post. There, I argued that there are two types of stagnation that economists like to talk about. The first is growth stagnation, where the argument is typically framed in the context of the standard workhorse growth theory developed by Solow, Cass, Coopmans, etc., many years ago. While growth theory is very useful in helping us understand cross-country growth experience, and to disentangle the factors contributing to economic growth in an individual country, it tells us little about what growth will be in the next 10 years in the United States, for example. Growth theory tells us that a substantial fraction of the growth in per capita income is accounted for by productivity growth, which in turn is driven by growth in the stock of knowledge. If anyone claims to be able to look into the future and see that, you shouldn't take them seriously. Thus, discussion about growth stagnation is just a guessing game.

The second type of stagnation is Keynesian stagnation. That's Larry Summers's version of secular stagnation, which he seems to have first discussed at an IMF conference in November 2013. Summers wasn't acting as the promoter of some well-developed research program. Indeed, the idea seems to have grown in Summers's brain and emerged from his mouth fully-formed. Most of us are longing for the day when this happens to us. No more fighting with editors, referees, colleagues, and various naysayers over our ideas. Just stand up in public, speak, and wait for the adulation. Taylor Swift never had it so good.

Nevertheless, as good scientists, we should flesh out Summers's idea, and check it for consistency and empirical plausibility. Macroeconomists are much better at this than they used to be - say, 50 years ago. So-called microfoundations - essentially, just using the best available theory in a judicious way - is about more than the Lucas critique. We want our models to include economic agents that are recognizably doing the things that real consumers and goods-producing firms do, interacting in ways that will somehow capture the real-world market interactions that we see going on. If the purveyors of particular theories are explicit, we can better understand what they are getting across, and we can check that their conclusions are correct, and that they are taking the right forces into account.

That's not to say that no one has attempted to formally capture what came out of Larry Summers's mouth. Eggertsson and Mehrotra have a paper about secular stagnation, which I wrote about in this blog post. Summers imagines that there exists a persistent inefficiency, reflected in a low real interest rate, that monetary policy can never fix, but which fiscal policy can. There is indeed an inefficiency in the Eggertsson/Mehrotra paper that will persist forever. But in their model it's easy to fix if the government simply provides an outside asset, as is well known for this class of models. I'm not sure this captures what Summers is getting at.

In any case, Summers summarizes what he means by secular stagnation in this reply to Bernanke:
The essence of secular stagnation is a chronic excess of saving over investment. The natural question for an economist to ask is how can such a chronic excess exist in flexible markets? In particular, shouldn’t interest rates adjust to equate saving and investment at full employment? The most obvious answer is that short term interest rates can’t fall below zero (or some bound close to zero) and this inhibits full adjustment.
So, suppose we consider a world with certainty - that will capture the long-run phenomena Summers is interested in. Then,

(1) r = R - i,

where r is the real rate of interest, R is the nominal rate of interest, and i is the inflation rate. Summers seems to be saying that, for some reason, the marginal product of capital is low, so the payoff from investing is low, and so the economically efficient real interest rate - what Woodford would call the "natural real rate of interest" or what Bernanke calls the "equilibrium interest rate" - is low. We'll let r* denote the natural real rate of interest. Then, if r* < -i, even with the nominal interest rate at the zero lower bound, the real rate of interest can't fall enough to correct Summers's "chronic excess of saving over investment." You should see where this is going now. You might have thought it odd that Summers mentions "flexible markets," but doesn't breathe a word about the flexibility of prices. How come? You tell me.

Summers's secular stagnation world appears to be one where the prices are sticky forever. He doesn't say as much, but I don't know how else he gets this to work. It seems to me that, in equation (1), i should be adjusting in the long run so that r* = R - i, no matter how the central bank sets R, if we think of this as, for example, a Wooford-type world. Further, in terms of conventional asset pricing, again in a world with certainty, we can write the real interest rate (approximately), as:

(2) r(t) = b + ag(t+1),

where r(t) is the real interest rate at time t, b is the subjective rate of time preference, a is the coefficient of relative risk aversion (assumed to be constant), and g(t+1) is the growth rate in consumption between this period and next period. It's hard to know for sure (as, again, Summers has not been explicit), but it seems that the effect he is discussing above is a level effect - the stagnation has to do with the level of output, not its growth rate. This translates in equation (2) into no effect on g(t+1), so in order to have a low real rate of interest, something else has to give. Some New Keynesians are fond of capturing real rate shocks as an increase in the discount factor, or a decrease in b in equation (2). This is hardly satisfactory, though. We're supposed that think that the economy will stagnate due to a contagious attack of patience? Maybe Summers thinks that (2) is not a good place to start in pricing assets? If so, he should tell us.

So, we're left wondering what Summers really has in mind, or if he's even thought about these problems. Why don't the prices adjust? What's the source of the low real natural rate?

Bernanke doesn't like Summers's secular stagnation ideas, but for the wrong reasons, I think. First, he gets a bit tangled up in interest rate logic:
The Fed cannot reduce market (nominal) interest rates below zero, and consequently—assuming it maintains its current 2 percent target for inflation—cannot reduce real interest rates (the market interest rate less inflation) below minus 2 percent.
As Summers points out, assuming that a central bank can maintain a 2% inflation target at the zero lower bound - particularly over an extended period of time - is a big leap. Indeed, if we add a time dimension to equation (1),

(3) r(t) = R(t) - i(t),

then (2) and (3) imply that, at the zero lower bound,

(4) i(t) = -b - ag(t+1)

So, conventional asset pricing theory tells us that, if monetary policy is irrelevant for the growth rate in consumption in the long run, then a central bank will have a hard time hitting an inflation target of 2% at the zero lower bound in the long run, unless there is a large enough sustained decrease in consumption. But, you might say, while many central banks in the world are indeed missing their inflation targets on the low side while at the zero lower bound - or even lower - we haven't yet seen sustained deflations, particularly in the United States. Even Japan, with about 20 years at the zero lower bound, experienced an average inflation rate of about zero over that period.

Now, note that, essentially by definition, the right-hand side of equation (4) is the real interest rate. If we're puzzled why we're not seeing deflation at the zero lower bound, we should also be puzzled by the low real interest rate. And, if we can figure out why the real interest rate is low, we also have a potential explanation for why inflation is higher than the conventional theory tells us it should be.

Here's another issue on which Bernanke seems confused. In the chart in this post, he shows us a real interest rate - the yield on 5-year TIPS. That's a security issued by the Treasury, of course. But when he starts taking issue with Summers, he's discussing the rate of return on investment - the marginal product of capital, in most macro models I know about. Maybe Bernanke is thinking that rates of return on all assets move together, and any differences in those rates of return are due to risk, but I don't think that's correct. For example, in this paper by Gomme, Ravikumar, and Rupert, the after-tax rate of return on business capital is measured. Their notion of capital is standard, but excludes residential capital and consumer durables. Basically, this is the average product of capital, which is proportional to the marginal product of capital with a Cobb-Douglas production function. On page 269 of their paper, they show a time series of their rate of return measure. The average is 5.16% for the period 1954-2008, and the rate of return is fairly smooth - bounded for the most part by 4% and 6%. But the real rate of return on short-term government debt (that's the ex post real rate) has much more variability, as can be seen in the following chart.
As well, there's a substantial downward trend, which we don't see in the time series of rates of return on capital that Gomme et al. calculate. Conclusion: There are some factors affecting the real rate of return on government debt that appear unrelated to what is determining the rate of return on capital.

What to make of this? Long ago, when people were interested in the equity premium puzzle, Mehra and Prescott showed that it was hard to reconcile standard asset pricing theory with observed returns on government debt and equities. Given empirical evidence on risk aversion, and the observed degree of aggregate risk from the time series, standard asset pricing predicts a much smaller risk premium than what we observe. Another way to think about this is that safe rates of interest in frictionless models are much higher than they are in practice. Indeed, in the conclusion to their paper, Mehra and Prescott suggest that people start looking at the frictions:
This is not the only example of some asset receiving a lower return than that implied by Arrow-Debreu general equilibrium theory. Currency, for example, is dominated by Treasury bills with positive nominal yields yet sizable amounts of currency are held.
The fact that certain types of contracts may be non-enforceable is one reason for the non-existence of markets that would otherwise arise to share risk. Similarly, entering into contracts with as yet unborn generations is not feasible. Such non-Arrow-Debreu competitive equilibrium models may rationalize the large equity risk premium that has characterized the behavior of the U.S. economy over the last ninety years.
Of course, most of the asset pricing literature didn't follow Mehra and Prescott's suggestions, but instead stuck to Arrow-Debreu pricing. I think they were missing something, and in the current context, Mehra and Prescott's suggestions are quite useful.

Take currency for starters. Bernanke gives an example of why negative real interest rates don't make sense. Basically, with a very small real interest rate, the present value of a small per-period payoff could be huge, making all kinds of seemingly ludicrous investment projects have positive net present value. But, of course, the real rate of return on currency is typically negative, and has been known to be quite large in absolute value. Why do people hold this asset if its rate of return is low - indeed lower, as Mehra and Prescott point out, than Treasury bills, which have essentially identical risk properties? We could say that the difference in the rates of return on money and T-bills reflects a liquidity premium - currency is more useful in exchange than are T-bills. So, extending the idea, why couldn't government debt bear a liquidity premium relative to other assets - capital for example? Government debt is indeed useful in exchange, in the sense that it is useful in credit contracts, as collateral - particularly in repo markets. This has to do with the non-enforceable contracts that Mehra and Prescott mentioned. Then, instead of equation (2), we can determine the real interest rate as:

(5) r(t) = b + ag(t+1) - l(t),,

where l(t) is a liquidity premium. The more liquid the asset, the higher is l(t), and the lower the real interest rate. Of course, equation (5) is a just a piece of a model. Has anyone written down fully-articulated general equilibrium models that determine such liquidity premia? You bet. Here are some:

Williamson (a)
Williamson (b)

That work isn't coming out of nowhere, of course. It's part of a broader research program involving other people - new monetarists, actually - and building on the work of many others. You can read about that in the papers. What the models show is that l(t) is an endogenous object, that depends in general on monetary policy, fiscal policy, and what is going on in credit markets.

Once we have the liquidity premium to work with, we have a potential explanation for why the real interest rate is so low - the liquidity premium is unusually high. Why would that be? We don't have to look too far to find the reasons. The financial crisis effectively destroyed part of the stock of eligible collateral, as did sovereign debt problems in parts of the world. U.S. government debt then became relatively scarce, and its price went up. Further, note that, at the zero lower bound,

(4) i(t) = -b - ag(t+1) + l(t),

so a higher liquidity premium on government debt also implies that we will tend to see higher inflation at the zero lower bound. In the models in the papers I refer to above, the real interest rate can be low due to suboptimal fiscal policy. If that suboptimal policy persists forever, the real interest rate can be low forever, and there is an inefficiency, reflected in low output, consumption, and employment. Looks a lot like what Summers would call secular stagnation. But it's a financial problem - there's insufficient government debt outstanding, not an insufficiency of government spending on goods and services. Faced with suboptimal fiscal policy, monetary policy matters in unusual ways - it's permanently non-neutral, and a severe shortage of government debt can mean that the central bank wants to be off the zero lower bound.

So, I think it would do Ben Bernanke good to get out more. Stop hanging out with big shots like Larry Summers, and make the acquaintance of some young macroeconomists, and other assorted riff-raff.


  1. Excellent piece of article. Bernanke should check this out!

  2. The fed is the main contributor to secular stagnation due to lowering rates to stimulate the economy. When it lowers rates to stimulate it grows credit, the financial sector and speculation too much drawing resources away from the rest of the economy undermining real GDP growth and generating greater instability which both also lead to lower levels of capital investment. The fed needs to stimulate with tools that don't promote financialization overly such as helicopter drops of central bank created e-money.

    1. That's a nonsense argument. If you worrty about financial instability you regulate the financial sector.
      Monetary policy can keep inflation expectations in line, stimulate the economy during a recession and play the role of lender of last resort (Europe!). It cannot sacrifice its last two goals in order to achieve a goal which other instruments could achieve more efficiently and without such horrible opportunity costs.

  3. "Leaving aside any effects of quantitative easing (QE), there has been no change in U.S. monetary policy since late 2008, so any nonneutralities of money dissipated long ago. For example, if the Fed had, in late 2008, gone to a fed funds rate range of 1.0%-1.25% instead of 0-0.25%, and stuck with that, real economic activity in April 2015 in the United States under that alternative policy would not be significantly different from what it actually is now."

    I don't think this follows from what Bernanke said. I assume Bernanke and Summers would both strongly disagree with both of your claims here.

    1. In his first post, Bernanke says:

      "Except in the short run, real interest rates are determined by a wide range of economic factors, including prospects for economic growth—not by the Fed."

    2. Right. In the (New)-Keynesian framework, to which I think Bernanke roughly subscribes, if the central bank tries to set r > r*, it gets high unemployment and deflation, and if it tries to set r < r*, it gets low unemployment and inflation. So this is the mechanism that keeps r ~= r* in the long run. You can have r != r* for a while, but at the cost of high unemployment or high inflation.

      But (I think) Bernanke would say that r > r* has been true for a while now because of the liquidity trap, and the absence of deflation is due to something else (Krugman likes to cite downward nominal wage rigidity). So he would probably say that if you had set r to a higher level over the last 7 years, unemployment would have come down more slowly, inflation would be lower, and we might have had deflation.

      Now I know that you disagree with this, and think that r gets back to r* on its own pretty quickly, but that's not what (I believe) Bernanke thinks.

    3. There's not much point in having a conversation about what Bernanke thinks, unless we're having it with him. But, we know what he stated in his post, which is what I quoted above. Thus, if we take central bank actions to be setting the target for a short-term nominal interest rate, Bernanke says that if the central bank changes its nominal interest rate target, then this will have an effect on the real interest rate only in the short run. That's consistent with how an NK model works. Changing the nominal interest rate matters temporarily for the real allocation, but not permanently. Unless you're thinking of the short run as much longer than I am, I'm not sure why you have a problem with what I stated.

    4. Here's what he had to say in that post about raising rates prematurely:

      "In the weak (but recovering) economy of the past few years, all indications are that the equilibrium real interest rate has been exceptionally low, probably negative. A premature increase in interest rates engineered by the Fed would therefore have likely led after a short time to an economic slowdown and, consequently, lower returns on capital investments. The slowing economy in turn would have forced the Fed to capitulate and reduce market interest rates again. This is hardly a hypothetical scenario: In recent years, several major central banks have prematurely raised interest rates, only to be forced by a worsening economy to backpedal and retract the increases. Ultimately, the best way to improve the returns attainable by savers was to do what the Fed actually did: keep rates low (closer to the low equilibrium rate), so that the economy could recover and more quickly reach the point of producing healthier investment returns."

      So it sounds like he thinks that the real rate set by the Fed has been above the natural rate since 2008, since he thinks r*<0, and he says that keeping rates low is "closer to" the equilibrium rate than keeping them high. And he thinks that if the Fed had set rates higher, this would have caused a slowdown, and they would have had to lower them again.

      And I think this is a fairly widespread view among (New)-Keynesian economists. I think most such people think that the real rate has been above the natural rate since the Fall of 2008. So we're still in the "short run" if you like.

    5. That statement is not inconsistent with the one I quoted. He's justifying his policy choices, but implicit in that is the idea that he can only affect the real outcomes temporarily. That's not to say I agree with everything in your Bernanke quote. For example, he says "several major central banks have prematurely raised interest rates." A standard example people use is Sweden, but I think that case is debatable.

      "And I think this is a fairly widespread view among (New)-Keynesian economists. I think most such people think that the real rate has been above the natural rate since the Fall of 2008. So we're still in the "short run" if you like."

      I don't disagree with you that this view is widespread. But that's a hard position to defend, I think. NK is about price and wage stickiness. The shock was the financial crisis. Prices and wages are still adjusting to the shock more than six years later?

    6. "The shock was the financial crisis. Prices and wages are still adjusting to the shock more than six years later?"

      In a way. But your statement sounds like this just required a single adjustment of all prices to a new equilibrium level, and once that happens we are back to the flexible-price equilibrium.

      I think this is misleading in at least two respects. First, there are nominal rigidities across many markets, and they reinforce one another, which can imply very slow adjustment, or even moving away from the ultimate equilibrium for a time.

      Second, we're not talking about going from one stationary equilibrium to another, but about shifting to an entirely different equilibrium path. I think it's plausible that the financial crisis required lots of adjustment of real variables, including the distribution of lots of assets across different agents. Then if nominal rigidities slow down every step of this adjustment process this could imply a very different path of real variables for a very long time.

  4. Is there supposed to be a negative sign in equation (3)?

  5. Great post, though I'm unconvinced by the conclusion that there's a shortage of safe assets. There was; but not any more: European yields across-the-board trade lower than treasuries. The criticism of Bernanke is apt. His quote from Samuelson effectively assumes the corporate sector can fund capital expenditure at the Fed funds rate - they can't. But if the Fed offered zero interest rate loans at infinite maturities, to anyone - sure there would be a capex boom. To that extent, monetary policy has never run its course. But it's never clear to me when I look into the detail of macro models what interest rate is being used. For example, is the interest rate in the Consumption Euler equation the fed funds rate? If so its even more of joke. It should be some weighted average expected return on all assets. Not that that compensates for the fact that the sign should be reversed! On the methodological point, why Larry doesn't bother anymore with detailed, rigorous models and peer-review publications - and instead settles for holding forth at conferences, the Financial Times, and every now-and-then the blogosphere. Maybe he has concluded that the former lose sight of what's relevant, and on reflection, relatively obvious. Talking to big Larry is not a waste of time ... he's getting close.

    1. "European yields across-the-board trade lower than treasuries."

      There's a lot going on in the U.S. relative to Europe that affects bond yields. Certainly the market seems to think that a lot of European debt is as safe as U.S. debt. But the Fed is talking about tightening, while the ECB is going the other way - below zero. That of course matters for the differential in nominal bond yields. Another factor I forgot to mention, which has come into play more recently, increases the demand for safe assets at the world level. That's Basel III regulations imposing restrictions on banks' holdings of liquid assets:

  6. On the equity premium puzzle, have you ever read Ahimud? He attributes the puzzle to a premium for stock illiquidity. Stock excess returns reflect not only the higher risk but also the lower liquidity of stock compared to Treasury securities.

    1. Finance people and market participants typically think of liquidity this way. How thick is the market, i.e. what's the volume of trade for a particular asset? That's not so far from how monetary economists would think about it - "monetary" assets are the ones with a high velocity of circulation. But liquidity premia aren't always associated with trading of the particular asset in question. For example, an asset can be widely used as collateral, and bear a liquidity premium as a result, but the asset could just sit in the portfolio of a financial intermediary indefinitely, and be used as collateral for a sequence of overnight repos.

    2. I agree. Ultimately, the best measure of liquidity is the price that people need to be paid as compensation for forgoing the ability to use it in trade, whether as a collateral object or for outright sale.

    3. Exactly. If you write this down in a model, the liquidity premium is the difference between its price and its "fundamental" value - the appropriately discounted present value of future payoffs, which is what I would lose if I couldn't trade it (or use it for collateral).

  7. "Further, note that, at the zero lower bound, (4) i(t) = -b - ag(t+1) + l(t), so a higher liquidity premium on government debt also implies that we will tend to see higher inflation at the zero lower bound."

    I don't get this. Why would the liquidity premium on government debt affect the inflation rate? We don't set the prices of things in terms of government debt like t-bills, but central bank liabilities. The only liquidity premium that should have an influence on the price level is the liquidity premium on central bank liabilities.

    1. That's with everything else held constant, of course. It's a general equilibrium effect, so you can't see what's going on in one equation. This involves the interaction of fiscal and monetary policy in determining inflation.

    2. Here's how you might think about it. In typical monetary models, there's no role for government debt, but there's a liquidity premium on money. That liquidity premium reflects an inefficiency, but we can get rid of the inefficiency by reducing the nominal interest rate to zero. That also makes the liquidity premium on money disappear. And in a stationary economy that has to imply deflation, as in equation (4). But, suppose that government debt has some role to play in this economy, and bears a liquidity premium. What happens if the nominal interest rate goes to zero? That means that liquidity premia are equal on money and government debt, but the liquidity premium is not zero, and inflation can be positive, as in equation (4).

      You can get into some interesting things if you consider what happens if the lower bound is not zero. For example, government debt is useful in some ways that currency is not, and vice-versa. Currency can be stolen, and takes up space, etc.

    3. I'm still not getting it. You start out saying that in reducing the nominal interest rate to zero, the "liquidity premium on money disappears."

      Then you imagine a world in which government debt also has a liquidity premium, and ask: "What happens if the nominal interest rate goes to zero?" Your answer: the liquidity premia on money and government debt are equal, and the liquidity premium is not zero.

      How can the nominal rate on money go to zero in both situations, but in one the liquidity premium on money disappears and in the other the liquidity premium is greater than zero?

    4. i is the interest rate spread between money and bonds. If bonds have no liquidity value, this is the liquidity premium on money (relative to all assets, including bonds, claims on capital, etc).

      If bonds have a liquidity premium, then i is the DIFFERENCE between the liq. premiums on money and bonds. This difference could be zero, while both bear a positive (and very high!) liquidity premium.

      We can imagine that there's another return r, which is the (risk-adjusted) return on illiquid capital projects. Then the liquidity premium on bonds relative to capital is r-i, and on money relative to capital is r, and between money and bonds is i.

      So you can have i=0, but r-i high, which is an economy where liquidity is scarce.

    5. I like that explanation. What I'm wondering is why a change in the liquidity premium on bonds relative to capital (r-i) would have an effect on the rate of inflation if the liquidity premium on money relative to capital (r) stays constant. It seems to me that near the end of his post, Steve is implying this when he says that "a higher liquidity premium on government debt also implies that we will tend to see higher inflation at the zero lower bound." But maybe I'm not reading him properly. If I'm reading him properly, I'm wondering what the intuition behind this is.

    6. This is just the Fisher equation plus liquidity premium at a fixed nominal interest rate. If you have inflation, then the real return on bonds is (i - pi), and so the liquidity premium on bonds (capital-bond spread) is:

      liq = r - (i - pi)

      If we assume that r and i are fixed, then a higher liquidity premium implies higher inflation.

      Here's another way to frame it: For a given r, a higher liquidity premium on bonds implies that the nominal interest rate consistent with a certain level of inflation is LOWER. A Keynesian way of saying this is that a higher liquidity premium on bonds lowers the natural rate of interest.

    7. Ok, I'm fine with that. We're talking about accounting identities.

      What I'd find odd is the existence of a causative connection whereby a higher liquidity on bonds doesn't just imply higher inflation, it leads to higher inflation. I'm not sure if this is the story that Steve (or yourself) is going for.

    8. Small (but important!) correction: This is NOT an accounting identity. It's an equilibrium relation.

      You should think about it as an arbitrage equation. It says that the risk AND liquidity-adjusted returns on two assets (claims on illiquid capital and bonds) are equal.

      Sometimes people say that r = i - pi is an identity, because we're just defining the real return on bonds r. That's correct. But here r is the return on a DIFFERENT asset (i.e. illiquid capital).

      Here's another way to put it: Let r* be the real return on bonds. That's just a definition, which yields the identity r* = i - pi.

      Then the equation above becomes:

      liq = r - r*

      Definitely NOT an identity. (By the way, "liq" above is going to be the shadow price on a liquidity constraint in some agent's problem).

      However, I agree with you that the causal interpretation of the equation is not clear from the relationship. In particular, the Keynesian interpretation I gave above has quite different implications than Steve's interpretation! But you need the rest of the model to flesh that out -- one equation doesn't get you (all the way) there.

    9. Yes, exactly, it's not causal. In some models I play with, interest rates (real and nominal), inflation, and liquidity premia are all endogenous. We can certainly talk about causation in terms of how the endogenous variables depend on the exogenous ones. But we can't say that the liquidity premium causes inflation.

    10. Thanks folks, question answered.

  8. Bernanke writes

    "If global imbalances in trade and financial flows do moderate over time, there should be some tendency for global real interest rates to rise, and for US growth to look more sustainable as the outlook for exports improves. To make sure that this happens, the US and the international community should continue to oppose national policies that promote large, persistent current account surpluses and to work toward an international system that delivers better balance in trade and capital flows."

    I am following this debate with interest. I/m very sceptical that the problems in the US relating to "secular stagnation" and trade deficits when they appear are the results of things happening abroad in places like Germany. In some ways it surprises me that Bernanke who is historically relatively literate has taken this approach. In very large countries the sources of such problems are more likely to be found at home. Pressures on Japan for example to close its bilateral current account surplus with the US was a big cause of the financial and real estate bubble (sorry Fama the Japanese can assure you that these things definitely exist) which was to start in the 1980s and it barely made a dent in the bilateral deficit.

    I think there is a problem though with "emerging markets" - and more particularly with those that are not emerging - much of the world - think of the Middle East, Africa, South America. Obviously there are a lot of potential returns to capital in these countries for countries looking for places to put their large amounts of idle capital and low returns . But that involves imaginative and brave measures to tackle poverty, political instability and inequality. The answer may be here, but not in places like Germany or the Eurozone.

    But more likely it is tackling issues at home.

  9. What about the literature on firm turnover and how it relates to productivity - isn't there some work on this by Hopenhayn ? With lower turnover and fewer start-ups, this reduces productivity. doesn't that show up as lower MPK ? So maybe the real interest rate is low for real reasons, and safe assets is just a red herring

    1. We have a lot of models in which technology affects MPK. Suppose we take this Hopenhayn effect seriously. You need to explain to me what the financial crisis, turnover, and startups has has to do with the rate of return on government debt.

  10. That is not how one write Koopmans, of course.