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"Do you want a central bank that sometimes needs to own all [the government bonds, all the commercial bonds, all the shares,] all the farmland, all the houses...to keep inflation (or NGDP) on target?"

Presumably the CB pays with currency for those assets so you would have very little to buy and lots of currency around; would that not mean very high inflation? Plus, with lost of assets and lots of liabilities (outstanding currency) I think the CB balance sheet would be large not small.

"If the central bank targets 100% inflation (or 103% NGDP level growth) the central bank's balance sheet would be very small (relative to GDP). That's because currency would pay minus 100% real interest per year, so the demand for currency would be very small relative to GDP."

I am wondering whether not the opposite would happen: With savings providing a high negative real return there will be a higher demand for liquidity as the people will try to convert their savings into real assets. However, the overall size of bank deposits can only be reduced by paying back loans which is not attractive during high inflation. Selling bonds to the central bank for liquidity purposes will then increase its balance sheet.

How is the CB actually targeting 100% inflation in practice? It says it targets 2% but has been unable to do so for the last years.

Problem: liquidity is endogenous, particularly with respect to market size. If the Fed bought up all but \$10 million in government debt, then remaining \$10 million would probably not be very liquid.

"If the central bank targets 100% inflation (or 103% NGDP level growth) the central bank's balance sheet would be very small (relative to GDP). That's because currency would pay minus 100% real interest per year, so the demand for currency would be very small relative to GDP."

Not sure I understand what you are getting at. If inflation is 100% per year, then after one year's time money will buy half as much, right? Wouldn't that be like minus 50% real interest?

Min: Damn maths! We always approximate (1+i)=(1+r)(1+p) with i=r+p. Which only works if r and p are small enough that rp can be ignored. I think you are (roughly) right. It won't affect my point though.

Alex: Good point. There is both an extensive margin and an intensive margin when the central bank buys assets along the spectrum. I ignored the inte3nsive margin.

Odie: No. This is basic monetary economics. Simple version (with no real growth in the economy). For 100% inflation, you need a 100% growth rate in the nominal money supply. But the real money supply M/P will be very small.

The Bank of Canada has been keeping inflation fairly close to 2% for the last few years.

Nick says, “If the central bank targets 100% inflation…”. I’m not sure that a CB would be able to do that. The CB could try printing money and buying up a vast range of assets so as to achieve that 100% inflation, but asset owners would just refuse to sell: who wants to part with their house or other assets in exchange for dollars which rapidly lose their value? As Nick says, “demand for currency would be very small..”.

Is the Real Bills Doctrine relevant here? RBD states very roughly that the private non-bank sector gets banks to supply it with a stock of money that the private non-bank sector wants or which it thinks makes sense.

Interest on reserves decouples the issue of the central bank size from the issue of the optimal target.

"How big do you want the central bank to be? How big do you want the fluctuations in size of the central bank to be?"
Friedman Rule is one answer. Central bank should be big enough with fluctuations of size big enough so that it earns zero economic profit. If it is too small, it is a harmful monopoly.

The Bank of Canada has paid "interest on reserves" for fifteen years. The Bank sets a target corridor with its Overnight Lending Rate and Overnight Deposit Rate, and the overnight money market generally stays within those bounds. If it goes outside the bounds, there is an instant arbitrage opportunity between the Bank Rate and the Market Rate.

"In that world the ZLB would always be binding on some asset, the one at the margin of the central bank's operations..."

If the central bank were to swap assets that are more liquid than the marginal asset for those that were less liquid, would that have a comparable effect to simply buying them for currency? Say for example, if the government issued new bonds to the central bank which then swapped them with the private sector for less liquid assets (assuming government bonds are more liquid than the marginal asset at that point).

At the ZLB, the central bank that hits the macroeconomic targets is earning an economic loss. Expected economic loss is the best indicator that the ZLB has caused the central bank become too big.

Hi Nick, I had a similar question to Ralph Musgrave at 1:12 PM, but with regards to expectations. If everyone expected the inflation rate to rise, why would anyone sell their real assets? The most eager sellers would be fixed interest contracts (debt, swaps etc.) owners who would sell, but the market would have renormalized immediately before the CB started buying (because markets are great at front running!) ... the CB would then be buying these assets at fair market value (i.e. with the new inflation expectations). In other words, how could the process ever get started if everyone thought the CB was perfectly credible?

Nick, You said:

"WIll the ZLB be a binding constraint, so that fiscal policy is needed?" is not the right question. Instead we should ask: "How big do we want the central bank to be?""

This is a point I am also trying to make. And the implication is that the actual "zero lower bound" is not zero rates, it's when you reach "zero eligible assets left to buy."

Regarding the "extreme socialists," I like to sometimes tease conservatives who want really low inflation by pointing out that that they are advocating socialism.

"Think of a world with a continuum of assets of different liquidity....The central bank would buy up all of that asset, then move on to the next asset along the liquidity spectrum, if it needed to. Monetary policy would mean moving the ZLB back and forth along the spectrum of assets."

Nick, just trying to wrap my head around this. When we talk about differing liquidity, are we talking about total, average, or marginal liquidity? If a central bank issues enough of its liabilities and simultaneously reduces the quantities of other liquid assets outstanding, at some point it could reduce the marginal liquidity of it's own liabilities below those of others. It could even reduce the marginal liquidity of central bank liabilities to 0, at which point it has hit its own ZLB constraint.

Let's use the criteria I gave in the comment above to examine which central banks are constrained by the ZLB. I wrote that the ZLB constrains the central bank only if the macroeconomic equilibrium requires that the central bank is expected to earn an economic loss. Only in this situation we can say that the ZLB has caused the central bank to become too big.

Switzerland is constrained by the ZLB, as the Swiss central bank is unable to charge the negative rates on reserves needed to compensate it for the extra safety of Swiss franc. Switzerland is a small open economy, it imports the equilibrium interest rate from the global markets, and this rate is not affected much by the changes in domestic conditions. Swiss macro equilibrium would require a temporary peg at a much lower exchange rate of the franc. At this exchange rate, SNB would face an extra demand for franc due to expected appreciation when the macroeconomic situation normalizes, and SNB is unable to offset the expected losses from the asset portfolio during the exit from the peg by charging the negative interest on reserves. Thus, the Swiss central bank was forced by the ZLB to peg the franc at the exchange rate that is suboptimally high.

The Fed is not constrained by the ZLB right now. It was constrained by the ZLB in early 2013 when Bernanke was complaining about the negative term premium on treasury securities the Fed was acquiring. The Fed has escaped the ZLB constraint by switching the focus of the policy from asset purchases to forward guidance, and the term premium on treasuries is positive again. Thus, the temporary ZLB constraint in early 2013 was caused by the lack of policy transparency and by the legal limitations on the assets the Fed can acquire.

The ECB is not constrained by the ZLB, and it never was. There are plenty of undervalued Eurozone assets that the ECB is legally allowed to acquire or to take as a collateral in refinancing operations. Unfortunately, the policymakers of the ECB have a clear preference for a small balance sheet, and this preference for a suboptimally small balance sheet means that the ECB is forced to take extra steps in cutting the interest rates. The ECB has cut the interest rates on reserves to levels lower than in the US or in the UK, and is discussing slightly negative interest rates on reserves.

What was TARP - monetary policy, fiscal policy, or neither? (I know, Nick said not to ask...but I'm asking!)

Does it make any difference whether it was funded with t-bills or Fed money (besides t-bills being a less(!) expensive funding source)?

1) I believe you are ignoring demand deposits as medium of account (MOA). If so, that is a problem.

2) Central banks run currency "passively" (elastic currency). They don't refuse to take back currency. They sometimes, but not always, refuse to take back central bank reserves.

3) It appears you are making monetary policy about only buying assets. That is not completely right.

4) "Think of a world with a continuum of assets of different liquidity." Let's say all assets were perfectly liquid and not mispriced. However, some assets go down in value. Do the assets going down in value matter?

The model you describe is one where there is a correlation between NGDP (or inflation) and the size of the monetary base. If this correlation s not good (the monetary base needs to increase by a lot to increase NGDP (or inflation) by a little then you may end up with a situation where the CB owns way more assets than would seem health for a free economy and the target is still missed. I think the underlying problem is that people are not just trying to hold more of their wealth in money but are also trying to increase their wealth. The path by which swaps between money and other assets increases wealth is a roundabout one.

Perhaps setting expectations about the future path of NGDP will prevent this from arising - perhaps not.

However suppose the authorities hit the NGDP target by increasing the monetary base via running a deficit of the appropriate size. As well as increasing the base and satisfying any expanded desire to hold liquid assets this deficit will also increase total income and total wealth.

To my way of thinking this is route one to stable NGDP growth.

Vaidas: Take the extreme case: suppose the SNB bought Swiss farmland, and held it forever. As long as the rents are positive, and the price of farmland finite (and the notes didn't wear out too quickly or cost too much to print), that would seem a profitable investment.

JP: " It could even reduce the marginal liquidity of central bank liabilities to 0, at which point it has hit its own ZLB constraint."

What would the price of land, and the rents on land, be in that case?

Nick: the problem is with the "held it forever" part. The demand for Swiss currency is fluctuating, with sharp episodes of flight to safety, and if you never sell the land, you'll get inflation when when things go back to normal. And if the market for Swiss land is efficient and in international equilibrium, the price of the land will jump high enough when the SNB announces the devaluation, so that the SNB will realize losses during revaluation when things go back to normal.
To sum up, money is a liability of central bank if central bank cares about the macroeconomic stabilization. If your liabilities yield too much due to ZLB, you will do less stabilization than is optimal.

Holding land forever is a solution favored by Krugman. He is calling it "credibly promise to be irresponsible". SNB does a large devaluation, and says it will never sell the acquired assets at a loss. The problem is that you get an overheating later on.

Scott Sumner has called the Swiss devaluation one of the greatest successes of market monetarism:
"A few years ago Switzerland successfully depreciated the franc against the euro, then pegged at 1.20, despite the skepticism of Keynesians. The peg held in 2013."

I am not so sure. Even though we market monetarists have won that particular debate (see http://krugman.blogs.nytimes.com/2010/06/04/policy-and-the-tinkerbell-principle/), maybe the problem is that Krugman has applied the ZLB logic at the point where the ZLB was not binding yet. Based on the analysis above, SNB has just moved the exchange rate closer to the level where ZLB starts to bite.

Nick,

If the Fed buys assets, it transfers their risk (assume it is equity risk) to the taxpayer via the higher expected volatility of Fed remittances to Treasury relative to baseline.

Private investors end up with too much liquidity; taxpayers end up with too much equity risk. What do you think would happen barring some market failure (i.e. information costs)?

Diego Espinosa,

taxpayers should care not about the volatility of remittances, but about the volatility of the net present value of future remittances. If you own shares of Wal-Mart, you care not about the volatility of dividends, but about the volatility of the net present value of future dividends (the volatility of share price). Furthermore, most of all you will care about the share price, that is the absolute value of discounted future dividends. Accordingly, taxpayers care most about the absolute net present value of future remittances to Treasury, and this absolute value may be increased or reduced by the extra asset purchases by the Fed.

Further complication arises from the fact that the source of these remittances to the Treasury is the monopoly power of the Fed. For reasons of efficiency, you may want to reduce this monopoly power, even if remittances are reduced.

Ralph and jt:

Distinguish between levels and rates of change. The price level and the inflation rate.

the nominal demand for money is a positive function of the price level, and a negative function of the rate of inflation. The real demand for money (or the demand for money relative to NGDP) is a negative function of the rate of inflation.

If the central bank credibly announces a higher rate of inflation, the real demand for money falls, so either the central bank reduces the nominal money supply, or else the price level increases.

Vaidas: Suppose there is some durable good X, that you can costlessly store. If demand for that good fluctuates, you could make a profit by buying it when demand is low, and selling it when demand is high. Let X be money.

"What would the price of land, and the rents on land, be in that case?"

Pretty high, I'd guess. Although if a central bank pays interest on reserves like the Bank of Canada, and therefore the majority of the return on reserves comes in the form of pecuniary interest, it might not take much in the way of purchases to reduce the marginal liquidity of reserves to 0. Although even if marginal liquidity hit 0, the total and average liquidity of reserves would probably be superior to almost all assets, in which case your continuum's order would be upheld insofar the continuum's scale is average or total liquidity. Dunno, I'm just brainstorming here.

Nick: yes, such a scheme would be profitable, but what makes you think it will stabilize the aggregate demand?

JP: I'm brainstorming a bit too. But I think the price of land would be infinite, if currency paid 0% nominal, and had no liquidity premium over land, at the margin.

Vaidas: well, if the (real) demand for currency increases/decreases, we would want the central bank to sell/buy currency to stabilise AD.

Scott: you and I are very much on the same page here, I think. This post was clearly influenced by you. You said somewhere recently, something like "monetary policy merging into fiscal policy, if the central bank needed to get too big due to too low an NGDP level-growth target."

There is a bit of a paradox in Milton Friedman's thought on the OQM. We can't really accuse MF of being a crypto-commie.

Valdas,
The volatility of the NPV of Fed remittances is captured in the equity risk premium. The "hot potato" thesis ignores the fact that taxpayers absorb this risk when the Fed purchases residual claims on assets. If sellers are left with too much liquidity, taxpayers are left with too much risk. The attempt to re-balance will simply result in a transfer from one to another. This is very different than the view, often expressed, that the Fed's balance sheet is somehow exceptional. The more accurate view is that assets held by the Fed create risk for the taxpayer, such as Fed asset swaps are merely risk transfers between investors and taxpayers.

One could argue the Fed could pay constant remittances by issuing reserves. This would not be possible in an inflation targeting regime. In other words, you can target NGDP, inflation, or the FFR, or you can target remittances, but you cannot do both.

Thanks, Nick.
"nominal demand for money is a positive function of the price level"
Specifically, for real assets, that requires a positive wealth effect, or a net positive effect on owners' equivalent rent (the largest real asset portion of CPI). For OER, the paradoxical effect of buying liquid assets such as MBS is it will reduce the OER, which is balanced against the real asset price increases. (Thus, even with the massive MBS QE and rapid recovery in home prices, current OER is only running at 2%.)

The other paradoxical effect is if real asset owners believe in the Fed credibility they won't part with real assets (as experienced in many countries with hyperinflation), but every Wed. when they see the Fed balance sheet and they are not buying real assets, then they will sell! Weird world.

Cheers.

Nick: "let X be money"
how is that different from the gold standard? We know that the gold standard did not stabilize the aggregate demand enough.

"But I think the price of land would be infinite, if currency paid 0% nominal, and had no liquidity premium over land, at the margin."

That's like saying the purchasing power of reserves would fall to 0, right? But if reserves were to have no liquidity premium over land, why wouldn't their purchasing power in the present fall to such a low level relative to their future purchasing power that they promised to appreciate? The lack of a liquidity premium would be replaced by an expected capital gain, so we'd never see purchasing power hit zero.

Vaidas: start with inflation targeting. Switch from 2% to 0% inflation target. Switch from a 0% inflation target to a fixed price level target. Now delete all the items from the CPI except gold. You get the gold standard.

JP: But that would be an unstable bubble, where people only hold worthless bits of paper because they expect a greater fool to pay even more for them in future.

"But that would be an unstable bubble, where people only hold worthless bits of paper because they expect a greater fool to pay even more for them in future."

Not necessarily. Smart investors might choose to hold reserves because they expect the central bank to buy them back at a better future price, or they might anticipate that the central bank will start paying out a pecuniary return in the future in the form of interest/dividends... in which case it's no longer the greater fool story.

Nick: "Now delete all the items from the CPI except gold". This is the step where the ZLB starts to matter, as the central bank is unable to store service and perishable good components of the CPI. And for small open economies, financial assets and durable goods are priced in international markets, their movements having very little to do with the movements in the domestic items of CPI.

Consider Switzerland again, using an extreme example. Suppose major central banks of the world tighten the monetary policy for one year, then return to normal. Monetary tightening drives the global real short term interest rates below zero. Before the global tightening, the EURCHF exchange rate is 1.20. SNB could preserve the monetary equilibrium by devaluing the franc to 1.50, and returning to the 1.20 exchange rate after one year when global monetary conditions normalize again. After the devaluation to 1.50, franc is expected to appreciate against euro by 25% in one year. Euro nominal interest rates are zero, per uncovered interest party we can calculate that swiss short term interest rate should be negative 25%. SNB should charge negative 25% IOR, but this is impossible because of the ZLB. Two scenarios remain - either SNB is unable to devalue as markets trust its commitment to low inflation and are forecasting 1.20 exchange rate after one year, or SNB is able to devalue by doing massive purchases of financial assets, but takes huge losses during the revaluation, as it is unable to generate 25% return on asset holdings measured in euros. Buying Swiss land doesn't help, as Swiss land is priced in global markets. In practice, the second scenario means that SNB is unable revalue to 1.20 absent a recapitalization of SNB, and you get excess inflation after one year.

The scenario above uses extreme figures, but the forces it describes are present in Switzerland. This is an actual quote from Bloomberg half a year ago:
"Swiss National Bank President President Thomas Jordan is unlikely to make good on his threat of negative interest rates for now so as not to fuel the booming housing market, economists said. ... Swiss consumer prices, on the other hand, have kept falling in Switzerland. They were down for their 20th-month running in May. "

Diego Espinosa: "In other words, you can target NGDP, inflation, or the FFR, or you can target remittances, but you cannot do both."

This is not true, as you can target both NGDP and remittances, if you adjust the interest paid on reserves accordingly.

Vaidas: "Buying Swiss land doesn't help, as Swiss land is priced in global markets."

No it isn't. Swiss land is priced in Swiss Francs. If the SNB announced it wanted to double the price of Swiss land, in Swiss francs, and would keep on buying Swiss land until the price doubled, it would succeed. Now the *real* value of Swiss farmland might be set in global markets, independently of the SNB, but that just confirms my point. The SNB is halving the value of the Swiss Franc, not doubling the value of Swiss land.

Nick, FWIW I think the dilemma Vaidas discusses is theoretically possible, but as an empirical matter I don't see it as a big concern. He isn't claiming unconstrained policy impotence, he's claiming there might be policy impotence if the SNB is constrained not to lose money on the assets it buys, if it later sells the assets, and also is constrained to keep prices stable. The second constraint may force a sale of assets at some point.

Scott: if a central bank *expects* to make nominal losses by buying then selling assets, wouldn't that violate EMH?

Nick -- not if the CB has private information about the bona fides of its future reaction function. That is, if it begins buying real assets to induce inflation but believes it will have to steadily buy assets over time to lend credibility to its stated reaction function, it can expect nominal losses form the early purchases. Of course, the Fed may surprise itself and change its mind or be ousted in which case the wisdom of crowds wins and private information loses.

"if a central bank *expects* to make nominal losses by buying then selling assets, wouldn't that violate EMH?"

Why? If the price start at 1 \$, and everyone expect the CB to buy until the value is 2 \$, the CB will have to pay 2 \$ for each unit.

If, at a later point, the CB is expected to keep on selling until the price is 1 \$, the CB will not get more than 1 \$ for any of those units.

or?

Nick: "No it isn't. Swiss land is priced in Swiss Francs"

According to EMH, if there is a temporary devaluation of the franc, after the devaluation the CHF price of the land immediatly increases, and it drops to the previous level when the previous exchange rate is restored. So SNB is buying land at a high price in CHF terms and is selling it at a low price in CHF terms.

"If the SNB announced it wanted to double the price of Swiss land, in Swiss francs"

The problem is that this announcement is not time consistent, as the monetary stability requires the land prices to double first when the global monetary conditions are too tight, and it also requires that land values return to the previous levels when global monetary conditions normalize.

" if a central bank *expects* to make nominal losses by buying then selling assets, wouldn't that violate EMH?"
In my example, according to the EMH it is impossible to devalue the franc temporarily to 1.50. If price stability mandate is perfectly credible, markets will have an infinite demand for francs for example at a level of 1.30 (see the examle with the uncovered interest parity in my previous example). If the mandate is not credible enough, the franc will go down to 1.50, and markets will expect an above target inflation on average for Switzerland.

Realistically, SNB is a big enough player to cause prices to deviate from the EMH somewhat, so it is possible to expect to have a loss-making trading strategy.

Scott, Nick,
My claim is that if the quantity of money is below the Friedman Rule quantity at the ZLB, you can do monetary stimulus at the ZLB, and Krugman's model is not applicable yet. It is only when you reach the Friedman Rule quantity you are in a ZLB trouble.

As an empirical matter, I believe the ZLB problem has constrained the aggressiveness of SNB devaluation, but for large countries it should not be a problem. Unfortunately, the Fed is legally constrained in the range of assets it can buy, and in early 2013 the Fed has estimated the treasury term premium has turned negative (i.e. the Fed was expecting losses from treasury purchases at that time). So I am a little bit worried about the next recession in the US. While the forward guidance will ensure the eventual return to normal monetary conditions, we may get excess cyclical movements due to ZLB.

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