I often hear that the Federal Reserve can't hike interest rates too much (perhaps not enough to control inflation) because then the federal government would be unable to service its debts. Is this actually true?
targeting the price of various other financial assets (such as inflation futures or nominal GDP futures)
Link to explanation of how/why this would work?
I often hear that the Federal Reserve can't hike interest rates too much (perhaps not enough to control inflation) because then the federal government would be unable to service its debts. Is this actually true?
The Fisher relation says such a hike has to either raise real interest rates or raise expected inflation. If you believe the interest rate hikes would go more into real interest rates than inflation then worrying about this is justified in principle, but in general there's no good explanation of why the central bank raising nominal interest rates would raise real interest rates for a long time, say more than the few years it might take for prices and wages to adjust.
If the hike goes into expected inflation instead, then it's true that the US government has to pay more nominal interest to roll over short-term debts, but they also collect more taxes because of inflation as the tax base becomes larger in nominal terms. Inflation is actually a fiscal benefit to the government in this case, as it ends up devaluing the long-term debt that the government owes.
The US government is sufficiently creditworthy that a few years of higher real interest rates would most likely not leave it in any danger of being unable to service its debts, but I admit there is some small risk every time real interest rates go up that markets end up losing confidence in the US government and refuse to roll over the trillions of dollars of Treasury bills that would need to be rolled over to prevent a debt default, either explicitly or implicitly through an inflating away of nominal debts.
Link to explanation of how/why this would work?
Market monetarists are one group that has been vocal in recommending this kind of policy, specifically with NGDP futures. From the wiki page:
Market monetarists advocate that the central bank clearly express an NGDP target (such as 5–6 percent annual NGDP growth in ordinary times) and for the central bank to use its policy tools to adjust NGDP until NGDP futures markets predict that the target will be achieved.
Alternatively, the central bank could let markets do the work. The bank would offer to buy and sell NGDP futures contracts at a price that would change at the same rate as the NGDP target. Investors would initiate trades as long as they saw profit opportunities from NGDP growth above (or below) the target. The money supply and interest rates would adjust to the point where markets expected NGDP to reach the target. These "open market operation"s (OMOs) would automatically tighten or loosen the money supply and raise or lower interest rates. The bank's role is purely passive, buying or selling the contracts. This would partially or completely replace other bank's use of interest rates, quantitative easing, etc., to intervene in the economy.
The way a government normally services it's debts is to create new money, and use that to pay off the debts. However, the principle way that government creates new money these days isn't to print it, it's to lower the interest rate so that private banks will borrow more money from it. This represents a credit, that then balances the debts the government owes (typically from selling bonds). Raise the interest rates, and banks will borrow less money from the government, tilting the balance toward debt. There is, however, another way to reduce debt, which is to sell fewer bonds.
Thanks for writing this! I tried to find materials about monetary policy suitable for someone with zero prior knowledge and this is the clearest introduction I have found.
I'm in my final year of econ undergrad and this is a clearer explanation of monetary policy than any of my course materials has managed, so thank you.
Definitely not an area I've done too much research into, but it's always seemed obvious to me that interest rates should simply be allowed to float through market forces. Sometimes money should be cheap to get more of to encourage investment, and in those cases, people are already not taking out enough new loans. In some cases money should be expensive to keep the economy from being effectively manic, and in those cases people are already taking out far too many loans. If you have a system that simply lets that happen, you don't need any interest rate targeting at all.
That isn't to say that the government would be uninvolved in monetary policy at all, of course. There would still be things like, what fraction of loans need to backstopped by real money, deposit insurance to prevent runs, etc. Of course, the government would simply go through the same process as everyone else to get loans at whatever the rate is. These things could all be changed in response to actual conditions that matter, while letting interest rates do what they're for.
You seem to favor the idea of targeting inflation which I don't really. Some things that increase inflation are good. Some things that cause deflation are good. Getting both is far more important than the resultant rate. For instance, efficiency of manufacture decreasing costs is an unalloyed good, but so is the amount that people can afford on their salary. I'll do a deflationary (not rare in some industries, very rare in others) example because so many people already defend having some inflation.
Suppose, for instance, that a worker is currently making half of what it costs to employ them including all costs. The company makes a nice 10 percent of the revenue as profit.
An outside advance causes a dramatic increase in efficiency, and that company can make twice as much with the same worker. Suppose that the worker's salary doubles because everyone in the industry is hiring, but other costs stay the same. Total cost has gone up 50% to double production. Further suppose the price is lowered to 80% of what it was due to the glut.
(I apparently completely forgot how to solve math word problems. I hope the following math is right, but the point doesn't rely on exact numbers at all.)
newRevenue=1.6oldRevenue newExpenditures=1.5oldExpenditures oldProfit=oldRevenue - oldExpenditures oldRevenue= (10/9)oldExpenditures
newProfit= newRevenue - newExpenditures= 1.6OldRevenue - 1.5oldExpenditures= (16/9)oldExpenditures - (3/2)oldExpenditures= ((32-27)/18)oldExpenditures=5/18OldExpenditures=(2/3)(5/18)newExpenditures=10/54 of new revenue=5/27newRevenue
The worker is better off, making twice the money. The customers are better off, with people who would have formerly bought it paying only 80%, and those who wouldn't have presumably having improved on their next best option. If the worker's income were denoted in units of what they made, their income is up 250%. The company brings in 60% more revenue for 50% more cost, and their profit has improved from 10% of revenue to 5/18 of their former revenue or 27.777777(etc) percent of their old revenue in profit, which is 5/27 of their new revenue or 18.518% of new revenue.
Literally everyone is doing better, and there is no reason for the companies to stop advancing, despite a truly massive deflation.
I have unfortunately run out of time to keep working on the comment and make it shorter or better.
Can we just fire these central bankers and replace them with a simple program? They are political operators rather than calculating economists.
There have been proposals to do this, but in practice I think getting rid of central bankers and replacing them entirely with programs would not work so well. The problem is you often need humans to react to unexpected situations - a financial crisis, for instance.
I think routine implementation of monetary policy could actually be largely automated if only there were CPI futures or NGDP futures available in sufficient liquidity. The central bank could subsidize the creation of these markets if they thought it to be necessary, but central banks are bureaucratic organizations and so generally don't want to take actions that would limit their discretion.
For similar reasons, central banks often have a difficult time being seen as credible by market participants when they attempt to commit to some policy on a medium to long time horizon, as they really have no formal process which would bind them to a promise they had given years ago.
In theory, of course, you can also privatize money if you think market incentives and competition would result in more efficient money management. My guess is there would be a strong pressure for private monies to aggregate together until a small number of them accounted for most of transaction volume and money balances, and then the institutions managing them (which could e.g. be a consortium of banks) would still be faced with the same monetary policy problems that central banks are faced with today. Still, policy could improve if there were some mechanism for people to dump poorly managed monies and transact in better managed ones.
"Chinese officials forcibly detained one
Federal Reserve Bank employee on four separate occasions during a 2019 trip
to Shanghai, including at his hotel. Chinese officials threatened the
individual’s family unless the individual provided them with economic
information and assistance, allegedly tapped the employee’s phones and
computers, and copied the contact information of other Federal Reserve
officials"
from https://www.hsgac.senate.gov/imo/media/doc/HSGAC%20Report%20-%20China%20Threat%20to%20the%20Fed.pdf
If you replace them with an algorithm, with human intervention only in a president declared emergency , there wuld be no need for this stuff.
I've been seeing more discussion of monetary policy recently, I suspect in large part due to the wave of high inflation that's sweeping the globe right now. As such, I thought this is a good time to make a post about the wonderful website The Reader's Guide to Optimal Monetary Policy.
This website gives you access to a collection of hundreds of macroeconomics papers that are designed to specifically answer the question "what is the optimal monetary policy?" The results are then presented in a scatter-plot format, along with various properties of the optimal policy recommended in each paper, such as the first and second moments of inflation for the optimal policy.
Now that I've sufficiently advertised the website, I'll first discuss what monetary policy is about and what goals it tries to achieve, and then I'll explain the fundamental questions and tradeoffs that come up when we try to come up with an optimal monetary policy. I'll then link this to the estimates from the hundreds of papers listed in the website and broadly how each paper comes up with the recommendations they end up endorsing.
If you're already familiar with what monetary policy is about then feel free to skip the next section.
Monetary policy is fundamentally about the issuer of a money using their power of issuing or retiring currency in circulation to achieve various aims they find to be desirable. When a country has its own currency, this currency is (usually) managed by the central bank. The central bank has the power to issue[1] new currency or to retire existing currency by buying it back and removing it from circulation, and as counterfeit money printing is illegal, they are the only institution to legally have this power.
While central banks fundamentally exercise control over the money they manage, they can do this in ways that are somewhat less transparent. The most popular way to implement monetary policy nowadays is some form of nominal interest rate targeting. The simplified version of this is that the central bank announces a nominal[2] interest rate target, say 3% per year. The central bank then stands ready to accept unlimited deposits from banks and to make unlimited loans to banks at this interest rate.
Ideally, as the central bank has unlimited capacity to issue or retire currency, they can keep accepting deposits or making loans until arbitrage by banks brings the borrowing costs between banks in line with the central bank's target. This then influences (again by arbitrage) the borrowing rates that consumers or businesses face when they go to take out a loan from their local commercial bank, through what's called the monetary transmission mechanism. The central bank can, in principle, always achieve their target assuming they are willing to make transactions that are of sufficient size to do so, and with sufficiently many counterparties.
This is not the only way central banks can implement monetary policy, however. Historically, commodity standards were a much more popular way to implement policy, especially the gold standard. In this policy regime, instead of having a nominal interest rate target, the monetary authority instead has a gold price target. They maintain some fraction of the total money stock in gold reserves, and intervene in the market as required to maintain a fixed dollar price of gold. At times, monetary authorities could also devalue the currency by increasing their target dollar price of gold, much like modern central banks can raise or lower their target interest rate. This policy was abandoned throughout the 20th century, as fixing the price of gold was seen to have serious problems as a mechanism for implementing monetary policy.
Many alternative monetary policy implementations have been proposed, such as targeting some measure of the money supply or targeting the price of various other financial assets (such as inflation futures or nominal GDP futures). Ultimately, the decision has to be based on the goals the central bank is trying to achieve with its policy, which brings us to the next subsection.
Historically, monetary policy had a rather circumscribed role in trying to keep the value of the currency, equivalently the overall price level of goods and services in the economy measured in units of currency, stable. This role was often weighed against the benefits of seigniorage, or the profit made by the monetary authority through the "inflation tax" by issuing new money, as this is often one of the most convenient means of taxation available to a government with its own currency.
Seigniorage fell out of favor over time as the capability of governments to collect taxes through other means improved, as seigniorage is a tax with particularly undesirable properties. In contrast, some version of price stability remains one of the primary objectives of monetary policy today. However, over time monetary policy has experienced substantial mission creep as more and more factors began to influence the decisions of central bankers.
In the US, the Federal Reserve (hereafter referred to as "the Fed") didn't even exist until the early 20th century, and the role of managing monetary policy in a gold standard regime was left to the Treasury Department. The Fed was created by the Wilson administration in order to fight financial panics that had become commonplace in late 19th and early 20th century US. The Fed would lend money to banks that were facing bank runs and therefore coming under pressure to liquidate their long-run investments at big losses. If the bank was not fundamentally insolvent, the Fed would accept its assets as collateral and provide the bank with short-term financing to meet its obligations to depositors.[3] The hope was with such a commitment bank runs themselves would become less frequent, as depositors would know that the Fed would step in to provide a lifeline to a solvent bank that was threatened with a bank run. This is now known as the Fed's role as "lender of last resort", and has become part of the Fed's broader objective of promoting financial stability.
The Phillips curve, an inverse relationship between unemployment and inflation proposed by William Phillips, led to a further expansion of the role of monetary policy. (More on the motivation behind expecting such a relationship to exist later.) Now, the goal was not to simply have price stability, but to actively trade off inflation against unemployment. When inflation was judged to be too high, the central bank would push it down at the expense of creating some unemployment; and when unemployment was judged to be too high they would do the reverse. Over time, this would evolve into the macroeconomic stabilization objective of monetary policy: while monetary policy can't by itself make a country wealthy, it was thought that it could be used to lower the variance of economic growth.
As monetary policymakers got access to increasing amounts of higher frequency information, it became apparent that demand for money fluctuates a lot over time. Some of the fluctuations are predictable: people go shopping in Christmas week, so in this week demand for money spikes in a seasonal pattern. Other changes in demand are less predictable; and occur either in acute spikes due to financial distress in some sector of the economy, or due to long-run technological changes such as the use of credit cards for transactions becoming commonplace. Faced with this situation, central bankers decided the best high-frequency tool for mitigating this volatility in money demand was to target the opportunity cost of money[4] instead of its supply, which is how a brief experiment with money supply targeting in the 1980s came to an end and how nominal interest rate targeting became dominant.
Even this list does not fully cover the wide range of goals modern central banks aim to pursue, but it will be enough for this post. In short, we're looking at the following goals:
Before moving on to discussion of optimal monetary policy, there are a few important points to understand about how monetary policy works.
The zero lower bound (ZLB) on nominal interest rates is a consequence of the fact that most monetary systems offer people the ability to hold cash. Cash pays 0% interest, so in principle if interest rates ever fell below 0%, lenders and depositors would hold cash paying 0% interest instead of loans or deposits that pay negative interest. Ideally this puts a lower bound of 0% on nominal interest rates.
In practice this doesn't quite work because holding cash has a cost, but these costs are usually not much larger than 1%/year, so while the strict zero lower bound is not true in the real world some weaker version of it still poses a serious constraint to how low monetary policy can push nominal interest rates to be.
The Fisher relation is an equation that ties nominal interest rates, expected inflation and real interest rates together. It's a consequence of arbitrage between nominal and real investments.
Suppose you have $1. You can either lend this for one year at a nominal interest rate of , or you can lend it on an inflation-indexed basis at a real interest rate of . An inflation-indexed loan is one such that the borrower pays back an amount that's proportional to a price level index, such as the CPI, when the loan is due instead of a fixed dollar amount.
The Fisher relation says that in expectation these investments should have the same rate of return. The first investment nets you dollars at the end of the year, while the second nets you where is the inflation rate over the period. So the Fisher relation says
and on a first order approximation this is roughly . As an example, if normal US Treasuries are trading at a yield of 5%/year but inflation-indexed TIPS bonds are trading at a yield of 2%/year, that means[5] the market expects roughly 3%/year inflation over the period of the maturity of the bonds.
Now that we have some grasp of which goals monetary policy aims to achieve, let's think about which policies would be optimal for each goal individually. I'll make a separate section for each goal, as some of them require more in-depth discussion.
Well, this one is the easiest, in principle. If you want price stability, just pick some measure of the price level, such as the CPI or the PCE index, and target it at its current level forever. This will produce, on average, a 0%/year inflation rate as inflation is just the rate of growth in such an aggregate price index.
This does have a problem though, and it comes from a combination of the Fisher relation and the zero lower bound. Note that if you put these two together, we get the constraint that or : on average, inflation should be at least as large as the negative of the real interest rate. Historically this was not a common phenomenon, but nowadays it's actually not unusual to see real interest rates being negative. In such situations it will be impossible for the monetary authority to have a monetary policy that produces, on average, 0% inflation.
This problem is only minor, though, because it's possible to adjust the policy such that the central bank targets the price level in year to be for a fixed average inflation rate , say 2%/year. This has the benefit that it still makes price levels far in the future predictable, so such a policy can still serve essentially the same purpose with a sufficiently large to not violate the zero lower bound. So optimal policies trying to address price stability concerns in general have this form, where is chosen to optimize other goals of policy.
Note that this is not quite an inflation target, because in this policy the central bank commits to offsetting above target inflation in year with below target inflation in year and vice versa. An inflation target would instead try to have an expected inflation rate of each year regardless of whether the central bank overshot or undershot its inflation target in previous years. The benefit of targeting the price level instead of inflation is that it makes long-term contracts indexed to the currency much more predictable, ensuring greater price stability.
Financial problems are generally caused by the maturity mismatch on the portfolio of banks or bank-like institutions[6], which nowadays extend far beyond ordinary commercial banks.
These institutions borrow money short-term and lend it out long-term, and try to profit from the spread they charge between the two interest rates. This is beneficial because depositors or lenders to a bank often don't know when they will need to take out their money, but when this risk is averaged over many such depositors it becomes much more manageable from the bank's point of view. Therefore the bank is able to use short-term financing to support long-term investment projects and eliminate a source of inefficiency in the capital markets.
The main problem is that this makes banks particularly exposed to interest rate risk. The value of the long-term loans they own are often much more sensitive to interest rates than the short-term debts they owe to lenders or depositors, and this means a sudden increase in interest rates can leave a bank insolvent if it didn't sufficiently hedge against this risk. Likewise, a sudden decrease in interest rates can leave long-term borrowers in a bad position, as it makes it much more difficult to service long-run debts. For all these reasons, trying to stabilize the financial system usually pushes monetary policy towards stabilizing the nominal interest rate at some level .
In fact, there's a nice theoretical argument that the correct target value for is just zero. This is because is essentially the opportunity cost of holding money, as explained here[4:1]. So the fact that is not zero means people will economize on money holdings as it costs them some return to hold money instead of e.g. bank deposits or bonds. This is not desirable, because money is actually very cheap to produce, so it makes no sense for people to have to economize on it as if it were scarce. Therefore the optimal monetary policy from the point of view of minimizing the inefficiency caused by the necessity to hold money for transactions is to target the nominal interest rate at zero: the Friedman rule.
Initially it may be tempting to think that monetary policy has macroeconomic effects primarily because money is used as a medium of exchange: people pay for goods and services using money, so it seems intuitive that monetary policy can have an effect on the real economy. This is true, but the problem is that this effect usually turns out to be second-order in the nominal interest rate, which as discussed above is a measure of how scarce money is in the economy. This is because is optimal, so you can imagine welfare as a function of having a global maximum at . This means the first derivative vanishes at and consequently deviations from only have second order effects on welfare. So unless we have a hyperinflation and therefore gets very large as a consequence of the Fisher effect, it's unlikely that deviations of from will have much explanatory power when it comes to macroeconomic volatility.
The most commonly accepted explanation for why monetary policy has substantial macroeconomic effects comes from money's role in the economy as a unit of account. If prices and wages are quoted in dollars, and for whatever reason they are adjusted at less than the optimal frequency, then monetary policy can affect relative prices in the economy and therefore have an impact on real production in the economy.
For instance, if workers resist nominal wage cuts and the monetary authority implements a deflationary monetary policy that drives the overall price level down, then in real or purchasing power terms the wages of workers will be going up. As employers can't afford to hire workers at this higher real wage, and as workers are unwilling to take nominal pay cuts, they end up having to fire workers instead. This continues until the marginal product of labor rises sufficiently to compensate for the higher real wage businesses must pay to workers, and therefore the deflation results in an increased rate of unemployment and a lower amount of total production. There are other similar frictions that have the same effect, but the essential ingredient is always that nominal prices are slow to adjust for one or another reason and this allows monetary policy to have real effects.
"Wait", you might say. "You just said that the deviations of the nominal interest rate from zero can't have big macroeconomic effects because is optimal. So if relative prices on the market are set optimally, then shouldn't first order deviations from those prices still only have second order effects on welfare?"
You would be right: in ideal market conditions this argument would fail for essentially the same reason that the argument fails. The way macroeconomists get around this is to assume that relative prices in the economy are not set optimally, because the economy has a lot of agents trading with each other with various amounts of market power, and this leads relative market prices to be different from the frictionless optimal values they ideally would take. If this is true, then inflation messing up these prices and wages further can have first order effects.[7]
In this case, the way for monetary policy to remedy the inefficiency is to create inflation when real wages need to fall (for example due to a recession), so employers don't actually have to cut nominal wages. In addition, having some average level of inflation that's somewhat above 0%/year can also help because not raising wages may be somewhat easier than cutting wages on nominal terms even in ordinary economic circumstances, so some amount of inflation can be generally useful to achieve the necessary adjustment in real wages without nominal wages needing to be cut.
Working out the optimal policy for achieving this usually gives a result that looks like a nominal GDP level target, with the same caveats as I've already discussed in the context of price level targets. The idea is that as nominal GDP growth is the sum of real economic growth and inflation, at a time when real growth slows down a nominal GDP target pushes up inflation to compensate for this. This higher inflation then enables real wages throughout the economy to adjust to the economic shock without anyone needing to get nominal wage cuts or a slower pace of nominal wage raises.
If you think the decisive friction is the difficulty of other prices to adjust and not of wages, the optimal policy can end up looking somewhat different, e.g. it could end up being a price level target.
As you can check on the website, averaging the recommendations of 124 papers published about optimal monetary policy from 2010 to 2020 gives an average expected inflation of 0.55% and an average inflation volatility of 1%.
This might seem quite low, but it shouldn't be surprising in light of the discussion in the previous section. If we took all goals into consideration, we could end up with a nominal GDP level target that aims for a slightly positive inflation rate on average, as this compromise is not far from the optimal policy on all fronts. It would also end up with similar numbers to this: inflation would be slightly above zero and the volatility of inflation would be roughly the volatility of real growth, which in the US is indeed on the order of 1%/year. In addition, if you look at the specific papers in detail, you'll see that they indeed get their results by optimizing for one or more of the goals I've discussed earlier.
There is a good reason to target inflation to be higher than the 0.55%/year average recommendation in the real world, and it again has to do with the zero lower bound. Modern central banks operationally implement monetary policy through interest rate targets, even if their high level goal is more like a 2%/year inflation target. This means the zero lower bound on nominal interest rates seriously limits their ability to conduct monetary policy effectively in some situations, so they have a temptation to set a higher inflation target so as to "have room" to reduce nominal interest rates in a recession if necessary.
The literature does not care much about this because using interest rate targets to implement monetary policy when your actual goal is to target inflation is not optimal to begin with. In this case, you're better off implementing policy by buying and selling NGDP futures or CPI futures. However, as these assets don't actually exist in a large enough scale for central banks to use them in operational implementation of policy, they are stuck with using interest rates even though they don't actually want to be targeting interest rates at a high level. This discrepancy means there's some reason for them to push inflation higher than what would be optimal, as it gives them more room to maneuver in operational terms.
Overall, my considered view is that targeting interest rates operationally doesn't make sense unless you also want to target interest rates as part of your policy regime, as in the Friedman rule for example. Unless you want to do this, you should be implementing monetary policy through buying and selling CPI futures, NGDP futures or other similar assets.
If you can't do this and are stuck with interest rate targeting as an implementation mechanism but you think difficulties of nominal wage and price adjustment are a big problem, then I would recommend a relatively high inflation target, possibly higher than 2%/year. This is because this raises the average level of nominal interest rates by the Fisher effect and thus gives central banks more room to cut interest rates during economic slumps, while the costs of this inflation are likely going to be second order. However, I'd make it clear that this is entirely an artifact of the poor way monetary policy is implemented and executed by central banks right now, and first best is definitely to get them to change the way they do this.
It's a misconception that central banks print money, at least in the US. The physical task of printing dollar bills is actually handled by the US Treasury Department. However, it's the Federal Reserve that issues new currency. So they do the economic equivalent of "printing money", which you'll often encounter in colloquial usage as a description of what the Federal Reserve does even though it's, strictly speaking, false. ↩︎
A nominal interest rate is one that's denoted in the money the central bank is managing. The Federal Reserve targets an interest rate in dollars, not in pounds or euros, because dollars are the currency that they manage.
It's important to note that this is not the real interest rate, i.e. the interest rate net of the expected change in the value of money, or in inflation. A money that is expected to lose value will generally have higher borrowing costs to compensate lenders for the additional expected loss they incur when they make a loan. More on this here. ↩︎
This continues to be relevant in the modern age. When AIG, an insurance company, experienced a severe run on its short-run debt financing in 2008; the Fed decided that they could accept AIG's portfolio of long-run investments as collateral and provide them with sufficient financing to save them from immediate bankruptcy. ↩︎
If you hold cash instead of investing your money in interest-bearing securities, the return you forgo is the nominal interest rate paid on those securities. So this is the opportunity cost of, or "the price you pay" for, holding money instead of such securities for some period of time. ↩︎ ↩︎
This argument doesn't quite work for two reasons. One is that the Fisher relation doesn't have to hold exactly, as the arbitrage between real and nominal investments is only statistical: it equates the average return of the two investments while these don't really have to be the same a priori. Two is that TIPS bonds are not quite inflation-indexed, though they are quite close to being so.
Still, as a first approximation the calculation should be fine; the deviations from it are going to come from higher order effects. ↩︎
Confusingly, nowadays institutions that are called "banks" often don't take interest rate risk at all, because they sell their loans to other financial institutions instead of keeping them on their balance sheet. However, there are still economic equivalents of banks, sometimes called "shadow banks", that do the same maturity transformation and are similarly vulnerable to interest rate shocks. ↩︎
Of course there are also somewhat exotic monetary economics models in which the optimal value of is actually negative, which can't be achieved due to the zero lower bound, and so deviations of from zero also have first order effects. These models seem even less compelling to me than the market power stories about relative prices, though. ↩︎