Wednesday, June 21, 2017

The optimal inflation rate

Anthony Diercks has a very useful review of the the academic literature on the question, what is the optimal inflation rate? He includes 150 papers, ordered from low to high inflation.

Broadly speaking, we start with the Friedman result that the optimal nominal interest rate is zero, so the optimal inflation rate is the negative of the real rate of interest. The optimal nominal interest rate is zero, so people feel no incentive to economize on money holdings, or devote effort to cash management, paying bills late and collecting early. Many sticky price models suggest an optimal inflation rate of zero, so you don't have to change sticky prices. Then,
Most all of the studies that have found a positive optimal inflation rate have been written in the last ten years. The increase in the number of studies with a positive optimal inflation rate can be explained predominantly by the rise of two modelling features: (1) inclusion of the zero lower bound and (2) financial frictions.  
The zero bound means the Fed may want some headroom, a higher nominal rate in normal times. (More on that issue in an earlier post here).

Then, economists get creative. Anthony provides a nice list of additional ingredients that have appeared in the literature:
Previous studies have outlined a deviation from strict inflation stabilization for some of the following reasons: 
• Money (opportunity cost of positive interest rate)
• Distortionary taxes (inflation can be shock absorber to reduce tax volatility)
• Govt. transfers (represent pure rents that inflation can conscate)
• Sticky wages (stabilize wages rather than inflation)
• Price and wage markup shocks (cost push shocks)
• Zero lower bound (inflation reduces chances of reaching ZLB)
• Capital accumulation (composition of demand between investment and consumption matters)
• Flexible prices (no costs associated with inflation)
• Foreigners demand for domestic currency (inflation generates seignorage)
• Price indexation (reduces costs of inflation)
• Collateral constraints (prevents borrowers from smoothing the way savers do)
• Endogenous firm entry (higher entry costs reduce number of firms but increase desired markups, inflation lowers markup and discourages welfare-inefficient entry)
I would add a few of my favorites: 1) Optimal taxation principles say not to tax rates of return. The tax code is not indexed. At low inflation, and low nominal interest rates, inflation-induced taxes on dividends and capital gains are reduced. That suggestion leads to zero or negative inflation. 2) I favor a price level target, not an inflation rate target, meaning that any unexpected inflation is eventually squeezed out. Among other advantages, this reduces the risk of long run contracts, and would reduce the inflation risk premium in long term bond yields. Others like it or nominal GDP targets because it provides more extended countercyclical stimulus. (There is a big literature on the latter issues. Anthony excluded it rightly, being on other questions.) There are more papers to be written. 

This is a hot topic, as you can see. The Fed is thinking how to adapt to lower real interest rates. The blogosphere and commentariat are echoing more calls for the Fed to raise the inflation target. Some of this seems to reflect a resurgence of belief in the 1960s era static Phillips curve, that a higher target would lead to a permanent stimulus. Discredited economic ideas never seem to really die.

Anthony closes with
Overall, the goal of this survey is to act as a definitive resource that policymakers around the world can use to evaluate their inflation targets going forward. Furthermore, it will provide the general public with a justification and understanding of the 2% inflation target.
The former is laudable. The latter seems wishful, though necessary given Anthony works for the Fed. I think this survey has the opposite effect: it makes clear just how thin the scientific understanding behind the 2% mantra is, just how much our central banks pulled 2% out of a hat and then repeated it over and over again until it seemed carved in to stone. The Fed's mandate is "price stability," not "2% inflation." It is also a nice reminder of the difference between academic and policy writing. A good academic paper focuses on one mechanism and really understands it. Policy makers have to find an optimal inflation rate that balances 150 different mechanisms. And counting.

But do not take that as criticism. The optimal inflation target is likely whatever the inflation target is. Most of the function of a target is to be a rock of stability. 0%, 2%, or 4% would each likely work as well as the other, but constant rethinking of any target would not. The point of a target is to "anchor expectations." The "justification and understanding" should not be that 2.000% is precisely optimal. The justification and understanding is that the Fed picks one number and sticks to it. My main complaint about many people who want a higher target, or a price level target conveniently backdated to the pre-2007 trend, is the sneaking suspicion that this is just about current stimulus and they will want a lower target or to abandon the price level commitment later. (Where were you when the price level or NGDP target said to lower inflation?) The inflation target should not respond to current policy concerns. Inflation targets are like constitutions -- change them infrequently,  and only for very good reasons.

If you think Anthony is missing an important and relevant paper, put the citation in the comments. This paper is special for its attempt to be comprehensive. But keep it relevant -- the paper should have a qualitative answer to "what is the right long-run inflation target?"


  1. It seems to me that "inflation" is not a well defined concept. We have arguments over whether the inflation rate should be 1% or 2% when we cannot define it to that accuracy. This, it seems to me, to be the strongest argument for the Fed to tolerate an inflation rate anywhere between 0 and 2%,

    All of the arguments for the Fed to pursue a higher inflation target seem to be deeply flawed with no plausible mechanism proposed for how inflation would stimulate the economy going forward. Looking back over my experience it seems to me that fear of inflation stimulated the economy by stampeding the middle class into over investing in housing. That mechanism is a spent force and we have suffered from the consequences of that mal-investment for a decade now.

    1. How long did you have to work to afford a day's food in 1700? How long do you have to work today to afford a day's food?

  2. If price was made tiny price quants arriving at a pricing machine, then queueing applies and the mean accumulation of price in the queue will have variance equal to mean. If the pricing machine, ultimately, quarantees zero price drift, then queue variance is inflation. It is also the discovery bounds on price discovery. Is our system price neutral? Dunno, we usually change monetary regimes before the count is done.

  3. This is a topic where I think macroeconomists should incorporate variables like crime, especially the murder rate. Inflation is closely tied to these phenomena and the social costs could be much larger than many microfounded justifications for optimal inflation rates.

  4. inflation and crime papers:

    1. If you're responding to the request for papers, the rules are they need to have been already written and they need a numerical optimal long-run inflation rate.

  5. I've seen Scott Sumner make the point, several times, that the central bank should target the stickiest prices i.e. wages. He cites a Mankiw and Reis 2003 paper providing justification, but also notes that he made the same argument (less rigorously) in 1995. In my view, the typical worker should be able to sign a contract with an agreed number for wages that is good for several years, without a need for frequent renegotiation. The central bank can adjust the currency for movements in productivity, to maintain equilibrium.

    This isn't quite the same as the Friedman rule (the justification is quite different). However, given the relationship between interest rates and productivity movements in frictionless general equilibrium models, these two regimes should be similar.

    So yes: zero inflation is a great target, but not if we use consumer prices as our measure of inflation. And besides: people who specialize in measurement of consumer prices are telling us that the task is becoming more and more difficult, due to rapid technological changes.

  6. "Answer" is right, John. Any argument suggesting that there's an "ideal" but constant CPI or PCE or other output-based inflation rate is credible--almost all of them abstract from the implications of persistent variations in the rate of TFP productivity growth--which is to say, the rate at which overall unit production costs decline. It's a point economists used to "get" (Gunnar Myrdal, for instance, made the argument about the benefits of stabilizing relatively sticky factor prices back in the '30s, for instance; but there are many other arguments supporting a like policy). I made these arguments at length in Less Than Zero, which Scott Sumner frequently mentions as a source, though he seemed to forget my reference to the sticky wage argument, and to Myrdal, when he cited Mankiw and Reis, who merely (but very formally) reinvented an old wheel.

  7. John,

    "Broadly speaking, we start with the Friedman result that the optimal nominal interest rate is zero, so the optimal inflation rate is the negative of the real rate of interest."

    First: There is NOT a single, magical interest rate that everyone and their brother borrows at. So what if the Fed lends at a 0% nominal interest rate. That doesn't stop a private bank from taking that money and relending at a 2%, 4%, or 10% real interest rate.

    And so to get to Friedman's optimal SINGLE interest rate, private banking would need to be eliminated.

    Second: Changes in the interest rate by the central bank offer a check on expansive government. Ultimately, this is why the central bank increases the nominal interest in the hopes of driving down inflation. When the federal government borrows, they do not use the borrowed money to fund the production of new goods.

    And so, to prevent inflation escalation driven by government largess, the federal government cannot (under Friedman's theory) borrow at any interest rate (real or nominal).

  8. Prof Cochrane: off topic.

    I recently moved from NYC to TX. This morning at around 730, I was driving to work when my path was blocked off by a giant crane and road construction crew, none of whom could speak English except the supervisor. This was the only road out of my neighborhood. I was going to file a complaint to local council for the inconvenient obstruction, when I realized that I have never seen construction in NYC before 930, and it almost always ends around 430. Construction often goes on for years at a time with no end in sight. The construction laborers in NYC are also very unionized.

    After reading your blog, I realized that these regulations (union labor, noise regulations, land use regulations) are probably responsible for the high construction costs and slow work rate of NYC infrastructure projects. I withheld my complaint. Chalk it up as a win for the YIMBYs.

  9. Professor Cochrane,

    The most sense I can make from the formation of a 2% inflation target is:

    If there is a shock to the real rate and it goes to -2% then the cb just hits the lower bound. And based on the expectations that the real rate might never get there anyway then maybe this was an okay bet while still trying to minimize the welfare loss of inflation. I don't think cb's expected this low neutral rate environment we are in now, but I would tend to agree there was never a very scientific procedure in its initial set up, and the fact that there is loads of literature retroactively explaining it's optimality is puzzling (putting that nicely).

    On the point of PLT. I prefer an ngdpplt but for political economy reasons a PLT rule may be the more practical alternative framework that I believe is a much better alternative to IT. I'd be interested to see a post about the implementation. Particularly the point you mention about catching up to a plt from 2008. I would hardly characterize myself as someone using a PLT as a means to inflate today, but I do think that there is an argument for us to catch up to the 2008 PL path if it helps with gaining CB credibility. I'm not sure it I believe in that argument, but I see it there.


  10. John,

    My co-author and I have a paper in the JEDC with capital (an Austrian-style of capital with a time structure), endogenous entry and exit, and financial frictions. We find that optimal policy is still the Friedman rule.

  11. Interesting that so many economists favor a zero percent inflation rate, as measured.

    George Selgin has pointed out there may be times when inflation is valid, say in years of crop shortages. If there is a bad corn crop, then corn prices would go up.

    To try to beat prices back down by limiting demand would crimp the economy but not lower prices. Indeed accommodating higher prices would result in the price signal stimulating more supply.

    The ideal zero inflation rate strikes me as a Holy Grail, something aesthetically pleasing, and perhaps invested with ideological undertones, or class bias.

    But measurement issues, and deeply embedded structural impediments (property zoning for starters) perhaps make zero inflation unwise as a policy goal.

    The US economy did fine with a long-term average of 3% inflation and 3% real growth from 1980 to 2007. That is not a theory, nor ancient history.

    I suspect may of us would be happy with 3% real long-term growth again!

  12. Hi John. Three remarks from my side:
    (1) I would like to emphasize your last point with an argument from Mario Draghi (made at an ECB press conference a while ago): this is the worst point in time to consider changing inflation targets. The public’s confidence in the central banks’ ability to reach their inflation targets is shaken. Look at market-based 5Yx5Y inflation expectations (falling again in the US after the Trumpflation story turned out to be unfounded) or at survey-based measures like UMich 5-10Y inflation expectations. Lowering the targets right now would appear to be an admission of their inability to reach 2%. Inflation expectations would fall further and – in any model where inflation expectations play a significant role in the inflation process – reaching the new lower target would turn out to be as difficult as reaching 2% nowadays is. On the other side, higher targets would be non-credible as long as central banks struggle to reach their current targets. This is what the Bank of Japan currently experiences. Once inflation targets are persistently reached central banks might discuss changing them. But not now.
    (2) I was astonished that you take the Friedman rule as your starting point. I had considered the paper of Vasco Curida and Michael Woodford (“The central-bank balance sheet as an instrument of monetary policy“, Federal Reserve Bank of New York Staff Report No. 463, July 2010) as indicating that it‘s not the inflation rate which matters, but the spread between a central bank‘s deposits rate and lending rate. If this spread were zero, seigniorage would be zero and Friedman’s argument against distorting seigniorage would still apply at any nominal interest rate. Did I get this wrong?
    (3) The next point that astonishes me is the fact that one argument is always missing in the discussion about optimal inflation: asymmetric price adjustment. I know the old paper of Laurence Ball and Greg Mankiw (“Asymmetric price adjustment and economic fluctuations”, The Economic Journal, March 1994), who argue that positive long-term inflation expectations create this asymmetry. But frankly, I am not sure if that’s the whole story. Having talked to Japanese companies in the last years, I got the impression that Japanese wage stickiness is less asymmetric than in Europe or in the US, but lowering nominal wages is still a hassle there – even after 25+ years of zeroflation. I know, this is just anecdotal and not evidence. But unfortunately I am not aware of empirical studies of price-adjustment asymmetries in Japan. I fear that this asymmetry is part of the story of Japan’s under-performance in the last 20 years (asymmetric nominal price stickiness + long-term zeroflation = distorted relative prices = inefficiencies).

    1. (1) Indeed. Moreover, when you respond to events by changing the long-run target, it stops being a target, the inflation anchor.

      (2) The Friedman rule points out that when cash pays 0 and the interest rate is positive, people economize on cash by going to the bank too often. Yes, now most money pays interest, so the "shoe leather" costs are related to the interest spread between "money" and "non money" assets, whatever that means these days. But I'm still getting 0.01 on my checking account, and there is a lot of cash out there. Anyway, we're reviewing literature, and most of that literature ignores interest paying money. As in the post, there are other distortions as well, such as taxes on inflation induced capital gains.

      (3) The eternal downwardly sticky wages. Three points: 1) an individual wage does not grow at the rate of inflation. You get the aggregate productivity increase and the age earnings profile. So average wages can be going down and each individual's wage is going up. 2) People change jobs frequently. 3) There is a huge spread in individual wages, with many people taking wage cuts. Moving the middle of that spread to the left or right a few percent has a small effect. Bottom line, if inflation is 0% rather than 2%, just how many individuals have to actually take pay cuts? Not as many as you'd think.

      But, again, the point is not to argue one way or the other -- these are just many of the mechanisms to think about.

    2. Well, regarding “aggregate productivity increase”: Japanese nominal wages have decreased by 23% between 1990 and 2016 (most of this development happening between 1997 and 2009), as the data from the Ministry of Health, Labor and Welfare show. And regarding the required wage cuts: The Ministry’s “Survey on Wage Increases” for 2012 (the last year available) shows that 12.8% of surveyed companies implemented wage cuts (when wages fell by 2%), affecting between 23.8% and 43.2% of the employees in these companies. Not such a small number of workers, I’d say… And yes, the more people change their jobs, the more you get aggregate wage flexibility without flexibility in individual wage contracts. The only problem with this approach is: These job changes destroy job-specific human capital, eroding productivity from this side.

  13. How long did you have to work to afford a long distance tel call in 1960? How long do you have to work today to afford the same?

  14. New technology make almost everything cheaper. This is the main reason today for inflation.


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