How to change the inflation target

The longer interest rates stay at the Zero Lower Bound (ZLB), the stronger the case (pdf) for raising the inflation target becomes. (No, that is not a good reason to raise interest rates today, but perhaps it helps explain why some are so keen to do so!) However there seem to be two political barriers to this happening. Central banks seem to live in mortal fear that any move to raise inflation targets will shatter their ‘hard won credibility’ and inevitably lead to inflation ‘taking off’ and inflation expectations becoming ‘unhinged’. Where politicians have control (as in the UK), they worry the public will interpret any increase in the inflation target as a further erosion of their living standards. Yes, I know Abe raised the target rate in Japan, but only to the 2% that has become the consensus for the major developed economies.

Tony Yates suggests a very British solution to this problem. In the past, a standard way that UK politicians have handled such tricky questions has been to establish an independent commission to examine the question. (One famous example in the past was the Macmillan committee, set up after 1929 to establish the causes of the UK depression. Keynes’s role on that committee is vividly described by Peter Temin & David Vines in their recent book.) Tony calls it the Inflation Remit Review Commission. This commission could take evidence (from the central bank and others) on issues such as what the medium term natural real interest rate is likely to be, and compute the costs and benefits of any change. This sounds like a good way of trying (as far as possible) to depoliticise the issue, and putting the central bank’s inflation paranoia in context.

I have just one suggestion to add. This commission, at the same time, should examine whether it remains appropriate that the inflation target should just involve the consumer price index (and in particular, whether the rate of change of wages should also be targeted), and whether the target should involve the inflation rate or a path for prices (a price level target), or indeed national income. These questions naturally go together with the choice of the level of any inflation target. If there is a target for the path of prices rather than its rate of change, then the consequences of hitting the ZLB are less severe, for example. In addition, the possibility of ending the tyranny of the consumer price index, or changing to a level target, suffer from much the same conservative bias from politicians and/or central banks as the value of the target itself.

Whether the idea of a commission would work in the US I do not know. In the Eurozone there are strong grounds for setting up a similar body, not only to review the questions set out above, but also to permanently oversee the performance of the ECB. At present the ECB has minimal accountability. Appearing every three months before the European Parliament just does not count, I’m afraid. (For further discussion, see this Bruegel paper by Claeys, Hallerberg and Tschekassin.) This in itself is a strange state of affairs for an institution with such power. In addition its performance since 2011 (at least) has been very poor relative to the Fed and Bank of England. (See for example this post written over a year ago which I think reflected the clear consensus among macroeconomists at the time.)

Tony does not suggest who might sit on this commission, except to say that they should not be part of the government, or the central bank. My own view is that it is vital that at least some are academic macroeconomists, because academic macroeconomists do understand these questions better. For the UK obvious candidates are ex-external members of the Monetary Policy Committee, unless you think they have become (or were perhaps selected because they were) too indoctrinated with the central bank view. Suggestions on who might comprise an oversight commission for the ECB would be very welcome.      

Price level targeting intuition

For students and maybe teachers of macroeconomics. The analysis here is standard: a more general discussion can be found in Woodford's Interest and Prices for example (see pages 497-501 in particular). All this adds is a bit of intuition which I at least found helpful. If there are any mistakes in the algebra or numbers below, please let me know and I will correct them 

When monetary policy can commit (i.e. follow a time inconsistent policy), why does the optimal response to an anticipated cost-push shock involve bringing the price level back to its original value? I do not think it is obvious why it should, yet the result is an important part of the justification for price level or nominal income targeting, so here is my attempt at some intuition.

To make things simple, ignore discounting in both the monetary policymakers objectives and the New Keynesian Phillips curve (NKPC). For notational clarity, assume perfect foresight. So the monetary policymaker tries to minimise the weighted sum of the output gap (y) and inflation (π), both squared (the inflation target is zero), from period zero onwards, subject to a series of NKPC constraints. The shock is a cost-push shock (u) in period zero, which is observed at the beginning of period zero.

To start us off, assume that the policymaker can only set period zero output and inflation. Expected inflation in period 1 is zero (the shock is not persistent, and the central bank is credible.) So the problem can be expressed as choosing output and inflation to minimise the Lagrangian:

This gives us two first order conditions:

which can be combined as

Equation (1) can be thought of as a policy rule: the combination of the output gap and inflation that optimal monetary policy would select if it cannot achieve zero for both. So, for example, if output has a large impact on inflation, then (1) gives a larger ‘weight’ to inflation. If people like diagrams, we can represent the loss function by indifference curves around the ‘bliss point’ zero, which are circles if β is one. The monetary rule (1) is the line joining the points where these indifference curves are tangent to the Phillips curves.

To take a concrete example, let the cost push shock be 10, and set α=β=1. Adding (1) to the Phillips curve implies that the central bank creates a negative output gap of 5, which gives an inflation rate of 5. The optimal policy involves one of intratemporal smoothing, balancing the costs of inflation against the costs of lower output. The welfare cost is 50, compared to a cost of 100 if the policymaker allowed no fall in output.

Suppose now that the policymaker can make promises about period 1 only. The Lagrangian then becomes

The first order conditions always imply that the Lagrange multiplier for any time period is equal to the output gap for that period divided by α. In addition to the first order condition (1) for period zero inflation, we also obtain

We can add (1) to this, to get

Equation (2) gives us the key intuition behind the price targeting result. Suppose αβ is large, so the final term is small. In this case (2) tells us that the sum of inflation in the two periods will be close to zero. Higher inflation in period zero will be almost balanced by negative inflation in period one. A moment’s thought implies that this must mean the price level at the end of period one will be close to its original value.

Inflation in period zero will be positive as a result of the cost push shock. We can reduce its size by creating negative inflation in period 1. By creating negative inflation of x in period 1, we reduce inflation in period zero by x. With a cost push shock of 10, creating negative inflation of 5 in period 1 balances positive inflation of 5 in period zero, which is the optimum combination. Creating less negative inflation in period 1 will lead to a greater welfare loss, but so will reducing inflation by more than 5 in period 1.

However, what if αβ is not large? Specifically, suppose we return to the example where α=β=1. Combining this with the NKPC for each period implies the optimal policy is

The optimal policy creates negative inflation in period one, but not by enough to keep the price level unchanged. Prices end up higher by 2, compared to 5 when we could only change period zero values. The welfare cost is now 40, which is an improvement on 50.

Why does the case non-negligible αβ stop approximate price level targeting in this two period case? Think about what exact price level targeting would imply. It would involve inflation of 5 in period zero and -5 in period one. This could be achieved with an output gap of -5 in period one, but no output gap in period zero. So although inflation would be balanced, output gaps would not be. A more balanced output combination involves a higher final price level.

(The policy is now time inconsistent: at t=1 there is an incentive for the policymaker to not carry through and reduce output, but instead set the output gap to zero. Unfortunately if this change in policy is anticipated in period 0, inflation will be 6 rather than 4 in period 0, and the overall welfare cost will be 52 (36+16), which is worse than the case where policy only operated in period zero.)

Suppose we now allow the policymaker to make promises in period 0 about the output gap in period 1 and 2. Instead of just reducing output in period one, we can spread lower output over periods one and two. The output costs become more balanced, which reduces the extent to which we fail to achieve a balanced inflation profile. We can then derive the following policy rule

                                                                  

As the fall in output in period 2 is likely to be lower than the previous fall in output in period 1, the deviation from price level targeting is reduced.

If we allow the policymaker to make commitments T periods ahead, then we can derive the following first order condition:

                                                  

High inflation in period 0 can now be balanced by negative inflation in many later periods. Intuitively the output gap in period T will become very small as T becomes large. This implies that the sum of inflation over all periods is almost zero. That means that the price level in period T is almost the same as the original price level. Thus the optimal policy in effect involves a long term price target, although that target is approached gradually.

Going beyond Quantitative Easing

                I’ve been away for a few days at the OECD, so have only just picked up Scott Sumner, fully endorsed by Tyler Cowen, asking why there are not more people advocating a higher inflation target, or a nominal GDP target, in the UK. (Being away did not in theory prevent me blogging, but I’m afraid in practice I prefer exploring Paris!) I think this is a good question. While there is a very active UK debate about fiscal austerity, most discussion on the monetary side tends to be within the parameters of current policy.  

                Those familiar with the case for raising the inflation target can skip the next couple of paragraphs. For those who are not, the idea is that the central bank/government could moderate the impact of the zero lower bound constraint on interest rates by announcing that it would allow inflation to go above 2% for a significant period after the recession was over. This would help stimulate the economy today through various channels. One is that expected lower future short interest rates should reduce long term interest rates today, which would in turn stimulate borrowing by firms and consumers. Another is that, according to the New Keynesian Phillips curve, expected inflation today depends on expected inflation tomorrow, so if the central bank allowed above 2% inflation in the future, this would raise actual and expected inflation today, lowering real short term interest rates today. One of the interesting things about this policy proposal is that it is very New Keynesian rather than Old Keynesian.

                This policy was first suggested as a way out of Japan’s lost decade (when nominal rates were also stuck at the zero bound) by Paul Krugman, and subsequently formalised by Eggertsson and Woodford (Gauti B. Eggertsson & Michael Woodford, 2003. "Optimal Monetary Policy in a Liquidity Trap," NBER Working Papers 9968) among others. This paper suggests that the optimal policy can be approximated by replacing an inflation target with a price level target, because a price level target implies a period of excess inflation would automatically follow a period of insufficient inflation. Scott Sumner in particular has championed nominal GDP targeting, which would have similar effects, and this policy has gained a lot of support in the US and elsewhere.

                So why relatively little debate on this issue in the UK? At the political level, simple politics combined with recent experience may be important. Price inflation has been, and still is, high in the UK, and this is highly unpopular because it has been associated with large falls in real wages. An argument by any political party that the Bank should target higher inflation, rather than be admonished for its inability to prevent it, would be a hard sell. Nominal GDP (NGDP) targeting may be much more palatable to a non-macro audience, as Krugman points out. However a problem here for the government may be the accusation that such a change reflects a failure of their austerity programme, for reasons discussed below. Whether this issue might be on the Labour Party’s agenda I have no idea, although I cannot see any reason in principle why it should not be.

                What is perhaps more puzzling is a lack of discussion by the Bank itself. As far as I am aware, the Bank has not discussed these various alternatives to its current 2% mandate. I am also not aware of any members of the current MPC discussing them in public. Of course any decision to change the mandate would not be for the Bank or MPC to make – it’s a decision for the Chancellor - but that does not rule out discussion of options. I think this lack of ‘official’ discussion may also discourage debate elsewhere. (I know I thought of writing something myself on this a few weeks back, looked for something from the Bank as a ‘hook’ to argue with, and on finding nothing let it slide.) In contrast to the US, macroeconomic blogs in the UK are not developed or influential enough to initiate a debate themselves.

                The lack of public analysis from the Bank, or MPC members, could perhaps be another example of ‘groupthink’ that Laurence Ball suggests in his analysis of Bernanke’s views on the zero lower bound. My first experience of this came at a conference organised by the Centre for Central Banking Studies in 2009. Chris Sims and Mike Woodford were the other guest speakers, and both my and Mike’s paper provoked discussion of this policy issue. I have often been in meetings where an option may be politely discussed, but you just know it has no chance of serious consideration, and this seemed like one of those. To be honest, I think this represents central bank conservatism more than anything else.

                One of the main arguments against this policy option is time inconsistency. Even if a promise to raise future inflation was effective today, when the recession ended and it was time to implement the policy, the temptation would be to renege on this commitment and return to the 2% inflation target. A smart private sector would realise this, so the promise to raise future inflation would not be believed, and so it would not be effective. A price level or NGDP target is partly designed to help overcome this problem. However, in the case of the UK, where a change in policy would almost certainly have to be decided by the Chancellor rather than the Bank, this should be seen as less of a problem for the Bank or MPC. Its credibility would not be on the line, and the government rather than the Bank would come under pressure to renege.

                Exactly the same could be said of another objection to raising the inflation target, which is that it might be perceived as a way of helping the government reduce the ratio of debt to GDP. This charge could be a more serious concern for the Chancellor, if it was perceived that his austerity program was not delivering the fiscal target he had set himself. However, it should be less of a concern for the Bank, because they have always deferred to the Chancellor’s authority to set the inflation target. So for both reasons, I suspect the lack of discussion by the Bank and MPC may reflect a taboo about deliberately raising inflation above 2%.

                I should add that I think the advocates of NGDP targets sometimes go too far in suggesting that this is an obviously preferable way to speed economic recovery compared to fiscal stimulus. Promises to raise future inflation are costly, which is why there is a time inconsistency problem. However the current recession is, in my view, much more costly, so it needs both monetary and fiscal action to help bring it to a speedy end. Furthermore, the current recession may well indicate an endemic problem with low inflation targets, which is that we are in danger of hitting the zero bound quite frequently. (With this in mind, can anyone explain to me why the Bank of Japan has just announced an inflation target of only 1%?) This seems like an excellent time to be discussing alternatives to inflation targeting. 

So it is a pity that this policy option is not being debated more actively in the UK right now, with help from the Bank and MPC members. In the absence of a discussion based around the Bank, then this seems to be exactly the kind of issue that the Treasury Select Committee of the House of Commons should investigate. The committee has always taken a keen interest in all aspects of monetary policy, and such an investigation would be a good follow-up to their recent report on Bank accountability.