Thursday, 31 May 2012

Austerity, Nominal GDP targets and the Zero Lower Bound


                One part of my earlier post on monetary policy and austerity was a little cryptic. OK, it was largely unintelligible to nearly everyone (see, for example, Arnold Kling here).  My apologies. As it’s an important point, let me elaborate. What I want to show is that with monetary policy aiming to hit some level for nominal GDP (NGDP), if we are at the Zero Lower Bound (ZLB) for nominal interest rates today, austerity today will reduce welfare (by, in part, raising inflation tomorrow), and fiscal stimulus will increase welfare. I will not use maths, as even when I use the most simple of equations, my posts are described by well known blogging economists as nerdy.
                Output today depends on real interest rates today. Anything else that changes output today is called a shock. There is no Quantitative Easing (QE). For simplicity we will assume no direct linkage between output across periods. Inflation today depends on output today, but also expected inflation tomorrow. Prices were on target yesterday, and let’s assume that inflation the day after tomorrow is fixed. Now hit output today with a negative demand shock, a shock which is not repeated tomorrow. If that shock is small enough, we can offset it entirely by lowering interest rates today. Inflation today is unchanged as a result. Nothing changes tomorrow. Everyone is happy: monetary policy has done its job, by lowering nominal and real interest rates today.
                Now suppose the negative shock today is so large, that even with nominal interest rates at zero, output remains too low. This reduces inflation today. With a target for NGDP, not only would this mean we missed our target today, but it would also mean that we would miss our NGDP target tomorrow, because lower inflation today would mean lower prices tomorrow if inflation tomorrow was unchanged. So monetary policy cuts interest rates tomorrow in order to raise tomorrow’s output and inflation. If this response is expected (we assume rational expectations throughout) it does two things. It raises inflation today directly (because inflation today depends on expected inflation tomorrow), and it reduces real interest rates today (real interest rates today are nominal rates today minus expected inflation tomorrow), which raises output today which in turn raises inflation today. This is why NGDP targets can be very helpful to combat the ZLB. If we instead targeted inflation, then monetary policy tomorrow might do nothing, because policy would still hit the inflation target tomorrow.
                Now suppose that, despite relaxing monetary policy tomorrow, we still hit the ZLB today. Output and inflation are too low today, even though we hit the NGDP target tomorrow. There is absolutely no reason why this might not happen. Although inflation is higher tomorrow to compensate for low inflation today, real interest rates today are still not low enough to prevent output falling today. Sure, we could relax monetary policy tomorrow by yet more (assuming we are not at the ZLB tomorrow), and this could increase inflation tomorrow by enough to get real interest rates low enough today. But that would mean we overshoot our NGDP target tomorrow.
                So, we hit the ZLB today, undershoot the NGDP target today, but meet it tomorrow. Now let output also depend on fiscal policy, and add some austerity today. This reduces output by yet more today. Interest rates are at the ZLB today, so monetary policy today can do nothing about it. Lower output lowers inflation today still further, but because this reduces the price level tomorrow, monetary policy relaxes by more tomorrow. This is good, because higher inflation tomorrow raises both inflation and output today, which moderates the impact of austerity. But the end result must be that the net impact of austerity is to reduce output and inflation today, and raise inflation tomorrow. (If output and inflation are not lower today, inflation will not change tomorrow. But if inflation tomorrow is unchanged, why has austerity not reduced output and inflation today?)
                That is how a negative demand shock today, like austerity, can raise inflation tomorrow. It only happens because we have a target for the level of NGDP, and we cannot use interest rates to kill the impact of the demand shock today, because we are at the ZLB. But the latter is where we currently are, if you ignore QE.
                It follows directly that excess austerity today reduces welfare, even with NGDP targets. We still hit the NGDP target tomorrow, but only by having additional excess output and inflation tomorrow, and a bigger recession today. People are clearly worse off both today and tomorrow.
                This little experiment also shows us why fiscal stimulus can be more effective than a NGDP target at stabilising the economy at a ZLB. Just put the story in reverse. Instead of excess austerity, now have a fiscal stimulus today sufficient to get NGDP back to target today. As there is no shock tomorrow (fiscal or otherwise), we also hit NGDP tomorrow. We are back to where we want to be. Now the fiscal stimulus may have meant more government spending than we might have wanted in the short term, so it’s not cost free. But in terms of output and inflation, we are clearly better off as a result of the fiscal stimulus, even though we have a NGDP target.
                  
                 

5 comments:

  1. As a student who attended your macro course twice (I hope that says more about your capabilities than mine)I've been extremely happy to see you begin this blog.
    Seeing Krugman on Newsnight taking down some of the worst zombie fallacies triggered a question: What barriers if any stop you from taking your arguments to such a forum?

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    1. Yes, I was struck by the fact that the opposing talking heads both had backgrounds in finance rather than economics. I was wondering if the BBC had been frantically scouring the country to find someone suitable who disagreed but had been unable to do so.

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  2. "People are clearly worse off both today and tomorrow."

    Under your assumptions (in particular, no ability to target a NGDP level target through monetary policy at the ZLB) they're clearly worse off today. But if you hit the NGDP level target tomorrow you're just as well of in either scenario since the real output level and the price level are exactly the same unless there is a difference in the AS curve. Rates of change do not matter under any form of level targeting and intuitively should not matter in any welfare calculation.

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    1. I'm assuming here, not unreasonably, that welfare each period is related to the rate of inflation and the output gap each period. As a result, welfare is lower in both periods as a result of austerity.

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    2. "I'm assuming here, not unreasonably, that welfare each period is related to the rate of inflation and the output gap each period."

      I have no quarrel with assigning a negative weight to the welfare cost of the output gap (of course), it's the inflation rate I am concerned with. In and of themselves more variable inflation rates have no welfare costs, as long as the level of NGDP is relatively stable over time. And in fact, over time, NGDP level targeting is much more likely than memoryless inflation rate targeting to produce a stable price level. (Levels matter more than rates.)

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