Tuesday, July 15, 2014

Trying To Understand Inflation

Scott Sumner makes the case that economists generally can’t agree on what inflation is, and even when they do, their understanding is at odds with the general population. Let’s explore this a little:

Imagine an economy with one laborer, me, one capital owner, you, two consumers, you and me, and two kinds of goods, apples and oranges. It takes me one hour to produce one apple and one hour to produce one orange. I can only work a maximum of 500 hours in total per year. I get paid one dollar an hour, but you get half of my wages (this makes it easier to introduce a monetary system into this fictional economy rather than having the capital owner retain the product--just assume after production the fruit is co-owned by you and me hence we "buy" it from the coop). Let's start with the price of apples at $1 and the price of oranges at $1. Another way of looking at it is to say the price of an orange is one apple and the price of an apple is one orange.

Fast forward to one year later where apples and oranges begin the year at the same price of $1 each (sticky prices) but then rise to $1.17 for apples and $1.05 for oranges (details how are below), my wage rate is still $1 per hour (sticky wages), but my productivity has increased whereby it only takes me 45 minutes to produce either fruit. In this story how can we meaningfully talk about "inflation"? Prices have risen, but so has productivity. In fact, productivity has potentially increased 33%. And wages are flat for the time being. None of these variables alone really tells the story. John Cochrane might say we’re on to something.

And if a monetary authority (an entity that controls the supply of money such as a central bank) targets "inflation", we start to see big problems. David Beckworth tells it better and more thoroughly than I can.

Picking up on one of Beckworth’s claims, we can see from our hypothetical apples and oranges economy that it will look like the supply of money needs to be loosened when in fact it needs to be tightened to allow total spending in the economy (nominal GDP) to be maintained.

Let's assume in the first year I produce 300 apples and 200 oranges, and then you and I each separately purchase/consume 150 apples and 100 oranges. Total spending in year 1 is $500 (500 fruits at $1 each). 

[here comes the yada, yada, yada...]
In the second year I produce 360 apples and 240 oranges taking just 450 hours to do so thanks to my enhanced productivity which leaves time every day to pretend I'm Rip Van Winkle while on the clock (you'll see below why I would stop working at some point short of maximum output--360 and 240 are somewhat arbitrary numbers). My total wages are $500 still since I'm still getting $1 per hour for 450 hours of labor and 50 hours of napping. You still get half of my wages, but additionally the central bank gives you $100 and me $75 (out of thin air) so as to maintain the monetary authority's desired ~2% inflation target in the face of a 33% rise in productivity* ($175 is about a 35% increase over the $500 monetary base). I have $325 and you have $350. As we attempt to make our purchases of apples and oranges presumably to get at a similar consumption arrangement as before (half of each type of fruit for each of us), we bid up the price of each good somewhat so that the market can clear and in the process we change the consumption arrangement some. Your greater purchasing power allows you to bid up your slightly preferred fruit, apples, a little relative to oranges. The prices settle at $1.17 for apples and $1.05 for oranges (these prices are arbitrary in the example—just one of many ways the math will work out). You walk away with 190 apples and 121 oranges while I get 170 apples and 119 oranges (just one of many possible outcomes). This makes total spending in period 2 $675 [$1.17 x (190+170) + $1.05 x (121+119)].

We can summarize the economic situation: Total spending, "nominal GDP", is up dramatically (35%) while the "real GDP" is only up 20%. The monetary authority wanted only about 2% price inflation but got a 15% level. The economy could potentially be producing 11% more fruit than it is actually producing. The Cantillon Effects of you getting $100 and me only $75 from the central bank may be unrealistic and are not central to the story. I believe there is something to it and it can have distributional effects as it does here (both in the price change and ultimately the quantities of apples and oranges we each get to enjoy). Don’t get lost in this, though; it is not the central theme—rather understand that inflation is a murky subject and policy based on it can have severely adverse consequences.

It was my expectation of the central bank's inflation targeting which led me to shirt instead of producing more--I happened to stop at 360 apples and 240 oranges. The high rate of money supply growth was a negative shock to my purchasing power. I should have seen my $1 per hour going further as the price of apples and oranges came down in nominal-dollar terms, labor-hour terms, and substitute-good terms (apples for oranges and vice versa). If instead of targeting inflation the central-bank targets nominal GDP to rise about 5% such that nominal GDP should be about $525 in year 2, prices will be allowed to fall and my purchasing power because my wages are sticky will be rising; hence I will be incentivized to produce closer to the the economy's full potential. In which case I will be doing a lot less shirking. Year 2 would look more like this: I produce close to 667 total fruit, the money supply increases about 5% rather than 35%, the prices of apples and oranges each fall about 25% (a 33% productivity increase implies a 25% price decrease) but is offset some with the 5% increase in money supply, and the economic distortions are minimized. Happily ever after . . .

*The key here is that the central bank doesn’t completely understand the increase in productivity, and it realistically wouldn’t. In a more realistic, fluid economy what they would see would be falling prices or at least downward price pressure for apples and oranges. Productivity gains would equally be disguised as underemployment (after all, I am napping). The feedback loop keeps telling them to fight deflation—i.e., increase the money supply.