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# The Fluttering Veil

23 Apr 2021

This is my primer on money in macroeconomics. In particular, I want to discuss how money affects the nominal world and how it affects the real world. And in turn, what this implies for the conduct and goals of monetary policy.

Money and the Nominal World

If we want to talk about the nominal world, we need to talk about money - this is the defining feature of the monetary exchange economy in which we live. And it is because we engage in monetary exchange that money exists - instead of relying on a double coincidence of wants where two people want each other’s stuff and barter, money gives us a medium of exchange to avoid that in our transactions.

Having established what money does, what is the value of money? Slightly facetiously, the nominal value of £1 is just £1, as it says on the tin. But its real value is what you can buy with it i.e. its purchasing power. As with any other good, this value is determined by the supply and demand of money. If we think of central banks as having a monopoly over the money supply, it can set any quantity $M$. Meanwhile, people’s demand for money depends on its role as the medium of exchange - if the amount of nominal output $PY$ in the economy is higher, people will want more money to buy things. Of course, people don’t hold all their wealth in the form of money, because doing so means that they forgo the earnings from putting it in interest-bearing assets. So we might think that the fraction of money they’re willing to hold is a decreasing function of the interest rate as $k(i)$. That means the equilibrium when the supply of money equals the demand is $M = PYk(i)$. If we think that the velocity at which people spend money is the inverse of the fraction of money they want to hold i.e. $V=\frac{1}{k(i)}$, we get the following equation of exchange.

$MV = PY$

Consider what happens when there is a one-off doubling of the money supply from the central bank. Although individuals may choose the amount of money they want to hold based on the money demand described above, this clearly isn’t possible in aggregate given that is controlled by the central bank. How is this resolved? When we see this doubling, the real value of the money people hold will be too much for what they want - consequently, they will get rid of the money they hold by buying things. This bids up the price level and it adjusts by doubling, until the purchasing power of money they hold is back to the level they want. In other words, people determine the real value of money they hold while the central bank determines the nominal value of money. This is the quantity theory of money, which says that the price level is directly proportional to the money supply in the long run. This is the long-run neutrality of money i.e. the money supply only affects the price level, as opposed to real variables like output.

However, consider what would happen if a central bank doubled the money supply today and promised to halve it tomorrow, as soon as inflation occurred. Would there still be the same effect on the price level? Probably not. So there is a difference between a temporary and permanent injection of money. And similarly, it seems likely that prices would rise immediately if people were told that the money supply would double tomorrow. Expectations matter. Another useful consideration is to think about what happens if the rate of money growth increases - this will lead to an increase in inflation $\pi$. Since the nominal interest rate $i$ is approximately the real interest rate $r$ plus the inflation rate $\pi$, this will raise the nominal interest rate and the velocity of money. So in this way, it is clear that a one-off rise in the money supply will raise nominal output by causing a rise in $M$, while a rise in the money growth rate will raise nominal output both via $M$ and $V$.

So this is the nominal world - here, the quantity theory and neutrality of money holds, and monetary changes affect nominal output. Yet as interesting as this is, the reason we care about money is because its changes have effects on real variables.

Money and the Disequilibrium Sticky World

So how does money affect the real world? To understand this, we have to go back to the reason why fluctuations from the full-employment level do not occur in the real world without money. We know from Walras’s Law that if there is an excess supply of goods in one market, it must be the case that there is an excess demand for goods in another market. In a world with a perfect barter system, any deviations from equilibrium would represent opportunities for mutually beneficial trade. People would simply negotiate and trade away these inefficiencies. In other words, Say’s Law would hold and supply would create its own demand.

Why does money change this? As it turns out, the introduction of money as a medium of exchange means that every market goes from being a goods-goods market to a goods-money market. And so if the money markets are out of equilibrium, the goods markets will be too. But how can the money market be out of equilibrium? This is because it is often the case that the exchange rate between money and a good is not easily changed i.e. the unit of account is sticky. So when there is suddenly an excess demand for money, the price of money would need to rise i.e. the price of everything else would need to fall. Because some prices for goods are sticky, those goods markets will go out of equilibrium - and when it is difficult to sell goods for money due to the price of goods being too high, people stop selling money for goods too i.e. the volume of trade falls. And so even a few sticky prices will result in all sorts of markets going out of whack. As Jack Gurley put it, “money is a veil, but when the veil flutters, real output sputters”.

This is best illustrated by looking at some real world examples. For example, some of the largest shocks did not produce biggest downturns, because the change in money demand was offset. The 1987 financial crisis saw the single largest one-day percentage fall in the Dow Jones Industrial Average, and yet output barely budged. The prelude to the Great Recession saw housing construction falling by half between early 2006 and mid-2008, and yet employment didn’t get affected till later in 2008. By many accounts, the Treasury market in March 2020 froze up in a way that wasn’t even seen during the Global Financial Crisis of 2008, and yet this never propagated into a wide scale financial crisis. And that’s because in those cases, monetary policy provided speedy, substantial and sustained access to money and liquidity. By contrast, all of these pale in comparison to the size of the business cycle fluctuations during the Great Depression or the Great Recession - that’s because monetary policy was not there to accommodate these shocks. So although real problems matter, they only become huge issues because of nominal problems. What does this mean for monetary policy?

Goal of Monetary Policy in Theory

Implicitly, we’ve already identified the role of monetary policy: it is to look at changes in money demand and offset it with the money supply - that is, to ensure that $M$ adjusts when $V$ fluctuates, because rapid fluctuations in $MV$ cause problems by forcing the money market (i.e. all markets) out of equilibrium. In other words, the idea is to stabilise the expected future path of nominal GDP. And this isn’t terribly surprising - insofar as people make decisions about employment contracts, debt contracts and all sorts of purchases based on the expected level of nominal GDP, changes off that path can cause problems.

There are three important notes on this approach. The first is about the word “expected” - this means looking forward at forecasts, and because it’s generally not a good idea given the Efficient Market Hypothesis to assume you can always outpredict the market, targeting market forecasts is particularly appealing. This has the additional advantage of reducing the “long and variable lags” associated with policy changes, since asset markets react quickly and will tell you if you’re on track. The second is about the word “future” - people are to some degree forward looking, and if they expect future nGDP to fall, they will start spending less and cause current nGDP to fall. Meanwhile, if future nGDP remains on target, people have far less incentive to spend less now and so it is hard for current nGDP to fall much. As such, monetary policy should be concerned with all future levels of nGDP, not just what it is right now. The third is about the word “path” - since people’s expectations of future nGDP matter, it is even better to commit to targeting a level rather than just an annual growth rate. In practice what this means is that any shortfalls in nGDP growth in a particular year are made up for in future years, rather than simply letting bygones be bygones. This commitment to correct for deviations means people have well-anchored expectations of the future level of nGDP, since a failure to hit the goal in any single year won’t drag it down.

How does this compare with the status quo? In many ways, this is very similar to how many economies like the US, UK, Canada, Australia, New Zealand and Israel conduct their monetary policy right now. They have some sort of dual mandate where the central bank cares about inflation and output, they are ostensibly forward-looking and target the forecast, they place a significant premium on affecting future expectations and in the case of the US with its new regime of average inflation targeting, will make up for shortfalls. But the difference is that nGDP level targeting treats nominal GDP as one thing, whereas most central banks currently treat the components of real output and inflation separately. Inevitably, this reduces some of the flexibility central banks can have, because it forces them to only care about real output and inflation as well as treating their deviations as equally important.

But the advantage of not splitting this into a flexible dual mandate comes in several ways. Firstly, it is just a lot easier to sell a central bank’s policy as one of raising nominal incomes than of raising inflation during a crisis, because many people associate the latter with a higher cost of living. Secondly, the measurement of inflation is notoriously difficult and arbitrary, whether this is in the use of hedonic adjustments or the imputing of rental equivalents for housing. It is a testament to this confusion that there are so many different price indices, not to mention different variants on each e.g. core inflation versus headline inflation, where the former excludes food and energy prices. Thirdly, inflation can be deceptive - insofar as prices change slowly, inflation will lag behind shocks to nGDP. And in fact, it may go the other way if there is a supply-side shock hitting the economy at the same time. The most obvious example of this causing a misdiagnosis is in mid-2008, when the rise in oil prices meant the Federal Reserve was too concerned about inflation and failed to arrest the fall in nGDP.

The other main disparity between nGDP level targeting and what we do right now comes down to how we measure the stance of monetary policy. In the past, economists often looked at monetary aggregates, though we now commonly look at interest rates. The danger with this is that interest rates fall for many reasons - one reason interest rates fall is due to monetary expansion i.e. a liquidity effect from an increase in the money supply. But over time, an increase in the money supply translates into more nGDP growth, raising the interest rate. So when the Fed lowered interest rates during the Great Recession, it seemed on the surface that they had an easy monetary stance. But in reality, the equilibrium interest rate had fallen even further due to low nGDP expectations, so their easing of policy still left them at an overall tight monetary stance. And although in theory a good measure would be the deviation of the interest rate from its equilibrium level, the difficulty of doing so in real time means a much better alternative is just to look at nGDP expectations, since it will be apparent if the monetary expansion is enough to offset the increased demand for money. And by doing so, we can infer the monetary stance with reference to the expected value of our policy goal and relative to our policy target.

Going Forwards

We can see clearly that money is crucial in our modern economy. In the long run, the effects are nominal, but in the short run, they are very real. And the consequence of that is the need for monetary policy to help alleviate these fluctuations. In practice, this looks like what the Fed has done, using a range of tools to meet its dual mandate.