A Simple Macroeconomic Model

In a recent article, I pushed back against Paul Krugman’s dismissal of microfoundations. However, I agree with his broader point: a simple model usually suffices. Indeed, I would argue that Krugman’s preferred model is not simple enough. In what follows, I offer an even-simpler model and explain how such a model would help Krugman avoid the inaccurate conclusion that monetary policy is ineffective when interest rates are at the zero lower bound.

Let’s start with the equation of exchange, which says that MV = PY. M is the stock of money: liquid assets used to make purchases. V is income velocity: the average number of times a unit of money changes hands in transactions involving final goods and services. P is the price level. Y is real output.

The equation of exchange is an identity. It says the amount of money changing hands (left-hand side) has to be equal to the nominal value of the goods and services purchased (right-hand side). Imagine you go into a convenience store and buy two cans of Coke for $1. A dollar changes hands one time (MV = $1 x 1 = 1); two Cokes at a price of 50 cents each are purchased (PY = $0.50 x 2 = 1). If you handed over more money, the cashier would return your change. If you handed over less money, the cashier would call the cops. The amount of money being spent has to equal the nominal value of the transaction being executed. This accounting principle holds for all transactions in the economy.

Next, we make some assumptions about the variables in the equation of exchange. In the long run, real output is determined by real factors (capital, labor, the level of technology, etc.). In the short run, prices are sticky and expectations are slow to adjust. Hence, we can characterize the effects of an increase in nominal spending (MV) as follows:

• P fails to fully adjust in the short run, meaning Y must increase.
• P fully adjusts in the long run, meaning Y must return to its long-run level.

In other words, an increase (decrease) in nominal spending (MV) will fool people into over- (under-)producing until they update their expectations and prices adjust.

If we are interested in monetary policy, we can expand the model to include a banking system. Suppose liquid assets (M) consist of currency (C) in circulation and deposits (D) held at private banks. Suppose further that the central bank controls the monetary base (B), where B = C + R and R is reserves held by banks. Hence, M = mB, where the money multiplier is m = (C+D)/(C+R) = [(C/D) + 1]/[(C/D) + (R/D)]. This suggests three ways the central bank might increase (decrease) the money supply (M):

• Increase (decrease) the monetary base (B).
• Encourage the average bank to decrease (increase) its ratio of reserves to deposits (R/D).
• Encourage the average household to decrease (increase) its ratio of currency to deposits (C/D).

Now, that is a pretty simple model. Indeed, it is the model I teach undergraduates. It is also the model I refer back to when reading the news or talking to other economists. It is far from complete. The microfoundations are implicit. A lot of institutional detail is omitted. But it is a useful tool for quickly thinking through complicated macroeconomic issues.

To illustrate, let’s consider the effectiveness of monetary policy at the zero lower bound. Krugman writes:

On the monetary side, old-fashioned macro says that once interest rates have been driven down to the zero lower bound, monetary policy loses traction. Even huge increases in the monetary base (bank reserves plus currency in circulation) won’t be inflationary. […] We all know what happened. The Bernanke Fed massively expanded the monetary base, by a factor of almost five. There were dire warnings that this would cause inflation and “debase the dollar.” But prices went nowhere, and not much happened to broader monetary aggregates (a result that, weirdly, some economists seemed to find deeply puzzling even though it was exactly what should have been expected.)

Hence, according to Krugman, the Fed’s decision to increase the monetary base (B) had little effect on broader monetary aggregates (M) and, correspondingly, real output (Y) and price (P) because monetary policy is ineffective when interest rates are sufficiently low.

I don’t buy it. Krugman is effectively arguing that monetary policy only works through the interest rate channel. In fact, there are other channels through which monetary policy might work. If monetary history teaches us anything, it is that central banks can always increase nominal spending (MV) and, therefore, nominal income (PY).

The even-simpler model I prefer suggests an alternative interpretation. The problem was not that expansionary monetary policy was tried and found wanting, as Krugman claims. Rather, it was that it was never really tried. The Fed systematically undermined its own efforts to increase the money supply. Sure, it increased the monetary base (B). But it offset that expansionary policy with the contractionary policy of paying interest on reserves, which significantly increased the reserve ratios of banks (R/D). The Fed increased B while decreasing m. The net effect on M was nil. In other words, the Fed did not engage in expansionary monetary policy on net. And the economy suffered as a result.

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