Macro

• Nominal and real wage growth, St. Louis Fed, 2012-2023.

A Model of Inflation and Interest Rates

John Cochrane has a good Substack on how hard it is to build a model in which a rise in nominal interest rates by the Fed will generate lower inflation, [https://www.grumpy-economist.com/p/monetary-ignorance-monetary-transmission "Monetary ignorance, monetary transmission, and a great time for macroeconomics," (Sept 8, 2024). He begins by rejecting the monetarist model, because the Fed doesn't control the money supply any more. It is endogenous. Money-- via credit cards, etc.-- will expand as money demand asks.

Here is my attempt. Start with inflation equalling inflation last period plus something if output is above normal. The rationale is that agents have to coordinate on some price rise, since the price level is arbitrary, so they coordinate on last period's inflation. It is costless for everbody to raise prices that much, because it requires no thinking, just coordination. We will have to get later to why above-normal output raises inflation.

The nominal interest rate is the real interest rate plus expected inflation. Also, it can be manipulated by the Fed. Let's suppose the real rate is 3% and expected inflation is 5% in steady state, so the nominal interest rate is 8%.

Now suppose the nominal interest rate rises. That could be because the real interest rate has risen, or expected inflation has risen, or the Fed did some manipulation. It isn't expected inflation rising that starts this off, though, because expected inflation is endogenous--- it is last period's inflation plus the real-output effect.

Assume the Fed does NOT follow a Taylor Rule or anything like that-- it is exogenous. We should revisit this later.

Assume that if the real interest rate rises, output falls. Borrowing has become more expensive, so people don't want as many houses, and the price of housing is sticky so it doesn't fall enough to clear the market. Also, nondurable prices are sticky, so they don't rise enough to clear the market either. Also, nondurables are at capacity, and it takes time to shift inputs to them. In the next period, some will shift, and unemployment will fall. The eventual adjustment will be at full employment again, but less durable goods and more nondurable. If it is a Fed trick, though, the shift is a mistake and somehow this will be discovered over time.

So far this is much like what Cochrane calls the Static Keynesian Model. I haven't explained why higher real interest rates reduce output.

1. Nominal interest rate appears. 2. Firms choose prices for this period. 3. Inflation is the difference between last period's price and this period's. 4. QUantity demanded depends on prices and the nominal interest rate. Quantity supplied is constant.

In period 1, nominal interest rates rises and prices fall, and output. Next period, prices fall more (stickiness) and output rises. Inflation is higher,

Ah-- I have people using last period's inflation has their expectation, and their expectations turn out to be wrong. I can't do that.