To analyze the transmission from interest rate policies to output and inflation, many academics and central bank economists use the basic New Keynesian (NK) ‘three-equation model’ and its various extensions. A key factor responsible for the model’s success is the seeming alignment with conventional wisdom—some of the model features can be framed in the language of familiar business cycle narratives, as found in newspapers, central bank communication, or introductory macroeconomics courses. But the resemblance between model and narratives is deceptive and the framing misleading. Practitioners and journalists might think that they base their reasoning on the NK model, but typically that’s not what they do.

So, what does the NK model really say? Few writers have identified the model’s fundamental elements more clearly than Stanford’s John Cochrane. In the context of his work on the ‘Fiscal Theory of the Price Level’ (FTPL), which partly overlaps with the NK model, he has thoroughly scrutinized the latter framework and compared it to prevalent views among policy makers and commentators. His verdict is harsh. In a recent blog post he writes:

There is a Standard Doctrine, explained regularly by the Fed, other central banks, and commentators, and economics classes that don’t sweat the equations too hard: The Fed raises interest rates. Higher interest rates slowly lower spending, output, and hence employment … slowly bring down inflation … So, raising interest rates lowers inflation …

The trouble is, standard economic theory, in essentially universal use since the 1990s, including all the models used by central banks, don’t produce anything like this mechanism. We do not have a simple economic theory, vaguely compatible with current institutions, of the Standard Doctrine.

At the heart of the NK model are three equations: One that nearly all macroeconomists take seriously, another one that many consider reasonable, and a final equation that only a few would wholeheartedly endorse. The first equation is the consumption Euler equation. It represents the fundamental concept of choice in the face of scarcity, capturing substitution towards cheaper goods: When the price of apples relative to oranges falls, households consume relatively more apples. The same logic applies with respect to current and future consumption: Higher real interest rates render future relative to current consumption cheaper, i.e., higher real interest rates go hand in hand with stronger growth. Accordingly, a higher nominal interest rate is associated with a *strengthening* of economic activity unless it triggers an even stronger increase in inflation.

Higher real interest rates make output

higherin the future than today, and soraiseoutput growth. The best we can hope [for in terms of reconciling Standard Doctrine and Euler equation] … is to have output jump down instantly today when the interest rate rises.

The second equation, the ‘Phillips curve,’ represents firms’ price setting. It relates current as well as expected future inflation to contemporaneous output. Underlying this second equation is the assumption that firms compete against each other and try to charge a markup over cost. Price increases by other firms as well as higher production, which pushes up costs, induce firms to raise their own prices as soon as they get a chance (sticky prices). But again, this is not easy to reconcile with the ‘Standard Doctrine:’

Again the sign is “wrong.” Suppose the economy does soften, lower [production] … A softer economy means lower inflation …

relative to future inflation. It means inflationrisesover time. At best, perhaps we can get inflation to jump down immediately, but then inflation still rises over time. … (This is an old puzzle, pointed out by Larry Ball in 1993.)

The final, least credible equation represents an interest rate rule whose coefficients satisfy the ‘Taylor principle.’ The assumption is that the interest rate set by the central bank systematically responds to inflation (and potentially output), and strongly so. The third equation and the ‘Taylor principle’ do not bear resemblance to real-world central banking, although many central bankers and journalists talk about ‘Taylor rules,’ which is not the same as the ‘Taylor principle.’ Rather, the equation and the principle are needed for technical reasons that relate to the dynamic properties of difference equations and more specifically, the number of unstable eigenvalues and jump variables. Paired with the assumption that output and inflation eventually return to their pre-shock trends, the equation subject to the ‘Taylor principle’ forces output and inflation to jump to specific values after the system is shocked.

Cochrane rejects the interest rate rule subject to the ‘Taylor principle’ as bogus. Instead, he favors an ‘FTPL’ mechanism to pin down output and inflation after a shock. According to the ‘FTPL,’ fiscal policy makers set primary surpluses ‘actively,’ i.e., independently of inflation. Inter temporal government budget balance then implies that changes in the economic environment, for instance a change in interest rates, give rise to an equilibrating jump in the aggregate price level, so fiscal policy pins down inflation.

Obviously, I think the fiscal theory story makes a lot more sense. The Fed does not have an “equilibrium selection policy.” The Fed does not deliberately destabilize the economy. The central story of how interest rates lower inflation is that the Fed threatens to blow up the economy in order to get us to jump to a different equilibrium. If you said

thatout loud, you wouldn’t get invited back to Jackson Hole either, though equations of papers at Jackson Hole say it all the time. The Fed loudly announces that it will stabilize the economy — that if inflation hits 8%, the Fed will do everything in its power to bring inflation back down, not punish us with hyperinflation.

Given the weak conceptual and empirical foundations of the third equation and the ‘Taylor principle,’ Cochrane is right to dispute the conventional argument that inflation is pinned down by this very equation—the Fed’s threat to ‘blow up the economy.’ But the FTPL mechanism he favors relies on a similar threat, in this case by fiscal policy makers. With ‘active’ fiscal policy, inflation is pinned down by the inter temporal government budget balance requirement; unless inflation assumes the ‘right’ value, government debt spirals out of control.

Independently of whether you believe in the third equation of the NK model subject to the ‘Taylor principle’ or in ‘active’ fiscal policy along the lines of the ‘FTPL,’ the implications are stark:

But we don’t have to take sides on that debate, because the result is the same, and the question here is whether current models can reproduce the Standard Doctrine. When interest rates rise, we can have an instantaneous jump down in inflation, that lasts one period before inflation rises again.

But this is a long way from the Standard Doctrine. First, we still have inflation that jumps down instantly and then rises over time, where the Standard Doctrine wants inflation that slowly declines over time. That sign is still wrong.

Second, the jump occurs because, coincidentally, fiscal policy tightened at the same time. Whether that happened independently, by fiscal-monetary coordination, or because the Fed made an equilibrium-selection threat and Congress went along doesn’t matter. Without the tighter fiscal policy you don’t get the lower inflation. So this is not really the effects of monetary policy. At best it is the effect of a joint monetary and fiscal policy.

Moreover, the fiscal/equilibrium selection business is doing all the work. You can get exactly the same unexpected inflation decline (or rise) with no change in interest rate at all. …

The mechanism is also a long way from the Standard Doctrine. The decline in inflation has nothing to do with the higher interest rates. There are no higher real interest rates anyway in this story. There is a fall in aggregate demand, but it comes entirely from tighter fiscal policy, having nothing to do with higher interest rates.

Cochrane is right to argue that the NK model’s transmission from interest rates to output and inflation has fiscal consequences, which the literature typically disregards. Consider the consequences of a shock. If we insist on the third equation subject to the ‘Taylor principle,’ then the inflation jump that guarantees stable system dynamics implies a revaluation of outstanding nominal debt (if there is some), which in turn requires fiscal policy makers to adjust future primary surpluses. So, the standard model subject to the ‘Taylor principle’—the Fed’s threat to blow up the world—implies that a shock to the interest rate (a ‘monetary policy shock’) forces fiscal responses. Cochrane asks, why researchers do not pay more attention to the fiscal consequences of ‘monetary policy shocks,’ and why they interpret the output and inflation dynamics resulting from the shock as the effects of monetary rather than monetary-and-fiscal policy.

If we instead dump the third equation and replace it with the notion of ‘active’ fiscal policy, then the shock cannot change future primary surpluses. Now, the inter temporal government budget balance requirement joint with the predetermined level of nominal debt (if some is outstanding) pins down contemporaneous inflation. And according to Cochrane, the traditional output and inflation adjustment paths to the ‘monetary policy shock’ are gone.

Cochrane discusses how the problems of the NK model transcend that model—they are not a consequence of the price stickiness assumption, i.e., the ‘Phillips curve.’ Even without price stickiness, the dynamics according to the ‘Standard Doctrine’ are hard for the Euler equation and the third equation to match.

The only way to get inflation and output to decline at all is to pair the interest rate rise with a FTPL fiscal shock or a multiple-equilibrium-selection-threat by the Fed, which induces a fiscal shock. Even then, we still get inflation that jumps down and then rises, and has nothing to do with the mechanism of the Standard Doctrine. The fiscal shock or equilibrium-selection threat is still coincidental with raising interest rates, and indeed has to fight the fact that higher interest rates want to raise inflation.

Cochrane suggests long-term debt as a potential model ingredient to better align model predictions under the ‘FTPL’ approach with the data. He also speculates why the NK model has been so successful in academia and central banks in spite of its dubious mechanics:

How could this state of affairs have gone on so long, that the basic textbook model produces the opposite sign from what everyone thinks is true, for 30 years? Well, interpreting equations is hard.

This paper contains more discussion and analysis. Have a look yourself and be prepared for a new business cycle framework.