About mid-way through the blog post, you assert the following puzzling statement:
"It works much like a money growth target: inflation eventually settles down to the nominal rate plus real rate, as it settles down to money growth."
Irving Fisher's equation is (1 + r ) = ( 1 + i )/( 1 + f ), where f is the rate of inflation, r the real rate of interest and i the nominal rate of interest. An approximate expression, if and only if f << 1, is given by r = i - f . Solving for f, given i and r, yields f = i - r. Your statement, however, asserts that f = i + r , a contradiction of Fisher's equation. Has the world turned upside-down, overnight?
In my opinion, your analysis omits something important: the banking system. I could be wrong, but QE did not create trillions in cash. Since most of the bonds were sold by banks, QE just replaced bonds with new bank reserves. Due to draconian bank regulation (including payment of interest on reserves), loan growth was tepid throughout the 2010’s. Banks maintained immense excess reserves which could have been turned into money (purchasing power) but never were. Similarly, in the COVID response, loan growth has remained subdued (except for PPP.) Inflation was driven entirely by checks written from the treasury account, and QE suppressed long term rates that would have mitigated the inflation. This post from 2021 presents my forecast of COVID inflation. https://charles72f.substack.com/p/aint-nothin-but-a-party
"We don’t see decisive experiments like this very often in macroeconomics."
You're pushing this way harder than it warrants, and haven't convinced me in the slightest that the three outcomes of episodes with a bunch of other really weird stuff going on simultaneously are anything more than coincidental (especially since market monetarism seems to provider cleaner predictions and explanations as well).
Equation (30) on page 205, namely, x = ( 1 – β ) / κ π , appears to be incorrect. The dimensionally correct equation for the steady-state formula, derived from the standard new-Keynesian Phillips curve πₜ = β 𝔼ₜ{πₜ₊₁} + κ xₜ , is x = ( 1 – β ) π / κ .
Was Friedman wrong about inflation being a monetary issue, as I learned many years ago, or can “excess” money in an economy be absorbed by equities, bonds, real estate, or other illiquid vehicles? As the oceans soak up CO2, is money being sequestered, masking its effects? If this were true, enormous sums could lay dormant, barely effecting inflation statistics, until some exogenous event releases these quiescent hoards into the general economy.
The basic new-Keynesian two-equation model (Eqn.s (1) and (2)) is a representative agent model of a closed economy. The author notes that equations (1) and (2) describe the small variations from the presumed steady-state system that underlies the system (1)-(2). The variations x(t), π(t) and i(t) must be small relative to the steady-state values x̅ , π̅ , and i̅ of the underlying complete model. That is to say, | x(t)| / x̅ , | π(t) | / π̅ , and | i(t) | / i̅ must be much less than unity for all time, t > 0.
The basic model is unlike the U.S. economy, or any developed nation's economy. Keeping this in mind, and accepting that the restrictive assumptions have implications for the conclusions drawn in the course of the paper's evolution through the several layers of specialization of the models to bring forth interesting aspects of the monetary and fiscal possibilities, the purpose of the paper is not so much elicidation of how contemporary monetary and fiscal policy work in harness, but to stimulate academic economists' focus on model development to explain the real world of central bankers, congressmen and presidential advisors, and the members of the FOMC. The giveaway is found at the end of the paper in the statement that no data was used in writing the article.
The simplifying assumptions used to make tractable the exposition end up making the arguments more in the way of a 'gedanken Experiment' (a 'thought experiment') rather than an exposition of the mathematical economics of the proffered models. The simplifications eliminate the complicating features of the models presented, and the reader is led down cul-de-sacs that bear no relation to the original model and which though interesting in and off themselves fail to shed useful light on the fundamental problem. If the exceptions were the rule, then would life not be much simpler for all and sundry? An aerodynamicist would gladly trade-in the Navier-Stokes equations for the simplicity of inviscid mediums any day of the week, rather than undertake the grinding non-linear mathematics that the real world forces her to deal with if the aeroplane is to fly from point A to point B successfully. Only if..., eh?
“Still, it’s hard to digest.”:) To say much with little, such is the goal of good science(and prose). Something about Necessary and Sufficient Conditions. Conflations of Correlation and Causation. A commendable bold attempt for a new hypothesis beyond the gravitational force of the ruling new-Keynesian priesthood school of Economics which only sees Central Banks as Central. Deserving of the Galileo Prize ? Special Theory of Relativity ? Max Planck Award ? Are asset value inflations and consumer price inflation separate and distinct, and are rulers with which we measure these suitable to the tasks. Wittgenstein’s ruler: Unless you have confidence in the ruler’s reliability, if you use a ruler to measure a table you may also be using the table to measure the ruler.” Nassim Nicholas Taleb, “Fooled by Randomness”, 2001.
"Old-Keynesian and policy analysis states that inflation is unstable at an interest rate peg or zero bound. Inflation or deflation “spirals” will break out."
This idea is older than the Old Keynesians: it was expressed by Wicksell. He would have added an important qualifier that you omitted: inflation is unstable at an interest rate peg or zero bound *if that rate differs substantially from the natural rate of interest.*
Evidently the central bank rate at close to zero was not too far from the natural rate in United States, the euro area, and Japan after the Great Recession. Such is not the case at most places and times.
To this Wicksellian, you seem to be making the old mistake of thinking of the interest rate as the price of money rather than as the rental price of money.
Great paper, and a great demonstration of the importance of getting to the (seemingly only) technical details of models, as they may hide deep economic insights.
And on technicalities… I am puzzled by the long-run non-neutrality of the model (equation 30 in the paper).
My understanding is that the FTPL addition to the NK model does nothing to the steady-state. The FTPL addition determines the equilibrium path outside the steady-state, but does not affect it, so the model must share the same steady-state as the standard NK model.
In its simplest form, the NK model displays long-run non-neutrality due to price dispersion across producers, which leads to inefficient production. Zero steady-state inflation eliminates the price dispersion in the long-run and the inefficiency. This type of non-neutrality is easy to fix by assuming full price indexation to steady-state inflation, i.e. producers that cannot re-optimize in period t automatically adjust their price by the rate of steady-state inflation.
However, equation 30 is derived from a linearized version of the model. Price dispersion is second-order. Therefore, the non-neutrality displayed by equation 30 cannot possibly come from price dispersion. Where does it come from? Is it really a property of the *exact* model, or is it an artifact of using its linear version?
About mid-way through the blog post, you assert the following puzzling statement:
"It works much like a money growth target: inflation eventually settles down to the nominal rate plus real rate, as it settles down to money growth."
Irving Fisher's equation is (1 + r ) = ( 1 + i )/( 1 + f ), where f is the rate of inflation, r the real rate of interest and i the nominal rate of interest. An approximate expression, if and only if f << 1, is given by r = i - f . Solving for f, given i and r, yields f = i - r. Your statement, however, asserts that f = i + r , a contradiction of Fisher's equation. Has the world turned upside-down, overnight?
/s/ "Puzzled"
In my opinion, your analysis omits something important: the banking system. I could be wrong, but QE did not create trillions in cash. Since most of the bonds were sold by banks, QE just replaced bonds with new bank reserves. Due to draconian bank regulation (including payment of interest on reserves), loan growth was tepid throughout the 2010’s. Banks maintained immense excess reserves which could have been turned into money (purchasing power) but never were. Similarly, in the COVID response, loan growth has remained subdued (except for PPP.) Inflation was driven entirely by checks written from the treasury account, and QE suppressed long term rates that would have mitigated the inflation. This post from 2021 presents my forecast of COVID inflation. https://charles72f.substack.com/p/aint-nothin-but-a-party
"We don’t see decisive experiments like this very often in macroeconomics."
You're pushing this way harder than it warrants, and haven't convinced me in the slightest that the three outcomes of episodes with a bunch of other really weird stuff going on simultaneously are anything more than coincidental (especially since market monetarism seems to provider cleaner predictions and explanations as well).
Equation (30) on page 205, namely, x = ( 1 – β ) / κ π , appears to be incorrect. The dimensionally correct equation for the steady-state formula, derived from the standard new-Keynesian Phillips curve πₜ = β 𝔼ₜ{πₜ₊₁} + κ xₜ , is x = ( 1 – β ) π / κ .
Was Friedman wrong about inflation being a monetary issue, as I learned many years ago, or can “excess” money in an economy be absorbed by equities, bonds, real estate, or other illiquid vehicles? As the oceans soak up CO2, is money being sequestered, masking its effects? If this were true, enormous sums could lay dormant, barely effecting inflation statistics, until some exogenous event releases these quiescent hoards into the general economy.
The basic new-Keynesian two-equation model (Eqn.s (1) and (2)) is a representative agent model of a closed economy. The author notes that equations (1) and (2) describe the small variations from the presumed steady-state system that underlies the system (1)-(2). The variations x(t), π(t) and i(t) must be small relative to the steady-state values x̅ , π̅ , and i̅ of the underlying complete model. That is to say, | x(t)| / x̅ , | π(t) | / π̅ , and | i(t) | / i̅ must be much less than unity for all time, t > 0.
The basic model is unlike the U.S. economy, or any developed nation's economy. Keeping this in mind, and accepting that the restrictive assumptions have implications for the conclusions drawn in the course of the paper's evolution through the several layers of specialization of the models to bring forth interesting aspects of the monetary and fiscal possibilities, the purpose of the paper is not so much elicidation of how contemporary monetary and fiscal policy work in harness, but to stimulate academic economists' focus on model development to explain the real world of central bankers, congressmen and presidential advisors, and the members of the FOMC. The giveaway is found at the end of the paper in the statement that no data was used in writing the article.
The simplifying assumptions used to make tractable the exposition end up making the arguments more in the way of a 'gedanken Experiment' (a 'thought experiment') rather than an exposition of the mathematical economics of the proffered models. The simplifications eliminate the complicating features of the models presented, and the reader is led down cul-de-sacs that bear no relation to the original model and which though interesting in and off themselves fail to shed useful light on the fundamental problem. If the exceptions were the rule, then would life not be much simpler for all and sundry? An aerodynamicist would gladly trade-in the Navier-Stokes equations for the simplicity of inviscid mediums any day of the week, rather than undertake the grinding non-linear mathematics that the real world forces her to deal with if the aeroplane is to fly from point A to point B successfully. Only if..., eh?
“Still, it’s hard to digest.”:) To say much with little, such is the goal of good science(and prose). Something about Necessary and Sufficient Conditions. Conflations of Correlation and Causation. A commendable bold attempt for a new hypothesis beyond the gravitational force of the ruling new-Keynesian priesthood school of Economics which only sees Central Banks as Central. Deserving of the Galileo Prize ? Special Theory of Relativity ? Max Planck Award ? Are asset value inflations and consumer price inflation separate and distinct, and are rulers with which we measure these suitable to the tasks. Wittgenstein’s ruler: Unless you have confidence in the ruler’s reliability, if you use a ruler to measure a table you may also be using the table to measure the ruler.” Nassim Nicholas Taleb, “Fooled by Randomness”, 2001.
"Old-Keynesian and policy analysis states that inflation is unstable at an interest rate peg or zero bound. Inflation or deflation “spirals” will break out."
This idea is older than the Old Keynesians: it was expressed by Wicksell. He would have added an important qualifier that you omitted: inflation is unstable at an interest rate peg or zero bound *if that rate differs substantially from the natural rate of interest.*
Evidently the central bank rate at close to zero was not too far from the natural rate in United States, the euro area, and Japan after the Great Recession. Such is not the case at most places and times.
To this Wicksellian, you seem to be making the old mistake of thinking of the interest rate as the price of money rather than as the rental price of money.
Great paper, and a great demonstration of the importance of getting to the (seemingly only) technical details of models, as they may hide deep economic insights.
And on technicalities… I am puzzled by the long-run non-neutrality of the model (equation 30 in the paper).
My understanding is that the FTPL addition to the NK model does nothing to the steady-state. The FTPL addition determines the equilibrium path outside the steady-state, but does not affect it, so the model must share the same steady-state as the standard NK model.
In its simplest form, the NK model displays long-run non-neutrality due to price dispersion across producers, which leads to inefficient production. Zero steady-state inflation eliminates the price dispersion in the long-run and the inefficiency. This type of non-neutrality is easy to fix by assuming full price indexation to steady-state inflation, i.e. producers that cannot re-optimize in period t automatically adjust their price by the rate of steady-state inflation.
However, equation 30 is derived from a linearized version of the model. Price dispersion is second-order. Therefore, the non-neutrality displayed by equation 30 cannot possibly come from price dispersion. Where does it come from? Is it really a property of the *exact* model, or is it an artifact of using its linear version?