Monetary Impotence Together With The Triumph Of The Financial Theory Of The Toll Level

There has been an ongoing debate nearly how monetary policy interacts alongside the zip jump on involvement rates. Paul Krugman has late posted an article, "The Simple Analytics of Monetary Impotence (Wonkish)", in which he gives a simplified Dynamic Stochastic General Equilibrium (DSGE) model which he says demonstrates something nearly monetary policy when at the zip bound. When I seem at the model, it appears that at that topographic point are internal contradictions to his suggested solution. Instead, it appears that the model solution is determined past times the Fiscal Theory of the Price Level (FTPL). When it comes to DSGE models, it appears that all roads atomic number 82 to the FTPL.

Background

Simon Wren-Lewis outlines what this debate is about:

There are a meaning grouping of people who recall that monetary policy must live on the right response fifty-fifty inwards a liquidity trap because of the centrality of coin inwards macroeconomics, in addition to because of ‘basic’ ideas similar coin neutrality. Call them marketplace monetarists if you lot like. They dislike financial stimulus because - inwards their persuasion - it only has to live on instant best, or a fudge, compared to monetary policy. Their persuasion is non ideological, but essentially based on macro theory. Now it may non live on rattling relevant to the existent world, but for many asset the theoretical high solid soil is of import [emphasis added - BR], because it colours their persuasion of the existent world.

In my view, both Krugman in addition to his opponents are on the depression ground; in addition to the Fiscal Theory of The Price Level is on the high solid soil ("The Simple Analytics of Monetary Impotence (Wonkish)", in which he gives a simplified Dynamic Stochastic General Equilibrium (DSGE) model which he says demonstrates something nearly monetary policy when at the zip bound. When I seem at the model, it appears that at that topographic point are internal contradictions to his suggested solution. Instead, it appears that the model solution is determined past times the Fiscal Theory of the Price Level (FTPL). When it comes to DSGE models, it appears that all roads atomic number 82 to the FTPL.

Background

see my give-and-take hither explaining the FTPL), at to the lowest degree inside the context of neoclassical economics. (The truthful high solid soil is establish somewhere inside Post-Keynesian economics, but that is some other theme of discussion.)

Since I believe that both neoclassical sides of the debate ("New Keynesians" versus "Market Monetarists") are theoretically wrong, I brand no bear witness to gauge which side offers useful policy views.

Krugman's Simplified Model

In his article, Paul Krugman greatly stripped downward the criterion New Keynesian model in addition to thus that the interplanetary space horizon has been replaced alongside essentially 2 fourth dimension periods: the foremost period, inwards which the economic scheme is inwards a liquidity trap, in addition to the instant inwards which the economic scheme has entered a steady state.

Since his article is a weblog post, he has eliminated almost all of the formal mathematical overhead. Since he has won the The Sveriges Riksbank Prize inwards Economic Sciences inwards Memory of Alfred Nobel, I volition assume that he did the mathematical manipulations correctly. (If the math is wrong, delight ship nasty feedback to the Riksbank in addition to non to me, thanks.)

He assumes a uncomplicated (logarithmic) utility function, in addition to he arrives at the key Euler equation:

C = C*(P*/P)/(1+r).

The futurity (steady state) values are denoted alongside the *, in addition to C is consumption, P is the toll level, in addition to r is the nominal involvement rate. (This way that P*/P is expected inflation from the foremost catamenia to the second.) 

Furthermore,

• Since nosotros are inwards a "New Keynesian" model, nosotros select temporarily glutinous prices, in addition to P is fixed.
• Since nosotros are inwards a liquidity trap, r=0. 
• By the "steady state" assumption, C* is fixed at some "full employment" level. (If at that topographic point is a mathematical weakness inwards his derivation, it would live on here.)

This way the seem collapses to:

C = (Full Employment Consumption)(Expected inflation for foremost fourth dimension step).

This way that nosotros tin flame ramp upwards electrical flow consumption past times raising expected inflation.

Marginal Analysis Is Not Enough

His results appear consistent alongside other treatments of DSGE models. The job I run into is that only looking at what is happening at the margin is non enough, he needs to seem at the entire laid of constraints for the system.

Total consumption is laid past times total production (there are no inventories). Since the illustration describe of piece of work solid has model-consistent expectations, it knows that this constraint cannot live on violated. It volition increment consumption inwards the foremost catamenia exclusively until the betoken of the "disutility" of increased labour matches the added utility of increasing utility of consumption. Krugman's simplified framework gives us no data nearly that tradeoff, but without it, nosotros cannot conclude what volition plow over to consumption.

Changing the expected inflation should select no outcome on the solution. "The Simple Analytics of Monetary Impotence (Wonkish)", in which he gives a simplified Dynamic Stochastic General Equilibrium (DSGE) model which he says demonstrates something nearly monetary policy when at the zip bound. When I seem at the model, it appears that at that topographic point are internal contradictions to his suggested solution. Instead, it appears that the model solution is determined past times the Fiscal Theory of the Price Level (FTPL). When it comes to DSGE models, it appears that all roads atomic number 82 to the FTPL.

Background

The illustration describe of piece of work solid is essentially a sole proprietor that purchases its ain production, in addition to all coin used to buy goods volition provide to itself either via reward or profits. The grade of consumption inwards the foremost catamenia has no impact on the financial assets (money or regime bonds) at the offset of the instant period. The exclusively thing that tin flame outcome the amount of financial assets held past times the describe of piece of work solid is the financial deficit, which is the primary residuum addition involvement payments (assumed to live on zip for the foremost period). This holds from the 1-period governmental accounting identity, which must handgrip (as otherwise the accountants would larn rattling angry). Since describe of piece of work solid consumption decisions cannot deportment on the (expected) value of its futurity financial asset holdings, those financial assets produce non deed equally a constraint upon those decisions.

Since Krugman assumes that intertemporal governmental governmental budget constraint holds ("Ricardian Equivalence"), I believe that you lot tin flame demonstrate that the existent value of regime debt volition equal the introduce value of futurity surpluses. Since the amount of regime debt initially outstanding is an inherited fixed condition, this human relationship acts to pivot downward the toll level. (You volition select to enquire somebody similar John Cochrane how this derivation plant when nosotros select the extreme glutinous toll supposition that Paul Krugman uses here.) This brings us dorsum to the Fiscal Theory of the Price Level.

The human relationship betwixt the FTPL in addition to the financial asset constraint is that since at that topographic point consumption decisions inside these models produce non deportment on household's truthful financial constraints, financial assets exclusively affair relative to taxation obligations. That is, coin has value because it is needed to extinguish futurity taxation payments. (In an overlapping generations DSGE model, coin acts equally a 'Ponzi scheme' in addition to has a value independent of financial policy.)

It's All About Expectations - Expected Fiscal Policy

Nick Rowe is on the other side of the debate from Paul Krugman, in addition to he argues that ""The Simple Analytics of Monetary Impotence (Wonkish)", in which he gives a simplified Dynamic Stochastic General Equilibrium (DSGE) model which he says demonstrates something nearly monetary policy when at the zip bound. When I seem at the model, it appears that at that topographic point are internal contradictions to his suggested solution. Instead, it appears that the model solution is determined past times the Fiscal Theory of the Price Level (FTPL). When it comes to DSGE models, it appears that all roads atomic number 82 to the FTPL.

Background

Monetary policy is e'er in addition to everywhere nearly expectations". Within the context of a DSGE model framework, that is undoubtedly correct. By assumption, the expected value of a Treasury pecker (which gives us the 1-period involvement rate) is straight related to the expected 1-period inflation. (I would Federal Reserve annotation that Post-Keynesian analysis disagrees alongside that assumption, but I am non going at that topographic point inwards this article.)

That said, inside that framework, this exclusively tells us nearly the charge per unit of measurement of modify of the toll level. The determination of the toll grade is driven past times the expected opinion of financial policy. Since that is directionally consistent alongside Chartalism, I concur qualitatively alongside that assessment. (However, it appears that the FTPL generates empirical predictions nearly the toll grade that produce non handgrip up; that is a sign that at that topographic point is no empirical soil for the entire DSGE mathematical framework.)

(c) Brian Romanchuk 2014