Understanding The Financial Theory Of The Cost Marker Amongst Flexible Prices

In this article, I summarise some of the results inwards the working newspaper in this article. John Cochrane’s article is fairly wide-ranging as well as interesting. The newspaper likewise clarifies the logic behind toll degree determination inwards Dynamic Stochastic General Equilibrium (DSGE) models. The toll degree is driven past times what he terms “fiscal backing” – futurity taxation is what gives a currency value. (This is similar to the sentiment of Chartalism.) In this article, I speak over how this concept plant inwards the illustration of flexible prices. I receive got concerns virtually the DSGE model mathematical framework, but I volition speak over those points inwards follow upwards articles.

The Model Economy

This model economic scheme is a simplified version of the flexible toll model discussed inwards the appendix of the working paper. This model is a Real Business Cycle (RBC) DSGE model, amongst a “pure endowment” economic scheme (there is no labour required to create output).

1. You are the caput of the “representative household” (which is assumed to receive got heirs for all time), as well as your decisions somehow stand upwards for the whole household sector.
2. You receive got an apple tree tree inwards your dorsum yard that produces 100 apples per year, as well as that is the total economical output for the economy. 
3. You grip $1 inwards coin at present, which nosotros label equally fourth dimension zero.
4. You desire to maximise your household utility over from t=0 to infinity. Your utility is based exclusively upon the seat out of apples you lot eat inwards each period. Future consumption likewise gives utility, but you lot apply a discount charge per unit of measurement on futurity consumption.

So the inquiry is: what is the trajectory of economical variables that maximises your utility?

Price Level Indeterminacy

The occupation amongst this province of affairs is that it is unclear what the toll of apples should be. You teach no utility from holding money, exclusively past times eating apples. It is rattling clear that the optimal solution is that you lot eat all 100 apples every year. (In other words, the economic scheme fully utilises all the existent resources of the economy, which is a feature of Real Business Cycle models.)

Although at that spot is no debate virtually the trajectory of the existent variables, the inquiry is what is happening inwards the monetary economy. Since the optimal strategy for the household is to eat all of its apples as well as at that spot are no other apples to buy, the household has no utilisation for its coin inwards transactions.  You could translate this inwards 2 ways:

1. Money is worthless, as well as the toll of apples are infinite.
2. The value of coin is unknown (indeterminate), but the seat out of apples that volition endure supplied at whatever toll is zero.

In social club to create a need for money, the authorities has to impose taxes. (This is the key declaration behind Chartalism, which is the theory of the world money.) The household wants to grip coin to pay futurity taxes, equally the authorities volition non loan it coin inwards social club to allow it to come across taxation obligations. For some unknown ground it is assumed that the household gets no utility from coming together taxation obligations (by avoiding the “disutility” of existence thrown inwards jail for non paying taxes), rather this obligation is enforced equally a constraint on the optimal solution.* This constraint leads to what he refers to equally the Government Bond Valuation formula:

(This formula is described inwards my previous post.)

For simplicity, I volition short-circuit the infinite amount inwards the formula as well as cut it to a single-period condition.

What is assumed that the authorities pays off the debt inwards the side past times side period, as well as runs a balanced budget for all fourth dimension thereafter. In this case, the Bond Valuation Formula collapses to:

The existent (face) value of authorities debt = the acquaint value of the existent primary surplus inwards menstruation 1, discounted at the existent charge per unit of measurement of return.

The declaration is that the value of the debt must endure this value because:

1. If the surplus is to a greater extent than than that, the household sector would halt the menstruation amongst a negative amount of money, as well as nosotros assumed that the authorities volition non lend coin to households.
2. The surplus is less than that (or at that spot is a deficit), the household volition halt upwards amongst positive financial assets at the halt of the period, which volition never endure taxed away. He argues that the household would desire to merchandise away the excess financial property holdings (which are authorities liabilities – debt as well as money).

(I believe at that spot is a throttle inwards logic inwards the 2nd case, but I volition speak over that elsewhere.)

One of import affair to banker's complaint that inwards this simplified framework, the authorities undertakes no operations inwards the existent economic scheme – it does non furnish or need goods (apples, inwards the electrical flow example). This simplifies the analysis, but it is likewise what helps drive the indeterminacy of the toll level. The operations inwards financial assets are completely decoupled from the transactions inwards apples (since the household is both buying as well as selling the same amount of apples, the internet cash flows due to apples are ever zero).

The interesting affair is how the surplus has to endure defined – it has to endure defined inwards existent terms. For my example, assume that the household discount charge per unit of measurement as well as the involvement charge per unit of measurement is null to decease along the numbers simple. In this case, the toll degree would endure expected to endure constant. Since the initial amount of authorities liabilities is $1, the surplus would receive got to $1 at fourth dimension 1 inwards social club eliminate the outstanding authorities liabilities. But if that financial strategy was specified inwards nominal terms, at that spot is null to pivot downwards the toll level.

Instead, Cochrane’s newspaper defines the amount of taxation equally a per centum of nominal income. If the taxation charge per unit of measurement was laid at 1% of nominal income, the household would laid the toll of 1 apple tree at $1.  This agency that the household nominal income is $100 (100 apples times $1), as well as so it has a taxation liability of $1. If the taxation charge per unit of measurement were 2%, the toll of an apple tree would endure $0.50, equally 2% of $50 gives the required $1 inwards taxes. Since the amount of taxes is the same per centum of gross domestic product regardless of the toll level, the taxation is effectively defined inwards existent terms.

As he notes, having taxes existence specified inwards existent terms makes sense. This matches do for most modern taxes, equally nosotros rarely regard caput taxes that are fixed nominal amounts.

Monetary Policy – Pah!

Looking at the Bond Valuation Formula carefully shows an interesting belongings of the toll degree – its path volition endure determined past times the path of surpluses. The exclusively role of monetary policy is to touching the degree of involvement payments, which influences the amount of authorities debt outstanding.

In the working paper, John Cochrane discusses this inwards detail, as well as he gives examples how monetary policy “works” past times creating a financial response. I do non receive got a lot to add, other than agreeing amongst the yell for that financial policy as well as monetary policy yell for to endure coordinated. This should non endure a surprise to most economists, but it may endure tidings to some members of the ECB.

Budget Constraint Or Valuation Rule?

There is a small-scale literature discussing the Fiscal Theory of the Price Level, as well as the primary debate is whether the Bond Valuation Formation/Governmental Budget Constraint is a constraint on behaviour, or a valuation formula. The criterion sentiment is that it is a constraint on behavior that must grip (largely past times assumption); the option sentiment is that the valuation of authorities debt and/or the toll degree adjusts to the expected financial path.

If the initial toll degree for the economic scheme has non been determined, such equally inwards flexible toll models, as well as at that spot are no “monetary frictions”** the valuation interpretation seems to endure the most tenable. (UPDATE: I speak over monetary frictions farther inwards this article.) There is no other way of fixing the initial toll level. The fundamental banking concern tin determine the path of inflation, but that is the charge per unit of measurement of modify of the toll degree relative to an indeterminate initial level.

If the initial toll degree is fixed (that is, it was assumed to endure fixed inwards the previous fourth dimension step), as well as so the valuation dominion runs into difficulties. The left manus side of the equation is fixed, as well as at that spot is null that forces the correct manus side to jibe the left manus side. For example, the authorities could merely create upwards one's hear to run deficits, as well as so the correct manus side would never amount to the positive quantity on the left manus side of the equation. That said, if the initial toll degree is assumed to endure fixed, it is unclear that the authorities budget constraint must hold, for the same reason.

Equilibrium Versus Off-Equilibrium

Part of the word of the Fiscal Theory of the Price Level inwards the literature revolves merely about “equilibrium” versus “out of equilibrium” states. To my mind, this word is confused, as well as based on verbal discussions of furnish as well as need curves inwards the absence of modelled time. In DSGE models, the trajectory of economical variables (or at to the lowest degree their expected values) are the solution to an optimisation occupation – which is implicitly assumed to be as well as endure unique. The possibility that economical variables (like prices) do non follow this optimal trajectory (or trajectories) is rejected. If nosotros allow the possibility of non-optimal solutions, the models tell us nothing, since whatever trajectory that meets accounting constraints becomes a valid solution, as well as at that spot is no way to distinguish which 1 to use.

In the mathematics of dynamic systems, an equilibrium is a yell for inwards the the world infinite where the the world variable would stay if it starts at just that point. It is non a belongings of the entire trajectory of the the world variable, which is what DSGE model solutions are. Broadly speaking, the word of equilibrium appears to endure a verbal projection of the properties of the existent basis onto a organisation of mathematical equations. Obviously, mathematical proofs tin tell us null virtually those verbal formulations.

Concluding Remarks

The Fiscal Theory of the Price Level is a way of determining the initial toll degree inwards a DSGE model that does non receive got monetary frictions. Given that nosotros mostly do non regard societies waking upwards each 24-hour interval as well as struggling to determine the toll level, the existent basis implications of this are rather remote. I would instead utilisation this equally an indication that such DSGE models are underdetermined as well as so somewhat questionable.

Once nosotros innovate monetary frictions, the Fiscal Theory of the Price Level starts to facial expression upwards problems. But equally I volition speak over inwards upcoming article, this same is truthful for the entire “governmental budget constraint”.

Footnotes:

* The household could conceivably borrow from the authorities to pay taxes. The DSGE model frameworks may or may non allow this to happen, but the supposition is that household borrowings receive got to decease to null equally fourth dimension goes to infinity (the “No Ponzi” condition). Realistically, governments do non lend to households to allow them to pay taxes, so it would brand feel to enforce the no-borrowing dominion at all times. This would require a slight change to the proofs inwards the working paper, but that is already known.
** Monetary frictions would include having coin inwards the utility function, or having a cash-in-advance constraint. The simplest such constraint would endure adding the constraint MV=Py (Money × Velocity = Price Level × Real Output). The amount of coin creates a constraint on the toll level, eliminating the under-determination inwards the model. See this article for a longer discussion.

(c) Brian Romanchuk 2014