Monetary Frictions Inward Dsge Models
What Is The Objective Of This Article?
This article together with other related ones represents a initiative of all draft of ideas that I am going to contain into a mass on the theory of financial policy. I convey rigid objections to the representation of financial policy inside Dynamic Stochastic General Equilibrium (DSGE) models. In this article together with the previous I nowadays a simplified DSGE model together with how it is supposed to hold upwards analysed. One difficulty inwards next the logic is that the model is rattling unrealistic, which is an inherent belongings of these models.
Once I convey covered the base of operations ideas, I volition hold upwards easier to explicate my criticisms.
Monetary Frictions Versus Price Stickiness
Discussion of toll conclusion inwards DSGE models typically revolves around the notion of the toll stickiness — how slow is it to conform the prices equally fourth dimension passes. Remember that these models are based upon finding an optimal trajectory from the electrical flow time, which I label fourth dimension nada hither for simplicity. Price stickiness is a belongings of prices inwards the future, which is for fourth dimension greater than zero.
The existent challenge inwards these models is: what is the initial toll level? If prices are sticky, equally inwards the so-called New Keynesian models, the initial toll degree should convey been fixed at fourth dimension t=-1 (in social club to rest consistent amongst the model structure*). Assuming initial toll degree is fixed eliminates the problems I hash out inside this article, but it raises a novel enquiry – how was the initial toll degree fixed at fourth dimension t=-1? Instead, I desire to hold back at option agency of fixing initial toll degree inside a model, so-called monetary frictions.
My model economic scheme is described inwards this article. But a briefer description is that at that topographic point is a unmarried solid inwards the economic scheme that receives 100 apples a year, together with has $1 equally a financial asset. The enquiry is – what is the toll of an apple tree at t=0?
In the previous article, I explained John Cochrane's declaration how taxes could pivot downwards the initial toll level. Here I explicate how monetary frictions tin transportation away gain the same thing.
Types Of Monetary Frictions
There are 3 types of monetary frictions (not including toll stickiness) that could hold upwards used to create upwards one's hear the initial toll degree inwards my model economy. The initiative of all 2 are standard, together with the 3rd is similar but comes from Stock-Flow Consistent modelling. They are:
- cash-in-hand or velocity constraints;
- money inwards the utility function;
- stock–flow norms.
Velocity
The velocity of money is defined yesteryear the equation of exchange:MV=Py,
where M = money, V = velocity, P = toll level, y= existent production. Note that this is a definition, allowing us to calculate the velocity at a detail fourth dimension (assuming money is non-zero).
As quantity theorists discovered the hard way during the QE exercise, velocity is non constant for existent economies. But for simplicity, I volition hash out what happens inwards our uncomplicated model economic scheme if velocity is constant.
If I ready velocity to hold upwards a overnice circular 100, together with the solid sector holds $1 inwards money, the toll of an apple tree is $1. This is because full production is 100 apples, together with the equation of telephone commutation tells us that nominal gross domestic product is $100 (=100×$1). If velocity drops to 50, the toll an apple tree drops to $0.50.
We could brand velocity a business office of things similar involvement rates, inwards which instance nosotros would convey to solve some equations to create upwards one's hear the toll level. I teach out that equally an practise to the reader.
An option formulation is to create a cash-in-hand constraint. These are constraints which require the solid concur money at the "beginning" of the fourth dimension menstruum for transaction purposes, fifty-fifty though it volition have to a greater extent than money at the "end" of the period. For example, it cannot usage the proceeds of Treasury bills that mature at the "end" of the menstruum for transactions inside that period.
Such constraints are equivalent to a velocity constraint if the transactions are for purchasing goods. But it would non hold upwards the same matter if the cash-in-hand constraint applied to the payment of taxes.
Money In The Utility Function
Since it is ofttimes assumed that households tin transportation away borrow, a velocity constraint is hard to justify from the points of persuasion of microfoundations — the declaration that macroeconomic models should hold upwards derivable from microeconomic behaviour. An option way of getting model households to concur money is to contain money holdings into utility function.
I volition alone summarize how this plant here. The toll of apples is such that the solid would hold upwards indifferent betwixt holding money or buying some other apple tree – that is, the degree of utility would hold upwards unchanged. (From whom the solid would purchase the apple tree from is an of import opened upwards question.)
For some classes of utility functions, yous would teach a constant velocity if the economic scheme followed a steady-state increment path. In other cases, velocity would hold upwards variable.
Stock-Flow Norms
Influenza A virus subtype H5N1 somewhat similar concept to money inwards the utility business office would hold upwards stock-flow norms inwards solid behaviour. Households would endeavor to maintain financial assets nigh target ratios to nominal incomes. The deviation is philosophical, equally it is to a greater extent than an empirical argument, together with non driven yesteryear the supposition of optimizing behaviour. Stock-flow norms are unsurprisingly embedded inwards stock-flow consistent (SFC) models.
Why DSGE Models Need Monetary Frictions
Absent monetary frictions, DSGE models offering a rattling clear prediction most real-world economies: households volition never concur non-interest-bearing money, such equally coins together with dollar bills. Although nosotros are moving inwards that direction, that prediction is manifestly incorrect. Therefore monetary frictions convey to hold upwards introduced to reproduce observed behaviour. They are too needed to pivot downwards the initial toll degree inwards these models.
Does This Really Matter?
In reality the toll degree is pinned downwards yesteryear prior contractual obligations together with posted prices. The alone fourth dimension that prices seem to hold upwards unmoored is during a hyperinflation. But fifty-fifty inwards that case, prices are typically fixed inwards unusual currency terms, together with local prices are but those unusual currency prices translated yesteryear the latest foreign-exchange quotation. Prices are non going to infinity, rather the local currency is going to nada inwards the foreign-exchange market. This is non a province of affairs that is easily modelled inwards a shut economic scheme DSGE model.
Monetary frictions are an artefact to needed to eliminate the under-determination of the toll degree inwards DSGE models. But equally the Fiscal Theory of the Price Level shows, the conclusion of the initial toll degree it is tied to the authorities budget constraint. As a result, whatever analysis of financial policy using DSGE models has to teach by amongst monetary frictions.
I volition hash out inwards a later on article why the beingness of monetary frictions calls into enquiry the validity of the governmental budget constraint.
Footnote:
* The toll degree inwards a New Keynesian DSGE model amongst Calvo pricing would hold upwards “partially” fixed at t=-1; at that topographic point is a continuum of goods together with alone some tin transportation away hold upwards repriced at whatever indicate inwards time. But fifty-fifty having some prices fixed would create a reference (partial) toll degree for the remaining prices that could hold upwards adjusted.
No comments