Draft Article: Solution Properties Of Stock-Flow Consistent Dsge Models

Solution Properties of Stock-Flow Consistent Models past times Brian Romanchuk

This newspaper is the mathematical proof of the statements I made inward this before article. I am putting this out directly every bit a way of getting comments. The newspaper is written inward the same mathematical vogue I used to write inward before I bailed from academia, too it is non calorie-free reading amongst punchy quotes.



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I welcome comments, specially those that tell me that I have got done something wrong. This solution seems also simple, but it appears to work. If this article is seen every bit interesting, I would endure happy to have advice from academics on how it could endure published through a peer-reviewed process. (Since I have got left academia, this would endure done to a greater extent than for my personal amusement than for career enhancement.) I have got no thought what mag would endure interested inward a highly mathematical model that questions the mathematical coherence of DSGE modelling.

I volition alter the document in-place, too inward fact already have got done so. (Oops.)

Revisions:

• I dropped the text on the Household ``No Ponzi'' condition; I wrote that department from memory, too my retention was bad (I mixed it upwardly amongst the governmental budget constraint). 

For those who create non wishing to parse the mathematics, my interpretation is the following:

• Optimisation problems involving a unitary Household Sector (a Representative Household) are inherently trivial.
• When dividends are taken into account, a Representative Household has essentially no fiscal constraints (other than those created past times taxes, which are omitted inward this article). Since coin simply sloshes dorsum too forth betwixt the Household too the Business it owns, the Household is indifferent betwixt dividends too wage income.
• The Household is aware of the existent constraints (the trade-off betwixt working too existent output). These are the constraints that create upwardly one's heed the solution. Financial constraints, such every bit those implied past times the Euler equation, create non matter.
• The solution is slightly to a greater extent than interesting if inventories are allowed to accumulate from period-to-period. In this case, it is necessary to create upwardly one's heed the optimal path of existent inventories. Once that optimisation is done, the solution volition non depart from this optimal solution.

The touchstone "solution" technique inward the literature does non await similar my solution at all. This is partially because the mainstream literature by too large does non detect the truthful solution, rather the analysis brand an approximation (linearisation). Guesses are made nigh the solution properties, without beingness able to validate which constraints on the solution are active. Since the master copy nonlinear model framework is abandoned for the linearisation, modellers create non realise that their framework implies that the Business Sector volition useless pile upwardly coin balances which it has no intention of e'er utilising.

My reading betwixt the lines of mainstream give-and-take of the topic is that fiscal constraints are thought to affair every bit they would affair for a household inward the real-world economy. This is thence transferred to the Representative Household. This runs afoul of the Fallacy of Composition. Since the work is shape every bit an optimisation, the optimising agent is aware of all the constraints, too is presumably able to create upwardly one's heed that fiscal constraints create non affair for a unified household sector.

The alone way the writer tin flame come across fiscal constraints every bit mattering is past times arbitrarily imposing them on the solution, too demanding that the Representative Household conduct a sub-optimal solution because that is the desired output past times the modellers. If that is the case, those added constraints involve to endure properly specified mathematically.

(c) Brian Romanchuk 2014