The Tricky Interrogation Of Matching Render In Addition To Ask Inward Sfc Models

One of the to a greater extent than challenging parts of developing my stock-flow consistent (SFC) models library was the enquiry of how to jibe upwards render in addition to demand inwards a market. I generalised a technique used inwards Godley in addition to Lavoie's Monetary Economics; I am all the same unsure whether at that topographic point is a to a greater extent than full general technique. [Update: I added merely about explanatory text.]

(This article is fairly tentative, in addition to likely would non brand into the volume inwards this form. Suggestions from anyone familiar with the literature are welcome. I accept non actually tried excavation into whatever inquiry on this topic.)

Context for this Discussion

The argue why I wrote this article is that I bespeak to develop the guide of my Python SFC model framework. Note that this is my framework, in addition to does non capture the entire academic SFC literature. This framework generates the model equations with algorithms, based on the high-level construction of sectors that are laid past times the user. This framework could travel placed inside a graphical user interface: the user drags in addition to drops sector objects into a model, in addition to hence the framework generates the equations that are implied past times the high-level parameters.

It is non plenty to plow over a laid of equations that mightiness accept a solution from the perspective of mathematics; the equations accept to travel built to fit inside the constraints of an equation solver.

The enquiry hither is how to jibe upwards render in addition to demand betwixt competing sectors inside the same market. Examples are given below.

Differences Between the Real World in addition to SFC Models

There are 2 ways of creating coherent macro models.

1. We could create a representative sample of transactions, in addition to rails the effects of the transactions on the model entities. (I believe this is how nosotros would characterise agent-based modelling techniques.) Each transaction mightiness occur at a unlike price.
2. We aggregate transactions alongside sectors. We produce non crusade to model the prices of private transactions; nosotros utilization the same toll for all transactions inwards the model accounting period. (This is the conventional stock-flow consistent (SFC) modelling strategy.)

The get-go strategy would create models that jibe our intuition; real-world transactions produce occur at unlike prices. The work with the agent-based approach is that the overall complexity of the model is extremely high. H5N1 unmarried agent would likely accept to a greater extent than equations than a few sectors of a criterion SFC model. We tin plow over the axe run the economical simulations, but it is hard to brand authoritative statements most the model's aggregate behaviour: nosotros tin plow over the axe only comment on the simulations that nosotros accept run.

The work with the aggregated approach is that guide tin plow over the axe travel non completely intuitive.

For 1 unproblematic example, imagine that nosotros calibrated 2 models against the same data, but 1 runs at a quarterly frequency, in addition to the other monthly. The monthly model would mostly non jibe the quarterly one, every bit it forthwith has iii toll points that correspond to a unmarried quarterly point, in addition to hence it has information that the quarterly model cannot replicate.

The relaxation of this article discusses a to a greater extent than complicated problem: matching render in addition to demand inwards markets. I needed to honor a means to allocate render or demand alongside multiple competing sectors inwards my Python SFC model framework.

The Case of Importers

If nosotros are matching render in addition to demand betwixt 2 sectors, matching them should travel straightforward. The enquiry hence arises: what happens if at that topographic point are multiple sectors?

In the relaxation of this article, I am discussing how to grip imports from a unmarried country, but this matching work is to a greater extent than general. Examples:

• Three or to a greater extent than countries with imported goods. For example, inwards a model of the euro area, nosotros could accept the euro core, euro periphery, in addition to the relaxation of the world. How produce nosotros decide marketplace shares for iii competing draw of piece of work concern sectors inside this model?
• What happens if nosotros disaggregate the draw of piece of work concern sector into a labour-intensive versus capital-intensive subsectors? They would travel competing for the same demand, but with unlike production profiles.
• What happens if a labour marketplace is running at capacity, in addition to nosotros accept 2 draw of piece of work concern sub-sectors competing for labour? (For example, a consumer goods in addition to a upper-case missive of the alphabet goods sector.) In the existent world, payoff rise, but non necessarily real quickly. Instead, 1 or to a greater extent than sectors would halt upwards with staffing levels below the desired target.

The get-go models developed for the framework were straightforward: the draw of piece of work concern sector was ever able to run across all the demanded goods from the consumer in addition to authorities sectors. Therefore, at that topographic point was no effective demand side competition, in addition to at that topographic point was only a unmarried supplier.

The problems I depict hither arose when it came fourth dimension to create opened upwards economic scheme models. In this case, nosotros had 2 suppliers of goods:

1. the domestic draw of piece of work concern sector; and
2. imported goods from the unusual draw of piece of work concern sector.

(This contest was mirrored inwards the unusual goods market.)

How should demand travel allocated betwixt the competing draw of piece of work concern sectors? 

The instinctive reaction is to rely on price: consumers would but from the cheaper supplier.

However, this does non work, since nosotros assume that all goods are traded at the same toll inside the accounting period. By assumption, at that topographic point is no means of competing on price. (If nosotros fixed the prices of the 2 sectors at unlike levels, why would demand non travel 100% fulfilled past times the cheaper supplier? We mostly produce non catch massive high frequency switches inwards suppliers inwards real-world data, which is what would hap if demand sectors optimally allocated alongside suppliers with flexible prices.)

(Upon re-reading what I wrote, I realise that classical arguments most render in addition to demand curves would seem to solve this issue. Since the post-Keynesian SFC models refuse merely about of the embedded assumptions that are required inwards this declaration -- on the exclusively reasonable declaration that the assumptions are rejected past times real-world information for existent goods in addition to services -- I ignored this angle of attack.* That said, render in addition to demand flexibility is a characteristic of fiscal markets, in addition to 1 of the items to travel implemented inwards the framework is the utilization of currency adjustments to residue the unusual telephone commutation markets. I may seek addressing the render in addition to demand declaration for goods declaration later, but this is non a high priority. Most engineers involved inwards turbine pattern produce non pass fourth dimension reflecting on what the phlogiston theory of combustion would accept to say; similarly, I catch fiddling value-added inwards discussing arguments that are manifestly wrong.)

The solution to this detail work from the models inside  Chapter half-dozen of Monetary Economics was to prepare the propensity to import. This meant that imports were determined past times multiplying domestic income past times this parameter. The domestic draw of piece of work concern sector supplied the remaining demand.

(The full general solution to the matching work inside the Python framework was that if at that topographic point are N suppliers, the first N-1 accept fixed resources allotment functions, in addition to the final sector is the residual sector that supplies all remaining demand.)

Therefore, nosotros accept to assume that the goods inwards enquiry were non perfect commodities inwards which the demand side only distinguishes suppliers past times price. Instead, at that topographic point is an resources allotment dominion betwixt the suppliers, in addition to toll does non matter. (Complicating matters is that the unproblematic models that accept been dealt with produce non rails prices, but they tin plow over the axe travel interpreted every bit the toll grade beingness fixed.)

In gild to larn contest based on price, it appears necessary for us to process the 2 suppliers output every bit beingness distinct goods. In which case, the resources allotment business office volition occur inwards the consuming sectors' demand functions. 

Concluding Remarks

Supply in addition to demand matching is an illustration where intuition most private transactions does non jibe upwards with the assumptions most aggregation inwards SFC models.

Footnote:

* The doctrinaire render in addition to demand declaration most allocations would rely on 2 primal arguments: that prices are non administered, in addition to that production functions accept a negative render to scale. The get-go supposition is rejected past times whatever empirical analysis of toll setting, in addition to the instant flies inwards the aspect upwards of the engineering in addition to empirical economical literature. The signal most economies of scale is non obvious, hence I volition seek to apace explicate my logic. The implication is that firms would travel happy to render goods at a lower toll if they could guarantee a larger volume of sales. Since sales volumes cannot travel guaranteed, setting prices becomes a real complex game, in addition to depends on sentence calls most the province of the market.

(c) Brian Romanchuk 2017