Primer: Agreement Stock – Menses Norms
The models I introduce hither are based on those inside the text Monetary Economics past times Godley in addition to Lavoie, from Chapter 2. I cause got simplified the notation. It should live on noted that these concepts are similar to those industrial plant life inside before Keynesian models. Since I desire to focus on how stock-flow norms piece of work inside these models, I do non desire to instruct distracted amongst the history of the concept. The text discusses the history equally good equally giving farther references.
What Are Stocks And Flows?
H5N1 stock variable is an economical variable that is a quantity (and non a parameter) that is measured at the goal of an accounting period. For example, variables that would appear on the remainder sheet, such equally coin holdings or inventory at the goal of the month.
H5N1 flow variable is somewhat harder to define. For variables associated amongst money, flows are transactions that alter of a monetary stock variable during accounting period. For example, variables that would appear on income statements. For the other side of transactions (since coin is exchanged for goods or services), things are to a greater extent than complex. Flows for goods would live on a alter of condition of the unwrap of goods over a period, such equally a the unwrap of cars sold (which affects the stock of inventory). However, in that location are no stocks associated amongst transactions inwards services.
(A fuller Definition is given on Wikipedia. Note that the previous paragraph was corrected cheers to the input of Ramanan inwards the comments.)
For bond marketplace economics, the classic stock variable is the amount of authorities debt outstanding, in addition to the corresponding flow variable is the authorities deficit over a fourth dimension period. Also, gross domestic product is a flow variable. Therefore, a debt-to-GDP ratio is the ratio of a stock to a flow variable. Many economists warn that y'all should non mix stock in addition to flow variables. Correspondingly, a debt-to-GDP ratio looks similar a mix of concepts. However, it is necessary to necktie the relationships betwixt flow variables to the relationships betwixt stock variables, in addition to hence economical models cause got to include something that tells us close those ratios.
Inventory Ratios
Stock-flow norms tin live on expressed inwards existent terms. An of import lawsuit is the inventory-sales ratio. The nautical chart higher upward shows the inventory/sales ratio of motor vehicles in addition to parts inventories (at the wholesale level) inwards the United States. As an example, if the ratio is 1.4, that agency it would cause got 1.4 months of sales at that electrical current charge per unit of measurement to clear that electrical current grade of inventory.
Production decisions past times businesses are non modelled rattling good inwards mainstream economical models (that is, Dynamic Stochastic General Equilibrium – DSGE – models). Those models focus on family behaviour equally the driver for the economy. Within those models, businesses adjust prices to forbid a ascent inwards inventories (which are oftentimes assumed to live on zero). Although this may occur inwards only about industries, such equally the commodity industry, this does non appear to reverberate reality rattling well, equally shown above. The spectacular ascent inwards auto inventories during the terminal recession was non the outcome of deliberate selection past times automakers.
Stock-flow consistent models are to a greater extent than complete, equally they elbow grease to create behavioural rules for every sector of the economy. Within my models (which are fairly basic adaptations of the models inwards the Godley in addition to Lavoie textbook) my model occupation concern sectors adjust production — hence job — based on the amount of inventory they concord relative to sales. This is a thus stock-flow norm embedded inwards the behaviour of businesses.
Household Consumption
The most visible application of stock–flow norms is inwards the expanse of modelling the consumption role of the family sector. This is a large expanse of query in addition to economical squabbling.
H5N1 typical consumption role for the family sector is given past times (using my non-standard notation):
C = (1-s)*I + d*W;
where:C = consumption,
s = savings rate,
I = total income = wage income + dividend income + involvement income,
d = wealth drawdown,
W = wealth.
The fact that I include involvement income inside total income income is a modelling selection that affects the dynamics. If it is non included inwards the income measure, family asset/income ratios volition choke theme upon the charge per unit of measurement of interest.
This consumption role is unremarkably called the Modigliani consumption function.
For simplicity, let's assume that households alone concord banking corporation deposits equally fiscal assets. Since I cause got included involvement equally part of income, the alter inwards fiscal assets (bank deposits) is given by:
ΔW = I - C.
If nosotros substitute the consumption equation into previous, nosotros get:
ΔW = s*I - d*W.
We tin in addition to so recast this to:
ΔW =I*d*(s/d - W/I).
The ratio W/I is the wealth to income ratio. We tin translate this terminal equation equally an adjustment of the wealth to income ratio towards a target ratio which is given past times s/d. If the wealth to income ratio already equals the target, in addition to income is non changing, wealth volition non change. If the wealth to income ratio is below target, in that location volition live on positive internet savings which volition force the wealth to income ratio towards target.
The linearity of the consumption role creates a duality betwixt 2 possible models of family behaviour. We could either specify consumption directly, or nosotros tin specify family behaviour inwards terms of attempting to accomplish a target grade of wealth. If nosotros brand our behavioural relationships to a greater extent than complex (nonlinear) the duality volition in all likelihood intermission down. For example, if nosotros cause got a to a greater extent than complex consumption function, the wealth to income ratio may non tend towards a constant value.
(As an aside, these dynamics are kickoff gild linear system, which also describes the criterion Adaptive Expectations model, equally discussed inwards this primer.)
Example Simulation Results
Within a total stock-flow consistent model, the results are complicated past times the impact of the dissimilar sectors upon each other. I volition give an lawsuit of how family savings react to a stride alter inwards income, but I assume that this steady income tin live on maintained despite the interaction of the family amongst the other sectors inside the economy. The parameters for the family sector behaviour are:
- The family saves 20% of income, putting the savings into coin holdings.
- It draws downward (spends) 10% of its coin holdings.
- Money does non pay involvement (for simplicity).
- Income before t=0 was $100/period, which in addition to so jumps to $110 at t=0.
(Note: these parameters are non meant to live on realistic estimates.)
The nautical chart higher upward shows the simulation results. The ratio of the savings charge per unit of measurement to the drawdown charge per unit of measurement was 2:1, which is why the initial stock of savings was $200. At t=0, the amount of spending rose higher upward the amount of coin drawn down, in addition to so the stock of coin saved rises. The stock of coin asymptotically converges towards $220 (=2×$110).
Impact Of Income Growth
One cardinal belongings of these models is that the ratio of property holdings to income drops equally the charge per unit of measurement of increase of nominal income rises. In the nautical chart below, I demo what happens if the initially static income of the family (growth charge per unit of measurement of 0%) rises to 5% per catamenia (keeping other parameters constant).
Although the stock of savings rises, the stock-flow ratio drops from an initial 200% to converge towards a novel steady acre of 140% of income. This behaviour agency that if y'all desire to specify the consumer behaviour inwards terms of seeking a target assets-to-income ratio inside a linear model, the parameters are theme upon the assumed nominal income growth.
(UPDATE) It is possible to define SFC models where the steady acre debt-to-GDP ratio is stable, fifty-fifty if nominal gross domestic product increase rates change. This comes from an supposition that households elbow grease to stabilise their existent assets versus existent income. As Ramanan noted inwards the comments, in that location is such a model inwards Chapter eleven of the Godley in addition to Lavoie text. However, the dynamics of family behaviour inwards that model are to a greater extent than complex than what I desire to verbalize over inside this article.
In practice, the dependence of the assets-to-income ratio to nominal increase rates is strong. In my view, it is no accident that the authorities debt-to-GDP ratio moved inversely to nominal gross domestic product increase rates throughout the developed footing during the post-WWII era, equally authorities debt is an of import element of private sector assets. I volition encompass this subject to a greater extent than fully inwards subsequently articles.
Comparison To Mainstream Models
In modern mainstream models (DSGE models), family savings behaviour is specified inwards terms of the solution of an optimization problem. Households are assumed to optimize utility over time. The uncomplicated behavioural rules used higher upward facial expression primitive relative to an optimizing framework.
In practice, the difference is smaller than mightiness appear. If nosotros created 2 parallel models, the consumption role used higher upward would in all likelihood live on a rattling proficient kickoff gild approximation of the behaviour of an optimizing family over a reasonable fourth dimension interval. Additionally, fifty-fifty optimising models remove to cause got into occupation concern human relationship that in that location are broad divergences betwixt savings patterns betwixt the dissimilar historic catamenia cohorts, in addition to so aggregate behaviour volition deviate from what looks optimal for an private household.
We would remove fairly extreme changes inwards economical behaviour to create pregnant deviations inwards the behaviour betwixt the models. I suspect that the differences would live on larger inwards an inflationary environment. But if nosotros were calibrating to real-world information at present, it would live on difficult to distinguish the model classes.
On the other hand, SFC models tin live on solved without relying on fairly dubious assumptions in addition to linearisations. Correspondingly, if y'all desire to truly instruct a model that y'all tin use, the best line of assault is to facial expression into stock-flow consistent modelling.
See Also:
- The text Monetary Economics by Wynne Godley in addition to Marc Lavoie offers an first-class introduction to SFC models. (Amazon affiliate link.)
- My "theme article" amongst links to my principal articles on SFC models.
- sfc-models.net
(c) Brian Romanchuk 2014
No comments