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amv: that's almost compatible with my view. Minor differences:

1. At the level of individual firms, relative prices will be "wrong" even if the monetary authority gets it right.

2. Given imperfect information, or information lags, the "optimal" policy rule may not be perfectly optimal.

3. Because of imperfect competition, so that P exceeds MC, the output market will always "look like" a perfectly competitive market with price above the market-clearing equilibrium and excess supply, even when monetary policy is optimal of prices are perfectly flexible. (This is one of my pet themes, that I bore readers with by posting about it from time to time -- just search "excess supply monopolistic competition" if you want to fully explore this idee fixe of mine).

But, basically, agreed.

Thanks. I'll check.

Re: stock/flow inconsistencies, my core criticism is that capital -- which is a stock -- is treated as a flow. Then you get all sorts of problems.

Take a continuous model and imagine the economy is engaging in some continuous market clearing (at each point in time). At each point in time, stocks do not increase or decrease, the growth rate (flow) of the stock changes.

You have to integrate the flows across time to get the change in the stock.

That means that at each point in time, the stock inputs into production are fixed, and the flow inputs are variable, so there is no problem with increasing returns to scale industries in a stock-flow consistent competitive equilibrium model. As long as the industries have declining marginal product in their flow inputs, you are OK, as the stock inputs are fixed in each period. So when talking about convexity of production sets, we need to only look at the flow inputs rather than the stock inputs, and the production set needs both flow inputs (e.g. labor, intermediate inputs) as well as stock inputs (capital).

It is just like population -- there is no problem with production functions that have increasing returns with respect to population (which is properly treated), but for some reason there is a problem with increasing returns with respect to capital (which is not properly treated).

And the problems cascade from there on.

You can clear flows with prices, but excess demands for stocks are going to be cleared with a combination of price and rate of change of price (with respect to time), as the "equilibrium" investment flows give rise to a growing capital stock.

The concept of equilibrium with both stocks and flows is different -- it means that the rates of change of prices and quantities are at equilibrium.

And from there you get problems with the budget constraint, as flows of goods are purchased with with flows of money -- dm/dt, whereas stocks (e.g. capital goods) are not. You need two budget constraints, one for the income statement and another for the balance sheet. Capital transactions do not go on the income statement -- they are not expenditures in the flow.

RSJ: 5 thoughts:

1. There is (usually) a contradiction between increasing returns and perfect competition. With IRS (unless it's external to the firm) you get natural monopoly.

2. There's an equilibrium time-path for prices. That time-path will generally be continuous, unless something discrete happens at a point in time, like sudden new information.

3. Flows of goods or assets are bought with flows of money; stocks of assets are bought with stocks of money.

4. In practice, we always buy everything in lumps, with stocks of money. Monetary exchange is like batch-processing, because there's a fixed cost to each batch. (I buy apples in batches too, and consume them in batches too, not as a pure flow.) For example, right now I am consuming a pure flow of electricity, but I am paying for it with a flow of trade credit, and at the end of 2 months I pay a stock of money to pay off a stock of trade credit (my hydro bill). The stock of money I hold is like an inventory. If I paid for everything I bought in pure flows of money, and received payment for everything I sell in pure flows, I might be able to arrange my affairs so that my stock of medium of exchange was usually zero. My "demand for money" is best understood as some average desired holdings over the cycle of payday and trips to the supermarket.

5. If we ignore point 4, and coarsen the measurement of time so that they all look like pure flows of money receipts and expenditures, my demand and supplies of assets will also be pure flows, and the equilibrium time-path of prices will be continuous, unless there's some discrete lump of new information that happens at a "point" in time.


In a continuous time model, the stock of capital does indeed change at each point in time, called the instantaneous rate of change (Wicksell's Verzinsungsenergie). Increasing returns are excluded by assumption (as you say, convex technology): Increasing returns means that your list of inputs is incomplete. Thus, constant return to scale means that you have a complete list of inputs. I think this is a legitimate assumption. Further, do you mean the physical stock of capital or its value? If you have the value concept in mind, please take into account that this stock is nothing else then the present value of future flows. So stock-flow consistency is given.

@ Nick Rowe,

I have a question with regard to monopolitic competition and "excess supply":

Let us assume a competitive economoy with A agents/firms with convex preferences and technology and N goods/markets. All goods, including entrepreneurial activities are traded (so zero profit to the firm in competitive equilibrium). Assume that - for whatever reason - from one moment to the other preferences show a love for variety. Thus, on each of the N-markets, there is a potential for firms to differentiate itself from the other firms in the N-th market so that each firm can earn positive equilibrium profits (the mark up). One way to think of this to enlarge the list of commodities: Instead of thinking of N markets with heterogenous firms, think of M>N markets with homogeneous firms. Since the number of agents is fixed, i.e., remains A, the number of agents per market is lower in the M-market economy. Since A only ensures perfect competition in a N-market economy, the M-market economy may allow for strategic behavior: since buyers don't have perfect outside options firms can increase prices by REDUCING output (realizing a positive profit).

So if opportunistic behavior indicates suboptimal reductions in output, why do you think of 'excess supply'?


"When a bank securitizes loans and sells it in the market, the amount of deposits in the banking system goes down "

Why does the amount of deposits go down ? A securitized "product" is just a mixture of vanilla loans.

Take MBS for example.

Or CDO ;)


When a bank makes a loan, the assets and liabilities of the bank increases because loans make deposits.

Securitization is a complicated thing but lets consider a loan sale - most of it will hold for the former since securitization is just a complicationization of loan sales.

Let us say a bank makes a loan of $100. Banks assets increase by $100 and deposits increase by $100. If the bank sells this loan to a non-bank, the non-bank's purchase of the loan will result in the deposit of the non-bank going down because the payment is done by the bank debiting the non-bank's account. Even if the non-bank has an account at a different bank, this holds.

So while loan making causes deposits to go up by $100, loan sale causes it to go down by $100.

This can be checked from Z.1 - Banks' assets have less loans as compared to liabilities to banks in the household and corporate sectors' balance sheet.

amv: first let me ask a rhetorical question: who do you think sets the prices in your model? A Walrasian auctioneer? They don't exist.

In economics, we normally think of a perfectly competitive firm as choosing quantity, not price, and a monopolstically competitive firm as choosing a point on its downward-sloping demand curve -- which we can think of as choosing either price or quantity.

Let me give you another way of thinking about it. Any firm, even a perfectly competitive firm, can be though of as choosing two variables: a price; and the maximum amount it is willing to sell at that price. And that way of thinking corresponds to the way we normally think, as shoppers. "What's the price?" "Do you have any in stock you are willing to sell me?"

(In perfectly competitive equilibrium, of course, the individual firm would lose profits if it set any price different from what other firms selling identical products are selling. But out of equilibrium it would want to set either a higher (if there's excess demand) or lower (if there's excess supply) price than the other firms, if it wants to maximise profits.)

If we think of a firm that way, in the normal way we think when we go shopping, the answers to the two questions are:

For a perfectly competitive firm:

1. Set P= the same as all the other firms are setting.

2. Be willing to sell as many units of output Qmax that people will buy up to the point where MC(Qmax)=P.

And for a monopolistically competitive firm:

1. Set price such that P=(1/(1-E))MC where E is elasticity of demand.

2. Be willing to sell as many units of output Qmax that people will buy at that price, up to the point where MC(Qmax)=P.

The difference is that the Qmax will equal Qd for a perfectly competitive firm. But Qmax will be greater than Qd for a monopolistically competitive firm.

And Qmax is the profit-maximisising Q *given P*. So it can make sense to think of Qmax as "quantity supplied" (it's the quantity the firm *would like* to sell, given P).

So a person who thinks of firms setting both P and Qmax, the way normal people think when they go shopping, would see a monopolistically competitive firm in profit-maximising equilibrium as having what looks like excess supply.

Consider this thought experminent: take a firm in equilibrium, hold its price fixed by law, then increase demand. Will it be willing to sell more? For a perfectly competitive firm, the answer is "no". For a monopolistically competitive firm, the answer is "yes please!"

One possible advantage of stock/flow consistent models in economics is that they make it easier (or rather, more feasible) to model processes of adjustment towards equilibrium, by borrowing well-established models from physics. There is a folk analogy (see e.g.: Karnopp, Margolis & Rosenberg; System Dynamics: a Unified Approach [1990]) which relates the following quantities:

(a) displacement: q; (b) flow: q';(c) momentum: p; (d) effort: p'

In translational mechanics: (a) is position; (b) is velocity; (c) is momentum; (d) is force.
In rotational mechanics: (a) is angle, (b) and (c) are angular velocity and momentum, and (d) is torque.
In electric circuits: (a) is charge, (b) is current, (c) is flux linkage, (d) is voltage.
In hydraulics, (a) is volume, (b) is flow, (c) is a quantity we could call 'pressure momentum' and (d) is pressure.
In thermodynamics, (a) is heat, (b) is heat flow, (c) is 'temperature momentum' and (d) is temperature.

Such systems are often described using so-called "bond graphs", which look rather like a generalization of electrical circuit diagrams. For a description, see e.g. John Baez's This Week in Physics, week 288 to week 297.

Some econophysicists have extended this model to economics, where (a) is inventory (dimensioned as physical quantity), (b) is flow of product (quantity / time), (c) is 'economic momentum' (dimensioned as money × time / quantity, or money / flow) and (d) is price (money / quantity). The role of "money" (p'q, or p'q') in this analogy matches the one of "energy" in physical systems.

The basic models known from physics (e.g, damped harmonic oscillator) resemble a continuous-time version of what is known as "cobweb model" in economics. The cobweb model is quite problematic, in that it lacks empirical support and implies that agents are not fully rational. But perhaps one could draw from control theory and engineering so as to reach more satisfactory results.


LOL, there is no need to bring german into this :)

This is simple. There is position x(t), and velocity, dx/dt. There is K(t), and Investment, I(t). Now assume the economy is following some trajectory, and at each point in time there is a warlassian clearing process happening. The clearing process adjusts _flows_, but it cannot adjust stocks (unless you allow for interior solutions, or for capital to be thrown away). If you want to increase the size of the capital stock, you have to produce more capital. That is a flow. By adjusting the flow, you can cause dK/dt to change, and this will alter the _future_ size of the capital stock, but the present size of the capital stock is fixed.

Therefore in order to have a CE solution in a stock-flow consistent CE framework, you do not need convex production technologies in all inputs, you only need convex production technologies in the flow inputs -- in those inputs that can be varied in response to the allocation process, which is occuring at each point in time.

But capital (real, physical capital), cannot be varied instantly. Only its speed of production, which is a flow, can be varied. And an adjustment to a flow does not cause an instant adjustment to the stock. It takes time for the adjustment to the flow to result in an adjustment to the stock, whereas the clearing process is happening at each point in time. Prices continuously clear throughout the trajectory.

So you will still get an equilibrium solution if your production function is K^4*L, because K cannot increase as a result of the allocation process, only its derivative with respect to time can increase.

Again, there are serious stock/flow problems here, relating to how you embed the CE framework into time.

In the above, I meant (if its not clear) that the aggregate size of the stock cannot be changed as a result of the market clearing process.

@ Nick Rowe

I come to believe that we have no disagreement in content, yet differ in the way we frame the problem and in our semantics.

Since I entered the discussion with regard to the New Keynesian model, I remained within the canonical general equilibrium framework modified by the assumption of monopolistic competition. In theoretical discussions, I hesitate to refer to everyday experience which by and large is anectodical. This may explain my recourse to the Walrasian auctioneer: for our discussion the way prices come about is neglible, since we want to know how a firm's behavior can be understood for given prices.

I have particular problems with your shift between equilibrium and disequilibrium semantics. Let us remain in New Keynesian models. Here the term "excess supply" indicates that you are out of equilibrium. This is why I was confused. If the representative firm is monopolistic in the sense you described, which is a perfect description of the standard assumption of New Keynesian firms, it is of course true that the firm is constraint by demand only: since they realize a mark-up, the firm can make profit on each additional unit sold. But this is an equilibrium position, that is, supply equals demand independent of the fact that the constraint on output is one-sided. True, since the firm would like to supply more than it can for given equilibrium prices, this equilibrium is not efficient, that is, it is Pareto dominated by competitive allocations. But it is an equilibrium nevertheless. However, your notion of "excess supply" indicates that the firm actually produces more goods than there is demand for it, and that it piles up involuntary inventories (accounting view).

That disequilibrium rules the real-world depends on your definition of equilibrium. Before WWII, long-run equilibrium meant deterministic long-run stationary states. If equilbrium is such a restrictive notion, everyday trades must be grasped as disequilibrium phenomena. Today, general equilibrium implies a stochastically stable system under continuous market-clearing that can account for the variations of real-world data. Given such a broad understanding of equilibrium, it is not so clear that real-world processes cannot be thought of as equilibrim processes. Equilibrium as well as disequilibrium is an invention of the humand mind. What matters is the relative productivity of the equilibrium notion (in generating excess empirical content and excess corroborations).


Sure, the initial level of stock is given. Optimal growth problems take the intial size of capital as given (why not?). Intial period is t=0. From t=1 to t=infinity, the stock level is endogenously determined, it's all about intertemporal allocation of consumption, that is, the size and time shape of consumption FLOWS. Technology is summarized by an aggregate production function, usually displayimg diminishung returns to capital accumulation (constant returns to scale for proportional increases in all input; modifications granted). Abstracting from depreciation and resource growth, the optimal stock of capital is determined by marginal productivity of capital (MPK) = pure rate of time preference (PRTP). For K(t)

Where do you see the inconsistency between stocks and flows for this simple Ramsey problem?

sorry, something went wrong with my post. Here is the part missing:

... For K(t)

ha, now I know. So here a third attempt:

For K(t) smaller than K(opt), the speed of convergence is controlled by MPK minus PRTP.


Growth theory doesn't suggest that the capital stock is changed by the market-clearing process. In the social planner framework, there is no need for a price system to aggregate information. So the stock varies according to the real data of the system independent of market clearing (there are no markets at all). In a competitive framework, the stock varies for a given set of equilibrium prices, indicating the relevant tradeoffs. How the equilibrium price system is generated, is a different questions that asks for additional theory: for instance, if transaction costs are zero and thus markets complete (no need for expectation formation), the auctioneer process suffices (for some additional restrictions) to explain convergence to a market-clearing price system in the initial period before all production takes place. The accumulation of capital just follows the mutually consistent plans of all agents. Since the stock-flow problem already manifests itself in the social planner framework, it is independent of the market-clearing assumption in the competitive equilibrium framework.

amv: "I come to believe that we have no disagreement in content, yet differ in the way we frame the problem and in our semantics."

Yep. Basically agreed. It's an equilibrium, even if I want to say it's an equilibrium with excess supply. Just that I think that my way of framing the problem can be useful for *some* purposes. For example:

1. Start with a competitive general equilibrium, hold P temporarily fixed, then increase AD. Output will not increase, because firms are selling as much as they want already. But if we do the same thing in monopolistically competitive equilibrium, output will increase. It is *as if* we started in competitive *dis*equilibrium with excess supply.

2. When we go shopping, there is almost never a problem in buying as much as we want. The sellers are always really pleased to see an extra customer. They work hard trying to find willing buyers so they can sell more; we don't work hard trying to find willing sellers so we can buy more. More people have jobs in sales than in purchasing. The world *looks like* a world with excess supply. Go to Cuba, for example, and it's the exact opposite was round. This all makes sense with monopolistic competition.

Minor quibble: "However, your notion of "excess supply" indicates that the firm actually produces more goods than there is demand for it, and that it piles up involuntary inventories (accounting view)."

Not really. It indicates that they are *willing* to produce more goods than there is demand for, at existing prices. They would be very happy to produce more if needed. They *may* produce more bread than they usually sell (if demand is stochastic and they need to produce in advance of the realisation), and *may* have hairdressors waiting for a customer most of the time. But it's more a *willingness* to produce than actual production.


I misspoke. The number of bilateral contracts won't go down. If you buy a loan from the bank, you exclude the bank as an intermediary. The fact that one leg of the bilateral contract happens to be a deposit is unimportant.

But, yes, you are right the number of deposits(the bank liability "leg" of the contract) will go down as a result of the bank exclusion from the contract.


Okay I see an agreement.

Securitization is nothing but a part of liability management but with various goodies for the bank.

To be more accurate, the loan is hidden in the SPE's balance sheet as receivables (which is owned by the bank).

What I was aiming at was that even though credit has increased, deposits haven't. The money stock is a residual.


What I was aiming at was that even though credit has increased, deposits haven't. The money stock is a residual.

I am not sure what you mean by "credit has increased". If you sell the original contract, in a simple case, the credit understood as a quantity of outstanding contracts remains the same.

To be more accurate, the loan is hidden in the SPE's balance sheet as receivables (which is owned by the bank).
If the loan (in any shape) is sold to, e.g., a pension fund, the bank no longer owns it.


Poor specification on my part.

"Credit has increased" was with reference to the point the loan was not made. Didn't clarify.

"If the loan (in any shape) is sold to, e.g., a pension fund, the bank no longer owns it."

Yes true. But in a sense it is better to see the asset of the pension fund as a liability of the Bank+SPE ... which makes it clearer that securitization is liability management - an alternative to financing with deposits. The loans appear in the SPE's assets, though the bank does not "own" them.

Take another example, banks also market covered bonds. The holders of the covered bond (say a pension fund) can be said to the owner of the loan .. it still remains in the banks' balance sheet as liabilities.

What I was originally aiming at was that the money stock has no particular significance.


With "true sale", the bank gets cash from the SPV who raises cash by selling its bonds backed by the original loans, now owned by SPV, to the investors. The investors, in this arrangement, bear credit risk. Therefore, you cannot consolidate Bank+SPE(V) -- they are separate, that's the whole point.

Perhaps, you had a different arrangement in mind ?

@ Nick Rowe

Ok, I got it. If output prices are fixed, and profit per unit of output equals zero due to competitiveness, there is no incentive to respond to excess AD by producing more zero-profit units. If, however, there is a mark-up due to monopolistic competition, excess AD is accommodated, since each unit sold earns positive profit. You are right.

amv: Yep. Except it's profit *at the margin*.

Sure. To grasp your argument, I wrote down a simple and highly restricitve model with labor as sole factor of production and a single output. Thus, no increase in marginal costs at given wages. So I resumed to unit costs and profits. My bad. In general, you are right ... only margins of choice matter.

amv (or Walt),

Don't want to hijack the discussion, but you seem to understand the canonical NK model well, so I'd love to hear your thoughts on a previous issue discussed here (feel free to ignore). In previous posts, Nick has argued that Woodford's cashless limit in the NK model does allow for particular kind of demand-recession that is available in a model with monetary disequilibrium. Specifically, that Woodford's cashless limit with no medium of exchange must allow for some kind of barter system (though it isn't explicit in Interest and Prices or the relevant papers), and that such barter would allow the economy to comply with Walras' Law. Note: This of course doesn't preclude recessions altogether as relative price changes and resorting to barter can still decrease Y, just that it would prevent the kind of recession where there seems to be oversupply of everything and an excess demand for money.

My question for you: Is some kind of barter system necessarily a component of Woodford's cashless limit, or is it merely credit-as-money? And if it's barter, do you think the model leaves out an important "kind" of recession that isn't just about relative price changes amid nominal rigidities and monopolistic competition or the effects of second-best choices on Y, but is about a freezing that might come from monetary disequilibrium (everybody trying to hold the MOE and having no second-best option because barter doesn't exist or is too costly) in a true medium of exchange economy without barter? I am mainly thinking about the conversation between Nick and Adam P., who also understands NK models well.



In previous posts, Nick has argued that Woodford's cashless limit in the NK model does not allow for a particular kind of demand-recession


Its a bit of a digression from what I was originally aiming at.

Plus I gave the example of covered bonds, which are very similar to securitized products, but the former is on balance sheet. These are legal hurdles .. though of course true .. who bears the credit risk ... though not always... sometimes there are trigger conditions which leads to the bank moving the SPEs back to their balance sheet .. some banks had issues during the crisis due to this ...

But all these are digressions... the main point being ... the money supply being determined by the private sector activity and details of transactions ... the central bank rate setting affects credit of course ... but not the money supply... I took a complicated example to show this ...


can you tell me which posts you are referring to? In concrete, what is the particular kind of demand recession you/Nick refer(s) to? In general, the cashless economy can mimic demand recessions: there is a price level, there is real income, so there is PY which measures AD. Further, in the standard model without investment, where aggregate demand equals consumption. Thus, manipulations of the real rates lead to intertemporal substituion such that present consumption (=AD) may fall (and planned future consumption =AD increases). Finally, the cashless economy can display NGDP-level targeting, my favorite policy, which by and large is demand managment (the avoidance of demand-recessions).

read: ... where aggregate demand equals consumption, manipulations of real rates ...

amv: This is the pst dlr is thinking about:


But try this post instead, since I managed to simplify the argument:


Or this one (the bit about the hairdresser, masseuse, and manicurist) where I simplify it still further:


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