A question for Modern Monetary Theorists

What, in your opinion, is the shape of the Long Run Phillips Curve?

Supplementary: if you use the words "full-employment" in your answer, can you do your best to explain what you mean by this. (This is not a "gotcha!" question. I know that's a tall order, because it's not always easy to come up with a simple theoretically and empirically watertight definition of theoretical concepts; many orthodox economists have equal difficulty explaining what they mean by the "natural rate of unemployment".)

I think that Modern Monetary Theorists want "orthodox" macroeconomists to engage them more. I'm not sure that I'm really orthodox, but anyway; I sympathise with their desire, and this is an attempt to meet it.

Here is my "rational reconstruction" of the MMT answer. By that I mean here is what I can best assume they believe if I want to make sense of what they say:

"The Long Run Phillips Curve in {inflation, unemployment} space is L-shaped. Alternatively, the Long Run Aggregate Supply curve in {Price level, real income} space is reverse-L-shaped. The price level, or rate of inflation, is exogenous with respect to Aggregate Demand until you hit "full employment" (or "full employment output"). Then it turns vertical. So increases in Aggregate Demand (for example, due to money-financed increases in government spending, transfers, or tax cuts) will cause output to increase and unemployment to fall, with no effect on the price level or inflation, until you hit "full-employment". Thereafter they only affect inflation."

That's what I used to believe in 1972, when I was studying A-level economics and politics. (I only got a D; but perhaps, I hope, it was because I did very badly on the politics part?)

In 1972 I couldn't define what I meant by "full employment". But now i think I can rationally reconstruct what I would or should have meant by "full employment". Here it is:

"An economy is at "full employment" when an increase in Aggregate Demand won't increase employment even in the short run."

To put it another way, I made no distinction between the Long and Short Run Phillips and Aggregate Supply curves.

OK. Now for the comments.

Comments

[Finster]

Besides the modern veracity of a 'Phillips Curve,' the problem is that interest rates and employment have globalized. I greatly admire Prof. Pettis for his work and quote his blog entry here:

http://mpettis.com/2010/04/the-rmb-and-the-magic-of-accounting-identities/

The connection might not be obvious at first, but if you start thinking about the current and capital accounts and their effect on unemployment you might get a new perspective on the matter in question. I do not presume to completely understand it.

[Anon]

I read the Pettis piece, and I am a Pettis fan. He posits the China problem with the lack of reliable information in China about China. So the Phllips curve in China will be highly volatile as the information is not available to hedge the future.

In the USA, we can hedge against inflation for longer due to more accurate information. But eventually, constraints of important inputs appear, and we restructure. Hence the long term Phillips curve defines the non linear restructuring, that is the definition of long term is that Phillips no longer holds.

[Too Much Fed]

Here is mine on page 20 of this .pdf.

http://www.thomaspalley.com/docs/research/MoneyControlPosenSubmission.pdf

Figure 1 The backward bending Phillips curve showing the Minimum Inflation Rate of
Unemployment (MURI).

IMO, the price inflation rate that minimizes the unemployment rate is ABOVE 2%.

[Too Much Fed]

Not sure if the link showed up correctly.

http://www.thomaspalley.com/docs/research/

MoneyControlPosenSubmission.pdf

[Too Much Fed]

What if there is a shortage of something else that causes price inflation (going vertical) before "full employment"?

Here is an example. What if "full oil" occurs before "full employment"?

[RSJ]

By Phillips curve -- do you mean the relationship between unemployment and wages, or the relationship between unemployment and inflation? Phillips drew several curves..

It's certainly possible to have low unemployment without rising unit labor costs -- many nations adopted a disinflation policy that consisted of negotiations with labor unions rather than using the CB to bankrupt large swathes of the private sector -- c.f. Wassenaar Agreement -- and these policies worked!

Volcker's approach was not the best, or third best, way to control inflation. At the same time, it's possible for there to be inflation without the cause being rising unit labor costs. A large expansion of credit can lead to demand-led inflation, for example, and low unemployment would not be to blame. In fact, the casual chain might be: unwarranted expansion of credit --> increased prices, with decreased unemployment as a side-effect, rather than a cause, of the inflation.

So the topic is a bit like asking how much liquor do you need to drink before you get pregnant. The whole question is loaded with a lot of assumptions that many reasonable people would object to, even though there is no doubt a statistical relationship between unwanted pregnancy and liquor consumption.

[RSJ]

And as an aside, when asking "Is low unemployment a consequence of a booming economy with rising prices, or does low unemployment cause the rising prices?" The first place to look as unit labor costs, which do *not* lead rising prices, but are a coincident indicator, so there is evidence that the same forces that cause demand to increase also cause unemployment to fall at the same time, bolstering the excess credit as a driver of inflation argument, rather than rising unit labor costs.

I remember once looking at this relationship and have dug up an old chart:)
http://1.bp.blogspot.com/_fevQMK7kLEI/SuO8zBL__1I/AAAAAAAAAGQ/LIGmU3iBo_Q/s1600-h/ULC_CPI.png

[Jon]

TMF: Employment is maximized at any stable inflation target. To deny this, really is to deny 30 years of progress.

Nick: If low unemployment leads to hard nominal bargaining, then employment leads to wage inflation, and the data need not admit any possibility of inflation boasting employment even in the short-run.

[Nick Rowe]

RSJ: "By Phillips curve -- do you mean the relationship between unemployment and wages, or the relationship between unemployment and inflation? Phillips drew several curves.."

Whatever you (they) like. Put some real variable (unemployment, employment, output..), on the horizontal axis, and a nominal variable (prices, wages, their rates of change...) on the vertical axis, and describe the curve(s) traced out in the long run when aggregate demand varies. Call it the Phillips Curve, Aggregate Supply curve, whatever.

[Panayotis]

We must ralize that any long run relationship between inflation and full employment of resources not just labor but also productive capacity and other materials depends on the level of inefficiencies/inadequacies of resources. These are variable with policies that expand human capital embedded in labor,skill development,technology/innovation of existing productive capacity, infrastructure that reduces frictions, etc. For example, capital adequacy instead of being measured only in monetary value it should also be measured in terms of its real capacity to produce. For a given financial capital measurement, there is a variable adequacy to produce output and reduce inflationary pressures. This can be viewed as an inflation at risk estimation of capital adequacy!In any event, at the long run the curve is shifting with private spending in R&D, education and training programs and discretionary fiscal spending as development policy.

[Lord]

"mployment is maximized at any stable inflation target. To deny this, really is to deny 30 years of progress."

At nearly 10% unemployment, it is long past time to revisit this.

[RSJ]

Nick,

Ok, I put y/y change in unit labor costs on the y-axis, and unemployment on the x-axis, and find no correlation in the data. Theoretically, you could assume it would be "L" shaped for very low levels unemployment that are in practice unreachable, and in times of depression unit labor costs would be falling while unemployment is rising, but generally there is no relationship.

The real question is, why single out labor, if not for political reasons? Do we require 5% of homes to be vacant? 5% of the population to be homeless? 5% of capital to be idle? 5% more oil to be produced than is sold? We are able to distinguish between a market *clearing* and the price. But for some reason we are afraid of the labor market clearing and are not afraid of the other factors of production clearing. So I object the casual relationship implied by NAIRU, rather than the act of plotting nominal variables against real ones to infer that an economy suffers from nominal effects.

[Nick Rowe]

RSJ: "The real question is, why single out labor, if not for political reasons?"

None. "Unemployment" could mean unemployment of *any* resource, if you like. Labour is the most important, quantitatively, but all resources can be unemployed. And if you put output, or real income, on the x axis, then all productive resources are implicitly included.

[Nick Rowe]

Put it another way: if you believe in a natural rate of unemployment, you almost certainly have to believe in a natural rate of unemployment of any resource, not just labour.

[RSJ]

"Put it another way: if you believe in a natural rate of unemployment, you almost certainly have to believe in a natural rate of unemployment of any resource, not just labour."

Agreed! But in that case, you are believing that there is a "natural" failure rate of the market to clear. Now -- there is nothing wrong with believing in that per se, but why would this natural failure to clear rate be dependent *only* on the price of the good in question, and not on the quantities/prices of the other factors of production?

So this is again an aggregation problem. If you believe that there is an aggregate production function with the following characteristics:

* Adding an additional unit of labor without increasing the capital stock will result in a positive marginal increase in output.

* Capital and labor are substitutable for each other

* All combinations of labor and capital will result in non-zero output

Then indeed you can argue for a NAIRU.

But, at the micro-level, all of the above are false. At the micro level, businesses lose money, cannot substitute labor for capital, and cannot increase output by increasing only a single factor of production. So the quantity and price demanded for each factor depends on the quantity and price demanded for all other factors. A business short of capital cannot hire more labor. And a business short of labor cannot deploy more capital. Because of this constraint, if the cost of capital is too high, then a business will not hire more labor even if labor is fairly priced. As a result, you have an *explanation* of why the aggregate labor market would fail to clear.

Therefore in aggregate, you would expect U(Labor) to also be a function of U(capital) and of the price of capital. And in that case, you lose the ability to say that a low U(labor) will "cause" the price level to increase. It could just be that at the micro level, capital and not labor tends to be the constraining factor on production (because the ratios are constrained), and so you can max out labor utilization without maxing out production and therefore prices.

Or, it could be the other way around, and labor is more constrained. So if you aggregate from the bottom up, U(L) just doesn't supply enough information to draw a relationship between it and the price level. But I agree that when you put "Output" on the x-axis, you can get a relationship -- but perhaps not a very interesting one.

[Nick Rowe]

RSJ: "But I agree that when you put "Output" on the x-axis, you can get a relationship -- but perhaps not a very interesting one."

I could see an Austrian taking that position, because they don't think aggregates are meaningful and interesting (in some sense). But I don't interpret MMTers as thinking that. As far as I know, since they do commonly talk about aggregate concepts, like aggregate demand, output, employment, etc., they do think aggregates are meaningful. (Of course, when pressed, no doubt like any sensible people they would agree that aggregation can leave out some other interesting information.)

You have sketched out a theory of the natural rates of unemployment for each of the various inputs (and even "labour" can be disaggregated into the millions of different types of labour), based on Leontieff (y=min{k,l} ) production functions at the micro (individual firm) level. I disagree with your theory. But that's a bit beside the point of this post. Unless you are saying that your theory is also the MMT theory of the natural rate?

[Adam P]

"if you believe in a natural rate of unemployment, you almost certainly have to believe in a natural rate of unemployment of any resource, not just labour."

Really?

[Nick Rowe]

Adam P: Yes, (allowing of course that some of those natural rates might be zero).

You get a natural rate of unemployment under neutrality and super-neutrality of money. If money were non-neutral, then it would be a big coincidence if some real variables (like some unemployment rates) changed but other real variables stayed the same. Mostly, in General Equilibrium, everything depends on everything else.

I suppose if there were a zero natural rate of unemployment in some resource, (due to zero search and other frictions etc.), then that zero natural rate might stay invariant to other real changes.

Is that what you had in mind?

[RSJ]

Nick:

I'm not the MMT expert, but I think everyone believes aggregate quantities are meaningful and important -- I'm only disputing the relevance of this particular pair of variables. I know that MMT likes to focus on sectoral balance sheet identities and other aggregate accounting identities. But accounting identities are not "real" identities.

About the min{} functions, yes, this is an example of how a natural failure of the market to clear would arise. But you don't need to believe in Leontieff production functions per se.

If you are looking at micro-firms that grow in size, then each firm is a price taker for all factors of production other than capital, which is unique to the firm.

Suppose you have a whole distribution of micro-firms. That means you get a distribution of marginal products of labor, for example, and a distribution of marginal products of other factors. At any wage rate, there will be some firms for whom labor is too expensive and other firms for whom labor is too cheap.

You can hope that the firms for whom labor is too cheap will grow in size, and as they do, their MPL will fall to the "equilibrium" wage. And the small firms will shrink so that the MPL will rise to the equilibrium rate. But what if there is more than 1 factor of production? Now, you need *either* all the factors of production to be perfectly substitutable *or* you need the production curve to be exactly the same function for each firm. If there is variance in the shape of the production function or some non-infinite elasticity of substitution of factors of production, then a model with more than one firm will in general not be able to reach a state where every firm has the exact same marginal products for all factors of production. And as long as that happens, the market will fail to clear. So this is a much more general result than a requirement that each PF be Leontieff.

And it has *nothing* to with frictions -- it holds with zero frictions or search costs. Variance in production functions and substitutability of factors is sufficient to get the market to fail to clear.

[RSJ]

And it's Saturday, so here is a mini example:

Assume not one, but two production functions in a very general form: f_1(K_1, L_1) and f_2(K_2, L_2). And let the total *employed* labor be L = L_1 + L_2, and the total *deployed* capital be K = K_1 + K_2. Then the requirement that the marginal product of f_1 with respect to L_1 = marginal product of f_2 with respect to L_2 = wage rate

forces L_1 to be a function of X(L, K, K_1). And the similar requirement on capital forces K_1 to also be a function of Y(L, K, L_1). These curves will generally intersect in disjoint loci, and each loci will describe a surface Z(L,K). What this means is that a change in the *total* K forces a change in the total L. But changes in K -- dK/dt = Investment -- are volatile and depend on expectations, therefore the total size of the labor force is similarly volatile. And this assumes perfect flexibility in wages and no frictions as well as perfectly competitive markets.

So even if you start out with generic micro production functions, in which capital and labor are substitutable, you still end up with the conclusion that only certain types of (capital, labor) combinations are feasible -- *regardless* of the wage rate or interest rate.

And that is just with 2 production functions, and no requirements that they be Leontieff.

There are many such emergent effects when you disaggregate production that explain well the aggregate economic phenomena that we see, but are completely hidden and inexplicable if you assume the entire economy is a single corn farm, or that all production functions are identical.

[Panayotis]

Even at full employment of resources a variable adequacy of these resources to produce can reduce inflationary pressures and expectations.In my research the adequacy factor is calibrated to incorporate random/stochastic steps and jumps with an asymptotic hyperbolic function in order to avoid decay with size. Why assume that there are no inadequacies of resources? These can be assisted and remedied by discretionary fiscal policy of allocative nature such as reorganization, innovation, skills formation and other qualitative measures of development policy that reduce frictions.These measures are given the stock of resources and productive capacity. On the other hand, growth policy is thew discretionary fiscal measures that expand the stock of resources. Finally,the automatic endogenous fiscal policy performs the role of stabilizing the effective utilization of these resources at or near full employment.In this hypothesis with a variable adequacy to produce, the relationship between full employment of resources and inflation is unstable and shifting. Actually there is a case of inflation at risk given the degree of inadequacy.

[Nick Rowe]

RSJ: I just don't see it.

Assume there are 2 farms, that both produce the same good, corn, and wages and capital rentals are measured in corn. (You assumed that the output prices are the same for both production functions, and equal to one, so I'm just echoing your implicit assumptions here.) Assume the 2 farms have different production functions (because, say, one has sandy and one clay soil). OK.

So the competitive equilibrium (and the solution to the social planner's problem of maximising total output of corn) is defined by:

Farm 1's MPL1(L1,K1) = Farm 2's MPL2(L2,K2)

Farm 1's MPK1(L1,K1) = Farm 2's MPL2(L2,K2)

L1+L2 less than or = L

K1+K2 less than or = K

4 equations and 4 unknowns, so look good so far.

I can imagine production functions where we don't get an interior solution, i.e. where one or both of the resource constraints is non-binding (is a strict inequality). That would be where the MPL and/or MPK is zero in equilibrium. So it would be efficient for the social planner to leave labour and/or capital unemployed in equilibrium. But in competitive equilibrium that would mean that wages and/or capital rentals are zero. In other words, labour and/or capital isn't scarce, so some is unemployed.

Is that what you are saying?

If so:
1. You can get that result with a single farm; you don't need 2 farms. Just assume strongly diminishing returns and abundant labour.
2. I don't think it's realistic. Unless you are talking about really Malthusian economies, marginal labour seems to be capable of producing some extra output, and would be employed if the firm could sell the extra output and hire the worker at a low enough real wage.

[RSJ]

OK, a couple of points:

What do you mean by "boundary"? For example, in the special case of two CRS CDPF with exponents a and b, then the result is

Labor 1 = lambda_1 Capital 2
Labor 2 = lambda_2 Capital 1

where lambda_i is some ugly function of a and b. The point is that the total labor demand is a function of the size of the capital stock, *regardless* of the wage rate.

But the rate of change of the capital stock is investment, which is volatile. Even if the the total labor demand were maximal, any variation in investment will push the utilized labor away from maximum. So you get into the situation that you previously dismissed, which is fixed capital/labor ratios leading to unemployment independent of the wage rate due to a shortage of capital. In this case, these ratios are fixed because there is more than one production function. By the way, I am not saying that in the "real" economy the ratios are _fixed_, but I am saying that a shortage of capital can force unemployment regardless of the wage rate, and you don't need leontieff PF for this. standard constant return to scale production functions will do the trick, and rapidly diminishing production functions will work even more strongly, as in that case you get bounded solution sets -- e.g. ellipses, etc.

re: point 2

"marginal labour seems to be capable of producing some extra output, and would be employed if the firm could sell the extra output and hire the worker at a low enough real wage."

That is the point! From whence would this "extra" spending power come?

You can start out with perfectly flexible wages, and still have equilibria that have unemployment if your model consists of a flow of (overlapping) production functions, each of which have rapidly diminishing returns. In fact, you can have a growing economy and still experience these multiple equilibria in case of shocks to the expected return of each micro-production function.

So I am not saying that full employment is impossible, but that whether or not there is full employment depends on the capital stock size, which itself depends on expectations, even with perfectly flexible wages.

[RSJ]

oops, should have previewed:

it should read: labor 1 = lambda_1*capital_1, etc.

The point is that with a single PF, K^aL^1-a, if you take MPL and set it to w, you get:

K^a/L^a = w

so even with a very small K, you can make w small enough so that L is at full employment. And people took this toy and climbed mount everest with it.

But as soon as you have *two* production functions, then w drops out and you get a relationship of the form

K_i= lambda_i * L_i --> and no "w" appears to bail you out and provide you with full employment by being small enough.

-- regardless of the form of your production function. Only in the degenerate case where all production functions have the same exponent can you fall back on the "let's lower wages" to boost employment argument.

In all other cases, you need to increase capital to boost employment. And we all know how volatile capital is.

Hope that makes sense...

[Panayotis]

Guys,

I am sure you are familiar with the problems of heterogeneity and indivisibilities of resources, the Cambridge aggregation controversy and the Samuelson reswitching issue of non monotonicity. The relation between the employment of resources and their remumeration is not so clear and stable, and their markets cannot clear.

[Nick Rowe]

Panayotis: I *used* to know something about the Cambridge^2 Capital Controversy, 30 years ago!

RSJ: OK. I think I follow you now.

First off, forget my "farm" example above. Since you are assuming Constant Returns to Scale in Labour and Kapital, there obviously cannot be a third fixed factor, land. So your firms are not "farms" (because farms have land).

OK. So we have 2 firms, both producing the exact some good (so the two firms have the same price of output), each with a different technology. Both firms' technologies are Constant returns to Scale Cobb-Douglas:

Y=L^a.K^b where a+b=1

But one firm has a more labour intensive technology than the other. (One firm has a higher a/b ratio than the other).

Perfect competition.

Those are your assumptions, right?

Since I am crap at math, I'm going to "solve" for the aggregate labour demand curve intuitively.

Hold aggregate K constant for the moment, while we vary L, and so vary aggregate L/K.

Imagine we start of with zero L, and slowly increase L, and watch what happens to MPL as we do this.

With very small L, and so very small L/K, only the capital intensive firm produces output. The labour intensive firm shuts down. With only one firm operating, we get the standard downward-sloping MPL curve as L/K rises.

When L (and L/K) increases past a certain point, call it L', both firms start operating. As L increases further, each firm holds its K/L ratio constant, but the capital-intensive firm produces less and less output (using less and less K and L), and the labour-intensive firm produces more and more output (using more and more K and L). The MPL at each firm is constant; it does not diminish as aggregate L increases.

(This is where, as you say, it looks *as if* each firm has a fixed coefficients technology, even though they don't).

When L (and L/K) increases still further, past a certain point, call it L", the capital-intensive firm shuts down completely, and only the labour-intensive firm operates. As L increases past this point, we again get the standard diminishing MPL as more and more L is added to a fixed K.

Under perfect competition, the MPL curve is the same curve as the labour demand curve. So what does this curve look like, under your assumptions?

Holding aggregate K constant, the labour demand curve slopes down between 0 and L'. Then it becomes horizontal (perfectly elastic) between L' and L". Then it slopes down again as L increases past L". But the MPL is always positive.

What happens if aggregate K increases? The whole labour demand curve shifts horizontally to the right. If K doubles, for example, L' and L" will both double. We get double the quantity of labour demanded at any given wage (or MPL). (That's because, under CRS, only the ratio K/L matters for MPL.)

Sure, it's a weird labour demand curve. It has a kink at L' and at L". And it's horizontal between L' and L". But that labour demand curve cannot create unemployment. You would only get unemployment if: wage was stuck above MPL; or there's a shortage of Aggregate Demand. But if wages were above MPL, or there were a shortage of AD, we could get unemployment even with a regular labour demand curve.

(If we drop the assumption that both firms produce the exact same good, so the relative price of the two goods varied as their relative outputs varied, we would get rid of the 2 kinks and the horizontal section. the labour demand curve would be a regular downward-sloping one.)

You don't get unemployment under your assumptions.

Plus, I don't think this is what the MMTers are talking about anyway.

[Nick Rowe]

Yep: Micro theory is slowly coming back to me.

Draw the unit isoquant for each technology in {K,L} space. Two convex curves, that intersect, so the envelope of those two curves is not convex. But it can be convexified easily.

Draw the isocost line that is tangent to both those unit isoquants. The slopes of the rays from the origin to those two tangency points points define the K/L ratios of each technology, under the assumption that both technologies are being used. They will both be used if the aggregate K/L ratio lies somewhere between the slopes of the two rays. By varying the ratios of the outputs of the two technologies, you can vary the aggregate K/L ratio even if both technologies hold their K/L ratios fixed. So that constructs an aggregate unit isoquant that is weakly convex. (The aggregate unit isoquant is a straight line between those two tangency points, and outside those two tangency points it simply follows the convex locally superior technology, because only one technology is being used.)

[Nick Rowe]

So the aggregate production function is well-defined, and weakly concave ("weakly", because it has a triangular-shaped flat section in the middle). And the aggregate labour demand curve is also weakly downward-sloping (it has a horizontal section in the middle). And the aggregate capital demand function is also weakly downward-sloping.

[RSJ]

OK, good. Now I point out that

1. Kink region -- the non-convex region -- is the general case

* The economy does have more than 1 firm. It has many industries, even.
* The labor pool, or occupations if you prefer, service many different industries, so there can never be 1 firm.
* Capital of all firms competes
* All firms in all industries compete for Land, energy, etc.

So we are *always* operating in the "kink" region in which the economy has more than 1 firm. Moreover, it is a pretty reasonable assumption that the production characteristics of firms are not the same.

2. You need equilibrium in both markets simultaneously.

Suppose you are at a point (K_1,K_2, L_1, L_2) such that:

MPL1 > MPL2 and MPK2> MPK1.

I claim that in this situation, there does not exist a wage that allows both markets to clear. As firm 2 sheds labor to make MPL2 rise to equal MPL1, and firm 1 takes on labor to make MPL1 fall to MPL2, MPK1 will also rise and will not equal MPK2.

So there is a feasibility region of certain tuples of (K_i, L_i) that are needed for the market to clear. And this feasibility region is actually a surface that can be described as

Total Labor Employed = f(Total Capital).

This is a simple implicit function result -- as long as the gradients {(MPL1, MPK1), (MPL2, MPK2)} are not identically the same, they will be equal on a set of dimension 2, which can be viewed as a curve in (Total K, Total L) space. Independent of the interest rate or wage rate, simultaneous equilibrium in both markets requires the firms to operate at some point on this curve. And this curve will intersect "full employment" only for a single magical size of the total capital stock. Any other size of the capital stock, and employment will not be full.

If the number of firms > then the number of factors of production, then this result still holds -- the total quantity employed of each factor of production can be viewed as a function of the total capital stock, so that

Total Labor = f_1(Total K),
Total Land = f_2(Total K),
etc.

What this means is that if you start at full employment, say, but the level of total capital decreases, then the level of total labor employed must decrease as well. And no change in the wage rate will help you, unless somehow a shift in the wage rate causes the capital stock size to increase. This is important because, in practice, the level of the capital stock is volatile and dependent on forward looking expectations. A change in these expectations, lowering K, will force a certain level of unemployment even if wages are perfectly flexible.

3. It seems to me that you are trying to find equilibrium in the labor market, and then say that you can find equilibrium in the capital market, and just assume that this means you can simultaneously find equilibrium in both. You can't do this except in the degenerate case of a single production function. In the general case, you will only be able to choose pairs (equilbrium wage, equilibrium return on capital) in which lowering the wage rate also requires lowering the MPK, and this forces you to hold certain capital/labor combinations.

None of this requires Constant Return to Scale, but it's easy to explicitly solve for the constraints in that case. All it requires is that production functions be independent (e.g. that their gradients not be multiples of each other). This is all just calc 101 or wherever you learn the implicit function theorem, which I admit is a deep result, as it requires a contraction mapping argument, but nevertheless should not be up for dispute.

[RSJ]

Ugh, it should read

"As firm 2 sheds labor to make MPL2 rise to equal MPL1, and firm 1 takes on labor to make MPL1 fall to MPL2, MPK1 will fall and MPK2 will rise, so the two will diverge. In that case, both firms need to add large amounts of capital to bring MPK into equilibrium. Therefore decreasing the wage rate forces the equilibrium MPK to decrease, and it forces K to increase."

Basically, if you don't want to look at the implicit function argument, the "pictorial" way to see this dynamic is that with more than 1 firm, the equilibrium wage rate moves in the same direction as the equilibrium MPK. So if you need a low wage rate to make the labor markets clear, you will get a low MPK as well. But a low MPK requires a high total capital stock. So full employment will only be possible with a high enough level of the total capital stock, and changes in the capital stock will cause unemployment.

With only a single firm, MPK becomes decoupled from MPL, and you can make the labor markets independently of the capital markets by adjusting the wage rate for any given equilibrium MPK.

And I agree that I have hijacked this thread -- sorry! If you want, you can move these posts to some other thread? The minimum wage thread?

[Nick Rowe]

RSJ: "And this curve will intersect "full employment" only for a single magical size of the total capital stock. Any other size of the capital stock, and employment will not be full."

Nope.

Start at that magical size of the total capital stock. Now remove one unit of capital, holding the labour force constant, so the aggregate capital/labour ratio falls. Here's how we stay at full employment:

The capital-intensive firm (with the higher K/L ratio) contracts both K and L, holding K/L constant, and so MPL and MPK constant.

The labour-intensive firm (with the lower K/L ratio) expands both K and L, holding K/L constant, and so MPL and MPK constant.

Intuitively, the aggregate K/L ratio is a weighted average of the high K/L ratio in the capital-intensive firm and the low K/L ratio in the labour-intensive firm. By varying the relative size of the two firms, you vary the weights in the weighted average, and get to full employment.

[RSJ]

"Start at that magical size of the total capital stock. Now remove one unit of capital, holding the labour force constant, so the aggregate capital/labour ratio falls. Here's how we stay at full employment:"

No, here is an example of the math:

L_1 = lambda_1 K_1 (lambda_1 is the ratio for firm 1)
L_2 = lambda_2 K_2 (lambda_2 is the ratio for firm 2)

You do agree that the "equilibrium" in both markets solution requires this, right?

Now, subtract 1 unit of capital -- say from firm 1.

Then L_1 must fall by lambda_1 in order to stay at equilibrium in both markets. You have reduced the capital stock and created unemployment as a result. let's see if we can get back to full employment without increasing the capital stock:

You add that labor to firm 2. But in order to stay at equilibrium, then K_2 must increase by 1/lambda_2. So you have only achieved full employment as a result of increasing the total capital stock from the level it was when you had unemployment.

"Intuitively, the aggregate K/L ratio is a weighted average of the high K/L ratio in the capital-intensive firm and the low K/L ratio in the labour-intensive firm. By varying the relative size of the two firms, you vary the weights in the weighted average, and get to full employment."

Yes, but you are still constrained by the largest ratio. You cannot vary the size of the firms *arbitrarily* and obtain full employment independent of the size of the total capital stock.

In this case, say lambda_1 = 2 and lambda_2 = 3. Then if the capital stock is 1/4, nothing you can do will give you full employment. There does not exist a wage rate that can achieve full employment in this case.

This is unlike the situation in which you have just a single firm. In that case, even with a capital stock of .000001, you can lower the wage rate to a level that achieves full employment.

In the more realistic case of a large number of firms that are not constant return to scale (e.g. monopolistic competition), you have more complicated curves instead of straight lines -- e.g. hyperbolas

L_1^2 - lambda_1*K^2 = 1
...
L_N^2 - lambda_N*K^2 = 1, etc.

and get into a situation in which no shift in relative firm sizes will give you a lower capital/labor ratio, and yet still have a large number of firms.

[RSJ]

I forgot to finish the example

Drop 1 unit of capital from firm 1, and you lose lambda_1 units of labor

To add lambda_1 units of labor back to firm 2, you need to add lambda_2/lambda_1 units of capital.

In other words, only if lambda_1 = lambda_2 -- the production functions are the same function -- can you keep the capital stock constant and add or subtract labor to the economy.

Now, in general, you can argue that this process will get rid of one of the firms. But it wont -- as competing firms die out in a given industry (or sub-industry), the remaining firms begin to operate under monopolistic competition, not constant returns to scale. So you will no longer be in a situation in which there are fixed ratios and one firm will be more capital intensive than another only for some levels of K, and it will be more labor intensive for other values of K. In other words, the ratios are no longer fixed, and if you remove "too much" capital from one industry, it becomes the most labor intensive industry. So you are stuck with multiple firms as long as you have multiple industries (or subindustries), or geographic regions, etc.

[Nick Rowe]

RSJ: "Yes, but you are still constrained by the largest ratio. You cannot vary the size of the firms *arbitrarily* and obtain full employment independent of the size of the total capital stock.

In this case, say lambda_1 = 2 and lambda_2 = 3. Then if the capital stock is 1/4, nothing you can do will give you full employment. There does not exist a wage rate that can achieve full employment in this case."

Yes you can.

Just to repeat your question, to show I've understood it, and to clear up some notational difficulties:

Suppose that, with both firms operating, the K/L ratio in the labour intensive firm is 1/2, and the K/L ratio in the capital-intensive firm is 2.

So if the ratio of the total supplies of capital to labour is between 1/2 and 2, we can always find a mix of output of the two firms that makes the weighted average K/L ratio of the two firms equal to the ratio of the total supplies, and so get to full employment.

But what happens, you ask, if the ratio of the total supplies of K/L is (say) 1/4?

Answer: the capital-intensive firm stops production. We are only left with one firm operating. And it operates at a K/L ratio of 1/4. And as the K/L ratio varies between 0 and 1/2, with only that one technology being used, the MPL/MPK ratio varies accordingly, and so does the wage/rental ratio.

The reason the capital-intensive firm stops production is that it will have higher costs per unit of output than the labour intensive firm. So it will make losses and shut down, You can see this from the isoquant/isocost diagram.

(In {K,L} space, a "unit isoquant curve" defines the combinations of K and L that will produce 1 unit of output. With Cobb-Douglas production functions Y=L^a.K^(1-a) the unit isoquant will be convex to the origin. If 'a' is different between the two firms, each will have a different unit isoquant, and the two curves will cross once. The isocost lines are downward-sloping straight lines that show combinations of K and L that cost the same to rent. The slope of an isocost line will equal the wage/rental ratio. Competitive equilibrium is at a point where the isocost is at a tangent to the isoquant.)

[Nick Rowe]

Just to add some intuition:

RSJ's "lambda' is defined (I think) as the L/K ratio. The convention in economics is the inverse, the K/L ratio, which we denote by lower case k.

Under Constant Returns to Scale, MPL and MPK are a function of k only.

There are 3 types of equilibrium in this case:

1. Both firms operating. In this case, MPL1=MPL2=W, and MPK1=MPK2=R (where W is wage and R is rental on labour). In this case, the aggregate k lies somewhere between k1 and k2. As you vary aggregate k (by varying the total supplies of K and L), neither k1, k2, W, or R change. The only thing that changes is the relative output of firm 1 to firm 2. Define k1* and k2* as the K/L ratios for the two firms when both are operating. Assume k1* is less than k2* (so firm 1 is labour intensive and firm 2 is capital intensive).

2. If aggregate k is less than k1*, then only firm 1 operates. W=MPL1 and R=MPK1. Firm 2 would make losses at this W and R, so does not operate. W is greater than MPL2 and R is greater than MPK2, for any k2. As k increases in this range, MPL=W rises, and MPK=R falls.

3. If aggregate k is greater than k2*, then only firm 2 operates. W=MPL2 and R=MPK2. Firm 1 would make losses at this W and R, so does not operate. W is greater than MPL1, and R is greater than MPK1, for any k1.

[RSJ]

"But what happens, you ask, if the ratio of the total supplies of K/L is (say) 1/4?

Answer: the capital-intensive firm stops production."

No, because the firms are in different industries -- or sub-industries, and there is a large number of them. As competitors go out of business the production characteristics of the remaining firms in each industry change, shifting more towards monopolistic competition in which it is no longer the case that the ratio of capital to labor is constant, but it is a curve. In that case -- the general case of non-constant returns to scale and changing production functions -- does not allow you to get rid of all of the firms but one -- you can get rid of some, of course, but you still do not reach the single firm-single production function case, and so you are still stuck with the fact that a downward shift in the equilibrium wage rate forces a downward shift in the MPK. You cannot independtly tweak wages in order to get the labor market to clear without also tweaking the MPK downwards as well. And the latter is a volatile function of expectations.

We do live in an economy with a large number of sectors and a large number of firms. Although this line of reasoning might be a good argument as to why monopolistic competition is inevitable even if you start with perfect competition -- i.e. this is an argument that perfect competition is not "stable" if there are multiple markets all drawing from the same pool of resources.

[RSJ]

I would add that this is a bit similar to your earlier "black hole" question. You are taking a model applicable only at the margins -- e.g. constant returns to scale -- and using it drive the capital of an entire firm to zero, with the assumption that this linearization of constant returns to scale will continue to hold independently of the size of the firms capital stock, or the number of competing firms. There will be at least one firm in each industry, and so you will never reduce the number of firms to 1 unless all industries but one disappear. But firms will become monopolies long before then, so that CRS will no longer be valid.

In general, the scale-behavior of a firm will change as the number of competitors changes and as the size of that firm's own capital stock decreases. In the beginning, all firms have increasing returns, then they reach the point of diminishing returns, and then they finally hit the consol rate. If you shrink the capital stock of the firm too much, you will push it back to a different production function, and so you can't use these linearization to deduce that all firms will disappear but one.

[Nick Rowe]

OK. Suppose the two firms are in different industries, producing different goods. Then we have to drop the assumption that both goods have the same price.

And instead of MPL1=W etc., we have to write P1.MPL1=W=P2.MPL2 and P1.MPK1=R=P2.MPK2. Where P1 is the price of the good produced by firm 1, and P2 the price of the good produced by firm 2. And we would also assume, if demand curves for the two goods slope down, that P1/P2 is a decreasing function of Y1/Y2. And what that assumption does is to get rid of the "flat spot". So the whole model changes. But you still don't get unemployment, as long as wages are flexible, and there's no shortage of AD, regardless of the stock of K.

All that assumes perfect competition. If we drop that assumption, then we replace P1 with MR1, and P2 with MR2. But in "normal" cases, MR1/MR2 is still a decreasing function of Y1/Y2. And we have to do this if we want to assume Increasing Returns to Scale, also.

Monopolistic competition by itself will mean lower real wages, and lower capital rentals, in equilibrium. If the labour supply curve slop[es upwards, that will give you lower employment, but still no excess supply of labour. You can get unemployment, however, if demand is inelastic enough.

[RSJ]

"Then we have to drop the assumption that both goods have the same price."

I think you are confusing goods (= firm output) with factors of production. Different industries still draw from the same labor pool, they pay the same price for oil, and electricity, etc. and all capital competes with all other forms of capital for return.

This is the distinction between *occupations* and industries. An accountant can work for an airplane manufacturer or for Disney. So assume that there is one price for each occupation, or with 2 factors of production, you can assume that there is one common price for each factor.

This is really the key distinction here between assuming that the economy contains a single firm and multiple firms. In the case of a large set of micro-firms, all drawing from a similar (and it need not be *exactly the same* pool of resources), but selling the output in one of several different markets, you naturally get monopolistic competition as an outcome even if you start with perfect competition. Perfect competition is extremely unstable when you have more than one firm (a requirement) due to the dynamics that you point out.

The requirement that there be a single price for each factor of production, even though the price of the finished goods is different, is a strict (and realistic) transformational constraint that forces a lot of dependencies between the quantities of factors of production used in competitive markets. All of that is missed by assuming there is only one firm.

[Nick Rowe]

"I think you are confusing goods (= firm output) with factors of production."

Nope. I was talking about the prices of firms' output goods. If firms 1 and 2 produce different output goods, those goods will have different prices. But if they hire the same labour and capital goods, they pay the same wages and rentals (assuming competitive factor markets).

And the first-order conditions for profit maximisation are, as I said, P1.MPL1=W=P2.MPL2 etc.

Look. My guess is that you probably have a graduate degree in math (or similar). But you are largely self-taught in economics. Right? Because you are obviously really intelligent, and know some stuff well, but also have some gaps in mainstream micro theory.

I'm crap at math, and my micro is very rusty. But remember, a load of guys who are very good at math and extremely good at basic micro theory have been ploughing this field for many decades. And they haven't come up with a theory of unemployment from this stuff. You need to throw something else into the mix. Playing around with Cobb-Douglas production functions alone won't do it.

[Greg]

Nick

Thanks for encouraging this dialogue. I'm not even going to chime in on the technicalities of this discussion (RSJ is clearly capable and I would in effect simply be saying "What HE said"!) but I think a stark contrast I can already see and Im only third of the way through the comments, is that the mainstream laws, theorems and relationships have been created in so many instances to simply satisfy a small set of "perfect" conditions which almost never exist. They dont do "messy" very well. Often times when its pointed out that such and such a real world situation doesnt meet these relationships described in this particular curve (like the Phillips curve) the response too often is "Well it would if the govt werent in the way" or something like that. Explaining things away is not the same as explaining.

[Nick Rowe]

Greg: I look at it a little differently. It is really hard to understand "messy". We are forced to make simplifying assumptions so we can understand it, define a question clearly, and answer it. So we face a trade-off.

In this case, RSJ made some simplifying assumptions, so the question was well-defined, and it has an answer. (And if my maths were better, or I could draw diagrams in these comments, I could have answered it much more conclusively and clearly.)

But when we go to a messier set of assumptions, it's not so clear that the question is well-defined, and it's so easy for everyone to just wave their hands around and BS.

[Panayotis]

Nick Rowe and RSJ,

the issues of heterogeneity of resources, indivisibilities, the aggregation measurement problem and reswitching of non monotonicity are at the core of your discussion. There is complex math involved beyond the simple assumptions of this discussion but the bottonm line is that there is no stable relation between resources and their renumeration!

[Nick Rowe]

Sure. But has anyone ever worked out a coherent model of unemployment based on all that stuff? (Without assuming sticky wages etc. that could generate unemployment without needing all that stuff). Because, I confess, my immediate reaction is to suspect obscurantism.

[Nick Rowe]

By the way, let's take the simple model that RSJ and I have sketched out above. The equations that define the equilibrium are:

P1.MPL1=W=P2.MPL2 and P1.MPK1=R=P2.MPK2

RSJ (in particular): Notice anything peculiar about that system of equations, just looking at it as a mathematician?

P1, P2, W, and R all have $ in the units. (We call them "nominal variables"). And that system of equations is Homogenous (of degree one, IIRC?) in those nominal variables. That means, if you start in any equilibrium defined by those equations, whether or not there is or is not unemployment in that equilibrium, if you double all those nominal variables you remain in that same equilibrium. For any solution to that system of simultaneous equations, there exists a whole range of solutions where all nominal variables are multiplied by an number you care to think of.

And that, dear readers, is the fundamental insight that lies behind the vertical Long Run Phillips Curve.

Which brings us back to the topic of this post.

[RSJ]

hmmm

If you are using CRS, then

P1.MPL1=W=P2.MPL2 and P1.MPK1=R=P2.MPK2

implies that both production functions are exactly the same.

Ugh.

I want to look at an economy with more than one firm, and with multiple production functions that are not all identical, or homogenous of degree anything -- it seems that statements like "I can always tweak the wage rate to achieve full employment independent of the MPK" should not require production functions that are of a highly specific form, as production is a fluid and changing thing -- you should be able to deform the production function a bit and still end up with the same general conclusions.

But I still think that what I am saying is fairly simple, and not obscurantism. When there are two production functions, unless you are in a degenerate situation, then in general the equations:

MPK1/MPK2 = MRTS(K1,K2) = MR1/MR2 (1)
MPL1/MPL2 = MRTS(L1,L2) = MRTS(K1,K2) (2)

Should take away 2 degrees of freedom from (L1, L2, K1, K2), in which case they would leave you with a constraint of the form total labor = f(total capital). That is a pretty simple argument.

The reason for believing that these two constraints are non-degenerate is that in general, you wont have constant elasticity of substitution for micro-level firms.

For the MR1/MR2 non-degeneracy condition, the right hand side is going to be a function of the PED1 and XPED12 of the two goods, which will depend on consumer preferences rather than the technical factors of production. You can argue that, over the long run, capital will be invented with the exact substitution characteristics to match the (changing) consumer preferences -- but it's hard to argue this is a general case at all periods of time.

Btw, I did go through some micro-texts but suffered with a lot of boredom. It's my own laziness, so thanks for being a gracious host. I will force myself to go look at them again. Feel free to call any BS as and when you see it!

[begruntled]

I think it is more about what you count as important than any fancy math.

Most MMTers think that 'full employment' - with the simple meaning of 'everyone who wants a job can get one at a living wage' - is more important than inflation. This is a political question, not an economic one.

From this position they aren't really interested in Phillips curves. They see the primary economic job of government to achieve full employment. If a government can do that cleverly with labor market policies - training etc - great. If they can't, then just do it anyway with aggregate demand and wear whatever rise in prices you get while the economy adjusts.

If anything, they think the most important aspect of a 'long run phillips curve' is that it is actually U shaped. High unemployment leads in the long run to an unskilled labor force that actually increases production costs - a sort of 'supply shock'. We are seeing this in Australia right now, where twenty years of not employing trainees and apprentices has led to a real lack of skilled workers that must be obtained from overseas at great cost.

[Nick Rowe]

RSJ: "But I still think that what I am saying is fairly simple, and not obscurantism."

I fully agree. Sorry, I wasn't accusing you of obscurantism. In this thread, you are (almost always) being the exact opposite. (What is the opposite of "obscurantism"?) You made a clear claim, and laid out your assumptions clearly. (Or, as clearly as you could). And you gave a simple (or fairly simple) example to back it up. Just like a good economist should. And that's why I wanted to fully engage you on it.

Any obscurity in our argument here is an accident of my bad math, your bad micro, and the difficulty of writing equations and drawing diagrams in TypePad.

[Nick Rowe]

RSJ: Let's switch back to perfect competition, as it makes the model simpler, and I don't think the results should depend on it, in this case.

Let me try to lay out the model more clearly.

There are two firms (or two industries each comprised of identical firms). The two firms produce different output goods. Each firm has a different CRS technology.

Your 2 equations:

Replace "MR" with "P" to reflect perfect competition. The P1/P2 should be a function of Y1 and Y2 (the outputs of goods 1 and 2), as well as consumer preferences. A simple assumption (sort of the equivalent to CRS in preferences) would be that P1/P2 is a (decreasing) function of Y1/Y2.

"For the MR1/MR2 non-degeneracy condition, the right hand side is going to be a function of the PED1 and XPED12 of the two goods, which will depend on consumer preferences rather than the technical factors of production."

Nope. The ratio MR1/MR2 (or P1/P2 under perfect competition) will depend *both* on consumer preferences (the shape of the indifference curves) *and* on the relative supplies of the two factors of production. Intuition: as capital becomes more abundant relative to labour, that will increase the supply of the capital intensive good relative to the labour intensive good, and will reduce the marginal utility of the capital intensive good relative to the labour intensive good (change the MRS), and lower the price of the former relative to the latter.

If the ratio P1/P2 were fixed, determined by preferences independently of Y1/Y2, then your equations would indeed do as you say (I think), and let you derive an equation "total labor = f(total capital)".

Here's the economic intuition for that case: your indifference curves would be straight lines. The two goods would be perfect substitutes. Formally, this is mathematically equivalent to the one good model (except that 1 unit of good 1 might be equivalent (say) to 3 units of good 2.) So if the aggregate K/L ratio were outside those bounds I mentioned above, one of the firms would stop producing.

[Nick Rowe]

begruntled: "From this position they [MMTers. NR] aren't really interested in Phillips curves."

That would be a totally incoherent position.

Suppose (for example) the Long Run Phillips Curve sloped the "wrong" way, so that an increase in inflation caused an *increase* in unemployment. Don't you think (if they cared about unemployment) they would then recommend very different policies?

[vimothy]

Nick, see Marc Lavoie's ppt, especially slide 16, here for a depiction of the post Keynesian Phillips curve: http://aix1.uottawa.ca/~robinson/Lavoie/Presentations/en/DR06.ppt

The PKE position is that there are multiple rates of path determined growth, inflation and capacity.

[Nick Rowe]

vimothy: Thanks. Marc does address the question of what the Phillips Curve looks like. Personally, I am sympathetic to his view that there may be a range of natural rates (so the LRPC is vertical but "thick"). And you can build a formal model where you get that result. But that result does tend to be very "fragile", in the sense that very small changes in the assumptions can make big changes in that result. I am less sympathetic to his drawing the Phillips Curve as having a stable non-vertical slope on either side of that range (but maybe that's just the Short Run Phillips Curve?)

But I don't think Marc classifies himself as a MMTer.

[Greg]

Begruntled,

Well said. I've said the same thing in a different way

Nick

In begruntleds model high inflation CANT lead to high unemployment because employment is always guaranteed.

---------------------------------------------

A note about something I said earlier Nick.

My comment about messy was certainly vague so Ill try to be a little clearer. Textbook economics with its formulas and theorems and laws ends up forcing micro principals that often times dont survive the composition fallacy. They dont aggregate well for various reasons and it really doesnt seem to bother them because they view aggregation perspectives as socialism (in a sense). All that matters is that the formulas are neat and explain something that has been seen in economic behavior at one time (even if its in a widget factory). They dont want to get into the messy questions of whether this will really apply or be explanatory for an ENTIRE populace of widely varying desires and choices. Thats a PROBLEM!! None of us exist only as individuals and we are all very dependent whether we want to admit it or not on the collective. So if your ideas dont apply well to the collective and dont even consider the collective something to think about how can you really be relevant? The collective is messy.

Here's my suggestions for Laws of economics
As worker
1) I will do extra work for you if you pay me enough extra (or if I really like you) but I reserve the right to change my mind about the arrangement in a couple months

As Boss
2) I will hire the guy who can do the same quality of work for the least amount (unless your my son)
3) I will lay you off as soon as my expenses get to high and your not my son

4) Getting educated is fun and will lead to better conversations at break time but there are no guarantees you will get a god paying job unless you work for your dad
5) Working hard will keep you at work longer and will piss your coworkers off

------------------------------------------

This article by James Galbraith discusses the fact that labor markets do not function like markets and the thinking on labor needs to be revised.
He uses the term "job structure". Very interesting.

http://www.levyinstitute.org/pubs/ppb36.pdf

[RSJ]

Nick,

"The ratio MR1/MR2 (or P1/P2 under perfect competition) will depend *both* on consumer preferences (the shape of the indifference curves) *and* on the relative supplies of the two factors of production."

Yes, but I only need it to not be *exactly equal* to the technical production characteristics. An epsilon of income effects, preferences, whatever -- is all I need for the system (1) and (2) to be non-degenerate.

Whereas you are saying something much stronger -- that P2/P1 is identically the same as MPK1/MPK2 on the 3 dimensional subset where MPK1/MPK2 = MPL1/MPL2.

And actually, you need something even stronger, because condition (1) -- that MPK1/MPK2 = MPL1/MPL2, will cut a codimension 1 subset that in general moves as the capital and labor stocks vary, so you really need P2/P1 to be identically equal to MPK1/MPK2 on an open subset of the entire 4 dimensional space. Arguing that P1/P2 is a downward sloping function, or that there are similar influences is not enough to argue that MPK1/MPK2 is exactly the same function.

For example,

Say
Y_1 = K_1^a L_1^(1-a)
Y_2 = K_2^b L_2^(1-b)

Then MPL1/MPL2 = MPK1/MPK2 on the codimension 1 set cut out by:

m = C/p

where m = L_1/K_1, and p = L_2/K_2, and C = (1-a)b/((1-b)a)

On that set,

(3) MPL1/MPL2 = Dp^(a+b) where D = [(1-a)/(1-b)]^(1-a) * (b/a)^a

"If the ratio P1/P2 were fixed, determined by preferences independently of Y1/Y2, then your equations would indeed do as you say (I think)"

No, P1/P2 just needs to be something other than

[(1-a)/(1-b)]^(1-a)*(b/a)^a*(L_2/K_2)^(a+b)

for some combinations of L_2 and K_2 within an open neighborhood of the equilibrium point. Certainly, it does not need to be constant. It can be anything other than the above messy function, and my claim would hold.

I think this is interesting -- because if we were in the single consumer case, then you would be saying that the consumer's 1/MRS(1,2) is exactly the same as MPK1/MPK2 away from the equilibrium points (they would of course be equal when (2) holds). In other words, in the presence of capital volatility, full employment is only guaranteed if there is a first order tangency condition relating the production substitution characteristics and utility substitution characteristics not just at the equilibrium points, but identically on an open neighborhood where (1) and (2) hold. Certainly if this were the case, it would be more advantageous for capital, since it would allow more points (K,L) to be potential equilibrium points -- that choice is economically valuable, but will it always occur? If so, what are the mechanisms forcing the derivatives of micro-production functions to be exact copies of the derivatives of micro-utility functions at almost all points in the space of potential factor ratios?

So we can talk, in addition to wage flexibility, about production flexibility, in that over time, you might expect new techniques to be invented whose pairwise technical substitution rates get closer to the whole space of option, say by anticipating what consumer preferences would be in more and more likely equilibria.

But there is no reason to believe that with changing preferences and changing technologies, that you would always be in the maximal state where (1) and (2) are redundant. In that case, the production frontier would be less flexible in response to shifts in the size of the capital or labor stock.

And -- correct me if I screw up the micro -- you get the same situation with utility functions. By changing prices, you can get a single consumer with $1 and a fixed utility function to purchase any desired combination of two quantities (Q(A), Q(B)).

But as soon as you have *two* consumers with a total budget of $1, then it is no longer the case that by changing prices, any combination of quantities is possible, and you get a constraint between Q(A) and Q(B).

For example,
if the first consumer has utility = (x^2 + y)^(.4)
and the second consumer has utility (x + y^2)^(.4),

then MRS1(x_1,y_1) = 2x_1, with MRS2(x_2,y_2) = 1/(2y_2) = p_x/p_y

Both are satisfied on the (non-convex) hyperbola

(*) 4x_1y_2 = 1

And we can use this to bound total X in terms of total Y and vice versa. For example,
Multiply (*) by p_y and use p_y*y_1 <=1 to get

p_y = 4x_1 (y_2 p_y) <= 4x_1, so that

4x_1 > p_y, and then from the budget constraint:

p_x/p_y total X + (total Y) = 1/p_y <= 4x_1

Total Y <= 4x_1 - 2_x1(x_1 + x_2)

And similarly we can bound total Y in terms of X, etc. With more work, we could draw out the exact boundaries, but this is enough :)

Only in the degenerate case -- e.g. both consumers have the same utility function, or each has a separable utility function, can we control Q(X) independently of Q(Y) by adjusting the relative prices of X and Y. The situation of a single consumer is not representative, qualitatively.

What you are arguing is that the "generic" micro-production function always has a similar separability property -- such a claim needs to be justified, particularly if claims about wages and the labor market end up hingeing on obscure separability properties of micro production functions.

[Nick Rowe]

RSJ:

OK, there are two goods X and Y. In {X,Y} space, draw the Production Possibilities Frontier (PPF) that shows the maximum amount of Y that can be produced, for given X, given K and L, and given technologies. The PPF will be concave to the origin.

(Don't trust me when I use the words "concave" and "convex"; I always muddle them!)

I need to assume just one consumer, or that all consumers have identical homothetic preferences (the MRS depends only on the ratio Y/X), if I want to work in 2-dimensions.

Each indifference curve is convex to the origin. (It must be convex to the origin otherwise it won't satisfy the second-order conditions for utility-maximisation).

General equilibrium is that single point where the concave PPF is tangent to a convex indifference curve. (Remember there are an infinite number of indifference curve, each one drawn for a particular level of utility, so there's always one that is tangent to the PPF.

In particular, the slope of the Indifference curve (the MRS) *cannot* be *identically* equal to the slope of the PPF (the MRT). They are equal only at one point, the competitive equilibrium.

There is a Budget Line that passes through that same point. It is tangent to the Indifference curve and to the PPF. The slope of the budget line is -Px/Py.

At that one point:

The slope of the budget line Px/Py equals the consumer's MRS between Y and X, which satisfies the first order condition for Utility maximisation;

The slope of the budget line Px/Py equals MRT, which equals MPKy/MPKx which equals MPLy/MPLx, which is consistent with both firms maximising profits;

The consumer's income, which equals WL+RK, which equals Px.MPLx.Lx + Py.MPLy.Ly + Px.MPKx.Kx + Py.MPKy.Ky will also equal (given CRS technologies) Px.X+Py.Y so the consumer can just afford to buy the goods his labour and capital produces. Ignoring any excess supply or demand for money (here's where I slip in the assumption that Aggregate Demand is just right) his expenditure will equal his income.

I've probably got a couple of the ratios upside down (I normally do).

But what I have just done is sketched the existence of competitive equlibrium.

In graduate micro we spent a few weeks doing exactly the same thing with waaaaay more math, with an unlimited number of firms, goods, households, factors, etc. Somebody or other's Fixed Point Theorem. I have forgotten it all, thank God! The above is all I can remember, because it was about all I really understood!

You would almost certainly understand those proofs better than me. All I have been trying to do is give you the economic intuition behind those math proofs. I hope it works, because that's all I've got!

[Panayotis]

Nick Rowe,

It is not obscurantism to point out a series of academic work using more complex math than what you are presenting here in this debate. Simplistic assumptions and math will not deal with the problem. This is the problem with much economics that attempts with unrealistic assumptions and elementary math to deal with problems when there are measurement issues, heterogeneous non representative units or resources, indivisibilities and non smooth and non monotonic functions. The bottom line is that RSJ has a point, regarding the nonstable relation between resources and their renumeration independently of each other! Any mathematician will understand that and only economists are still not getting it because they still are attempting to analyze as if complexity does not exist.I would not say anything more about entropies from complexity that I use in my work because I will be called obscurantist!
Furthermore, in earlier comments I pointed out that the Long Run Phillips curve is unstable and shifting. I wanted to thank you for the opportunity to comment in your blog and the serious comments it receives!

[Nick Rowe]

Greg: "In begruntleds model high inflation CANT lead to high unemployment because employment is always guaranteed."

But that just begs the question: "*Could* employment, be guaranteed? And if so, *how*?" For example, if the Long Run Phillips Curve had the "wrong" slope, a policy to create jobs financed by printing money could actually increase unemployment.

I wouldn't call your list "Laws of Economics" in the same sense that (e.g. the "'Laws' of supply and demand" are "Laws of Economics". Your "Laws" are more like "moral"(?) rules.

In my opinion, your Law 2 would reduce unemployment a lot, if it were generally accepted.

"As Boss
2) I will hire the guy who can do the same quality of work for the least amount (unless your my son)"

But I am in a distinct minority in liking your Law 2. It definitely breaks all current conventions. Your Law 2 would shock most people.

And the fact that it does break current conventions is one of the reasons why the labour market is indeed, as you say, different in many ways from other markets.

[Nick Rowe]

Panayotis: Dunno. Most of the time people criticise mainstream economists for using too much fancy math! Sometimes I think we can't win.

[RSJ]

Re: competitive equilibrium -- yes I agree entirely, but I think we are talking past each other.

You are pointing out that given any (convex) feasible set, there will be a set of prices such that (in the PC CRS case), satisfy (2), namely MPK2/MPK1 = P2/P1 = 1/MRS(1,2) as well as (1) = MPL1/MPL2= MPK1/MPK2

I am pointing out that not all combinations (L1, L2, K1, K2) are in the feasible set.

And this is a no brainer. Write down a utility function, use the two production functions with a neq b, and solve for the condition that that MPK2/MPK1 = 1/MRS(1,2) as well as MPK1/MPK2 = MPL1/MPL2, and you will find that this restricts the possible values of (L1, L2, K1, K2). Then you should declare victory.

Only in very degenerate cases, such as MPK1/MPK2 = constant = MPL1/MPL2 = 1/MRS(1,2) will all tuples of L, K be in the feasible set.

Competitive Equilibrium results have *nothing* to say about what the feasible set is. You have to be told what it is, and use that as an input to the theorem. So my approach was to first treat as variables L1, L2, K1, K2, and then determine what the constraints on them were, assuming an equilibrium price existed. And you do get non-trivial constraints when your MRS, MPL, MPK are not constant. Write it out and see for yourself!

[Nick Rowe]

RSJ: You lost me (again!).

Given that 1 and 2 hold (i.e. both firms are maximising profits, and the consumer is maximising utility), then it is indeed true, as you say, "I am pointing out that not all combinations (L1, L2, K1, K2) are in the feasible set." In fact, only *one* possible combination of (L1, L2, K1, K2) will satisfy both equations 1 and 2 (except in degenerate cases). [EDIT. and satisfy the conditions that L1+L2=L and K1+K2=K , I should have added]

If both firms are choosing the cost-minimising mix of K and L to produce a given level of output ( MPL1/MPL2= MPK1/MPK2 ) we must be *on* the PPF, and not *inside* the PPF. And this will (except in degenerate cases) require that both firms have the right mix of K and L. If you give one firm too much K, and the other firm too much L, they won't be maximising profits, you will be inside the PPF, and production will not be as big as it could be, even with both K and L fully employed. You could get more Y and more X by rearranging K and L between the two firms.

"Only in very degenerate cases, such as MPK1/MPK2 = constant = MPL1/MPL2 = 1/MRS(1,2) will all tuples of L, K be in the feasible set."

Agreed. [EDIT or nearly agreed] For example, if the two factors are perfect substitutes in production, like Y=Ky+Ly and X=2(Kx+Lx) for example, then the mix of K and L between the two firms won't matter. And in this case the PPF is a straight line with slope -(1/2). [EDIT. And in that case, Py/Px must be 2, and the MRS=Py/Px condition determines which particular point on the PPF the consumer will choose]

Intuitively, except in that degenerate case, equation 1 determines the optimal mix of the two factors between the two firms, and ensures that we are somewhere along the PPF curve, then the MRS=MRT equation ensures we are on the utility maximising point on the PPF.

I know we must be talking past each other.

[Nick Rowe]

RSJ: I'm obviously doing a really bad job of teaching micro. My only excuse is that I never have taught it past the 1000 level, where we never do any math anyway! Sorry.

[Nick Rowe]

Try this: suppose you were the central planner in this economy? You were trying to choose {L1,L2,K1,K2} to maximise U(X,Y) subject to the two production functions, and the two resource constraints (that you can't use more than the available labour or capital). Would you leave any labour or any capital unemployed? (Would either of the two resource constraints be slack?) No. Not if that resource had a positive marginal product in either good, and that good had a positive marginal utility.

Now check the first order conditions of that problem. You will find they are the same as the first order conditions for consumer utility maximisation and firm profit maximisation (they are the same as your equations 1 and 2). Therefore the competitive equilibrium duplicates the solution to the central planners problem (first theorem of welfare economics, more or less). And since the planner won't leave resources unemployed, neither will the competitive equilibrium.

Does that help explain it?

[Panayotis]

Nick Rowe,

regarding your comment on "math", my response is that I am competent but against its use for its own sake (out of knowledge)! Many economists base their analysis on elementary math presentation and given their limited competence on the tool they end up adopting simplified assumptions that fit their calculus! Their analysis is conditioned by their level of math application as their assumptions are correlated by their modeling. Even if their analysis cannot be refuted or confirmed by math proof, how can this be used to explain a complex reality? One should also realize that math presentation is a language imperfect in explaining itself and mathematical logic is not fully consistent as Wittgenstein showed in "Tractatus Logicophilosophicus". Sorry, but the rest reads as Introductory Math for Economists that some of us have been bored to learn and teach in the past! Please save us!

[Nick Rowe]

Panayotis: I try to avoid math as much as possible. But sometimes you need it, unfortunately. Yes, math is imperfect. All languages are imperfect, English, graphs, as well as math. (Wittgenstein's arguments in English were sometimes less than perfect models of clarity!)

"Sorry, but the rest reads as Introductory Math for Economists that some of us have been bored to learn and teach in the past! Please save us!"

Sure. What do you want me to do? Ignore RSJ's argument? Refuse to speak math to him? (It's the language he's more comfortable in, so I'm doing my best to speak it, as well as speak English and graphs to him).

[Nick Rowe]

RSJ: I think I now see where you got hung up.

With Cobb-Douglas technology, the ratio of the two firms' K/L ratios, i.e. k1/k2, is determined solely by the technology, independent of the total K/L ratio and consumer's preferences.

With k1/k2 determined by technolgy, how does the weighted average of k1 and k2 adjust to match the total K/L ratio determined by the supplies of the two factors (and also meet the constraint of the consumer's preferences)?

Answer: there are two degrees of freedom to meet those two extra constraints:

1. k1 and k2 can both increase (or decrease), provided they do so in the same proportions, to meet the total K/L ratio.

2. The relative size of the two firms can adjust, holding k1 and k2 constant, to match consumer's preferences, and this will also change the weights in the weighted average of k1 and k2 that must equal K/L, so might require adjusting on point 1 above.

[RSJ]

Ok, Nick, I think we are in agreement.

I was pointing out that with two firms, L1,L2 is in general a function of K1,K2.

But that does not mean that full employment is impossible, as you point out, there are degrees of freedom -- in K -- so that K1, K2 can adjust and full employment is reached.

But why would they? Each individual firm is in equilibrium, paying the market rate for labor and the market rate for capital, which are both equal to their marginal products. If a firm were to try to hire an additional worker -- say a desperate worker who is willing to work for less than his marginal product -- then the increase in L would cause MPL/MPK of the firm to change, bringing it out of equilibrium. You would need simultaneous coordination in which all the other firms adjust their L and K as well.

And with a large number of firms, the feasible sets become disconnected and horribly ugly. Even with 2 firms, in the simple example I gave with two CRS CDPF but with different exponents, and a separable utility function = log(xy), the feasible set was not compact. Add N firms, for N large, with all firms using the same 2 production factors, K and L, and your feasible production set becomes the intersection of N-1 convex surfaces -- it could be anything. I'm sure that given changing utility functions and changing technologies, that there is always some (changing) magic combination of K_i's that ensure full employment, but why would we exactly follow this ideal point, given the volatility of capital, without any lags or deviations?

And you can certainly imagine a situation in which K1/K2 is not always at the magic level -- maybe foresight about future preferences or future interest rates is not perfect. Suppose that the actual level of K_i is equal to the ideal level plus some white noise term. Then the mean error of that white noise term is going to give you a mean "natural" unemployment rate, but due to capital market mis-coordination, rather than labor market rigidities, or a desire for leisure. Any deviation will force unemployment to occur, regardless of the wage rate, and this unemployment rate wont have anything to do with inflation -- it will be the rate of unemployment caused by a less than perfect distribution of capital.

With the single firm model, this is not true -- K1 can be anything, and you can adjust the wage to get full employment. But that's just an artifact of the model, and cannot be applied to an economy with more than 1 firm.

Why don't we hear more about the multiple firm intuition -- unemployment due to a maldistribution of capital -- rather than the single firm intuition of unemployment due to excess wages?

[Nick Rowe]

RSJ: "Why don't we hear more about the multiple firm intuition -- unemployment due to a maldistribution of capital -- rather than the single firm intuition of unemployment due to excess wages?"

Good question. Maybe because only people like me can do intuition, and we can't do the math for multiple firms; and the people who can do the math for multiple firms can't do the intuition!

".....You would need simultaneous coordination in which all the other firms adjust their L and K as well."

Here's my intuition: suppose we start at full employment equilibrium, then some new workers appear. They are unemployed. The market wage gets bid down, relative to rentals on capital. P.MPL is now greater than W, so both firms switch to a more labour intensive method of production (reduce k).

One puzzle is: what ensures that aggregate demand increases enough so that people want to buy the extra output that the extra workers can produce? Then you remember that this is implicitly a barter economy. There's no money. Workers get paid in kind, using the firm's output. So the unemployed worker goes to the shoe factory and gets paid in shoes.

" Add N firms, for N large, with all firms using the same 2 production factors, K and L, and your feasible production set becomes the intersection of N-1 convex surfaces -- it could be anything."

The mathEcon tell me it's still convex, as long as you don't have Increasing Returns to Scale. I was taught the proof as a grad student, didn't really understand it at the time, and wouldn't have a hope of explaining it to you now. But we (not me) still torture our grad students with it every year. Actually, your asking me this question is the first and only time in my life when my understanding this proof might have been useful. Maybe those MathEcon guys are doing something worthwhile after all.

"Suppose that the actual level of K_i is equal to the ideal level plus some white noise term."

OK. Good model. And suppose the white noise term fluctuates every week, and it takes more than a week to change K1 and K2.

We now have to distinguish the Short Run (less than a week) from the Long Run (more than a week).

The LR model is what we described, in expected value terms (or, roughly as we described, because it's non-linear, so Jensen's Inequality will apply). The SR model is now exactly like the SR model in ECON1000. Each firm has a fixed factor, capital. So the equation P.MPK=R does not hold in the short run. Only P.MPL=W holds, if labour can be changed daily. If W is flexible, we still get full employment, even in the SR.

You would have a great time doing a grad degree in Econ. (Or maybe not, I don't know; but you would be good at it, because it's all this sort of stuff, only taught by people who know it, and who know math.)

[Too Much Fed]

Jon said: "Employment is maximized at any stable inflation target."

Maybe or maybe not. I'd rather concentrate on what happens if currency denominated debt is required for the (price) inflation target. For example, what if the fed wanted/allowed currency denominated debt to be created and wanted/allowed that debt to go into a housing bubble to get people to spend and employ people? I think I read somewhere that about 1/3 of the jobs created between about 2002 to 2008 were related to housing in the USA.

[Too Much Fed]

Jon said: "To deny this, really is to deny 30 years of progress."

I really don't see much progress in macroeconomics in the last 30 years, especially related to the proper understanding of the nature of currency denominated debt.

If there was, people could accurately describe what a liquidity trap actually is.

[Too Much Fed]

Nick said: "I'm crap at math, and my micro is very rusty. But remember, a load of guys who are very good at math and extremely good at basic micro theory have been ploughing this field for many decades. And they haven't come up with a theory of unemployment from this stuff. You need to throw something else into the mix. Playing around with Cobb-Douglas production functions alone won't do it."

How about adding changes in retirement date(s) to macroeconomics?

[Too Much Fed]

Nick said: "One puzzle is: what ensures that aggregate demand increases enough so that people want to buy the extra output that the extra workers can produce? Then you remember that this is implicitly a barter economy. There's no money. Workers get paid in kind, using the firm's output. So the unemployed worker goes to the shoe factory and gets paid in shoes."

How about what ensures that aggregate demand increases enough so that people want to buy the extra output that the same amount of workers can produce (positive productivity growth)?

Now add in money (as in currency and currency denominated debt).

It seems to me that the question should then be if positive productivity growth and cheap labor produce price deflation and there is a positive price inflation target and probably a positive real GDP target, what should happen?

[Too Much Fed]

RSJ said: "Why don't we hear more about the multiple firm intuition -- unemployment due to a maldistribution of capital -- rather than the single firm intuition of unemployment due to excess wages?"

Let's concentrate on bank capital. Let's say it went up a little bit, but currency denominated debt went up a good bit more with the bankers not believing there would be many defaults.

The bankers were wrong, and there were many defaults. What happens?

[RSJ]

I would have great fun being a grad student in economics. But I'm not sure how that would pay the bills :) It does make me wistful, though.

But I object to this part:

"So the equation P.MPK=R does not hold in the short run. Only P.MPL=W holds"

I think the opposite occurs. Why?

Look at the prices of capital -- they are much more volatile than wage rates. Investment is much more volatile than changes in employment. If anything, we live in an economy in which investors and firms try to ensure that

P.MPK=R

at all times by varying investment and interest rates quite rapidly -- much more rapidly than wage rates and employment. And in fact labor hoarding occurs so that as capital is cut, employers try to hang onto the labor.

Why would this happen?

Because the capital is forward looking. If tomorrow, you stop believing that your plant -- or project -- will be profitable, then you shut it down that day. Even if it will continue to be profitable over the next 2 years. I've experienced this many times -- profitable projects were cut now because management peered into the future and decided that year X from now, the project wont be profitable any more, and for the project as a whole to break-even, there was a requirement that it be profitable for 10 years, not just the current year.

And they were right to do this.

Anytime you have a factor of production that requires a greater time commitment, then utilization of that factor will respond more rapidly to changing outlooks that the factor that requires a lesser time commitment -- provided that you have many firms. Just as a small change in outlook will cause house purchases to tumble, whereas candy bar purchases will remain unchanged.

And this is even more true for taking on new capital commitments. If you assume that depreciation/labor force growth is such that X new projects must be taken on each week in order to maintain the right capital ratios for full employment, then a change in outlook can quickly bring X down to zero. In the aggregate, deferral of capital investments is the same as liquidation -- so for an economy with many firms and sizeable depreciation, I think that the aggregate K varies much more than employment in the short run, even though for a single firm "K" is assumed to be fixed in the short run.

I think I could make a case from the data that K moves first, and L follows.

[Panayotis]

Nick Rowe,

My point about math is that you should use it appropriately. You are employing elementary calculus and optimization theory for a problem that includes resources that you cannot measure like capital, and/or are heterogeneous like labor and mode of technology that is indivisible and discrete and functions that are smooth, continuous and monotonic. I pointed out the Samuelson reswitching problem. I agree with the conclusion of RSJ but not with the modeling you are applying to a problem recognized and settled partially long time ago against neoclassical theory!

[Nick Rowe]

RSJ: Yep. Implicitly, in that sort of model 'K' has to be interpreted as machines, that the firm rents by the hour, and are owned by households. Formally, there's no difference at all between K and L in that model. And since no firm in that model is producing K, it's not even really capital at all. It's more like land.

Panyotis: it is just as easy/hard to measure capital as it is to measure labour. Just count the number of machines, like we count the number of workers!

[Panayotis]

I am stunned! You really believe that that all capital is the same?!?! All labor is homogeneous with no differences?!?!Not even the Cambridge theorists (US) will say that!

[Nick Rowe]

Nope! I did say "easy/hard" ;-) I mean it's no easier or harder to assume that all workers are the same than that all capital goods are the same.

[Panayotis]

Exactly my point! That is why I question the math used! I sympathise with the fact that more advanced math can not be easily used and/or displayed in the blog. Mathematical logic can help under the circumstances.

[RSJ]

"Formally, there's no difference at all between K and L in that model"

Hmm, then why is it that P.MPK would not change in the short run but P.MPL would?

re: math

To P -- I would read Joan Robinson's essay "On the unimportance of re-switching".

In any model, you need to capture simple effects via a stylized presentation. The issue is not whether all details are presented accurately, since that is not the role of models. Models are Gedanken experiments to gain some insight about the world. I claim that the PK'ers and a lot of the heterodox people have jumped the shark here. They looked at some of the neo-classical conclusions, disagreed, and then reject math as a result. I don't think there is anything wrong with models per se, but rather with some assumptions behind the models and also their interpretation.

For example, Ricardian equivalence is nothing more than the government budget constraint -- you could read it as a theory of crowding out, or you could read it as saying that government deficit spending always creates enough assets to buy the government debt. Mathematically, the two interpretations are equivalent, but for political reasons people choose to focus on one of them and ignore the other.

Models are not to blame for that. And a similar result holds for looking at labor market rigidities as the source of unemployment as opposed to capital market rigidities. That doesn't come from models, but from politics.

[Nick Rowe]

"Hmm, then why is it that P.MPK would not change in the short run but P.MPL would?"

P.MPK would change, if L changed. Why did K not change in the short run, but L would? Only because we assumed it, just to see if it would make any difference. We could as easily have made the opposite assumption.

I agree with the rest of your comment. Except that Ricardian equivalence is the government budget constraint *plus* some other assumptions that tell you whether people will want to save or spend those assets that the government creates.

[RSJ]

I was assuming that they would both change in the short run, and that this would lead to the white-noise caused unemployment. But if you assume only P.MPL would change, then there wouldn't be white noise unemployment given enough wage flexibility.

For Ricardian equivalence, part of the assumption is that deficit spending must be financed by selling debt. So RE is telling you that households will in fact elect to save by buying that debt, allowing the deficit spending to occur in the first place.

It's not saying that in addition to saving enough to buy the debt, that they will save even more -- say that they will save 2X of what is deficit spent. Perhaps I'm missing something, but it seems like just the government budget constraint to me, and you could interpret it as a statement that governments will always be able to run deficits of whatever magnitude they want, as people will always elect to save enough to purchase enough bonds to finance whatever deficit spending the government chooses to do. I'm not saying that you should necessarily read it that way, but the statement that should the government run a deficit of X, people will elect to buy X worth of government bonds is pretty much an accounting identity.

Anyways I don't mean to gum up the boards. Am sick now and blogging is better than watching television :)

[Nick Rowe]

RSJ: sorry to hear you are sick.

"...the statement that should the government run a deficit of X, people will elect to buy X worth of government bonds is pretty much an accounting identity."

This is where you really have been badly lead astray by the MMTers. Some of the stuff they say might be right, or might be wrong; it's an empirical and/or theoretical question. But when you misuse an accounting identity, and mistake it for an empirical or theoretical statement about how the world works, you are just logically wrong.

Let me just pretend that I think that Ricardian equivalence is wrong. It makes my job easier.

Yes it's true (in a closed economy) that if the government sells bonds people buy those bonds. That's trivially true by definition. If I sell you a car, you must buy a car from me. But that doesn't mean you want to buy the car at the existing price. It doesn't mean that an increase in supply has no effect on prices. I must persuade you to want to buy the car by lowering the price enough that you will want to buy it. Same with bonds. The government can only manage to sell the bonds if it can lower the price enough to persuade people to buy them. That means bond sales will cause the rate of interest to rise, which will reduce investment, persuade people to hold less money, etc. So selling bonds will have lots of real effects on people's behaviour. Ricardian equivalence is false.

[RSJ]

"I must persuade you to want to buy the car by lowering the price enough that you will want to buy it. Same with bonds."

I guess I believe that for liquid instruments, the price is purely a function of expected return. Too much government spending can cause inflation, which would raise nominal rates. But inflation can arise even without too much government spending, in which case rates would also rise. So it's better to just look at expected return -- that is the "right" thing to look at. If that is influenced by quantity, then yes, quantity will affect the price, but only indirectly. I think this holds for open or closed economies.

This is only for liquid instruments, but the central bank ensures that government debt is liquid. And the 'fair' price is the liquid price. In the long run, I think all debt is liquid.

[Too Much Fed]

Nick said: "The government can only manage to sell the bonds if it can lower the price enough to persuade people to buy them."

Put a 0% capital requirement on the gov't bonds. Why can't "banks" buy an unlimited amount of them at the current price?

IMO, the gov't/the rich/the bankers will then get their real return by inflicting negative real earnings growth on the lower and middle class.

[Too Much Fed]

RSJ said: "the statement that should the government run a deficit of X, people will elect to buy X worth of government bonds is pretty much an accounting identity."

Why can't the federal gov't (if it is the currency printing entity) run a deficit with currency (no currency denominated debt issuance)?

Hope you feel better.

[RSJ]

Sure, the government can create money and spend it. Often without inflationary consequences. I claim it makes no difference, in that household wealth is unchanged whether the government offsets deficit spending with bond sales or whether it creates more money. Inflation, household wealth, and output will be the same in both cases, as will interest rates. I know this is an idiosyncratic view, but I'm sticking to it :)

I believe the MMT position is that it is better to issue currency than to issue bonds. I say that when assets are fairly priced, the effect is the same.

In defense of the MMT paradigm, they are well aware of the inflationary risks of deficit spending, but correctly argue that in many cases there is excess capacity that can absorb deficit spending without causing inflation. In any case, the choice of whether to deficit spend or not should be a political choice, based on public purpose, rather than a choice made by the central bank or the bond markets.

[Panayotis]

RSJ,
I agree with Joan Robinson which by the way I have met when she was very old. The reswitching issue is that the relations are more complex and can reverse and cannot be examined only in the locality that is convenient for us!It is not because is important for the measurement of capital issue. My point is that the math we use must be consistent with the assumptions relevant to the reality of the situation we examine and not what assumptions fit our simplified model.This is circular thinking leading to local solutions.

[Mandos]

Bingo. We should democratically elect the people who govern the Bank of Canada (or the Fed, or whatever).

[Mandos]

BTW, I was *at* the MMT meeting in DC that I suspect inspired this blog. Click my name-link for more.

[winterspeak]

RSJ: I believe the MMT position is that sovereign bond sales (for a currency issuer) merely shuffle extant private sector assets (public sector liabilities) but do not change the size of either balance sheet, and are certainly unneccessary for enabling Government expenditure.

All Government expenditure is done via marking up accounts, and all taxation is done via marking down accounts. There are no goblins shuttling wheelbarrows of gold around, it's just numbers in excel.

Therefore, why bother to issue debt at all? You need to drain bank reserves to hit a positive federal funds rate. If the Fed is happy with rates at zero, it can stop issuing Treasuries and there will be no impact on anything. In today's reserve rich environment I believe that is even more true.

So, in sum: all Government spending is currency issuance. Bond sales do not "off set" this issuance, they merely alter its term structure for purposes of mechanically setting the FFR.

[Panayotis]

RSJ,
Accounting balances are a static representation, usually in matrix form of a situation at a period of time and not time itself. Its a "black box" with no behavioral dynamics to it. You can be stock flow consistent but you need to add behavioral relations.

As about your statement of RE is circular and has no meaning. I sympathise with the MMT position but it says something more. Particularly, that there no future tax liabilities to cover and repay any debt because the debt issue is demanded for net financial savings purposes. This is behavioral. Similarly, there is no crowding out effect as in the presence of a banking system any reserves created by the central bank can be used to validate credit expansion in response to increasing effective demnad. If there are unutilized resources, rates will not have to change as inflationary pressures are contained. This is also behavioral.

[Nick Rowe]

Panayotis: "Accounting balances are a static representation, usually in matrix form of a situation at a period of time and not time itself. Its a "black box" with no behavioral dynamics to it. You can be stock flow consistent but you need to add behavioral relations."

Yep. Exactly. Especially that last part about needing to add behavioural relations. (For once we totally agree on something.)

Welcome back Winterspeak! I enjoyed and agreed with a couple of your recent posts. Wish you allowed comments. I especially wanted (off-topic) to ask you about your rather cryptic statement that the Eurozone does not insure deposits. I had a guess at what you might mean, but I wasn't sure. Is it because the individual countries can't create money, so their insurance promises aren't credible?

[Nick Rowe]

Mandos: I saw that all you guys were off partying in DC. But it was reading Billy's blog that originally inspired this question.

[winterspeak]

Nick: Your wish is my command! Had to move blog to a new host, and I'm seeing if blogger comments work if I run on blogger itself.

You guessed at my meaning exactly re the Eurozone.

[Nick Rowe]

Winterspeak: That's an important insight re Eurozone deposit insurance. Only the ECB can credibly insure deposits (if it breaks the rules). But will it? Let's hope it's not tested empirically. But I'm not optimistic.

[RSJ]

P,

MMT'ers do not believe that there is no crowding out effect. That is a gross misrepresentation.

The difference is operational and political-- most people have a fear of currency issuance and assume that in all cases, each dollar issued causes some inflation, raises interest rates, and is harmful.

MMT'ers argue that instead of assuming that deficit spending is always harmful, that the government should deficit spend up until the point where inflation exceeds some publicly agreed upon target. And this may require large amounts of deficit spending or large amounts of surpluses (depending on the circumstance), but that the reaction function that determines how much deficit spending the government engages in should be based on these inflation/output trade-offs as decided by the political system, rather than medieval fears that all printing of money is harmful, or that this should be left to cloistered experts in the CB.

The second point is that they do not want the CB to engage in this reaction function, but the fiscal arm -- i.e. true "helicopter" drops of money, or rather not giving the money away but paying for goods and services. Whereas the CB is only allowed to purchase assets at market prices, and therefore monetary operations cannot stimulate the economy in the way that fiscal operations can.

I.e. with a monetary "stimulus" -- e.g. lowering borrowing costs -- you are requiring the private sector to stimulate itself, by encouraging more debt growth and deficit spending by members of the private sector.

With fiscal stimulus, the government engages in the deficit spending, which does not leave a debt overhang in the private sector.

I believe that because of this, a government that repeatedly resorts to monetary stimulus will end up with debt deflationary pressures, as the private sector eventually reaches a point that it is not willing to self-stimulate via borrowing anymore. This is another form of "crowding out" that should be talked about more, since we are experiencing it now in the U.S., whereas we are not in a situation of experiencing fiscal spending crowding out.

So the general principles are:

use fiscal policy rather than monetary policy
deficit spend based on politically agreed upon inflation/output trade-offs
do not offset bond sales with deficit spending, but issue more currency

None of the above suggests that there is no crowding out, but rather the MMTers are aware of the inflation crowding out that happens with deficit spending as well as the balance sheet crowding out that happens with monetary stimulus.

[winterspeak]

I hope the EU is not tested either. But there you have it, exogenous currency in action! I'm sure there are austrians somewhere talking about how they got it *almost* right ; )

RSJ: Small quibble, but I think MMTers would say that is that CB *cannot* engage in the stimulus effort you describe as CBs cannot add to the private sector's net financial assets, they can merely alter their term structure. This is why (as I said above), MMT do not believe that bond sales "offset" (or "sterilize" to use an old gold standard term) currency issuance.

[RSJ]

Winterspeak,

I don't want to re-argue all these points here, but I was engaged in lengthy debates over at Billyblog in which they argued that the payment of interest on government bonds enriched the private sector above and beyond the deficit spending, and that therefore bond sales (might be) more inflationary than net currency issuance. Because of this, they argued that selling bonds was the unfair granting of "annuities" to private sector households.

My position was that whenever a financial asset is sold at market prices, you cannot assume that the interest received is more than the opportunity cost of the funds necessary to buy the asset, and that therefore it is completely irrelevant whether bonds are sold to the private sector or not. The private sector is enriched by the deficit spending, not any subsequent financial asset sales or purchases, provided that all assets are sold at market prices.

Aggregate household financial net-worth will be exactly the same regardless of whether the government has a policy to offset some or all of that deficit spending with bond sales.

Many pixels were spilt on this, because on the one hand, people "counted" the money -- always a dangerous undertaking, as you need to "value" the money rather than count it -- and said "look, before households have $X and next year they have X+ rX -- they must be rX richer! Government is sending them rX, that, in aggregate, they would not have. And I was trying to point out the whole concept of a growing economy, in which all financial assets are expected to grow by rX, that in fact all assets will grow by rX, -- hence r is the risk-free rate -- regardless of whether the quantity of "cash" grows by rX, or who sends what to whom.

[RSJ]

...and I'll continue with this thought because I think it has a lot of relevance for some of my other discussions with Nick.

The belief that it doesn't matter whether the government is sending rX interest payments to households, or whether the households are receiving rX from the business sector seems to suggest a theory of crowding out -- that households have a choice of investing in the private sector or in government bonds, and 1 dollar of government debt purchased "crowds out" 1 dollar of private sector debt. This is false -- in the exact same way that the loanable funds theories are false.

It is false because of the possibility of *balance sheet expansion* -- which is something I've never seen allowed for in any RA model (although I've only looked at a handful). Balance sheet expansion screws up equilibrium boundary conditions, and so you must assume that the debt --> 0, which is not really observed. Balance sheet expansion is a bit like increasing returns in that way.

In general, I don't think economists have taken balance sheet expansion into account, and so because of this, they believe that an increased desire to save must result in lower interest rates. But this is not true if households take the money that they saved, and use it as collateral to short a security instead of going long. You can equally go short or long -- you can buy a put option or a call option. There is no reason to believe -- a priori -- that increased purchases of financial assets will always result in more call options being purchased than put options.

This is why unlike the goods markets, the financial asset markets do not have a downward sloping interest rate curve with respect to the amount of money saved. And in fact periods of high volume transactions tend to be market crashes -- something that is not observed in the goods markets.

This is not just an artifact of financial engineering. Even if it were impossible to buy put options or to short securities, in a world of endogenous capital, you can "short" capital by purchasing the net capital producing firms, or go long capital by purchasing the capital consuming firms. For example, if you believe that housing is over-priced, you can buy stock in the homebuilders, lowering their cost of funds, and bringing more houses onto the market, therefore you are net seller of houses, and your actions raise the yield of the house as an asset class.

In the financial markets, increased purchases can result in downward pressure on yields *or* upward pressure on yields -- it depends on what the expected return is. But if you view the financial market as just another good market, then increased purchases will only result in falling yields, and your loanable funds theory will hold, and your (financial) crowding out theory will hold as well.

There is only a "real" crowding out, in the sense that there is a finite capacity to produce real goods. The capacity to produce financial assets is infinite. Assuming liquid markets, there is never any shortage of money to buy a bond, as you can always borrow to the buy the bond, and you will as soon as the price of the bond is less than the expected return. Then you will make money off the spread. And in the same way, you can always short the bond, as soon as the price of the bond is greater than the expected return.

Back to the situation of government bonds -- or really all bonds -- in aggregate they are *always* purchased via balance sheet expansion. The household sector is a net holder only of equity. All bonds are purchased solely for financial engineering purchases, with some households being (directly or indirectly) net short and others being (directly or indirectly) net long, and any bond interest payments, whether those payments are made by government or not -- exactly cancel to give no benefit to the household sector.

In a closed economy, aggregate household sector net worth exactly tracks the net present value of the equity of the private sector, and is not affected by the quantity or yield of bonds at all. But this can be a non-intuitive result, and without this view, you will start believing that it is possible to "run out of cash" to buy bonds, and so if the government tries to sell too many, then private sector bonds must increase in yield, regardless of what happens to expected return. They may increase in yield, but only because of the "real" crowding out -- not because of the size of the auction.

[winterspeak]

RSJ: I don't want you to re-argue anything, just pointing out the standard MMT perspective (which I think is correct, although I'm always open to learning more).

If you have a link to the right thread in billyblog I'd appreciate it.

Your point on whether interest paid on Treasuries is really fiscal expansion or not is a good one. A simple reading of MMT would argue that it is, although it could be wrong (for the reasons you lay out). There is an interesting extension that you may have already had on whether Treasury rates are really at a "market" price. In normal conditions they are (although they don't need to be) and under QE who knows. Still, the Treasury currently sets quantity to manipulate price (instead of setting price and letting quantity float) and that sounds like "market price" to me.

I don't know what you mean by "RA" model, but I agree, I have yet to see an economist demonstrate any understanding of what a balance sheet is -- with the exception of MMT. It's certainly possible that even they have not pushed this far enough.