Econophysics: Financial White Noise Switch. Thought of the Day 115.0


What is the cause of large market fluctuation? Some economists blame irrationality behind the fat-tail distribution. Some economists observed that social psychology might create market fad and panic, which can be modeled by collective behavior in statistical mechanics. For example, the bi-modular distribution was discovered from empirical data in option prices. One possible mechanism of polarized behavior is collective action studied in physics and social psychology. Sudden regime switch or phase transition may occur between uni-modular and bi-modular distribution when field parameter changes across some threshold. The Ising model in equilibrium statistical mechanics was borrowed to study social psychology. Its phase transition from uni-modular to bi-modular distribution describes statistical features when a stable society turns into a divided society. The problem of the Ising model is that its key parameter, the social temperature, has no operational definition in social system. A better alternative parameter is the intensity of social interaction in collective action.

A difficult issue in business cycle theory is how to explain the recurrent feature of business cycles that is widely observed from macro and financial indexes. The problem is: business cycles are not strictly periodic and not truly random. Their correlations are not short like random walk and have multiple frequencies that changing over time. Therefore, all kinds of math models are tried in business cycle theory, including deterministic, stochastic, linear and nonlinear models. We outline economic models in terms of their base function, including white noise with short correlations, persistent cycles with long correlations, and color chaos model with erratic amplitude and narrow frequency band like biological clock.



The steady state of probability distribution function in the Ising Model of Collective Behavior with h = 0 (without central propaganda field). a. Uni-modular distribution with low social stress (k = 0). Moderate stable behavior with weak interaction and high social temperature. b. Marginal distribution at the phase transition with medium social stress (k = 2). Behavioral phase transition occurs between stable and unstable society induced by collective behavior. c. Bi-modular distribution with high social stress (k = 2.5). The society splits into two opposing groups under low social temperature and strong social interactions in unstable society. 

Deterministic models are used by Keynesian economists for endogenous mechanism of business cycles, such as the case of the accelerator-multiplier model. The stochastic models are used by the Frisch model of noise-driven cycles that attributes external shocks as the driving force of business fluctuations. Since 1980s, the discovery of economic chaos and the application of statistical mechanics provide more advanced models for describing business cycles. Graphically,


The steady state of probability distribution function in socio-psychological model of collective choice. Here, “a” is the independent parameter; “b” is the interaction parameter. a Centered distribution with b < a (denoted by short dashed curve). It happens when independent decision rooted in individualistic orientation overcomes social pressure through mutual communication. b Horizontal flat distribution with b = a (denoted by long dashed line). Marginal case when individualistic orientation balances the social pressure. c Polarized distribution with b > a (denoted by solid line). It occurs when social pressure through mutual communication is stronger than independent judgment. 


Numerical 1 autocorrelations from time series generated by random noise and harmonic wave. The solid line is white noise. The broken line is a sine wave with period P = 1. 

Linear harmonic cycles with unique frequency are introduced in business cycle theory. The auto-correlations from harmonic cycle and white noise are shown in the above figure. Auto-correlation function from harmonic cycles is a cosine wave. The amplitude of cosine wave is slightly decayed because of limited data points in numerical experiment. Auto-correlations from a random series are an erratic series with rapid decade from one to residual fluctuations in numerical calculation. The auto-regressive (AR) model in discrete time is a combination of white noise term for simulating short-term auto-correlations from empirical data.

The deterministic model of chaos can be classified into white chaos and color chaos. White chaos is generated by nonlinear difference equation in discrete-time, such as one-dimensional logistic map and two-dimensional Henon map. Its autocorrelations and power spectra look like white noise. Its correlation dimension can be less than one. White noise model is simple in mathematical analysis but rarely used in empirical analysis, since it needs intrinsic time unit.

Color chaos is generated by nonlinear differential equations in continuous-time, such as three-dimensional Lorenz model and one-dimensional model with delay-differential model in biology and economics. Its autocorrelations looks like a decayed cosine wave, and its power spectra seem a combination of harmonic cycles and white noise. The correlation dimension is between one and two for 3D differential equations, and varying for delay-differential equation.


History shows the remarkable resilience of a market that experienced a series of wars and crises. The related issue is why the economy can recover from severe damage and out of equilibrium? Mathematically speaking, we may exam the regime stability under parameter change. One major weakness of the linear oscillator model is that the regime of periodic cycle is fragile or marginally stable under changing parameter. Only nonlinear oscillator model is capable of generating resilient cycles within a finite area under changing parameters. The typical example of linear models is the Samuelson model of multiplier-accelerator. Linear stochastic models have similar problem like linear deterministic models. For example, the so-called unit root solution occurs only at the borderline of the unit root. If a small parameter change leads to cross the unit circle, the stochastic solution will fall into damped (inside the unit circle) or explosive (outside the unit circle) solution.

Austrian Economics. Some Further Ruminations. Part 2.

There are two Austrian theories of capital, at least surfacially with two completely different objectives. The first one concentrates on the physical activities roundabout, time-consuming production processes which are common to all economic systems, and it defines capital as a parameter of production. This theory is considered to be universal and ahistorical, and the present connotation of Austrian Theory of Capital falls congruent with this view. This is often denoted by physical capital and consists of concrete and heterogenous capital goods, which is nothing but an alternative expression for production goods. The second and relatively lesser known theory is the beginning point for a historically specific theory, and shies away with the production process and falls in tune with the economic system called capitalism. Capital isn’t anymore dealing with the production processes, but exclusively with the amount of money invested in a business venture. It is regarded as the central tool of economic calculations by profit-oriented enterprises, and rests on the social role of financial accounting. This historically specific theory of capital is termed business capital and is in a sense simply money invested in business assets.

A deeper analysis, however, projects that these divisions are unnecessary, and that physical capital is not a theory of physical capital at all. Its tacit but implicit research object is always the specific framework of the market economy where production is exercised nearly exclusively by profit-oriented enterprises calculating in monetary terms. Austrian capital theory is used as an element of the Austrian theory of the business cycle. This business cycle theory, if expounded consistently, deals with the way the monetary calculations of enterprises are distorted by changes in the rate of interest, not with the production process as such. In a long and rather unnoticed essay on the theory of capital, Menger (German, 1888) recanted what he had said in his Principles about the role of capital theory in economics. He criticized his fellow economists for creating artificial definitions of capital only because it dovetailed into their personal vision of the task of economics. In respect of the Austrian theory of capital as expounded by himself in his Principles and elaborated on by Böhm-Bawerk, he declared that the division of goods into production goods and consumption goods, important as it may be, cannot serve as a basis for the definition of capital and therefore cannot be used as a foundation of a theory of capital. As for entrepreneurs and lawyers, according to Menger, only sums of money dedicated to the acquisition of income are denoted by this word. Of course, Menger’s real-life oriented notion of capital does not only comprise concrete pieces of money but

all assets of a business, of whichever technical nature they may be, in so far as their monetary value is the object of our economic calculations, i.e., when they calculatorily constitute sums of money for us that are dedicated to the acquisition of income.

An analysis of capital presupposes the historically specific framework of capitalism, characterized by profit-oriented enterprises.

Some economists concluded therefrom that “capital” is a category of all human production, that it is present in every thinkable system of the conduct of production processes—i.e., no less in Robinson Crusoe’s involuntary hermitage than in a socialist society—and that it does not depend upon the practice of monetary calculation. This is, however, a confusion (Mises).

Capital, for Mises, is a device that stems from and belongs to financial accounting of businesses under conditions of capitalism. For him, the term “capital” does not signify anything peculiar to the production process as such. It belongs to the sphere of acquisition, not to the sphere of production.  Accordingly, there is no theory of physical capital as an element or factor in the production process. There is rather a theory of capitalism. For him, the existence of financial accounting on the basis of (business) capital invested in an enterprise is the defining characteristic of this economic system. Capital is “the fundamental notion of economic calculation” which is the foremost mental tool used in the conduct of affairs in the market economy. A more elaborate historically specific theory of capital that expands upon Mises’s thoughts would analyze the function of economic calculation based on business capital in the coordination of plans and the allocation of resources in capitalism. It would not deal with the production process as such but, generally, would concern itself with the allocation and distribution of goods and resources by a system of profit-oriented enterprises.

How Permanent Income Hypothesis/Buffer Stock Model of Milton Friedman Got Nailed?

Milton Friedman and his gang at Chicago, including the ‘boys’ that went back and put their ‘free market’ wrecking ball through Chile under the butcher Pinochet, have really left a mess of confusion and lies behind in the hallowed halls of the academy, which in the 1970s seeped out, like slime, into the central banks and the treasury departments of the world. The overall intent of the literature they developed was to force governments to abandon so-called fiscal activism (the discretionary use of government spending and taxation policy to fine-tune total spending so as to achieve full employment), and, instead, empower central banks to disregard mass unemployment and fight inflation first. Wow!, Billy, these aren’t the usual contretemps and are wittily vitriolic. Several strands of their work – the Monetarist claim that aggregate policy should be reduced to a focus on the central bank controlling the money supply to control inflation (the market would deliver the rest (high employment and economic growth, etc); the promotion of a ‘natural rate of unemployment’ such that governments who tried to reduce the unemployment rate would only accelerate inflation; and the so-called Permanent Income Hypothesis (households ignored short-term movements in income when determining consumption spending), and others – were woven together to form a anti-government phalanx. Later, absurd notions such as rational expectations and real business cycles were added to the litany of Monetarist myths, which indoctrinated graduate students (who became policy makers) even further in the cause. Over time, his damaging legacy has been eroded by researchers and empirical facts but like all tight Groupthink communities the inner sanctum remain faithful and so the research findings haven’t permeated into major shifts in the academy. It will come – but these paradigm shifts take time.

Recently, another of Milton’s legacy bit the dust, thanks to a couple of Harvard economists, Peter Ganong and Pascal Noel, who with their paper “How does unemployment affect consumer spending?” smashed to smithereens the idea that households would not take consumption decisions with discretion, which the Chicagoan held to be a pivot of his active fiscal policy. Time traveling back to John Maynard Keynes, who outlined in his 1936 The General Theory of Employment, Interest and Money a view that household consumption was dependent on disposable income, and, that in times of economic downturn, the government could stimulate employment and income growth using fiscal policy, which would boost consumption.

In Chapter 3 The Principle of Effective Demand, Keynes wrote:

When employment increases, aggregate real income is increased. The psychology of the community is such that when aggregate real income is increased aggregate consumption is increased, but not by so much as income …

The relationship between the community’s income and what it can be expected to spend on consumption, designated by D1, will depend on the psychological characteristic of the community, which we shall call its propensity to consume. That is to say, consumption will depend on the level of aggregate income and, therefore, on the level of employment N, except when there is some change in the propensity to consume.

Keynes later (in Chapter 6 The Definition of Income, Saving and Investment) considered factors that might influence the decision to consume and talked about “how much windfall gain or loss he is making on capital account”.

He elaborated further in Chapter 8 The Propensity to Consume … and wrote:

The amount that the community spends on consumption obviously depends (i) partly on the amount of its income, (ii) partly on the other objective attendant circumstances, and (iii) partly on the subjective needs and the psychological propensities and habits of the individuals composing it and the principles on which the income is divided between them (which may suffer modification as output is increased).

And concluded that:

1. An increase in the real wage (and hence real income at each employment level) will “change in the same proportion”.

2. A rise in the difference between income and net income will influence consumption spending.

3. “Windfall changes in capital-values not allowed for in calculating net income. These are of much more importance in modifying the propensity to consume, since they will bear no stable or regular relationship to the amount of income.” So, wealth changes will impact positively on consumption (up and down).

Later, as he was reflecting in Chapter 24 on the “Social Philosophy towards which the General Theory might lead” he wrote:

… therefore, the enlargement of the functions of government, involved in the task of adjusting to one another the propensity to consume and the inducement to invest, would seem to a nineteenth-century publicist or to a contemporary American financier to be a terrific encroachment on individualism, I defend it, on the contrary, both as the only practicable means of avoiding the destruction of existing economic forms in their entirety and as the condition of the successful functioning of individual initiative.

For if effective demand is deficient, not only is the public scandal of wasted resources intolerable, but the individual enterpriser who seeks to bring these resources into action is operating with the odds loaded against him …

It was thus clear – that active fiscal policy was the “only practicable means of avoiding the destruction” of recession brought about by shifts in consumption and/or investment. That view dominated macroeconomics for several decades.

Then in 1957, Milton Friedman advocated the idea of Permanent income hypothesis. The central idea of the permanent-income hypothesis, proposed by Milton Friedman in 1957, is simple: people base consumption on what they consider their “normal” income. In doing this, they attempt to maintain a fairly constant standard of living even though their incomes may vary considerably from month to month or from year to year. As a result, increases and decreases in income that people see as temporary have little effect on their consumption spending. The idea behind the permanent-income hypothesis is that consumption depends on what people expect to earn over a considerable period of time. As in the life-cycle hypothesis, people smooth out fluctuations in income so that they save during periods of unusually high income and dissave during periods of unusually low income. Thus, a pre-med student should have a higher level of consumption than a graduate student in history if both have the same current income. The pre-med student looks ahead to a much higher future income, and consumes accordingly.Both the permanent-income and life-cycle hypotheses loosen the relationship between consumption and income so that an exogenous change in investment may not have a constant multiplier effect. This is more clearly seen in the permanent-income hypothesis, which suggests that people will try to decide whether or not a change of income is temporary. If they decide that it is, it has a small effect on their spending. Only when they become convinced that it is permanent will consumption change by a sizable amount. As is the case with all economic theory, this theory does not describe any particular household, but only what happens on the average.The life-cycle hypothesis introduced assets into the consumption function, and thereby gave a role to the stock market. A rise in stock prices increases wealth and thus should increase consumption while a fall should reduce consumption. Hence, financial markets matter for consumption as well as for investment. The permanent-income hypothesis introduces lags into the consumption function. An increase in income should not immediately increase consumption spending by very much, but with time it should have a greater and greater effect. Behavior that introduces a lag into the relationship between income and consumption will generate the sort of momentum that business-cycle theories saw. A change in spending changes income, but people only slowly adjust to it. As they do, their extra spending changes income further. An initial increase in spending tends to have effects that take a long time to completely unfold. The existence of lags also makes government attempts to control the economy more difficult. A change of policy does not have its full effect immediately, but only gradually. By the time it has its full effect, the problem that it was designed to attack may have disappeared. Finally, though the life-cycle and permanent-income hypotheses have greatly increased our understanding of consumption behavior, data from the economy does not always fit theory as well as it should, which means they do not provide a complete explanation for consumption behavior.

The idea of a propensity to consume, which had been formalised in textbooks as the Marginal propensity to consume (MPC) – which described the extra consumption that would follow a $ of extra disposable income, was thrown out by Friedman.

The MPC concept – that households consume only a proportion of each extra $1 in disposable income received – formed the basis of the expenditure multiplier. Accordingly, if government deficit spending of, say $100 million, was introduced into a recessed economy, firms would respond by increasing output and incomes by that same amount $100 million. But the extra incomes paid out ($100 m) would stimulate ‘induced consumption’ spending equal to the MPC times $100m. If the MPC was, say, 0.80 (meaning 80 cents of each extra dollar received as disposable income would be spent) then the ‘second-round’ effect of the stimulus would be an additional $80 million in consumption spending (assuming that disposable and total income were the same – that is, assuming away the tax effect for simplicity). In turn, firms would respond and produce an additional $80 million in output and incomes, which would then create further induced consumption effects. Each additional increment, smaller than the last, because the MPC of 0.80 would mean some of the extra disposable income was being lost to saving. But it was argued that the higher the MPC, the greater the overall impact of the stimulus would be. Instead, Friedman claimed that consumption was not driven by current income (or changes in it) but, rather by expected permanent income.

Permanent income becomes an unobservable concept driven by expectations. It also leads to claims that households smooth out their consumption over their lifetimes even though current incomes can fluctuate. So when individuals are facing major declines in their current income – perhaps due to unemployment – they can borrow short-term to maintain the smooth pattern of spending and pay the credit back later, when their current income is in excess of some average expectation.

The idea led to a torrent of articles mostly mathematical in origin trying to formalise the notion of a permanent income. They were all the same – GIGO – garbage in, garbage out. An exercise in mathematical chess although in search of the wrong solution. But Friedman was not one to embrace interdependence. In the ‘free market’ tradition, all decision makers were rational and independent who sought to maximise their lifetime utility. Accordingly, they would borrow when young (to have more consumption than their current income would permit) and save over their lifetimes to compensate when they were old and without incomes. Consumption was strictly determined by this notion of a lifetime income.

Only some major event that altered that projection would lead to changes in consumption.

The Permanent Income Hypothesis is still a core component of the major DSGE macro models that central banks and other forecasting agencies deploy to make statements about the effectiveness of fiscal and monetary policy.

So it matters whether it is a valid theory or not. It is not just one of those academic contests that stoke or deflate egos but have very little consequence for the well-being of the people in general. The empirical world hasn’t been kind to Friedman across all his theories. But the Permanent Income Hypothesis, in particular, hasn’t done well in explaining the dynamics of consumption spending.

Getting back to the paper mentioned in the beginning, it finds deployment of a rich dataset arguing to point where the permanent income hypothesis of Friedman is nailed to the coffin. If the permanent income hypothesis was a good framework for understanding what happens to the consumption patterns of this cohort then we would expect a lot of smoothing going on and relatively stable consumption.

Individuals, according to Friedman, are meant to engage in “self-insurance” to insure against calamity like unemployment. The evidence is that they do not.

The researchers reject what they call the “buffer stock model” (which is a version of the permanent income hypothesis).

They find:

1. “Spending drops sharply at the onset of unemployment, and this drop is better explained by liquidity constraints than by a drop in permanent income or a drop in work-related expenses.”

2. “We find that spending on nondurable goods and services drops by $160 (6%) over the course of two months.”

3. “Consistent with liquidity constraints, we show that states with lower UI benefits have a larger drop in spending at onset.” In other words, the fiscal stimulus coming from the unemployment benefits attenuates the loss of earned income somewhat.

4. “As UI benefit exhaustion approaches, families who remain unemployed barely cut spending, but then cut spending by 11% in the month after benefits are exhausted.”

5. As it turns out the “When benefits are exhausted, the average family loses about $1,000 of monthly income … In the same month, spending drops by $260 (11%).”

6. They compare the “path of spending during unemployment in the data to three benchmark models and find that the buffer stock model fits better than a permanent income model or a hand-to-mouth model.”

The buffer stock model assumes that families smooth their consumption after an income shock by liquidating previous assets – “a key prediction of buffer stock models is that agents accumulate precautionary savings to self-insure against income risk.”

The researchers find that the:

the buffer stock model has two major failures – it predicts substantially more asset holdings at onset and it predicts that spending should be much smoother at benefit exhaustion.


7. Finally, the researchers found “that families do relatively little self-insurance when unemployed as spending is quite sensitive to current monthly income.” Families “do not prepare for benefit exhaustion”.