20 June 2008

The Social Laffer Curve

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This was borrowed and adapted from
Monissen (1999)

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Wikipedia: Revised version of Martin Gardner's
Neo-Laffer curve.
The Laffer Curve was intended to illustrate a correlation between tax rates as a share of GDP and tax revenue. The x-axis is supposed to represent taxes as a share of GDP, and the y-axis is supposed to represent tax revenue. The problem with the Laffer curve is pretty severe: even as a thought experiment, it's impossible to map out an observable y-axis. Suppose we take a unitary government with a total overall tax rate of 0.75 of GDP (see upper figure). We surmise that the peak of the curve is at .55, and at 0.33, it's back down to whatever it was at x = .75. If that's true, then the effect of cutting taxes 26.3% is an increase in revenue to the state, and the effect of a halving taxes is to make revenue the same. This cannot be what Arthur Laffer meant, of course; surely some time is required before the tax cuts work their supply-side magic.

Ah, then in that case we have to say that the tax base is increasing now because the tax cut stimulated investment and labor. So what are we saying the y-axis measures? It must be tax revenue at some as-yet-unspecified future date.

I could be very generous and surmise that the Laffer Curve is based on the Ramsey-Cass-Koopmans model (which is pretty fundamental to modern economics), and that the values of y corresponding to each value of x are determined by the usual utility-maximizing objective function; at some point in the future the labor market reaches a new equilibrium of output at which point revenues reach their new equilibrium as well. But, in such a case, the derivative of the curve at each point is dependent on conditions under which taxes are cut or raised, and on expectations of future tax increases.1 This means that the derivative is entirely indeterminant, and hence the function that the Laffer Curve is supposed to represent has no fixed value. In other words, there's no sense in which the y-axis means anything at all.2

Even intuitively it is not much help because there's no consideration of what the government actually does with the money, which may be more important than the precise amount levied or raised. That's even assuming all the economic assumptions that orthodox economists make.

Aside from the trivial observation that tax rates of 0 or 100% of GDP will fetch zero revenues, while for rates between % and 100%, it'll be >$0, the Laffer Curve says nothing.

A Possible Analogy to the Laffer Curve
A modest proposal

Now, let's look at the Laffer Curve as a measure of social policy. We could say that the x-axis represents the rate of government spending on social welfare per person. We make some minor assumptions:

  1. social welfare spending mostly targets illiteracy, preventable diseases, and other obstacles to earning a living;
  2. social welfare spending has some marginal utility; it might not be perfect, and we assume there is some waste, but more spending in any given time period t­­i leads to greater income in period ti + 1.
In that case, it is reasonable to expect that if social welfare spending Gi is 0% of GDP, then total income will be low since poverty rates will be high and have dire consequences for civil order. If social welfare spending Gi is 100% of GDP, then the customary incentive effect is going to be bad, as everyone would expect: everyone is guaranteed everything that they could possibly have to consume, so productivity wastes away (albeit, probably not to nothing). For that matter, bureaucrats would probably be the worst offenders, so we'd never reach that point, but if we did, it's not controversial to claim that the economy would grind to a halt.

But in between there is going to be an optimal level of social welfare spending which might possibly be measured in terms of the total factor productivity (TFP), or perhaps an index that incorporates TFP and the human development index (HDI). Growth rate, in my opinion, is not really useful because so many things affect growth rates, such as saving (which can be distorted upward by the absence of a social welfare system, as it is in China, or distorted upward by the presence of one, as in Scandinavia or Japan).

So what about TFP? Why is this important?

It's not as important as the actual well-being or sense of connectedness that people in a [morally] good society feel towards their neighbors, but TFP may well be a good numerical surrogate. That's because TFP measures the effectiveness of utilization of economic inputs. In a society where crime rates are high, the GDP will be padded by spending on law enforcement, courts, and corrections. Since it is necessary, the money will be spent, but it will not contribute to productivity. Likewise, if the polity refuses to spend money on education for the ignorant masses, then productivity increases may occur, but they'll be mainly caused by the accumulation of capital (which is subtracted from productivity growth to get TFP). Also, extreme misery among the permanently poor and hopeless will require an immense wall around the squalid quarters where they live, wastage of money on armored Hummers for the affluent (to avoid getting carjacked and held for ransom), a less efficient transit system, a less efficient sewage and drainage system (with every house needing its own septic tank, whether the water table can sustain one or not), and so on.

When a social problem is not very intense, fighting it is comparatively cheap per victim.

Drug addiction is a good example. In the USA, there are reportedly six million users of cocaine, or 3% of the population aged 15-65. There are 3.6 million ATS users, some of whom also use cocaine. Possibly ten million Usonians use a class A drugs on a regular basis.3 Prevalence for class A drugs in the USA is usually several times what it is in Western European countries, especially for cocaine. The enormous number of users, particularly of ATS, has created a market for more pernicious drugs than were used in the past. While there are doubtless many explanations for the extraordinarily high US rates of class A drug use, one has to be the weak social model. During the period 1990-2000, drug use declined in the US (as did most types of crime) but it did so at a terrible cost: record-busting incarceration rates, a compromised judicial system, paramilitary policy forces, and ultimately, the loss of basic Usonian freedoms.4 In effect, the people of the United States paid very heavily for a reduction of crime to average OECD levels. Measuring this with TFP indices is unreliable, but clearly turning huge regions of modern cities into armed camps, and adopting the highest rates of incarceration in the world (mostlly for nonviolent drug offenders) had a dire impact on the productive deployment of labor, capital, and energy.

I am aware that the last sentence is obscene. Please accept my apologies; if you've read this far, you probably sense that I think the real cost is not in terms of output or measurable welfare, but in terms of human freedom and moral decency. But when one attempts to analyze the impact of a large number of heterogeneous policies on the large set of heterogeneous human activities known as an "economy," one has to use the language and methods of economics.)

Another compelling example is poverty itself. Poverty is closely tied to location; the poor are less mobile and usually can leave a depressed community only with difficulty. In many cases, a policy change of reducing welfare/food stamps causes a loss of jobs in retailing in the community; firms that were viable at the prior level of custom go out of business, and unemployment rises. The community will experience a multiplier effect, and finally settle at a much greater level of unemployment.While the initial policy might have supplied $1000/person per month on average, the new policy might supply $500/person per month; but there's twice as many aid recipients, and since poverty is more intense, the community where they live can no longer sustain schools or internet access. Poverty there has become virtually hopeless, and the surrounding community has to be defended from a desperate, sick, ignorant, and antagonistic enclave. Public libraries contrive ways of excluding the poor, denying them access to job opportunities. Private property, such as cars used for business or construction tools, are stolen or impounded (because the owner can't keep up the registration).

Even outside of blighted ghettos, the effect of reduced public spending below a certain point can sharply worsen the ability of people to be productive, and thereby make the usual business of government costlier.

For example, the US government is organized so that most social services are provided by state and local governments, while the federal government takes care of the military, foreign relations, some law enforcement, and some supplemental R&D for big corporations (Department of Energy, Department of Transportation, the BLS, etc.). During business cycles, the federal government not only continues to spend the same amount on soldiers, narcs, and gizmos, it actually increases spending during recessions. The states, cities, counties, and school districts are compelled to cut back. In fact, their budget typically decreases by much more than the local gross state product does, because tax revenues are volatile. When a recession hits, the proportion of governmental expenditures directed at things people actually need, like health care services, schools, local infrastructure, public transit, and law enforcement, declines; government spending actually shifts to things that are largely destructive and pointless, such as preparing for another optional war or rescuing the coal industry.

As a result, the Usonian educational system is subject to violent budgetary swings and enormous local variance in quality. Mathematically, education spending per student per year averages out to something quite high, but with programs like education, extra spending in boom years is mostly wasted; the bad years ruin the progress in building up a strong, committed cohort of educators. Police forces react to reduced funding by shifting energies to traffic tickets and impoundings. This, of course, negatively impacts safety and makes the worsened social problems costlier to deal with.


The Laffer Curve has towered over policy debate in the USA for almost 30 years now. While it is not helpful for describing the behavior of revenues in response to tax policy (except at the extreme points of 0 and 100%), it actually has some practical relevance for social spending. To wit, assuming that
  • social spending moves within reasonable limits (say, the levels encountered in OECD countries during the last forty years),
  • social spending is managed in good faith and does not vary greatly in efficiency over the relevant domain,
  • social spending is mostly directed at assisting the ability of people to become or remain productive,
then TFP is a curve that is concave downwards with respect to the horizontal axis. The peak value of TFP will correspond to "pre-emptive redress" of social problems like poverty, public health risks, education, infrastructure, and safety (G*). "Pre-emptive redress" implies that problems are redressed at a level of thoroughness such that they remain at a relatively low, manageable level; do not impinge on the general quality of life; and do not jeopardize the resource-base of the economy.

Levels of social spending in excess of G* will of course pose the expected problems posed by exorbitant taxes and hyperactive states. But at levels significantly below G*, social problems will grow in size so that maintaining them at a higher degree of severity (e.g., higher crime rates, worse poverty, more cases of tuberculosis) becomes more expensive, and government expenditures will have to rise at a later date just to contain them. The surprising inference is that attempting to reduce the cost of government by slashing social spending will likely lead to increased government spending in subsequent budget cycles, as routine governance gives way to putting out fires.

1 There is a Keynesian method of predicting the stimulus caused by a particular tax cut under particular circumstances, and there's a rational expectations (REH) method. The latter method requires that one know what the future fiscal balances will be after the cuts. The REH method incorporates (to some degree) the Ricardian Equivalence Hypothesis, in which taxpayers adjust their savings and investment strategies in expectation of future deficits (and a probable tax increase).

The short version of this is that, if the government slashes taxes without reducing spending, then taxpayers will anticipate the approximate size of the deficit and include a future tax increase in their personal financial planning. The effect, according to Robert Barro, was that the intended stimulus of deficit spending will be entirely thwarted. Instead of actually increasing aggregate demand, consumers will hoard wealth because they know they'll need it when the government has to balance the budget again.

How do households know when or how big the tax increase will be? They don't, but a very rough guess of both is surprisingly effective. The reason is that the longer the government waits to restore a balanced budget, the larger the tax hike will have to be. Economists assume that households value future income/spending less; so if the government waits a short time and raises taxes a little bit, then that little bit will have about as much effect as a long wait and big tax increase far in the future. Based on past experience and cultural expectations, households will tend to guess correctly what the most likely course of action will be.

For an introduction to this idea, see Douglas W. Elmendorf & N. Gregory Mankiw, "Government Debt" , originally an excerpt from Handbook of Macroeconomics Federal Reserve Board (1998), p.28.

2 A Mr. Hans G. Monissen wrote "Explorations of the Laffer Curve" (1999) in which in included a large number of assumptions to allow the Laffer Curve to "mean something." Specifically, a cut in taxes reduces the demand for leisure and consumption, and increases the willingness to work and to save. Investment increases the productivity of labor, and workers will accept longer hours (bidding down the price of labor). According to the Swan-Solow Classical Growth Theory, this stabilizes at a new GDP, which is definitely higher than the old one. Under certain assumptions one can calculate what that new GDP level will be; but it corresponds to a future date which has to be specified. In order for the Laffer Curve to work, however, workers will need to "know" that it will work, because if they assume that deficit spending will be followed by a comparably-sized surplus, they will not make the virtuous adjustments that a Keynesian would automatically expect them to, and that would lead to increased revenue. If they guess wrong, no stimulus will occur and deficits will in fact follow (as they expected), which means that they weren't wrong at all. Monissen's attempt to salvage some meaning for the Laffer Curve leads to a paradox in which there are actually infinitely many rational expectations with self-fulfilling prophesies.

3 United Nations Office on Drugs and Crime, World Drug Report 2008 , table 7, p.84; see also The Threat of Narco-Trafficking in the Americas, p.21. Please note that cocaine is not the only serious drug problem. See also the Global ATS Assessment, which mentions that amphetamine-type stimulants (ATS; includes methamphetamine, crystalline methamphetamine, and ecstasy) are much more prevalent than either heroin or cocaine. See p.11. Exact comparisons of different "habits" are difficult, but the prevalence of ATS in the USA is massively greater than in any other region. This, despite a near-halving of ATS usage since 2001. See p.14. Heroin usage is much larger outside of the Western Hemisphere than in it, but heroin is used by far fewer people in Europe than cocaine is by North Americans.

Class A drugs are ecstasy, LSD, heroin, cocaine, crack, magic mushrooms, amphetamines (if prepared for injection). The term is British but fits standard penal classification in other countries as well.

4 It is difficult to make a fair comparison between crime rates internationally, but see the International Crime Victimization Survey (ICVS), 1989-2000, ICVS International Working Group (United Nations 2006). The ICVS is the most thorough international study of crime; it is probably unique insofar as it consists of survey of many different national populations, directly, by a single organization. The Codebook is part of the data package that one downloads at the link above; it has a section called "Key Findings from the 2000 ICVS" which is an outstanding summary of the data. Most types of crime monitored by the ICVS declined in the USA (1990-2000; see the Codebook in the data download, "Findings"), but increased sharply through 1996 everywhere else. As a result, except for murder, the crime rates in the USA are no longer particularly high.

Incarceration rates: see Christopher Hartney, "US Rates of Incarceration: A Global Perspective" , National Council on Crime and Delinquency (Nov 2006); see chart, p.2. The rates of incarceration in the USA are about 5x that of the UK and Spain, which are (in turn) the highest rates in the rest of the industrialized democracies. France has one eighth the incarceration rate. In contrast, the Stalinist GULAG held only a slightly larger share of the Soviet population at its peak in 1950.

Compromised legal system: I am to blame for such a vaguely-worded rebuke, but one exceptionally good source (on DVD) is Frontline: the Plea, PBS (2004). Bearing in mind that the vast majority of criminal cases are resolved through plea bargaining, "plea bargaining" is almost synonymous with "criminal justice system." Hence, another excellent source is George Fisher, Plea Bargaining's Triumph: A History of Plea Bargaining in America, Stanford University Press (2004), especially III: "On-file Plea Bargaining and the Rise of Probation." Fisher is very restrained in making any sweeping editorial claims. Another, more plaintive work is Jonathan Simon, Governing Through Crime: How the War on Crime Transformed American Democracy and Created a Culture of Fear, Oxford University Press (2007).

Paramilitary policing: a widely-cited reference is "Botched Paramilitary Police Raids" and Radley Balko, "Overkill: the Rise of Paramilitary Police Raids in America" , both hosted by the Cato Institute (2006); see also Christian Parenti Lockdown America, Verso Press (2000), Chapter VI.

Loss of basic Usonian freedoms: technically, the Military Commissions Act of 2006 rendered the Bill of Rights null and void. Text of Act ; ACLU fact sheet; Amnesty International report. The Act does not include language that precludes US citizens or legal residents from being designated "illegal combatants" and held without charge. Since military commissions do not include a grand jury and are not subject to writs of habeas corpus, it is potentially irrelevant to them whether any US citizen/legal resident is plausibly engaged in any "combat," illegal or otherwise.

Additional Sources and Reading:

Barbara Sard & Jeff Lubell, "
The Value of Housing Subsidies to Welfare Reform Efforts," Center for Budget & Policy Priorities (2000)

Hans G. Monissen, "Explorations of the Laffer Curve" University of Wuerzburg, Germany (1999)



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