Category Archives: Economics

Confusion about the "Law of Large Numbers"

An important concept in the theory of risk that seems to confuse a lot of people (journalists in particular) is the law of large numbers. The law of large numbers is a statistical law which implies that the average value of a randomly selected sample is likely to be close to the average value of the population from which the sample is drawn. The law of large numbers makes important risk pooling mechanisms such as insurance economically feasible. For more information on the law of large numbers, see the Wikipedia entry on this topic, entitled “Law of large numbers”.

Lately in the media, I have heard numerous (incorrect) references to examples of the “law of large numbers” at work. For example, this morning on Bloomberg Radio, an analyst was droning on about how the “law of large numbers” works to the “disadvantage” of large companies like Walmart. This analyst correctly observed that as large firms such as Walmart grow even larger, their opportunities for further growth in the future diminishes. This is an example of the “law of diminishing returns”, not the law of large numbers.

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Riskprof on adverse selection

In my opinion, Marty Grace at Georgia State has the most useful weblog on the internet for people who are interested in risk management/insurance-related research and public policy issues, called Riskprof.  For example, check out today’s entry about empirical evidence (or the lack thereof) concerning adverse selection in insurance markets, complete with a holiday theme!

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Finance to the Rescue

For what it’s worth, I am one of four people (along with Jeff Holland, Liongate Capital Management founder, John W. Howton Rockbrook Capital founder, and John C. Bogle, founder and former CEO of the Vanguard) interviewed in “Finance to the Rescue”, an article that appears in the Fall 2005 issue of Baylor Business Review.  My interview is on the topic of cat bonds, which is a topic that I have previously blogged about.

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Hurricane Katrina and the Great New Orleans Flood

Here is a collection of readings that I have been wading through (pardon the pun) in order to try to gain some perspectives on the tragedy that we see unfolding in the Gulf Coast generally and in New Orleans in particular:

1. Katrina, Cost-Benefit Analysis, and Terrorism, by Richard Posner, Senior Lecturer in Law, University of Chicago.
2. Major Disasters and the Good Samaritan Problem, by Gary Becker, 1992 Nobel Laureate in Economics, Professor of Economics at the University of Chicago and Senior Fellow at the Hoover Institution, Stanford University.
3. Rebuilding New Orleans — and America, by Thomas Sowell, Rose and Milton Friedman Senior Fellow, The Hoover Institution, Stanford University.
4. A Fuller Picture: Beginning to understand what we are seeing in New Orleans, by Michael Novak, George Frederick Jewett Scholar in Religion, Philosophy, and Public Policy at the American Enterprise Institute.

In retrospect, it would appear that the man-made aspects of the disaster are by far and away much worse than the storm itself.  The initial damage report from risk modeling firm Risk Management Solutions (RMS) was $20–$35 billion.  Later that same day (September 2), the levees failed in New Orleans and RMS immediately revised its estimate to $100 billion.  On September 7, the Wall Street Journal published a page 1 article entitled “First Estimates on Katrina Costs For Washington Hit $200 Billion”.  The biggest long term problem (at least from a loss prevention standpoint) has been a chronic underinvestment in levee protection for most of the history of the city of New Orleans.  Interestingly (as noted in John Berlau’s piece entitled Greens vs. Levees), the Army Corps of Engineers was sued sometime back in the mid-90’s in order to prevent them from raising and fortifying Mississippi River levees.  The Corps’ rationale for this project at the time was that it was needed “…because a failure could wreak catastrophic consequences on Louisiana and Mississippi which the states would be decades in overcoming, if they overcame them at all.”

Late today (September 8), Congress approved $51.8 billion in emergency spending to pay for Hurricane Katrina recovery efforts, and thankfully this will be directed through channels other than Louisiana public officials (see Congressman Tom Tancredo (R-CO)’s letter to Speaker Dennis Hastert (R-IL) on the problem of public corruption in Louisiana).

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Cat bonds

The very concept of insurance is based on risk. So it’s no surprise that important innovations in risk management and finance often come from the insurance industry. One such innovation that is growing in popularity is the so-called catastrophe bond, or “cat bond.”

Common sense as well as theory suggests that proper diversification of any risk involving a remote possibility of enormous loss (such as a natural or man-made catastrophe) makes such a risk more manageable. Traditionally, catastrophe, or “cat” risk was transferred and shared through the insurance and reinsurance markets. However, in spite of the dramatic growth in the magnitude of human and economic losses from natural and man-made catastrophes in recent years, it is surprising how little cat risk transfer actually occurs. Property owners fail to adequately insure catastrophe risk, and even when they purchase insurance, their insurers tend to retain most (as much as 70 percent) of this risk rather than distribute it more broadly through the reinsurance market. The reason why cat reinsurance is so limited is due to inadequate global capacity and correspondingly high reinsurance premiums.

Cat bonds came into existence due to this lack of capacity in the reinsurance market. Although they have been used primarily as an alternative to cat reinsurance, there are examples of corporations and other non-insurance entities issuing cat bonds. For example, during the summer of 1999, Tokyo Disneyland issued cat bonds because management found at the time that it was cheaper to have the capital markets insure its earthquake exposure than the insurance markets. More recently, the Fédération Internationale de Football Association (FIFA) issued a $260 million cat bond to protect itself against (a terrorism-related) cancellation of the 2006 World Cup in Germany.

Cat bonds represent a form of insurance securitization in which risk is transferred to investors rather than insurers or reinsurers. Typically, an insurer or reinsurer will issue a cat bond to investors such as life insurers, hedge funds and pension funds. The bonds are structured similarly to traditional bonds, with an important exception: if a pre-specified event such as a terrorist attack or hurricane occurs prior to the maturity of the bonds, then investors risk losing accrued interest and/or the principal value of the bonds.

Although the cat bond market is still relatively small compared with the traditional insurance and reinsurance markets, it is already having a particularly important effect on reinsurers. Since the cat bond market provides insureds with a credible alternative to traditional reinsurance, the cat bond market has forced reinsurers in particular to become more competitive in their pricing and underwriting practices. Furthermore, investors value cat bonds in part because returns on these securities tend not to be very highly correlated with returns on other asset classes such as stocks, conventional bonds, commodities and real estate.

Given the benefits that cat bonds offer both insureds and investors, the market for cat bonds is expected to continue to grow and exert an important check and balance upon pricing and underwriting practices in conventional insurance and reinsurance markets. Ironically, as documented by a recent Wall Street Journal article, the growth of the cat bond market is in turn fueling the growth prospects of the reinsurance industry, as a number of hedge funds that were early cat bond investors are now starting to launch their own reinsurance firms.

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Tax compliance costs and related issues

It is well known that the U.S. income tax system has enormous compliance costs.  Economists generally view compliance costs as the sum of direct payments made to tax lawyers and tax accountants for tax-related services plus the opportunity cost of time spent by everyone else.  Everyone else basically includes firms and individuals who complete their own tax forms and deal directly with the IRS with respect to tax audits and litigation (rather than employ tax professionals to do the “dirty work” for them). A cursory survey of the tax compliance literature yields estimates (based upon this specific compliance definition) ranging from $200 to $300 billion, or approximately 1.7 to 2.5% of GDP. 

In 2002, it is estimated that individuals, businesses and non-profits spent 5.8 billion man-hours complying with the federal income tax code, which is the financial equivalent of imposing a 20.4-cent surcharge for every dollar that the income tax system collects.  Apparently it is quite expensive to figure out what taxable income actually is.  This is not surprising in light of the substantial and growing complexity of the Internal Revenue Code.  The number of words in the Internal Revenue Code that specifically address the topic of income taxation has grown from 172,000 words in 1955 to 982,000 by 2000, an increase of 472 percent. Income tax regulations, which provide taxpayers with the “guidance” they need to calculate their taxable income, have grown at an even faster pace from 572,000 words in 1955 to 5,947,000 words by 2000, an increase of 939 percent. Combined, the federal income tax code and regulations grew from 744,000 words in 1955 to 6,929,000 by 2000—an increase of 831 percent.  (Source: “The Cost of Tax Compliance”).

Interestingly, the CNNMoney website published an article yesterday that points out another yet another important cost related to the current U.S. income tax system that is of a similar order of magnitude as the cost of compliance.  This relates to the cost of noncompliance.  Preliminary findings from a recently published IRS study show that the gap between what’s owed and what’s actually paid is between $257 billion and $298 billion (see the article entitled  “Taxpayers stiff IRS by nearly $300B”).  So let’s summarize.  The current U.S. income tax system has substantial transactions costs (1.7 to 2.5% of GDP) and at the same time produces a net shortfall of tax revenues to the government of a similar order of magnitude (i.e., an additional 2.1 to 2.5 percent of GDP).  Relative to the amount of money actually collected by the IRS, these costs total around 40%.

In the risk management literature, it is well known that the asymmetric nature of the corporate income tax creates incentives for firms to prefer hedging over retaining risk.  Tax asymmetries derive from two important features of the corporate income tax; specifically, tax rate progressivity and incomplete tax loss offsets.  Thus the incentives conveyed by the manner in which the tax system is structured creates yet another cost; specifically, firms and individuals have a tendency to underinvest in risky (but potentially profitable) assets, which in turn limits the economy’s prospective growth potential.   Thus the current U.S. income tax system gives rise to underinsvestment problems in the economy and is also very costly to administer.

Clearly, very powerful vested economic interests (with lots of money to “invest” in lobbyists) prefer the status quo, so it will be interesting to see whether Congress is able to reform the tax system such that administrative costs are substantially reduced and economic incentives with respect to risk bearing are less distorted.  Most of the proposals (e.g., a “flat” income tax or a consumption tax) that are on the table presently have the potential (at least in theory) to accomplish both of these goals, which in turn would bode well for the future growth and competitiveness of the U.S. economy.

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Some thoughts concerning the economics of the “Loser Pays” rule

It is widely believed that the U.S. tort system needs to be reformed in order to ensure that the U. S. remains globally competitive.  Of course, this begs the obvious policy question: what kinds of reforms are likely to be most effective without significantly compromising beneficial aspects of the tort system?  One reform proposal which has been debated for quite some time involves requiring that the loser reimburse the winner’s legal fees. The rationale for “Loser Pays” is that it would likely have the effect of reducing the number of cases brought to court (along with the associated legal expenditures).  Other legal systems (such as exist in the U. K. and throughout most of Europe) typically require losers to compensate winners for a portion of their legal costs, and the evidence appears to suggest that such rules do in fact reduce the frequency of litigation and related expenses.

The economics of “Loser Pays” compared with “Loser Doesn’t Pay” would appear to be fairly straightforward.  Under the “Loser Doesn’t Pay” that is actually practiced in the U.S., the payoff from litigation resembles a call option.  From the plaintiff’s perspective, downside risk is limited to the option premium, which comprises the legal costs (if any) that are directly borne by the plaintiff.  Although the plaintiff will typically share upside risk (in the form of contingency fees), her payoff is not bounded from above.  Since the plaintiff does not fully internalize the cost of litigation, this creates an apparent moral hazard.  By linearizing the payoffs from litigation so that the plaintiff bears downside as well as upside risk, one would expect that such a rule would likely reduce the frequency and expense of litigation, a result that is corroborated by Baye, Kovenock, and de Vries (2004) in an auction-theoretic framework.

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Insurance Reform in the State of Texas

Starting today, the state of Texas will be taking a sorely needed step in the direction of more competitive insurance markets by reforming insurance regulation. The specific reform involves the adoption of an alternative rate regulation protocol known as “File and Use” in place of “Prior Approval”. Under Prior Approval, insurers must submit information concerning the rates they wish to charge to the state insurance regulator and get these rates formally approved prior to their use. While the File and Use protocol requires that rate information be submitted to the state insurance regulator, the submitted rates do not require formal regulatory approval.[1]

As an applied economist, I candidly find the notion that insurance rates ought to be regulated by regulatory fiat rather than competitive markets to be somewhat peculiar. In the economics literature, typical arguments for regulation of prices rely upon the existence of monopoly or some form of market failure. In the case of the insurance business, neither argument is particularly compelling. If anything, a more compelling argument is that society is better served by relying upon competitive markets rather than regulatory fiat. Anyway, in what follows, I will sketch some of the public policy issues that are at play in this particular insurance reform.

1. Theory of price regulation[2]

According to George Stigler, public price control has two aspects:

1. Correction of monopolistic pricing (e.g., most public-utility regulation in the United States).

  • By granting firms monopoly licenses in various local domiciles, policymakers are hoping to take advantage of economies of scale in production. If there are scale economies, monopolists will face significantly lower costs of production on a per unit basis than will firms competing with each other in a competitive market environment.
  • This is a “have your cake and eat it too” strategy. Without price regulation, the benefits of these scale economies would naturally accrue to the owners of such firms. However, price regulation is imposed so that benefits accrue instead to consumers in the form of lower prices.
    • Ideally, the objective is to regulate rates so that the firm still earns a “fair” return while providing the scale economies which lead to lower consumer prices.
    • The “fair” return standard was set by a U.S. Supreme Court case which was argued in 1943 and decided in 1944 (Federal Power Commission et al. v. Hope Natural Gas Co.).
    • By providing a “fair” return, the government does not violate the “Takings” clause of the U.S. Constitution (the last clause of the 5th amendment, which reads, “nor shall private property be taken for public use, without just compensation”).

2. Provide private benefits at public expense to special interest groups.

  • Prices of farm products are regulated (raised) in most nations with the intention of improving farmers’ incomes.
  • Prior to the deregulation of the banking industry more than twenty years ago, the fixing of interest rates paid by banks was undertaken to improve bank earnings.
  • Such policies are invariably defended on various economic and ethical grounds but reflect primarily the political strength of large and well organized interest groups.

There are no natural scale economies in the production of insurance services. This is a fact that is well documented by at least two generations of rigorous empirical research. Therefore, it would appear that Stigler”s second rationale better fits the case of insurance. Originally, insurance rate regulations were imposed because there was a stated concern that insurers might be motivated to cut prices to unsustainably low levels as a way to acquire market share. Therefore, it would seem that price regulations were initially intended to benefit producers of insurance services by providing excess rates of return on their investments in the insurance business. The argument here is that such groups were successful in coalescing and bringing political pressure to bear on the regulatory authorities to produce such an outcome. This idea of regulatory “capture” was quite insightful and profound, and it (among other things) helped Stigler win the Nobel Prize in 1991.

In recent years, however, the pendulum has swung in such a way that rate suppression (as opposed to expansion) has become more the rule rather than the exception. The special interests here include regulatory agencies, the plaintiff”s bar, and consumer groups.[3] Economic theory suggests that over time, persistent regulatory suppression of insurance rates will likely cause product quality to deteriorate and limit insurance availability as insurers seek opportunities to exit the market (sound familiar?).

2. Empirical evidence on the effects of rate regulation[4]

Previous studies (using U.S. and Canadian data) have found that rate regulation:

  • reduces competition,
  • reduces availability of coverage, and
  • increases volatility of insurance premiums.

Competition is reduced by prior approval regulation because the ability to compete on price is by definition (arbitrarily) limited by the state. Availability is reduced by prior approval regulation because this form of rate regulation tends toward rate suppression; since one cannot earn a fair return in a rate-suppressed environment, there is little incentive to expand one”s business of writing insurance policies! Finally, increased volatility in insurance premiums likely results from delays in the rate approval process under prior approval rate regulation. Regulatory lags typically produce lower rate increases during periods of rapid cost growth and larger rate increases or a slower rate of reduction in periods of stable or declining claims costs (see Harrington, 2001 AEI-Brookings, available at”id=48).

The state of Illinois is unique because it does not have any formal rate regulation of automobile insurance rates whatsoever. Steve D’Arcy notes that the Illinois auto insurance market is amongst the most competitively structured insurance markets in the U.S. economy.[5] He finds that insurer loss ratios and premiums are less volatile than in regulated markets, and premium levels tend to be lower than in comparable areas. Illinois also boasts the lowest percentage of uninsured drivers, one of the lowest residual market shares, and lowest costs of insurance regulation in the entire U.S. economy.

3. Texas has a longstanding reputation for suppressing auto insurance and workers compensation rates

Although the Kramer study cited below is obviously dated, its findings are qualitatively consistent with Texas”s longstanding reputation of persistent regulatory suppression of insurance rates.

Kramer (1991) Study Rate Suppression States
Private Automobile Insurance Workers’ Compensation Coverage
Delaware Alabama New Hampshire
District of Columbia Arkansas New Mexico
Louisiana Florida North Carolina
Massachusetts Georgia Oregon
Nevada Iowa Pennsylvania
New Hampshire Kansas Rhode Island
New Jersey Kentucky South Carolina
Pennsylvania Louisiana South Dakota
Rhode Island Maine Tennessee
South Carolina Massachusetts Texas
Texas Mississippi Vermont
Missouri Virginia

Source: Kramer, S. Rate Suppression and Its Consequences. New York: Insurance Information Institute Press, 1991.

[1]For a more detailed explanation and analysis of insurance rate regulation, see the recently published Insurance Information Institute white paper entitled Rates and Regulation, available on the web at

[2]This section elaborates primarily upon George Stigler”s excellent essay entitled “Economic Theory: Price”, available online at, and applies his insights to an analysis of the insurance industry in particular.

[3]The cynical view here is that by suppressing rates, regulatory agencies are given more work to do, which enables them to expand their staffing and overall influence. The plaintiff”s bar likes rate suppression because this process renders the insurance ratemaking process into a very opaque and largely unintelligible process which makes it all the more difficult for consumers to discern the relative magnitude of the impact that the U.S. civil justice system has upon insurance rates. The reason why consumers” groups prefer low rates should be apparent, but an often overlooked second order effect derives from that fact that many of these groups are funded primarily by plaintiff”s attorney associations (e.g., Ralph Nader”s Public Citizen group is known to receive as much as 2/3 to 3/4 of its funding from plaintiff”s attorneys).

[4]For more detailed information concerning empirical evidence on the effects of rate regulation, see the recent working paper by Leadbetter, D., J. Voll, and E. Wieder, 2004, The Effects of Rate Regulation on the Volatility of Auto Insurance Prices: Evidence from Canada, presented at the 38th Annual Meeting of the Canadian Economics Association, June 2004, Ryerson University, Toronto, Ontario (available at

[5]See D’Arcy, Stephen P., 2001, “Insurance Price Deregulation: The Illinois Experience”, paper presented at the Brookings Institution Insurance Rate Regulation Conference (January 18, 2001).

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“Infectious Politics” – article about the flu vaccine shortage in today’s Wall Street Journal

In today’s Wall Street Journal, there is a very interesting and insightful article entitled “Infectious Politics” that explains why flu vaccines in particular and vaccines for infectious diseases generally are in such short supply in the United States.  The contributing factors appear to involve a combination of price controls, regulation and tort lawyers.  Of course, I made the latter point (concerning tort) the other day in my blog entry entitled “Impact of the tort system on flu vaccine availability in the United States“.

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