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Recently in Statistics/Empirical Work Category

By Martin F Grace

One of the problems in the tort reform debate is the use of simplistic statistics.  The identification of particular problems in assessing the existence of the need for tort reform or the effect of tort reform has generated a number of studies.  Many of them conflicting.  This is because they tend to be advocacy briefs rather than  disinterested research.  Robert Hunter, writing under the aegis of the Americans for Insurance Reform, is the latest into the fray.  His report finds that doctors are being gouged by their insurers.  He uses a pretty good data set of loss costs by state and he finds that the losses have not risen to reflect the crisis that is supposed to exist.  Further, he finds that the growth in losses are not that much different in the last five years (so-called crisis years) from the previous five years.  In fact the report claims that tort reform did not make a difference.  While he does show statistics, he does no statistical tests.  Not one.

Essentially what he does is look at states with a set of certain tort reform and states with fewer reforms.  He then looks at the percentage loss cost growth and uses the eyeball (it looks close to me) test to say there are no differences.  He also says that during the crisis years loss costs grew less in states with relatively few reforms and more in states with the most reforms.  Now this is pretty interesting as one would expect the reverse at first glance. However, one might actually expect states under more pressure (higher increases in loss costs, higher premiums, etc.) are more likely to put in place new reforms.  States without loss cost growth are not likely to put additional reforms in place.  This failure to control for causation or at least control for the fact that the choice of reform is an endogenous choice is quite important.

I looked at the NAIC�s page 14  (state page data) and did some simple statistical tests for the years 1994-2004.  (I looked at firms that wrote more than $200,000 in premiums in any given state and year.  This excludes companies that are not really in the medmal business.  I also didn't adjust for inflation as I was just doing this to avoid grading. I took the damage cap and non-economic damage cap information from the Appendix in Mr. Hunter's study.)


First, in Table 1 (click on Table to enlarge) I looked at the med loss ratio by state and regressed it against whether the state had a punitive damage cap limitation or a non-economic damage cap limitation. (I used a state and year fixed effect model) and found that there appears to be no statistical influence of the damage caps on the mean of the loss ratio.  This result is not uncommon and it seems to lend support to the group complaining that tort reform is a sham.  However, note that the standard deviation of the loss ratio is significant and positive.  This implies that if in the previous year the loss ratio was more volatile, one saw a higher mean loss ratio this year.  if we think about insurance pricing, price =expected losses + expense+ cost of risk.  As cost of risk increases, prices go up.  One can think of the standard deviation of the loss ratio as a proxy for the cost of risk.  As the loss ratio becomes more "uncertain", a prudent insurer will have to hold more capital to support the risk.

The question then becomes, does the cost of risk depend upon tort reforms?  In Table 2, I estimate a similar regression looking at the standard deviation of the loss ratio as the dependent variable against the dummy variables for the damage caps and the lag of last year's loss ratio.  Note that the punitive damage cap seems to have  a significant negative effect on the standard deviation �thus reducing the cost of risk. 

The only point I want to make is that the the tort reform story is more complicated than some simple averages might lead one to believe.  My regression models are also simplistic and if I had more time I'd do a better job before running off the the New York Times to make an authoritative claim. The standards for analysis in this debate are too low.  Every group has their favorite whipping boy and their statistics to back it up.  However, just looking at point estimates and saying this estimate is bigger than another to make a conclusion ... is so 1930s.   I don't think these reports would even get an average grade as an undergraduate term paper.  Shouldn't we expect more?

[cross posted at RiskProf]

By Ted Frank

I attended yesterday's AEI forum debating the Texas study of Professors Black, Silver, Hyman, and Sage. Based on their study, the authors made a broad statement in a NY Times op-ed: "The medical malpractice system has many problems, but a crisis in claims, payouts and jury verdicts is not among them. Thus, the federal 'solution' that Mr. Bush proposes is both overbroad and directed at the wrong problem." At AEI, however, Professors Black and Hyman made the following two concessions (which I paraphrase from my notes):

  • Over the long run, malpractice insurance prices reflect claim outcomes.
  • Caps on non-economic damages should reduce insurance rates.

Don't expect ATLA to acknowledge these straightforward economic principles in its above-the-fold front-page link to its press release on the study. But once everyone agrees on this central common ground, then, to paraphrase Rabbi Hillel, that's the whole tamale and the rest is just commentary.

After all, it doesn't appear to be the case that the doctors complaining about a "crisis" are concerned only about the first derivative of claims costs. The claim is also the subjective one that insurance costs are "too high" relative to the benefits of the current system of malpractice liability. One can agree or disagree with that value proposition but, once one acknowledges that insurance premiums are a function of claim costs, and further acknowledges that non-economic damage caps would reduce premiums, the authors' op-ed becomes a non sequitur. Perhaps claims costs aren't rising in such a way to cause insurance costs to rise. But proving that premise does not demonstrate that there isn't a "crisis", and doesn't demonstrate flaws in the administration proposal. Ironically, it's the op-ed that is "overbroad and directed at the wrong problem."

And it's far from clear that the premise--that there is no problem of rising risk to insurers from a change in the malpractice environment--is true. As Professor Klick noted at the conference, insurance premiums reflect not just the expected incurred cost, but a risk premium to compensate for the variance of that expectation. And the Texas study did not look at variance. Let's take a look at the Texas Department of Insurance data set used by the Texas study. What does the closed cost data look like in 2000, the year that insurance costs started to rise in earnest?

Extseq #32300902 was a $65,000,000 verdict issued by a jury on December 13, 1999. �The case appears to have been subject to a hi-lo settlement, so it wouldn't have much impact on the closed claims paid data that the Texas study relies upon -- but the fact of such a large verdict has to have had some impact on insurers' pricing. �In addition, there was a verdict of over $33 million that closed in 2000 after settling for about $11 million. �

Let's compare this to the world in 1990, the pre-2000 year in the TDI data set with the highest mean verdict. That year, the most aggressive outlier Texas jury awarded $17 million, a bit less than $23 million in 2000 dollars.

In 1990, there were about seven closed claims with verdicts above $1 million. In 2000, there were about sixteen closed claims with verdicts above $1.32 million (about $1 million in 1990 dollars).

The tail is about twice as tall at the $1 million mark in 2000 than in 1990. There are two outlier verdicts in the 2000 TDI closed claims data that average nearly twice as much as the single largest verdict in the 1990 TDI closed claims data, even after inflation. Yet the Texas study makes the blanket statement that juries weren't any more aggressive over time. Just from the TDI data, this seems to be false.

But wait, there's more. On November 3, 2000, a Dallas jury awarded $268 million to the family of a 15-year-old cerebral palsy patient who died of a medication overdose. This verdict, twelve times the size of the largest 1990 verdict in real dollars, is not in the TDI closed claims data at all, and was thus excluded from the study. The authors acknowledge the incompleteness of their data set, which omits certain self-insured entities that need not report to TDI. I don't think this critique is ambiguous, but let me make clear that I'm not accusing the authors of doing anything unethical by failing to include this data point. But they do err in overestimating the power of the conclusions that can be drawn from the data they do have. Their regressions don't account for increased variance or for the fact that the top three verdicts in twelve months averaged a record $100 million, nearly an order of magnitude higher than those of a decade ago, but the actuaries calculating insurance rates in Texas certainly did. This evidence is certainly evidence is anecdotal, but these anecdotes are large enough pebbles to distort the entire market; in the world of insurance, it's the outliers that create the need for reserves.

By Ted Frank

Dear Professors Black, Silver, Hyman, and Sage,

I was surprised at the counterintuitive preliminary results in your study covered in Reuters for which Professor Hyman was quoted. I read your paper. It seemed that 1990 figures were unusually high, so I downloaded and took a quick look at the 1990 data from the TDI website. Your paper mentions the 1988 and 1989 data collection problems, and it appears to my eye that these problems were resolved by filing closed claim forms in 1990 for a number of settlements that were actually made in 1989. See, e.g., the $14.7 million of settlements and defense costs in TDI #7800282, #7800283, #7900170, and #7900318. The payments were made in 1989, but the claims "closed" in May and June 1990. TDI #9700276 settled in August 1989, but wasn't closed until October 1990, adding $7.9 million in settlement and defense costs to the latter year. If I took the time to construct a spreadsheet macro, rather than just scrolling through, I'm sure I could find additional and similar errors. In contrast, I used 1998 as a control, and a spot-check of the "closed claim" dates for larger settlements seemed to take less time to report, and much more likely to be in the same year.

Did your paper sort data by the Q1G "closed claim" field, or by the Q1E "Date of settlement" field? Because it would appear that there is a strong possibility that the 1990 "closed claim" data, sorted by Q1G, is not directly comparable to that of later years, where data collection was more consistent. From the tables and graphs in your paper, it would appear that a 1991-2002 dataset would result in substantially different conclusions than a 1990-2002 dataset.
In addition, it seems to me that, given the variance involved in medical malpractice verdicts, there are problems of small sample size even in a state as large as Texas. An outlier of two $14 million settlements (as happened in 1990 TDI #7700251 and #8500332) can throw off the entire study. Was there a reason that a three-year moving average wasn't considered?

Finally, how much do malpractice rates increase when subjected to the same deflationary factors that your paper applied to malpractice expenses? I didn't see a chart on that subject, though the former was repeatedly described as a "spike." It seems unfair to compare the real rates of malpractice insurance expenses to the nominal malpractice insurance rates.


Ted Frank



Rafael Mangual
Project Manager,
Legal Policy

Manhattan Institute

Published by the Manhattan Institute

The Manhattan Insitute's Center for Legal Policy.