Reducing Medical Malpractice Loss Reserve Volatility Through Tort Reform

North American Actuarial Journal

ISSN: 1092-0277 (Print) 2325-0453 (Online) Journal homepage: https://www.tandfonline.com/loi/uaaj20

Patricia H. Born, Evan M. Eastman & W. Kip Viscusi

To cite this article: Patricia H. Born, Evan M. Eastman & W. Kip Viscusi (2020) Reducing Medical Malpractice Loss Reserve Volatility Through Tort Reform, North American Actuarial Journal, 24:4, 626-646, DOI: 10.1080/10920277.2020.1733616 To link to this article: https://doi.org/10.1080/10920277.2020.1733616

Published online: 14 Apr 2020.

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Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=uaaj20 North American Actuarial Journal, 24(4), 626–646, 2020 # 2020 Society of Actuaries ISSN: 1092-0277 print / 2325-0453 online DOI: 10.1080/10920277.2020.1733616

Reducing Medical Malpractice Loss Reserve Volatility Through Tort Reform

Patricia H. Born,1 Evan M. Eastman,1 and W. Kip Viscusi2 1Dr. William T. Hold/The National Alliance Program in Risk Management/Insurance, College of Business, Florida State University, Tallahassee, Florida 2Vanderbilt Law School, Vanderbilt University, Nashville, Tennessee

This study examines how tort reform affects uncertainty in insurance markets by testing whether noneconomic damage caps influence reserving volatility for medical malpractice insurers. Using a panel of insurers from 1986 to 2009, we estimate the determinants of loss reserve error volatility and focus on how this volatility is influenced by the percent of premiums an insurer writes that are subject to noneconomic damage caps. We find empirical evidence that tort reform reduces reserve volatility over the subsequent 3- and 5-year periods, consistent with tort reform improving insurers’ loss forecasting ability. Our findings address outcomes of tort reform that are prominent concerns of legislators, regulators, and policyholders. This article contributes both to the literature examining the insurance market effects of tort reform and to the literature examining loss reserving practices.

1. INTRODUCTION For decades now, states have considered reforms of the legal environments in which courts consider medical malpractice tort cases. The impetus for tort reform is generally based on a range of goals that target problems in the legal environment, the health care environment, and the medical malpractice insurance environment. Overarching objectives typically include reducing the frequency and severity of medical malpractice lawsuits, restoring the availability of high-risk medical procedures, reducing the number of unnecessary medical services performed for defensive reasons, and mitigating the rising cost of malpractice insurance coverage. Despite the long history of reform efforts, beginning with California in the 1970s, and following several waves of activity since the mid 1980s, additional reforms continue to draw the attention of state legislatures. In early 2019, for example, Florida began reconsidering a cap on noneconomic damages in medical malpractice cases. The previous cap enacted in 2003 was declared unconstitutional in 2017.1 The enduring interest in “tinkering” with the medical malpractice tort environment has important implications for research- ers. First, evaluations of 30-plus years of tort reform enactments should provide ample evidence as to the consequences of various measures; the existing literature is, in fact, fairly consistent in identifying significant consequences of reform to the affected markets, such as an increase in the underwriting profitability of medical malpractice insurers.2 Still, among those states that have enacted reform measures, there is no consistency in the particular bundle of reform measures enacted from state to state or any noticeable convergence in state approaches over time.3 In this context, we propose the evaluation of an important consequence of reform that, to our knowledge, has not received attention in previous empirical analyses. Our findings contribute to the research on tort reform, with an explicit consideration of how medical malpractice insurers establish reserves to pay estimated claims, and how these reserves are adjusted over time as claims are resolved. Our focus on reserving

Address correspondence to Patricia H. Born, Dr. William T. Hold/The National Alliance Program in Risk Management/Insurance, College of Business, Florida State University, Tallahassee, FL 32306. E-mail: [email protected] 1The 2003 caps on noneconomic damages were set at $500,000 for most cases. If malpractice caused death or a vegetative state, the cap was set at $1 million. See Fla. Stat. Ann. § 766.118. 2See Mello and Kachalia (2016) and Viscusi (2019). While the unique effects of reform measures that occur in bundles are difficult to isolate, the noneconomic damages cap is consistently reported to have significant influence on insurer underwriting performance. 3Impetus from changing exogenous conditions, such as changes in the health insurance market, might explain this inconsistency in reform over time. State differences on other dimensions—e.g., demographic, political—also appear to explain why some states take an interest in enacting reform or why some reform measures are more palatable than others (Deng and Zanjani 2018).

626 MEDICAL MALPRACTICE RESERVE VOLATILITY 627 behavior in reformed versus nonreformed environments provides a perspective on the benefits of tort reform that extend beyond their influence on insurer profitability. Specifically, we find that tort reform is associated with lower reserve volatility, which has important implications for pricing and, consequently, for capital requirements and reinsurance adequacy.4 Economists and legal studies scholars have had a long-standing interest in the overall effects of tort reform dating back to the mid 1970s, when state legislatures enacted the first rounds of tort reform. Much of the impetus for the initial tort reform effort was to address the effect of the changes in tort law on uncertainty in insurance markets (e.g., Priest 1987). A subset of the subsequent empirical literature on the effect of tort reform on insurance markets has addressed the impacts on premiums, losses, and profitability (e.g., Born and Viscusi 1994; Viscusi and Born 1995; Viscusi and Born 2005; Born, Viscusi, and Baker 2009; Grace and Leverty 2013). However, to the best of our knowledge, this literature has not examined the impact of tort reform on the uncertainties that tort liability generates in insurance markets. Medical malpractice liability insurance has been a prominent focus of tort reform efforts. This market is of particular interest because crises in medical malpractice markets have adverse ramifications for supply in health care markets (e.g., Avraham, Dafny, and Schanzenbach 2012; Born, Karl, and Viscusi 2017). In its 2012 decision upholding the constitutionality of noneconomic damages caps, the Kansas Supreme Court concluded: “We hold that it is ‘reasonably conceivable’ under the rational basis standard that imposing a limit on noneconomic damages furthers the objective of reducing and stabilizing insurance premiums by providing predictability and elimi- nating the possibility of large noneconomic damages awards.”5 Despite the pertinence of the relationship between tort reform and insurance market stability to the constitutionality of tort reform, ours is the first study, to our knowledge, to show that medical malpractice tort reform reduces insurer reserving volatility. Our research provides new insight into insurer claim operations, particularly relating to the effects of tort reform on reserving practices. The determination of adequate initial reserves for a liability claim relies largely on the interpretation of the eligibility of the claim, the extent of coverage dictated in the contract, and the expected damages award. Insurers can estimate the damages award level using historical information on past claims of a similar nature, although the amount remains uncertain for many reasons, including the inability to assess the extent of long-term injury at the time the claim is filed. A claims investigation process reduces the uncertainty with respect to injuries as the case is resolved, but information about how similar cases are currently resolving in the legal system can increase uncertainty if award amounts for these similar claims are inconsistent.6 To the extent that a reform measure, such as a cap on noneconomic damages awards, leads to more consistent legal outcomes, the need to adjust reserves over the course of the case should be lessened. Since loss reserves are typically a property and casualty insurer’s largest balance sheet liability, improved accuracy reduces pressure on insurer surplus, improving capital allocation and capital budgeting.7 Our findings regarding reserve volatility also have implications for state insurance regulators. One of the primary tasks of state insurance regulators is to ensure the solvency of insurers. Since inadequate reserves are one of the leading causes of property-casualty (P/C) financial impairment (A.M. Best 2009; A.M. Best 2018) and volatile reserving is associated with lower financial strength (Carson, Eastman, and Eckles 2018), how tort reform influences reserving practices has important implications for solvency.8 The estimates of the impact of tort reform on the volatility of reserves also have potential implications for medical malpractice policyholders (i.e., health care providers). Prior research indicates that insurance consumers are risk sensitive in that they demand lower prices when insolvency risk is higher (Sommer 1996; Epermanis and Harrington 2006). If higher reserve volatility is associated with higher insolvency risk, then reserve volatility can influence the price insurers are able to charge. This relationship suggests that tort reform has the potential to have an indirect effect on rates charged by medical malpractice insurers (Danzon 1986). In a similar vein, prior work finds evidence that reserve volatility is priced into an insurer’s debt capital, proxied as the price of insurance (Eckles, Halek, and Zhang 2014). Any finding of a relation between tort reform and reserve volatility, therefore, has implications for insurance prices in medical malpractice markets. Using ordinary least squares, we regress insurer-level reserve volatility on the percent of premiums written in environments with a cap on noneconomic damages and control variables theorized to determine insurer reserve volatility. Our sample covers all property-casualty (P/C) insurers with operations in medical malpractice insurance from 1986 to 2009. Since each state forms its own insurance market and since states adopted tort reform measures at different points across time, our measure of

4For a particular block of business, the size of the loss reserves in successive years may influence the setting of premiums since incurred losses include estimates of loss reserves. 5Miller v. Johnson, No. SC 99,818 (Kan. Oct. 5, 2012), at 40. 6Geistfeld (2011) refers to this as “legal ambiguity” and suggests that it increases insurer cost of capital. 7Reserve adjustment processes vary from ad hoc extrapolation or “detrending” of historical data to the use of Bayesian models (Zhang, Dukic, and Guszcza 2012). See, for example, Froot (2007) for considerations for capital budgeting, including carrying and adjustment costs. 8Seven percent of all P/C insolvencies between 2000 and 2016 were medical professional liability insurers, indicating that these insurers are at risk of potential insolvency (A.M. Best 2016). 628 P. H. BORN ET AL. tort reform is unlikely to be influenced solely by either time series or state-specific factors, allowing us to accurately isolate the relation between tort reform and reserve volatility. Our results are robust to different reserve volatility windows, to the inclusion of state fixed effects, and to different econometric specifications. We find that caps on noneconomic damages are negatively and statistically significantly associated with ensuing reserve volatility. Insurers that have a higher proportion of medical malpractice premiums written in states with caps tend to experience lower reserve error volatilities over the subsequent 3- and 5-year periods. This finding is consistent with tort reform providing a benefit to medical malpractice liability insurers and indicates that losses become more predictable with tort reform in place. This article makes several contributions to the literature. First, we contribute to the literature examining the impact of tort reforms, generally, and the impact of tort reforms on insurance markets, specifically. As we noted in the preceding, a large literature has tested how tort reform impacts liability insurance markets, with a focus on how premiums, losses, and profitability are affected by tort reform. Notably, Born, Viscusi, and Baker (2009) test how tort reform influences medical malpractice insurer ultimate losses by accounting for reserve development over time. Our study extends Born, Viscusi, and Baker (2009) by testing how tort reform influences reserving volatility following the enactment of tort reform.9 We also contribute to the literature that examines insurance reserving practices. Insurer loss reserves are regularly used in the accounting and insurance literature as a measure of accounting discretion or earnings management (e.g., Petroni 1992; Gaver and Paterson 2004; Grace and Leverty 2010). This literature generally focuses on predictions related to the signed reserve error—for example, an insurer can underestimate losses to avoid reporting negative earnings (Beaver, McNichols, and Nelson 2003) or can overestimate losses to convince regulators to approve a rate increase request (Grace and Leverty 2010). Recent studies also examine how reserve volatility influences the cost of capital (Eckles, Halek, and Zhang 2014) or financial strength ratings (Carson, Eastman, and Eckles 2018). We contribute to this literature by studying how the legal environment influences reserving practices by specifically looking at how changes in the tort environment affect loss reserve volatility. In the context of insurer reserving, prior studies examine how rate regulation (Nelson 2000; Grace and Leverty 2010) and solvency regulation (Petroni 1992; Gaver and Paterson 2004) influence reserving; our study is the first, to our knowledge, to examine how changes to the tort environment affect the volatility of insurer accounting estimates. Finally, we contribute to the literature examining dynamics of medical malpractice insurance markets (e.g., Neale, Eastman, and Drake 2009; Born and Boyer 2011). To the extent that tort reform reduces volatility in loss reserving, it may free up more capital for insurers to invest in other strategic purposes. State tort reform activities might, therefore, help to explain changes in market share, competitiveness, and entry and exit across state markets. The rest of this article proceeds as follows. In section 2 we provide background on tort reform and insurer loss reserves. In section 3 we provide our testable hypotheses. Section 4 describes our research design and section 5 presents our results. We briefly conclude in section 6.

2. BACKGROUND 2.1. Tort Reform Over the past several decades, states have enacted various reforms in their legal environments designed primarily to combat the growing frequency and severity of tort claims. In most states, the specific targets of these efforts were torts against medical providers, where the increasing magnitude of judgments against providers has had serious consequences for the medical com- munity: A growing fear of litigation affected the supply of certain health care services and the availability of medical malpractice insurance coverage. State tort reform efforts—defined by various packages of reform measures—have changed the behavior of medical providers (Kessler and McClellan 1996; Kessler and McClellan 2002; Sloan and Shadle 2009; Avraham, Dafny, and Schanzenbach 2012; Paik et al. 2012; Born, Karl, and Viscusi 2017), the composition of medical malpractice cases (Danzon 1986; Lee, Browne, and Schmit 1994; Holtz-Eakin 2004; Avraham 2007; Hyman et al. 2009; Paik et al. 2012), and efficiency in the courts (Friedson and Kniesner 2012). Consequently, these measures have had a significant effect on the performance of medical malpractice insurance companies (e.g., Born and Viscusi 1994; Viscusi and Born 1995; Viscusi and Born 2005; Born, Viscusi, and Baker 2009; Grace and Leverty 2013).10

9In unreported tests we also confirm that Born, Viscusi, and Baker’s(2009) result holds in our sample. We do this by testing how the percent of medical malpractice premiums in tort reform environments impacts signed insurer loss reserve errors. We find that there is a positive and statistically significant coefficient estimate on our tort reform variable when estimating the determinants of signed, scaled reserve errors, indicating that insurers in tort reform environments tend to overestimate initial losses, consistent with what Born, Viscusi, and Baker (2009) find using a different methodology. 10We do not evaluate here the drivers for state tort reform enactments, but several theories have been proposed. See, for example, Stigler (1971), Peltzman (1976), Joskow and Noll (1981), Dixit (1996), Berry et al. (1998), and Deng and Zanjani (2018). MEDICAL MALPRACTICE RESERVE VOLATILITY 629

Tort reform measures that are commonly considered in the existing literature include reform of joint and several liability rules, modifications to the consideration of collateral sources, caps on damages (noneconomic, punitive, or total), periodic payments, limitations on liability, and limitations on attorney contingency fees.11 Tort reform measures take different forms across states. For example, some states modified the collateral source rule to allow courts to reduce the plaintiff’s damages by the amount of other benefits received, while others require this reduction. Further, while most measures refer specifically to medical malpractice torts, some extend to a broader set of torts (e.g., automobile liability). States enacted most reforms in several waves over the past decades, but there is significant variation across states and over time in the particular measure or bundles of measures enacted. The most consistently influential tort reform is that of noneconomic damages caps (Viscusi 2019), which is the primary focus of our analysis here.12 Tort reform has the avowed purpose of reducing the cost of tort litigation and damages by reducing the frequency and/or severity of claims. The implication of these changes for the insurance industry is a change in the nature of liability claims against medical providers, creating an environment with, presumably, greater certainty as to how these claims would be disposed. Existing evaluations of the effects of tort reform confirm that medical malpractice insurers—the primary payer of claims against providers—benefited from these measures; most notably, caps on noneconomic damages awards are associated with a significant increase in underwriting performance following reform (e.g., Barker 1992; Viscusi et al. 1993; Weiss, Gannon, and Eakins 2003; Viscusi and Born 2005).13 The evidence also suggests that reforms are responsible for maintaining a more stable market for coverage through potential crisis periods (Born, Karl, and Montesinos-Yufa 2019). In addition, Grace and Leverty’s (2013) analysis indicates that reforms that were eventually declared unconstitutional or otherwise struck down had little effect on insurer losses, but reforms that were unchallenged or upheld in court served to reduce the level of losses incurred by medical malpractice insurers. The existing literature provides some evidence that the process of resolving claims is affected by tort reform. For example, using the Texas closed claims database for a period before and after the state’s 2003 reform enactment (i.e., 1988 to 2007), Friedson and Kniesner (2012) find that tort reforms are associated with smaller but quicker payouts. The authors evaluate only settlement amounts and time to resolution for claims that are settled in 3 years or less, but their finding of quicker payouts implies that tort reform may be associated with more timely information about how claims will be resolved.14 Nonetheless, while evidence supports the assumption that tort reform has reduced uncertainty in how claims will be disposed for medical malpractice insurers, it is unclear how this effect plays out over time. Born, Viscusi, and Baker (2009) compare reported losses to 5- and 7-year developed losses and find that tort reforms are associated with even larger improvements in underwriting performance when the analysis considers developed medical malpractice losses incurred by insurers as opposed to initially reported values.15 They conclude that insurers are initially pessimistic regarding the benefits of reform measures; insurers tend to over-reserve following reform, but adjust loss estimates down over time. This result motivates our consideration of how these adjustments occur over time. Specifically, we expect that reduced uncertainty in the legal environment will manifest in smaller absolute adjustments in loss reserves from year to year, as the insurer has fewer uncertain outcomes from which to base these adjustments.

2.2. Insurer Loss Reserves Insurer loss reserves are typically the largest liability for property-casualty insurers. The insurer loss reserve consists of three components: (1) losses reported and adjusted, but not yet paid; (2) losses reported, but not yet adjusted; and (3) incurred but not reported (IBNR) losses.16 Due to the inherent uncertainty of the loss reserve—particularly for IBNR losses—this liability account requires estimation from actuaries and management. Management will typically pick the actual loss reserve from within a range recommended by company actuaries. Over time, insurers are required to report updates to their initial loss

11Avraham (2019) provides a comprehensive review of tort reform measures. State tort reform enactments are summarized by the American Tort Reform Association and published on its website, www.atra.org. 12We consider the potential influence of other reforms in our robustness tests. 13Born and Neale (2014) find evidence that noneconomic damage caps set under $250,000 are more effective at reducing medical malpractice losses incurred by insurers than caps above that amount, which are less likely to be binding. 14While few claims actually go to trial, outcomes of both trials and settlements can influence the damages awarded by juries and settlement amounts in current and future cases. This is one reason why reserves on many known claims are adjusted over time. 15Losses reported in a given year are an estimate of the amount that will ultimately be paid for claims filed that year. Insurers must report any adjustments to these losses in subsequent years. Born, Viscusi, and Baker (2009) analyze this development of losses 5 and 7 years out, as they may more accurately reflect the influence of the reforms. 16Insurers have more information about the likely disposition and their liability for reported losses that are adjusted versus those that are not yet adjusted. However, there remains some uncertainty in all reported losses until they are paid. 630 P. H. BORN ET AL. reserve estimates, which are referred to as development. Comparing developed loss reserves to initial estimates provides information on how far off the initial loss estimates are. This difference is referred to as the loss reserve error. A large academic literature examines the determinants of insurer loss reserve errors. These errors provide a strong measure of accounting discretion since they are a material accrual and they provide lower measurement error compared to traditionally used measures of accounting discretion (e.g., Jones 1991) since insurer statutory reporting allows for an explicit comparison between initial and ultimate losses. While a portion of the insurer loss reserve error is considered nondiscretionary (i.e., it is inherently difficult to estimate future losses), reserve error studies argue that managers exercise discretion over reserve estimates in response to financial reporting incentives (Grace and Leverty 2012). Specifically, this literature proposes that property-casualty insurers can intentionally overestimate or underestimate initially reported losses relative to ultimately paid losses. This stream of literature has found evidence that insurers manage their reported loss reserves in response to incentives related to solvency regulation (Petroni 1992; Gaver and Paterson 2004), rate regulation (Nelson 2000; Grace and Leverty 2010), and earnings smoothing (Beaver, McNichols, and Nelson 2003). Within the reserve error literature, there are several studies that have specifically examined reserving practices for medical malpractice insurers. Harrington, Danzon, and Epstein (2008) examine loss development of medical malpractice insurers during the soft market in the late 1990s. They find evidence that insurers underestimated losses during this soft market period and that growing insurers specifically tended to experience positive loss development. Lei and Schmit (2008) and Born and Boyer (2011) test how organizational form influences medical malpractice reserving. Lei and Schmit (2008) find evidence that physician-directed medical malpractice insurers tend to reserve more conservatively. Born and Boyer (2011) examine differences in reserving between stock, mutual, reciprocal, and risk retention groups (RRGs) differentiated by whether they wrote claims made or occurrence policies. They find that stock and mutual insurers exhibit more variability in their reserving, while RRGs tended to reserve more accurately. Finally, Barth, Eastman, and Eckles (2019) examine determinants of reserving errors across all lines of business, which includes an examination of medical malpractice reserving errors, specifically. Though medical malpractice reserve errors are not the focus of their study, their findings indicate that medical malpractice insurers manage reserves in response to, among other factors, group membership, percent of long-tailed lines, and taxes. While most of the reserving literature focuses on intentional misstatements of the signed reserve error, recent studies have examined the determinants and outcomes associated with reserve volatility. Eckles, Halek, and Zhang (2014) use the volatility of insurer loss reserve errors as a measure of accruals quality and test whether lower accruals quality (higher reserve volatility) is related to the cost of equity and debt capital. While they find evidence that accruals quality is priced into debt capital (i.e., the price of insurance), they are unable to conclude that accruals quality is priced into equity capital.17 Song (2016) examines the determinants of insurer reserve volatility, specifically focusing on the influence of group membership and internal capital market (ICM) transactions. She finds empirical evidence that suggests insurers use reserving and group membership as substi- tutes—insurers that are members of groups tend to have lower reserve volatility, consistent with internal capital market transactions serving to smooth performance. Carson, Eastman, and Eckles (2018) examine the role reserve volatility plays in determining insurer financial strength ratings.18 Their evidence is consistent with a ratings penalty being applied to insurers with noisy reserves, indicating higher insolvency risk.

3. HYPOTHESIS DEVELOPMENT By design, caps on noneconomic damages should reduce reserving uncertainty if they effectively constrain the amounts for which medical malpractice insurers are held responsible and, consequently, facilitate a more accurate assessment of the ultimate damages arising from claims. Unlike economic losses, noneconomic damages are less predictable because jurors receive limited guidance on how to measure the types of damages they are allowed to award.19 Consistent with this expectation, Born, Viscusi, and Baker (2009) find empirical evidence that medical malpractice insurer ultimate losses are lower in tort reform

17Chen, Lu, and Weiss (2018) extend Eckles, Halek, and Zhang (2014) by introducing direct and indirect effects of information risk (accruals quality) on the cost of equity capital. They find evidence that the overall effect of information risk on the cost of equity capital is negative. 18Eckles, Halek, and Zhang (2014) and Carson, Eastman, and Eckles (2018) decompose reserve volatility into innate and discretionary components. We do not perform a similar decomposition, for two reasons. First, we do not have a theoretical reason to differentiate between innate and discretionary reserve volatility when examining the impact of tort reform. Second, both previous studies use reserve volatility as an independent variable, allowing them to separately examine the impact of innate versus discretionary volatility. Our study is interested in the determinants of reserve volatility, meaning this variable is used as a dependent variable. We are already, therefore, examining the impact of tort reform after controlling for relevant (discretionary and innate) factors. 19Bavli and Mozer (2019, 405) indicate that “damage awards for pain and suffering and punitive damages are notoriously unpredictable. Courts provide minimal, if any, guidance to jurors determining these awards, and apply similarly minimal standards in reviewing them.” MEDICAL MALPRACTICE RESERVE VOLATILITY 631

TABLE 1 Sample Selection Table Insurer-years in P/C Annual Statements from 1985 to 2016 68,393 Less insurer-years unable to merge with DSTLR or Schedule P (17,739) 50,654 Less insurer-years with negative initial or developed reserves (267) 50,387 Less insurer-years with non-positive Medical Malpractice net premiums (41,575) 8,812 Less insurer-years with insufficient data to calculate Reserve Vol 3 (3,887) 4,925 Less insurer-years with missing control variables (2,828) 4,310 Less insurer-years with percent of medical malpractice business < 75 percent (2,213) Full Sample 2,097 Note: This table summarizes our sample selection process. Our final sample of 2,097 insurer-year observations represents insurers from 1986 to 2009 when using our 3-year loss reserve error volatility measure. Our analyses using our 5-year loss reserve volatility measure require lead data from 2008 and 2009, so these analyses consist of 1,803 insurer-year observations from 1986 to 2007. environments. Our expectation here is that beyond reducing ultimate losses, caps on noneconomic damages also decrease the variability in amounts awarded in medical malpractice cases, and thereby reduce the need for annual reserve adjustments. By making ultimate losses more certain, insurers should be able to reserve with more consistency, thereby reducing reserving volatility in tort reform environments. We therefore propose the following hypothesis: H1: Higher percentages of medical malpractice premiums subject to noneconomic damage cap tort reforms are associated with lower subsequent reserve volatility. Many, but not all, noneconomic damages reform measures were enacted by states in bundles with other tort reform measures, including modifications to joint and several liability, modifications to collateral sources rules, and caps on punitive damages. We focus on the noneconomic damages cap in our research because it is consistently the most influential reform measure when evaluating insurer underwriting performance. Prior research that has attempted to estimate the unique influence of other reform measures has met with limited success (Viscusi and Born 2005), but we consider their potential influence on reserve volatility in our robustness tests in the following.20

4. RESEARCH DESIGN 4.1. Data We use data from several sources. First, we use data from annual statutory filings P/C insurers make with state insurance regulators that are compiled by the National Association of Insurance Commissioners (NAIC). These filings contain detailed financial information on each insurer including their loss development and geographic distribution of premiums. Our data on tort reforms are from Avraham’s(2019) Database of State Tort Law Reforms (DSTLR), edition 6.1. Table 1 provides a description of our sample selection process. We start with all insurers in the NAIC P/C annual statutory filings between 1985 and 2016. We then exclude observations that we are unable to merge with either our tort reform or reserve error measure (which we describe in detail in the following). We then further exclude insurer-years with negative initial or developed reserves (Beaver, McNichols, and Nelson 2003). Since we expect reforms will have a bigger impact on insurers that are primarily involved in writing medical malpractice, we include only insurers that have positive premiums written in

20Since approximately one in five tort reforms in the United States was ruled unconstitutional between 1985 and 2005, the potential for tort reform to be undone by the courts is a serious possibility (Grace and Leverty 2013, 1253). Grace and Leverty (2013), however, note that while insurers will respond to their institutional and legal environments, their response is also partially based on expectations regarding whether a law will eventually be ruled unconstitutional. Specifically, Grace and Leverty (2013) hypothesize that tort reform that is eventually overturned (i.e., temporary tort reform) will have less of an effect on insurer premiums and losses relative to tort reform that remains in place (i.e., permanent tort reform). In analysis not reported here, we find that both temporary and permanent tort reforms are associated with decreasing reserving volatility. Moreover, we document no statistically significant differences between permanent and temporary reforms. 632 P. H. BORN ET AL. medical malpractice, and those for whom medical malpractice accounts for more than 75% of their underwriting business.21 We then exclude insurer-years with insufficient data to construct our reserve error volatility measure.22 Finally, we exclude observations without necessary data to construct our control variables. We winsorize all continuous variables at the 1 and 99% levels. For our Reserve Vol 3i,t (Reserve Vol 5i,t) variable, described in detail in the following, this results in 2,097 (1,803) insurer-year observations representing 233 (216) unique insurers from 1986 to 2009 (1986 to 2007).

4.1.1. Measuring Tort Reform As already noted, we rely on Avraham’s(2019) DSTLR database to construct our tort reform measure. This database is fre- quently used in studies examining various aspects of tort reform (e.g., Grace and Leverty 2013; Deng and Zanjani 2018). We focus on noneconomic damage caps in our analysis of tort reforms because prior research indicates that this measure has had the greatest influence on insurer underwriting performance (e.g.,Viscusi 2019). Following Born (2001) and Born, Viscusi, and Baker (2009), we collect data from the state pages of the annual statutory statements. These data include information on direct premiums written in each state for certain lines of business. As the focus of our study is on medical malpractice insurance, we collect the amount of direct premiums written in medical malpractice in a given state in a given year.23 Combining each state page with the DSTLR data on noneconomic damage caps, we construct the following variable: P ðPremiums Written Nonecon Þ ¼ i, s, t P i, s, t s, t Noneconi, t ð Þ (1) i, s, t Premiums Writteni, s, t

where Premiums Writteni,s,t is insurer i’s direct premium written in medical malpractice in year t in state s. Nonecons,t is a binary variable equal to 1 if state s had passed noneconomic damage cap tort reform in year t and 0 otherwise.24 Overall, the variable, Noneconi,t represents the percentage of insurer i’s medical malpractice direct premiums written that are subject to noneconomic damages tort reform in year t. Table 2 provides a summary for the initial year of passage for states that passed noneconomic damage caps between 1980 and 2016, and the year in which the cap was declared unconstitutional (listed in italics), if relevant.

4.1.2. Measuring Reserve Volatility To construct our measure of reserve volatility, we first construct each insurer’s loss reserve error. We require data from Schedule P of each insurer’s annual statutory filings. Schedule P—Part 2 provides data on incurred losses and loss development for each insurer.25 Notably, in addition to providing loss reserve development for the entire insurer (i.e., the sum of all lines of business), Schedule P also provides loss development broken down by certain lines of business. For our study, we focus on loss development for medical malpractice insurance.26 Table 3 provides an example of Schedule P—Part 2F Section 1 from the Medical Professional Mutual Insurance Company in 2016. The numbers in the table are losses incurred, which statutory accounting defines as the sum of paid losses and the

21Born, Viscusi, and Baker (2009) require insurers to have at least $1 million in premiums to remain in their sample. We perform a robustness test keeping only insurers with at least $1 million in medical malpractice premiums written. Our results are unchanged. 22 We require lead years to construct the Reserve Vol 3i,t and Reserve Vol 5i,t measures since they are measured from t to t þ 2 and from t to t þ 4, respectively. For each measure we require only 2 years of scaled reserve errors to calculate the volatility, aside from insurer-years at the end of the sample, since all observations in these years would have only two observations. Therefore, our analysis sample for Reserve Vol 3i,t is from 1986 to 2009 and the Reserve Vol 5i,t sample is from 1986 to 2007. 23Medical malpractice direct premiums are listed on line 11 of the “Exhibit of Premiums and Losses (Statutory Page 14),” which an insurer files annually for each state in which it operates. From 1986 to 2008 this line is labeled “Medical malpractice.” From 2009 to 2016 this line is labeled “Medical professional liability.” 24Avraham (2019) indicates that reforms that are effective on or after July 1 are coded as belonging to the following year. Noneconomic damage caps range from $200,000 to $1.16M and some states have changed the cap amount over our sample period. For tractability, we treat all caps equally in our

Noneconi,t variable, although we expect that smaller caps will have a larger influence on loss reserve error volatility. 25The incurred losses reported in Schedule P—Part F include both reported losses and IBNR losses. 26Medical malpractice insurance loss development reporting in Schedule P has changed over the years. From 1986 to 1988 medical malpractice development was reported in Schedule P—Part 2C and only 5 years of development were reported. Starting in 1989, insurers began reporting 10 years of loss development. The schedule reporting medical malpractice development was renamed to Schedule 2—Part F from 1989 to 1992. Starting in 1993, insurers began reporting medical malpractice occurrence and medical malpractice claims-made policies separately in Schedule P—Part 2F Section 1 and Schedule P—Part 2F Section 2, respectively. Since early years of our sample report medical malpractice loss development on an aggregate basis, we combine loss development for occurrence and claims-made policies in our analyses. A separate analysis for claims-made and occurrence policies using only data from 1993 yielded quantitatively similar results. MEDICAL MALPRACTICE RESERVE VOLATILITY 633

TABLE 2 Tort Reform Summary—Enactments and Strike Downs

Year States

1980 1981 1982 1983 1984 1985 South Dakota 1986 Alaska, Missouri, Washington, West Virginia, Wisconsin 1987 Alabama, Colorado, Florida, Florida, Hawaii, Kansas, Maryland, Massachusetts, Michigan, Minnesota, New Hampshire 1988 Idaho, Oregon, Utah, Washington 1989 Minnesota 1990 1991 Alabama, New Hampshire, Ohio 1992 1993 1994 1995 Illinois, Wisconsin 1996 Montana, North Dakota, South Dakota 1997 Illinois, Ohio, Ohio 1998 Alaska 1999 Oregon 2000 Maine 2001 2002 2003 Florida, Mississippi, Nevada, Ohio, West Virginia 2004 Oklahoma, Texas 2005 Georgia 2006 Alaska, Illinois, South Carolina, Wisconsin 2007 2008 2009 Georgia, Illinois 2010 2011 2012 Mississippi, Missouri, North Carolina, Tennessee 2013 2014 2015 Utah 2016

Note: This table summarizes the passage and repeal of state noneconomic caps over time. Certain states appear twice if they either passed an update to the existing noneconomic damage cap or if a law was struck down but subsequently passed again. Italics mark the year that a reform was struck down. Most states that do not appear in the table have not passed noneconomic damage cap tort reform, although some states passed tort reforms prior to 1980. These data are from Avraham’s(2019) Database of State Tort Law Reforms (DSTLR) edition 6.1, available from SSRN. loss reserve. Losses incurred are estimated and reported in the year incurred (the accident year) and subsequently revised. For example, in column 6 of Table 3, Medical Professional Mutual estimated losses for 2011 in 2011 to be $144,027 (reported in thousands). By 2016, Medical Professional Mutual revised this initial estimate to be $90,030 (in column 11). The difference 634

TABLE 3 Schedule P—Part 2F—Section 1 Summary

incurred net losses and defense and cost containment expenses reported at year end ($000 omitted) 1 Accident Year 2 2007 3 2008 4 2009 5 2010 6 2011 7 2012 8 2013 9 2014 10 2015 11 2016

Prior 722,279 645,054 579,581 542,333 507,515 493,365 483,176 472,852 470,785 470,408

2007 169,099 164,064 151,163 150,695 135,613 123,814 119,054 113,583 110,753 111,105 AL. ET BORN H. P. 2008 168,805 162,729 142,996 121,533 119,050 111,538 105,522 106,296 105,630 2009 164,267 148,917 117,290 105,081 100,845 92,041 90,075 87,102 2010 159,437 138,169 128,977 118,798 113,973 103,150 101,374 2011 144,027 134,788 124,773 107,912 104,649 90,030 2012 141,743 139,501 134,775 108,483 109,987 2013 135,247 133,779 116,138 114,920 2014 132,885 130,428 119,828 2015 131,108 127,195 2016 122,339

Note: This table contains data from the National Association of Insurance Commissioner’s annual statutory filing. This excerpt is from the 2016 annual statement submitted by the Medical Professional Mutual Insurance Company (NAIC# 10206). We construct reserve errors as Incurred Lossest – Incurred Lossestþn .Since we use 5-year errors, n is 5. From the table, we take the bold value in column 6 (144,027) and subtract from that total the bold value in column 11 (90,030). This difference is the raw reserve error for 2011, which equals 53,997 in this example. This total will be positive if an insurer over-reserved and negative if an insurer under-reserved. MEDICAL MALPRACTICE RESERVE VOLATILITY 635 between these two values is referred to as the insurer loss reserve error. For Medical Professional Mutual, therefore, its reserving error for 2011 is $53,997 ($144,027-$90,030). Positive values indicate over-reserving (i.e., initial estimates were higher than ultimate losses), while negative estimates indicate under-reserving (i.e., initial estimates were lower than ultimate losses). In this study, we calculate accident year reserve errors instead of the more commonly used calendar year reserve errors (Bath, Eastman, and Eckles 2019).27 Given our research question—focusing on the impact of tort reform on reserving accuracy—using accident year reserve errors is consistent with tort reform influencing policies written in a given accident year, but not necessarily having a retroactive influence on previously written policies. For example, if a state were to enact tort reform in 2011, we would expect this change to the legal environment to affect policies written (and losses incurred) in 2011, but not necessarily policies (or losses incurred) in 2010. Using calendar year losses would include prior accident years, which is not appropriate given our research question.28 We calculate our reserve error variable, Errori,t, as follows:

Incurred Lossesi, tIncurred Lossesi, tþ5 Errori, t ¼ (2) Assetsi, t

Note two characteristics of our measurement of insurer loss reserve errors. First, we scale by total assets to account for differences in insurer size. Prior studies have generally found their results to be robust to using different scaling factors (e.g., Petroni 1992; Beaver, McNichols, and Nelson 2003; Grace and Leverty 2010).29,30 Second, we use developed losses 5 years in the future as our proxy for ultimate losses (5-year errors). Five-year errors are generally the standard across the reserving literature as this allows for a trade-off of allowing sufficient development without losing too many years of data (e.g., we require data from the 2016 annual statement to calculate the 2011 error—calculating a 10-year error for 2011 would require annual statement data from 2020, which are not yet available.).31 While medical malpractice liability insurance, the focus of our study, has a relatively long tail, using a 5-year error allows for comparability with prior studies. From a more practical standpoint, we are also limited by insurer data reporting. Specifically, in the early years of our sample period (1988 and prior), Schedule P— Part 2C, where medical malpractice development is reported during this period, reported a maximum of 5 years of development. While later statement years report 10 years of development, for consistency across the entire sample we are limited to calculating 5-year reserve errors.32 While most prior studies examining insurer loss reserve errors focus on signed reserve errors and incentives to manage earnings (e.g., Petroni 1992; Beaver, McNichols, and Nelson 2003; Grace and Leverty 2010), we are instead focused on reserve error volatility. Two prior studies, Eckles, Halek, and Zhang (2014) and Carson, Eastman, and Eckles (2018), construct reserve volatility variables measured as the standard deviation of scaled insurer loss reserve errors. Similarly, we construct the following variable as our measure of reserve volatility: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u P ! u tþðj1Þ Errori, t uP þð Þ t u t j 1 Error t t i, t j Reserve Vol j ¼ (3) i, t j

27To calculate calendar year reserve errors we would calculate initial incurred losses as the sum of all values in column 6 of Table 3 ($1,164,147), while the updated estimate is equal to the sum of the first six rows of column 11 of Table 3 ($965,649). The calendar year error is then calculated as the initial estimate minus the developed reserve ($1,164,147 – $965,649 ¼ $198,498). 28We note that using calendar year errors is appropriate for most research designs since financial reporting outcomes are impacted by discretionary management of all accident years. Barth, Eastman, and Eckles (2019) find evidence that coefficient estimates statistically significantly differ depending on whether calendar year or accident year errors are used as the dependent variable. 29One commonly used scaling factor is ultimate losses. Since we expect ultimate losses to be lower for insurers in tort reform states (e.g., Born, Viscusi, and Baker 2009), this scaling factor would systematically result in higher scaled reserve errors (due to the lower denominator). We therefore report results using assets as the scaling factor. 30Since we control for (the natural log) of firm assets as one of our control variables, it is potentially unnecessary to scale reserve errors to account for differences in firm size. Accordingly, we estimate our models using the standard deviation of the unscaled reserve errors to see if our results are robust to this alternative definition of our dependent variables. The coefficient estimates on Noneconi,t remain negative and statistically significant. 31Barth, Eastman, and Eckles (2019, 151) report that 92.55% of ultimate incurred losses are paid after 5 years. 32Friedson and Kniesner (2012, 119), using medical malpractice claims data from the Texas Department of Insurance Closed Claims Database (CCD), report that the average length of a case that reaches a court verdict is 5.5 years, suggesting that a little more than 5 years is appropriate in our current setting. Settled cases, which comprise the majority of claims, are resolved earlier, 636 P. H. BORN ET AL.

33 where Errori,t is insurer i’s 5-year reserve error scaled by total assets in year t and j 2 [3,5]. For example, in order to calculate Reserve Vol 3i,t for Medical Professional Mutual in 2009, we first require loss development data from 2014, 2015, and 2016 annual statements in order to calculate scaled reserve errors for 2009, 2010, and 2011, respectively. Returning to the preceding example where we calculate the reserve error for Medical Professional Mutual in 2011, the raw error is equal to $53,997. Medical Professional Mutual’s assets in 2011 are $3,003,736.175, so the resulting scaled reserve error for 2011 is 0.0180.34 We then use loss development from Schedule P—Part 2F Section 1 in 2015 to calculate Medical Professional Mutual’s reserve error for 2010 (scaled by 2010 assets) and loss development from Schedule P— Part 2F Section 1 in 2014 to calculate the reserve error for 2009 (scaled by 2009 assets) using the same methodology as described earlier. The scaled reserve error for 2010 is equal to 0.0196 and the scaled reserve error for 2009 is equal to 35 0.0284. In order to calculate Reserve Vol 3i,t for 2009, we then take our scaled reserve error values for 2009, 2010, and 2011 (equal to 0.0284, 0.0196, and 0.0180, respectively) and calculate the standard deviation. Therefore, Reserve Vol 3i,t is equal to 0.0046 for Medical Professional Mutual in 2009. In general, higher values of Reserve Vol ji,t indicate higher uncertainty regarding reserve estimates, while a lower value indicates more certainty regarding reserve estimates. Compared to the mean of our sample of medical malpractice insurers (described in greater detail in the following), Medical Professional Mutual has a relatively low value for Reserve Vol 3i,t—while the mean for the entire sample is 0.0364, Medical Professional Mutual’s value of Reserve Vol 3i,t for 2009 is 0.0046, suggesting that it has relatively lower reserve volatility.

4.2. Empirical Methodology 4.2.1 Modeling Determinants of Reserve Volatility In order to test the impact of tort reform on reserving accuracy we estimate the following model using ordinary least squares (OLS):

Reserve Vol ji, t ¼ a þ bNoneconi, t þ wXi, t þ /It ½þ cSi, t þ i, t (4)

36 where Reserve Vol ji,t is the standard deviation of insurer i’s scaled reserve error from year t to year t þ (j – 1). Noneconi,t is the percentage of insurer i’s medical malpractice direct premiums written in noneconomic damage cap tort reform states in year t. Xi,t is a vector of insurer-level control variables. It is a vector of year indicators and Si,t is a vector of 51 state-year par- 37 ticipation indicators. i, t is a random error term. We adjust standard errors for insurer-level clustering. Positive coefficient estimates indicate higher reserve volatility (lower reserve estimation consistency), while negative coefficient estimates indicate lower reserve volatility (higher reserve estimation consistency). Therefore, a negative and statistically significant coefficient estimate for Noneconi,t (b < 0) would be consistent with our hypothesis that tort reform results in more consistent loss estimates for medical malpractice insurers. In order to isolate the statistical impact of our variable of interest, it is important to control for other factors that could potentially determine reserve volatility.38 We include controls for the levels and changes in premiums written (Harrington, Danzon, and Epstein 2008). We additionally include variables to account for an insurer’s organizational structure. These variables include controls for whether an insurer is organized as a risk retention group, mutual, or reciprocal (Born and Boyer 2011), as well as whether an insurer is a member of a group (Song 2016). We control for the amount of reinsurance an insurer

33The reserve volatility measure for t is calculated over a 3- or 5-year window (e.g., the 3-year measures is calculated using reserves at t, t þ 1, and t þ 2). Since the reserve volatility measure for t þ 1 also includes reserves for t þ 1 and t þ 2, there is a degree of overlap that may introduce some bias in our analysis. To address this potential issue, we estimated our model using every 3 years of data, which ensures that each volatility measure is non- overlapping. We find that the results are consistent with our reported results. 34Note that while Schedule P—Part 2 is reported in thousands, balance sheet information is reported in whole dollars. Therefore, for our example calculations we omit the thousands from assets. Medical Professional Mutual’s reported assets on their balance sheet in 2011 total $3,003,736,175.00. 35The calculation for the 2010 error is (159,437 – 103,150)/2,869,992.841 ¼ 0.0196. The calculation for the 2009 error is (164,267 – 92,041)/ 2,540,902.868 ¼ 0.0284. 36While prior studies point out that there is the potential for reverse causality in tort reform adoption (e.g., Durrance 2010), since our dependent variable is forward-looking this concern is not relevant in our tests. Moreover, while our main reported measures of Reserve Vol ji,t include the year t loss reserve error, robustness tests calculating Reserve Vol ji,t as the volatility from year t þ 1 to year t þ j yield results that are unchanged from what we report, indicating that our results are not driven by current-year reserving only. Other robustness tests, described further in the following, include clustering the standard errors by state of domicile, limiting our sample to include only insurers that operate in only one state, and inclusion of other “traditional” loss reserving controls for managerial discretion and incentives to manipulate claims. 37An insurer “participates” in a state if it reports positive direct premiums written in medical malpractice in that state. We include insurers operating in all 50 states and the District of Columbia. 38See Table A.1 in the Appendix for complete descriptions of all variables. MEDICAL MALPRACTICE RESERVE VOLATILITY 637 has ceded (Harrington and Danzon 1994). Finally, we also include variables relating to insurer operations, specifically, insurer size, the number of states in which an insurer writes medical malpractice, and the percent of net premiums written in medical malpractice.39 All models include year fixed effects. We also present models with and without state fixed effects.40

5. RESULTS 5.1. Descriptive Statistics We present summary statistics for our sample in Table 4. The mean values of our main dependent variables, Reserve Vol

3i,t and Reserve Vol 5i,t, are equal to 0.0364 and 0.0411, respectively. The reported percentiles highlight the skewed nature of the reserve error distribution, which has a long upper right tail. Our main independent variable, Noneconi,t, has a value of 0.4332, which indicates that just over 40% of medical malpractice direct premiums written were subject to noneconomic damage cap tort reform over the sample period.41 Around 40% of our sample insurers are organized as groups under common ownership structure. This percentage is lower relative to prior studies on property-casualty insurers (e.g., Grace and Leverty 2010; Carson, Eastman, and Eckles 2018). This is due to our focus on medical malpractice insurers, who are more likely to specialize in this particular line of business. Finally, we note that the average insurer in our sample has medical malpractice premiums written in 8.1583 states, while the median insurer has medical malpractice premiums written in two states. This suggests that for most insurers, tort reform should impact a substantial proportion of their business even if it occurs in only one state where they have operations.

5.2. Determinants of Reserve Volatility We present results of our empirical estimation of Equation (4) in Table 5. The dependent variable in columns (1) and

(2) is Reserve Vol 3i,t, while the dependent variable in columns (3) and (4) is Reserve Vol 5i,t. All columns include year fixed effects, while columns (2) and (4) include state fixed effects. Each coefficient is presented along with standard errors in parentheses beneath it. Standard errors are clustered at the insurer level. Positive coefficients indicate higher reserve volatility (less consistent loss estimation), while negative coefficients indicate lower reserve volatility (more consistent loss estimation). Overall, the results in Table 5 are consistent with our hypothesis. The estimated coefficients on Noneconi,t are negative and statistically significant—at the 1% level in all four models. The magnitudes of the coefficient estimates are also economically meaningful, ranging from –0.0092 to –0.0111. Therefore, a single-state insurer operating in a state that enacts tort reform (i.e.,

Noneconi,t changing from 0 to 1) would see its loss reserve volatility decline by –0.0094 over the ensuing 3 years (using the estimate from column (1)). The magnitude of this estimate is approximately 26% of the mean 3-year reserve volatility over our sample (–0.0094/0.0364). For the total industry, insurer reserve errors for policies sold in 2009 totaled nearly $1.4 billion as of 2011—a reduction in volatility of 26% is, therefore, sizable. These results provide evidence that as medical malpractice insurers have more operations in environments subject to noneconomic damage caps, their reserves tend to become less volatile— our results are both statistically and economically significant. This result is expected if one of the goals of tort reform is to provide more certainty to medical malpractice insurers. We find that insurers writing more premiums tend to have higher reserve volatility (positive estimated coefficient on ln(Premiums)i,t), while we find that larger insurers tend to have lower reserve volatility (negative estimated coefficient on 42 ln(Assets)i,t). Finally, insurers that cede more business to reinsurers tend to have more accurate reserves, consistent with reinsurance serving to smooth losses for primary insurers.

39While we use the natural log of the number of states for consistency with prior research on property-casualty insurers (e.g., Ke, Petroni, and Safieddine 1999; Berry-Stolzle,€ Eastman, and Xu 2018), we also perform robustness tests including the raw number of states. Our findings are robust to this change. 40Specifically, we include state fixed effects based on whether an insurer has positive direct premiums written in medical malpractice in a given state. We include these effects to account for state-specific factors that may influence medical malpractice markets in certain states (Deng and Zanjani 2018). 41See Appendix Tables A.2 and A.3 for correlations and univariate differences, respectively. 42One possible explanation for this result is that premium volume and assets are correlated. Results in Table 5 remain unaffected by omitting ln(Assets)i,t—the estimated coefficient for Noneconi,t remains negative and statistically significant in all four models. 638

TABLE 4 Summary Statistics

Percentiles Variable Mean Std. Min 10th 25th 50th 75th 90th Max

Reserve Vol 3 0.0364 0.0624 0.0000 0.0060 0.0114 0.0234 0.0441 0.0755 1.6629 Reserve Vol 5 0.0411 0.0801 0.0000 0.0086 0.0160 0.0270 0.0488 0.0766 1.8606 Nonecon 0.4332 0.4312 0.0000 0.0000 0.0000 0.2883 0.9790 1.0000 1.0000 ln(Premiums) 16.3428 1.7334 11.5129 14.0153 15.1819 16.4087 17.6046 18.5918 20.5512 RRG 0.2704 0.4443 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000 .H ONE AL. ET BORN H. P. Mutual 0.2027 0.4021 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 Reciprocal 0.1536 0.3606 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 Group 0.4044 0.4909 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000 ln(Assets) 17.9910 1.7390 14.3911 15.6945 16.6509 17.9368 19.3288 20.3516 22.4508 Medical Malpractice Premium % 0.9754 0.0486 0.7500 0.9106 0.9756 0.9994 1.0000 1.0000 1.0000 Reinsurance 0.2596 0.2519 0.0000 0.0000 0.0658 0.1979 0.3627 0.6341 0.9812 ln(Number States) 1.1119 1.2938 0.0000 0.0000 0.0000 0.6931 1.9459 3.3673 3.9318 ln(Premium Growth) 0.1385 0.5696 3.1483 0.1905 0.0422 0.0680 0.2348 0.5358 3.6848

Note: This table contains summary statistics for our sample of 2,097 observations from 1986 to 2009. Reserve Vol 3 (Reserve Vol 5) is the standard deviation of an insurer’s loss reserve errors scaled by total assets from years t to t þ 2(t to t þ 4). Nonecon is an insurer’s percentage of direct premiums written in medical malpractice in states that have passed noneconomic damage cap tort reform. Permanent Nonecon (Temporary Nonecon) is the percent of medical malpractice direct premiums written in states with permanent (temporary) noneconomic damage cap tort reform. ln(Premiums) is the natural log of net premiums written. RRG is a binary variable equal to 1 if an insurer is a risk retention group, and 0 otherwise. Mutual is a binary variable equal to 1 if an insurer is a mutual, and 0 otherwise. Reciprocal is a binary variable equal to 1 if an insurer is a reciprocal, and 0 otherwise. Group is a binary variable equal to 1 if an insurer is a member of a group, and 0 otherwise. ln(Assets) is the natural log of total assets. Medical Malpractice Premium % is the percentage of net premiums written in medical malpractice. Reinsurance is reinsurance ceded divided by the sum of direct premiums and reinsurance assumed. ln(Number States) is the natural log of the number of states in which an insurer has positive direct premiums written in medical malpractice. ln(Premium Growth) is the natural log of current-year premiums divided by prior-year premiums. MEDICAL MALPRACTICE RESERVE VOLATILITY 639

TABLE 5 Determinants of Reserve Error Volatility

Reserve Vol 3 Reserve Vol 5 (1) (2) (3) (4) Nonecon 0.0094 0.0111 0.0092 0.0097 (0.0026) (0.0030) (0.0031) (0.0033) ln(Premiums) 0.0116 0.0125 0.0121 0.0130 (0.0021) (0.0022) (0.0026) (0.0026) RRG 0.0040 0.0023 0.0040 0.0027 (0.0035) (0.0036) (0.0041) (0.0040) Mutual 0.0002 0.0017 0.0007 0.0023 (0.0040) (0.0039) (0.0050) (0.0050) Reciprocal 0.0004 0.0013 0.0010 0.0014 (0.0027) (0.0030) (0.0030) (0.0033) Group 0.0021 0.0046 0.0014 0.0041 (0.0028) (0.0031) (0.0031) (0.0035) ln(Assets) 0.0184 0.0201 0.0183 0.0199 (0.0022) (0.0022) (0.0026) (0.0026) Medical Malpractice 0.0108 0.0039 0.0207 0.0153 Premium % (0.0288) (0.0258) (0.0363) (0.0314) Reinsurance 0.0118 0.0116 0.0098 0.0099 (0.0058) (0.0063) (0.0068) (0.0072) ln(Number States) 0.0018 0.0013 0.0018 0.0017 (0.0009) (0.0026) (0.0009) (0.0029) ln(Premium Growth) 0.0015 0.0018 0.0009 0.0009 (0.0012) (0.0012) (0.0015) (0.0014) Intercept 0.1977 0.2027 0.1969 0.2034 (0.0312) (0.0309) (0.0375) (0.0353) Year FE Yes Yes Yes Yes State FE No Yes No Yes R2 23.75% 27.76% 24.20% 30.00% F-Stat 6.85 9.16 5.92 20.00 Observations 2,097 2,097 1,803 1,803

Note: This table reports estimated coefficients from OLS estimation of the determinants of reserve error volatility. The dependent variables are the standard deviation of reserve errors scaled by total assets. Columns (1) and (2) use 3-year standard deviations (from year t to year t þ 2) and columns (3) and (4) use 5-year standard deviations (from year t to year t þ 4). Nonecon is an insurer’s percentage of direct premiums written in medical malpractice in states that have passed noneconomic damage cap tort reform. ln(Premiums) is the natural log of net premiums written. RRG is a binary variable equal to 1 if an insurer is a risk retention group, and 0 otherwise. Mutual is a binary variable equal to 1 if an insurer is a mutual, and 0 otherwise. Reciprocal is a binary variable equal to 1 if an insurer is a reciprocal, and 0 otherwise. Group is a binary variable equal to 1 if an insurer is a member of a group, and 0 otherwise. ln(Assets) is the natural log of total assets. Medical Malpractice Premium % is the percentage of net premiums written in medical malpractice. Reinsurance is reinsurance ceded divided by the sum of direct premiums and reinsurance assumed. ln(Number States) is the natural log of the number of states in which an insurer has positive direct premiums written in medical malpractice. ln(Premium Growth) is the natural log of current-year premiums divided by prior-year premiums. All models include year fixed effects. Columns (2) and (4) include state fixed effects. Standard errors are clustered at the insurer level and are presented in parentheses beneath each coefficient estimate. , , and represent significance at the 1%, 5%, and 10% levels, respectively. 640 P. H. BORN ET AL.

TABLE 6 Determinants of Reserve Error Volatility—Additional Tort Reform Controls

Reserve Vol 3 Reserve Vol 5 (1) (2) (3) (4) Nonecon 0.0102 0.0110 0.0101 0.0099 (0.0028) (0.0032) (0.0034) (0.0035) Punitive 0.0005 0.0009 0.00 0.0006 (0.0028) (0.0031) (0.0033) (0.0036) Collateral Source 0.0026 0.0014 0.0020 0.0002 (0.0030) (0.0036) (0.0034) (0.0040) Joint and Several 0.0026 0.0008 0.0033 0.0006 (0.0031) (0.0042) (0.0035) (0.0043) ln(Premiums) 0.0116 0.0125 0.0122 0.0130 (0.0021) (0.0022) (0.0026) (0.0026) RRG 0.0040 0.0022 0.0041 0.0027 (0.0035) (0.0035) (0.0040) (0.0040) Mutual 0.0006 0.0016 0.0012 0.0023 (0.0040) (0.0040) (0.0051) (0.0052) Reciprocal 0.0001 0.0013 0.0004 0.0014 (0.0027) (0.0030) (0.0031) (0.0034) Group 0.0030 0.0045 0.0023 0.0041 (0.0030) (0.0033) (0.0034) (0.0038) ln(Assets) 0.0187 0.0201 0.0185 0.0199 (0.0022) (0.0022) (0.0026) (0.0026) Medical Malpractice Premium % 0.0066 0.0041 0.0164 0.0150 (0.0275) (0.0254) (0.0344) (0.0306) Reinsurance 0.0111 0.0117 0.0088 0.0099 (0.0056) (0.0062) (0.0065) (0.0071) ln(Number States) 0.0019 0.0013 0.0019 0.0017 (0.0009) (0.0026) (0.0009) (0.0029) ln(Premium Growth) 0.0016 0.0018 0.0011 0.0009 (0.0012) (0.0012) (0.0015) (0.0014) Intercept 0.1947 0.2035 0.1929 0.2034 (0.0308) (0.0305) (0.0367) (0.0345) Year FE Yes Yes Yes Yes State FE No Yes No Yes R2 23.93% 27.79% 24.43% 30.01% F-Stat 6.37 8.99 5.51 7.65 Observations 2,097 2,097 1,803 1,803

Note: This table reports estimated coefficients from OLS estimation of the determinants of reserve error volatility. The dependent variables are the standard deviation of reserve errors scaled by total assets. Columns (1) and (2) use 3-year standard deviations (from year t to year t þ 2) and columns (3) and (4) use 5-year standard deviations (from year t to year t þ 4). Nonecon is the percent of medical malpractice direct premiums written in states with noneconomic damage cap tort reform. Punitive is the percent of medical malpractice direct premiums written in states with punitive damage cap tort reform. Collateral Source is the percent of medical malpractice direct premiums written in states with collateral source rule tort reform. Joint and Several is the percent of medical malpractice direct premiums written in states with joint and several tort reform. ln(Premiums) is the natural log of net premiums written. RRG is a binary variable equal to 1 if an insurer is a risk retention group, and 0 otherwise. Mutual is a binary vari- ableequalto1ifaninsurerisamutual,and0otherwise.Reciprocal is a binary variable equal to 1 if an insurer is a reciprocal, and 0 otherwise. Group is a binary variable equal to 1 if an insurer is a member of a group, and 0 otherwise. ln(Assets) is the natural log of total assets. Medical Malpractice Premium % is the percentage of net premiums written in medical malpractice. Reinsurance is reinsurance ceded divided by the sum of direct premiums and reinsurance assumed. ln(Number States) is the natural log of the number of states in which an insurer has positive direct premiums written in medical malpractice. ln(Premium Growth) is the natural log of current-year premiums divided by prior-year premiums. All models include year fixed effects. Columns (2) and (4) include state fixed effects. Standard errors are clustered at the insurer level and are presented in parentheses beneath each coefficient estimate. , ,and represent significance at the 1%, 5%, and 10% levels, respectively. MEDICAL MALPRACTICE RESERVE VOLATILITY 641

5.3. Robustness Tests We perform several additional tests to ensure the robustness of our results. First, we note that many state approaches to tort reform involved enacting a bundle of measures including, for example, modifications to joint and several liability, modifications to collateral sources rules, and caps on punitive damages. Although prior research has had limited success in disentan- gling the relationships between these measures and insurer performance, we consider the possibility that exposure to other reform measures would similarly affect reserve volatility. We reestimate Equation (4) with three additional reform measures— modifications to joint and several liability, modifications to collateral sources rules, and caps on punitive damages—which we calculate in the same manner as Noneconi,t (see Eq. (1)). The results, shown in Table 6, are consistent with our previous findings: The estimated coefficients on Noneconi,t remain negative and statistically significant in all four specifications. Next, given that our dependent variable is the standard deviation of scaled reserve errors, it is truncated at zero. While we perform OLS regression previously, a Tobit model is arguably more appropriate given this truncation.43 Therefore, we estimate Equation (4) using a Tobit model with standard errors clustered at the insurer level. In all four specifications our results are consistent with the 44 results we obtain from OLS estimation: The estimated coefficients on Noneconi,t are negative and statistically significant. We also test whether our results are robust to using 4 years of reserve errors in our volatility measure instead of 3 or 5. We estimate Equation (4) using Reserve Vol 4i,t as the dependent variable, defined as the standard deviation of scaled loss reserve errors from year t to year t þ 3. As with our previous reserve volatility measures, we require at least 2 years of data to construct this variable. In both specifications (without and with state fixed effects) the estimated coefficient on Noneconi,t is negative and statistically significant at the 1% level, indicating that our results are not sensitive to the number of years used to calculate reserve volatility. In our original definitions of Reserve Vol 3i,t and Reserve Vol 5i,t we require only 2 years of nonmissing values for scaled reserve errors to calculate a value for each variable. We also construct versions of these variables where we require all reserve error values to be nonmissing to calculate the variable (i.e., we require scaled reserve errors for years t, t þ 1, and t þ 2forReserve Vol 3i,t and for years t, t þ 1, t þ 2, t þ 3, and t þ 4forReserve Vol 5i,t). Our results are robust to this sample restriction—the estimated coefficients on Noneconi,t are negative and statistically significant in all four specifications, consistent with our main results. Our only sample restriction for inclusion in the sample of medical malpractice insurers is that an insurer has at least 75% of total premiums written in medical malpractice. This restriction excludes insurers in our sample with relatively low levels of medical malpractice business, who may be less impacted by tort reforms since medical malpractice is relatively unimportant to the firm’s overall operations. As an alternative, we reestimate Equation (4) for all insurers with strictly positive medical malpractice premiums, but include an interaction term, Medical Malpractice Premium %i,t Noneconi,t. We find that the coefficient on the interaction term is negative and statistically significant, indicating that exposure to noneconomic damages caps has a larger negative effect on reserve volatility as the insurer’s business in medical malpractice increases. We also reestimate Equation (4) limiting our sample to insurers that write at least $1 million in medical malpractice premiums. Again, our results are robust to this sample restriction—the coefficient estimate on Noneconi,t is negative and statistically significant in all four specifications, indicating that our results are not driven by insurers writing a small amount of medical malpractice business. Our approach to measuring exposure to tort reform aggregates and weights exposure across states to create an insurer-level measure that can be compared to insurer-level reserves. To confirm that this approach does not bias our findings, we reestimate Equation (4) limiting our sample to insurers that write medical malpractice coverage in only one state. Our results are robust to this sample restriction—the coefficient estimate on Noneconi,t is negative and statistically significant in three of the four specifications. Existing research on insurer loss reserving incorporates a variety of additional variables designed to capture managerial discretion and motives for manipulation. While these insurer-specific variables are important for explaining under- and over- reserving behavior and, consequently, reserving error levels, it is likely that they would also be related to volatility. Therefore, we reestimate Equation (4) with several variables from this literature, including controls for earnings smoothing (Beaver, McNichols, and Nelson 2003), whether a firm paid taxes (Petroni 1992), the estimated probability of insolvency (Grace and Leverty 2010), and proxies for the length of time between the claim and the ultimate settlement (Petroni and Beasley 1996). While we find that many of these are significantly related to volatility, the inclusion of these additional controls does not affect our main results. The coefficient estimate on Noneconi,t is negative and statistically significant in all four specifications. Finally, although our analysis is conducted at the insurer level, we consider whether the errors in our estimation might be correlated with unobserved state of domicile characteristics, such as capital requirements or regulatory stringency in the state.

43An alternative to using a Tobit model would be to log our dependent variable, thereby admitting negative values and making OLS estimation more appropriate. We perform this test in unreported tests and find that the coefficient estimates for Noneconi,t remain negative and statistically significant. 44For the sake of brevity, the results of this analysis and the results of further robustness tests described in the following are not reported. These are available from the authors upon request. 642 P. H. BORN ET AL.

We reestimate Equation (4) with standard errors clustered by state of domicile and our results hold. Again, the coefficient estimate on Noneconi,t is negative and statistically significant in all four specifications.

6. CONCLUSION While prior studies examining the impact of tort reform on insurance markets have largely focused on premiums, losses, and profitability, there is little evidence on how changes to the legal environment influence the accounting practices of insurers with respect to insurance reserves. Our examination of how tort reform affects medical malpractice reserving behavior speaks to potential benefits of tort reform beyond improving insurer underwriting profitability and therefore provides evidence that is relevant to state legislators as they continue to consider adopting tort reform measures. In this study we evaluate reserving practices of insurers writing medical malpractice insurance for the period 1986 to 2009. We identify when states adopted noneconomic damage cap tort reform and use these data to determine the percentage of an insurer’s premiums written in tort reform environments. We then test whether 3- and 5-year reserving volatility is reduced when insurers write proportionally more business in tort reform environments. We find evidence that noneconomic damage caps substantially reduce reserving volatility and that this result is driven by both permanent and temporary tort reforms. We conclude that a benefit not documented in prior literature examining the impact of tort reform on liability insurance markets is a reduction in reserving volatility. This impact is consistent with tort reform advocates’ belief that tort reform could potentially foster insurance market stability. Our study is of interest to economists and legal scholars who study the interactions between tort reform and insurance markets. We also contribute to the accounting and insurance literature that examines the determinants and consequences of insurer loss reserves. Finally, our results suggest that insurers are better able to forecast future losses in a tort reform environment—a finding that has potential implications for insurer solvency as well as pricing.

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APPENDIX TABLE A.1 Variable Definitions

Variable name Description

Reserve Vol ji,t Standard deviation of insurer i’s reserve error scaled by assets from year t to year t þ (j – 1) where j is equal to 3 or 5. Errori,t Difference between insurer i’s original medical malpractice loss reserve estimate in year t and the developed loss reserve in period t þ 5 scaled by total assets. Noneconi,t Percentage of insurer i’s medical malpractice direct premiums written in states with noneconomic damage cap tort reform in year t. ln(Premiums)i,t Natural log of insurer i’s net premiums written in year t. RRGi,t Binary variable equal to 1 if insurer i is organized as a risk retention group in year t and 0 otherwise. Mutuali,t Binary variable equal to 1 if insurer i is organized as a mutual in year t and 0 otherwise. Reciprocali,t Binary variable equal to 1 if insurer i is organized as a reciprocal in year t and 0 otherwise. Groupi,t Binary variable equal to 1 if insurer i is a member of a group in year t and 0 otherwise. ln(Assets)i,t Natural log of insurer i’s total assets in year t. Medical Malpractice Premium %i,t Percentage of insurer i’s net premiums written in medical malpractice in year t. Reinsurancei,t Insurer i’s reinsurance ceded divided by the sum of reinsurance assumed and direct premiums written in year t. Ln(Number States)i,t Natural log of the number of states in which insurer i reported positive direct premiums written in medical malpractice insurance in year t. Ln(Premium Growth)i,t Natural log of insurer i’s ratio of medical malpractice net premiums written in year t to medical malpractice net premiums written in year t – 1. Permanent Noneconi,t Percentage of insurer i’s medical malpractice direct premiums written in states with permanent noneconomic damage cap tort reform in year t. Temporary Noneconi,t Percentage of insurer i’s medical malpractice direct premiums written in states with temporary noneconomic damage cap tort reform in year t. TABLE A.2 Correlation Matrix

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

(1) Reserve Vol 3 0.8492 20.0848 20.3230 0.1917 20.1442 0.0277 20.1913 20.4254 0.1231 20.0571 20.1114 0.1550 (2) Reserve Vol 5 0.8223 20.1049 20.3293 0.1738 20.1383 0.0391 20.1868 20.4390 0.1181 20.0619 20.1137 0.1734 EIA APATC EEV VOLATILITY RESERVE MALPRACTICE MEDICAL (3) Nonecon 20.0739 20.0750 0.0321 0.0174 0.0330 20.0782 0.0697 0.0226 0.0443 0.0471 0.1055 0.0314 (4) ln(Premiums) 20.1459 20.1026 0.0384 20.3803 0.3164 0.1631 0.3165 0.9449 20.2162 20.2507 0.1888 20.0563 (5) RRG 0.1599 0.1508 0.0070 20.3533 20.3069 20.2593 20.4207 20.4295 0.1162 0.0302 0.1660 0.0122 (6) Mutual 20.0658 0.0557 0.0328 0.3013 20.3069 20.2147 0.0366 0.3155 0.0374 20.1608 20.1115 0.0246 (7) Reciprocal 0.0223 0.0220 0.0535 0.1660 20.2593 20.2147 0.1611 0.1374 0.0212 0.0009 20.1141 0.0261 (8) Group 20.1303 20.1153 0.0465 0.3056 20.4207 0.0366 0.1611 0.3803 20.2030 0.0671 0.1395 20.0620 (9) ln(Assets) 20.2360 20.1874 0.0148 0.9280 20.4180 0.3119 0.1360 0.3852 20.2516 20.1629 0.1918 20.1641 (10) Medical Malpractice 0.0101 0.0204 0.0101 0.0129 0.0445 0.0969 0.0570 20.1314 0.0174 0.0520 20.0741 0.0374 Premium % (11) Reinsurance 0.0047 0.0431 20.0582 20.3756 0.0454 20.1904 20.0608 0.0445 20.2214 20.0806 0.1438 0.0417 (12) ln(Number States) 20.0744 20.0598 0.0160 0.2033 0.1835 20.1210 20.1165 0.1268 0.1973 0.0071 0.0995 0.0153 (13) ln(Premium Growth) 0.0544 0.0436 0.0077 0.0171 0.0104 0.0270 0.0110 0.0497 20.1378 0.0248 20.0725 0.0436

Note: This table reports correlations for our sample of insurers. Pearson correlations are reported in the lower triangle, while Spearman correlations are reported in the upper triangle. Reserve Vol 3 (Reserve Vol 5) is the standard deviation of an insurer’s loss reserve errors scaled by total assets from years t to t þ 2(t to t þ 4). Nonecon is an insurer’s percentage of direct premiums written in medical malpractice in states that have passed noneconomic damage cap tort reform. Permanent Nonecon (Temporary Nonecon) is the percentage of medical malpractice direct premiums written in states with permanent (temporary) noneconomic damage cap tort reform. ln(Premiums) is the natural log of net premiums written. RRG is a binary variable equal to 1 if an insurer is a risk retention group, and 0 otherwise. Mutual is a binary variable equal to 1 if an insurer is a mutual, and 0 otherwise. Reciprocal is a binary variable equal to 1 if an insurer is a reciprocal, and 0 otherwise. Group is a binary variable equal to 1 if an insurer is a member of a group, and 0 otherwise. ln(Assets) is the natural log of total assets. Medical Malpractice Premium % is the percentage of net premiums written in medical malpractice. Reinsurance is reinsurance ceded divided by the sum of direct premiums and reinsurance assumed. ln(Number States) is the natural log of the number of states in which an insurer has positive direct premiums written in medical malpractice. ln(Premium Growth) is the natural log of current-year premiums divided by prior-year premiums. Bolded figures are significant at the 0.01% level. 645 646 P. H. BORN ET AL.

TABLE A.3 Summary Statistics: Tort Reform States

(1) (2) (1)-(2) Nonecon 50% Nonecon < 50% Difference n ¼ 889 n ¼ 1,208 Mean Median Std. Dev. Mean Median Std. Dev. Mean Median Std. Dev. Reserve Vol 3 0.0302 0.0212 0.0320 0.0410 0.0244 0.0772 0.0108 0.0032 0.0452 Reserve Vol 5 0.0326 0.0252 0.0309 0.0473 0.0297 0.1018 0.0147 0.0045 0.0709 ln(Premiums) 16.4103 16.3985 1.6221 16.2931 16.4266 1.8100 0.1172 0.0281 0.1879 RRG 0.2632 0.0000 0.4406 0.2757 0.0000 0.4470 0.0125 0.0000 0.0064 Mutual 0.1935 0.0000 0.3952 0.2094 0.0000 0.4071 0.0159 0.0000 0.0119 Reciprocal 0.1451 0.0000 0.3524 0.1598 0.0000 0.3665 0.0147 0.0000 0.0141 Group 0.4319 0.0000 0.4956 0.3841 0.0000 0.4866 0.0478 0.0000 0.0090 ln(Assets) 18.0289 17.8847 1.6606 17.9631 17.9726 1.7947 0.0658 0.0879 0.1341 Medical Malpractice 0.9755 0.9985 0.0467 0.9754 0.9997 0.0500 0.0001 0.0012 0.0033 Premium % Reinsurance 0.2485 0.1680 0.2471 0.2677 0.2072 0.2551 0.0192 0.0392 0.0080 ln(Number States) 1.0693 0.6931 1.2265 1.1432 0.6931 1.3408 0.0739 0.0000 0.1143 ln(Premium Growth) 0.1356 0.0547 0.6178 0.1407 0.0831 0.5316 0.0051 0.0284 0.0862

Note: This table reports summary statistics and univariate differences for means, medians, and standard deviations for our sample between insurers operating mostly in and out of tort reform environments. Statistical significance of differences is based on t-tests for means and nonparametric k-sample tests for medians. Nonecon is an insurer’s percentage of direct premiums written in medical malpractice in states that have passed noneconomic damage cap tort reform. Reserve Vol 3 (Reserve Vol 5) is the standard deviation of an insurer’s loss reserve errors scaled by total assets from years t to t þ 2(t to t þ 4). ln(Premiums) is the natural log of net premiums written. RRG is a binary variable equal to 1 if an insurer is a risk retention group, and 0 otherwise. Mutual is a binary variable equal to 1 if an insurer is a mutual, and 0 otherwise. Reciprocal is a binary variable equal to 1 if an insurer is a reciprocal, and 0 otherwise. Group is a binary variable equal to 1 if an insurer is a member of a group, and 0 otherwise. ln(Assets) is the natural log of total assets. Medical Malpractice Premium % is the percentage of net premiums written in medical malpractice. Reinsurance is reinsurance ceded divided by the sum of direct premiums and reinsurance assumed. ln(Number States) is the natural log of the number of states in which an insurer has positive direct premiums written in medical malpractice. ln(Premium Growth) is the natural log of current-year premiums divided by prior-year premiums. , , and represent significance at the 1%, 5%, and 10% levels, respectively.