Small Firms Demand for Health Insurance: The Decision to Offer Insurance

Transcription

1 Jack Hadley James D. Reschovsky Small Firms Demand for Health Insurance: The Decision to Offer Insurance This paper eplores the decisions by small business establishments ( 100 workers) to offer health insurance. We estimate a theoretically derived model of establishments demand for insurance using nationally representative data from the 1997 Robert Wood Johnson Foundation Employer Health Insurance Survey and other sources. Findings show that offer decisions reflect worker demand, labor market conditions, and establishments costs of providing coverage. Premiums have a moderate effect on offer decisions (elasticity.54), though very small establishments and those employing low-wage workers are more responsive. This suggests that premium subsidies to employers would be an inefficient means of increasing insurance coverage. Greater availability of public insurance and safety net care has a small negative effect on offer decisions. Despite a booming economy and the lowest unemployment in decades, the proportion of nonelderly people without health insurance continued to grow through most of the 1990s, from 17.4% in 1994 to 18.4% (approimately 44 million people) in 1998 (Hoffman and Schlobohm 2000). More than 80% of the uninsured are workers or their dependents, and 60% of these workers are employed by small firms with fewer than 100 employees (Hoffman and Schlobohm 2000). Nearly half of uninsured adults say that their employers do not offer insurance, and the vast majority of these employers are small firms (Hoffman and Schlobohm 2000). The importance of small firms offer behavior was also a key element of the debate over the health care reform proposals of former President Bill Clinton (McLaughlin, Zellers, and Frick 1994). One strategy for epanding insurance coverage involves subsidies or ta breaks designed to induce firms to offer insurance to their employees; this is based on the assumption that the cost of health insurance is an important factor in firms decisions to offer insurance. Similarly, small market reforms are intended to lower the premium cost of health insurance to small firms. A recent survey of small businesses reported that one in seven would drop coverage if their premiums increased by 10% (Freudenheim 2000). Will subsidies or market reforms in fact increase small firms offer rates? Similarly, if premiums for employer-sponsored insurance (ESI) increase sharply over the net few years (Gabel et al. 2001; Hogan, Ginsburg, and Gabel 2000; Hewitt Associates 2000), how many small firms that currently offer insurance will drop their coverage? Jack Hadley, Ph.D., is a senior fellow at the Center for Studying Health System Change, and a principal research associate at the Urban Institute. James D. Reschovsky, Ph.D., is a senior health researcher at the Center for Studying Health System Change. Funding for this research came from the Robert Wood Johnson Foundation through its support of the Center. Address correspondence to Dr. Hadley at the Center for Studying Health System Change, 600 Maryland Ave., S.W., Suite 550, Washington DC Inquiry 39: (Summer 2002) Ecellus Health Plan, Inc /02/ $1.25

2 Small Firms Demand We address these questions in this paper by estimating a comprehensive model of small firms decisions to offer health insurance using data from a nationally representative sample of employers surveyed primarily in Our main objective is to estimate small firms premium elasticity of demand in order to measure how responsive their decisions to offer insurance are to variations in health insurance premiums. We also eplore how this elasticity varies across firms with different characteristics, and estimate the effects of other public policies that provide alternative sources of health care coverage or influence premium levels. We employ a modified version of the selection-correction technique used by Feldman et al. (1997), who imputed an insurance price variable derived from a premium equation corrected for sample selection bias. Their elasticity estimates ranged from 3.9 to 5.8, which are much larger than other studies estimates. As we will show, however, their method does not satisfy the overidentifying restriction test for an eogenous instrumental variable. Our modified approach satisfies this test and produces a much smaller elasticity of.54, which is in the range of elasticity estimates found by most other studies. We conclude that subsidizing insurance premiums paid by small firms is a blunt policy instrument that is likely to have only a modest impact on epanding workers insurance coverage. Background Previous studies have employed various methods to derive the premium elasticity of demand, producing a very wide range of estimates. At one etreme, Feldman et al. (1997) used a selectivity-correction model to predict insurance premiums faced by firms offering and not offering health insurance. They estimated elasticities of 3.91 for single coverage premiums and 5.82 for family coverage premiums for approimately 2,000 small firms in Minnesota in Several studies investigated changes in offer rates over time for small firms participating in demonstration projects of alternative strategies for reducing the cost of insurance (Helms, Gauthier, and Campion 1992; Thorpe et al. 1992). Firms in these demonstrations were generally unresponsive to changes in the cost of insurance, with elasticity estimates ranging from.1 to.7. However, the lack of awareness about these programs and their temporary nature have been cited as reasons for the low elasticities found (Helms, Gauthier, and Campion 1992; Dyckman and Burnette 1992; Thorpe et al. 1992). Studies that used observational data faced the dilemma that the reservation premium that is, the threshold premium level that prompts a firm to offer insurance is not observed for firms that do not offer insurance. To solve this problem, some investigators derived a hypothetical demand for health insurance benefits by asking firms how they would respond to insurance policies offered at various prices (Buchanan and Marquis 1999; Morrisey, Jensen, and Morlock 1994; Thorpe et al. 1992). These studies estimated elasticities from.3 to 1.6. Other researchers attempted to impute insurance prices to firms that do not offer policies by eploiting variations in the after-ta cost of insurance across states and over time. Gruber and Lettau (2000) used the Bureau of Labor Statistics Employment Cost Inde annual ( ) survey of a sample of employees from 2,500 to 5,000 establishments, and variations in marginal ta rates. For small firms with fewer than 100 employees, they estimate an elasticity of.61. Leibowitz and Chernew (1992) used list prices from a small group insurer along with ta rate variation; Jensen and Gabel (1992) used state average premium levels and state income ta rates; and Marquis and Long (2001) employed premium quotes reported by recent shoppers of health insurance benefits. Estimates from these studies range from.1 to 2.5. Theoretical Framework Demand for Insurance Following Feldman et al. (1997), we assume that firms act as their employees agents, offering insurance if their employees collective reservation price (the amount they are willing to pay on average for insurance of a given benefit level) eceeds the price at which the employer can make insurance available. 1 Accordingly, the theoretical framework begins with a standard model of the individual s demand for insurance. Translating employees demand for insurance into a firm s decision to offer insurance adds factors that reflect the firm s cost of agency. We also assume that employees decisions to 119

3 Inquiry/Volume 39, Summer 2002 purchase insurance are based on maimizing an epected utility function defined over alternative insurance states (e.g., Pauly 1986; Marquis and Holmer 1986). In this analysis, we consider four possible discrete choices: to go without insurance and either pay for medical care out-of-pocket and/or rely on free care (the safety net); to seek coverage from free or subsidized public insurance, if eligible; to purchase insurance directly from an insurance company as an individual; or to purchase insurance through an employer. Individuals compare epected utilities across these options and choose employment-sponsored insurance (ESI) if its epected utility eceeds those of the others. This approach leads to a model that specifies the choice of a particular insurance state as a function of the premiums associated with each choice and other factors that affect the demand for insurance, such as the price of medical care, income, preferences, and health, which affects the epected use of medical services. Firms Cost of Offering Insurance Even though we assume that firms act as employees agents, agency is not costless, as firms must search for and administer the insurance. If these costs have a large fied component, the average cost per worker should decline with firm size and with the number of hours worked per employee. Therefore, larger firms and firms with a higher proportion of full-time workers should be more likely to offer insurance relative to smaller firms or firms with a low proportion of full-time workers. As illustrated by the following quotation from an employer, small firms offer decisions also will be affected by the nature of competition for workers in their local market: I was almost coerced into [providing health insurance] because of the job market. All these big companies have every benefit... and I was losing guys because I wasn t offering them benefits. Health care was the big one (Duggan and Levine 2000). Thus, if a small firm operates in a market where potential workers have good job opportunities in other firms that offer insurance, then it will be more likely to offer insurance in order to attract workers. Adding the cost of agency to the underlying demand for insurance, we write the firm s offer equation as: Prob(Offer) g(p esi,d, P j, X, Z), (1) where P esi,d is the firm s demand or reservation premium for employer-sponsored insurance; P j represents the premiums or costs associated with the other insurance states; X is a set of eogenous factors influencing workers demand for insurance; and Z represents factors affecting either the firm s cost of acting as its employees agent or market factors that affect the payoff to the firm of offering insurance. The Supply of Insurance We write the supply of insurance (an insurance company s willingness to provide insurance) in inverse form that is, the premium at which an insurer is willing to write a policy depends on the epected payout (medical claims) under the policy; the loading fee (Phelps 1992, p. 293), which includes administrative costs; the price of risk bearing; mark-ups due to insurer market power and normal profit; and the effects of any state insurance regulations on insurance premiums. Medical claims are assumed to reflect the firm s health characteristics and the generosity of the benefit package. Thus, we represent the supply of insurance to firm f by equation 2: P esi,s h(p m, M f, B f, L, R), (2) where P m is the price of medical care; M represents the epected medical care use of firm f based on the health characteristics of its workers; B represents the generosity of the benefits offered (i.e., the combined effects of coverage, coinsurance, deductibles, and other plan-specific factors that might influence actual service use); L represents variables that influence the loading factor, such as firm size and insurance industry market structure; and R stands for state insurance regulations. Equilibrium Following Feldman et al. (1997), we assume that equilibrium occurs (i.e., the firm offers insurance) when the demand price just equals (or eceeds) the supply price. In other words, we can rewrite equation 1 as 120

4 Small Firms Demand Prob(Offer) Prob(P P P ) esi,d esi,s esi g (P esi, P j, X, Z). (3) Equation 3 is the structural offer equation we seek to estimate. As described in the net section, we also estimate equation 2 in order to construct an instrumental variable estimate of P esi. Statistical Estimation Unbiased estimation of equation 3 faces two fundamental problems: P esi is not observed for firms that do not offer insurance and it is endogenous. To address these problems, we constructed an instrumental variable estimate of P esi from a selection-corrected premium equation using the two-stage Heckman procedure to account for the fact that premiums (P esi ) are observed only for establishments that offer insurance (Heckman 1979; StataCorp 1999). For firms that do not offer insurance, P esi,d P esi,s, and we do not observe any value of P esi. Therefore, using only data from firms that offer insurance to construct an instrument for all firms would systematically understate the premium faced by firms that do not offer. Implementing this procedure requires the following steps: using a probit specification to estimate a reduced-form offer equation with data for all firms, since no information on either insurance premiums or benefits is required; estimating a selection-corrected premium equation 2; using the premium equation 2 to create an instrumental variable by assigning the selection-corrected predicted premium value for a policy of fied benefits to each firm based on each firm s predicted probability of offering insurance (from the reduced-form offer equation); and estimating the structural offer equation 3. Our approach is similar to the one used by Feldman et al. (1997), but differs in one important respect. They assigned the selection-corrected premium to each firm based on whether the firm actually offered insurance, thus reintroducing an endogenous factor into their instrument. In our strategy, both the calculation of the predicted premium and its assignment to firms based on the predicted probability of offering insurance are strictly functions of eogenous variables. 2 Therefore, the ESI premium used to estimate equation 3 can be considered a selection-corrected instrumental variable. In constructing the instrument for P esi, we assumed that a small firm that does not offer insurance would consider a relatively lower-cost bare bones policy, defined as a health maintenance organization (HMO) plan with an actuarial value of.7 (approimately the 15th percentile of the distribution of actuarial values). The reduced-form probit offer equation and the selection-corrected premium equation were estimated jointly using maimum likelihood estimation (StataCorp 1999, pp ). The dependent variable in the premium equation is the natural log of the observed premium. (We applied a smearing correction to retransform the predicted premium back into dollars for the estimation of the structural offer equation.) The structural offer equation was estimated as a logit specification using SUDAAN software to adjust the standard errors for the effects of comple sampling (Shah, Barnwell, and Bieler 1996). 3 All monetary variables (premiums, average worker income, price of medical care) were deflated by a cross-sectional cost-of-living inde produced by the American Chambers of Commerce Researchers Association (ACCRA) to eliminate the effects of variations in general price levels across areas. 4 The premium equation was identified by the eclusion of several variables hypothesized to influence firms offer decisions, but not premiums. We conducted both a weak instrument test (Bound, Jaeger, and Baker 1995; Staiger and Stock 1997) and a test of the overidentifying restrictions used to construct the instrumental variable estimate of P esi (Greene 1990). The unit of analysis is the establishment, rather than the firm, because insurance decisions may vary across establishments that are part of a geographically diverse firm. As a consequence, however, some of the small establishments in our sample are parts of firms that have more than 100 employees. The empirical specification accounts for differences in both establishment and firm size, since larger firms still may be able to take advantage of scale economies and greater risk pooling even when employees are spread across multiple establishments. (Limiting the sample to establishments 121

5 Inquiry/Volume 39, Summer 2002 and firms with fewer than 100 employees had very little effect on the results.) Data Information on employers insurance and establishment characteristics comes from the 1997 Robert Wood Johnson Foundation (RWJF) Employer Health Insurance Survey, which is a nationally representative telephone survey of business establishments and government employers. This analysis uses data from the Community Tracking Study (CTS) portion of the sample, that includes 11,613 small (fewer than 100 employees), private establishments, which were oversampled in 60 randomly selected local health care markets. Local health care markets are defined as Metropolitan Statistical Areas (MSAs) or groups of nonmetropolitan counties defined by the Bureau of Economic Analysis (Metcalf et al. 1996). Taken together, data from the 60 markets are representative of the continental United States. Etensive information about each establishment, its workers, and health benefit plans offered to workers was collected from the person(s) most knowledgeable about health benefits and worker characteristics. Health plan information included premiums, benefits, cost sharing, and enrollments. (Weighted averages based on plan-specific enrollment were constructed for establishments that offered more than one plan.) The CTS conducts several surveys, collected at the same time and in the same 60 communities (Kemper et al. 1996). This allowed us to supplement the employer survey data with variables obtained from other sources. In particular, we used the CTS Household Survey which samples 54,000 individuals in the same 60 markets to derive instrumental variables for the availability of public insurance, health care through the safety-net system, the price of nongroup insurance, average worker income, and workers family health status. (See Reschovsky et al for details concerning the Household Survey.) Information on each household survey respondent s insurance coverage was obtained in the CTS Insurance Followback Survey. Merged data from these two surveys were used to calculate a local market Herfindahl concentration inde for insurers of workers. Hospital cost data came from the American Hospital Association s (AHA) Annual Survey of Hospitals. Variable Specification In this section, we briefly summarize the variables used in the empirical estimation. (Detailed information on variable construction is available from the authors.) Table 1 indicates the equations (the reduced-form offer equation, the supply function [premium equation] or the structural offer equation) in which each variable appears. Premium Variables The employer-sponsored insurance premium is the full (employer plus employee shares) cost per month for a policy that covers only the worker. (Family premiums were highly correlated with the worker-only premiums. 5 ) Premiums are observed only for establishments that offer insurance. A variable related to the ESI premium is the state income ta rate. Workers with ESI in states with high marginal income ta rates will face a lower after-ta premium than workers with ESI in other states 6 because the portion paid by the worker s firm is treated as a nontaable fringe benefit (Gruber 2000; Gruber and Poterba 1994). Altering the after-ta cost of ESI should influence the underlying utility of ESI relative to the utilities of the other insurance states. The premium for self-purchased insurance (i.e., insurance purchased directly from an insurance company rather than through an employer) was constructed from the CTS Household Survey. We estimated a selection-adjusted, self-purchased premium equation with independent variables corresponding to information available about worker characteristics from the employer survey: gender, age, wage level, industry, policy type (HMO, a restricted feefor-service, or preferred provider organization [PPO] policy, or an unrestricted indemnity policy), and dummy variables for the 60 CTS sites. We then combined these parameters with establishment-level data for the common set of variables to compute a firm-specific value representing the average premium for self-purchased insurance faced by the establishment s workers. The variables representing the availability of public insurance and perceived safety-net capacity also were constructed from the CTS Household Survey data. The availability of public insurance is measured by the predicted probability of having at least one member of a work- 122

6 Small Firms Demand Table 1. Variable specification, by model equation Variable Reduced-form offer Equation Premium Structural offer Offers health insurance a b b Price terms Employer-sponsored insurance premiums Self-purchased insurance premiums Availability of public insurance Availability of safety net services (site) Average state income ta rate facing workers Average worker income Price of medical care (hosp. cost/patient day, site) Epected medical care use Proportion female workers Proportion workers aged 30 Proportion workers aged Proportion workers aged Proportion with family member in poor health (site) Industry Establishment/firm size combinations Proportion full-time workers Proportion workers in firms with 500 workers (site) Proportion workers in unions (site) Firm has high turnover ( 30%) a Insurance industry concentration (site) Employer concentration (site) State insurance regulation No rate regulation a Weak rate regulation a Insurance policy attributes Actuarial value Plan is HMO a Plan is POS a Plan is PPO a Policy has waiting period a Policy has pre-eisting condition eclusion Firm is self-insured a Enrollee characteristics Proportion of enrollees retired, age 65 Proportion of enrollees retired, age 65 Proportion of enrollees through COBRA a Constructed as 0 1 dummy variable. b Dependent variable in equation. b er s family covered by public insurance. This variable was constructed using essentially the same variables and methods as in the construction of the premium for self-purchased insurance, ecept that the underlying equation was not adjusted for selection. 7 We define perceived safety-net capacity as the perception that one can get care if uninsured. We used the CTS Household Survey to calculate the percentage of uninsured people in each of the 60 CTS sites who did not report any problems in obtaining needed care because of financial reasons (Herring 2000, 2001). This variable, which is modestly correlated with the percentage uninsured (.33), had a mean of 70% across sites and ranged in value from just under 123

7 Inquiry/Volume 39, Summer % (Lansing, Pittsburgh, Columbus) to around 85% (St. Louis, Los Angeles, Riverside). We assume that the greater this proportion, the more likely a worker is to choose being uninsured as an alternative to ESI. 8 Demand Variables Related to Workers Characteristics Other demand variables in the model are average worker income in the establishment, a measure of the cost of medical care, indicators of epected medical care use related to age, gender, and health, and the establishment s industry. Average income per worker at the establishment level was imputed from the CTS Household Survey. We first calculated average family income per worker by wage level, industry, firm size, and state. These estimates then were mapped to establishments in the same industry, size category, and state using the percentage of workers at each wage level to weight the income estimates from the household data. 9 The cost of medical care (P m ) enters the demand function because it affects epected outof-pocket payments for services not covered by insurance. It was defined as the average cost of an adjusted-patient-day in the hospital (using data from the AHA s Annual Survey of Hospitals). 10 To control for variations in workers epected use of medical care, we included several demographic variables that describe the establishment s workforce and are plausibly related to the epected use of services: the percentage of female workers and the percentages of workers in the age categories younger than 30, 30 to 39, and 40 to 49 (with 50 and older as the omitted reference group). We also used data from the CTS Household Survey to construct a site-level variable measuring the percentage of workers with at least one family member (including themselves) in fair or poor health. We epect that ESI demand will be greater in sites where workers anticipate greater medical use due to poorer health among family members. Finally, following many earlier studies, we included dummy variables for industry to allow for possible variations in both the mean level of epected medical care use and its variance (riskiness) associated with the worker s industry. A Firm s Incentives to Offer Health Insurance Given workers demand, firms decisions to offer insurance will be influenced by the cost to the firm of offering insurance and the consequences of not offering. 11 As noted earlier, the per employee costs of searching for and administering insurance are likely to decline as the number of employees increases. However, there is some ambiguity as to whether the establishment or firm is the relevant structural unit for insurance offer decisions. To allow for both establishment-size and firm-size effects, we constructed a set of dummy variables that uniquely assigns each establishment to joint establishment-firm size categories. The establishmentsize classes are fewer than 10 employees, 10 to 24, 25 to 49, and 50 to 99; the firm-size classes also include the category of 100 or more employees. The omitted reference category is establishments with 50 to 99 workers that are part of a firm with 100 or more workers. Two other establishment characteristics that may affect the cost of administering ESI are the percentage of workers who are full time and whether the establishment has a high turnover rate (defined as greater than 30%). 12 Feldman et al. (1997) hypothesized that small firms decisions about whether to offer insurance would be influenced by the behavior of competing firms. Their data allowed them to construct direct measures of whether a firm s closest competitor offered health insurance. The 1997 RWJF employer survey did not repeat these questions, so we cannot directly measure whether competitors offered health insurance. Instead, we used two other characteristics of the 60 CTS sites: the percentage of workers in very large (500 or more employees) firms and the percentage of workers belonging to unions. Since nearly all very large firms offer ESI and nearly all union members have access to ESI through either their employer or their union, these variables should capture general labormarket pressures on small employers to offer ESI. Alternatively, a high concentration of large employers or high union membership also increases the likelihood that workers in small firms can obtain ESI coverage at lower cost as spouses of people who work for a large firm or belong to a union. This phenomenon might lead small employers to lower their likelihood of of- 124

8 Small Firms Demand fering insurance. Thus, the epected effect is ambiguous. The Premium Equation (Supply of Insurance) The supply equation includes variables representing epected medical payout, which depends on the price of medical care and characteristics of the establishments workers (described previously). The premium also depends on plan benefits, factors affecting the loading fee, and states regulations of health insurance premiums. Plan benefits are measured by the actuarial value of the policy, which was calculated for each policy offered from detailed information on plan characteristics (Callahan 1999), and the type of policy. Policy type is represented by three dummy variables for HMO, point-of-service (POS), and PPO policies, with indemnity policies being the omitted reference group. 13 We also include dummy variables for whether the policy has a waiting period for new employees and whether it ecludes coverage of pre-eisting health conditions for up to one year; other dummy variables include measures of the proportions of enrollees who were retirees under age 65, retirees 65 or older, or those eligible under provisions of the Consolidated Omnibus Budget Reconciliation Act (COBRA). We attempt to measure variations in the loading fee with variables that focus on insurers administrative costs, the riskiness of insuring an establishment of a particular size, and the structure of the market for health insurance. As with employers, we assume that insurers administrative costs are related to establishment/firm size and employee turnover. We also assume that the size of the risk premium is related to establishment/firm size, with costs generally decreasing as size increases. However, risk (and marketing costs) should be lower if the firm self-insures, which we measure with a dummy variable. 14 To control for insurance industry market structure, we constructed a Herfindahl inde using data from the CTS Insurance Followback Survey, which identified privately insured household respondents plans. The Herfindahl inde was constructed by applying CTS Household Survey weights to insurance plans to calculate insurers market shares in each CTS site. 15 Since concentration on the seller s side of the insurance market could be offset by concentration on the buyer s side, we also constructed a Herfindahl inde for employers in each site, using data from the employer survey on total employment by firms in each market. During the 1990s, a number of states instituted regulations designed to constrain premiums that insurers could charge small groups (Hing and Jensen 1999). We created two dummy variables to capture differences in rate-setting approaches: one indicates the absence of any rate regulation and the other the use of ratesetting bands or prohibitions against using groups health characteristics to set premiums. The reference group was states with community rating, which in principle should be most advantageous to small groups. Results Sample Characteristics and Descriptive Statistics Table 2 reports means and standard deviations of the models variables, for all establishments and by whether they offer insurance. Just under half (47.9%) of the establishments offered at least one general medical/surgical health insurance plan. The average monthly premium for single coverage in establishments that offered insurance was $ Almost two-thirds of the establishments were parts of firms with fewer than 10 employees, and another 14% were from firms with fewer than 25 employees. These smallest establishments and firms made up over 90% of the sample of establishments that did not offer insurance. Establishments that did not offer insurance also were more likely to be in the retail trade and nonprofessional services sectors. Although workers age and gender distributions in offering and nonoffering firms were fairly similar, a much smaller proportion of workers were full-time employees in nonoffering firms (75.8% compared to 90%). Lastly, estimated average family income per worker was about 20% lower in nonoffering firms ($30,110 compared to $36,246). Reduced-Form Offer Equation Table 3 reports results of the reduced-form probit model of small establishments decisions to offer insurance. The two key variables used to identify the Heckman estimation procedure are the percentage of workers in the area who are 125

9 Inquiry/Volume 39, Summer 2002 Table 2. Variable means and standard errors (SEs) (weighted), by establishment insurance offer Variable All establishments (N 11,613) Mean SE No insurance offer (N 4,296) Mean SE Insurance offer (N 7,317) Mean SE Offers health insurance a Price terms Employer-sponsored insurance premiums Self-purchased insurance premiums Availability of public insurance Availability of safety net services Average state income ta rate facing workers Average worker income ($1,000) Price of medical care (hosp. costs/patient day, site) Epected medical care use Proportion female workers Proportion workers aged 30 Proportion workers aged Proportion workers aged Proportion with family members in poor health (site) Industry Construction a Mining and manufacturing a Transportation, communications, and utilities a Wholesale trade a Retail trade a Finance, insurance, and real estate a Professional services a Other services a Establishment/firm size combinations Estab. size 1 9, firm size 1 9 a Estab. size 1 9, firm size a Estab. size 1 9, firm size a Estab. size 1 9, firm size a Estab. size 1 9, firm size 100 a Estab. size 10 24, firm size a Estab. size 10 24, firm size a Estab. size 10 24, firm size a Estab. size 10 24, firm size 100 a

10 Small Firms Demand Table 2. (continued) Variable Estab. size 25 49, firm size a Estab. size 25 49, firm size a Estab. size 25 49, firm size 100 a Estab. size 50 99, firm size a Proportion full-time workers Proportion workers in firms with 500 workers (site) Proportion workers in unions (site) Firm has high turnover ( 30%) a Local insurance industry concentration (site) Employer concentration (site) State insurance regulation (site) No rate regulation a.09 Weak rate regulation a.38 Insurance policy attributes Actuarial value Plan is HMO a Plan is POS a Plan is PPO a Policy has waiting period a Policy has pre-eisting condition eclusion a Firm is self-insured a Enrollee characteristics Proportion of enrollees retired, age 65 Proportion of enrollees retired, age 65 Proportion of enrollees through COBRA All establishments (N 11,613) Mean SE a Constructed as 0 1 dummy variable. No insurance offer (N 4,296) Mean SE Insurance offer (N 7,317) Mean SE

11 Inquiry/Volume 39, Summer 2002 Table 3. Reduced-form probit offer equation Independent variable Coefficient T-ratio Intercept Self-purchased insurance premiums Availability of public insurance Availability of safety net services Average state income ta rate facing workers Average worker income ($1,000) Price of medical care (hosp. costs/patient day) % female workers % workers aged 30 % workers aged % workers aged % with family members in poor health Construction Mining and manufacturing Transportation, communications, and utilities Wholesale trade Retail trade Finance, insurance, and real estate Professional services Other services Firm has high turnover ( 30%) Estab. size 1 9, firm size 1 9 Estab. size 1 9, firm size Estab. size 1 9, firm size Estab. size 1 9, firm size Estab. size 1 9, firm size 100 Estab. size 10 24, firm size Estab. size 10 24, firm size Estab. size 10 24, firm size Estab. size 10 24, firm size 100 Estab. size 25 49, firm size Estab. size 25 49, firm size Estab. size 25 49, firm size 100 Estab. size 50 99, firm size % of full-time workers % workers in firms with 500 workers % unionized workers in local market Employer concentration Insurance industry concentration No rate regulation Weak rate regulation Notes: Log likelihood 4, N 11,414. *** p. ** p 01. * p ***.111E ***.821** *** 4E 2** ** *** 1.588*** 1.562*** 1.428***.795*** 1.621*** 1.062***.709***.489*** 1.212*** 1.118***.205*.758***.632***.886***.582* ***.316***.157** union members and the percentage of workers in the area who are employed by large establishments (500 workers). It was hypothesized that these variables would influence small establishments willingness to offer insurance, but not the ESI premiums that insurance companies would charge small establishments. Both variables were positive and highly significant, suggesting that a small establishment was significantly more likely to offer insurance in markets with higher levels of either union membership or employment in large firms. Four variables in the reduced-form model represent supply-side effects. In this reducedform model, small establishments in states with no or less restrictive regulation of small group insurance premiums were significantly less likely to offer insurance relative to small establishments in states with some type of community rating. The other two supply-side variables are 128

12 Small Firms Demand the Herfindahl indees for the structure of the health insurance market. Establishments in areas with greater insurer concentration were significantly less likely to offer insurance. However, there was no relationship with buyer concentration. Selection-Adjusted Premium Equation Table 4 reports the results of the selection-adjusted premium equation. Most variables effects were consistent with our hypotheses. Premiums faced by small establishments were higher in markets where the insurance industry was relatively concentrated. (Again, buyer concentration was not significant.) Premiums also increased with the price of medical care and with the proportion of workers who had at least one family member in fair or poor health, but were lower for establishments that had higher proportions of younger workers. The actuarial value of the policy had a relatively large, though less than proportional, positive effect on the premium. Controlling for actuarial value, HMOs were about 10% cheaper, but we found no differences among POS, PPO, and indemnity plans. Premiums also increased with the number of retirees covered by the plan, and were somewhat higher for firms that self-insured. As in the reduced-form offer equation, premiums did not appear to be related to establishments industries. Premiums were largest for the smallest establishments, by roughly 10% to 15% for those with fewer than 25 workers. Once establishment and/or firm size increased past 50 workers, the premium difference shrunk to roughly 2% to 7% and was not statistically significant. Finally, premiums appeared to be significantly lower in states with no or weak regulation of small-group insurance premiums. Although this finding seems to contradict some other research (Buchanan and Marquis 1999; Nichols 1999; Chollet and Paul 1995), there are several key differences between this analysis and earlier studies. First, those studies typically analyzed employees offers of insurance or ESI coverage, rather than ESI premiums. Increases in premiums were inferred from a negative relationship between rate regulation and coverage. Second, the premiums we analyzed were obtained from establishments that offered insurance. If high-risk establishments in unregulated states faced higher insurance quotes than similar firms in regulated states, they would be less likely to offer insurance. Consequently, the average premium for establishments that actually offer insurance could be lower in unregulated states due to unobserved differences in the risk profiles of offering establishments in regulated and unregulated states. Third, the premiums in this analysis were adjusted for cross-sectional variations in the cost of living. When premiums were measured in nominal terms, the coefficients of the rate regulation variables became much smaller, which suggests that the rate regulation variables may be partially confounded with other, unobserved state characteristics. Thus, it may not be appropriate to interpret these results as strictly due to differences in insurance rate regulation. The bottom panel of Table 4 reports the correlation between the premium and the reducedform offer equations, lambda, and the weak instrument test. As epected, lambda was negative and statistically significant (p.01). The negative correlation suggests that firms not offering insurance do in fact face higher, though unobserved, premiums than firms offering insurance, and that the unobservable factors influencing both the offer decision and the premium are correlated between the two equations. Adjusted for selection bias, the predicted average single monthly premium for firms that did not offer insurance was $180, which was 18.4% greater than the predicted monthly premium of $152 for firms that did offer insurance. The weak instrument test indicates that the eogenous identifying variables were significantly and strongly related to the probability of offering insurance. The partial-r 2 of.042 represents 14% of the variance eplained by the model, and the F-statistic for the test of joint insignificance of the identifying variables is 60.2, which rejects the null of joint insignificance at p. Structural Offer Equation Test of overidentifying restrictions. A key element of our estimation strategy is the assignment of the premium instrument based on the predicted probability of offering insurance generated from the reduced-form offer model reported in Table 3, which is a function of eogenous variables only. The overidentifying re- 129

13 Inquiry/Volume 39, Summer 2002 Table 4. Selection-adjusted logged premium regression equation Independent variable Coefficient T-ratio Intercept Price of medical care (hosp. costs/patient day) ($100) % female workers % workers aged 30 % workers aged % workers aged % with family members in poor health (site) Construction Mining and manufacturing Transportation, communications and utilities Wholesale trade Retail trade Finance, insurance, and real estate Professional services Other services Firm has high turnover ( 30%) Estab. size 1 9, firm size 1 9 Estab. size 1 9, firm size Estab. size 1 9, firm size Estab. size 1 9, firm size Estab. size 1 9, firm size 100 Estab. size 10 24, firm size Estab. size 10 24, firm size Estab. size 10 24, firm size Estab. size 10 24, firm size 100 Estab. size 25 49, firm size Estab. size 25 49, firm size Estab. size 25 49, firm size 100 Estab. size 50 99, firm size Employer concentration Insurance industry concentration No rate regulation Weak rate regulation Actuarial value Plan is HMO Plan is POS Plan is PPO Policy has waiting period Policy has pre-eisting condition eclusion Firm is self-insured % of retired enrollees, age 65 % of retired enrollees, age 65 % of COBRA enrollees ; p. Lambda (Wald test of independent equations 6.72; p.009) Weak Instrument test F(7,7118) 60.2 Note: N 7,118. *** p. ** p 01. * p ***.134** ***.242** ** ** ** ***.202***.229***.366**.105** *** strictions test (Greene 1990) for the premium instrument produced an R 2 of 1 and a corresponding 2 of 12.2, which is well below the critical value of 22.3 for rejecting the null hypothesis at p.01. In contrast, estimating equation 3 using the same approach as Feldman et al. (1997) produced a highly significant and quantitatively large elasticity estimate for P esi of 130

14 Small Firms Demand Table 5. Structural logit offer equation Independent variable Coefficient T-ratio Intercept Employer-sponsored insurance premiums Self-purchased insurance premiums Availability of public insurance Availability of safety net services Average state income ta rate facing workers Average worker income ($1,000) Price of medical care (hosp. costs/patient day) ($100) % female workers % workers aged 30 % workers aged % workers aged % with family members in poor health (site) Construction Mining and manufacturing Transportation, communications and utilities Wholesale trade Retail trade Finance, insurance, and real estate Professional services Other services Estab. size 1 9, firm size 1 9 Estab. size 1 9, firm size Estab. size 1 9, firm size Estab. size 1 9, firm size Estab. size 1 9, firm size 100 Estab. size 10 24, firm size Estab. size 10 24, firm size Estab. size 10 24, firm size Estab. size 10 24, firm size 100 Estab. size 25 49, firm size Estab. size 25 49, firm size Estab. size 25 49, firm size 100 Estab. size 50 99, firm size % of full-time workers % workers in firms with 500 workers *** 5***.0089E ***.2482* 6 0*** ***.2832***.2638***.2326***.0828**.2900***.1345**.0743* ***.1552* *.1788***.2531*** % unionized workers in local market.2035* * Normalized log-likelihood full model: 7, Pseudo R 2 :.31 Note: n 11,613. *** p. ** p 01. * p , which is somewhat smaller than their estimate but considerably larger than other estimates of small establishments sensitivity to premium variations. However, the overidentifying restrictions test for this approach produced a R 2 value of.245, substantially in ecess of the critical value of approimately. This result strongly suggests that assigning values of the premium instrument based on actual offer behavior violates the eogeneity assumption and could be one reason for the large elasticity estimates obtained by Feldman et al. (1997). Premium estimate for all small establishments. In Table 5, we present the estimates of the structural offer equation estimated over the sample of establishments with fewer than 100 workers. The premium for employer-sponsored insurance was negative and highly significant, but moderate in magnitude. The average marginal probability of 5 means that a $1 de- 131

15 Inquiry/Volume 39, Summer 2002 Table 6. Premium coefficients, predicted premiums, predicted offer rates, and elasticities, by selected establishment characteristics Establishment characteristic Establishment size Percent low-wage ($7 per hour) workers 75% 50% 75% 50% Average family income per worker $15,940 (0 5 th percentile) $15,940 $18,401 (5 th 10 th percentile) $18,401 $23,158 (10 th 25 th percentile) $25,158 (25 th 100 th percentile) Coefficient a (NS) a All coefficients are significantly different from 0 at p.01, unless noted by (NS). b Adjusted for selection bias. Predicted premium ($) b Predicted offer probability Elasticity crease in premium would increase the probability of offering insurance by 5 percentage points, for eample, from.4800 to The corresponding elasticity,.54, suggests that a 10% decrease in the average monthly premium ($16.68) is predicted to increase the probability of offering insurance by about 5.4%, or from the sample mean of.48 to Variations in Premium Estimates by Establishment Characteristics We re-estimated the structural offer equation using interaction variables to allow the premium coefficient to vary with establishment size, with the percentage of workers who receive low wages, and with the estimated average family income per worker. The establishment/firm size dummy variables were collapsed into four categories corresponding to establishments with fewer than 10, 10 to 24, 25 to 49, and 50 to 99 employees. Low-wage workers were defined as workers earning less than $7 per hour. Establishments then were grouped by whether the percentage of low-wage workers was less than 50%, between 50% and 75%, or greater than 75%. Finally, to approimate establishments with a high proportion of low-income workers, we assigned establishments to categories based on whether the estimated average income per worker was less than the 5th percentile ($15,940), between the 5th and 10th percentiles ($18,401), between the 10th and 25th percentiles ($23,158), or above the 25th percentile of the distribution of average income per worker across all small establishments in the sample. In Table 6, we report the premium coefficient estimates, predicted offer rates and selection-adjusted premiums, and elasticity estimates for each of the three alternative ways of grouping small establishments. In general, establishments responsiveness to changes in premiums did vary with establishment characteristics. The very smallest establishments, those with fewer than 10 employees, had the lowest offer rate, faced the highest average premium, and were most responsive to a reduction in premium, with an elasticity estimate of.63. In other words, a 10% reduction in those firms average premium (from $176 to $158) would increase their offer rate by 6.2% (from.40 to.425, or 2.5 percentage points). While relatively small, this elasticity is much larger than the estimate of only for establishments with 50 or more employees, which essentially were unresponsive to variations in premiums. Establishments with a high proportion ( 75%) of low-wage workers or low average income per worker (below the 25th percentile) 132

16 Small Firms Demand showed higher degrees of price sensitivity, with elasticities ranging from.88 to The elasticity estimates for other establishments were smaller, ranging from.30 to.58. Other Determinants of Small Establishments Offer Decisions Small establishments offer decisions also appeared to be sensitive to the estimated value of average worker income and to the prices of public alternatives to ESI. The coefficient of the average income variable was highly significant and suggests that the establishment s offer decision is influenced by worker demand. A 10% higher average income was associated with a 4.9% increase in the offer rate. Both the availability of public insurance coverage through Medicaid (or a similar state-subsidized insurance program) and care from the perceived safety net had negative and statistically significant effects on small establishments offer decisions. These variables negative coefficients are consistent with the hypothesis that they are substitutes for employer-sponsored insurance. The mean proportion of workers in small establishments with at least one family member covered by public insurance was 4.4%. Doubling this proportion is estimated to reduce small establishments offer rate to.37, or by 23%. A 10% increase in the percentage of uninsured people feeling that they can get needed medical care without financial difficulty (from 70.7% to 77.8%) would reduce the offer rate by about 5.5% (to.45). (In contrast, the coefficient estimates for the price of an individually purchased insurance policy and of the state marginal ta rate were not statistically significant.) In terms of factors affecting the establishment s offer decision, we see that the percentage of full-time workers, and establishment and firm sizes were all highly significant, as epected, since insurance is essentially a fied cost per worker. The effects of industry, however, were trivial. Measuring both establishment and firm sizes indicated that the effect of establishment size decreased as firm size increased. Finally, it does appear that market-level competition for workers between small and large establishments has a significant influence on small establishments offer behavior. The offer-rate elasticity associated with the percentage of workers in large firms was.2: a 10% greater concentration of workers in large firms should increase the offer rate by about 2%. The percentage of workers in large firms (mean 28.4%) varied substantially across the 60 CTS sites, with eight sites having values less than 20% and nine sites with values greater than 40%. The elasticity estimate suggests that a twofold difference in this key market factor would result in about a 20% difference in the probability of offering insurance. Implications for Policy How responsive would small establishments be to subsidies that lower the cost of health insurance? Our primary finding, that small establishments premium elasticity of demand is only.54, suggests that the subsidy-induced response would be modest at best, and that subsidies would have to be large to entice a significant number of additional establishments to offer insurance. How reliable is our estimate? Although other studies have estimated both much higher and much lower elasticities (Feldman et al. 1997; Jensen and Gabel 1992; Marquis and Long 2001), several have produced similar values, falling between.3 to.8 (Gruber and Lettau 2000; Leibowitz and Chernew 1992; Buchanan and Marquis 1999; and the upper range of estimates found by Helms, Gauthier and Campion 1992 and Thorpe et al. 1992). Moreover, our estimate is based on data from a recent large and nationally representative survey applied to a comprehensive model that included measures of the costs of alternative insurance options adjusted for variations in plan benefits and controlled for important worker, establishment, and market characteristics. In addition, our econometric methods adjusted for the possible effects of selection bias and satisfied tests for valid instrumental variables. We also found that the smallest establishments faced the highest premiums and were least likely to offer insurance, and that the premium elasticity declined rapidly as establishment size increased. Although the smallest establishments were the most price sensitive, their small size also means that relatively few people worked there. Thus, premium subsidies targeted to very small establishments would have a smaller impact on the percentage of workers offered employer-sponsored insurance than on the 133

17 Inquiry/Volume 39, Summer 2002 Table 7. Effect of $1,000 premium subsidy to firms on number of workers without offers of health insurance Target group Number of workers (millions) Workers without offers Number (millions) % All small establishments ( 100 workers) With $1,000 subsidy Low-wage ( $7/hour) workers in small establishments With $1,000 subsidy Firms with less than 25 workers With $1,000 subsidy percentage of establishments offering health insurance. Indeed, we estimate that the increase in the percentage of workers offered health insurance as the result of a reduction in premiums would be about one-third as large as the percentage of small establishments that would be induced to start offering health benefits. To illustrate, several recent proposals have offered a ta credit of up to $1,000 for purchasing individual insurance. The inefficiency of employer premium subsidies is shown in Table 7, which presents the simulated impact of a $1,000 reduction in annual premium costs (which is roughly equivalent to $840 in 1997 prices). Although 52% of small establishments failed to offer health benefits, only 32% (18.3 million) of the 56 million workers in these establishments actually lacked offers from their employer. A $1,000 subsidy is estimated to lower the proportion without offers to 27%. Targeting subsidies to low-wage workers in establishments with fewer than 100 workers or to only very small establishments (those with fewer than 25 workers) has a greater proportional impact, though only one million and two million additional workers, respectively, are estimated to gain offers of coverage. Moreover, three in five workers who lack insurance offers do not have low wages, according to our definition, and one in five works for establishments with 25 or more workers. It is important to note that the effect of an employer premium subsidy on the number of workers who gain insurance offers from their employer would be substantially greater than the number of workers who actually gained coverage as a result of the subsidy. This is because a majority of workers in firms that do not offer health benefits (59%) are covered through a spouse s policy, purchase individual coverage, or receive public insurance coverage. Moreover, even with subsidized premiums, some would fail to take up offered coverage. Epansion of public insurance (for eample, Medicaid and the State Children s Health Insurance Plan) is another option for increasing health insurance coverage. Our results suggest that epansions in public insurance enrollment would induce a very small number of firms to stop providing health insurance. Presumably, firms induced to stop offering insurance would employ mostly low-income workers. Take-up rates among these workers are likely to be low, so this aspect of displacement (often termed crowd-out) is unlikely to significantly dilute the number of people who would gain coverage. Similarly, investments in the capacity of the safety net to provide direct care to the uninsured would reduce demand for employer-sponsored coverage, but would be unlikely to have very large effects on the number of workers with offers of employer-sponsored insurance. After a long period of flat insurance premiums and tight labor markets, we are now in a period where premiums are rising faster than inflation and unemployment is increasing. These trends forebode a weakening system of employer-sponsored health insurance and a probable increase in the already large number of uninsured. Although establishments demand for insurance is partly a reflection of workers demand, targeting subsidies at small establishments appears to be a blunt and inefficient policy instrument. Targeting subsidies directly to low-income workers, regardless of their employment setting, 134

18 Small Firms Demand would be a more efficient way of epanding insurance coverage. Future research should focus on gaining a better understanding of individuals demand for health insurance, the nature of the employer s agency role, and how characteristics of health benefits (e.g., plan benefits, cost sharing, plan choices) affect worker labor supply and take-up decisions. Notes The authors are very grateful to Roger Feldman, A. Bowen Garrett, Katherine Swartz, and two anonymous referees for their helpful comments, although they bear no responsibility for the final content of this manuscript. The authors also acknowledge and thank Nancy Odaka of Social and Scientific Systems, Inc., for her ecellent computer programming support, and Bridget O Leary for her help with manuscript preparation. Financial support was provided by the Robert Wood Johnson Foundation through its support of the Center for Studying Health System Change. 1 In developing this framework, we also make the simplifying assumptions that employees bear the full cost of insurance (Gruber 2000) and that workers heterogeneous preferences can be represented by simple averages (Gruber and Lettau 2000). We believe that relaing these assumptions would complicate both the model and its empirical estimation without appreciably altering our basic conclusions. 2 More formally, the instrument for P esi in the structural offer equation is given by: (Pesi Pesi,d P esi,f ) (V *) h(p m, M f, B f, L, R) (V *) (firm predicted to offer), (Pesi Pesi,d P esi,f ) (4a) (V *) h(p m, M f, B f, L, R) (1 (V *)) (firm predicted to not offer). (4b) The epression h(), the premium equation 3 from the tet, depends on P m,m f,l,and R, which are observed for all firms. In calculating 4a and 4b, we hold constant the level of benefits, B f, setting it to the value of a policy at the lower range of observed policies, one presumably relevant to a firm that does not offer insurance. The epression V * represents the predicted value from the reduced-form probit equation of whether the firm offers insurance, where V is the set of eogenous variables in the model. The term is the product of the correlation between the reduced-form offer equation and the supply (premium) equation, rf, and the correlation between the error terms of the two equations. The epressions () and () are the standard normal and cumulative normal density functions, respectively, evaluated at the predicted value V * estimated for each firm from the reduced-form offer model. Our formulation differs from 4a and 4b, which Feldman et al. (1997) employed, in that we conditioned the equations on (V *).5 and (V *).5, respectively, where (V *) is the predicted probability from the reduced-form offer equation. 3 Standard errors in the reduced-form and selection-corrected premium equations were not adjusted for comple survey design because SU- DAAN lacks the capability to estimate a Heckman selection model and because other statistical software lacks the capability to account for all aspects of the survey s sampling structure. 4 Information on the ACCRA cost of living inde can be found at Values for local market areas that were missing from the ACCRA series were imputed using a technique developed by McMahon (1991). 5 We chose to use single premiums because of complications that arise from varying definitions of a family. Although most firms policies quote the same premium for all multi-person coverage, some policies quote different premiums depending on family structure and/or the numbers of adults and/or children in the family. Rather than try to standardize these variations, we simply used the premium for worker-only coverage. 6 We computed an estimate of the marginal state income ta rate faced by the average worker in each firm using data from the CTS household survey on workers wage rates, industry of employment, and family incomes. For each combination of wage rate, firm size, industry, and state, we calculated average family income using data from the household survey. We then used the corresponding information from the employer survey to calculate a firm-specific, average family income per worker. This value then was compared to the income ta tables for each state to identify the appropriate marginal ta rate for the average worker in that firm. 7 We estimated both logistic and linear probability models with data for 28,091 people who were interviewed by the CTS Household Survey and were employed by a small establishment. The dependent variable was a dichotomous indicator of whether the person had a family member covered by public insurance. The independent variables were those common to the household and employer surveys: age categories, wage categories, 135

19 Inquiry/Volume 39, Summer 2002 gender, industry, and establishment size. The linear and logistic models had very similar eplanatory power (about 5%) and generated very similar and highly correlated predicted probabilities (mean 9,.91). We used the logistic model, since it constrains the predicted probabilities to fall between 0 and 1, to assign values to establishments. The predicted probabilities ranged from to.481 across all establishments. 8 Other researchers have tried alternatively to capture the availability of providers that typically provide substantial amounts of charity care (the safety net) by measuring the availability of public hospitals, major teaching hospitals, and public clinics, which are usually thought of as making up the bulk of the safety-net (Rask and Rask 2000; Cunningham 1999). This approach has three potential difficulties: 1) the actual amount of free care provided varies considerably within each of these classes of providers; 2) other important providers of free care may be omitted; and 3) it is difficult to account for geographic proimity between potential safety-net providers and the uninsured population. 9 The calculations were subject to a minimum sample size of at least 20 observations per category. If the sample size was inadequate, industry groupings were collapsed or eliminated. 10 This market-level variable is highly correlated with measures of average physician compensation derived from the CTS Physician Survey. 11 These variables correspond to the measures of competitor s behavior used by Feldman et al. (1997) to identify the structural demand equation. 12 A turnover rate of 30% was approimately the 75th percentile of the distribution of turnover rates across establishments. 13 Although the estimated actuarial value makes an adjustment for plan type, the adjustment may be imperfect. In addition, premiums may vary across plan types because of variations in pricing behavior not captured by the actuarial adjustment. 14 Premiums for self-insured firms were derived from a question asking for the premium equivalent of these plans. Self-insured respondents then were asked whether the premium equivalent included administrative costs and reinsurance or stop-loss coverage costs. The costs of these items also were solicited. In calculating self-insured premiums, the premium equivalents were edited so that they included administrative costs. Information on reinsurance costs was not included because it was deemed to be unreliable and had high rates of item nonresponse. When premium equivalents were not provided, information on COBRA premiums were used, again adjusted if necessary to include administrative costs, but not reinsurance costs or the 2% COBRA surcharge. 15 A given insurer often will market numerous types of insurance products, spanning major categories of plans (HMOs, PPOs, etc.). 16 We also estimated alternative, more general specifications of the reduced-form offer equation to assure that results were not sensitive to the Heckman specification. Results were robust. We also evaluated the instrumental variable created by our approach by comparing mean predicted values to mean observed values across firms with differing predicted probabilities of offering insurance. The predictions corresponded closely with observed values. In contrast, a standard instrumental variable approach created a variable that produced a similar elasticity estimate, but the predictions tended to underestimate premiums when firms had low offer probabilities. 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