The Welfare Effects of Provider Reimbursement Rates: Evidence from the Nursing Home Industry

Transcription

1 The Welfare Effects of Provider Reimbursement Rates: Evidence from the Nursing Home Industry Martin B. Hackmann Job Market Paper November 20th, 2013 Abstract This paper estimates the welfare effects of Medicaid provider rate changes in the nursing home industry. To disentangle the effects on Medicaid spending, consumer welfare, and provider profits, I estimate a model of demand and supply. Applying the model to provider and consumer micro data from Pennsylvania delivers two main results. First, I find that nursing homes increase the number of skilled nurses per resident by 2-3% in response to a universal 1% increase in the Medicaid reimbursement rates. Second, I find that staffing levels are on average inefficiently low. The demand estimates suggest that the total willingness to pay of all residents in a given nursing home equals $109,000 per year for an additional skilled nurse. On the other hand, detailed information on wages and fringe benefits from cost reports indicate that it costs providers only $82,000 per year to employ another skilled nurse. Combining the demand and cost estimates with the evidence on provider responses suggests that an increase in Medicaid rates can enhance social welfare. Specifically, I find that a universal increase in Medicaid reimbursement rates of 5% would lead to an annual welfare gain of $27 million in Pennsylvania, about 24% of the underlying increase in Medicaid spending, ignoring the deadweight loss from raising the additional Medicaid dollars. I am deeply indebted to my advisers Steven Berry, Philip Haile, and Amanda Kowalski for their invaluable guidance and support. I thank Nikhil Agarwal, Joe Altoni, Zack Cooper, Camilo Dominguez, Maximiliano Dvorkin, Mitsuri Igami, Adam Kapor, Fabian Lange, Costas Meghir, Nora Müller-Alten, Christopher Neilson, Vincent Pohl, Ted Rosenbaum, and Seth Zimmerman for their thoughtful comments. Jean Roth and Mohan Ramanuan provided invaluable help with the data. Funding from the National Institute of Aging is gratefully acknowledged. All errors are my own. martin.hackmann@yale.edu. Please visit my webpage to access the most recent version of this paper. 1

2 1 Introduction Reductions in provider rates for Medicare and Medicaid consumers are frequently used to contain public health care spending both at the national and the state level (see e.g. Brill, Lundy and Bookman (2013) and Kaiser Family Foundation (2013)). However, reimbursement cuts also lower the profitability of providing services to beneficiaries, which may lead providers to cut back on doctors, nurses, and other key inputs for the production of health care quality. This introduces a tradeoff between benefits from lower public health expenditures on the one hand and costs from a reduction in consumer surplus and provider profits on the other. In this paper, I investigate this tradeoff for Medicaid rates in the nursing home industry. Nationally, Medicaid covers about two thirds of the 1.5 million nursing home residents and spends annually about 69 billion dollars on nursing home care (about 17% of total Medicaid spending). Understanding the effects of Medicaid rate changes on quality of care and social welfare is critical for the design of reimbursement policies and of growing importance as the US population ages. Over the course of the next 40 years, the US population share of people aged 80 and older is expected to double from 3.7% to 7.4%. To disentangle the effects of Medicaid price changes on the quality of care, provider profits, and consumer surplus, I estimate a model of demand and supply in this industry. The supply side model describes providers optimal nurse staffing decisions as well as the optimal private rates charged to consumers who pay out-of-pocket. Both depend on the regulated Medicaid reimbursement rates. The demand model describes consumer preferences for proximity and staffing levels, as well as the role of private rates for consumers who pay out-of-pocket. This industry model allows me to quantify the key effects of the policy tradeoff. Specifically, I use the model to quantify a) the equilibrium effects of changes in Medicaid provider rates on the providers optimal staffing and pricing decisions and b) the effects of these decisions on consumer surplus, provider costs, and provider revenues. Combining these results, I can quantify the effects of Medicaid rate changes on public spending, consumer surplus, and provider profits. To estimate the industry model, I combine detailed provider and consumer micro data from Pennsylvania. On the supply side, I estimate the providers equilibrium strategies, which determine the equilibrium effects of changes in Medicaid rates on optimal staffing as well as pricing decisions. 2

3 One empirical advantage of this approach, as opposed to the estimation of first order conditions, is that I do not have to simulate the new equilibrium in order to quantify the supply responses to changes in Medicaid rates. One empirical challenge of both approaches is that each provider s Medicaid rate is determined based on previously reported own costs as well as costs of all other providers from a size- and region-based peer group. This introduces an endogeneity problem to the extent that the provider s costs as well as costs from local competitors affect the optimal staffing and pricing decisions directly. To address this concern, I first isolate the reported cost variation of those providers in the peer group that operate in different nursing home markets. I assume that these cost shocks affect optimal input and pricing decisions of providers located in the given market through the reimbursement rule only. In a second step, I simulate a Medicaid rate that varies in provider costs from other nursing home markets only and use this rate as an instrument for the actual rate. This simulated instrument exploits knowledge about the reimbursement formula and thereby increases statistical power. Finally, to quantify the effects of changes in nurse staffing decisions on each provider s costs, I exploit information from Medicaid cost reports on wages and fringe benefits for nurses by skill type. On the demand side, I estimate the consumers indirect conditional utility functions, which depend on distance and nurse staffing levels, as well as the private rate if the consumer pays outof-pocket. There are two main empirical challenges to the estimation of demand. First, staffing and pricing decisions are endogenous and potentially correlated with unobserved demand shocks, which affect consumer utility as well. Second, Certificate of Need (CON) laws restrict entry and capacity investments in this industry. Therefore, nursing homes may reach their physical capacity in which case they have to reect potential residents. The demand estimation has to take into account that these capacity constraints restrict the consumer s choice set. To isolate the effects of prices and staffing levels on the consumer s indirect utility, I use instrumental variables. These include the exogenous simulated Medicaid rate described above as well as other supply shifters that are excluded from the indirect utility function. To address the second concern, I exploit admission and discharge information on the universe of nursing home residents to construct the number of open beds of all facilities on each day in the sample period. In the demand estimation, I include only those providers in the consumer s choice set that have at least one open bed on the day the consumer was admitted to any nursing home. In other words, consumers are admitted on a 3

4 first-come-first-serve basis. Applying the model to the data delivers two main results. First, I find that nursing homes increase the number of registered and licensed practical nurses per resident, henceforth skilled nurses per resident, by 2-3% in response to a universal 1% increase in the Medicaid rate. I do not find evidence in favor of other meaningful input or price adustments. Second, I find that current staffing levels are on average inefficiently low. The demand estimates suggest that the oint willingness to pay of all residents in a given nursing home equals $109,000 per year for an additional skilled nurse. On the other hand, detailed information on wages and fringe benefits from cost reports indicates that it costs providers only $82,000 per year to employ another skilled nurse. Based on a social planner s problem, I conclude that current staffing levels fall short of optimal staffing levels by about 29%, suggesting that higher minimum staffing standards may enhance social welfare. These findings also indicate that the social costs from lower consumer welfare and provider profits can outweigh the benefits from lower public spending if the regulator reduces Medicaid rates. Conversely, an increase in Medicaid rates can enhance social welfare. Specifically, I calculate the welfare effects of a universal increase in Medicaid reimbursement rates of 5%. My estimates suggest that the rate increase raises Medicaid spending annually by $114 million dollars in Pennsylvania. However, the rate increase also raises consumer welfare and provider profits annually by $142 million. This suggests an annual welfare gain of $27 million, about 24% of the additional Medicaid spending, ignoring the deadweight loss from raising the additional Medicaid dollars. While the estimates for the deadweight loss from taxation vary considerably in the public finance literature, ranging from 5% to 30%, they generally suggest that the potential industry gains may be offset entirely by additional tax distortions. Because of diminishing marginal utilities for skilled nurses, as shown in the empirical analysis, these findings encourage small Medicaid rate increases and discourage Medicaid cuts. However, the findings do not indicate that modest to large Medicaid rate increases are adequate to address the inefficiently low staffing levels because the deadweight losses from taxation can outweigh the welfare gains in this industry. Finally, I test the validity of the main parameter estimates by estimating the nursing homes first order conditions. These first order conditions identify the firm-specific cost structure that is consistent with the observed staffing and pricing decisions. I address the role of capacity constraints 4

5 in the first order conditions, which can mitigate the firm incentives to raise quality or lower prices. Specifically, I model consumer arrivals and discharges of residents as continuous time Poisson processes and obtain a closed-form expression for the steady-state probability that a provider operates at full capacity. This probability depends on the primitives of the economic model and reflects the idea that capacities bind on only some days during the year. I compare the cost estimates with evidence from cost report data and find that both the estimated marginal costs and the estimated input prices are very similar to the observed average variable costs and observed wages and fringe benefits respectively. This evidence supports the main modeling assumptions and the magnitude of the estimated preference parameters. This paper contributes to three strands of literature. First, this paper contributes to the literature on the effects of Medicaid reimbursement rates on nursing home staffing decisions (see e.g. Nyman (1989); Gertler (1989); Gertler (1992); Cohen and Spector (1996); Grabowski (2001); Feng et al. (2008); Harrington et al. (2008)). Despite important policy implications for the design of Medicaid reimbursement policies, there is still only limited and mixed empirical evidence on this relationship. This study aims to provide new empirical evidence on the equilibrium effects of changes in Medicaid rates on optimal nurse staffing decisions using a novel source of plausibly exogenous variation in Medicaid rates. Although several studies employ instrumental variable strategies to investigate this relationship, concerns regarding the validity of these instruments persist. 1 Second, this paper builds on studies on the demand for nursing home care. Most studies in this literature focus on the extensive margin, that is whether consumers choose nursing home services or other forms of care in the long term care spectrum (e.g. Grabowski and Gruber (2007); Goda, Golberstein and Grabowski (2011)). 2 This paper focuses on the intensive margin, the choice of a specific nursing home, and is closely related to the demand model in Ching, Hayashi, and Wang (2012), henceforth CHW. The authors use nursing home survey data from Wisconsin to quantify the role of rationing in this industry. There are two maor differences between this analysis and their approach. First, CHW focuses on consumer demand and abstracts from endogeneity in nurse staffing levels, which is key in my analysis. Second, CHW assumes that the admission process is centralized for the entire year and that nursing homes offer priority access to more lucrative private 1 For example, Gertler (1989) uses the nursing home s reported capital costs as a source of exogenous variation in the cost-based Medicaid reimbursement rate. The exclusion restriction is violated if consumer value capital costs as they may be correlated with room size. 2 Giacalone (2000) provides a summary of earlier demand studies. 5

6 payers before they fill the remaining beds with Medicaid consumers. This abstracts from the fact that the payer sources may vary between Medicare, Medicaid, and private sources over the course of a nursing home stay and that consumers are admitted and discharged at any time during the year. Using micro data on admission dates, discharge dates, and the consumer s mix of payer sources, I can address both aspects in the empirical analysis. Third, this paper is also related to the industrial organization literature on endogenous product characteristics (see e.g. Fan (2013) for an overview). These studies emphasize the computational burden of simulating equilibria with endogenous prices and product characteristics. I avoid these challenges in the baseline analysis by estimating the equilibrium strategies directly. However, I revisit the baseline supply side estimates in the extension section, where I estimate the firms first order conditions as well. Similar to Fan (2013), I add an endogenous product characteristic to the typical Berry, Levinsohn and Pakes (1995) supply side model. I innovate on former approaches by providing a novel framework to address the role of rationing in the firm s first order conditions. The remainder of this paper is organized as follows. In Section 2, I provide a brief discussion of the institutional background before I discuss a theoretical model in Section 3 and the empirical strategy in Section 4. I describe the data in Section 5 and I discuss the results as well as the counterfactual exercise in Section 6. In Section 7, I revisit the baseline estimates using the first order conditions. Finally, I conclude in Section 8. 2 Institutional Background Before I turn to the theoretical and the empirical analysis, I discuss three important institutional details concerning the mix of payer sources, health care related inputs, and the CON law, which motivate the design of this analysis. First, Medicaid is the predominant payer source for nursing homes services, which covers about two thirds of the nursing home residents. The program covers financially indigent consumers that typically struggle with multiple chronic disabilities. The remaining resident days are typically either paid out-of-pocket (about 20-25%) or covered by Medicare (about 10-15%). 3 Medicare is designed 3 Some consumers are covered by a private long-term-care insurance plan or a veteran s insurance policy but these programs pay for only about 2% of the resident days in the sample population. This is consistent with evidence from Giacalone (2000), who notes that out-of-pocket payments constitute the largest private source of financing for nursing home care by a large margin, see page 96 and Table 5.5 on page 97. 6

7 to cover post-acute rehabilitative care services and pays up to 100 days of a given nursing home stay. If the patient stay exceeds the Medicare covered length of stay, then the patient typically either pays the additional days out-of-pocket or becomes eligible for Medicaid depending on the person s financial background. Both programs, Medicaid and Medicare, pay the nursing home a pre-determined reimbursement rate per resident day. It is important to emphasize that these programs may heavily distort the provision of health care quality in this industry. The nursing home demand of the beneficiaries is perfectly price inelastic. In other words, the beneficiaries do not internalize the cost of service. Therefore, providers may provide inefficiently high or inefficiently low quality of service depending on the generosity of the reimbursement rates. Second, to provide adequate quality of care, nursing homes employ a mix of nurses with different skill levels. Registered nurses and licensed practical nurses monitor patients, assess their health status, and can give medications and treatments, whereas nursing aides typically provide basic level of care including moving, repositioning, and bathing residents, as well as helping patients with their meal. Evidence from the literature as well as cost reports suggest that skilled nurses are key inputs in the labor intense nursing home production technology. 4 In addition to nurses, nursing homes also employ specialized therapists who typically provide intensive and more expensive rehabilitative care for a short-stay oriented resident population. In the empirical analysis, I use staffing ratios for nurses and therapists as measures of input quality and test whether nursing homes change these inputs in response to changes in Medicaid rates. Third, a CON law restricts entry and capacity investments in the nursing home industry in Pennsylvania. Based on these legislative barriers to invest, I treat the location and the size of facilities as exogenous and model endogenous pricing and staffing decisions in a static industry model. These barriers may also exacerbate the role of binding capacity constraints on consumer demand. I address this effect in the empirical demand analysis using detailed micro data on dayto-day occupancy levels of all nursing homes. Finally, these barriers to entry and invest can further reduce the competitiveness of local nursing home markets, which may lead nursing home providers to offer inefficiently low quality of service. 4 Evidence from the literature suggests a positive relationship between skilled staffing ratios and quality outcomes (see e.g. Lin (2012); Konetzka, Stearns and Park (2008)). With respect to the evidence from costs reports, I find that nurses account for about 49% of variable costs and 39% of total costs in Medicaid certified facilities in Pennsylvania. 7

8 3 Theoretical Model of Demand and Supply I consider a static model of the nursing home industry in which providers compete in local markets for nursing home residents (e.g. the county). Nursing home providers obtain revenues from nursing home residents and incur costs from providing services. The revenues depend on the resident s payer source which may be Medicaid, private, or Medicare. Medicaid and Medicare pay a pre-determined reimbursement rate per resident day, R caid and R care, which the provider takes as given. The provider may, however, choose an arbitrary daily price P from consumers who pay out-of-pocket. Nursing homes also choose a vector of quality inputs (e.g. the number of registered nurses per resident), which is summarized by a quality index θ. These inputs determine the quality of service and are valued by all payer types. 5 The total cost of nursing home services depends on the total number of provided resident days Q and the quality index θ as well as observable cost shifters X c and unobservable (from the perspective of the econometrician) cost shifters ω. The provider observes both types of shocks. I assume constant marginal costs per resident day such that the cost function for provider is given by C = MC(θ, X c, ω ) Q + F C, where F C refers to fixed costs. Consumers value the quality of service and dislike the distance to facility, D i, and the private rates, P, if they pay at least some days of their stay out-of-pocket. In contrast, I assume that consumers who are covered by Medicare and Medicaid for their entire stay act completely inelastic with respect to prices. I express consumer i s preferences for facility in terms of her conditional indirect utility function u i = u NH (D i, θ, X d, ξ, X d i, η i ) + β p (W i P i ), (1) which combines preferences for the nursing home good, u NH, and preferences for the consumption of W i P i units of a numeraire good. Here, W i denotes the consumer s wealth and X d and ξ refer to observable and unobservable facility characteristics respectively. Finally, observable and 5 I assume that the quality of service is common across payer types within a facility, which is consistent with the legislative environment that prohibits health care quality differentiation based on the payer type. 8

9 unobservable differences in consumer tastes are captured by Xi d and η i. I assume that new residents evaluate the facilities in their local market based on these grounds and choose the provider that best meets their needs. Therefore, the payer-type specific residual demand curve for provider depends not only on s characteristics but also on the characteristics of his competitors denoted by. The total residual demand for provider is given by Q = Q caid + Q care + Q priv = Q(θ, θ, P, P, X d, X d, ξ, ξ ). Combining the payer type-specific residual demand curves and the cost function, I can express provider profits as follows: π = R caid Q caid + R care Q care + P Q priv C. 3.1 Equilibrium I assume that nursing homes maximize profits. While this assumption can be relaxed and does not affect the estimates in the baseline analysis, I maintain this assumption as a natural starting point and revisit the implications in additional robustness checks, see Section 7. In Nash equilibrium, each nursing home chooses the private rate and quality inputs optimally given the quality and pricing decisions of the competitors. These optimality conditions, the first order conditions, define a system of equations of the following form: θ = f θ (P, P, θ, R caid, X, X, ɛ, ɛ ) J (2) P = f P (θ, P, θ, R caid, X, X, ɛ, ɛ ) J (3) where X = (X d, X c, R care ) and ɛ = (ξ, ω) summarize observable and unobservable demand, cost, and profit shifters respectively. Expressing the endogenous right hand side variables as a function of exogenous demand, cost, and profit shifters allows me to rewrite equations (2) and (3) as follows: θ = f red θ (R caid, R caid, X, X, ɛ, ɛ ) J (4) 9

10 P = f red P (R caid, R caid, X, X, ɛ, ɛ ) J. (5) These equations are the reduced form solutions to the system of first order conditions and represent the equilibrium strategies that map exogenous state variables into endogenous actions. The equilibrium strategies are the key obects of interest in the empirical supply side analysis. Specifically, I aim to quantify the equilibrium effects of changes in Medicaid rates on optimal input and pricing decisions. The sign of these effects is theoretically ambiguous and ultimately an empirical question that I address in the remainder of this paper The Welfare Effects of Medicaid Rate Changes in Theory In this section, I briefly discuss the welfare implications of a change in Medicaid rates, which changes the equilibrium allocation, described by inputs, prices, and consumer demand from {θ 0, P 0, Q 0} { to θ 1, P 1, Q 1}. The change in welfare is given by W = i CV i + π (R caid Q caid + R care Q care ), (6) which combines the compensating variation for each consumer i CV i, the effects on provider profits, π, and the effects on public spending. For simplicity, I abstract from the deadweight loss of raising additional Medicaid spending. I come back to the cost of taxation in the counterfactual experiment, see Section 6.4. To simplify the illustration, I decompose the change in welfare into two effects: 7 where MB i (θ) = W = ˆ θ1 Q 0 i (MB i (θ) MC ) (θ) dθ i θ 0 θ }{{} u i (θ) θ u i W i + [ u NH i (θ 1 Q ] i u i MC (θ 1 ) i } W {{ i } B A, (7) denotes consumer i s marginal (dollar valued) benefit for the quality input θ. The effect A holds the consumer demand in the old equilibrium constant and addresses 6 See the appendix section 9.1 for additional details on the theoretical predictions of the model. 7 I derive the decomposition in the Appendix Section

11 the welfare effects from changes in quality inputs. 8 Figure 1 describes this welfare effect per resident day for a specific consumer in a specific facility. Since quantities are held fixed I endogenize a onedimensional input on the x-axis. 9 The y-axis measures marginal benefits and changes in marginal costs in dollars. The downward sloping marginal benefit curve indicates diminishing marginal utilities for the quality input. The horizontal curve describes the effect of a marginal increase Figure 1: Welfare Effect per Resident Day with Constant Demand Marginal Benefit/Cost in $ MB(θ) MB(θ 0 ) MB(θ 1 ) dmc dθ θ 0 dr caid θ 1 Input: θ in the quality input on the marginal costs per resident day. The vertical difference between the marginal benefit curve and this cost curve describes the per-person welfare effect of a marginal increase in the input, holding consumer demand constant. Therefore, the per-person welfare effect of the change in Medicaid rates is given by the integral over the difference between these curves, as depicted by the light gray area. Effect B holds the new input and pricing decisions constant and captures the welfare effects of changes in consumer demand. Changes in demand are relevant for welfare to the extent that consumers switch systematically towards more or less efficient providers from a social welfare perspective. Specifically, efficiency is defined by the difference between consumer utility for the nursing home good, measured in dollars, and the variable per-person cost of service: unh i (θ 1 ) u i W i MC (θ 1 ). To quantify both welfare effects, I need to quantify a) the equilibrium effects of changes in 8 Notice that changes in prices are a transfer between consumers and providers if we hold consumer demand constant. 9 I consider a one-dimensional input to simplify the exposition. 11

12 Medicaid rates on optimal staffing and pricing decisions of all providers b) consumer preferences for inputs and the private rates, and c) marginal costs as well as changes in marginal costs stemming from changes in inputs. In the empirical analysis, I first estimate the equilibrium strategies of all providers to quantify equilibrium effects of changes in Medicaid rates on optimal staffing and pricing decisions. Second, I use consumer micro data to estimate consumer preferences. Third, I use information from Medicaid cost reports to quantify average variable costs and changes in average variable costs. I assume that average variable costs equal marginal costs, which is consistent with the described theoretical model of constant marginal costs. 4 Empirical Model 4.1 Supply To quantify the equilibrium effects of changes in Medicaid rates on optimal staffing and pricing decisions, I estimate the nursing home s equilibrium strategies, equations 4 and 5. This approach offers two advantages compared to the estimation of first order conditions. First, I can quantify the relevant equilibrium effects directly and do not need to simulate new equilibrium under alternative Medicaid rates. Second, I use this method to identify the main endogenous input variables for this analysis. For example, I test whether nursing homes adust the number of therapists, nurse aides, and skilled nurses in response to changes in Medicaid rates. These findings motivate the choice variables in the firm problem and thereby determine the first order conditions. In other words, this analysis is a prerequisite for the estimation of first order conditions. 10 In the remainder of this subsection, I discuss the empirical analogue of the equilibrium strategies and the instrumental variables that identify the equilibrium effects. 10 I return to the estimation of first order conditions in the robustness check section 7. 12

13 4.1.1 Empirical Supply Model In the empirical analysis, I estimate linear versions of the equilibrium strategies, which have the following form ct = γ1 k MA t log(rt caid ) + γ2 k log( 1 Rlt caid ) (8) J Y k + α k 1X t + α k 2 X ct + φ MA t MA t + φ t + φ c + ɛ k t + ɛ k ct. l J Here Y k ct denotes the respective decision variable of provider located in county c in year t. Specifically, k indicates either a particular staffing measure or the private rate charged to consumers who pay out-of-pocket. The key parameters of interest are γ k 1 and γk 2. γk 1 denotes the equilibrium effect of an increase in the own reimbursement rate on staffing and pricing decisions for providers that are Medicaid certified, MA t = γ k 1 + γk 2 and γk 2 denote the equilibrium effect of a universal increase in Medicaid rates on staffing and pricing decisions for Medicaid certified and non-certified providers respectively. Xct and ɛ k ct refer to common observable and unobservable demand and cost characteristics at the county-year level. X t and ɛ k t refer to analogous providerspecific characteristics. 12 Finally, φ t and φ MA t effects and φ c denotes county fixed effects. 13 MA t denote certification-type-specific year fixed One concern that challenges the identification of the main parameters of interest is the potential correlation between Medicaid reimbursement rates and unobserved demand and cost shocks. Several states, including Pennsylvania, employ a cost-based Medicaid reimbursement methodology. While the methodologies vary across states, it is often the case that the Medicaid reimbursement rate for a provider, Rt caid, depends on s costs as well as costs of s competitors. Costs, however, depend on input decisions, which introduces an endogeneity problem. 14 To address these concerns, I exploit a novel source of exogenous variation in Medicaid reimbursement rates, which is tied to the reimbursement methodology in Pennsylvania. I discuss the details of the reimbursement 11 About 93% of the providers in the sample population are Medicaid certified. Non-certified providers cannot accept Medicaid residents. I return to this point in the data and the result section. 12 I discuss the specific control variables in Section The year fixed effects control for common input price shocks at the state level (e.g. the price for energy or common wage trends). The county fixed effects control persistent cost or demand differences between markets. For example, housing prices are, controlling for inflation, persistently higher in urban counties than in rural counties. 14 For instance, facilities located in markets with higher wage levels may, all else being equal, hire fewer nurses or fewer skilled nurses per resident. This clearly affects the costs of these providers and thereby their reimbursement rates. 13

14 methodology in the next Section The Reimbursement Methodology and the Instruments The state of Pennsylvania uses a prospective, cost-based reimbursement methodology that assigns Medicaid certified facilities into one of fourteen different peer groups. Two of these fourteen peer groups contain hospital operated and special rehabilitation facilities respectively. Rehabilitative care facilities are not considered in this study and hospital operated facilities are excluded from the baseline sample population because they may respond differently to changes in Medicaid prices, see the data section 5. Therefore, I focus the discussion of the reimbursement methodology and the instruments on the remaining peer groups, which comprise the baseline sample population. 15 Figure 2: Reimbursement Peer Group Regions in Pennsylvania Erie Warren McKean Susquehanna Potter Tioga Bradford Crawford Wayne Forest Wyoming Cameron Elk Sullivan Lackawanna Venango Lycoming Mercer Pike Clinton Clarion Luzerne Jefferson MontourColumbia Monroe Lawrence Clearfield Centre Union Butler Carbon Northumberland Armstrong Snyder Northampton Beaver Schuylkill Indiana Mifflin Lehigh Juniata Allegheny Cambria Blair Perry Dauphin Berks Lebanon Westmoreland Huntingdon Bucks Washington Cumberland Montgomery Lancaster Somerset Bedford Chester Philadelphia Fayette Fulton Franklin York Delaware Greene Adams Chester Reimbursement Regions MSA-Pop: <100k MSA-Pop: 100k-250k MSA-Pop: 250k-1million MSA-Pop: >1million The remaining twelve peer groups cluster facilities by size (<120 beds, beds, >269 beds) and location. There are four distinct geographic regions that oin Metropolitan Statistical Areas by population size (<100k, 100k-250k, 250k-1million, >1 million), see Figure I revisit the analogous reimbursement details for hospital operated nursing homes in Section 6.1.3, where I document their responses to changes in Medicaid rates. 16 The population size definition follows the former definition of the Office of Management and Budget, see Bulletin No : 14

15 Each facility within a given peer group reports previous average costs per resident day for different cost categories from typically two, three, and four years ago on a quarterly basis. The different cost categories are resident care costs (rc), which comprise spending on health care related inputs, other resident related care costs (orc), administrative costs (admc), and capital costs (capc). The regulator computes the facility specific arithmetic mean of the reported average costs by category and assigns the peer group and category specific median cost level for all but capital costs to each facility in the peer group. Capital costs are reimbursed directly. The final category specific reimbursement rate for facility in year t depends on the median rate and s previous average costs according to the following formula: t = min ({ med + min ({ med R caid ({ med + AC capc t 2. AC admc k,t 2 ({ 1.17 med AC rc k,t 2 ({ 1.12 med } ACk,t 2 orc ) P (k)=p () } ) ACk,t 2 rc P (k)=p () } ) P (k)=p () } ) ACk,t 2 orc P (k)=p () } ) P (k)=p (), AC rc t 2, AC orc t 2 cmi MA t (9) Here, AC rc denotes the Case Mix Index and inflation corrected average costs for resident care. 17 Average resident related care costs, average administrative costs, and average capital costs (AC orc, AC admc, and AC capc ) are corrected for inflation but not for the Case Mix Index of the residents. Finally, cmi MA t measures the Case Mix Index of Medicaid patients in facility and P () P 1, P 2,..., P 12 refers to facility s peer group, defined by size and geographic region. In words, resident care costs, other related care cost and administrative costs are reimbursed according to a weighted average of own costs and the median cost level in the peer group unless own costs exceed the median cost level. In this case, facilities receive the median cost level. This methodology resembles the yardstick competition regulatory scheme in which the regulator uses the costs of comparable firms to infer a firm s attainable cost level. Following the theoretical model, I assume that nursing homes compete in locally segmented 17 The Case Mix Index is a resource utilization index, which I explain in Section 5. 15

16 markets (counties). In equilibrium, nursing homes choose inputs and prices optimally based on local demand shocks, input price shocks, and other market characteristics as shown by the equilibrium strategies, see equations 4 and 5. These decisions affect the provider costs in this market directly but they also change the Medicaid reimbursement rate of providers located in different markets through the median component in the reimbursement rule, see equation 9. The exclusion restriction is that local market characteristics as well as local input price and demand shocks do not enter the equilibrium strategies of providers located in different markets. Therefore, these shocks affect optimal input and pricing decisions of providers located in different markets through the reimbursement rule only. For example, the income and the age distribution in Butler County, which is located in the Pittsburgh MSA (see Figure 2), affect the number and the payer source distribution of potential nursing home residents in this specific market. These demand characteristics markedly affect provider revenues and therefore their input decisions and costs. However, the income and the age distribution do not directly affect the input and pricing decisions of providers located in Bucks County, which is located in the Philadelphia MSA, because these providers are not competing for residents from Butler County. Therefore, the income and the age distribution in Butler County affect the input and pricing decisions in Bucks County through the reimbursement rule only because both counties belong to the same peer group region. There are two potential concerns to this exclusion restriction. First, the exclusion restriction is violated if the market is too narrowly defined. Most studies assume that nursing homes compete at the county level and more recent evidence suggests that nursing home markets tend to be even more concentrated (see Zwanziger, Mukamel and Indridason (2002)). I find that that the median travel distance equals only 7km in the sample population, see Section 5. Second, the exclusion restriction can be violated if there are price shocks and demand shocks that are common to several nursing home markets. All baseline specifications control for year fixed effects to address common shocks at the state-year level. Furthermore, I control flexibly for nursing home size and include county fixed effects to control for persistent differences across providers between and within peer groups. In the baseline analysis, I assume that reported average costs (which summarize the effect of input price shocks, demand shocks, and market characteristics on costs) affect staffing and pricing 16

17 decisions of providers located in different counties through the reimbursement rule only. According to this exclusion restriction, reported average costs of all providers located in different markets that belong to the same peer group are valid instruments. Instead of using this large number of instruments directly, I employ the method of simulated instruments. This method increases statistical power by exploiting knowledge of the functional relationship between instruments and the endogenous variables (see Currie and Gruber (1996a); Currie and Gruber (1996b) and Shan (2010) for a more recent application). To apply this method, I first express the actual reimbursement rate of a given provider in terms of endogenous and exogenous average cost components using equation 9. Endogenous cost components comprise all formula relevant cost components of nursing homes located in the provider s county (which also belong to the same peer group). Exogenous cost components, on the other hand, comprise all formula relevant cost components of nursing homes located in different counties. In a second step, I integrate out the endogenous cost components by repeatedly drawing costs from the population of providers in the entire state. For each iteration, I replace the endogenous cost components by a sample of randomly drawn cost components and evaluate the formula at the random sample and the fixed set of exogenous cost components. I repeat this procedure multiple times and finally calculate the average reimbursement rate for the given provider over the different random samples. Therefore, the simulated reimbursement rate varies in the exogenous cost components only and maintains the detailed knowledge about the reimbursement formula. I provide additional details to this approach in the Appendix Section 9.4. Finally, I use the simulated reimbursement rate to identify the parameters of interest in a two-stage least squares regression approach. Notice, that this approach provides simulated cost block specific rates. In other words, I can not only simulate the overall reimbursement rate but also the reimbursement block for resident care costs, other resident related care costs, and administrative costs. I come back to this in the result section Demand In this section, I discuss the estimation of consumers conditional indirect utility functions. I start with the discussion of the consumer s choice set. Next, I describe the empirical version of consumer s conditional indirect utility function and discuss the instrumental variables that address 17

18 endogeneity in prices and nurse staffing levels. Finally, I discuss the estimation strategy Consumer Choice Set This demand model addresses consumer selection at the intensive margin, the choice of a specific nursing home, and abstracts from consumer selection at the extensive margin, the choice of the level of care (e.g. nursing home care, assisted living facility, or home health care). Specifically, I assume that the level of care is primarily determined by the consumer s health profile and the family background and not by prices and nurse staffing levels chosen by nursing home providers. This is consistent with the evidence from Grabowski and Gruber (2007), who conclude that nursing home demand is very inelastic at the extensive margin. 18 Therefore, the empirical consumer choice set does not include providers that offer other forms of long term care. Next, I drop nursing homes from the consumer s choice set if they are not located within 50km of the consumer s former residence. 19 I do this for two reasons. First, consumers who travel long distance may choose the respective facility because of proximity to their relatives. This is inconsistent with the underlying choice model, discussed in the next section, which evaluates nursing homes based on the proximity to the consumer s former residence. 20 Second, this modeling assumption reduces the storage needs of the estimation algorithm, which are sizable. Finally, to address the role of capacity constraints for consumer demand, I combine information on residents admission and discharge dates with nursing home data on the number of licensed beds to calculate the number of open beds of all providers on any day in the sample period. I assume that consumers are admitted on a first-come-first-serve basis and include all providers in the consumer s choice set that have at least one vacant bed on the day the consumer was admitted to any nursing home Another reason for this modeling choice is data quality. The consumer micro data provide detailed information on consumers that choose nursing home care but it does not provide data on consumers that decided to consume different forms of long term care. 19 About 98% of the residents choose a nursing home within 50km of their former residence. 20 Data limitations do not allow me to include the residence of relatives in the choice framework. 21 This modeling assumption is consistent with the fact that more than 80% of the consumers in the sample population are admitted from a hospital and need nursing home care within a few days, less than a week. In fact, Medicare eligibility may expire if consumers are not admitted within 30 days. 18

19 4.2.2 Indirect Conditional Utility function In the empirical analysis, I estimate a parametric version of the theoretical indirect conditional utility function displayed in equation 1. Specifically, I assume that the indirect conditional utility function per day of consumer i with payer type τ at nursing home is given by u iτ = β d D i + βi sn log(sn Res ) + }{{}}{{} Distance Endogenous Quality + β p ( W }{{} i υτ p P τ }{{} ). W ealth P rice P er Day βi x X x }{{} Exogenous Quality + ξ τ + ɛ i }{{} Error Structure (10) Here, the first and the second row express the utility over consumption of the nursing home good (see u NH in equation 1) and the numeraire good respectively. Residents dislike distance between the former residence and the facility, D i, and value the log number of skilled nurses per resident, log(sn Res ). The latter is the key endogenous input measure in this analysis, because providers primarily change this input variable in response to changes in Medicaid rates, see the result section 6.1. Consumer preferences for nursing homes also depend on additional exogenous facility characteristics, represented by X, which include the facility s ownership type, the size of the facility, the number of therapists per resident, and whether the facility has an Alzheimer unit. Residents may also value unobserved facility characteristics, unobserved to the econometrician but observable to consumers and providers, which are captured by ξ τ. These characteristics capture, for example, the atmosphere, the values of the facility, and the quality of room and board, which are difficult to monitor and measure but potentially relevant for consumers. I allow for differences in preferences for these unobserved characteristics across three different payer types: consumers that pay all days out of pocket, henceforth private payers, consumers that pay none of the days out-of-pocket, henceforth public payers, and consumers that pay some but not all of the days out-of-pocket, henceforth hybrid payers. These unobservable preference components are given by ξ private ξ hybrid, ξ public, and respectively. ɛ i captures a consumer-nursing home specific unobserved taste shock which is distributed i.i.d. extreme value. Finally, wealth W i 22 and the payer-type specific daily price P τ determine the consumption of the numeraire good. I assume that consumers who pay none 22 Notice that wealth drops out of the estimation since it does not depend on the nursing home choice. 19

20 of the days of their stay out-of-pocket face a price of zero. 23 Consumers, on the other hand, who pay at least some days of their stay out-of-pocket, face a price per day equal to the reported daily semi-private room rate. 24 I include a price adustment factor, υ p hybrid, for consumers who pay some but not all days out-of-pocket to address differences in perceived prices between these consumers and consumers who pay every day out-of-pocket. In the remainder of this analysis I refrain from the utility decomposition and simply treat the daily price as an additional facility characteristic. Preferences for observable characteristics are captured by β, which may vary across consumers. For example, the taste for skilled nurses per resident may depend on the consumer s health profile at the time of admission. I model heterogeneity in preferences based on the number of assigned rehabilitative care minutes, based on whether the resident struggles with an Alzheimer disease, and based on the the consumer Case Mix Index, which summarizes the consumer health profile into a single index. I provide more information on this index in the data section. Mathematically, I express differences in preferences as follows β x i = β x + z β x z Z i. (11) Here, β x measures common preferences for characteristic x, common across all consumers. β x z measures differences in preferences that are related to differences in observable consumer characteristics, measured by Z, (e.g. the number of assigned rehabilitative care minutes). The preference parameters for skilled nurses (β SN, βz SN ) and prices (β P, υ p hybrid ) are the key parameters of interest in the demand estimation. To identify these parameters empirically, I exploit exogenous variation in prices and skilled nurses, exogenous with respect to unobserved quality measured by ξ τ. This is important, because providers choose prices and the number of skilled nurses endogenously conditional upon consumer relevant characteristics that are potentially unobserved to the econometrician, see equations 4 and 5. In other words, the correlation between unobserved demand shifters on the one hand and skilled nurses and prices on the other biases the parameter estimates if left unaddressed. I discuss the sources of exogenous variation in the next section. 23 Medicare consumers must pay a daily copay-rate for the days , which does not vary across facilities. This copay-rate will, however, not affect the particular nursing home choice since I am only modeling the intensive margin, the choice of a particular nursing home. 24 I assume that private pay consumers are indifferent between private rooms and semi-private rooms. Specifically, I assume that the value of privacy is outweighed by the higher daily room rate. 20

21 4.2.3 Identification This empirical model allows for sources of endogeneity at the payer type-nursing home level. That means, however, that consumer preferences that vary within these payer types are identified directly and do not require exogenous variation in prices and skilled nurses, exogenous with respect to these unobserved characteristics. This applies, for example, to differences in preferences for skilled nurses across consumers with different health profiles as well as preferences for proximity. To illustrate the identification problem that applies to the estimation of the common preference components β x as well as differences in preferences across payer types, I define the mean utilities for specific payer types following the notation in Berry, Levinsohn and Pakes (1995). These mean utilities equal: β sn log(sn Res δ i = ) + x βx X β p P + ξ private β sn log(sn Res ) + x βx X β p υ p hybrid P + ξ hybrid if #P rivate Days = #Days if 0 < #P rivate Days < #Days β sn log(sn Res ) + x βx X + ξ public if #P rivate Days = 0, (12) where u i = δ i + β d D i + X z β x z Z i + ɛ i (+β p W i ). (13) Following the tradition of empirical demand studies in the industrial organization literature, I assume that the facility characteristics other than skilled nurses and prices, captured by X, are exogenous with respect to the unobserved demand shocks. Therefore, the preference parameters for these exogenous characteristics, β x, are identified off from variation in these exogenous facility characteristics. To identify the common preference parameter for the log number of skilled nurses per resident, β sn, I use instrumental variables that are orthogonal to unobserved demand shifters, ξ private, ξ hybrid and ξ public, but correlated with the number of skilled nurses. I combine the exogenous variation in Medicaid rates with variation in exogenous characteristics of rival firms, X, to increase statistical power. While the exogenous variation in Medicaid rates is powerful enough to identify the key parameters of interest in the equilibrium strategies, it is not particularly suitable for this exercise. This is because the Medicaid instruments affect a large number of providers within the same market 21