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- Abstract
- 1. Introduction
- 2. Background
- 3. Conceptual Model
- 4. Data
- 5. Empirical Strategy
- 6. Results
- 7. Conclusion
- References

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J Health Econ. Author manuscript; available in PMC 2017 August 10.

Published in final edited form as:

Published online 2016 December 30. doi: 10.1016/j.jhealeco.2016.12.006

PMCID: PMC5551673

NIHMSID: NIHMS876886

Neeraj Sood,^{*,}^{a,}^{b} Abby Alpert,^{c} Kayleigh Barnes,^{a} Peter Huckfeldt,^{d} and José J. Escarce^{e}

The publisher's final edited version of this article is available at J Health Econ

Policymakers are increasingly interested in reducing healthcare costs and inefficiencies through innovative payment strategies. These strategies may have heterogeneous impacts across geographic areas, potentially reducing or exacerbating geographic variation in healthcare spending. In this paper, we exploit a major payment reform for home health care to examine whether reductions in reimbursement lead to differential changes in treatment intensity and provider costs depending on the level of competition in a market. Using Medicare claims, we find that while providers in more competitive markets had higher average costs in the pre-reform period, these markets experienced larger proportional reductions in treatment intensity and costs after the reform relative to less competitive markets. This led to a convergence in spending across geographic areas. We find that much of the reduction in provider costs is driven by greater exit of “high-cost” providers in more competitive markets.

With the passage of the Patient Protection and Affordable Care Act (ACA),
policy makers are increasingly looking to reduce both health care costs and
inefficiencies in care by restructuring the ways that Medicare pays health care
providers. High costs and inefficiencies have long been attributed to the
traditional “cost-based” reimbursement model, where health care
providers are paid separately for each service provided. In addition, competition
has been shown to *increase* costs under cost-based reimbursement,
with health care providers competing for patients based on quality and amenities
which generate higher costs (Robinson &
Luft, 1987; Zwanziger & Melnick,
1988). In this way, competition may also drive geographic variation in
costs of care since there is considerable variation in market concentration across
areas.

Over the past 30 years, Medicare has progressively moved away from cost-based reimbursement towards prospective payment, where a health care provider receives a set payment for an episode of care based on the characteristics of the patient. These payment reforms occurred in 1983 for hospitals and in the late 1990s and early 2000s for providers of post-acute care (e.g., skilled nursing facilities, home health agencies, and inpatient rehabilitation facilities). Extensive evidence shows that the shift to prospective payment had varying effects on health care costs across setting, with more “prospective” reforms and those reducing marginal payments leading to larger cost reductions (Grabowski, Afendulis, & McGuire, 2011; P.J. Huckfeldt, Sood, Escarce, Grabowski, & Newhouse, 2014; Newhouse & Byrne, 1988; N. Sood, Huckfeldt, Grabowski, Newhouse, & Escarce, 2013). In addition, there is some evidence that the relationship between competition and quality (or costs) also changed after prospective payment. For example, data from California show that costs fell more for providers in the most competitive markets after the Inpatient Prospective Payment System was implemented in 1983 (Meltzer, Chung, & Basu, 2002). However, the implementation of the Inpatient Prospective Payment System coincided with the implementation of selective contracting and rapid penetration of managed care in California. Thus, it is unclear the extent to which the differential effects on costs were related to implementation of prospective payment versus other contemporaneous trends.

In this paper we revisit the question of whether provider payment reforms, which reduce the marginal reimbursement to health care providers, may have a differential effect depending on the level of provider competition in a health care market. We start with the premise that differences in the level of competition across health care markets is an important source of geographic variation in health care costs, with markets with greater competition under cost-based reimbursement having higher costs or intensity of care. Prior research also suggests that greater competition in health care markets with administered prices might lead to socially wasteful spending (Gaynor, 2006). We next develop a stylized model that evaluates how the impact of payment reform on costs or intensity of care might vary by the level of competition in the market. We predict that payment reform reduces costs more in more competitive markets. Thus, it is possible that payment reform can simultaneously reduce costs and reduce geographic variation in care as it will lead to convergence in costs across more and less competitive markets.

We empirically test our predictions by investigating a significant Medicare payment reform for home health agencies: the 1997 Interim Payment System (IPS). The IPS offers an interesting case study as it imposed limits on payments to home health agencies in what was a cost-based reimbursement system, dramatically reducing reimbursement to home health agencies by nearly 50 percent (US Government Accountability Office, 2000). Moreover, there is evidence that post-acute care is a key driver of the still-substantial geographic variation in Medicare spending (Newhouse & Garber, 2013), suggesting significant scope for payment reforms targeted at post-acute care in reducing overall geographic variation in spending. Although several studies have analyzed the effects of IPS, none have looked at how the effects of the IPS on costs or intensity of care varied by the initial level of competition in the market (P.J. Huckfeldt et al., 2014; Peter J Huckfeldt, Sood, Romley, Malchiodi, & Escarce, 2013; Liu, Long, & Dowling, 2002; McCall, Komisar, Petersons, & Moore, 2001; Murtaugh, McCall, Moore, & Meadow, 2003; Porell, Liu, & Brungo, 2006). In this paper we add to this literature by analyzing how the effects of IPS varied by the level of competition. We also analyze the pathways or mechanisms that might explain the heterogeneous impact of IPS across markets with different levels of competition.

The empirical results are consistent with the predictions from the theoretical model. We find that there was significant variation in costs by level of competition in the pre-IPS period, with more competitive markets having higher costs. After the IPS, costs declined in all markets but there were larger declines in costs in more competitive markets. The decline in costs was driven by both changes in the probability of any home health use (extensive margin) and a decline in the number of home health days among existing users (intensive margin). As a result of the heterogeneous response to the payment reform, costs and the number of home health days converged in more and less competitive markets and the significant variation in costs or intensity of care by level of competition in the pre-IPS period nearly disappeared in the post-IPS period.

Although the empirical findings are consistent with our theoretical model, a competing explanation for our findings is that IPS payment limits gave greater financial incentives in more competitive markets. We find evidence that IPS payment limits had greater “bite” in more competitive markets. However, we find larger cost reductions in more competitive markets even after controlling for heterogeneity in the reform’s bite across areas. These results suggest that the heterogeneous impacts of IPS by level of competition are not only driven by differences in the bite of IPS payment limits by level of competition, but also by differences in responsiveness by level of competition for a given financial incentive. Finally, we show that the larger impact of IPS in more competitive markets is driven by two factors. First, we observe greater exit of home health agencies in more competitive markets. Second, the home health agencies that exited more competitive markets were more likely to be “high-cost” agencies. Thus, payment reform serves to eliminate some of the most inefficient providers, especially those that are operating in highly competitive markets.

Overall these findings imply that payment reform is not only an important tool for reducing health care costs but it can affect geographic variation in care and health system efficiency by changing incentives and influencing market dynamics. Under the ACA, Medicare is adopting new provider payment reforms such as bundled payment and accountable care organizations, which represent further shifts towards capitation. The extent to which these reforms can further reduce costs and improve efficiency – and potentially reduce variation in health care spending- depends in part on the differential effects of such reforms across markets with different levels of competition.

The rest of the paper proceeds as follows. Section 2 describes the IPS. Section 3 builds a conceptual framework. Section 4 describes the data. Section 5 discusses our empirical strategy and section 6 discusses the results.

From 1989 to 1996, Medicare home health expenditures more than quintupled, rising from $3.4 billion to $19.2 billion. In addition, between 1990 and 1996 the number of beneficiaries using the home health benefit almost doubled from 1.9 million to 3.7 million and the number of visits per patient grew from 33 visits to 76 visits (United States Congress, 2000). Much of this growth was spurred by the 1988 Duggan v. Bowen court case, which drastically broadened the eligibility criteria for the Medicare home health benefit. In response to rising costs, the Balanced Budget Act of 1997 (BBA) mandated that the home health payment policy be reformed. The BBA called for a Prospective Payment System (PPS) and immediately enacted an Interim Payment System (IPS) to address the rising costs while the PPS was being developed. The IPS went into effect in October 1997 and lasted for 3 years before being replaced by the PPS in October 2000.

Before the IPS, Medicare home health payment policy was a cost based
reimbursement system subject to a per-visit limit on costs. This limit was set at
the lower of an agency’s “reasonable costs” or 112%
of the national average of per visit costs. The implementation of IPS imposed
stricter per-visit cost limits (reduction in average reimbursement) and introduced a
per-beneficiary total annual cost limit (reduction in marginal reimbursement).
Specifically, IPS introduced per-visit limits equal to 105% of the national
median cost per visit for newer home health agencies that entered the market after
1994. Older home health agencies faced a limit that was a weighted average of the
agency’s average per patient costs in 1994 (75%) and their census
division per patient costs (25%). This means that firms with costs above the
average cost in their census region faced a limit lower than their historical costs,
which would be binding; while a firm with costs lower than the average cost in their
region faced a limit above their historical costs, which would not be
binding.^{1} Consequently, we
would expect to see a larger reduction in costs after IPS for firms with historical
costs above the average cost in their region. A home health agency received payment
equal to the lower of its actual costs, its per-visit cost limit, or the
per-beneficiary cost limit.

McCall et al. (2001) and McKnight (2006) found a large decrease in home health utilization and the number of visits per user following IPS. Huckfeldt et al. (2014) found that the IPS reduced average payments and that this decline in reimbursement decreased utilization of home health services with little change in readmission and mortality. The decline in use of home health care coupled with lack of changes in readmission rates and mortality suggests that the IPS increased efficiency in the home health care industry. While prior work has investigated heterogeneous effects of the IPS by geography, such work has focused on variation in the average reimbursement change after IPS across markets which stems from payment limits being based on average census division costs (McKnight, 2006). One study does look at entry and exit effects by level of competition (as measured by the number of home health agencies in a market) and find that markets with more home health agencies experienced more supply changes after IPS (Porell et al., 2006). However, no studies have looked at how the impact of IPS on costs or utilization varies by level of competition, which is the focus of this paper.

Other related work has investigated trends in hospital costs in California during a period when California experienced several important cost containment measures including the introduction of Medicare inpatient prospective system, introduction of selective contracting for Medicaid patients and diffusion of managed care in private insurance markets. This literature finds that during this time reduction in costs were largest for the most competitive markets (Meltzer et al., 2002; Zwanziger & Melnick, 1988). We examine whether there was a differential impact of IPS in more versus less competitive markets. The IPS provides an important case study due to the large magnitude of overall reductions in payments. Moreover, the wide variation in home health competition across markets generates an ideal context for studying how competition affects responses to payment reform. Understanding how the effects of prior Medicare payment reforms varied across more and less competitive markets provide important evidence on the potential effects of reforms underway, and how they may affect geographic variation in Medicare spending.

In this paper, we are interested in how agencies adjust their intensity of care (in this context intensity can be viewed as the number of visits per episode of care or costs) in response to payment reform across markets with different levels of competition. We develop a conceptual model based on papers by Brekke, Siciliani, and Straume (2011) and Hodgkin and McGuire (1994). We build upon these models by incorporating the use of average and marginal reimbursement from Hodgkin and McGuire (1994) into the analysis of quality competition from Brekke, Siciliani, and Straume (2011). Hodgkin and McGuire (1994) predicts how hospitals will adjust intensity of care in response to changes in marginal or average reimbursement but is silent on how these effects may vary with market competition. Brekke, Siciliani, and Straume (2011) develop a model of the effects of market competition on hospital quality. Our model bridges these two models to fill the gap in the literature and evaluates how the effects of payment reform vary with competition.

In our model, price is regulated and takes the form *P*
= *α* + *β* *
*c*(*q _{i}*), where α is average
reimbursement, β is marginal reimbursement, and

$${\pi}_{\mathrm{i}}=\left(\alpha +\beta \ast c({q}_{i})\right){X}_{i}({q}_{i},{q}_{-i})-c({q}_{i}){X}_{i}({q}_{i},{q}_{-i})$$

(1)

With the first order condition for intensity allocation being:

$$\frac{\partial \pi}{\partial {q}_{i}}=\alpha \frac{\partial {X}_{i}}{\partial {q}_{i}}+\beta \left(\frac{\partial c}{\partial {q}_{i}}{X}_{i}+c({q}_{i})\frac{\partial {X}_{i}}{\partial {q}_{i}}\right)-\left(\frac{\partial c}{\partial {q}_{i}}{X}_{i}+c({q}_{i})\frac{\partial {X}_{i}}{\partial {q}_{i}}\right)=0$$

(2)

The model is explained in detail and formally derived in Appendix A. We summarize the key propositions relevant for the empirical analysis as follows.

The intensity of care increases with number of firms.

(See the appendix for a formal proof). To understand why this relationship is positive, we consider the first order condition, which simplifies to:

$$\mathit{\text{ProfitMarin}}(q)\ast \frac{\partial {X}_{i}}{\partial {q}_{i}}=\frac{\partial c}{\partial {q}_{i}}(1-\beta )\ast {X}_{i}$$

(3)

The right hand side (RHS) of the equation is the marginal cost of increasing intensity and the left hand side (LHS) of the equation is the marginal benefit of increasing intensity. The marginal benefit curve slopes downwards as profit margins decline with intensity. The marginal benefit term or the LHS is independent of the number of firms as the profit margin is a function of reimbursement policies and the slope of marginal cost curve while and the responsiveness of demand to intensity is a function of patient preferences (see expression for $\frac{\partial {X}_{i}}{\partial {q}_{i}}$ derived in the Appendix). However, the number of firms in the market does affect the RHS as an increase in the number of firms reduces the number of inframarginal patients a firm has. Thus the marginal cost curve for intensity shifts downwards as the number of firms rises (see Appendix Figure 1) and consequently intensity is higher in more competitive markets.

A decline in marginal reimbursement has a larger effect on intensity of care in more competitive markets.

(See the appendix for a formal
proof.) A decrease in marginal reimbursement reduces the marginal benefit of
intensity since decreasing reimbursement reduces profit margins (see first order
condition above). This reduction in profit margins is higher in more competitive
markets as equilibrium intensity is higher in more competitive markets and
*c*(*q _{i}*) increases with intensity.
Similarly, a decrease in reimbursement also increases the marginal costs of
intensity as providing care to inframarginal patients now has a larger effect on
profits. Again this shift produces a larger effect in more competitive markets
as equilibrium intensity is higher in more competitive markets and $\frac{\partial c}{\partial {q}_{i}}$ increases with intensity. This result is
illustrated in Appendix Figure 1 and
discussed in the corresponding section in the Appendix.

Reducing marginal and average reimbursement reduces intensity of care.

(See the appendix for a formal proof). As seen in equation (3), the marginal benefit of intensity of care increases with the profit margin per patient. Since reducing marginal or average reimbursement reduces the profit margin, it reduces the returns to intensity of care.

Reducing average and marginal reimbursement will lead to greater firm exit in more competitive markets.

(See the appendix for a formal proof). The intuition for this result is as follows. Firms will exit the market if profits fall below zero. This determines minimum threshold levels of marginal and average reimbursements below which firms will exit the market. These thresholds are an increasing function of intensity of care. In Proposition 1 we determined that intensity of care increases with competition, which implies that the minimum average or marginal payment thresholds for participation are higher in more competitive markets. Thus, reductions in reimbursement are more likely to lead to firm exit in more competitive markets. The above assumes that firm exit is non-zero, that is, due to internal friction and inefficiency, some firms are unable to reduce intensity sufficiently to keep profits above the minimum participation thresholds.

Motivated by these propositions we expect to see the following patterns in our data:

- More competitive markets have higher intensity of care (and consequently, higher costs).
- Because IPS lowered both average and marginal reimbursement we expect to see a decrease in intensity of care for all markets.
- Because the effects of changes in marginal reimbursement are magnified in markets with more competition we expect to see a greater decrease in intensity of care (and costs) following the IPS in more competitive markets. This implies a convergence in the costs or intensity of care in more versus less competitive markets after the reform.
- Because the effects of changes in average and marginal reimbursement on firm exit are magnified in markets with more competition we expect to see greater firm exit following the IPS in more competitive markets. Similarly, we expect to see greater exit of firms with higher intensity of care (costs) following the IPS.

It is important to note that the model is silent on the effects of competition on patient outcomes. On the one hand, one can argue that if patients value intensity it must improve patient outcomes. However, on the other hand one can argue that patients might be uninformed and even though they value higher intensity care, beyond a certain level, changes in intensity of care do not improve patient outcomes and represent “wasteful” spending. Thus, in our empirical models we will evaluate both changes in intensity of care and also changes in patient outcomes.

The primary source of data for this paper comes from a 100 percent
sample of Medicare claims from the Medicare standard analytic file (SAF) for
home health care. In our main analysis, we restrict the sample to individuals
who were discharged from an acute care hospital for stroke between 1996 and
2000^{2} and we include
individuals discharged for hip fracture and lower extremity joint replacement in
sensitivity analyses. We focus on these three conditions because these
conditions account for a significant proportion of home health use. We use the
Medicare claims to obtain the total number of days that beneficiaries received
home health visits and total Medicare payments for home health during the 90-day
post-acute period following each individual’s initial hospital
discharge. Any additional acute hospital stay occurring within the 90-day
follow-up period is considered a readmission.

Costs to home health providers are computed using data on facility costs from Medicare cost reports. To construct total costs for each 90-day post-acute episode, we multiply the number of visits from the claims data by the facility’s average calendar year cost per visit.

Our data contains hospital discharges for stroke, hip fracture, and
lower extremity joint replacement. We focus on stroke for the majority of our
results. We do this for simplicity and because stroke represents the largest
number of hospital discharges in our data in addition to having a higher
intensity of home health care compared to hip fracture and joint replacement. We
test the sensitivity of our main results for hip fractures and joint replacement
and find very similar results as we will show below. While the conditions
treated by home health care are diverse, diseases of the circulatory system
account for the largest share of Medicare home health patients during our study
period (31.4% in 1999), followed by injury and poisonings
(15.9%), and then diseases of the musculoskeletal system and connective
tissues (14.1%) (Centers for Medicare and
Medicaid Services, 2001). The conditions contained in our
sample– stroke, hip fracture, and lower extremity joint replacement,
respectively—represent these three disease classes.^{3} These conditions also cover a range of
treatment intensity and severity of disease (for example, stroke is associated
with the highest mortality rate, while joint replacement is a condition with low
mortality and hip replacement falls in between the two conditions), making the
results more representative of the range of conditions treated with home health
care.

We use the Medicare denominator file to obtain demographic variables for each individual including gender, age (5-year age categories), race, Medicaid coverage, county of residence, and urban/rural status, as well as information about whether death occurred within 90 days of the initial hospital discharge. We use the hospital claims from the initial acute episode to measure comorbidities, as defined by Elixhauser, Steiner, Harris, and Coffey (1998), and complications during the index hospitalization. In the case of stroke, we also use the hospital claims to determine whether the stroke was hemorrhagic or ischemic. In a hemorrhagic stroke an artery in the brain ruptures while an ischemic stroke occurs when a blood vessel to the brain becomes blocked by a clot. The main descriptive statistics for our data for stroke discharges are shown in Table 1. The complete set of comorbidities and complications that are included as controls in our analysis, as well as other patient and provider characteristics, can be found in Appendix Table 1 for stroke, hip and joint discharges. HSAs are grouped into the least competitive and most competitive markets based on whether they have above or below median HHI. Patients in both high and low competition markets have similar demographic characteristics prior to the introduction of IPS, except that the most competitive HSA’s are more likely to be urban areas and the least competitive HSA’s are more likely to be rural areas. Although patient demographics, comorbidities, and complications are similar across areas, home health outcome variables and agency characteristics vary between markets with high and low levels of competition. The most competitive markets have a greater percentage of for-profit agencies and higher intensity of care. These patterns across high and low competition markets are markedly similar for all three conditions (stroke, hip fracture, and joint replacement) as shown in Appendix Table 1. Stroke discharges have the highest intensity of home health care (as measured by home health days) in the baseline year, followed by hip fracture and joint replacement discharges. The reverse is true for the likelihood of receiving any home health care.

Provider characteristics for the acute care hospital are derived from
the CMS Medicare Provider of Services file and Acute Impact file. These
provider-level databases include information about ownership status, number of
beds, wage index, average daily census, acute case-mix index, DSH patient share,
and Medicare patient share.^{4}

The empirical analysis compares changes in home health use and costs across areas with high and low levels of competition. Our primary measure of the level of competition in the market is the Herfindahl–Hirschman Index (HHI). Though many measures of competition exist, HHI captures both the number of firms in the market and the relative market share of those firms and is the industry standard (Baker, 2001; Rhoades, 1995). We define markets using Hospital Service Areas (HSA) as defined by the National Center for Health Statistics (M Makuc, Haglund, Ingram, Kleinman, & Feldman, 1991; National Cancer Institute, 2008). An HSA is defined as one or more counties in which the residents receive the majority of their hospitalizations. Since home health care is typically received after a hospitalization we believe that the market definition for hospitals is a good approximation of the market for home health care. As we will show in Section 6.2, the results are also robust to an alternative market definition in which we split HSAs that cross state lines into separate markets (or exclude these HSAs from the sample) to account for the potential effects of state-based home health regulations on competition and outcomes.

The HHI is the sum of the squared market shares for home health providers within each HSA. Each home health agency’s market share is calculated separately by condition (stroke, hip fracture, or joint replacement) and is defined as the proportion of Medicare patients residing in the HSA who receive post-acute care (during the 90-days following their hospitalization) from that home health agency. We also compute the Four-Firm Concentration Ratio as the sum of the market shares for the four most dominant home health agencies within an HSA as a secondary measure of competition. We exclude small HSAs from our analysis sample that contain fewer than 28 home health claims (representing the bottom 25 percent of HSAs) where it is difficult to obtain a precise measure of competition. In some specifications, we examine firm exit and define a home health agency as exiting the Medicare market when there are no longer any Medicare claims for that provider. Figure 1 shows that HHI and the Four-Firm Concentration Ratio vary greatly across the home health industry; we will use this variation to study the differential effect of payment reform across more and less competitive markets.

We exclude individuals who died during the initial hospital stay for stroke, hip fracture, or joint replacement. We also exclude individuals under age 65, those enrolled in Medicare managed care plans, and those residing in Maryland since Maryland did not adopt prospective payment. We conduct our analysis at the discharge level and observe outcomes for a 90-day follow-up period. For stroke, our main analysis sample contains 1,178,430 post-acute episodes resulting from 1,178,430 unique stroke discharges over the study period. The other conditions have somewhat smaller analysis samples.

We perform OLS regression of home health outcomes on the level of competition interacted with a post-IPS indicator and controls taking the form:

$${Y}_{\mathit{\text{ijt}}}=\gamma (HH{I}_{j}^{\mathit{\text{Pre}}}\cdot {\mathit{\text{Post}}}_{t})+{\delta}_{j}+{\mu}_{t}+{X}_{\mathit{\text{ijt}}}\beta +{\epsilon}_{\mathit{\text{ijt}}}$$

(4)

where *Y _{ijt}* is an
outcome such as the number of home health days, provider costs, or the
probability of any home health care for patient

We estimate an event study version of the primary specification where we add in interactions of HHI with each quarter leading up to and following the introduction of IPS to test our identifying assumption of parallel trends in outcomes across markets with different levels of HHI. The omitted interaction term is the quarter before IPS is introduced (quarter 3 of 1997). We expect the coefficients on the interaction terms for the quarters leading up to the IPS to be statistically insignificant, implying that pre-IPS trends in outcomes were similar in more versus less competitive markets. We expect the coefficients on the interaction terms for the quarters after IPS to be positive and significant suggesting that IPS had smaller negative effects in less competitive markets.

Prior research and our data suggest that the level of competition in a market is strongly correlated with the market’s status as urban or rural. More densely populated urban markets are likely to be more competitive while rural areas have a more dispersed population and are therefore more likely to be less competitive. An analysis of changes in health outcomes after payment reform based on levels of competition could actually be capturing the difference in responsiveness between urban and rural markets. To test for this, we estimate our analysis for both urban and rural areas separately.

Geographic factors affecting competition may not only be driven by urban-rural differences but may also be influenced by state-based home health regulations. To address this, we repeat the main analysis using an alternative market definition in which we split HSAs that cross state lines into separate state-specific markets. Splitting HSAs creates two or three new sub-regions (or modified HSAs) within the original HSA, with the boundaries occurring along the state lines. We also repeat the main analysis excluding HSAs that cross state lines from the sample. About 15% of HSAs cross state lines. Standard errors are clustered at the modified HSA × state-level.

The method of payment reform instituted by the IPS imposed varying levels of reimbursement reductions for home health agencies depending on how long they had been in the market and the census averages of costs for their district. Firms that entered the market after 1994 were subject to a maximum per patient reimbursement of 105% of the national median in 1994. Agencies that had entered the market before 1994 were subject to a per-patient reimbursement limit which was a weighted average of the firm’s average per patient costs in 1994 (75%) and the firm’s census division weighted average of per patient costs (25%). Because of this, agencies with costs higher than the regional average faced larger reductions in reimbursement (since the payment limit was binding) than agencies with average or below-average costs (since the payment limit was not binding), which could affect their responses to the reform (see footnote 1). To account for this, we introduce a measure, IPS “Bite”. In a similar spirit as McKnight (2006), IPS Bite is defined as the difference between the average number of home health days in a HSA and the average number of home health days in the HSA’s census division. HSAs with more home health days than the average census region home health days (i.e., large positive value for IPS Bite) are likely to be areas where the per-patient payment limit was most binding and, consequently, IPS reduced payment the most. We plot how IPS “Bite” varies with HHI to determine whether there is a systematic relationship between the payment reduction and the level of competition in the market. We then control for the IPS “Bite” by including a triple-interaction term between post-IPS, HHI and IPS “Bite”.

In addition to characterizing the heterogeneous effects of payment reform by level of competition, we also want to understand the underlying mechanisms driving these differences. As discussed in the theoretical framework section, home health agencies may respond to payment reform by reducing the intensity of care or by exiting the market. We study each of these mechanisms.

First, we estimate equation 6 using the number of home health providers as the outcome variable. We also estimate models defining the outcome variable as the log number of providers. Changes in the number of home health agencies could be driven both by reductions in entry and an increased rate of exit.

Next, we compare the characteristics of exiting home health agencies (agencies that were in operation in 1996 but exited after IPS) with “stayer” home health agencies (agencies that were operating during the entire study period from 1996–2000), in order to identify changes in agency composition after the IPS that may have affected practice patterns. Specifically, we look at average home health days, Medicare payments, provider costs, and the demographic characteristics of patients seen by agencies.

In the third set of analyses, we directly investigate how much of the effect of the IPS occurred through a changing composition of home health agencies. Specifically, we estimate equation 6 for the home health days and provider costs outcomes, limiting the sample to just the agencies that stayed in the sample after IPS and compare the results to those for the full sample. Any differences in results between the two samples are driven by changes in agency composition due to exiting firms.

Figure 2 and Table 2 test a primary hypothesis generated by the conceptual model: that the IPS would have a greater impact on intensity of care (measured by the number of days of home health care) and costs in more competitive markets. Figure 2 shows reductions in average home health days, costs, and the probability of using home health for the case of stroke discharges across HSAs with different levels of competition during the period following the introduction of IPS but before the implementation of PPS (the introduction of IPS is indicated by a red vertical line after the third quarter of 1997). Consistent with the theoretical model and prior literature, the most competitive markets (HHI quantile 1) exhibit both the highest costs and days under cost-based reimbursement prior to the IPS and the largest reductions in costs and days after the IPS, converging towards the other HHI quartiles in the post-reform period. Figure 2 in the appendix shows the corresponding figure for two important patient outcomes: readmissions and mortality. In contrast to the results for intensity of care and costs we find little or no impact of the IPS on these outcomes and we find no differential effects by the level of competition. These results are consistent with (P.J. Huckfeldt et al., 2014) who also found large changes in costs but no change in patient outcomes after the IPS.

Table 2 displays the results from the analogous regressions for all three conditions (stroke, hip fracture, and joint replacement) for home health days, provider costs, and probability of any home health use on the interaction of HHI quantiles with a “post-IPS” indicator variable. The omitted quantile is the least competitive HSAs (HHI quantile 4). All of the regressions include fixed effects, quarter year fixed effects, and time varying patient and market level controls. In Appendix Table 2, we also show results from four specifications that progressively add controls for the case of stroke discharges: the first includes just HSA fixed effects, the second adds a linear time trend, the third replaces the linear time trend with quarter-year fixed effects, and the fourth specification adds time-varying patient and market-level controls (our main specification).

The results are markedly similar across conditions in both magnitudes and statistical significance. For all conditions, we observe a larger reduction in home health days and costs after the introduction of IPS in markets with higher levels of competition relative to the least competitive markets in Quantile 4 (as shown in Figure 2). For example, for stroke, we observe the largest reductions in home health days for the most competitive markets: home heath days fell by about 2.5 more days than the least competitive markets, and fell 1.5 more days more than the second quantile. The reduction in home health days after the IPS for the third quantile was not statistically different from the fourth quantile. For stroke, all quantiles also experienced a decline in costs, with home health agencies in the most competitive quantiles seeing a decline in costs of $220 more per patient than in the least competitive quantile. Home health agencies in the second quantile experienced an additional reduction of $84 in costs than agencies in the least competitive quantile. Hip fracture and joint replacement discharges had cost reductions of a similar magnitude. We find no significant difference between the reduction in provider costs for the third and fourth quantiles across all conditions. Although there was an overall reduction in the probability of using any home health care, we only find statistically significant differences in the magnitude of the reduction across different levels of competition for joint replacement discharges. However, although these results are significant they are small. In Appendix Table 3 (Panel A), we re-estimate the regressions to estimate proportional changes using log outcomes. The results are qualitatively similar. The lack of a differential change in probability of any home health implies that the competition effect on home health days is driven by changes in home health days conditional on use.

It is possible that payment reductions due to IPS led to substitution from home health care to other types of post-acute care services or longer stays in acute hospitals. In Appendix Table 4, we examine whether there was substitution of home health care to skilled nursing facilities (SNFs), inpatient rehabilitation facilities (IRFs), long term care hospitals (LTCHs), and acute care length of stay for all three conditions. Overall, we find little evidence of substitution to other post-acute or acute settings that is differential by level of home health competition. For example, while we find larger reductions in home health care days in areas with higher levels of competition, we do not find a differential increase in the use of SNFs or IRFs in these same areas, and only a relatively small differential increase in acute length of stay in the most competitive markets. One exception may be a slight substitution effect for long term care facilities. However, since long term care facilities are used in less than 1% of discharges, this is unlikely to have a significant offsetting effect on the differential reduction in home health costs from IPS.

Since the main results for stroke are very similar to the other conditions (hip fractures and joint replacement), we focus on stroke for the majority of robustness tests and secondary analyses in the remainder of the paper.

In Table 3, we estimate a regression for stroke that includes leads and lags of the policy to ensure that our findings in Table 2 are not driven by differential trends in outcomes in the pre-IPS period. Specifically, in the odd-numbered columns, the event-study replaces the $HH{I}_{j}^{\mathit{\text{Pre}}}\times {\mathit{\text{Post}}}_{t}$ variable in Equation 6 with a full set of quarter dummies interacted with the HHI measure. Each coefficient estimate gives the difference in the outcome variables (home health days, costs, or probability of any use) in high HHI versus low HHI areas relative to the omitted reference period: quarter 3 of 1997 (the quarter before IPS is introduced). We find no evidence of differences in trends by level of competition in the pre-IPS period, as reflected in the statistically insignificant coefficients prior to quarter 3 of 1997. However, there are significant differences in the trends immediately when IPS is introduced, as the coefficients for home health days and costs become positive and statistically significant in quarter 4 of 1997. The positive coefficients for the interaction terms indicate that there was a smaller reduction in the outcome variables in high HHI areas after the introduction of IPS. An advantage of the event-study specification is that a structural break is not imposed in any particular year. Still, the model identifies a trend break immediately when IPS is introduced.

Our data and prior research suggests that the level of competition might be correlated with urban/rural status, and thus the results could be related to other unobserved differences between urban and rural areas rather than competition. To investigate this, we re-estimate the main analysis for stroke separately for urban and non-urban HSAs (results shown in Table 4). To categorize our data into urban and non-urban groups we use data from the National Center for Health Statistics (NCHS). Table 4 shows that urban and non-urban areas exhibit patterns that are similar to the pooled sample in Table 2 – in both urban and non-urban areas the IPS had larger negative effects on costs and days in more competitive markets.

Although both urban and non-urban areas exhibit similar patterns the magnitude of the effects estimated are larger in the urban HSAs. We also re-estimate our main results splitting HSAs that cross state lines. We find that our results are largely robust to this alternative market definition and also to excluding HSAs that cross state lines from the sample. These estimates are reported in Appendix Table 5.

The IPS reduced reimbursement by different amounts for home health agencies depending on how long the firm has been in the market, as well as their average costs relative to census division costs. To account for this difference in reimbursement changes across HSAs, we introduce a measure called IPS “bite” which is the difference between the HSA’s average number of home health days and the census division’s average number of home health days. As discussed above, this measure predicts how much of an impact IPS had on reimbursement, since HSAs with average days exceeding their census region’s average days would be more likely to have a payment limit that was below their average costs and, consequently, would see a larger reduction in reimbursement. Figure 3 shows the relationship between HHI and IPS “bite”. There is a slight negative correlation meaning that a larger reduction in payment (i.e., larger IPS bite) is associated with more competitive HSAs. This is not surprising given the fact that competition is positively associated with costs. This suggests that correlation between IPS “bite” and competition could explain some of our results.

We explore this issue further in Table 5 for stroke discharges by including an interaction between Post-IPS and IPS-bite, and a triple-interaction between HHI Quantile, Post-IPS, and IPS bite. We find that the coefficient on the interaction between Post-IPS and IPS-bite is negative and significant. This is consistent with prior research which also finds that the IPS led to larger declines in costs in areas with larger bite (P.J. Huckfeldt et al., 2014; McKnight, 2006). We find that after controlling for the IPS bite, the differential effect for the most competitive markets is reduced slightly. Home health days are reduced by approximately 1 day more for markets in the first quantile of HHI compared to the fourth quantile (columns 2 and 3) relative to the 2.5 day reduction that we estimate without controlling for IPS bite (column 1). Similarly, including the IPS “bite” interactions reduces the magnitude of the difference in reduction of provider costs between quantile 1 and quantile 4 to approximately $130 (columns 5 and 6) rather than $220 (column 4). While accounting for IPS bite does affect the magnitude of the effect of competition it does not change our overall result that competition amplifies the impact of the payment change.

Since payment limits for a home health agency under IPS is a function of its own costs in 1994 and average costs in the census division where the agency was located, another possibility is that IPS payment might be more binding in more competitive markets if more competitive markets experienced higher cost growth between 1994 and the implementation of IPS in quarter 4 of 1997. Although our data does not go back to 1994, we can examine two years (1996 and 1997) of pre-IPS home health outcome trends in Figure 2. In the two years leading up to IPS, we find little growth in all home health outcomes. More importantly, these trends are uncorrelated with the level of competition, as we observe that all outcomes were growing at the same rate across HHI Quantiles. Thus, we believe that the analysis supports the conclusion that home health agencies in more competitive areas were both more responsive to the change in marginal reimbursement from IPS and that they faced larger financial incentives to respond to IPS due to the correlation between competition and IPS-bite. However, due to data limitations that prevent us from measuring the precise financial incentive faced by each home health agency, we are unable to fully disentangle these two mechanisms. Finally, we find that the coefficients on the triple interaction between HHI Quantile, Post-IPS, and IPS bite are statistically insignificant suggesting that IPS bite or average reimbursement changes do not affect how competition mediates the impact of IPS on costs.

We find substantial evidence that the IPS response varied with the level of market competition. Figure 4 shows that HSAs in the most competitive quantile experienced the largest reduction in the number of home health agencies after IPS while the other quantiles appear to have experienced much smaller reductions.

In Table 6 we present both
the level and log effect estimates of regressing the number of home health
providers on the same variables and controls as Table 2. We construct the HHI and compute the
number of providers separately for each of the three conditions. As we would
expect, these results are not very sensitive to the condition since the
number of providers is virtually the same for all conditions. For all
conditions, we find progressively greater reductions in the number of HH
providers after IPS as the level of competition increases. For stroke,
compared to the lowest competition markets (quantile 4), markets in the
third competition quantile lost approximately 0.4 more agencies, markets in
the second quantile lost 1 to 1.2 more agencies, and the most competitive
markets lost about 4 to 5.6 additional agencies. In total, the number of
agencies in the most competitive markets fell by 4.3 agencies compared to an
*increase* of 1.6 agencies in the least competitive
markets (see Appendix Table 6, column
2). The log effect results follow the same pattern as the level effects for
all conditions. For stroke, we find that markets in the first quantile
experience a 13.7% greater decrease in the number of providers after
IPS than markets in the fourth quantile. In Appendix Table 6 we show a more comprehensive table of the
effects of IPS on the number of providers focusing only on stroke discharges
that features progressive inclusion of control variables, inclusion of IPS
“bite”, and a comparison between urban and non-urban
HSA’s. Comparing urban and non-urban HSAs in columns 5 and 6, we
find that the number of agencies in competitive markets in urban areas fell
more than in non-urban competitive markets, however we find the same general
pattern across competition levels for both categories. Including the IPS
bite interaction terms attenuated the estimates slightly but did not change
the pattern by competition levels.

The results in Table 6 show that reductions in the number of home health agencies after the IPS were greater in more competitive markets. Table 7 displays characteristics of staying firms and exiting firms in markets with high and low competition. In the least competitive HSAs (columns 3 and 4) there is very little difference in baseline year characteristics between exiting and staying firms. In the most competitive HSAs (columns 1 and 2) we find larger differences, with exiting firms having about 8 more home health days and $500 more in Medicare payments and costs than staying firms in the baseline year (1996). Although exiting agencies provided more home health days and incurred higher costs, there is almost no difference in 90-day mortality and rehospitalization rates suggesting that exiting firms may have over-provided care intensity (as measured by days). In both more and less competitive HSA’s, exiting firms are much more likely to have for-profit ownership status than non-exiting firms and this is particularly true in the most competitive markets, suggesting that for-profit firms may be operating more inefficiently. Overall, these results suggest that payment reform is more likely to induce inefficient firms to exit the market when they are operating in high competition markets. Additionally, we re-estimate the analysis from Table 6 by ownership status. These results are shown in Appendix Table 7 for stroke discharges. Consistent with the above results, we find that the effect of IPS on agency exit is driven by for-profit firms.

Finally, in Table 8 we show results from repeating our analysis for stroke from Table 2, excluding firms that exited the market after IPS was introduced. In order to assess differences in home health days and costs between patients who receive care from exiting or staying firms, we restrict the sample to individuals who received any home health care after a stroke discharge. Excluding exiting firms attenuates the extra reduction in home health days in the most competitive markets, from a reduction of about 4 days receiving home health to a 2.4 day reduction (columns 1 and 2). Once we control for IPS bite, the estimates become attenuated and insignificant (column 4). This result implies that much of the difference in the reduction of home health days we found across levels of competition is likely due to home health agency exit rather than changes in internal structure. For provider costs, we also find a progressive attenuation in the estimates as the sample is limited to agencies staying in the market and when we include the IPS bite interaction terms. However, the extra reduction in the most competitive markets after IPS remains statistically significant (column 8). This result suggests that market exit plays an important role in reducing costs.

Cost-based payment of health care providers has been widely acknowledged as a driver of over-use of health care and the growth of health care costs in the US. Competition has been acknowledged to exacerbate this problem, with providers in more competitive markets attracting patients by providing more services and amenities, generating geographic variation in costs. In this paper, we examined whether the effects of reforms that shift provider payment away from fee-for-service towards more capitated models depend on the level of market competition. We developed a theoretical model generating predictions that reducing marginal reimbursement will have a greater effect on the intensity of care and costs in more competitive markets. Our empirical results are consistent with this prediction, with larger reductions after the IPS in the probability of receiving home health care and the intensity of care in more competitive markets. Overall these results suggest that payment reform can play an important role in reducing geographic variation in care across more and less competitive markets.

An alternative explanation for our findings is that IPS payment limits were
more binding in more competitive markets. In particular, payment limits for a home
health agency under IPS was a function of its own costs in 1994 and average costs in
the census division where the agency was located. The IPS payment limits could be
more binding in more competitive markets if more competitive markets had higher
costs relative to their census division average or if more competitive markets
experienced higher cost growth between 1994 and the implementation of IPS in 1997.
Contrary to the above hypothesis, in the two years leading up to IPS, we find little
correlation between growth in costs and level of competition. However, we do not
have data from 1994 so we cannot rule out the possibility of correlation between
competition and cost growth during that period. Consistent with the above
hypothesis, we find that more competitive markets have higher costs relative to
their census division suggesting that IPS payment limits had greater
“bite” in more competitive markets. Though, after controlling for a
measure of the reform’s bite, we find that payment changes still led to
larger responses in more competitive markets. We conclude that more competitive
markets both faced larger financial incentives under this reform
*and* were more responsive to these financial incentives.
However, without the data to compute the precise financial incentive faced by each
home health agency, we cannot fully disentangle these two mechanisms’
contributions to our findings.

We do not find a similar convergence in patient outcomes across markets with varying levels of competition suggesting that the reduction in costs might have improved efficiency. We also find a larger reduction in the number of home health agencies in more competitive markets and that exiting providers were more likely to provide high-intensity and high-cost care. Further, much of the reduction in more competitive markets comes from the exit of such providers.

Our analysis has several policy implications. First, our results indicate that payment reform is an important tool for controlling health care costs in general. We find that reductions in marginal and average reimbursement reduce intensity of care and lead to exit of high-cost firms, which could have long lasting effects on costs for both public and private payers. Second, we show that payment reform might be an important tool for reducing geographic variation in costs: we find that payment reform leads to a larger reduction in costs in more competitive markets and more competitive markets tend to have higher costs. This naturally raises the question of whether these reductions in costs could come at the expense of patient outcomes. Evidence from the existing literature on the health effects of payment reform is somewhat mixed (Cutler, 1995; Kahn et al., 1990; Kosecoff et al., 1990; Rubenstein et al., 1990; Shen, 2003). We find little or no changes in both mortality and readmissions, suggesting that the IPS for home health care had little effect on patient outcomes. Similarly, Huckfeldt et al. (2014) and McKnight (2006) also find that home health payment reform leads to reductions in costs or intensity of care and is not associated with adverse health outcomes (P.J. Huckfeldt et al., 2014; McKnight, 2006). Similar results were found by studies assessing payment reform in the inpatient rehabilitation facility market and in the post-acute care market in general (McCall, Korb, Petersons, & Moore, 2003; Neeraj Sood, Buntin, & Escarce, 2008). Overall these results suggest that both policies that reduce marginal payments such as bundled payment systems as well as policies that reduce average reimbursement such as reductions in Medicare payment rates could be effective tools for improving the efficiency of Medicare spending.

This research was supported by grants from AHRQ (R01HS018541) and NIA (R01AG046838)

In this section, we formally derive the model and proofs of the main propositions. We are interested in modeling how agencies adjust their intensity of care (in this context intensity can be viewed as the number of visits per episode of care or costs) in response to payment reform across markets with different levels of competition. We develop a conceptual model based on papers by Brekke, Siciliani, and Straume (2011) and Hodgkin and McGuire(1994). Brekke, Siciliani, and Straume model competition and quality under regulated prices and Hodgkin and McGuire model responses to payment reform, switching to a prospective payment system. In this model, we introduce the concept of marginal and average reimbursement from Hodgkin and McGuire to the theoretical framework built in Brekke, Siciliani and Straume to create predictions for how responses to payment reform are likely to vary with market structure.

Changes in an agency’s intensity of care can have two effects on
demand – a market stealing effect (attracting a patient from another
home health agency) and a market expansion effect (attracting a patient from
another post-acute care provider or a patient who was not planning on getting
any post-acute care). To illustrate and isolate these effects we consider two
types of patients. The first, *H* type patients have a high value
of home health care. These are patients who are much more suited to home health
care; they get a large amount of utility from remaining in their homes and will
not switch to other post-acute options as long as home health care is provided
at a baseline level of intensity. We assume this market is saturated such that
increasing intensity will not draw any new *H* type patients into
the market, increasing intensity will only steal them from other firms. So
changes in demand by *H* type patients isolates the market
stealing effect of changes in intensity of care. The second, *L*
type patients have a lower value of home health care. These patients are willing
to utilize other types of post-acute care, like nursing homes, or forgo
post-acute care if home health intensity is not high enough. To isolate the
market expansion effect we assume that the *L* type patient
market is never saturated; increasing intensity will draw in new
*L* type patients to the market but will not steal
*L* types from other firms. We can model patient utility as:

$${U}^{s}=\{\begin{array}{ll}V-t|x-{z}_{i}|+k{q}_{i},\hfill & H\phantom{\rule{0.2em}{0ex}}\mathit{\text{type}}\hfill \\ v-t|x-{z}_{i}|+k{q}_{i},\hfill & L\phantom{\rule{0.2em}{0ex}}\mathit{\text{type}}\hfill \end{array}$$

Where *V* or *v* is
the value that the patient puts on home health service at a baseline intensity
that we arbitrarily set as $\underset{\_}{q}\equiv 0$ for convenience. The extra utility that a
patient gets from a firm providing intensity above $\underset{\_}{q}$ is *kq _{i}*. For
simplicity, let

In our model, price is regulated and takes the form *P*
= *α* + *β*
* *c*(*q _{i}*), where α is
average reimbursement and β is marginal reimbursement. This formulation
allows Medicare’s payment of home health agencies to occur on a spectrum
ranging from cost based reimbursement system (

We normalize patient density on the circle and the total length of the
circle to one. There are *n* firms evenly distributed about the
circle, such that their distance apart is equal to *1/n*. The
patient population is split between *H* and *L*
types where a fraction *λ* are *H* type
and *1-λ* are *L* type. To find demand for
each patient type, we first find their point of indifference along the circle
between the first firm, *i*, and a second firm,
*j*, for *H* type:

$$\begin{array}{l}V-t{x}_{i}^{H}+{q}_{i}=V-t\left(\frac{1}{n}-{x}_{i}^{H}\right)+{q}_{j}\\ \phantom{\rule{0.5em}{0ex}}{x}_{i}^{H}=\frac{{q}_{i}-{q}_{j}+\frac{t}{n}}{2t}\end{array}$$

(1)

And for *L* type patients where
agencies have a local monopoly patients are indifferent between receiving home
health care and the outside option whose utility is normalized to zero:

$$\begin{array}{l}\phantom{\rule{0.5em}{0ex}}\phantom{\rule{0.5em}{0ex}}v-t{x}_{i}^{L}+{q}_{i}=0\\ {x}_{i}^{L}=\frac{v+{q}_{i}}{t}\end{array}$$

(2)

Total demand is given by multiplying (1) and (2) by two times the fraction of H or L type patients.

$${X}_{i}=2\lambda {x}_{i}^{H}+2(1-\lambda ){x}_{i}^{L}=\frac{2(1-\lambda )v+(2-\lambda ){q}_{i}-\lambda {q}_{j}}{t}+\frac{\lambda}{n}$$

(3)

The combination of having *H* and
*L* type patients in the model separates the “market
stealing” and “market expansion” effects of an agency
increasing its intensity of care. When a firm increases its intensity, it
“steals” *H* type patients from other agencies
and “expands” the market by attracting new *L*
type patients who otherwise would not receive home health. We gain greater
insight from looking at how demand changes with intensity:

$$\frac{\partial {X}_{i}}{\partial {q}_{i}}=\frac{2-\lambda}{t}>0\phantom{\rule{0.5em}{0ex}}\phantom{\rule{0.5em}{0ex}}\frac{\partial {X}_{i}^{H}}{\partial {q}_{i}}=\frac{\lambda}{t}>0\phantom{\rule{0.5em}{0ex}}\phantom{\rule{0.5em}{0ex}}\frac{\partial {X}_{i}^{L}}{\partial {q}_{i}}=\frac{2(1-\lambda )}{t}>0$$

Both the “market stealing” (the second inequality) and the “market growth” (the third inequality) components of demand contribute a positive, constant return to intensity. In addition, the market growth is usually the primary driver of the return to intensity; only at high levels of H types in the market (λ>2/3) does the “market stealing” component over power the “market growth” component. We also look at how demand changes with number of firms:

$$\frac{\partial {X}_{i}}{\partial n}=-\frac{\lambda}{{n}^{2}}<0\phantom{\rule{0.5em}{0ex}}\phantom{\rule{0.5em}{0ex}}\frac{\partial {X}_{i}^{H}}{\partial n}=-\frac{\lambda}{{n}^{2}}<0\phantom{\rule{0.5em}{0ex}}\phantom{\rule{0.5em}{0ex}}\frac{\partial {X}_{i}^{L}}{\partial n}=0$$

As the number of firms increase, there is a
decrease in demand for each firm coming from the *H* type
patients switching to new agencies, but no effect from the *L*
type patients.

For the initial analysis in this model we assume that firms are profit maximizing, while in reality they may exhibit altruistic behavior. A version of our model that includes altruism follows after our main theoretical findings. We find that our predictions are similar to the for-profit analysis presented here except when firms exhibit a high degree of altruism. However, the empirical literature suggests that the level of altruism in hospitals and post-acute care providers is not great enough to differentiate for profit from nonprofit utility maximizing actions. Pauly (1987) reviews theoretical and empirical literature and finds no significant differences in market behavior between for profit and nonprofit firms (Pauly, 1987). More recently, Duggan (2000) finds that nonprofit hospitals are no more altruistic than for profit hospitals and that they respond similarly to pricing incentives.(Duggan, 2000) Additionally, Sloan, Picone, Taylor, and Chou (2001) find no difference in outcomes for for-profit vs nonprofit hospitals (Sloan, Picone, Taylor, & Chou, 2001). For these reasons, we restrict our main analysis to classic for-profit profit maximization and treat altruism as a perturbation from the for-profit model.

Firms profit maximize, as in (4):

$${\pi}_{\mathrm{i}}=\left(\alpha +\beta \ast c({q}_{i})\right){X}_{i}({q}_{i},{q}_{-i})-c({q}_{i}){X}_{i}({q}_{i},{q}_{-i})$$

(4)

With the first order condition for intensity allocation being:

$$\frac{\partial \pi}{\partial {q}_{i}}=\alpha \frac{\partial {X}_{i}}{\partial {q}_{i}}+\beta \left(\frac{\partial c}{\partial {q}_{i}}{X}_{i}+c({q}_{i})\frac{\partial {X}_{i}}{\partial {q}_{i}}\right)-\left(\frac{\partial c}{\partial {q}_{i}}{X}_{i}+c({q}_{i})\frac{\partial {X}_{i}}{\partial {q}_{i}}\right)=0$$

(5)

We substitute equation (3) into (5) and set q_{i}=q_{j} to solve for optimum
intensity q*.

The intensity of care increases with number of firms.

To solve for dq/dn we take the total derivative of the first order condition:

$$\begin{array}{l}dq:-\left(\left((1-\beta )\frac{\partial c}{\partial {q}_{i}}\right)\frac{2(1-\lambda )}{t}+(1-\beta )\frac{\partial c}{\partial {q}_{i}}\left(\frac{2-\lambda}{t}\right)+(1-\beta ){X}_{i}\frac{{\partial}^{2}c}{\partial {q}_{i}^{2}}\right)\\ dn:\left((1-\beta )\frac{\partial c}{\partial {q}_{i}}\right)\frac{\lambda}{{n}^{2}}\\ d\alpha :\frac{2-\lambda}{t}\\ d\beta :c({q}_{i})\left(\frac{2-\lambda}{t}\right)+\left(\frac{2(1-\lambda )v+2(1-\lambda ){q}_{i}}{t}+\frac{\lambda}{n}\right)\frac{\partial c}{\partial {q}_{i}}\end{array}$$

We can see that dq is simply the second order condition of profit maximization, and is, by definition, always less than zero.

$$\frac{d{q}_{i}}{dn}=\frac{\left((1-\beta )\frac{\partial c}{\partial {q}_{i}}\right)\frac{\lambda}{{n}^{2}}}{\left((1-\beta )\frac{\partial c}{\partial {q}_{i}}\right)\frac{2(1-\lambda )}{t}+(1-\beta )\frac{\partial c}{\partial {q}_{i}}\left(\frac{2-\lambda}{t}\right)+(1-\beta ){X}_{i}\frac{{\partial}^{2}c}{\partial {q}_{i}^{2}}}\ge 0$$

The denominator is the negative of the second
order condition therefore is positive, so the sign is determined by the
numerator. The numerator is also positive given that costs are increasing
and there is a non-zero amount of *H t*ype patients in the
market.

A decline in marginal reimbursement has larger effect on intensity of care in more competitive markets.

To see this, consider how dq/dn changes with marginal reimbursement:

$$\frac{\partial}{\partial \beta}\left(\frac{d{q}_{i}}{dn}\right)=\frac{\frac{\partial c}{\partial {q}_{i}}\frac{\lambda}{{n}^{2}}}{\frac{\partial c}{\partial {q}_{i}}\left(\frac{\partial {X}_{i}^{L}}{\partial {q}_{i}}+\frac{\partial {X}_{i}}{\partial q}\right)+{X}_{i}\frac{{\partial}^{2}c}{\partial {q}_{i}^{2}}}\ge 0$$

To understand why this relationship is positive, we look back to the first order condition, which simplifies to:

$$\mathit{\text{Profit}}\phantom{\rule{0.2em}{0ex}}\mathit{\text{Margin}}(q)\ast \frac{\partial {X}_{i}}{\partial {q}_{i}}=\frac{\partial c}{\partial {q}_{i}}(1-\beta )\ast {X}_{i}$$

The right hand side (RHS) of the equation is the marginal cost of increasing intensity and the left hand side (LHS) of the equation is the marginal benefit of increasing intensity. An increase in intensity decreases profits because it increases the marginal cost of providing care for inframarginal patients (RHS). However an increase in intensity raises profits because it increases demand and firms enjoy a positive margin on the marginal patients (LHS). The marginal benefit curve slopes downwards as profit margins decline with intensity. The marginal benefit term or the LHS is independent of the number of firms as the profit margin is a function of reimbursement policies and the slope of marginal cost curve while and the responsiveness of demand to intensity is a function of patient preferences (see expression for $\frac{\partial {X}_{i}}{\partial {q}_{i}}$ derived earlier in the theory section). However, the number of firms in the market does affect the RHS as an increase in the number of firms reduces the number of inframarginal patients a firm has. Thus the marginal cost curve for intensity shifts downwards as the number of firms rises (see Appendix Figure 1) and consequently intensity is higher in more competitive markets.

A decrease in marginal reimbursement pivots the marginal benefit curve for intensity downwards as increases in intensity have a smaller effect on profit margins when marginal reimbursement is higher. This has a larger effect on intensity in more competitive markets, as equilibrium intensity is higher in more competitive markets. Similarly, a decrease in reimbursement also pivots the marginal cost curve for intensity upward as providing care to inframarginal patients now has a larger effect on profits. Again this upward pivot induces a larger effect on intensity in more competitive markets, as equilibrium intensity is higher in more competitive markets. This effect is shown in Appendix Figure 1. In the figure, the points labeled A denote the level of intensity before a decrease in marginal reimbursement. It is clear that intensity of care in the market with more competition leads to a higher baseline level of intensity. When marginal reimbursement decreases, the marginal benefit curve pivots downwards and the marginal cost curves pivot upward as previously stated. A new equilibrium level of intensity is achieved at the points labeled B. The change in intensity for less competitive markets (low n) is less than the change in intensity for competitive markets (high n) as predicted.

Reducing marginal and average reimbursement reduces intensity of care.

This proposition is fairly intuitive and can be derived easily from the total derivative of the first order condition:

$$\begin{array}{l}\frac{d{q}_{i}}{d\alpha}=\frac{\frac{2-\lambda}{t}}{\left((1-\beta )\frac{\partial c}{\partial {q}_{i}}\right)\frac{2(1-\lambda )}{t}+(1-\beta )\frac{\partial c}{\partial {q}_{i}}\frac{2-\lambda}{t}+(1-\beta ){X}_{i}\frac{{\partial}^{2}c}{\partial {q}_{i}^{2}}}>0\\ \frac{d{q}_{i}}{d\beta}=\frac{c({q}_{i})\frac{2-\lambda}{t}+{X}_{i}\frac{\partial c}{\partial {q}_{i}}}{\left((1-\beta )\frac{\partial c}{\partial {q}_{i}}\right)\frac{2(1-\lambda )}{t}+(1-\beta )\frac{\partial c}{\partial {q}_{i}}\frac{2-\lambda}{t}+(1-\beta ){X}_{i}\frac{{\partial}^{2}c}{\partial {q}_{i}^{2}}}>0\end{array}$$

More competitive markets will experience greater firm exit.

Immediately after payment change is enacted, firms will adjust their intensity to profit maximize but in the months and years post payment change firms will exit the market if profits fall below zero:

$${\pi}_{\mathrm{i}}=\left(\alpha +\beta \ast c({q}_{i})\right){X}_{i}({q}_{i},{q}_{-i})-c({q}_{i}){X}_{i}({q}_{i},{q}_{-i})<0$$

Solving for α and β, we obtain threshold levels of average and marginal reimbursement below which firms will leave the market:

$$\begin{array}{l}\alpha <(1-\beta )c({q}_{i})\\ \beta <\left(1-\frac{\alpha}{c({q}_{i})}\right)\end{array}$$

In Proposition 1 we determined that intensity of care increases with the number of firms and thus more competitive markets will have higher levels of intensity. The marginal cost of an additional patient is increasing with intensity, therefore costs in more competitive markets will be higher. A higher marginal cost raises the payment threshold for exit in these markets making it more likely that reductions to average and marginal reimbursement from IPS will surpass these thresholds and cause firms to exit.

Although there is evidence that many not-for-profit health care
organizations behave as profit maximizing firms, we include a model that
takes into account the altruistic behavior that may be displayed by
not-for-profit home health agencies. To account for this, we include the
value the firm gets from providing services to patients as a fraction of the
value the consumers get, *θ* *
*B*(*q _{i}*,

$${B}_{i}({q}_{i},{q}_{-i})=2\lambda {\displaystyle {\int}_{0}^{{\scriptscriptstyle \frac{1}{2t}}({q}_{i}-{q}_{j}+{\scriptscriptstyle \frac{t}{n}})}(V+{q}_{i}-tx)dx+2(1-\lambda ){\displaystyle {\int}_{0}^{{\scriptscriptstyle \frac{v+{q}_{i}}{t}}}(v+{q}_{i}-tx)dx}}$$

(6)

Differentiating with respect to quality gives:

$$\frac{\partial {B}_{i}}{\partial {q}_{i}}={X}_{i}({q}_{i},{q}_{-i})+\frac{\lambda}{t}\left(V+\frac{{q}_{i}+{q}_{j}}{2}-\frac{t}{2n}\right)>0$$

(7)

There are two components that make up the
change in patient benefit from a change in quality, the first part,
*X _{i}*(

$${\pi}_{\mathrm{i}}=\left(\alpha +\beta \ast c({q}_{i})\right){X}_{i}({q}_{i},{q}_{-i})+\theta B({q}_{i},{q}_{-i})-c({q}_{i}){X}_{i}({q}_{i},{q}_{-i})$$

With the first order condition for intensity allocation being:

$$\frac{\partial \pi}{\partial {q}_{i}}=\alpha \frac{\partial {X}_{i}}{\partial {q}_{i}}+\beta \left(\frac{\partial c}{\partial {q}_{i}}{X}_{i}+c({q}_{i})\frac{\partial {X}_{i}}{\partial {q}_{i}}\right)+\theta \frac{\partial B}{\partial {q}_{i}}-\left(\frac{\partial c}{\partial {q}_{i}}{X}_{i}+c({q}_{i})\frac{\partial {X}_{i}}{\partial {q}_{i}}\right)=0$$

(8)

We substitute equations (3) and (7) into (8) and set q_{i}=q _{j} to solve for
optimum intensity q*. The total differentiation of equation (8) that is used to
estimate how intensity changes with the number of firms in the market and
with changes to marginal and average reimbursement becomes:

$$\begin{array}{l}dq:-\left(\left((1-\beta )\frac{\partial c}{\partial {q}_{i}}-\theta \right)\frac{2(1-\lambda )}{t}-\theta \frac{\lambda}{t}+(1-\beta )\frac{\partial c}{\partial {q}_{i}}\left(\frac{2-\lambda}{t}\right)+(1-\beta ){X}_{i}\frac{{\partial}^{2}c}{\partial {q}_{i}^{2}}\right)\\ dn:\left((1-\beta )\frac{\partial c}{\partial {q}_{i}}-\frac{\theta}{2}\right)\frac{\lambda}{{n}^{2}}\\ d\alpha :\frac{2-\lambda}{t}\\ d\beta :c({q}_{i})\left(\frac{2-\lambda}{t}\right)+\left(\frac{2(1-\lambda )v+2(1-\lambda ){q}_{i}}{t}+\frac{\lambda}{n}\right)\frac{\partial c}{\partial {q}_{i}}\\ d\theta :\frac{2(1-\lambda )v+2(1-\lambda ){q}_{i}}{t}+\frac{\lambda}{n}+\frac{\lambda}{t}\left(V+{q}_{i}-\frac{t}{2n}\right)\end{array}$$

We find that intensity of care increases with the number of firms only for certain θ:

$$\frac{d{q}_{i}}{dn}=\frac{\left((1-\beta )\frac{\partial c}{\partial {q}_{i}}-\frac{\theta}{2}\right)\frac{\lambda}{{n}^{2}}}{\left((1-\beta )\frac{\partial c}{\partial {q}_{i}}-\theta \right)\frac{2(1-\lambda )}{t}-\theta \frac{\lambda}{t}+(1-\beta )\frac{\partial c}{\partial {q}_{i}}\left(\frac{2-\lambda}{t}\right)+(1-\beta ){X}_{i}\frac{{\partial}^{2}c}{\partial {q}_{i}^{2}}}$$

If a firm is above a certain threshold altruism level the sign is negative. Otherwise for modest levels of altruism we find the same result as for a profit maximizing firm. The threshold level of altruism is:

$$\overline{\theta}=2(1-\beta )\frac{\partial c}{\partial {q}_{i}}$$

For a profit maximizing firm, we found that intensity of care increased as the number of firms in the market increased due to increased competition. Although this result applies to altruistic firms up to the altruistic threshold, very altruistic firms are predicted to actually decrease quality as the number of firms increases. In the profit maximizing case, we obtained a positive relationship due to the fact that when the number of firms increased, the demand for each firm decreases, this lower demand increases marginal profits which makes it more profitable to increase intensity of care in order to attract more patients. Altruistic firms a have a second effect coming into play. Because they value the patient benefit, lower demand from an increase in firms also lowers the marginal patient benefit for high intensity of care giving the hospital less incentive to increase intensity of care. At high enough levels of altruism, this lowered patient benefit effect overshadows the increased marginal profit effect and firms actually decrease quality.

Our estimates of how intensity of care changes with the marginal and average reimbursement remain unchanged in sign, as payments increase (decrease) intensity of care increases (decreases). Similarly, effects on firm exit remain mostly unchanged. Threshold levels of average and marginal reimbursement, below which firms will leave the market in the long run, are lowered by the inclusion of the welfare term, θB.

Introducing the parameter, θ, lets us analyze the effect of changes in the level of altruism have on intensity:

$$\frac{d{q}_{i}}{d\theta}=\frac{{X}_{i}+\frac{\lambda}{t}\left(V+{q}_{i}-\frac{t}{2n}\right)}{\left((1-\beta )\frac{\partial c}{\partial {q}_{i}}-\theta \right)\frac{2(1-\lambda )}{t}-\theta \frac{\lambda}{t}+(1-\beta )\frac{\partial c}{\partial {q}_{i}}\frac{2-\lambda}{t}+(1-\beta ){X}_{i}\frac{{\partial}^{2}c}{\partial {q}_{i}^{2}}}>0$$

Although quality responsiveness to market competition is lowered by altruism, overall altruism leads to higher quality due to the value firms place on patient wellbeing. Altruistic firms are willing to forgo profits in order to provide higher quality and provide higher levels of equilibrium quality than do profit maximizing firms with the same level of reimbursement. Including altruism in our analysis leads to similar, though smaller in magnitude, results as profit maximizing firms except for at high levels of altruism. Prior research suggests that non-profit firms do not behave very altruistically and therefore we expect to see results similar to those of for-profit firms.

Motivated by these propositions and our subsequent analysis of altruistic behavior we expect to see the following patterns in our data:

- More competitive markets have higher intensity of care (and consequently, higher costs).
- Because IPS lowered both average and marginal reimbursement we expect to see a decrease in intensity of care for all markets.
- Because the effects of changes in marginal reimbursement are magnified in markets with more competition we expect to see a greater decrease in intensity of care (and costs) following the IPS in more competitive markets. This implies a convergence in the costs or intensity of care in more versus less competitive markets after the reform.
- Altruism, if present, is likely to reduce the magnitude of effects from payment reform. Thus we expect to find the largest effects in for-profit home health agencies and smaller effects in non-profit and government run agencies.
- More competitive markets will have greater firm exit.

One caveat is that the model is silent on the effects of competition on patient outcomes. The model predicts changes in intensity of care only and not patient outcomes. On the one hand, one can argue that if patients value intensity it must improve patient outcomes. However, on the other hand one can argue that patients might be uninformed and even though they value higher intensity care, beyond a certain level, changes in intensity of care do not improve patient outcomes and represent “wasteful” spending. Thus, in our empirical models we will evaluate both changes in intensity of care and also changes in patient outcomes.

^{1}For example, if a high cost firm had historical average costs of $200 and
the average cost in the region was $150, the firm would face a cost limit of
$187.5. Similarly, if a low cost firm had historical average costs of $100 and
was also in the $150 average cost region, it would face an average per visit
cost limit of $112.5, which would not be binding.

^{2}Stroke patients are defined as those with a principal diagnosis in the acute
hospital stay of intracerebral hemorrhage (diagnosis code 431.xx), occlusion and
stenosis of precerebral arteries with infarction (433.x1), occlusion of cerebral
arteries with infarction (434.x1), or acute but ill-defined cerebrovascular
disease (436.xx). Hip fracture patients are defined as patients with a primary
diagnosis of fractures of the neck or the femur (820.xx). Lower extremity joint
replacement patients were defined as patients with a primary diagnosis for joint
replacement, excluding hip fracture patients and patients with reattachment
procedure.

^{3}Specifically, in more recent data from 2008–2013, stroke, hip fractures,
and lower extremity joint replacement represented about 16% (3%
stroke, 4 % hip fracture, 9% joint replacement) of Medicare home
health patients and about 11% (3% stroke, 3.5% hip
fracture, 4% joint replacement) of Medicare home health days
(authors’ calculations from MEDPAR and HHA base claims files
2008–2013).

^{4}The data have unique provider identifiers for each home health agency operating
in a particular location. However, the data do not have any information on
ownership or participation in a chain. Thus, while two or more home health
agencies may be under the same ownership, we are unable to account for this in
our market concentration measures.

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