QUANTIFYING THE IMPACTS OF LIMITED SUPPLY: THE CASE OF NURSING HOMES

• Published date: 01 November 2015
• Author: Fumiko Hayashi,Hui Wang,Andrew T. Ching
• Date: 01 November 2015
• DOI: http://doi.org/10.1111/iere.12138

INTERNATIONAL ECONOMIC REVIEW

Vol. 56, No. 4, November 2015

QUANTIFYING THE IMPACTS OF LIMITED SUPPLY:

THECASEOFNURSINGHOMES

∗

BYANDREW T. CHING,FUMIKO HAYASHI,AND HUI WANG 1

University of Toronto, Canada; Federal Reserve Bank of Kansas City, U.S.A.; Peking University,

P.R. China

This article develops a new estimation method that accounts for excess demand and the unobserved component

of product quality. We apply our method to study the Wisconsin nursing home market in 1999 and find that nearly

20% of elderly qualified for Medicaid were rationed out. However, our counterfactual experiment shows that the net

welfare gain of fulfilling all nursing home demands may be small, because the welfare gain could be largely offset by the

increase in Medicaid expenditures. We also find that a 1% increase in quality would crowd out 3.2% Medicaid patients

in binding nursing homes.

1. INTRODUCTION

Products or services with limited supply are prevalent in our economy. Examples include

hotels, schools, public housing, hospitals, nursing homes, etc. Due to the stickiness of prices

or government regulations, these services commonly experience excess demand from time to

time. When demand exceeds supply, consumers would either need to wait in line or choose

their second best options. This poses a challenge to researchers who are interested in re-

covering consumer preferences from market shares/sales data available to them—in general,

one cannot use such data alone to infer true underlying consumer preferences. In particu-

lar, without properly taking the extent of rationing into account, the preference parameters

and product quality obtained from the standard estimation procedure could be very mislead-

ing. In this article, we develop an estimation strategy that accounts for excess demand and

the unobserved component of product quality. Our methodology is motivated by the institu-

tional details of the nursing home market. It allows us to quantify the extent of rationing,

price, and quality elasticities of demand and shed light on the potential welfare gain/loss

if we try to fulfill all rationed demand. We apply our framework to study the Wisconsin

nursing home market in 1999, which has been thought to face two main problems: limited

∗Manuscript received December 2012; revised March 2014.

1We are very grateful to Gautam Gowrisankaran and Tom Holmes for their advice in the early stages of the project.

We thank Holger Sieg (the editor) and two anonymous referees for providing many constructive comments. We also

thank Ig Horstmann, Juanjuan Meng, Kanishka Misra, Matt Mitchell, Judith Mortimer, Ed Norton, John Nyman,

Andrew Sweeting, participants at the AEA annual meeting, Annual Health Econometrics Workshop, CKGSB Mar-

keting Conference, Cowles Foundation Structural Microeconomics Conference, International Industrial Organization

Conference, SICS, FTC Microeconomics Conference and seminar participants at UCLA, UC-Davis, U of Toronto,

John Hopkins University, U of Texas-Dallas, U of Texas-Arlington, U of Guelph, CUHK, NUS, Indiana U, and Carl-

son School of Management for their helpful comments. The views expressed in this article are those of the authors

and do not necessarily reflect those of the Federal Reserve Bank of Kansas City or the Federal Reserve System.

We acknowledge the financial support provided by the Michael Lee-Chin Family Institute for Corporate Citizenship

at the Rotman School of Management, University of Toronto. Please address correspondence to: Andrew T. Ching,

Rotman School of Management and Department of Economics, University of Toronto, Toronto, ON M5S 2J7, Canada.

Phone: 1-416-946-0728. Fax: 1-416-978-5433. E-mail: aching@rotman.utoronto.ca.

1291

C

(2015) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1292 CHING,HAYASHI,AND WANG

access/rationing and low quality (e.g., Gruenberg and Willemain, 1982; Norton, 1992; Ettner,

1993).2

Besides being a market that commonly experiences excess demand, the nursing home mar-

ket is important on its own because of the substantial growth of the elderly population. To

control for the expenditures on nursing home care, most state governments regulate the in-

dustry in two important ways. First, many state governments restrict supply so that a cer-

tificate of need (CON) is necessary for new nursing homes to enter the market or even

for existing ones to increase their number of beds. Second, state governments regulate the

price that they pay for a large percentage of nursing home care through Medicaid programs.

These regulations have led to two groups of studies.3One group of studies focused on the

effect of Medicaid reimbursement, such as how the level of Medicaid reimbursement rates

affects nursing home quality of care and whether the difference in reimbursement method—

prospective or cost-based payment—affects nursing home outcomes (e.g., Nyman, 1985, 1988a,

1994; Gertler, 1989, 1992; Cohen and Spector, 1996; Grabowski, 2001). Another group of stud-

ies investigated the effects of the CON laws. Because the CON laws can potentially create

excess demand in the market and allow existing nursing homes to establish and preserve mar-

ket power, some of the studies have aimed at examining the empirical relationship between

excess demand/market concentration and market outcomes (e.g., Lee et al., 1983; Nyman,

1988a, 1988b, 1994; Gertler, 1989, 1992; Cohen and Spector, 1996; Spector et al., 1998). Ex-

tending Scanlon’s (1980) pioneering work, studies that used data in the 1970s and early 1980s

found evidence of excess demand (e.g., Nyman, 1985, 1988a, 1988b, 1989, 1994; Gertler, 1989,

1992). Studies that used more recent data, however, suggest that excess demand may become

less prevalent (e.g., Cohen and Spector, 1996; Grabowski, 2001; Grabowski and Angelelli,

2004).

We have learned much from previous work; however, due to the reduced-form modeling

approach, there remain some important questions that this work cannot answer. In general, there

are three limitations. First, many previous studies used market tightness as a proxy for excess

demand. However, a tight market does not always imply that the market has excess demand;

rather, it could be consistent with nursing homes being nearly fully occupied at equilibrium.

More importantly, their approach cannot quantify the extent of rationing because it does not

measure the number of patients who prefer to live in a particular nursing home but which they

cannot enter. Second, when measuring quality provided by a nursing home, most of the previous

studies used either input-based or outcome-based methods, which did not take into account

factors that are unobserved to the econometrician (e.g., reputation). Unobserved factors are

potentially important. They may adjust between the actual quality the nursing home provides

and the average quality that can be produced with the staffing intensity used by the nursing

home. Unobserved factors can also lead to an endogeneity problem of price if one ignores their

presence in estimation. Third, as is well known, the reduced-form approach cannot measure

patient welfare under counterfactual experiments.

In light of these shortcomings in the previous literature, the goal of this article is to develop

a structural demand model and a new estimation strategy that enables us to account for excess

demand and the unobserved component of nursing home quality. After obtaining the structural

parameters of the model, we can quantify the extent of rationing and the potential welfare

gain/loss if we try to fulfill all the rationed demand at prevailing private-pay prices, Medicaid

reimbursement rates, and nursing homes qualities. Motivated by several institutional features

of the nursing home industry, our model assumes that (i) some nursing homes may face excess

2See the report to Congress made by the Health Care Financing Administration in July 2000 (Health Care Financing

Administration, 2000). It is also worth pointing out that a nursing home shortage is a public concern even today. See

“The coming nursing home shortage,” the Fiscal Times (2012) http://www.thefiscaltimes.com/Articles/2012/01/26/The-

Coming-Nursing-Home-Shortage, accessed on Feb 17, 2014.

3Norton (2000) provides an excellent survey on this topic.

IMPACTS OF LIMITED SUPPLY 1293

demand from Medicaid patients; (ii) nursing homes are free to admit private-pay patients first,

who typically pay more than the Medicaid reimbursement rate; (iii) the potential number of

private-pay patients is not large enough for them to face the capacity constraints problem; and

(iv) both private-pay and Medicaid patients rank nursing home quality similarly. The key idea

of our identification strategy is that we need to observe the demand by one group of patients

who do not face the rationing problem (in this case, the private-pay patients), and hence we

can use the revealed preference argument to recover the quality of nursing homes based on

their observed demand. By further assuming that both Medicaid and private-pay patients share

similar preferences for nursing home quality (i.e., the nursing homes’ qualities recovered from

private-pay patients’ demand also apply to Medicaid patients), we can then use our model to

infer the true demand for each nursing home and measure the extent of rationing. Our modeling

assumptions, together with our data set, allow us to extend the estimation approach developed

by Berry (1994), Berry et al. (1995), and Petrin (2002) to obtain the structural parameters of

the model, when we only have access to market share data. Taking this approach allows us

to measure quality of care from patient demand by constructing a “quality index,” which can

potentially lessen the problem of input-based or outcome-based quality measure and address

the endogeneity problem of private-pay prices.4

To estimate our model, we use the 1999 Wisconsin Annual Survey of Nursing Homes, which

contains each nursing home’s characteristics and some statistics of its patients. We also supple-

ment it with the Special Tabulation on Aging from the 2000 Census and the 1999 Wisconsin

Health Survey. We study the nursing home market in 1999 because excess demand for nurs-

ing homes was believed to be common back then, but the limitations of previous empirical

methods were not able to quantify the extent of rationing. Therefore, this environment should

serve as a useful place to illustrate our proposed empirical framework for investigating excess

demand.

Our estimation results suggest that excess demand was still prevalent in Wisconsin in the

late ‘90s. Approximately half of the nursing homes used for this study are estimated to face

binding capacity constraints; about 20% of potential patients who qualified for Medicaid are

rationed out for nursing home care (i.e., they would have chosen to enter nursing homes

if the capacity constraints did not exist); and about 26% of the Medicaid nursing home

patients could not enter their first-choice nursing homes. However, we also find evidence that

the net social welfare gain of removing the capacity constraints may be small, because it is

expensive for the state government to cover additional nursing home care. Our estimation

results show that the unobserved component of quality accounts for 40% of the quality index

and plays an important role in explaining market shares. Moreover, our estimated quality

index suggests that nursing homes tend to provide lower quality of care in counties with tight

supply. Interestingly, it also implies that not-for-profit nursing homes tend to provide better

quality than for-profit nursing homes, which is consistent with what the health service literature

finds.

The rest of the article is organized as follows. Section 2 summarizes some important nursing

home regulations in Wisconsin. Section 3 presents the demand model. Section 4 details the

data, and Section 5 presents the estimation procedure. Estimation results, their implications,

and limitations are provided in Section 6. Finally, Section 7 concludes.

4Unlike our approach, Geyer and Sieg (2013) make use of individual level data on exit rate and an equilibrium model

to infer the unobserved waiting list in public housing. Our article is also closely related to Conlon and Mortimer (2013),

who propose an estimation approach that applies to a situation where all types of consumers could face stock-out

problems. However, their approach is computationally very challenging to implement when there are many products

experiencing stock-out, because it needs to integrate out all possible unobserved orders of stock-out to obtain the

likelihood. Our proposed approach completely avoids this computational problem, given the crucial assumptions we

made. Our article is also related to the marketing literature that focuses on the out-of-stock situation: Bruno and

Vilcassim (2008), Che et al. (2012), Musalem et al. (2010). These papers rely on using proxies to indicate which products

experience out-of-stock.