Empirical model

The objective of the paper is to answer the following two questions: does expansion of the assisted living industry affect nursing home market structure and does this expansion have an effect on the price that nursing homes charge? To answer both questions, data from 1999 and 2005 are used to construct a two-period panel of nursing homes in order to estimate two separate sets of regressions. Given how the market is constructed, which is discussed later, each nursing home is considered a separate market, making the unit of observation a market year.

In the first set of regressions, the dependent variable of nursing home market structure ( $$)(--><$>S_{{mt}}^{{NH}} <$><!--$$ ) is regressed against assisted living market structure ( $$)(--><$>S_{{mt}}^{{RCF}} <$><!--$$ ), market demographic characteristics (D_mt), an indicator for observation year (τ_t), and market fixed effects (a_m), where the subscript m denotes each nursing home market. Specifically, the equation to be estimated is

$$S_{{mt}}^{{NH}} \, = \,\beta S_{{mt}}^{{RCF}} \, + \,\theta {{D}_{mt}}\, + \,{{\alpha }_m}\, + \,{{\tau }_t}\, + \,{{{\epsilon}}_{mt }}$$

In the second set of regressions, the dependent variable is average daily private pay price charged by nursing homes ( $$)(--><$>P_{{mt}}^{{NH}} <$><!--$$ ). Along with variables in equation (1), this set of regressions also controls for nursing home market structure and a vector of facility characteristics (F_mt). Formally, the regression models to be estimated are

$$P_{{mt}}^{{NH}} \, = \,{{\beta }_{\rm{1}}}S_{{mt}}^{{RCF}} \, + \,{{\beta }_{\rm{2}}}S_{{mt}}^{{NH}} \, + \,\gamma {{F}_{mt}}\, + \,\theta D_{{mt}}^{{}} \, + \,{{\alpha }_m}\, + \,{{\tau }_t}\, + \,{{{\epsilon}}_{mt }}$$

There are few econometric issues that need to be addressed in estimating both equations. The error term is found to have a non-constant variance and shocks in a market that affect one year are likely to be correlated with shocks in the other year. Therefore, standard errors are estimated to allow for heteroscedasticity and clustering within market. Additionally, unobserved demand and cost shocks can lead to an evolutionary process that causes market structure to be endogenous. To address this issue, equations (1) and (2) include market-specific fixed effects, which captures a time-invariant demand or cost shock that affect market structure or price (Evans et al., Reference Evans, Froeb and Werden1993; Moriya et al., Reference Moriya, Vogt and Gaynor2010). For reference, the tables also report results that do not include market-specific fixed effects [i.e. pooled ordinary least squares (OLS)].

Data sources

The empirical analysis utilizes data from three main sources on long-term care providers in the State of Ohio for the years of 1999 and 2005 to construct a panel of nursing homes: the Online Survey Certification and Reporting (OSCAR) System, the 1999 and 2005 Biennial Survey of Long-Term Care Facilities, and the Area Resource File.Footnote ⁵ OSCAR is a uniform database that contains state surveys of all federally certified nursing homes every 9–15 months and contains information about the nursing home characteristics and location. The Biennial Survey of Long-Term Care Facilities is a survey of Ohio nursing homes and assisted living facilities collected by the Ohio Department of Aging in conjunction with the Scripps Gerontology Center with the purpose of providing the state information on the supply of long-term care beds. The nursing home component of the survey provides the average daily private pay price that nursing homes charge residents, whereas the assisted living component provides information on the location of assisted living facilities. Finally, the Area Resource File provides demographic information at the county level.

To construct the analytical data set, all nursing homes surveyed in OSCAR in the calendar years of 1999 and 2005 are merged with price data from the Biennial Survey of Long-Term Care Facilities using the nursing home's provider identification number. County demographic characteristics from the Area Resource File are merged into the data based on county the nursing home is located. The assisted living facility component of the Biennial Survey of Long-Term Care Facilities is used to identify the number of assisted living facilities in each market. Given the time between surveys in the OSCAR data, some nursing homes may not have surveys in 1999 or 2005. Therefore, data from 1998 to 2006 is used to identify nursing homes that are in the market in 1999 and 2005. Nursing homes and assisted living facilities are assigned markets based on their zip code. This assignment process is discussed below. The resulting analytical data file contains 1902 market-year observations across the two years.

Market definition and market structure variables

The definition of the relevant geographic market is important in obtaining accurate measures of market structure. While prior research has used the county to define the market, this market definition can over- or underestimate the true level of market concentration (Zwanziger et al., Reference Zwanziger, Mukamel and Indridason2002). Therefore, one of the common approaches is to use a fixed circular distance around each facility.Footnote ⁶ One of the first to use this approach in the nursing home industry is Grabowski and Stevenson (Reference Grabowski and Stevenson2008), which used a fixed radius of 25 km. However, as pointed out by Bowblis and North (Reference Bowblis and North2011), the size of radius can be different based on the population density in the local area. Therefore, markets are defined using a fixed radius around each nursing home based on population density. Specifically, the radius for nursing homes in the population density ranges of 0–99, 100–249, 250–599, and over 600 are 16.35, 13.73, 13.01 and 9.91 miles, respectively.Footnote ⁷

Using a fixed radius implies that each nursing home is in a separate market, resulting in 1902 market-year observations in 1039 markets.Footnote ⁸ To determine the nursing homes and assisted living facilities that compete within each market, the latitude and longitude of each facility is identified from zip codes and the distances between facilities are then computed using the ‘great circle’ distance formula. Any nursing home or assisted living facility that has a distance smaller than the fixed radius is considered within the market.

As discussed earlier, Ohio had a moratorium on new nursing home beds during the study period. The moratorium allowed nursing homes to trade beds within a county but not across county lines. This implies the number of nursing homes and distribution of beds among nursing homes within a county could change, but not the maximum number of beds. To account for this, two measures of nursing home market structure are used. The first is a measure of nursing home market concentration that accounts for the distribution of beds among nursing homes within a geographic area. The market concentration is measured as 1 minus the HHI.Footnote ⁹ The second measure is the number of nursing home facilities per 10,000 people. Assisted living market structure is measured as the number of assisted living facilities per 10,000 people. For all three measures, higher values imply more competitive markets and summary statistics for these measures are reported in Table 1.

Table 1

Variation in market structure

^†The concentration measure is defined as 1 minus the Herfindahl–Hirschmann Index. Higher values imply less market concentration.

***p < 0.01; **p < 0.05; *p < 0.1.

Since the regressions are based on regression to the mean, areas of Ohio with a greater population and hence more nursing homes will get a larger weight in the analysis. Variation in market structure is likely to be small in larger markets. For example, the largest three counties in Ohio (Cuyahoga, Franklin and Hamilton) have about 25% of all nursing homes in state in 1999 and combined with the next four largest in terms of number of nursing homes (Lucas, Montgomery, Stark and Summit), the seven largest counties represent about 40% of all nursing homes. Therefore, results are also reported for regressions in ‘small’ markets. A small market is defined as any nursing home not located in these seven counties.

Nursing home price variable

The nursing home price variable is the average daily private pay price charged by nursing homes in the calendar year. To account for inflation, private pay prices in 1999 are adjusted to 2005 dollars using the Consumer Price Index. Of the 1902 market-year observations, 211 observations are excluded from the analysis because private pay price is not reported, reported as zero, or is three standard deviations from the average price. This implies that equation (2) uses data from 1691 market-year observations.

Other controls

Equations (1) and (2) contain additional controls for market demographic characteristics. As pointed out by Stevenson and Grabowski (Reference Stevenson and Grabowski2010), assisted living facilities are more likely to locate in more affluent areas. Failure to control for market demographics could bias the effect of market structure. Market characteristics include per capita income, Medicare HMO penetration rates, percent of population aged 65+, percent of population that is female and population density. Equation (2) also controls for nursing home facility characteristics that can influence private pay price and can be broadly characterized as facility structure, case-mix and quality. Summary statistics for all control variables used in equations (1) and (2) are reported in Table 2.

Table 2

Summary statistics for market structure and private pay price regressions

Notes: The table reports summary statistics for the nursing home market structure and nursing home private pay price regressions. Standard deviations for summary statistics are reported in parentheses.

^†The concentration measure is defined as 1 minus the Herfindahl-Hirschmann Index. Higher values imply less market concentration.

Facility structure includes ownership status (i.e. for-profit, not-for-profit and government), number of beds, chain membership, hospital-based facility, payer-mix, occupancy rate and the presence of special care units. Each ownership status may be able to charge different prices, whereas nursing homes that are part of a chain or are hospital based have different cost-structures that are reflected in prices. The number of beds, together with occupancy rate, captures economies of scale in the regression equations. Finally, special care units, which include indicator variables of Alzheimer's and any other form of special care unit, can reflect price premiums consumers are willing to pay for specialized care.

Case-mix needs to be controlled for to capture the amount of care the average resident in each nursing home requires. Nursing homes that have residents that are more heavily dependent on nurse staff increase the cost of care, and this cost could be passed on to residents in the form of higher private pay prices. Physical case-mix is measured using the Acuindex (Cowles, Reference Cowles2002), and the percentage of residents that are chair bound and bedbound. Mental case-mix is captured by the percentage of residents with dementia and psychiatric illnesses.

The final set of nursing home facility characteristics included in the private pay price regressions are nursing home quality measures. There are multiple measures of nursing home quality and the quality measures used are reported in nursing home quality report cards available in Ohio before the federal implementation of national quality reporting in 2002. These quality measures include the total hours per resident day of nurse staffing, the percentage of nurse staffing that is licensed (i.e. registered nurses or licensed practical nurses), and the total number of regulatory deficiencies. Occasionally, nurse staffing variables are inaccurate and these observations are identified as nurse staffing levels three standard deviations above and below the sample mean. Inaccurate staffing observations are identified with an indicator variable for inaccurate staffing level and the total staff nurse staffing hours and percentage of licensed staff are recoded as zero.