What Does Free Cash Flow Tell Us About Hospital Efficiency? A Stochastic Frontier Analysis of Cost Inefficiency in California Hospitals William R. Pratt Hospitals are facing substantial financial and economic pressure as a result of health plan payment restructuring, unfunded mandates, and other factors. This article analyzes the relationship between free cash flow (FCF) and hospital efficiency given these financial challenges. Data from 270 California hospitals were used to estimate a stochastic frontier model of hospital cost efficiency that explicitly takes into account outpatient heterogeneity. The findings indicate that hospital FCF is significantly linked to firm efficiency/inefficiency. The results indicate that higher positive cash flows are related to lower cost inefficiency, but higher negative cash flows are related to higher cost inefficiency. Thus, cash flows not only impact the ability of hospitals to meet current liabilities, they are also related to the ability of the hospitals to use resources effectively. Key words: stochastic frontier analysis (SFA), free cash flow (FCF), hospital efficiency, cost function.

T

he past decade has been remarkably challenging for hospital administrators as different financial pressures have led to over 65 hospital closures in California alone. Predatory health plan payment structures are on the rise, government reimbursement is incomplete, and the growth of uncompensated care and unfunded mandates are compounded by rising labor costs that are creating substantial financial difficulties in the hospital industry. These financial and economic factors clearly indicate that hospital capital use and operations have to become highly efficient and flexible to guarantee long-term survival. Recent work by Bernet, Rosko, and Valdmanis1 examines relationships between debt issuance, debt rating, and the effect of debt on firm efficiency using stochastic frontier analysis (SFA). They find that hospitals that have recently acquired debt are, on average, less inefficient. Jensen2 shows that debt may promote firm efficiency by a number of means, including decreased free cash flows (FCFs). In this study, FCF is examined to assess its effect on firm inefficiency. While

a number of studies have examined hospital efficiency and inefficiency, none have specifically examined how FCFs may affect hospital efficiency. The remainder of this article is organized as follows: previous research, which describes the applicable existing literature; data, which describe the data used in the study; methodology, which outlines and describes the methodology; the results, which summarizes the results; and the conclusion. Previous Research Previous research on FCF is abundant across topics, though comparably limited in health care. Kauer and Silvers3 provide a normative discussion of FCF theory with William R. Pratt, is with the University of TexasPan American, College of Business Administration, Department of Economics and Finance, Edinburg, Texas, and he is a research associate with the South Texas Border Health Disparities Center. He can be reached at [email protected]. J Health Care Finance 2010;37(1):35–44 © 2010 Aspen Publishers

35

36

JOURNAL OF HEALTH CARE FINANCE/Fall 2010

empirical evidence contrasting for-profit and not-for-profit firms. They postulate FCF is relative to the amount of leverage desired by firms, which can vary due to growth opportunities and marginal return. Langabeer4 reports a similar result by using a general comparison of financial ratio. Though, Langabeer warns that financial ratios are not always clear and generalizable targets, and are capable of portraying a misleading picture of financial health, thus, reaffirming the need for additional FCF and firm efficiency research. McCue and Diana5 examine environmental factors influencing positive and negative cash flows of hospitals. Employing logistic regression, they identify payer mix and HMO penetration among other variables as associated with positive cash flows. Financial theory suggests managers of firms with significant FCFs are predisposed to inefficiency due to personal interests conflicting with those of the shareholders.6 Instances of inefficiency occur when managers invest free cash in nonstrategic projects with low or negative present value. Such instances of inefficiency may occur with hospitals as growth opportunities are limited and more so in states requiring certificate of need.7 Studies investigating hospital efficiency with SFA typically test efficiency by assessing hospital operations as a cost/production function. The benefit of analyzing cost efficiency is realized when information on technical inefficiency is extrapolated from raw data.8 Assessing a firm’s performance as total cost of outputs stemming from the cost of allocated resources enables efficient frontier estimation. When resources are combined inefficiently, the firm incurs increased costs. Cost variance across firms allows for an analysis of technical and allocative

inefficiency, stemming from a comparison with the current best practice (the efficient frontier). This type of assessment typically provides an advantage over other methods such as data envelopment analysis (DEA), when input price data are reliable.9 An indepth discussion of assumptions and DEA comparison is provided by Coelli et al.,10 Fried et al.,11 and Hollingsworth.12 Rosko and Mutter13 provide a review of summary of efficiency studies examining US hospitals. They report on 19 published studies and provide a summary of variables and methods employed in those studies. The compilation by Rosko and Mutter and the previously cited work by Bernet, Rosko, and Valdmanis are used to structure the analysis, specifically drawing from variables utilized in the cost function and the Battese and Coelli14 model.15 Data This study uses financial and operations performance data from the 2006 and 2007 California Hospital Annual Data Files (HADF). The HADF is made available by the California Office of Statewide Health Planning and Development. The dataset was selected due to the depth of financial information available. Hospital-specific information on expenses such as the amount of labor by employee type, payer allocated costs, interest, and depreciation is available in much greater detail than in other available sources. Previous efficiency studies have recognized that available financial data are limited and that measures accounting for outpatient heterogeneity could be improved upon.16 The HADF also provides improved detail in financial data for each hospital.

Cost Inefficiency and Free Cash Flow

Most variables used are from the HADF, allowing for the calculation of the following: • • • •

The price of labor; The price of capital; Total costs; and FCF.17

Total cost is based on the specification of previous studies, where total cost is a logged value, normalized by dividing by the price of labor. FCF was transformed to take on nonnegative values as required.18 FCF data from the previous year is divided into positive and negative values, rescaled by dividing by 100,000, and then logged. Additionally, the dataset provides the following: • • • • • • • • •

Number of admits; Number of outpatient visits; Number of non-acute days; Percentage of Medicare admits; Percentage of Medi-Cal admits; Teaching status; Ownership; Geographical location (county); and System membership.

Teaching hospitals are stratified into two groups, COTH19 and Non-COTH.20 County location information was used to generate a Herfindahl-Hirschman Index to assess the competitiveness of the environment in which each hospital operates. Data were also obtained from the 2006 Medicare Provider Analysis and Review (MPAR), Medicare Outpatient Prospective Payment System (MOPPS), and the Medicare Hospital Compare (MHC) databases. The MPAR dataset provides a Medicare case mix index (MCMI), which is used in almost every US hospital SFA study to control for heterogeneity of inpatient care

37

requirements.21 The MCMI is obtained by comparing the claimed total cost for treating a patient with respect to the expected cost under the identified diagnosed related group (DRG). The MOPPS dataset provides an outpatient counterpart to the MCMI, the service mix index (SMI). The SMI controls for outpatient heterogeneity by taking into account the range of services utilized in outpatient care and is estimated by the Centers for Medicare & Medicaid Services (CMS). The SMI is estimated by analyzing average cost by payment codes with respect to the claimed cost of treatment and the quantity of services provided, similar to the MCMI. The SMI has not been used in previous SFA research. Hospital Compare is another database made available by CMS. The database offers an extensive amount of quality indicators. Variables obtained from Hospital Compare are the 30-day risk-adjusted mortality rate for: heart attacks, heart failure, and pneumonia. These measures have been used in previous research to account for quality of care heterogeneity.22 Below, Figure 1 provides descriptive statistics of the cost function variables included in the data set. See Figure 1. The initial dataset contained 443 hospitals. Of the 443 hospitals, 172 hospitals were removed from the data set, which included: 111 specialty hospitals,23 25 critical access hospitals, two nonoperational hospitals reporting partial data, and 34 hospitals with missing data that could not be adjusted by imputation. Various factors specific to these heterogeneous types of hospitals need to be measured independently and, thus, these hospitals were excluded from the analysis. The final analytical dataset included 270 hospitals.

38

JOURNAL OF HEALTH CARE FINANCE/Fall 2010

Figure 1. Descriptive Statistics of Cost Function Variables Variable

Mean

Std. Dev.

Total Cost

$178,025,412

$195,930,024

Total Cost/Price of Labor (log) Price of Capital (log) Admits (logged)

0.971

0.183

12.353

0.549

8.933

0.896

Outpatient Visits (log)

12.069

1.063

Non-Acute Days (log)

10.165

0.847

COTH Hospital

0.074

0.262

Non-COTH Hospital

0.156

0.363

Medicare Case Mix Index

1.393

0.273

Service Mix Index

3.024

0.956

Heart Attack Death Rate-30 Day

15.943

1.677

Heart Failure Death Rate-30 Day

11.126

1.522

Pneumonia Death Rate-30 Day

11.702

1.860

% Medicare Admits

0.408

0.137

% Medi-Cal Admits

0.249

0.166

For-Profit Hospital

0.270

0.445

Government Hospital

0.167

0.373

Hospital Part of a System

0.467

0.500

Hospital Competition (HHI)

0.213

0.234

HMO Penetration

0.425

0.149

Positive Free Cash Flow

2.236

1.925

Negative Free Cash Flow

1.188

1.850

N = 270

Methodology SFA was used to estimate the effect of FCF on hospital cost efficiency. This method was selected over standard ratio analysis or conventional ordinary least squares (OLS) methods to identify best practices. Previously mentioned studies, Kauer and Silvers24 and Langabeer,25 describe ratio analysis as

subjective and not generalizable across the population. Furthermore, SFA is a unit per unit comparison of single input to output— as is ratio analysis, and conventional OLS methods are predisposed to error due to mean reverting estimation.26 FRONTIER Version 4.1 was used to obtain stochastic frontier estimates. FRONTIER applies a maximum likelihood method

Cost Inefficiency and Free Cash Flow

to obtain frontier estimates of the stochastic cost function frontier.27 A firm’s total cost is decomposed by the assumed cost function as follows:28

TCi = f (Yi,Wi) + (vi,ui)

(1)

TC represents the total cost of the ith firm as a function of Y vector of outputs and W vector of input prices. Two error terms are identified, where v represents statistical noise that is assumed to be iid as n(0, σ 2v ) and u represents non-negative departures from the cost curve, indicating cost inefficiency of the ith firm. The first stage of estimation examines the cost function in the specified functional form, in this case a Cobb-Douglas cost function. The model is estimated by maximum likelihood to obtain a measure of inefficiency and to obtain error terms v and u. While the distribution of the composed error has been specified to follow the work of Bernet, Rosko, and Valdmanis and other studies, the assumed distribution can vary. The frontier is estimated with the following cost model:

⎛ TC ⎞ ⎛ Wki ⎞ ln ⎜ i ⎟ = β0 + β1 ln ⎜ ⎟ ⎝ Wli ⎠ ⎝ Bedsi ⎠ J

K

j =1

k =1

+∑ βj ln(Yji ) + ∑ βk PDki

account for variation across firm outputs. MCMI and service account for variance care-requirements attributable to in patient severity, controlling for heterogeneity in resource consumption. Inefficiency-effects specific to each hospital are defined as:

Ui = δZi + wi, with ui ≥ 0

Total cost (TC) is normalized by the hospital wage rate (Wl), specifically the price of labor. The price of capital, Wk, is normalized by the number of beds within the ith facility. Again, vector Y is the quantity of the ith firm outputs: hospital admits, outpatient visits, and non-acute patient days. Variables accounting for quality of care (the PD term)

(3)

Ui are non-negative random variables independent of vi and assumed to be iid as n(mi, σ 2u ). Z is a vector of the list variables selected to explain inefficiency effects. Delta is a vector of values to be estimated, dependent upon the number of Z-list variables. Unobservable random variables are captured in wi, assumed to be iid and obtained by truncation of the normal distribution with mean zero and unknown variance. Cost efficiency is identified as the total cost of each hospital with respect the stochastic cost frontier. A one to one ratio indicates a completely efficient hospital; however, a 1 to .75 ratio would indicate the degree of inefficiency captured in ui of .25. Battese et al.29 have shown that:

CEi = exp(−Ui)

(2)

39

(4)

with CEi as cost efficiency and Ui from (3). The values of Ui are non-negative, thus a CE value of .25 would describe the example above. Results Estimates for the SFA regression are reported in Figure 2. The hypothesis of no inefficiency effects will be captured is rejected, that is σu has a value of 0 (i.e., σ2u is positive and statistically significant).

40

JOURNAL OF HEALTH CARE FINANCE/Fall 2010

Figure 2. Variable Coefficients and T-Statistics Variable

Coefficient

Std. Err.

T-Stat

Constant

4.094***

0.293

13.967

-0.257***

Price of Capital (log)

0.024

-10.568

0.016

0.018

0.886

Outpatient Visits (log)

0.076***

0.016

4.838

Non-Acute Days (log)

-0.051***

0.016

-3.133

COTH Hospital

0.086**

0.038

2.260

Non-COTH Hospital

0.020

0.025

0.783

0.044

-2.818

Admits (log)

Medicare Case Mix Index

-0.125***

Service Mix Index

0.003

0.011

0.298

Heart Attack Death Rate-30 Day

0.001

0.006

0.201

Heart Failure Death Rate-30 Day

-0.018***

0.007

-2.585

Pneumonia Death Rate-30 Day

-0.002

0.005

-0.417

0.368***

0.091

4.060

% Medicare Admits

0.139

0.104

1.335

% Medi-Cal Admits

-0.144

0.089

-1.619

For-Profit Hospital

-0.005

0.027

-0.201

Government Hospital

0.040

0.031

1.295

Hospital Part of a System

0.033

0.027

1.236

Inefficiency Effects δ Constant

Hospital Competition (HHI)

-0.535***

0.105

-5.088

HMO Penetration

-0.244***

0.076

-3.192

Positive Free Cash Flow

-0.025**

0.010

-2.365

Negative Free Cash Flow

0.028**

0.010

2.860

γ

0.112*

0.059

1.882

σ2

0.014***

0.001

11.500

Significant at the *P