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IX. EMPLOYMENT RELATIONS FOR
HEALTH CARE WORKERS
Serving the Medicaid and
Medicare Populations:
Nursing Labor Market Dynamics
Matthew Bodah, John Burkett, and Leonard Lardaro
University of Rhode Island
Abstract
In this paper we examine the effects of
changes in Medicaid and Medicare coverage on the employment of registered
nurses, licensed practical nurses, and certified nursing assistants. With
estimates using time series data, we find that Medicaid coverage has a
significant positive effect on the employment of registered nurses in
the short run. A 10 percent increase in Medicaid coverage is associated
with a 2.74 percent increase in registered nurse employment. Results also
show that a model of monopsony power, previously applied to hospitals,
is relevant to nursing homes.
Introduction
The effective demand for nurses may depend
on not only the number of people who could benefit from nursing care,
but also their insurance coverage. From 1987 to 2001, the number of people
covered by Medicare rose steadily, from 30.5 million to 38.0 million,
while the number covered by Medicaid fluctuated between 20.2 million (1987)
and 31.9 million (1995). In this paper, we examine the effects of changes
in Medicaid and Medicare coverage on employment of registered nurses (RNs),
licensed practical nurses (LPNs), and nursing aides, orderlies, and attendants
(NAOAs). Employment has trended upward for RNs and NAOAs, while it has
risen and then fallen for LPNs. The fall in LPN employment in the 1990s
is probably due in large part to a move by hospital administrators to
replace LPNs with NAOAs in less complex tasks and with RNs in more complex
ones. If the wages of the three types of nurses were determined independently,
we would expect to see the wages of LPNs dropping relative to those of
RNs and NAOAs. In fact, the earnings of the three groups moved in near
parallel, calling to mind the wage structures discussed by Dunlop (1957).
The rigidity of wage structures among nurses has been noted by Krall (1995),
who observes that hospital administrators have feared that changes in
the customary wage differentials among RNs, LPNs, and NAOAs could create
dissension and undermine cooperation.
Monopsonistic Equilibrium
Considering the seeming rigidity of the
wage structure for nurses, we doubt that markets for nurses can be accurately
modeled as if in continuous equilibrium. Nonetheless, equilibrium employment
and wages may be of interest as attractors influencing disequilibrium
dynamics. A simple model of monopsonistic equilibrium in the nursing labor
market was introduced by Yett (1970). In this model, a local monopsonist
derives its marginal expenditure function from a given labor supply function,
chooses a quantity of labor to equate its marginal expenditure with its
marginal revenue product, and pays just enough to attract this quantity
of labor, given the labor supply curve. The gap between its chosen employment
level and that which would equate its marginal revenue product with its
chosen wage may be one source of frequent reports of nurse "shortages."
New Evidence of Monopsony Power
Because previous studies of monopsony
power in nursing labor markets have focused on hospitals as employers
of RNs and LPNs, we need new evidence to justify applying the monopsony
model more widely. Fortunately, we have recently gained access to a cross-sectional
data set pertaining to nursing homes in Rhode Island. Because nursing
homes far outnumber hospitals, one might suspect they would operate in
a more competitive labor market.
Of the three occupational groups considered
in this paper, NAOAs have the least specialized training. The wage differentials
separating nurses from non-health service workers are less for NAOAs than
for RNs or even LPNs. Thus, one might suspect that nursing homes compete
for NAOAs not only with each other and with hospitals, but also with many
non-health service sector employers. If the local monopsony model of nursing
labor markets has a weak spot, it is most likely in application to nursing
homes as employers of NAOAs. Our data set on Rhode Island nursing homes
provides information on employment and wages for an important subset of
NAOAs, certified nurse assistants (CNAs). To assess the relevance of the
local monopsony model to nursing homes as employers of CNAs, we estimate
the wage elasticity of CNA labor supply to individual nursing homes. In
monopsonistic markets, this elasticity is a finite positive number. The
smaller the elasticity, the greater the monopsony power. Data for the
year 2001 are used, which consist of a total of 52 nursing homes located
throughout Rhode Island. We specify the supply of labor to a nursing home
i as follows:
where L is average weekly hours, W is average weekly wages
paid to CNAs, CA is a vector of variables measuring amenities and
nonwage compensation, HW is expenditure on "Help Wanted" advertising,
RLU is the relative local unemployment rate, L0
is the employment level for the previous year, and * is a random disturbance.
All variables are in logarithmic form.
Because wages are endogenous, equation
(1) is estimated using an instrumental variable technique, where W
is regressed on a series of nursing home-specific variables related
to labor demand, and the predicted values of W are used in place
of the original variable when estimating the labor supply equation. Inclusion
of the lagged dependent variable reflects a partial adjustment framework,
where actual hours supplied require a period of adjustment before arriving
at their long-run equilibrium. The coefficient of L0
allows this equation to provide an estimate of the long-run elasticity
of supply, which is obtained by dividing the short-run elasticity *1
by (1 - * 5). The estimated equation fits the data well, yielding
an adjusted R2 of .977 and an F statistic of 307.5. The
estimates of primary interest (with t statistics in parentheses)
are *ˆ1 = .420 (3.767) and *ˆ5 = .537
(4.309). The estimated short-run wage elasticity of CNA labor supply,
0.420, is statistically significant at the 1 percent level and above.
The estimate of long-run wage elasticity is 0.908, which is also statistically
significant. A 1 percent rise in average weekly wages raises the supply
of weekly CNA hours to nursing homes, on average, by 0.420 percent in
the short run and by 0.908 percent in the long run, given fixed values
of the other regressors. Thus, the supply of CNAs to individual nursing
homes appears to be inelastic in both the short and the long run, confirming
the relevance of the local monopsony model.
The Role of Insurance in a Model of Monopsonistic Equilibrium for
Use with Time-Series Data
We assume that labor supply and hence
the marginal expenditure function depends on, inter alia, the labor force
and wages in alternative occupations, whereas the marginal revenue product
function depends on the population and the extent to which it is covered
by insurance. Thus, reduced-form equations for equilibrium levels of employment
and wages should have labor force, wages in alternative occupations, population,
and insurance coverage among their right-hand-side variables.
Medicaid coverage increases when (a) eligibility
criteria are relaxed or (b) people lose jobs and fall below poverty lines
defining eligibility. In the former case, increases in Medicaid coverage
should raise marginal revenue product curves, boosting nurses' equilibrium
employment and earnings. In the latter case, the reverse might occur,
particularly if the people being added to Medicaid roles had previously
been covered by more generous private insurance. Medicare coverage increases
when people turn 65 or become disabled more rapidly than people already
covered die. No doubt the old and disabled make greater demands on nursing
facilities than do younger and healthier people; however, the bulk of
people joining Medicare have previously had employment-based health insurance.
Since the early 1980s Medicare has used a prospective payment system that
probably put more cost-saving pressure on health care providers than does
traditional private insurance. The effects of growth of the Medicaid and
Medicare populations on employment of nurses are thus empirical questions.
Specification of Disequilibrium Dynamics
Allowing employment to depend on its equilibrium
level and its lagged level, we specify the following employment equation:
where L denotes full-time employment, X1 the
number of people covered by Medicaid, X2 the number
covered by Medicare, X3 the population (all three expressed
in millions), X4 average real earnings in all occupations,
and X5 labor force. All variables are expressed as natural
logarithms. The time subscript takes values ranging from 1988 to 2001.
An equation of this form pertains to all three types of nurses. The only
difference among the explanatory variables for the three types of nurses
is that we construct the labor force variable as a weighted average of
male and female labor forces with weights reflecting the sexual composition
of the three occupations in 1988. The lagged dependent variable may pick
up two effects. On the one hand, adjustment of employment takes some time.
On the other hand, adjustment of capital may take longer. In the transition
from one equilibrium to another, labor inputs may overshoot their terminal
values to compensate for the slower adjustment of capital inputs. Thus,
the sign on the coefficient of the lagged employment term is uncertain.
Time-Series Data and Econometric Results
Our data consist of annual observations
for 1988-2001 obtained from the Bureau of Labor Statistics's Employment
& Earnings and the Census Bureau's Statistical Abstract of
the United States 2001, table 12, and Historical Health Insurance
Tables, table HI-1. With seven parameters to estimate from only fourteen
observations, collinearity problems must be expected. Using diagnostics
suggested by Belsley (1991), we find that the RN data have a near collinearity
involving the constant, Medicaid coverage, population, and earnings; LPN
data have one involving the constant, Medicaid coverage, population, earnings,
and the labor force; and NAOA data have one involving all variables except
the labor force. Considering the pattern of collinearity in our data sets,
we may anticipate difficulty in getting precise and robust estimates of
five coefficients of particular interest (i.e., those indicating the effects
of Medicare coverage on RN employment, Medicaid coverage on LPN employment,
Medicaid and Medicare coverages on NAOA employment, and lagged NAOA employment
on current NAOA employment). These difficulties could in principle be
finessed by introducing extraneous information on the coefficients of
other variables involved in near collinearities. Although we may do so
in future research, for now we simply approach the ordinary least squares
(OLS) estimates with due caution and limited expectations.
OLS estimates of the reduced-form employment
equation for the three nursing categories are shown in the table. The
italicized numbers under coefficient estimates are t statistics.
Because the variables are all expressed in logarithmic form, the estimated
coefficients can be interpreted as elasticities. The summary statistics
indicate that in each nursing category the regression accounts for a large
share of the variance in employment and that a hypothesis of 0 autocorrelation
cannot be rejected at conventional significance levels. Bearing in mind
that the critical values of a t statistic with 7 degrees of freedom
are 1.895 at the .05 level and 2.998 at the .01 level, we can see that
Medicaid and Medicare coverages have estimated effects on RN employment
that are statistically significant at the .01 level and Medicare coverage
has an estimated effect on NAOA employment that is significant at the
.05 level. We suspect, however, that collinearity makes the estimates
of the effect of Medicare coverage on RN employment and the effects of
Medicaid and Medicare coverages on NAOA employment vulnerable to errors
in variables. Thus, our one robust finding with regard to short-run effects
is that Medicaid coverage tends to increase RN employment. In principle,
long-run effects could be calculated by equating current and lagged values
of employment. The coefficients on lagged employment, however, are estimated
with so little precision that this exercise would be of little substantive
interest.
Conclusions
Our analysis of a cross section of Rhode
Island nursing homes indicates that the supply of certified nursing assistant
hours to individual nursing homes is inelastic in both the short and the
long run. This result indicates that a model of monopsony power, previously
applied to hospitals as employers of RNs and LPNs, is also relevant to
nursing homes as employers of certified nurse assistants. The remarkable
persistence of the earnings structure for RNs, LPNs, and NAOAs in the
face of efforts by hospital administrators to replace LPNs with RNs and
NAOAs is suggestive of relative wage rigidity.
We have used a model involving monopsony
power and relative wage rigidity as a basis for specifying reduced-form
employment equations for RNs, LPNs, and NAOAs. Estimating these equations
from U.S. time-series data, we have found evidence that Medicaid coverage
has a significant positive effect on employment of RNs: a 10 percent increase
in Medicaid coverage is estimated to induce a 2.74% short-run increase
in RN employment. Because of the low precision of the estimate for the
coefficient of lagged RN employment, we are unable to say with confidence
whether the long-run effect is greater or less than that. The effects
of Medicaid on employment of LPNs and NAOAs and the effects of Medicare
on all three occupations remain in doubt pending analysis using richer
data sets or more extraneous information.
References
Belsley, David A. 1991. Conditioning Diagnostics:
Collinearity and Weak Data in Regression. New York: John Wiley &
Sons.
Dunlop, John T. 1957. "The Task of Contemporary Wage
Theory." In George W. Taylor and Frank C. Pierson, eds., New Concepts
in Wage Determination. New York: McGraw-Hill, pp. 117-39.
Krall, Lisi. 1995. "The Rise and Fall of Customary Wage
Differentials among Nursing Personnel in US hospitals: 1956-1985." Cambridge
Journal of Economics, Vol. 19, no. 3 (June), pp. 405-19.
Yett, Donald E. 1970. "The Chronic 'Shortage' of Nurses:
A Public Policy Dilemma." In Herbert E. Klarman, ed., Empirical Studies
in Health Economics. Baltimore: Johns Hopkins University Press, pp.
357-89.
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