Health care inflation and its implications for monetary policy.
Yagihashi, Takeshi ; Du, Juan
I. INTRODUCTION
For over a decade, rising health spending in the United States has
been a major topic of debate. During 2000-2007, nominal health spending
grew at an average of 7.5% per year compared with the nominal GDP growth
rate of 5.1% per year, and much of the health spending growth was due to
health care inflation. (1) In 2013, health spending in real terms
comprises almost one-fifth of total real GDP and this share is predicted
to exceed 30% by 2050 (Hall and Jones 2007). Despite the growing
presence of the health care sector in the economy and an aging
population in the United States and around the globe, there are few
studies that look at the interaction between health care inflation and
monetary policy. This is because in the monetary policy literature the
goal of monetary policy is, in part, to stabilize the aggregate price
level, instead of sector-level prices.
* We thank William A. Branch (Co-Editor) and two anonymous referees
for their constructive comments. We also thank the seminar participants
at Hitotsubashi University and Kyoto University for providing valuable
feedback and discussions. The first author acknowledges support from the
PSC-CUNY Research Fund, City University of New York, 2009-2010.
Yagihashi: Department of Economics, Old Dominion University,
Norfolk, VA 23510. Phone 757-683-3512, Fax 757683-5639, E-mail
[email protected]
Du: Department of Economics, Old Dominion University, Norfolk, VA
23510. Phone 757-683-3543, Fax 757-6835639, E-mail
[email protected]
This paper aims to answer the following questions: (1) are
inflation dynamics in the health care sector different from other
sectors? (2) If so, how is the effect of monetary policy different in
models that separate the health care sector from other sectors?
To address the first question, we obtain some stylized facts about
health care inflation in the United States using principal component
analysis (PC A) and a factor-augmented vector autoregression. We find
that during 1980-2013 the volatility of health care inflation is much
lower, and the persistence is higher than other services in the personal
consumption expenditure (PCE) category. The response of health care
prices to an innovation in the federal funds rate is found to be smaller
than that of other services.
To address the second question, we introduce a dynamic stochastic
general equilibrium (DSGE) model with two novel features. On the
household side, we include health status in the utility function and
distinguish health care demand from the demand for other goods. In the
model, health is a "quality of life" indicator. Households can
improve their quality of life by combining health spending with leisure.
On the supply side, we allow the frequency of price adjustment in health
care goods to be lower than regular goods, reflecting an empirical
regularity (Bils and Klenow 2004). We show that the model can
successfully replicate the low volatility and the high persistence of
health care inflation as seen in the data.
The main findings are summarized as follows. First, when the model
economy is subject to an expansionary monetary policy shock, it yields
an amplified response of the equilibrium output and a muted response of
the equilibrium inflation in the health care sector relative to the
regular goods sector, consistent with our empirical finding. Second, to
understand the implication for monetary policy, we compare the impulse
responses of our model with those of a two-sector model that does not
feature health care. When these models are subject to the same
expansionary monetary policy shock, the response of aggregate output is
stronger and the response of aggregate inflation is weaker under the
health care model. The differences between the two models lie in how
households balance health spending and leisure to achieve better health.
When health spending increases, health improves, which lowers the
marginal utility of health and allows households to work longer hours
and produce more output. Third, when the monetary policymaker shifts its
policy and assigns a higher priority to output stabilization relative to
inflation stabilization, it results in a smaller increase in the
standard deviation of inflation in the health care sector compared with
the regular goods sector, whereas in the simpler two-sector model the
changes in the standard deviation of inflation are of similar magnitude
across sectors.
This paper contributes to the literature that examines the role of
demand heterogeneity in monetary DSGE models. Existing studies have
focused on how a sector with a relatively small size could have a
disproportionately large effect on the aggregate economy. For example,
Barsky, House, and Kimball (2007) introduce the durable goods sector
characterized by a relatively small output share and a low depreciation
rate. They find that the aggregate inflation dynamics are mainly
determined by the inflation dynamics of the durable goods sector,
irrelevant of its size and price stickiness. One puzzle that they
encountered is that output in different sectors is negatively correlated
in response to a monetary policy shock, which is inconsistent with
empirical findings. Our model can generate positively correlated
sectoral output in response to a monetary policy shock, yielding strong
monetary non-neutrality in aggregate. This occurs because health status
in our model weakens the inverse relationship between relative demand
and relative price as seen in many two-sector models.
This paper also contributes to another strand of literature on the
relationship between business cycle fluctuations and health. Our DSGE
model allows us to explore conditions at which health becomes pro- or
counter-cyclical. We show that the cyclicality of health depends on
several structural parameters, such as how effective medical care is in
improving health, whether health contributes to the productivity of
labor, and how fast health depreciates.
Section II reports empirical facts of health spending, health care
inflation, and health status. In Section III, we introduce our model
economy with health care demand and a two-sector model with homogeneous
demand. In Section IV, we provide details on model parameters, and then
study the effect of a monetary policy shock and a policy shift. In
Section V, we conduct various robustness analysis and Section VI
concludes.
II. STYLIZED FACTS ON HEALTH
A. Facts on Health Spending
We study health spending in the United States using the PCE from
the Bureau of Economic Analysis. (2) The PCE uses broad categories of
durable goods, nondurable goods, and services. Health spending is under
the category of non-durable goods (e.g., drugs) and services (e.g.,
physician services, net payment on health insurance). For this exercise,
we focus on health care services that constitute much of the overall
health spending. Table 1 presents the detailed series in health care
services and their price index. In the second quarter of 2013, the PCE
for health care services totaled $1,902.9 billion, the second largest
category within service after housing and utilities.
Table 2 shows the average growth rate of major type of products
during the last three decades (1980Q1-2013Q2). On the one hand, nominal
spending on health care services grew at an annual rate of 7.8% and
average health care inflation during this period was 5.0%, outpacing the
growth of the aggregate PCE average of 5.9% and the aggregate inflation
of 2.9%. On the other hand, health spending in real terms grew only by
2.7%, slightly below the aggregate PCE average of 3.0%.
The time series of health spending is shown in Figure 1. We observe
that the growth rate of PCE for health care services in real terms
remained in close proximity to that of the aggregate PCE (panel 1). The
spending share of the PCE for health care services in real terms had a
mild decline from 1980 to 2000, but it reverted back toward the sample
mean of 16.6% after 2000 (panel 2). Lastly, health care inflation was
visibly higher than the aggregate inflation from 1980 to late 1990s, and
moved closer to the aggregate inflation after 2000 (panel 3).
On the basis of these results, we conclude that health care
inflation is accountable for much of the rise in nominal health spending
during the last three decades and that the fluctuation of real health
spending has its unique pattern, occasionally deviating from the
aggregate PCE.
B. Facts on Health Care Inflation
Volatility and persistence of inflation are of particular interest
to the policymaker because they directly relate to the objective of
price stabilization. In this section, we first present volatility and
persistence of inflation in the health care and other sectors, and then
examine whether health care prices respond differently to a monetary
policy shock.
A few issues arise when comparing inflation dynamics across
sectors. One is that the volatility of large sectors that cover many
items tends to be smaller than the volatility of small sectors because
aggregation averages out idiosyncratic components. Another issue is that
unobserved macroeconomic factors, such as trend inflation, could affect
volatility and persistence of sectoral inflation, making them
incomparable. (3) To overcome these complications, we decompose the
individual inflation series into common macroeconomic factors and
sector-specific components, and report the moments of the
sector-specific components only. We use PCA to generate the common
factors for decomposition (Boivin, Giannoni, and Mihov 2009a). The
details of this approach are included in Appendix A.
[FIGURE 1 OMITTED]
Table 3 summarizes the moments of the (filtered) inflation series
for major service categories. The standard deviation of health care
inflation is .4%, much lower than that for the PCE with all items
(=1.1%). This implies that the relative volatility of health care
services is .39 (=.4%/1.1%). The persistence for health care inflation
is .56, twice as high as that for other services (=.26) and all items
(=.24). Thus, the health care sector can be characterized by low
volatility and high persistence relative to other sectors. The only
sector that shares the same characteristics is education.
Next, we examine how health care prices respond to a monetary
policy shock using the factor-augmented vector autoregression (FAVAR)
(Bernanke, Boivin, and Eliasz 2005a) in Figure 2. FAVAR takes into
account unobserved macroeconomic factors by using the common factors
obtained through the PCA. Details are provided in Appendix B.
On the one hand, the price of health care services responds mildly
to an expansionary monetary policy shock (=negative innovation to the
federal funds rate). This is particularly evident in comparison with
aggregate PCE and items excluding health care services (panel 1), and
slightly less so when comparing health care services with other services
(panel 3). On the other hand, the output response of the health care
sector is larger than that of items excluding health care services
(panel 2). The same pattern is observed when comparing health care
services with other services (panel 4).
[FIGURE 2 OMITTED]
C. Facts on Health Status
In the past decade, there are many micro studies that examine the
cyclicality of health. Findings of these papers are mixed depending on
the health measure and time span used. For example, studies using total
mortality as the health indicator tend to find health is
counter-cyclical (e.g., Neumayer 2004; Ruhm 2000) whereas studies using
body weight and mental illness as the health indicator show that health
is procyclical (e.g., Charles and DeCicca 2011; Latif 2014). Several
studies further suggest that the relationship between health and
macroeconomic conditions may have become less cyclical in recent years
(e.g., Ruhm 2013; Stevens et al. 2011; Tekin, McClellan, and Minyard
2013)
In this section, we examine the correlation between health and
several macroeconomic variables. The purpose of this exercise is to
produce some empirical moments to check model performance, rather than
to provide direct evidence on the empirical relationship between health
and unemployment as some of the micro studies do. For our health
measure, we use a survey question in the National Health Interview
Survey (NHIS). Since 1972, annual household surveys of illness and
disability have been conducted for a large sample of
non-institutionalized population, in which respondents are asked to rate
their health based on a five-point scale from excellent to poor. We
define health status as the percentage of the sample that says their
health is good, very good, or excellent in a given year. (4) This
variable is adjusted using sample weight so that it represents the
overall population. Self-reported health is known to be correlated with
mortality and highly predictive of physical functions. (5)
In addition, it provides an overall evaluation of health status for
individuals who are alive at the time of the interview. Self-reported
health is likely to represent qualify of life, which is how we model
health later.
In Table 4, we present correlation coefficients of our health
measure and three macroeconomic variables relevant to our model. We find
that health status is positively and significantly correlated with real
GDP per capita, GDP gap, and weekly hours worked during 1980-2012. (6)
These results apply equally to the annual frequency data and the
quarterly frequency data for which linear interpolation of the health
measure is conducted. (7) The correlation of health and hours worked is
smaller than the correlation with the GDP measures, possibly because
health deteriorates with work. We show in a later analysis that our
model can produce both pro- and counter-cyclical health depending on
certain parameter values.
III. THE HEALTH CARE MODEL ("HC MODEL")
We first introduce the HC model and then highlight the differences
between the HC model and a simpler two-sector model.
A. Household
Our household utility function closely follows the functional form
in Hall and Jones (2007). Utility monotonically increases with both
regular goods spending C and health status X. More specifically,
households maximize their expected lifetime utility
(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [beta] is the subjective discount factor, [[eta].sub.X] is
the utility weight on health status, and [e.sub.X,t] ~ N (O,
[[sigma].sup.2.sub.X]) is the exogenous health shock. [[gamma].sub.C]
and [[gamma].sub.X] are the inverse of the intertemporal elasticities of
substitution (IES) for regular goods spending and health status,
respectively.
Health status X is subject to the following accumulation equation,
(2) [X.sub.t] = [I.sup.X.sub.t] + (1 - [[delta].sub.X])[X.sub.t-1],
where [I.sup.X.sub.t] is health investment and 5X is the
depreciation rate of health. Health investment is conducted by combining
health spending and leisure in the following manner
(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where H is health spending and 1 - N is (normalized) leisure hours
defined as total hours minus hours spent working. [[kappa].sub.H] and
[[kappa].sub.L] represent the elasticity of health investment with
respect to "health input" H and 1 - N. Households face the
following budget constraint,
(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [D.sub.t] is a one-period nominal coupon bond maturing at
time t + 1 that pays a gross nominal interest rate of [R.sup.n.sub.t],
[W.sub.t] is the nominal wage determined in a competitive factor market,
and P, is the economy-wide aggregate price index, [P.sub.R,t] and
[P.sub.H,t] are the price of regular goods and health care goods,
respectively, and [profit.sub.t] is the sum of real profits collected
from firms.
Let [[lambda].sub.X] be the Lagrange multiplier on the health
accumulation equation (Equation (2)) and [[lambda].sub.D] be the
Lagrange multiplier on the budget constraint (Equation (4)). The first
order necessary conditions for optimization yield the following
expressions for marginal rates of substitution and intertemporal
efficiency conditions,
(5) [[MU.sub.H,t]/[MU.sub.C,t]] =
[[[kappa].sub.H][[lambda].sub.X,t][[I.sup.X.sub.t]/[H.sub.t]]/exp
([e.sub.X,t])[C.sup.-[gamma]C.sub.t]] = [P.sub.H,t]/[P.sub.R,t]
(6) [[MU.sub.-N,t]/[MU.sub.C,t]] =
[[[kappa].sub.L][[lambda].sub.X,t][[I.sup.X.sub.t]/[1-N.sub.t]]/exp
([e.sub.X,t])[C.sup.-[gamma]C.sub.t]] = [W.sub.t]/[P.sub.R,t]
(7) [[MU.sub.1-N,t]/[MU.sub.H,t]] =
[[[kappa].sub.L]/[[kappa].sub.H]][[H.sub.t]]/1 - [N.sub.t]] =
[P.sub.H,t]
(8) [[lambda].sub.D,t] =
[beta][R.sup.n.sub.t][E.sub.t][[[lambda].sub.D,t+1]/[[PI].sub.t+1]],
(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [MU.sub.i] (i = C, H, 1 - N) is the marginal utility of
regular goods spending, health spending, and leisure, and [[PI].sub.t+1]
= [P.sub.t+1]/[P.sub.t] is the gross inflation. The optimality
conditions imply that the marginal utility of health input H, 1 - N is a
product of two terms, i.e., the marginal utility of health status
([MU.sub.X] [equivalent to] [[lambda].sub.X]) and the marginal product
of each input with respect to health investment ([MP.sub.H] [equivalent
to] [[kappa].sub.H]([I.sup.x]/H) and [MP.sub.L] [equivalent to]
[[kappa].sub.L]([I.sup.X]/1 - N)).
There are a few points worth noting. First, the adoption of
additive separable utility in Equation (1) implies that regular goods
and health care goods are substitutes in raising households'
utility. (8) Second, in our model the role of health shock is twofold,
one as an intertemporal preference shock that affects how households
smooth consumption and health status over time (Equation (1)), and the
other similar to the labor supply shock in a conventional model that
affects how households value leisure relative to consumption in a given
period (Equation (3)). (9) Third, the choice of the Cobb-Douglas
function for health investment (Equation (3)) implies that H and 1 - N
have unit elasticity of substitution. (10) While these model assumptions
can be relaxed, we do not further pursue them for the sake of clarity of
the model structure.
B. Producers
On the supply side, we introduce sector heterogeneity similar to
Barsky, House, and Kimball (2007) and Erceg and Levin (2006a). There are
two sectors in our model: the regular goods sector (k = R) and the
health care sector (k = H). (11)
The final good producers in both sectors purchase differentiated
goods [Y.sub.k](z) from the corresponding intermediate goods producers
who are indexed along the unit interval z = [0, 1]. The purchased goods
are then aggregated into the sectoral good [Y.sub.k] as in Dixit and
Stiglitz (1977),
(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [[epsilon].sub.k] is the elasticity of substitution across
varieties of intermediate goods. Taking prices [P.sub.k,t](z) as given
and solving the cost minimization problem subject to Equation (16)
yields the within-sector demand curve,
(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
and the sectoral price index of
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The sectoral final goods [Y.sub.R,t], [Y.sub.H,t] are absorbed as
either private spending or government spending. Thus we have
(12) [Y.sub.R,t] = [C.sub.t] + [G.sub.C,t],
(13) [Y.sub.H,t] = [H.sub.t] + [G.sub.H,t].
The aggregate output in both nominal and real terms is defined
following the GDP definition,
(14) [P.sub.t][Y.sub.t] = [P.sub.R,t] [Y.sub.R,t] +
[P.sub.H,t][Y.sub.H,t],
(15) [Y.sub.t] = [[[bar.R].sub.R]/[bar.P]] [Y.sub.R,t] +
[[[bar.P].sub.H]/[bar.P]] [Y.sub.H,t],
where [[bar.P].sub.R]/[bar.P], [[bar.P].sub.H]/[bar.P] are
steady-state relative prices for the two goods. The aggregate price
index [P.sub.t] is implicitly defined as the GDP deflator through
Equations (14) and (15).
Following the new Keynesian model of Gali (2008), we assume that
the intermediate firm z in each sector hires labor [N.sub.t] from the
competitive nationwide labor market to produce intermediate goods. The
firm's production constraint is given as
(16) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [[mu].sub.N] measures how efficiently labor is used in
producing output and [[mu].sub.X] measures how the (nationwide) health
status contributes to labor productivity. The sectoral productivity
shock Ask f is defined as
(17) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Labor demand can be obtained through solving the cost minimization
problem subject to Equation (16) while taking the nationwide real wage
[w.sup.t] [equivalent] [W.sub.t]/[P.sub.t] and health status as given.
This yields the following first order necessary condition,
(18) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [MC.sub.k,t] is the sector-specific real marginal cost. Total
labor demand has to satisfy the following constraint,
(19) [N.sub.t] = [N.sub.R,t] + [N.sub.H,t].
We assume that a randomly assigned fraction [[rho].sub.k] of
intermediate goods firms is prohibited from adjusting their prices in
each period. Within each sector, price-adjusting firms' profit
maximization problem can be written as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [[DELTA].sub.k,j,t+1] is the j-period ahead stochastic
discount factor for the firm in sector k. The first order necessary
condition for the optimal price is
(20) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [P.sup.*.sub.K,t] is the optimal price set by the adjusting
firms. The sectoral price index can be rewritten in a fixed-distributed
lag form,
(21) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
C. Government
We assume that fiscal policy provides an additional disturbance to
the economy,
(22) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
and j = C, H. Monetary policy follows the modified Taylor rule with
partial adjustment
(23) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where today's interest rate is set according to the realized
inflation, output gap, and the interest rate in the previous period, and
[S.sub.M,t] is the monetary policy shock. (12) The monetary policy shock
[S.sub.M,t] is defined as
(24) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
D. The Two-Sector Model
To compare the HC model and traditional models, we prepare a
simpler model with two sectors ("TS model" hereafter). The
basic structure of the TS model closely follows the conventional
two-sector model in the new-Keynesian literature (Aoki 2001a; Erceg and
Levin 2006a), and to save space, the details of the model are delegated
to Appendix C. On the supply side, the TS model shares many model
equations with the HC model. (13) On the demand side, demand for health
care is modeled as part of the aggregate spending and the resulting
first order necessary conditions imply
(25) [[Y.sub.R,t]/[Y.sub.H,t]] = [[omega]/[1 - [omega]]]
[([P.sub.R,t]/[P.sub.H,t]).sup.-1],
where 0 < [omega] < 1 represents the (nominal) spending share
of regular goods. This equation states that the demand for sectoral
goods is inversely proportional to the relative price. The implied
relationship between price and quantity is much simpler than the
equivalent equation in the HC model (Equation (5)).
IV. MODEL ANALYSIS
In this section, we introduce model parameters and then examine
model dynamics using stochastic simulation and impulse responses. The
implication of the HC model under a monetary policy shift is provided at
the end of the section. The linearized model equations used in the
simulation are shown in Appendix D.
A. Model Parameterization
The parameter values we choose reflect quarterly frequency, the
same as the moments reported in Section II, and they are shown in Table
5.
Common Parameters. For the parameters that are common in both
models, we largely follow the convention in the literature. The discount
factor is set to imply a 2.5% annual real return. The income share of
labor is two-thirds. The elasticity of demand is set to be the same
across sectors, implying a steady-state markup of 10%. The IES parameter
for consumption is 2, following Hall and Jones (2007). The steady state
level of labor is set to .38. (14)
The price stickiness parameter for the regular goods sector is set
to .5, which implies an average duration of 6 months between price
changes. Based on the estimates in Bils and Klenow (2004), the price
stickiness for the health care sector is set to .81, implying an average
duration of 15.9 months between price changes. (15)
For the steady-state expenditure share of health spending in the HC
model, we apply the value of .166 based on the average during our sample
period. The same value is used to pin down [omega] in the production
function in the TS model. The steady-state government spending share of
output is set to .21 in the TS model, based on historical observations
in the United States. We apply the same government spending share for
health care goods in the HC model so that simulation outcome is
comparable across models.
We set the labor supply elasticity to unity following Ham and
Reilly (2013). (16) For the TS model, labor supply elasticity can be
implicitly calculated as
[[epsilon].sup.TS.sub.w] = [1/[[gamma].sub.N]] [[1 -
[bar.N]]/[bar.N]],
which is determined by the curvature parameter on labor
[[gamma].sub.N] and the steady state level of labor [bar.N]. We set
[[gamma].sub.N] to 1.65 so that together with [[gamma].sub.N] = 0.38, we
have [[epsilon].sub.TS.sub.w] = 1.
Parameters Specific to the HC Model. There are five parameters
([[mu].sub.x], [[delta].sub.X], [[gamma].sub.X], [[kappa].sub.L],
[[kappa].sub.H]) unique to the HC model. These health-related parameters
are difficult to pin down because there are few studies estimating them.
To simplify the model and highlight the role of health spending and
leisure, we set the technology parameter [[mu].sub.X] to zero and the
depreciation rate of health [[delta].sub.x] to one in the baseline
specification. In the robustness analysis, we examine model performance
under more reasonable parameter values.
The intertemporal elasticity of substitution with respect to health
status (1/[[gamma].sub.X]) captures how averse households are to the
fluctuation in health status. The larger [[gamma].sub.X] is, the quicker
the marginal utility of health status falls in response to the rise in
health status (Equation (9)). To prevent the marginal utility from
falling too quickly, households may "smooth" their health
status over time by cutting down either health spending or leisure. We
prepare our own estimate of [[gamma].sub.x] using the self-reported
health status introduced in Section II.C and Euler Equations (8) and
(9). The method described in Appendix E yields a value of 5.46.
Once we assume [[delta].sub.X] = 1, the labor supply elasticity in
the HC model can be expressed as follows,
(26) [[epsilon].sup.HC.sub.w] = [1/1 - [[kappa].sub.L] (1 -
[[gamma].sub.X])] [[1 - [bar.N]]/[bar.N]].
We set [[kappa].sub.L] to .15 so that together with [[gamma].sub.x]
= 5.46 and [bar.N] = 0.38, we have [[epsilon].sup.HC.sub.w] = 1 (unit
elasticity).
Although there is no direct estimate of [[kappa].sub.H] in
aggregate, many studies in the medical literature show that medical
treatment improves health. Hall and Jones (2007) provide their own
estimates of the effectiveness of health care for different age cohorts.
We adopt their estimate of .25 (for the middle aged group, 40 to 50
years old) as our baseline value.
Policy and Shock Parameters. The monetary policy parameters follow
the estimates of English, Nelson, and Sack (2003), which allows for the
extrinsic inertia process. The persistence of the monetary policy shock
takes the value of the autoregressive parameter for the serially
correlated errors in their paper. (17) To simplify analysis, we set the
persistence of the government policy shock the same in regular goods and
health care goods spending. Likewise, we set the persistence of the
sectoral productivity shocks the same. These values are uniformly set at
.75.
The standard deviations of the monetary and fiscal policy shocks
are calibrated based on Smets and Wouters (2005). We apply the size of
the aggregate productivity shock in their paper for our sectoral
productivity shocks and apply the size of the preference shock for our
health shock. To facilitate comparison, the size of the preference shock
and the labor supply shock in the TS model is set to equal the size of
the health shock in the HC model.
B. Simulation Results
We first look at the unconditional moments generated using the HC
model and then compare them with the empirical counterparts. For
simulation, we generate artificial time series of one million periods
while activating all stochastic shocks at once. Results are shown in
Table 6.
We use output (y) and normalized labor hours (,n) as business cycle
measures. (18) The correlation coefficients between health status and
output and between health status and labor hours are .68 and .71,
respectively. The correlation between health status and output is close
to the empirical counterparts reported in Table 4. The correlation
between health status and labor hours is somewhat larger in the model
than in the data. This number becomes smaller once we allow certain
parameters to vary and these results are discussed in Section V. The
volatility of health care inflation relative to aggregate inflation is
.44, consistent with the observed low volatility in Table 3. The HC
model is also able to generate higher persistence of health care
inflation relative to aggregate inflation (.78 vs. .48). (19)
[FIGURE 3 OMITTED]
The impulse responses of inflation and output after an
unanticipated one standard deviation decline in the nominal interest
rate are shown in Figure 3. We observe that the monetary policy shock
increases both the aggregate inflation ([pi]) and the sectoral inflation
([[pi].sub.R], [[pi].sub.H]). The response of regular goods inflation
closely resembles aggregate inflation, whereas the initial response of
health care inflation is much more muted, reflecting the higher price
stickiness in the health care sector. We also observe that the aggregate
output (y) and sectoral output ([y.sub.R], [y.sub.H]) respond positively
to the expansionary monetary policy. Output in the health care sector
responds stronger than output in the regular goods sector. These
responses are consistent with our empirical finding in Figure 2.
C. The Role of Health Care Demand
From Table 6, we see that the relative volatility and persistence
of health care inflation generated using the HC model are closer to
those in the data comparing with the moments generated using the TS
model. We explore the mechanism below.
There are two key mechanisms that transmit the monetary policy
shock in the HC model. The first mechanism, which also exists in the TS
model, is the relative price channel. When the interest rate is lowered,
demand for both regular and health care goods is stimulated (Equation
(8)), causing prices to rise in both sectors. Because of the higher
price stickiness in the health care sector, the price of regular goods
rises relatively more. This higher relative price of regular goods
triggers a substitution from regular goods to health care goods. As a
result, the equilibrium output of health care goods rises further.
The second mechanism is the health status channel. This channel is
only present in the HC model. We illustrate the health status channel in
the bottom two panels of Figure 3 with the following steps.
1. The expansionary monetary policy shock stimulates spending on
both regular goods and health care goods through Equation (8). The
higher demand also increases the demand for labor, pushing up the
equilibrium wage.
2. The higher health spending in Step 1 results in higher health
status x and lower marginal utility of health status [mu.sub.x] (panel
3).
3. Households increase labor supply in response to the higher wage
in Step 1. Marginal product of leisure with respect to health investment
[mp.sub.l] increases because leisure becomes scarce relative to health
spending. Marginal utility of leisure [mu.sub.l] falls on impact because
the rise in marginal product of leisure (dash line, panel 4) is
dominated by the fall in marginal utility of health status (dash-dotted
line, panel 3).
4. In the subsequent periods, the fall in the marginal utility of
health status in Step 2 applies downward pressure on the marginal
utility of leisure (dash-dotted line, panel 4).
5. The "reduced" marginal utility of leisure in Step 4
effectively enables households to spend less time on leisure and work
longer hours (solid line, panel 4). This amplifies the equilibrium
response of the aggregate output.
[FIGURE 4 OMITTED]
In Figure 4, we compare the impulse responses of the HC and the TS
model under the same monetary policy shock. First, we observe that the
response of health care inflation in the HC model is smaller than that
in the TS model (panel 3). This is because the rise in health status in
the HC model results in a subdued health care demand, which adds
downward pressure onto the marginal cost of health care goods in
equilibrium.
Second, the response of the aggregate output is stronger in the HC
model (panel 4). This is because the improved health status applies
downward pressure on the marginal utility of leisure, inducing
households to work longer hours (panel 7). The rise in the relative
price (panel 8) further causes a substitution from regular goods to
health care goods (panels 5 and 6). This substitution is smaller in the
HC model because health status mitigates the substitution mechanism
(Equation (5)). As a result, health care goods output increases less and
regular goods output increases more in the HC model. Because the regular
goods sector is larger than the health care sector, the response of the
aggregate output is amplified. (20)
D. The Monetary Policy Shift
The main purpose of monetary policy is to remove the distortionary
effect of price changes, which is analogous to minimizing the volatility
of aggregate inflation. However, once we assign unique roles to
individual sectors, monetary policy may have an asymmetric effect on the
volatility of sectoral inflation. In this subsection, we examine how the
volatility of the aggregate and sectoral inflation changes under a
monetary policy shift.
We consider a hypothetical policy shift in which the policymaker
assigns a higher priority to output stabilization relative to inflation
stabilization. This is modeled as a simultaneous change in the policy
coefficient [[rho].sub.[pi]] from 1.83 to 1.50 and [[rho].sub.y] from
.21 to .25. This policy shift effectively sets the slope of the
aggregate demand curve "steeper," i.e., demand shock of a
given size would have a larger destabilizing effect on inflation
relative to output.
The same stochastic simulation under the new monetary policy rule
is conducted. Table 7 shows that after the policy shift the standard
deviation of health care inflation rises by only 3.69% in the HC model
versus 23.67% in the TS model. This is because in the HC model
households can freely combine health spending with leisure to change
health status (Equation (5)). In addition, the change in the volatility
of inflation is very different across sectors in the HC model: the
volatility of health care inflation increases by 3.69% compared with
13.80% for regular goods inflation. Such asymmetry is non-existent in
the TS model, implying that price stickiness alone does not produce much
asymmetry across sectors.
V. ROBUSTNESS CHECK
In this section, we examine model outcome under alternative
parameterization and study the cyclicality of health.
A. Elasticity of Health Investment
The two parameters that may affect model outcome are the elasticity
of health investment with respect to health spending [[kappa].sub.H] and
leisure [[kappa].sub.L].
Literature on the effectiveness of health spending generally agrees
that medical treatment improves health (Cutler and McClellan 2001;
McClellan, McNeil, and Newhouse 1994), though there is disagreement
about how effective medical care is as health spending increases (the
so-called "flat-of-the curve" phenomenon). (21) In this
exercise, we use the estimates in Hall and Jones (2007) for different
age groups for [[kappa].sub.H]. Their estimates range from .04 for
elderly to .4 for infants. Literature on the effectiveness of leisure in
improving health is mixed. Some studies show that working longer hours
negatively impacts health (Bell, Otterbach, and Sousa-Poza 2012; Caruso
2006; Shields 1999), while others suggest that too much leisure (e.g.,
unemployment) can result in an increased probability of mortality
(Catalano 2009; Eliason and Storrie 2009; Sullivan and von Wachter
2009). Thus, it is reasonable to conjecture that leisure has a positive
effect on health investment with diminishing returns, i.e., 0 <
[[KAPPA].sub.L] < 1.
For robustness check, we use two sets of parameters:
[[kappa].sub.H], [[kappa].sub.L]] = [0.04, 0.99] and [0.40, 0.01], This
first set assumes that health spending is not very effective in
improving health and health investment is mainly through leisure, and
the second set assumes the opposite. The impulse responses from the same
monetary policy shock are shown in Figure 5. The alternative
parameterization has almost no effect on aggregate inflation, and the
responses of aggregate output, health care inflation and output are also
qualitatively similar to the baseline. These parameters mainly alter the
response of health status and marginal utility of leisure (bottom two
panels of Figure 5). For example, under [[kappa].sub.w], [[kappa].sub.L]
= [0.04, 0.99], health status responds negatively to the expansionary
monetary policy shock, contrary to the baseline result. This occurs
because the negative health effect of having less leisure is so large
that it cannot be offset by the increase in health spending (which is
assumed to be less effective than the baseline).
B. "Health Smoothing"
As we mentioned earlier, a higher [[gamma].sub.X] (or lower IES)
implies that households are more willing to smooth health status over
time. Flail and Jones (2007) use the non-accidental mortality rate as
the health measure and estimate this parameter to be 1.05. Although
their health status is different from the quality of life aspect
stressed in our model, we nevertheless use their estimate as the lower
bound value in our robustness analysis. For the upper bound, we pick the
value of 10, which is within the range of estimates for the (implied)
IES for consumption in the literature.
Figure 6 shows the impulse response of selected variables to the
expansionary monetary policy shock. When [[gamma].sub.X] = 10, health
care inflation and output both rise by a little less than in the
baseline. A larger [[gamma].sub.X] "magnifies" the negative
response of marginal utility of health status, further inducing
households to work longer hours, which enhances the positive response of
aggregate output. Overall the impact of this parameter on inflation
measures is quantitatively small.
C. Cyclicality of Health and Moments for Inflation Revisited
In this subsection, we examine how alternative parameterization
affects the cyclicality of health using stochastic simulation. We also
examine whether our model outcome changes if we allow health to
depreciate slowly (0 < [[delta].sub.X] < 1) and to increase
productivity ([[mu].sub.X] > 0). We set [[delta].sub.X] = 0.0015
based on Cutler and Richardson (1997), implying an annual depreciation
rate of .6%.22 We set [[mu].sub.X] = 0.04 based on Bloom, Canning, and
Sevilla's (2004) estimates of how life expectancy affects labor
productivity. (23) Table 8 shows the moments obtained using the HC model
under alternative parameterization. We alter parameters one at a time
while keeping the baseline value fixed for other parameters. We also
provide another scenario in which changes occur for all parameters at
the same time.
There are several findings. First, health status becomes less
procyclical (particularly with labor) when health spending is less
effective and leisure is more effective in health investment (when
[[[kappa].sub.H], [[kappa].sub.L]] = [0.04, 0.99]). This is because
labor becomes more "costly" for health under the new
parameterization. Second, health status becomes less procyclical when
households are less willing to smooth their health status over time
(when [[gamma].sub.X] = 1.05). A smaller [[gamma].sub.X] mitigates the
positive effect of health status on output by making marginal utility of
health status less responsive, leading to weaker co-movement of health
and output. Third, introducing health depreciation in our model reduces
the cyclicality of health significantly (when [[delta].sub.X] = 0.0015).
The sluggish dynamics of health status effectively breaks the
contemporaneous link between health input and health status, making
health status weakly linked to the business cycle. Lastly, when health
status is allowed to contribute to production (when [[mu].sub.x] =
0.04), the correlation between health status and output increases and
the correlation between health status and labor decreases. The former
occurs because health status adds to the productivity of labor while the
latter occurs because improved health status allows firms to reduce
labor as an input for production. Lastly, when we apply alternative
values for all the parameters at once, the correlation between health
and labor becomes negative. This scenario is consistent with the studies
that find health to be countercyclical (e.g., Ruhm 2000, 2003).
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
The moments of inflation under alternative parameterization are
shown in the last two columns of Table 8. The relative volatility of
health care inflation varies between .43 and .63 whereas the persistence
of health care inflation varies between .78 and .86. In several cases,
the relative volatility and persistence are larger than those in the
data, but they are within a reasonable range.
VI. CONCLUDING REMARKS
This paper studies the role of monetary policy in relation to
health care inflation, which is increasingly becoming an important
policy topic in today's aging society. We show that health care
inflation is accountable for much of the increase in nominal health
spending in the past 30 years, and it is less volatile and more
persistent than aggregate inflation and inflation in other service
sectors. Under an expansionary monetary policy shock, health care
inflation does not increase as much compared with aggregate inflation
and other service items.
Based on the empirical findings, we construct a DSGE model that
distinguishes the health care sector from the regular goods sector. This
model includes health in the utility function and allows health spending
and leisure to play a role in improving health status. Comparing with a
traditional TS model that does not feature health care demand, the HC
model can better replicate the empirical facts of health care inflation.
It also yields a larger response in aggregate output and a notably
smaller response in health care inflation under an expansionary monetary
policy shock. We show that the main mechanism that drives the difference
between the two models is the response of health status and labor
supply. Another implication of our model is that a hypothetical policy
shift would cause asymmetric stabilization in the volatility of
inflation across sectors. This would necessarily complicate the
policymaker's goal of minimizing the distortional effect of
inflation on the economy.
There are several ways to extend our paper. First, in the
simulation we assume zero steady state level of inflation for both the
health care sector and the regular goods sector. Wolman (2011) and
others have worked on models in which average sectoral inflation is
allowed to differ in the long run. It may be helpful to explicitly
incorporate non-zero steady state inflation in future work. Second, our
model assumes separability between health status and consumption. As
Finkelstein, Luttmer, and Notowidigdo (2013) point out, marginal utility
of consumption may depend on health status. Allowing dependency between
consumption and health status may be a meaningful step forward.
ABBREVIATIONS
DSGE: Dynamic Stochastic General Equilibrium
FAVAR: Factor-Augmented Vector Autoregression
GMM: Generalized Method of Moments
IES: Intertemporal Elasticities of Substitution
OIR: Over-Identifying Restrictions
PCA: Principal Component Analysis
PCE: Personal Consumption Expenditure
doi: 10.1111/ecin.12204
Online Early publication March 9, 2015
APPENDIX A
ESTIMATING VOLATILITY AND PERSISTENCE OF HEALTH CARE INFLATION
USING PCA
We use the underlying detailed tables of the NIPA account (Table
2.4.4U) to construct a large balanced panel of disaggregated inflation
series. Starting from 1980Q1, N = 342 series are obtained at different
levels of aggregation over T = 134 quarters. Following Boivin, Giannoni,
and Mihov (2009a), we decompose individual inflation series as follows,
(A1) [[pi].sub.i,t] = [[lambda].sub.i][C.sub.t] +
[[pi].sup.e.sub.i,t],
where [[pi].sub.i,i] is the rate of inflation for sector i,
[C.sub.t] is a vector of K unobserved factors, [[lambda].sub.i] is a
vector of factor loadings that relate the factors to the observed
inflation rates, and [[pi].sup.e.sub.i,t] is the sector-specific
component for sector i.
Equation (A1) can be further written as
(A2) [PI] = C[LAMBDA]' + [[PI].sup.e],
where [PI] is a T by N matrix of original inflation series, C is a
T by K matrix of unobserved factors, [LAMBDA] is a N by K matrix of
factor loadings, and [[PI].sup.e] is a T by N matrix of
"filtered" inflation series net of unobserved factors. In
Equation (A2), C and [LAMBDA] are not separately identifiable, unless
restrictions are applied. To solve this problem, we apply the
restriction 1/T(C' C) = [I.sub.K] on the factors, following the
convention in the literature. The estimation procedure takes two steps.
First, we estimate the factor [??] by minimizing the squared residuals
in Equation (A2) while treating the unknown loading as given. Next, we
estimate the loading by using a PCA. Under certain regularity conditions
on the error structures (Stock and Watson 2005), the factor loading can
be consistently estimated as the first K eigen-vectors of the
variance-covariance matrix of [PI]. We choose three factors (K = 3),
based on a screen plot observation (not shown here).
For the sector-specific volatility, we calculate the simple average
of the standard deviations of [[pi].sup.e.sub.i,t] for a certain
category (e.g., health care services). For the sector-specific
persistence, we first calculate the sum of the four-lag autocorrelation
coefficients of it [[pi].sup.e.sub.i,t] and then calculate the simple
average of these summed autocorrelation coefficients for a given
category.
In addition to the individual service categories, volatility and
persistence measures for the PCE: all items, goods, services, and other
services are provided in Table 6 of the main text.
TABLE Al
Additional Macroeconomic Variables from FRED
Mnemonics Slowvars Transcode
1. IPFINAL * 5
2. IPCONGD * 5
3. IPDCONGD * 5
4. IPNCONGD * 5
5. IPBUSEQ * 5
6. IPMAT * 5
7. IPDMAT * 5
8. IPNMAT * 5
9. IPMAN * 5
10. INDPRO * 5
11. USASARTMISMEI * 5
12. MCUMFN * 1
13. NAPM * 1
14. NAPMPI * 1
15. DSPIC96 * 5
16. W875RX1 * 5
17. CE160V * 5
18. UNRATE * 1
19. UEMPMEAN * 1
20. UEMPLT5 * 1
21. LNU03008756 * 1
22. LNU03008516 * 1
23. LNU03008876 * 1
24. LNU03008636 * 1
25. PAYEMS * 5
26. USPRIV * 5
27. USGOOD * 5
28. USMINE * 5
29. USCONS * 5
30. MANEMP * 5
31. DMANEMP * 5
32. NDMANEMP * 5
33. USTPU * 5
34. USWTRADE * 5
35. USTRADE * 5
36. USFIRE * 5
37. SRVPRD * 5
38. USGOVT * 5
39. AWHMAN * 1
40. AWOTMAN * 1
41. NAPMEI * 1
42. PCE * 5
43. PCEDG * 5
44. PCEND * 5
45. PCES * 5
46. HOUST 4
47. HOUSTNE 4
48. HOUSTMW 4
49. HOUSTS 4
50. HOUSTW 4
51. PERMIT 4
52. NAPMII 1
53. NAPMNOI 1
54. NAPMSD1 1
55. SP500 5
56. DJIA 5
57. DJUA 5
58. TB3MS 1
59. TB6MS 1
60. GS1 1
61. GS5 1
62. GS10 1
63. AAA 1
64. BAA 1
65. M1SL 5
66. M2SL 5
67. CURRCIR 5
68. BUSLOANS 5
69. TOTALSL 5
70. NAPMPRI * 1
71. PPIFGS * 5
72. PPIFCG * 5
73. PPIITM * 5
74. PPICRM * 5
75. CPIAUCSL * 5
76. CPIAPPSL * 5
77. CPITRNSL * 5
78. CPIMEDSL * 5
79. CUSR0000SAC * 5
80. CUSROOOOSAD * 5
81. CUSR0000SAS * 5
82. CPIULFSL * 5
83. CUSROOOOSAOL2 * 5
84. CUSR0000SA0L5 * 5
85. CES2000000008 5
86. CES3000000008 5
87. CES0600000008 5
Mnemonics Description
1. IPFINAL IP: Final Products (Market Group)
2. IPCONGD IP: Consumer Goods
3. IPDCONGD IP: Durable Consumer Goods
4. IPNCONGD IP: Nondurable Consumer Goods
5. IPBUSEQ IP: Business Equipment
6. IPMAT IP: Materials
7. IPDMAT IP: Durable Materials
8. IPNMAT IP: Nondurable Materials
9. IPMAN IP: Manufacturing (NAICS)
10. INDPRO Industrial Production Index
11. USASARTMISMEI Total Retail Trade in United States
12. MCUMFN Capacity Utilization: Manufacturing (NAICS)
13. NAPM ISM Manufacturing: PMI Composite Index
14. NAPMPI ISM Manufacturing: Production Index
15. DSPIC96 Real Disposable Personal Income
16. W875RX1 Real Personal Income Excl. Current
Transfer Receipts
17. CE160V Civilian Employment
18. UNRATE Civilian Unemployment Rate
19. UEMPMEAN Average (Mean) Duration of Unemployment
20. UEMPLT5 Civilians Unemployed--Less Than 5 Weeks
21. LNU03008756 Number Unemployed for 5 to 14 Weeks
22. LNU03008516 Number Unemployed for 15 Weeks and Over
23. LNU03008876 Number Unemployed for 15 to 26 Weeks
24. LNU03008636 Civilians Unemployed for 27 Weeks and Over
25. PAYEMS All Employees: Total Nonfarm
26. USPRIV All Employees: Total Private Industries
27. USGOOD All Employees: Goods-Producing Industries
28. USMINE All Employees: Mining and logging
29. USCONS All Employees: Construction
30. MANEMP All Employees: Manufacturing
31. DMANEMP All Employees: Durable Goods
32. NDMANEMP All Employees: Nondurable Goods
33. USTPU All Employees: Trade, Transportation &
Utilities
34. USWTRADE All Employees: Wholesale Trade
35. USTRADE All Employees: Retail Trade
36. USFIRE All Employees: Financial Activities
37. SRVPRD All Employees: Service-Providing Industries
38. USGOVT All Employees: Government
39. AWHMAN Average Weekly Hours of Production and
Nonsupervisory Employees: Manufacturing
40. AWOTMAN Average Weekly Overtime Hours of Production
and Nonsupervisory Employees: Manufacturing
41. NAPMEI ISM Manufacturing: Employment Index
42. PCE PCEs
43. PCEDG PCEs: Durable Goods
44. PCEND PCEs: Nondurable Goods
45. PCES PCEs: Services
46. HOUST Housing Starts: Total: New Privately Owned
Housing Units Started
47. HOUSTNE Housing Starts in Northeast Census Region
48. HOUSTMW Housing Starts in Midwest Census Region
49. HOUSTS Housing Starts in South Census Region
50. HOUSTW Housing Starts in West Census Region
51. PERMIT New Private Housing Units Authorized by
Building Permits
52. NAPMII ISM Manufacturing: Inventories Index
53. NAPMNOI ISM Manufacturing: New Orders Index
54. NAPMSD1 ISM Manufacturing: Supplier Deliveries Index
55. SP500 S&P 500 Stock Price Index
56. DJIA Dow Jones Industrial Average
57. DJUA Dow Jones Utility Average
58. TB3MS 3-Month Treasury Bill: Secondary Market Rate
59. TB6MS 6-Month Treasury Bill: Secondary Market Rate
60. GS1 1-Year Treasury Constant Maturity Rate
61. GS5 5-Year Treasury Constant Maturity Rate
62. GS10 10-Year Treasury Constant Maturity Rate
63. AAA Moody's Seasoned Aaa Corporate Bond Yield
64. BAA Moody's Seasoned Baa Corporate Bond Yield
65. M1SL M1 Money Stock
66. M2SL M2 Money Stock
67. CURRCIR Currency in Circulation
68. BUSLOANS Commercial and Industrial Loans at All
Commercial Banks
69. TOTALSL Total Consumer Credit Owned and Securitized,
Outstanding
70. NAPMPRI ISM Manufacturing: Prices Index
71. PPIFGS PPI: Finished Goods
72. PPIFCG PPI: Finished Consumer Goods
73. PPIITM PPI: Intermediate Materials: Supplies &
Components
74. PPICRM PPI: Crude Materials for Further Processing
75. CPIAUCSL CPI: All Items
76. CPIAPPSL CPI: Apparel
77. CPITRNSL CPI: Transportation
78. CPIMEDSL CPI: Medical Care
79. CUSR0000SAC CPI: Commodities
80. CUSROOOOSAD CPI: Durables
81. CUSR0000SAS CPI: Services
82. CPIULFSL CPI: All Items Less Food
83. CUSROOOOSAOL2 CPI: All Items Less Shelter
84. CUSR0000SA0L5 CPI: All Items Less Medical Care
85. CES2000000008 Average Hourly Earnings of Production and
Nonsupervisory Employees: Construction
86. CES3000000008 Average Hourly Earnings of Production and
Nonsupervisory Employees: Manufacturing
87. CES0600000008 Average Hourly Earnings of Production and
Nonsupervisory Employees: Goods-Producing
Notes: Mnemonics are the abbreviations used in FRED.
* represents slow-moving variables.
Transformation code is 1 = no transformation,
4 = log transformation, 5 = quarter-to-quarter
growth rates.
TABLE A2
Estimates of (Inverse of) the IES for Health
Health Status Overall Sample Overall Sample
Interest Rate 3-Month TB 5-Year Constant
IES for health 5.46 ** 5.23 **
(Standard error) (.98) (.86)
OIR test 2.07 1.94
(p value) (.35) (.38)
Health Status 16 to 64 Years 16 to 64 Years Old
Interest Rate Old 3-Month TB 5-Year Constant
IES for health 4.39 ** 4.23 **
(Standard error) (.78) (.69)
OIR test 2.80 2.99
(p value) (.25) (.22)
Notes: The GMM method and quarterly data during 1980-2012
are used in estimation. The instruments are the third lag of
the interest rate, nominal health care expenditure, and
health status.
** Statistically significant at 5% level.
APPENDIX B
ESTIMATING THE RESPONSE OF HEALTH CARE INFLATION TO A MONETARY
POLICY SHOCK
To obtain the impulse responses of health care inflation to an
expansionary monetary policy shock, we use the factor-augmented vector
autoregression (FAVAR). Specifically, we modify Equation (A1) as follows
(B1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [[PI].sub.t], [[PI].sup.e.sub.t] are the vectors of N
original and filtered inflation series, [X.sub.t], [X.sup.e.sub.t] are
the vectors of M original and filtered macroeconomic variables that we
add into this exercise, [C.sub.t] is the vector of K extracted factors,
and [FFR.sub.t] is the federal funds rate which we treat as an
additional factor. We add M = 429 additional macroeconomic variables so
that the broad information available to the monetary policymaker is
incorporated in our analysis (Bemanke, Boivin, and Eliasz 2005a). These
variables consist of 342 quantity variables in the PCE that are obtained
through deflating the nominal series with the corresponding price
indexes, plus 87 macroeconomic variables obtained from the FRED website.
The latter variables are reported in Table A1.
We further assume that [F.sub.t] [equivalent to] [[C.sub.t],
[FFR.sub.t]] has a recursive structure
[F.sub.t] = [[PHI].sub.P][F.sub.t] + [[zeta].sub.t].
where [[PHI].sub.p] is a conformable lag polynomial matrix with p
number of lags and [[zeta].sub.t] is a vector of reduced form residuals.
Equation (B1) can be further written as
(B2) Y = F[PSI]' + e,
where Y [equivalent to] [[PI] X] is a T by N + M matrix of observed
variables, F is a T by K + 1 matrix of unobserved factors with [F.sub.t]
= [[C.sub.t], [FFR.sub.t]]', [PSI] is a N + M by K + 1 matrix of
factor loadings that relates factors to the observed variables, and e is
a T by N + M matrix of "residuals."
Next, we run the vector autoregression using the factors F. To
recover the structural shock from the reduced form residuals in Equation
(B2), we apply the standard recursiveness assumption that the factors
affect the federal funds rate within the same period, i.e., the variable
FFR is ordered the last.
To examine the effect of the orthogonal shock to the FFR on the
remaining factors (and eventually on variables), we need to remove the
effect that FFR has on [C.sub.1], ... [C.sub.K]. Following Bernanke,
Boivin, and Eliasz (2005a), we define a set of "slow-moving"
variables that cannot contemporaneously respond to the shocks to FFR.
All price and quantity variables in the PCE and the variables marked
with asterisk in Table A1 are regarded as slow-moving variables. We then
filter out the effect that the FFR has on the remaining factors by using
the above slow-moving variables. For more details on this procedure, see
Bernanke, Boivin, and Eliasz (2005a).
We choose three factors (K = 3) and lag length of two quarters (p =
2). When drawing the impulse response, the size of the shock is adjusted
to be equivalent of a 25 basis point drop in the federal funds rate.
APPENDIX C
THE TS MODEL
The basic structure of the TS model is similar to the models in
Aoki (2001a) and Erceg and Levin (2006a). (24) In the TS model, health
care demand no longer plays a distinctive role and health spending is
included as part of the aggregate consumption index. This means that
utility derived from health status X in the HC model is replaced by a
term representing utility derived from leisure in the TS model and the
health accumulation Equation (2) and the health investment Equation (3)
no longer exist. Below we present the model equations that are different
from the HC model.
We start with the supply side that shares many model equations with
the HC model. Final goods producer purchase differentiated goods
[Y.sub.k](z) from the corresponding intermediate goods producers and
aggregate them as in Equation (10). The intermediate goods
producer's production constraint is given as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where the sectoral productivity shock follows the dynamics as in
Equation (17). Note that the contribution of health status is suppressed
in the TS model. Consequently, the sectoral marginal cost is expressed
as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Total labor demand satisfies the constraint in Equation (19).
Intermediate goods producer faces the random opportunity of price
adjustment, same as in the HC model. Solving the profit maximization
yields the new-Keynesian Phillips curve in Equation (20).
On the demand side, households maximize their expected lifetime
utility expressed as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where C represents the aggregate consumption index that constitutes
of regular goods consumption and health care consumption (described
below). The second term in the bracket represents the utility derived
from leisure (or disutility of labor), which replaces the utility
derived from health status in the HC model. [e.sub.I,t] ~ N (0,
[[sigma].sup.2.sub.I]), [e.sub.N,t] ~ N ([[sigma].sup.2.sub.N]) are the
intertemporal preference shock and the labor supply shock, respectively.
They replace the health shock in the HC model. The budget constraint is
[C.sub.t] + [[D.sub.t]/[P.sub.t]] = [[W.sub.t]/[P.sub.t]] [N.sub.t]
+ [[R.sup.n.sub.t-1]/[P.sub.t]] [D.sub.t-1] + [profit.sub.t]. . Solving
the utility maximization problem yields the intertemporal efficiency
condition
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
and the labor-leisure choice
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
In the TS model, households and the government purchase sectoral
outputs and produce a composite good defined as
[C.sub.t] = [[C.sup.[omega].sub.R,t][C.sup.l-[omega].sub.H,t]]/[[[omega].sup.w] [(1 - [omega]).sup.1-[omega]]],
[G.sub.t] = [[G.sup.[omega].sub.R,t][G.sup.l-[omega].sub.H,t]]/[[[omega].sup.w] [(1 - [omega]).sup.1-[omega]]],
where [C.sub.k,t], [G.sub.k,t], are the sectoral goods spent by
households and the government, respectively, and 0 < [OMEGA] < 1.
Minimizing the total cost on the composite good while taking sectoral
prices [P.sub.k,t] as given yields the following relative goods demand,
[[C.sub.R,t]/[C.sub.H,t]] = [[omega]/1 - [omega]]
[([P.sub.R,t]/[P.sub.H,t]).sup.-1],
[[G.sub.R,t]/[G.sub.H,t]] = [[omega]/1 - [omega]]
[([P.sub.R,t]/[P.sub.H,t]).sup.-1],
which in aggregate yields the expression (25) in the text.
The aggregate price index can be derived from the above cost
minimization problem. It is expressed as the geometrical average of the
sectoral prices
[P.sub.t] = [P.sup.[omega].sub.R,t] [P.sup.l-[omega].sub.H,t]
The resource constraint in the TS model follows the GDP definition
[Y.sub.t] = [C.sub.t] + [G.sub.t],
where aggregate government spending [G.sub.t] follows the exogenous
process
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Finally, monetary policy follows the same modified Taylor rule with
partial adjustment in Equation (23).
APPENDIX D
LINEARIZED MODEL EQUATIONS IN THE HC MODEL
All variables are expressed in deviation terms.
Nominal variables
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Resource constraint
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Aggregate demand
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Aggregate supply
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Law of motion of shocks
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
APPENDIX E
THE IES FOR HEALTH
This appendix presents the method used to estimate (the inverse of)
the IES for health [[gamma].sub.X]. The value of this parameter is used
in our baseline analysis. The empirical method we apply is similar to
the method used to estimate the IES for consumption in the literature
(Hall 1988; Hansen and Singleton 1982, 1983), except that we use health
status in the Euler condition instead of consumption.
The first order necessary condition for the optimal choice of
health spending is
[MU.sub.H,t] = [[lambda].sub.X,t] ([[kappa].sub.H]
[[I.sup.X.sub.t]/[H.sub.t]]) = [[lambda].sub.D] [[P.sub.H,t]/[P.sub.t]].
Combining this equation with the two intertemporal efficiency
conditions (Equations (8) and (9) in the main text) and applying the
full depreciation condition [[delta].sub.X] = 1 used in the baseline
parameterization yields
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Log-linearizing the equation yields
([[gamma].sub.X] - 1) [DELTA] log ([X.sub.t+1]) = constant + log
([R.sup.n.sub.t]) - [DELTA]log([P.sup.H.sub.t+1] [H.sub.t+1]),
where the (log of) discount factor and the average growth rate of
health care shock are collected into one constant term. The equation
states that the representative household adjusts its health status in
response to the interest rate (=opportunity cost of spending) and the
growth rate of health spending.
To estimate [[gamma].sub.X], we use the generalized method of
moments (GMM). Following the literature, we construct lagged variables
as instruments. To ensure the instruments are exogenous, we avoid the
first and second lag, and instead use the third lag of the interest
rate, nominal health care expenditure, and health status.
We use two interest rate measures for this exercise (3-month
Treasury bill: secondary market rate and 5-year Treasury constant
maturity rate) and they are obtained from the FRED. For nominal health
care expenditure, we use quarterly PCE, health care services, obtained
from Bureau of Economic Analysis (Table 2.4.5). Health status is the
percentage of population reporting their health as good and excellent
based on a question in the NHIS micro data. We construct two health
measures based on the overall population and the 16 to 64 years old
working population separately. The original health measure is collected
at the annual frequency. We interpolate the annual data in a linear way
to obtain quarterly frequency data. Our sample period is 1980-2012.
Table A2 shows the results. The [[gamma].sub.X] for the overall
population is 5.46 (3-month TB) and 5.23 (5-year constant) depending on
the interest rate used. The [[gamma].sub.X] for the working population
is 4.39 (3-month TB) and 4.23 (5-year constant). All estimates are
statistically significant at the 5% level.
The test for over-identifying restrictions (OIR test) is performed
and the results are shown in the last row of Table A2. We fail to reject
the null hypothesis in all cases, implying that our instruments are
uncorrelated with the error term. We also perform a likelihood ratio
test by comparing the model that includes all the instruments and the
model without the instruments in predicting the interest rate. The test
strongly rejects the model without the instrument (test stat = 254.61
and 276.11 for the 3-month TB and 5-year constant), indicating that our
instruments are not weak. The [R.sup.2] for the models that include the
instruments are .85 and .87 for the 3-month and 5 year interest rate,
respectively.
In the baseline analysis, we use the value of 5.46 that corresponds
to the overall sample and the 3-month TB as the reference rate.
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(1.) Source: U.S. Department of Commerce, Bureau of Economic
Analysis.
(2.) There are several advantages using the PCE. First, the PCE
covers a comprehensive list of health care services, including those
financed by third-parties such as health insurance companies and
government agencies. Second, the PCE is used to prepare the National
Income and Product Account (NIPA), which is used by many government
agents including the Federal Reserve in its policymaking process.
Finally, the PCE ensures that price indexes are internally consistent
with real quantities of spending through cross-checking different data
sources, such as Economic Census, Service Annual Survey, and Quarterly
Services Survey.
(3.) Reis and Watson (2010) report that 20% of the sectoral
inflation dynamics can be explained by macroeconomic factors.
(4.) The survey question is "Would you say ... s health in
general is excellent, very good, good, fair, or poor?" Results are
grouped into five categories during 1982-2012 and four categories
(excellent, good, fair, or poor) during 1972-1981. Individuals who
report their health being good and excellent during 1972-1981 are
included in our health measure. On average, 91 % of the sample reports
their health being good, very good, and excellent between 1972 and 2012.
(5.) See for example, Idler and Kasl (1995).
(6.) We also constructed a health measure based on the average of
the five categories (excellent, very good, etc.). The signs and
magnitudes of the correlations are very similar.
(7.) Our results are not directly comparable to the findings of
microeconomic studies in the literature. Here are some of the
differences: (1) micro studies often examine total mortality or a
specific illness whereas our health measure is defined as the percentage
population above a particular health threshold in a given year.
Mortality is often caused by external reasons (such as traffic
accidents) whereas self-reported health likely reflects both physical
and mental health; (2) many of the micro studies focus on the
unemployment rate whereas we use hours worked conditional on employment.
Unemployment rate reflects the extensive margin of employment whereas
hours worked reflects the intensive margin; (3) micro studies often use
state-level data (such as, state unemployment rate) whereas we use
national-level data. This could make a difference because people may
migrate based on economic opportunities; (4) we simply look at
correlations and our sample period is different as well.
(8.) Hall and Jones (2007, p. 49) justify the use of additive
separability by arguing that such preference is a natural intermediate
case in which the marginal utility of consumption neither rises nor
falls with the change in health status.
(9.) For example, a positive health shock today increases the
marginal utility of both consumption and health status, making
households want more of both. The positive shock also makes households
value health status relatively more because the marginal utility of
health status rises further relative to consumption.
(10.) Medical care and time input can be both complements and
substitutes in health investment (Grossman 1972). Recent medical
literature has shown that better night sleep, time spent on physical
activities, cooking and eating meals at home (as opposed to fast food)
enhance health, so individuals may not need as much medical care. The
Cobb-Douglas functional form provides both substitutability and
complementarity between health input, allowing us not to take an extreme
stance on this debated issue.
(11.) In our model, health care "goods" covers both goods
and services following the PCE categorization.
(12.) We also conducted analysis using a forward-looking Taylor
rule specification (not shown). For the one-quarter forecast horizon,
results are almost unchanged from the baseline specification in the
paper. For the four-quarter forecast horizon, we encounter indeterminacy
of the equilibrium.
(13.) One notable difference is that in the TS model health status
neither contributes to the production process nor affects sectoral
marginal costs.
(14.) This value does not include time associated with home
production, such as, household chores and child care. According to
Rupert, Rogerson, and Wright (2000), time used in home production
(excluding sleeping time) accounts for 18% of total time.
(15.) Specifically, we chose six health care services listed in
their appendix and recalculated the weighted mean duration based on the
reported expenditure weights. These six services are (1) hospital
services; (2) physicians services; (3) dental services; (4) services by
other medical professionals; (5) care of invalids, elderly, and
convalescents in the home; and (6) nursing and convalescent home care.
(16.) Empirical estimates can vary by much depending on the data
and methods used. See for example, Blundell, Duncan, and Meghir (1998),
French (2004), and Ziliak and Kniesner (1999).
(17.) We also experimented with another set of policy parameters in
English, Nelson, and Sack (2003) that assume the autoregressive
parameter for serially correlated errors to be zero. This set of
parameters are [[rho].sub.[pi]] = 1.70, [[rho].sub.y] = 0.26,
[[rho].sub.n] = 0.72, and [[rho].sub.M] = 0. We find slightly lower
correlation between health and labor and slightly lower volatility for
health care inflation. The main findings using the alternative
parameters are qualitatively similar to our baseline.
(18.) Variables denoted in lower case letters or with a tilde are
measured in deviations from the steady state.
(19.) We do not attempt to exactly match the absolute level of
relative volatility and persistence in the model with those in the data.
This is because in obtaining these measures from data, we used the
principal component analysis that removed the effect of the common
macroeconomic factors, and obtained the average of the disaggregated
series. Both procedures cannot be performed in simulation.
(20.) If we allow [[mu].sub.x] to take a positive value in the HC
model, the output response becomes slightly larger and inflation smaller
than those in Figure 4, but the change is almost invisible in the
impulse response.
(21.) Recent studies attribute as much as 50% of life expectancy
increase to medical spending alone (Cutler, Deaton, and Lleras-Muney
2006; Ford et al. 2007), while several studies note that the
effectiveness of health spending has been diminishing in recent years.
For example, Cutler, Deaton, and Lleras-Muney (2006) find that the cost
of per year of life rose in the 1990s compared to earlier years. For
more on the "flat-of-the curve" phenomenon, see for example,
Garber and Skinner (2008).
(22.) Cutler and Richardson (1997) calculated quality-adjusted life
years (QALYs) for various diseases, such as diabetes. hypertension,
heart disease, arthritis, etc., and obtained age-specific QALYs for men
and women separately (see Figure 7 in their paper). They assume the QALY
is 1 for newborn. Their estimates of QALYs for men at age 16 and 64 are
0.96 and 0.72, respectively. Using these numbers, we calculated the
implied depreciation rate of health is 0.597% annually. For women, the
annual depreciation rate is 0.561%, which corresponds to the QALYs of
0.93 and 0.71 at age 16 and 64.
(23.) The economic growth literature has noted that a higher life
expectancy increases output growth, especially in developing countries.
Estimates of the elasticity of output with respect to life expectancy
range from 0.02 to 0.07. Bloom, Canning, and Sevilla's (2004)
estimate falls within that range.
(24.) Using this type of model, Aoki (2001a) and Carvalho (2006)
have studied how the asymmetry in the price stickiness across sectors
affects the optimal conduct of monetary policy. They find that monetary
policymakers should focus primarily on stabilizing inflation in the
sector with higher price stickiness.
TABLE 1
List of Health Care Services
Category Type of Service Price Index
Outpatient Physicians PPI for offices of physicians
services Dentists CPI for dental services
Paramedical services PPI for home health care
PPI for medical laboratories,
diagnostic imaging centers
CPI for services by other
medical professionals
Hospitals Nonprofit hospitals PPI for hospitals
Proprietary hospitals
Government hospitals
Nursing Nonprofit nursing homes PPI for nursing care
homes Proprietary and facilities
government nursing
homes
Notes: Type of service corresponds to the PCEs series from
the Bureau of Economic Analysis. The corresponding price
indices are obtained from the Bureau of Labor Statistics.
TABLE 2
Summary Statistics by Major Type of Products
Nom. Spending Real Spending Share in
Growth Rate Growth Rate Inflation Real PCE
PCE. 5.9% 3.0% 2.9% 100%
aggregate
Goods 5.0% 3.3% 1.7% 34.0%
Services 6.6% 2.8% 3.7% 66.0%
Health care 7.8% 2.7% 5.0% 16.6%
services
Excl. health 6.3% 2.9% 3.3% 49.4%
care
services
Notes: The numbers in columns 2-4 are the mean growth rate
for each category. Growth rates are annualized using
quarterly data. All statistics are based on NIPA Tables
2.4.4 and 2.4.5. The sample period is 1980Q1-2013Q2 and the
share in real PCE is calculated based on 2013Q2.
TABLE 3
Volatility and Persistence of Inflation Measures
Standard Relative Share in
Deviation Volatility Persistence Real PCE
PCE, all items (342) 1.1 1 .24 100.0%
Goods (143) 1.3 1.23 .19 34.0%
Services (157) 1.0 .93 .28 66.0%
Health care .4 .39 .56 16.6%
services (13)
Excl. health care 1.1 .97 .26 49.4%
services (144)
Housing and .8 .78 .56 18.4%
utilities (17)
Financial/ 2.8 2.63 .19 7.1%
insurance (20)
Food/ .4 .39 .24 6.3%
accommodations
(15)
Recreation .6 .54 .22 3.7%
services (22)
Transportation 1.4 1.28 .06 2.8%
(17)
Communication (7) 1.6 1.49 .19 2.4%
Education .4 .41 .54 2.2%
services (7)
Professional (9) .7 .60 .22 1.4%
Notes: The numbers in the parentheses are the number of
series in each category. We report the average of the
individual series within each category. For example, for
health care services, the standard deviation is the average
of the 13 individual series. The sample period is 1980Q1-
2013Q2 and the share in real PCE is calculated based on
2013Q2.
TABLE 4
Correlation of Health Status and
Macroeconomic Conditions
Macroeconomic Correlation Correlation
Variables (Annual Freq.) (Quarterly Freq.)
Real GDP per capita .69 .68
(p value) (.00) (.00)
GDP gap .56 .55
(p value) (.00) (.00)
Weekly hours worked .55 .48
(p value) (.00) (.00)
Notes: The health measure is based on a question from the
National Health Interview Survey, which asks the respondent
to rate their own health in one of the five categories. We
construct health status as the percentage of the sample
reporting good, very good, and excellent health in a given
year. The quarterly frequency health measure is constructed
using linear interpolation from the annual data. Real GDP
per capita is real GDP divided by total population. Real GDP
per capita is detrended using the residuals from regressing
the log of real GDP per capita on a linear trend. GDP gap is
calculated using logged real GDP minus logged potential GDP.
All macroeconomic variables are seasonally adjusted except
for potential GDP. They are obtained from the FRED website.
Sample period is 1980-2012.
TABLE 5
Baseline Parameters
HC TS
Parameters Model Model
Discount factor [beta] = 1/[bar.R] .994 .994
Labor share [[mu].sub.N] .67 .67
Elasticity of demand [[epsilon].sub.R = 11 11
[[epsilon].sub.H]
(Inverse of) IES for 2 2
consumption [[gamma].sub.C]
Steady state labor [bar.sub.N] .38 .38
Price stickiness [[rho].sub.R] .5 .5
Price stickiness [[rho].sub.H] .81 .81
Policy parameter [[rho].sub.[pi]] 1.83 1.83
Policy parameter [[rho].sub.y] .21 .21
Policy parameter [[rho].sub.n] .58 .58
Shock persistence [[rho].sub.M] .75 .75
Shock persistence [[rho].sup.s.sub.H] = .75 .75
[[rho].sup.s.sub.R]
Shock size [[sigma].sup.s] .0013 .0013
Shock size [[sigma].sup.s.sub.H] = .0036 .0036
[[sigma].sup.s.sub.R]
Shock size [[sigma].sub.G] .0043 .0043
Elasticity of health .15
investment [[kappa].sub.L]
Elasticity of health .25
investment [[kappa].sub.H]
(Inverse of) IES for health [[gamma].sub.X] 5.46
Depreciation rate for health 1
[[delta].sub.X]
Health share [[mu].sub.X] 0
Health spending share of .166
output [bar.H]+[[bar.G].sub.H]/[bar.Y]
Government spending share .21
of output [[bar.G].sub.C]/[[bar.Y].sub.R] =
[[bar.G].sub.H]/[[bar.Y].sub.H]
Shock persistence [[rho].sup.d.sub.H] = .75
[[rho].sup.d.sub.C]
Shock size [[sigma].sub.X] .0040
Curvature parameter on labor 1.65
[[gamma].sub.N]
Health spending share of .166
output 1 - [omega]
Government spending share .21
of output [bar.G]/[bar.Y]
Shock persistence [[rho].sub.G] .75
Shock size [[sigma]sub.I] = [[sigma].sub.L] .0040
TABLE 6
Relative Volatility and Persistence of Inflation
Series
HC TS
Model Model
Correlation:
Health status and output, corr(x, y) .68 n.a.
Health status and labor, corr(x, n) .71 n.a.
Relative volatility of inflation:
HC goods to aggregate, std([[pi].sub.H])/std([pi]) .44 .58
Regular goods to aggregate, std([[pi].sub.H])/ 1.16 1.12
std([pi])
HC goods to regular goods, std([[pi].sub.H])/ .38 .51
std([[pi].sub.R])
Persistence of inflation:
Aggregate, corr([[pi].sub.t], [[pi].sub.t-1]) .48 .49
HC goods, corr([[pi].sub.H,t], [[pi].sub.H,t-1]) .78 .85
Regular goods, corr([[pi].sub.R,t], [[pi].sub.R,t-1]) .47 .45
Notes: Moments are calculated from artificial time series of
1 million periods. Variables are expressed in terms of
deviation from the steady state. Relative volatility is
calculated as the ratio of standard deviations and
persistence is calculated as the one-period autocorrelation
coefficient. All model variables are in quarterly frequency.
TABLE 7
Change in Volatility Before and After a Policy Shift
HC Model
Before After
Shift Shift [DELTA] %
Volatility of inflation:
Aggregate, std([pi]) .419 .476 13.73%
HC goods, std([[pi].sub.H]) .183 .190 3.69%
Regular goods, std([[pi].sub.R]) .486 .553 13.80%
TS Model
Before After
Shift Shift [DELTA] %
Volatility of inflation:
Aggregate, std([pi]) .463 .582 25.75%
HC goods, std([[pi].sub.H]) .267 .330 23.67%
Regular goods, std([[pi].sub.R]) .518 .650 25.39%
Notes: Moments are calculated from artificial time series of
1 million periods. Variables are expressed in terms of
deviation from the steady state. Volatility is calculated as
standard deviations expressed in percent. Policy shift is
modeled as a simultaneous change in the policy coefficient
[[rho].sub.[pi]] from 1.83 to 1.5 and [[rho].sub.Y] from .21
to .25. [DELTA] % denotes percentage change in standard
deviation before and after the policy shift. All model
variables are in quarterly frequency.
TABLE 8
Robustness Analysis
Correlation:
With Output With Labor
corr(x,y) corr(x,n)
Baseline .68 .71
[[kappa].sub.H] = 0.04, .54 .22
[[kappa].sub.L] = 0.99
[[gamma].sub.X] = 1-05 .51 .30
[[delta].sub.X] = 0.0015 .16 .13
[[mu].sub.X] = 0-04 .69 .70
Change all parameters .05 -.06
Rel. Volatility Persistence of
of HC Inflation HC Inflation
std([[pi].sub.H]) corr([[pi].sub.H],t],
lstd([pi]) [[pi].sub.H,t-1])
Baseline .44 .78
[[kappa].sub.H] = 0.04, .54 .84
[[kappa].sub.L] = 0.99
[[gamma].sub.X] = 1-05 .58 .85
[[delta].sub.X] = 0.0015 .63 .86
[[mu].sub.X] = 0-04 .43 .78
Change all parameters .62 .85
Notes: Moments in the model are calculated from artificial
time series of 1 million periods. Variables are expressed in
terms of deviations from the steady state. All model
variables are in quarterly frequency.
