Investing in Health during Good and Bad Times:
An Application to the China Shock∗
Soojin Kim†

Sunham Kim‡

Chong Xiang§

October 18, 2024

Abstract
Many economic shocks affect not only workers’ wages and employment but also
health. We study their mechanism, welfare effects, and policy implications in a dynamic quantitative model with endogenous health investment. The health production
technology is flexible, allowing workers to optimally choose to forego or partially treat
sickness, or incur non-medical health investment. Applying this model to the China
shock, we estimate its causal effects on health and calibrate the model to the pre-China
shock economy. Our simulations suggest that, first, the health investment mechanism
is economically significant, with the model elasticity accounting for between 40-50% of
the empirical estimates. Second, the workers’ steady-state welfare loss is equivalent toan annual drop of 8.4% in consumption, and both endogenous health investment andhealth itself play important roles. Finally, while universal health insurance is effective
in reducing partial or foregone treatment, it offers little protection for non-medical
investment. Therefore, its overall efficacy would be nuanced.

JEL Codes: E20, I30, I10, F10
Keywords: dynamic quantitative model; heterogeneous agents; health; under-investment;
over-investment; the China shock∗
The paper was previously circulated under the title “Care for the China Syndrome: Trade Shock, Sick
Workers, and Access to Healthcare.” We thank R. Anton Braun, Yongsung Chang, Roozbeh Hosseini, Karen
Kopecky, Dirk Krueger, José-Vı́ctor Rı́os-Rull, Richard Rogerson, and participants at various conferences
and seminars for their feedback. All errors are our own.
†
Georgia State University, soojinkim@gsu.edu‡
Korea Development Institute, sunham.kim@kdi.re.kr§
Purdue University, cxiang@purdue.edu

11Introduction

Economic shocks, such as mass layoffs, business cycles, and international trade, affect not
only wages and employment but also health.1 What is the mechanism through which these
economic shocks affect health? What are the welfare effects of these shocks, incorporating
their health effects? What policies may help mitigate these adverse health effects?
There are several challenges in studying these questions. The change of health is inherently a dynamic process and it is affected by both exogenous sickness shocks and endogenous
health investment. The angle of health investment is especially relevant for the U.S., because
many in the U.S. may limit their healthcare utilization when they are sick due to the lackof health insurance coverage. According to the National Health Interview Survey (NHIS),
18.6% of working-age adults report not receiving medical care in 2011-2012 due to financial constraints.2 On the other hand, there are many ways to invest in one’s health beyond
receiving medical care, such as consuming healthy foods and investing in exercise equipment.
In this study, we take the first step in addressing these challenges. We develop a modelof endogenous health dynamics and apply the model to analyze the effects of the China
shock, a large increase in import penetration from China between 1990 and 2007 in the
U.S. manufacturing sector. Our quantitative analysis starts first by estimating the causal
effects of the China shock on workers’ health. We then calibrate the model to understandthe economic importance of the health investment mechanism, measure the welfare losses
from the China shock, and evaluate the effectiveness of health insurance.
In terms of methodology, we develop a quantitative dynamic model with heterogeneous
agents whose good health probability evolves endogenously. The workers in the model are
incentivized to invest in health as bad health incurs utility costs à la Low and Pistaferri(2015), and has adverse labor market consequences such as lower probabilities of employment
and lower earnings when employed. In every period, after a sickness shock is realized, workers
optimally choose health investments to improve the probability of future good health. A key
innovation of our model relative to the literature is that workers may optimally choose tounder -invest in health relative to sickness, where the health investment is insufficient for full
treatment. They may also choose to over -invest relative to sickness, above and beyond the1

Empirical studies include Sullivan and von Wachter (2009) for mass layoffs, Ruhm (2000) for businesscycles, and Adda and Fawaz (2020) and Pierce and Schott (2020) for international trade shocks.
2
This was more prevalent before the major provisions of the Affordable Care Act (ACA) were implemented in 2014, which subsequently expanded insurance coverage in the U.S. population.

2

.5

Good Health Share
.55
.6
.65

.7

Figure 1: The China Shock and Health1

2

IPW Quartile

3

4

full treatment through, e.g., massages or therapies.3 In other words, the health transition
depends on initial health, the sickness shock the worker experiences, and his choice of healthinvestment. We specify a flexible health transition function that depends on both the sizeof the sickness shock and health investment. It also features minimum investment, so thatworkers may optimally choose to not invest in health at all.
We apply this model to the China shock because previous studies (e.g. Autor et al., 2013;
Autor et al., 2014) have established econometric method for its causal inference and shown
its adverse effects in wages and employment. In addition, the China shock has clear effects
on health. To show their correlation in health, we organize the commuting zones in the U.S.
into quartiles of import penetration per worker (IPW) using data from Autor et al. (2013).
Then, combining it with restricted commuting-zone data from the Panel Study of Income
Dynamics (PSID), we construct Figure 1. It shows that the population share of good-healthworkers is monotonically decreasing across the IPW quartiles. In our empirical analysis,
we move beyond the correlation in Figure 1 to estimate the causal health effects of the
China shock, following the empirical strategy of Autor et al. (2013). Our estimates imply astatistically significant health effect and the elasticity of future good health probability withrespect to IPW is around −0.05, with larger effects among those with good initial health.
Having measured the health effect of the China shock, our next step is to calibrate themodel to the pre-China shock economy. We embed our worker-level model of health dynamics into a sector-level model of international trade. We use the Medical Expenditure
3

In our model, the workers always optimally choose their health investment. We say that a worker“under -invests” in health if his health investment is smaller than what is required to fully treat his sickness,and vice versa when he “over -invests” in health.

3Panel Survey (MEPS) data to obtain the exogenous parameters and targeted moments related to health transitions, medical expenditures, and the shares of workers without medical
utilizations by worker demographics. The medical utilization shares, which are overlookedin previous studies, are indicative of under-investment in health. In the data, they range
from 0.07 to 0.10 for the insured workers, but reach 0.28 to 0.34 for the uninsured ones, adifference by a factor of more than three. Our model captures such empirical features andendogenously generates heterogeneous health outcomes across workers.
The calibrated model has good fits with targeted moments. For example, the model
predicts that 27% of uninsured workers with bad health choose to forego health investment,
versus 28% in the MEPS data. It also generates reasonable predictions about the value of
health and workers’ health investment decisions relative to the corresponding non-targeted
data moments.
In the model, workers find it optimal to over-invest in health relative to sickness as ameans to self-insure against the future risks of transitioning to the bad health state. As aresult, over-investment is a common choice among the individuals with good health in themodel. On the other hand, individuals with limited resources, like the uninsured, often choose
to sacrifice their sickness treatment for consumption, sometimes by foregoing all treatment.
Together, the novel features of over- and under-investment imply that health investment
provides an additional channel for consumption smoothing in our model, a novel feature
relative to studies that assume exogenous health dynamics or that health investment is equal
to medical expenditures. In addition, given the model’s ability to capture such heterogeneity
and non-linearity in workers’ health investment decisions, it serves as a suitable laboratory
for studying the mechanism, welfare consequences, and policy implications for the workers
facing adverse economic shocks, which, in our application, is the China shock.
We simulate the China shock following the trade literature that models it as an exogenous
decrease in the domestic share of the U.S. manufacturing sector. In the simulation, we solve
for the change in manufacturing wage that balances the sector-level labor demand and obtaina 5.8% drop in wage, in line with the estimates in Autor et al. (2014) of 2.3%-7.2%.4
We now present our quantitative findings for the mechanism through which the China
shock affects health. Qualitatively, our model suggests that health deteriorates after the4

We also conduct a second simulation, where we assume instead, that the wage drop is 2.3%, the low
end of the range reported in Autor et al. (2014), and solve for the change in the job destruction rate thatbalances labor demand. The qualitative effects from the second simulation are similar to that of the first.

4

China shock because the loss of economic resources decreases the over-investment in healthand induces more workers to choose under-investment. Quantitatively, our model-generated
IPW elasticity of future good-health probability ranges from −0.02 to −0.03, accounting fora sizeable portion of our empirical estimate of −0.05. As a result, we see that the mechanism
through optimal health investment is economically important. Putting the model predictedelasticity into perspective, we show that the China shock led nearly half a million individuals
in the U.S. manufacturing sector into bad health, resulting in approximately 100,000 more
Emergency Room visits and 200,000 more inpatient hospital days per year. This health
implication of the China shock (or any adverse economic shock) is a novel feature of ourstructural model, that cannot be captured in models that abstract away from health or
those with exogenous health transitions.
The adverse health effect of the China shock has considerable heterogeneity across worker
types. For example, the loss of economic resources leads to but small changes in future
health outcomes for workers with bad initial health, because their calibrated health transition
function is fairly flat in the region around their optimal health investment. In contrast,
the health transition function of workers with good initial health is steeper with respect
to health investment, and so these workers experience substantial reductions in their future
good-health probability. These model predictions are consistent with our empirical estimates.
In terms of welfare, our simulations suggest that the average worker’s welfare loss fromthe China shock is equivalent to an annual drop in consumption of $1,721 (8.6%) when wecompare the pre- and post-China shock steady states. To measure the contribution of endogenous health investment in shaping welfare, we first shut down endogenous health investment
in our model. The resulting economy with exogenous health evolution over-estimates thewelfare losses from the China shock, with its magnitude varying across worker types. The
welfare loss is 10% higher for the average worker, but 30% higher for the unemployed worker
with bad health. We then completely remove health from our model to measure the significance of health in welfare effects. In this economy, the welfare cost is lower by almost
one-quarter for the average worker. These counterfactual experiments showcase the significance of both endogenous health investment and health itself in quantifying the welfare costsof an economic shock. A model that abstracts away from the former would over-estimate
the welfare cost, while a model that abstracts away from the latter would under-estimate it.
Finally, we explore the potential policy responses by simulating a post-China economy in5which all individuals are covered by health insurance. Universal health insurance substantially reduces under-investment, relative to the benchmark post-China economy, leaving very
few workers to forego treatment when facing a sickness shock.5 On the other hand, universal health insurance has little effect on the over-investment in health, because non-medical
expenditures are not covered by health insurance. Therefore, the overall effectiveness of
universal health insurance is nuanced and hinges upon the extent to which access to healthinsurance can compensate for wage losses and the types of sickness shocks workers face.
Related Literature Our study is most closely related to the quantitative dynamic models
in which health evolves endogenously. For example, Hall and Jones (2007) and Fonseca etal. (2021) focus on mortality, and Cole et al. (2019) and Lukas and Yum (2024) incorporate
health investment through efforts (e.g., exercise). Relative to this literature, we focus on sickness and monetary health investment, and our flexible health transition function implies thatworkers may optimally choose to invest less (under -investment) or more (over -investment)
than the size of the sickness shock. By using the China shock as an application, we showthat over- and under-investments play important roles in both the mechanism and policy
implications of the adverse health effects of economic shocks.
Another line of work studies the interactions of disability and healthcare policies, healthand welfare, assuming that health evolves exogenously (e.g. Low and Pistaferri, 2015; Aizawa
and Fang, 2020; Kim and Rhee, 2022; De Nardi et al., 2023; Chen et al., 2024; Hosseini et al.,2024).6 Relative to this literature, workers’ health transition probabilities in our model are
impacted by endogenous health investment decisions, and thus economic shocks. In addition,
endogenous health investment serves as an additional channel for consumption smoothing.
A number of recent studies have used structural models to study how specific mechanisms,
such as migration, labor force participation, and college education, contribute to the effectsof the China shock on earnings, employment, and welfare (e.g., Lyon and Waugh, 2018;
Caliendo et al., 2019; Carroll and Hur, 2020; Ferriere et al., 2021). We focus on the healthinvestment mechanism, and our results suggest that the estimated welfare loss from the
China shock is likely larger if its adverse health effect is taken into account.
Lastly, our study has been motivated by the applied micro studies of the health effects
5This result is consistent with the empirical finding that under-investment in health is far more common
in the U.S. than in high-income countries with universal health insurance (e.g. Davis and Ballreich, 2014).
6
In Aizawa and Fang (2020) and Chen et al. (2024), health insurance status directly affects healthtransition. In our model, health insurance affects health through the health investment choice of workers.

6

of economic shocks, as in, for example, Schaller and Stevens (2015), Ruhm (2000), andHummels et al. (2023). Additionally, Adda and Fawaz (2020) and Pierce and Schott (2020)
show using cross-sectional data, the effects of the China shock on workers’ health statuses.
Our empirical analysis complements theirs by measuring the health elasticity with respect
to IPW using a panel data set that allows us to control for unobserved worker heterogeneity.
The rest of the paper is organized as follows. Section 2 presents our model of heterogeneous agents with endogenous health evolution. In Section 3, we estimate the causal effectsof the China shock on health and embed our worker-level model into a sector-level modelof international trade. The calibration strategy is detailed in Section 4 and its results arepresented in Section 5. Our quantitative analyses, evaluating the mechanism, welfare andpolicy implications of the China shock, are presented in Section 6.

2

A Model with Endogenous Health Dynamics

In this section, we develop a heterogeneous agent model with endogenous health dynamics.
The key features of the health transition process in our model are first, that health investment
is determined after the realization of sickness shocks; and second, that the amount of healthinvestment is not restricted to equal the magnitude of the sickness shock. That is, workers
may decide to forego or partially treat their sicknesses (under -investment) or invest moreresources beyond treating the sickness (over -investment). Our model also specifies richheterogeneity in worker characteristics and various roles of health in line with empiricalobservations that we further detail in Section 4, incorporating multiples ways in which healthdynamics impact workers’ labor market outcomes and welfare.

2.1

Endowments and Preferences

There are infinitely-lived workers of measure one. These workers are endowed with healthstatus x, where x = G denotes Good health and x = B, Bad health. The workers’ utility
function follows that in the literature (e.g., Low and Pistaferri, 2015):
U (c; x) =[c · exp(ι (x))] 1−ρ
,1−ρ

where c denotes consumption and ρ, the relative risk-aversion parameter. The parameterι (x) captures how health affects both the utility level and marginal utility of consumption.
If ι (B) < ι (G), being in the unhealthy state incurs utility cost, providing incentives for7health investment.
The health status impacts workers in three ways. First, each period, a worker receives asickness shock ε (x) with probability f (ε; x). Good health implies mild sickness shocks, i.e.,ε(G) < ε(B). Second, the worker may be either unemployed l = U or employed l = E, andhis transition probability to employment 1−δ (l, x) is health-dependent. Good health workers
have higher job continuation rate and lower job separation rate. Finally, an employed worker
earns income of w · ν (x) · z, where w is the market wage and ν (x) captures the productivity
effect of health with ν(G) > ν(B). The last term z is his idiosyncratic productivity shock,which follows an AR(1) process in logs with persistence ρz and standard deviation σz .
Lastly, workers have access to risk-free savings with an exogenous rate of return, r.

2.2

Health Production

Having clarified the central role of health status in our model, we now specify how healthevolves over time. The health production in our model specifies the probability of being ingood health in the next period. Relative to the literature with endogenous health dynamics(e.g., Cole et al., 2019, Fonseca et al., 2021), our health production is unique in its dependence
on the sickness shock ε. The sickness shock impacts the health production directly throughparameters, and indirectly through the health investment choice of an individual because hemakes the choice after the realization of the sickness shock.
Specifically, the probability of being in good health in the next period is a function of thecurrent health status, x, sickness shock, ε, and health investment, H, which we parameterize
using the following flexible Weibull function:

F (H; x, ε) =
 1 − α (x, ε)if H ≤ Hmin (x, ε)
h
i
γ(x)

 1 − α (x, ε) exp − (H−Hmin (x,ε))if H > Hmin (x, ε) .
λ(x)

(1)

The health production function has the following properties. First, all the parameters ofF (·) depend on initial health status x, capturing the heterogeneity in future health outcomesby x that we empirically document in Section 4. In Figure 2(a), we plot the health production
for a low (mild) sickness shock εL and a high (severe) sickness shock εH by health investment
H in the x-axis, given initial health x. The second feature of the health production function,
as seen in Figure 2(a), is that it is non-decreasing in H, with a minimum health investment

8

Figure 2: Health Production and Investment(a) Health Production(b) Under -Investment(c) Over -Investment
Low Shock, L
High Shock, H"Other"Investment

1-

1- L

1Medical Expenditures:#Marginal Cost 1-q, if insured#Marginal Cost 1, if uninsured

Medical Expenditures:#Marginal Cost 1-q, if insured#Marginal Cost 1, if uninsured

1- H
Hmin,L

Hmin,H

Investment

Hmin

H*

Hmin

H*

required for its marginal effects to be strictly positive and concave. That is, when healthinvestment exceeds the minimum Hmin (x, ε), F (·) is increasing in H, ∂F (·) /∂H > 0 approaches +∞ as H approaches Hmin (x, ε) from above, and F (·) is concave with respect toH, as long as γ (x) < 1. We incorporate Hmin (x, ε) as many individuals report zero medical
utilization in the data. Further, the minimum investment increases with ε (the flat portionis longer under a more severe shock εH ), as when one is severely ill (e.g. cancer), a large(r)amount of investment is needed for treatment to be effective. Lastly, there is a baseline
probability of good health represented by 1 − α (x, ε) > 0: even if H = 0, the probabilityof future good health is 1 − α (x, ε) > 0. As illustrated in Figure 2(a), a large sickness
shock may lower one’s baseline probability of being in good health implying the α (x, ε) is
increasing in ε.
It is important to note that, given ε, the worker is free to choose whatever amount of
H he wants. While we do not impose any restrictions on the amount of health investment
relative to the size of the sickness shock, we assume that the health investment smaller
than the sickness shock is medical expenditures used to treat that sickness. This is an
assumption that helps us map the model to the data. Then, any investment beyond sickness
shock, max{0, H −ε}, is considered non-medical health investments (e.g., massage or healthyfood). Thus, implicitly, we assume that non-medical health investments are only useful after
the sickness has been fully treated, and they enter the production function additively withmedical expenditures. On the other hand, the non-medical investments do not enter into
consumption, and so do not directly contribute to utility.7
In summary, given the health production function, the worker chooses the optimal health7

This assumption represents a conservative modeling choice, because without it, the workers would haveeven stronger incentives for non-medical health investment.

9

investment after sickness shock, ε is realized. The above-discussed features of F (·) imply
that this optimum may be (i) H ∗ = 0; (ii) Hmin (x, ε) < H ∗ < ε; (iii) H ∗ = ε; or (iv)H ∗ > ε, but never 0 < H ∗ < ε. We denote (i) or (ii) when ε > 0, an under -investment; (iii),
a full -treatment; and (iv), an over -investment. Figure 2(b) illustrates under -investment byshowing case (ii) and the associated medical expenditure of H ∗ = min {H ∗ , ε}. Figure 2(c)illustrates over -investment by showing case (iv) and the associated medical expenditure of
ε as well as the non-medical health investment of H ∗ − ε = max {0, H ∗ − ε} > 0.

2.3

Health Insurance

In our model, the worker has the exogenous probability of ζ (l) to have health insurance ineach period, where l denotes employment status. The employed have a higher probabilityof getting health insurance (i.e. ζ(l = E) > ζ(l = U ) > 0), reflecting the prevalence of
Employer-Sponsored Health Insurance (ESHI) in the US, but still allowing the possibilityof unemployed individuals to have (some form of) health insurance. With the premium ofπ, health insurance covers a χ (ε; x) < 1 share of medical expenditures. However, healthinsurance does not cover non-medical health investment. Thus, for insured individuals, themarginal cost of health investment is 1 − χ (ε; x) for medical expenditures, min{H, ε}, but 1
for the non-medical health investment beyond ε, max{0, H − ε}.
Note that the health production technology is independent of insurance statuses. Thatis, health insurance affects health dynamics endogenously through the choice of health investment H in our model, distinct from the approach in papers where health transitions
exogenously differ by insurance statuses (e.g., Aizawa and Fang, 2020).

2.4

Government

The government does not consume final goods. Instead, it collects taxes on labor income
T (y), and uses the tax revenue to finance the unemployment benefit of b and the consumption
floor of c. The consumption floor, c, captures various means-tested government programs,
in a similar manner as in previous studies with medical expenditure risks, such as De Nardi
et al. (2023). We denote the transfers made for c as tr, and assume that the individuals
for whom tr > 0 are unable to save or invest in health. The government also ensures thatthe health insurance sector makes zero profits through lump-sum subsidies. Note healthinsurance companies collect premium π and pay the insured at coinsurance rate of χ (ε; x)10

up to ε. We assume that premium is exogenous and that the government makes transfers to
insurance companies to ensure zero profit.8

2.5

The Workers’ Optimization Problem

We now state the optimization problem of a worker with the state s̃ ≡ {x, a, in, ε, z} that
includes the health status, financial asset, insurance status, sickness shock, and labor productivity shock. The worker of status l ∈ {E, U } solves
V l (s̃) =max

U (c + tr; x)XPr (x′ ) δ (l, x′ ) EV U (s̃′ ) + (1 − δ (l, x′ )) EV E (s̃′ )c≥0,a′ ≥0,H≥0

+β

(2)

x′ ∈{B,G}s.t.

c + a′ + H̃ = I (l, x) + (1 + r) a + tr
I (E, x) = w · ν (x) · z − T (w · ν (x) · z) ;(3)
I (U, x) = b(4)

tr = max {0, c − (I (l, x) + (1 + r) a)}(5)

Pr (x′ = G) = F (H; x, ε) ; Pr (x′ = B) = 1 − F (H; x, ε)Hif uninsuredH̃ = π + (1 − χ (ε; x)) min {ε, H} + max {H − ε, 0} if insured.

(6)
(7)

The worker maximizes his utility (2) in the current period U (·) plus his discounted utility inthe next period. If he is unemployed, the expectation is over insurance and sickness shock
status; and if employed, he additionally takes expectation over labor productivity shock.
In the budget constraint (3), the worker’s expenses are consumption c, tomorrow’s asset a′ , and out-of-pocket health investment expenditures H̃. The worker’s resources on theright-hand side of the budget constraint (3) are his income, I (l, x), asset value, (1 + r) a,
and government transfer, tr. Equation (4) spells out the worker’s income. If employed, hereceives the wage w · ν (x) · z and pays the tax T (·). Otherwise, he collects the unemployment
benefit b. Equation (5) specifies the amount of transfers from the government that guarantees consumption floor c. As discussed in Equation (1), health transition probabilities in (6)depend on health status x, sickness shock ε, and health investment H. Finally, Equation(7) summarizes our earlier discussions about medical expenditures and non-medical health8

Employer-paid premiums for health insurance are excluded from federal income and payroll taxes, andemployee-paid premium is deducted from pre-tax income. Effectively, there is a tax subsidy to ESHI fromthe government that we may be capturing here.

11

investment. If the worker is uninsured, his total out-of-pocket health expenditure, H̃, equals
his total health investment of H. For the uninsured, his out-of-pocket health expenditureconsists of three components: the insurance premium π, the copayment of medical expenditures (1 − χ (ε; x)) min {ε, H}, and the non-medical health investment max {H − ε, 0}.
In summary, workers are heterogeneous in health status, and receive sickness and labormarket shocks in each period. In this dynamic setting, workers optimally choose consumption, savings, and health investment, recognizing the benefits of good health.

3

Application: The China Shock

We now apply our model to the China shock, a large increase in U.S. import from China inthe manufacturing sector. We first clarify why we choose the China shock as our applicationand then embed our worker’s problem into a sector-level model of international trade to map
the trade shock into our full model for counterfactual analysis.

3.1

Why the China Shock?: Empirical Motivation

Many empirical studies, including Autor et al. (2013) and Autor et al. (2014), have shownthat the China shock caused adverse labor market outcomes to manufacturing workers in the
U.S. Therefore, it can be a good laboratory for studying how changes in economic resources
can impact workers’ health and evaluating the role of health investment. Further, given thewell-established empirical approach to estimating its causal effects from previous studies,
we can validate its effects on workers’ health. While there are previous studies that usedcross-sectional data to estimate the negative health effects of the China shock (e.g., Adda
and Fawaz, 2020), in this section, we further corroborate its effects utilizing panel data andcontrolling for unobserved heterogeneity across workers. Additionally, these empirical results
provide both quantitative and qualitative validations for the predictions of our model.
3.1.1

Data

In this subsection, we outline our data and the construction of main variables, and illustrate
the salient features of our data.
Import Penetration per Worker We measure the size of the China shock as importpenetration per worker (IPW) following Autor et al. (2013):
IPWcz,t =X Lcz,j,t
j

Lcz,t
12

×

CHN
Mj,t
.
Lj,t

(8)

CHN
In Equation (8), Mj,tand Lj,t are, respectively, the US imports from China and employ-ment in industry j in year t, Lcz,j,t is the employment in commuting zone cz in industry j
and year t, and Lcz,t is the employment in commuting zone cz in year t. Intuitively, IPWcz,tmeasures the weighted average of Chinese imports per worker, across industries, in commuting zone cz in year t, where the weights are the industries’ employment shares in cz in t. In
order to control for potential endogeneity in US imports, we follow Autor et al. (2013) and
use the following instrument for IPWcz,t :IPWIV
cz,t =

OTH
Mj,t
×
.
Lcz,t−10
Lj,t−10

X Lcz,j,t−10j(9)

As compared with the IPW measure of (8), its instrument, (9), uses U.S. imports from eight
other high-income countries and 10-year-lagged labor employments.9
Panel Study of Income Dynamics The rest of our data come from the PSID. We
restrict our sample to those between the ages of 18 and 64 (working-age population) who
work full-time (1,600 annual hours) in their initial year of entry into the PSID sample.
We use self-reported health as our measure of health status, which is common in both thestructural estimation literature (e.g. Cole et al. 2019; De Nardi et al. 2023) and applied micro
studies of health (e.g. Currie and Madrian, 1999). Recent studies show that self-reported
health is also a good predictor of future health events, such as hospitalization (e.g. Nielsen,
2016). It also fits well with our inquiry, because the PSID data for self-reported health span
the years of the China shock, 1991 through 2011.10 In PSID, each respondent is asked torate his health into five levels (from excellent to poor). We combine the top two levels into
the single category of good health, and combine the other three levels into bad health. PSID
also includes detailed demographic information such as age, gender, income, and industry
affiliation. In addition, we obtain the restricted commuting-zone identifiers, to combine theworker-characteristics data with the IPW data discussed above.
Merged IPW-PSID Data The merged data set includes 508 unique commuting zones
and about 33,000 worker-year observations.11 We list the detailed summary statistics inAppendix A.1, and outline their main features. The average IPW is $1,440 per worker and
9

OTH
Mj,t
is U.S. imports from Australia, Denmark, Switzerland, Finland, Japan, Germany, New Zealand,
and Spain.
10
The objective health measures in PSID (e.g., indicator variables of diabetes, asthma, etc.) start in 2003,
which makes it impossible for us to exploit the IPW variations before 2003.
11
The number of all commuting zones is 722, implying that PSID covers around 70% of them.

13the IPW distribution features a large variation with quartiles ranging from $220 per worker
to $3430. Most of the workers in our sample are male and about two-thirds of them are ingood health. Importantly, the mean value of the good-health dummy, our measure of healthstatus, monotonically decreases across the quartiles of IPW, as we showed earlier in Figure
1. In the rest of this section, we establish the causality of the effects of IPW.
3.1.2

Effects of Import Penetration on Worker Health

We exploit the rich worker-level panel data to estimate the causal effects of IPW and theirheterogeneity across worker characteristics. The econometric specification is:X
GHi,cz,t = βi + βt +γk · Ik,t0 · IPWi,cz,t−1 + α · Zi,t + εi,cz,t .

(10)

k

In Equation (10), the indicator variable GHi,cz,t takes the value of 1 if worker i, living incommuting zone cz, has Good Health in year t. The coefficients βi and βt are, respectively,
worker- and year-fixed effects, and Zi,t is a vector of time-varying worker-characteristic controls (e.g., education). Given the annual frequency of the data, we include IPW in year t − 1,
to ensure that exposure to import competition had happened before the realization of thehealth status, GHi,cz,t . The coefficient of interest is γk , where Ik,t0 = 1 if a worker has acertain characteristic k (e.g., works in manufacturing sector) in his initial year t0 . Thus, thecoefficient γk allows us to measure the group-specific effects of the IPW.
The following features of the estimation of Equation (10) allow us to interpret γk as thecausal effect of import penetration. First, both the IPW measure and the worker characteristic are lagged relative to the dependent variable. Second, we instrument IPWcz,t−1,kusing the exogenous variations in IPWIV
cz,t−1,k as in Equation (9). Third, the worker fixed
effects, βi , control for the idiosyncratic and time-invariant factors that could be important
for workers’ health, such as early life experiences and genetic differences, some of whichhave been emphasized in previous studies.12 While the first two features have been used inprevious studies, the use of worker-fixed effects is novel. It implies that regression (10) asks
the following: as import penetration increases in a commuting zone for exogenous reasons,relative to the sample mean, do workers in the commuting zone suffer lower probabilities ofbeing in good health in the following year, relative to the sample mean? Because the error
term might be correlated across workers within cz by year, we cluster standard errors by cz.
12See, e.g. Maccini and Yang (2009) and De Nardi et al. (2023).

14

Table 1: Import Penetration and Future Healthγk
All
Manufacturing
Non-Manufacturing
Income Q1
Income Q2
Income Q3
Income Q4
Initial Good
Initial Bad
First-Stage F
Number of Obs.

Dependent variable: Probability of good health
(1)
(2)
(3)
(4)
-0.019(-1.60)-0.025∗∗∗(-2.10)-0.012(-1.13)-0.050∗∗∗(-2.81)-0.026(-1.44)-0.023∗(-1.84)-0.012(-0.98)-0.031∗∗(-2.51)0.019(1.62)
12.92
52.71
15.10
58.06
33,376

Elasticity(∆75-25%)-0.042(-2.8 pp)-0.054(-3.7 pp)-0.026(-1.8 pp)-0.110(-7.3 pp)-0.056(-3.7 pp)-0.050(-3.3 pp)-0.026(-1.8 pp)-0.068(-4.6 pp)0.042
(2.8 pp)

Note: The table reports regression coefficients γk from Equation (10). The first-stage F -statistics are forthe first endogenous variables. The standard errors are clustered by commuting zone and t-statistics are inparentheses. ∗ p < 0.10, ∗∗ p < 0.05, ∗ ∗ ∗ p < 0.01

Table 1 reports the results from our analysis. In column (1), we pool across all workers. While the coefficient on import penetration is negative, this effect is not statisticallysignificant. In columns (2) through (4), we divide the workers into their initial year characteristics, and report the coefficient estimates by subgroup. Column (2) shows that the effectof import penetration on manufacturing workers is negative and statistically significant, andabout twice as large in magnitude as compared to the effect on non-manufacturing workers.
This result is reassuring because during the China shock, import penetration primarily impacted the U.S. manufacturing sector. Our coefficient estimates in column (2) imply thatthe elasticity of IPW on the Good health probability is −0.054 for manufacturing workers
and −0.026 for non-manufacturing workers (although the latter is statistically insignificant),
and that the commuting zone at the 75th percentile of the IPW distribution has 3.7 pp
lower probability of future good health for manufacturing workers relative to the commuting
zone at the 25th percentile. These findings corroborate, and add to, the findings from prior15

studies by Adda and Fawaz (2020) and Pierce and Schott (2020), which investigate different dependent variables (e.g. incidences of hospitalization and mortality). Column (3) of
Table 1 indicates a particularly pronounced effect of import penetration on workers whose
initial-year income is in the first quartile, consistent with the results from Autor et al. (2014)indicating that the China shock had a larger effect on the earnings of low-income workers.
Lastly, in Column (4), we see that the IPW had more adverse health effects on workers withgood initial health than on those with bad initial health. We will show, in Section 5, that
this result is consistent with qualitative predictions of our model.
We have conducted the following additional empirical analyses, the details of which are
in Appendix B. First, we aggregate our data into the region level and then follow the longdifferencing specification of Autor et al. (2013). Our dependent variable is the long-termchange in the good-health population share, and we exploit the regional variations in longterm changes in IPW exposure. This alternative approach complements the estimation of
Equation (10) by capturing the overall effects of the China shock over long periods. We obtain
similar results as in Table 1, with the elasticity of the good-health population share withrespect to IPW ranging between -0.048 and -0.078, with the mid-point of -0.060. In addition,
we estimate Equation (10) with manufacturing-by-year fixed effects to address concerns thatworkers in manufacturing and non-manufacturing sectors could have experienced different
trends in health status during our sample period. The results are robust to the specification.
Finally, using subsamples of male and manufacturing workers yield similar results.
In summary, we have shown that the increase in import penetration from the China
shock caused statistically and economically significant adverse impacts on workers’ health,with IPW elasticities ranging around -0.054. We embed our worker-level model into a sectorlevel model of international trade, and then use it as a laboratory to study the mechanism,
welfare effects, and policy implications of the adverse effects of the China shock.

3.2

Closing the Model at the Sector Level

Production and Trade We close our model in Section 2 with the production and tradesides of the economy, where all markets are competitive. We assume a small-open economy
and use the specific-factors model from the trade literature for the manufacturing sector.
We start from goods demand. The price and quantity of the final good are P and Y ,respectively, and we normalize P = 1. The production technology of the final good is Cobb-

16

Douglas with respect to the manufacturing good, whose price and quantity are Pm and xm ,respectively, where m indexes the manufacturing sector. Let ϕm denote the manufacturingsector’s share in final good production and thus, xm = ϕm · Y /Pm represents the demand
for the manufacturing good from the final good production. Both the final good and the
manufacturing good are non-tradable, and we are agnostic about the rest of the economy,outside of the manufacturing sector.13
The manufacturing good, in turn, is assembled from domestic and imported inputs via
the following constant elasticity of substitution (CES) technology
h 1
i σ
1
σ−1 σ−1σ−1∗σσ,xmS = ωm nm σ + (1 − ωm ) (nm ) σwhere ωm is the weight of the domestic input, nm and n∗m are quantities of domestic andimported inputs, and σ > 1 is the elasticity of substitution. Let pm denote the price of thedomestic input. Meanwhile, the price of the imported input is τ ∗ p∗m , where τ ∗ ≥ 1 is thetrade cost of manufacturing inputs. The demand for these manufacturing sector inputs are
nm = ωm (pm ) −σ XmS Pmσ−1 ,∗ ∗ −σn∗m = (1 − ωm ) (τmpm ) XmS Pmσ−1 ,where XmS = Pm xmS is the total expenditure for the manufacturing sector, and
 1∗ ∗ 1−σ 1−σPm = ωm (pm ) 1−σ + (1 − ωm ) (τmpm )relates the prices of the manufacturing good to the those of domestic and imported inputs.
Turning to goods supply, the domestic input is produced with labor according to thelinear technology, zmS = ψm Lm , where ψm is productivity, and Lm is the labor supply (inefficiency equivalent units) of the manufacturing sector. Our use of the specific factors model
implies that manufacturing labor is immobile to the rest of the economy. The price of thedomestic input is thus proportional to the wage rate wm : pm = wm /ψm . The domestic input∗∗
is tradable. When it is exported, it faces the foreign demand of Dm(pm ) ≡ Dm
· (pm ) −σ ,∗where Dm
incorporates demand shifters as foreign expenditure and export costs. Finally,

because we assume that our economy is a small open economy with respect to the rest of13

Our model can be extended to incorporate a general equilibrium with multiple sectors. Such model
requires more assumptions (e.g., production technology in other sectors). As we focus on the outcomesof manufacturing workers, we choose to abstract away from production in other sectors. However, as we
describe in Section 4.4, we impose equilibrium conditions in the manufacturing sector, endogenizing theequilibrium wage effect in the manufacturing sector in response to the China shock.

17

the world, the supply of imported manufacturing inputs n∗m , is elastic.
Market Clearing When we simulate the China shock in our quantitative model, we impose market clearing conditions in the economy. Therefore, in response to the shock in theimport cost, the wage in the manufacturing sector in the post-China economy is determined
endogenously. Here, we outline the key equilibrium conditions, leaving the rest and theformal equilibrium definition to Appendix C.
Let the distribution of workers in the manufacturing sector over state space s ≡ (l, s̃) beµ (s). First, the aggregate labor supply, Lm , depends on workers’ health (x) and productivity(z) and the stationary distribution of µ (s):X
Lm =
ν (x) · z · Il=E · µ (s) .

(11)

s

On the other hand, the market clearing conditions for the manufactured good and forthe domestic inputs imply that when the labor market clears,D∗ 1−σ
wm Lm = πm
ϕm Y + Dm
pm ,

D
πm
=

ωm (pm ) 1−σ,∗ p∗ ) 1−σωm (pm ) 1−σ + (1 − ωm ) (τm
m

(12)

D
where πmis the domestic share of the manufacturing sector. On the right-hand side ofD∗ 1−σEquation (12), πm
ϕm Y represents the labor demand from domestic production, and Dm
pm

represents the labor demand from exports. Equation (12) says that the aggregate labordemand and labor supply, Lm , jointly determine the wage, wm , for the manufacturing sector.
Thus, our sector-level model ensures that the wage and labor supply are consistent withthe labor demand, through Equation (12). These two pieces of our model allow us to quantify
the China shock using the standard practice in the trade literature, and to endogenously
determine workers’ wage, wm , in the post-China economy, which we discuss in Section 4.4.

4

Calibration

In this section, we map our model to the data to quantify the effects of the China shock on
workers’ health and welfare. In addition to PSID, we use the Medical Expenditure Panel
Survey (MEPS), Current Population Survey (CPS), STructual ANalysis Database (STAN),
and World Development Indicators (WDI), to set parameter values and generate target
moments. We first lay out the predetermined parameters and discuss the key empiricalfacts concerning medical expenditures and health transitions. Then, we present calibrations
within the worker model (inner loop) and the sector model.
18

4.1

Predetermined Parameters

The left panel of Table 2 lists the household parameters whose values we take from outside
the model, with one model period corresponding to one year in the data. The coefficient ofrelative risk aversion ρ, discount factor β, and interest rate r are set to 1.5, 0.95, and 0.02,
respectively, which are standard values in the literature.
Then, we use the PSID data in pre-China years (1991–1996) to obtain the average incomeof workers in the manufacturing sector. One of the important components in our quantitative
analysis is the health gradient of income. Due to selection into employment, using theobserved incomes across health status may be biased. To correct for the bias, we follow Low
and Pistaferri (2015) and conduct a two-step wage estimation using the amount of “potential”
government transfers as an instrument variable to obtain ν (B), after normalizing ν (G) to
one.14 Given this procedure, the average labor income of a worker with Good health is$50,211 and the health gradient of income, ν (B) = 0.81. The productivity shock process
has the persistence and standard deviation parameters of 0.95 and 0.15, and we discretize
the process following Tauchen (1986). The job continuation and job finding rates by healthstatus are from the Annual Social and Economic Supplement of the CPS in years 1996-1999.15
We set the unemployment benefit to 20% of average wage income across health statuses, which amount to $9,086. Additionally, the consumption floor is $3,000, similar to one
estimated in De Nardi et al. (2023), and the income tax rate is 20%.
Note that these parameter values point to substantial economic benefits of being in good
Table 2: Predetermined Parameters
Parameter
Description
Household and Labor Market
ρRisk aversion
βDiscount factorrInterest rate
wm
Pre-China wage
ν (B)Health effect on wage(ρz , σz )Inc. shock: pers.; st.dev.
1 − δ (E, x) Job continuation: B; G
1 − δ (U, x) Job finding rate: B; G

Values1.5
0.9
0.02$50,2110.81
0.95; 0.15
0.87; 0.93
0.18; 0.32

14

Parameter Description
Government Policiesb
UI benefitcCons. floorτIncome tax rate
Production
ωmHome bias
σ−1
Trade elasticity
ϕmManuf. shareDπm,pre;post
Domestic share

Values$9,086$3,000
20%
0.5
3
0.17
0.85; 0.71

The “potential” government transfers refer to the amount of benefits from welfare programs (e.g.,
SNAP, TANF) that a representative individual worker would have received in his residential state. The
details regarding the first-stage and the second-stage estimation results are relegated to Appendix D.1.
15
The CPS allows us to track workers’ employment statuses for a larger sample of individuals than PSID.

19

health. Employed workers earn 20% more if in good health, and job continuation and finding
rates are 0.6pp and 0.14pp higher, incentivizing workers to invest in health.

4.2

Key Empirical Facts

As we showed in Section 2, a key element of our model is the workers’ optimal choiceof medical expenditures. Individual-level data on medical expenditures are available from
MEPS, which we use to establish the stylized facts in two areas: firstly, medical expendituresand medical utilizations, and secondly, transition probabilities to good health, by worker
characteristics.16 These stylized facts provide the starting point of our calibration process.
In Table 3, we document average medical expenditures and the shares of individuals
with zero medical utilization by health and insurance statuses. For the latter, we use theHousehold Component Event files of the Medical Conditions data to identify those who neverreported medical events or utilizations, such as outpatient visits and prescribed medicine.17
Next, to better understand the relationship between medical expenditures, insurance
status, and health transitions, we run the following regression:
Healthi,t+1 = β0 + β1 · Healthi,t +

10
X

med
β2,k · Di,t,k+ Γ · Xi,t + ε.

k=1

The variable Healthi,t(t+1) takes a value of one if the individual is in Good health, and 0
otherwise in year t (t + 1). We then construct deciles of medical expenditures among insured
Table 3: Medical Expenditures and Medical Utilizations
Average Medical Expenditures(positive only)
Share of Individuals
without medical utilizations

Bad
Good
Bad
Good

Insured$3,297$2,2460.07
0.10

Uninsured$1,755$1,2940.28
0.34

Note: For medical expenditures, we document group-level average expenditures among those who havepositive spending, after controlling for age, sex, race, education, Census region, marital status, and survey
panel dummies. An individual is considered to have utilized medical service if one had prescribed medicine,dental visit, outpatient event, home health provider event, office-based medical provider visit, emergency
room visit, or other medical expenses.

16

For parameters governing health production, we calculate moments using all workers in the sample
without restricting the sample to those in the manufacturing sector (as we do for wage moments) for a larger
sample size. The underlying assumption is that all individuals face the same health production technology
regardless of the sector they are employed in.
17
Event level data is a better measure than zero medical expenditure shares, because some individuals
might receive medical treatment free of charge, e.g., in emergency rooms or through charity care.

20

.6

.1

Predicted Prob. of Good Health
.2
.3
.4

Predicted Prob. of Good Health
.65
.7
.75
.8

.5

.85

Figure 3: Medical Expenditures, Insurance, and Future Health(a) Bad Initial Health(b) Good Initial Health

0

2

4
6
Med Expenditure Decile
Uninsured

8

10

0

2

Insured4
6
Med Expenditure Decile
Uninsured

8

10

Insuredindividuals with positive expenditures, and assign each individual i with a dummy variable
med
Di,t,kwhere k indicates either a zero expenditure or the decile of medical expenditure (totalof 11 groups) in year t. The individual-level controls Xi,t include the number of reported
medical conditions, employment, and insurance status. Figure 3 plots the predicted valuesof Healthi,t(t+1) against the medical-expenditure deciles. Figure 3(a) is for the individuals
with bad initial health, and Figure 3(b) for those with good initial health. Both subplots
distinguish the insured (circles) from the uninsured (crosses).
The salient features in Table 3 and Figure 3 are as follows. First, Figure 3 shows that the
future good-health probabilities are monotonically decreasing in current medical expendituredeciles for all groups, after controlling for various medical conditions. It implies that a large
expenditure this period reflects the severity of the sickness shock a worker experienced.
Second, initial health status matters. From Table 3, we note that individuals with good
health incur lower medical expenditures and are less likely to utilize medical services compared to those with bad health. From Figure 3(a), we note that for the individuals with badinitial health, the predicted future good-health probabilities range from 0.15 to 0.42, while in
Figure 3(b), they range from 0.60 and 0.84 for those with good initial health. These patterns
suggest that individuals with good health experience milder sickness shocks and have higher
probabilities of future good health; i.e. the health status is persistent.
Finally, insurance status also matters. From Table 3, we see that 7%-10% of insured
individuals report zero medical utilization but 28%-34% of uninsured ones do, and the insured
individuals’ mean medical expenditure (conditional on positive) is almost twice as large as theuninsured individuals’. Meanwhile, Figure 3 shows that the uninsured have lower probability
21

of being in good health in the future than the insured in every single medical-expendituredecile, regardless of initial health status. These suggest that the variations across insurance
status in Table 3 are not because the uninsured are healthier, but potentially because they
are not able to receive sufficient medical care due to their lack of resources and access.
We summarize these patterns as the following empirical facts and utilize them to calibrate
worker-level parameters.
Empirical Fact 1. Initial Health, expenditures, and future health(a) Individuals with good health have lower medical expenditures and are less likely to utilize
medical services than those with bad health (Table 3).
(b) Conditional on characteristics, individuals with good initial health have higher probabilities of being in good health than those with bad initial health (Figure 3).
Empirical Fact 2. Insurance, expenditures, and future health(a) Insured individuals incur higher medical expenditures and are more likely to utilize
medical services than uninsured individuals (Table 3).
(b) Conditional on medical expenditures and characteristics, insured individuals have higher
probabilities of being in good health than uninsured individuals (Figure 3).

4.3

The Worker-Level Model (Inner Loop)

On the household side, the remaining parameters are those governing (i) the sickness shockprocess {ε (x) , f (ε; x)}; (ii) the health insurance {χ(ε, x), ζ(l), π}; (iii) the health production
F (H; x, ε); and (iv) the preferences {ι (x)}. We obtain the parameter values in (i) and (ii)from the data, outside the model, and calibrate the remaining ones of (iii) and (iv) within.
Sickness Shocks and Health Insurance Qualitatively, high medical expenditures in
MEPS imply severe sickness shocks, ε, in our model, as shown in Figure 3. Quantitatively,
however, there are two additional issues related to data availability. First, although inthe model, ε is distinct from medical expenditures, min {H, ε}, we only observe medical
expenditures in the data.18 Second, although we observe whether an individual utilized
medical services or not (lower panel of Table 3), it does not perfectly coincide with whether
an individual experienced a sickness shock this period. To address these issues, we assume
that individuals who are insured and employed (those most likely to have sufficient resources)
18

Although MEPS asks respondents their medical diagnosis akin to sickness shocks in our model, it isdifficult, if not impossible, to translate the diagnosis into a numerical value.

22

Table 4: Predetermined Parameters Regarding Sickness Shocks and Health Insurance
Parameter

Description

ε (x)Sickness shocksf (ε; x)

Probability

1 − χ (ε; x)

Coinsurance rateζ (l)Insurance prob.

π

Insurance premium

Bad
Good
Bad
Good
Bad
Good
Emp.
Unemp.

ε0
$0
$0
0.07
0.10
-

ε1
$370
$220
0.23
0.23
0.38
0.39

Valuesε2
ε3$1,454 $3,599$769 $1,877
0.23
0.23
0.23
0.23
0.33
0.28
0.39
0.34
0.82
0.63
$1,889ε4$9,446$6,453
0.23
0.23
0.20
0.23

Note: All statistics are from the MEPS data (1996-2014). The values of sickness shocks ε (x) are constructedfrom the predicted values of medical expenditures among the insured population after controlling for age,sex, race, education, Census region, marital status, and survey panel dummies. We use fourth quantiles
conditional on positive spending for values ε1 –ε4 by health status. The probabilities of not experiencing asickness shock f (ε0 ; x) are those of the insured individuals from MEPS-HC data as described in Table 3. The
coinsurance rate is calculated from MEPS using out-of-pocket expenditures and total medical expenditures,and the insurance premium is defined as a weighted average of sickness shocks, using f (ε; x) as weights.

choose full treatment of sicknesses, and that the uninsured face the same distribution ofsickness shocks as the insured.19 These assumptions are consistent with Empirical Fact 2.
Given these assumptions, we are able to use the medical expenditures for the insured andemployed from MEPS to parameterize the sickness shock process in our model, {ε (x) , f (ε; x)}.
As reported in Table 4 below, we discretize ε(x) into five events. We refer ε0 to the event ofbeing sickness free (i.e. ε0 = 0), and its frequency is given by the shares of the insured andemployed with no medical events as reported in the lower panel of Table 3 above. Then weconstruct the values and frequencies of the remaining four sickness events, ε1 through ε4 , byhealth status using within-quartile averages of medical expenditures conditional on positive
values. Table 4 shows that the individuals with bad initial health have more severe sickness
shocks (ε (B) > ε (G)) and a lower probability of not getting sick (f (ε0 ; B) < f (ε0 ; G)), as
consistent with Empirical Fact 1.
The parameters for the health insurance are straightforward to obtain from MEPS andare reported in Table 4. We note that first, the expenditure-dependent coinsurance rates,1−χ (ε; x), help us parsimoniously capture such components of insurance plans as deductibles
and out-of-pocket maximum. Second, the coinsurance rate decreases with the severity of thesickness, implying that health insurance is more useful for severe sickness shocks than for
mild ones. Lastly, although we do not directly model insurance for low-income people, such
19

Implicitly, we abstract away from adverse selection in insurance status.

23

as Medicaid, the unemployed in our model have a positive probability of having healthinsurance.20 These features help our model predictions match the pattern in the upper
panel of Table 3 that the mean medical expenditure is higher for the insured, and generate,
endogenously, the heterogeneous effects of the China shock across workers (see Section 6).
Target Moments and Identification We are now ready to use our worker-level model tocalibrate the remaining parameters for the health production function and preferences. Thisis the inner loop of our computation. In order to limit the number of parameters to calibrate,
we parameterize Hmin (x, ε) = s (x) · ε, with s (x) ≤ 1; i.e., within health status x, the levelof minimum health investment increases as ε increases, but its share relative to ε is constant.
Further, we normalize ι(G) = 0, leaving us with 17 parameters to be calibrated: α (x, ε),s(x), γ (x), λ (x), and ι (B). Meanwhile, our data targets are group-specific averages of (i)the sickness shock-dependent probabilities of tomorrow’s good health (analogous to Figure
3 but with five sickness shocks, 20 moments); (ii) the share of population with zero medical
utilizations (Table 3, 4 moments); and (iii) the average medical expenditures (Table 3, 4
moments). We jointly calibrate the 17 model parameters to target the 28 data moments.
In order to develop the intuition for how the parameters are identified, we first describe
the most salient effects of these parameters on targeted model moments. First, from Figure2(a), we see that an increase in α (x, ε) lowers the baseline probability of future good health,and so α (x, ε) are identified from the variation of the good health probabilities across sickness
sock ε and health status x. Second, both λ (x) and γ (x) impact the marginal benefits ofinvestment, but differentially. An increase in λ (x) compresses the effective health spending,H − Hmin (x, ε), and drags down the concave portion of F (·). On the other hand, forγ (x) < 1, an increase in γ (x) changes the curvature of the concave portion of F (·) byrotating this portion counter-clockwise around the point (Hmin (x, ε) + λ (x) , 1 − α (x, ε) /e).
Thus, λ (x) and γ (x) are identified from the variation in the mean medical expenditures andprobabilities of future good health across current health status. Lastly, an increase in theminimum share, s (x), directly impacts the share of workers who choose zero utilization. It
also decreases the probability of future good health for large sickness shocks, but has more
limited effects on those of small sickness shocks. On the preference side, ι (B) < 0 affects
the utility loss of being in bad health. An increase in ι (B), or a decrease in its magnitude,
increases the zero shares for the uninsured. As a result, s (x) and ι (B) are identified from20

The consumption floor in our model proxies for other social insurance policies for low-income individuals.

24the population shares of zero medical utilizations across health statuses.

4.4

The Sector-Level Model (Outer Loop)

We now relate the worker-side decisions to the market clearing condition in the manufacturingsector, Equation (12), and clarify how we introduce the China shock into our model.
First, we normalize the manufacturing sector productivity ψm to one, and as describedin the right panel of Table 2, set the sectoral home bias, ωm , to 0.5, and the trade elasticity,
σ − 1, to 3, following Simonovska and Waugh (2014).
Next, consider the pre-China-shock economy, where we take wm as exogenous (Table 2).
The labor supply, Lm , is pinned down by the workers’ optimal choices and their distribution,
as expressed in Equation (11). Our remaining task is to ensure that the right-hand sideof Equation (12) stays in balance. As listed in Table 2, ϕm is set to 0.17, the mean ofD= 0.85 ismanufacturing value added as a share of U.S. GDP for 1990-1992 (WDI), and πmthe average for the years 1990-1992 (STAN). This means that we are left with two unknowns,∗, and the total output in the economy Y , in Equation (12).
the export-demand shifter Dm

We thus bring in the extra equation of the model-implied ratio of manufacturing export
to Gross National Expenditure (GNE),∗
Dm· pm 1−σ
Manufacturing Export
=
.
GN E
Y

(13)

From STAN, we obtain that this ratio is 0.057 (the average for 1990-1992). We then use∗
equations (12) and (13) to back out the values of Dm
and Y that are consistent with thesolutions from the inner loop.
For the post-China-shock economy, we follow the sufficient-statistics approach in theDtrade literature, and model the China shock as an exogenous drop in πm
to 0.71 (the averagevalue for the post-China-shock years of 2010-2012). This approach allows us to be agnostic
about the specific sources of this shock, because the shock reduces labor demand for the manufacturing sector by the same degree, whether it is caused by a drop in p∗m (which may result∗
from an increase in foreign productivity), a drop in import cost τm, or combinations of thetwo. On the other hand, because we have remained agnostic about the non-manufacturing
part of the economy, our model is unable to predict how the China shock affects total output, Y . We expect such effects to be small, however, because the trade literature estimates
limited output gains from trade relative to autarky, a much larger change than the China
25

shock we model (e.g. Costinot and Rodriguez-Clare, 2014).21 Therefore, we assume that∗
there is no change in Y , as an approximation, and that Dmremains unchanged.

Under these assumptions, there are two endogenously determined outcomes in Equation(12), the wage rate wm and the total labor supply Lm . We use two approaches to simulate
the effects of the China shock, keeping the parameter values for the health production andworker utility functions at the pre-China-shock levels. In the first approach, we assume thatthe job continuation rates remain unchanged. Equation (12) allows us to solve for the postChina-shock wage that clears the labor market in Equation (11), using the labor supply, Lm ,from workers’ problems and that pm = wm . In the second approach, we allow both wm andjob continuation rates to change. In order to contrast with the first approach, we set thewage decline to be 2.3%, the lower end of the estimates from Autor et al. (2014), and search
for the change in 1 − δ (E, x) that balances equation (12).

5Calibration Results

In this section, we focus on our calibration results of worker-side parameters. We report anddiscuss the calibrated parameter values and model fit, show model validation, and clarify
the key model features.

5.1

Parameter Values and Model Fit

Table 5 reports the values of our calibrated parameters. In order to illustrate their intuition,
we plot the health production function, F (·), as implied by these parameters by sickness
shock in Figure 4 by initial health.
First, the ten baseline probability parameters, 1−α (x, ε), determine the vertical interceptof the health production function, F (·). We see that the vertical intercept is always above
0.5 in Figure 4(b) but always below 0.5 in Figure 4(a): the baseline probability of future
good health is high when current health is good. We also see that the vertical intercept
shifts down from ε0 through ε4 in both Figures 4(a) and (b), that is, the baseline probabilityof future good health is low when sickness is severe.
Second, the remaining six parameters of the health production function determine its
shape, which differs substantially across initial health status. This happens for two reasons.
One, the production function is more concave for bad initial health, because γ (B) is smaller
21

This literature examines the change in real GDP, which is closely related to Y , the real GNE.

26

Figure 4: Calibrated Health Production(a) Bad Initial Health(b) Good Initial Health($10K)
0.6($10K)
1

0.5

0.9

0.4

0.8

0.3

0.7
(No Shock)
0

0.2

1
2

0.1

3
4

0

0.6

($370)

1($1,454)2

0.5($3,599)3($9,446)

4

0(No Shock)($220)($769)($1,877)($6,453)

0.4
0

2500

5000

7500

10000

12500

0

2500

Investment

5000

7500

10000

12500

Investmentand λ (B) is larger than their counterparts for good health. Two, the ratio of minimum
health investment to ε for bad health, s (B), is smaller than that for good health, s (G),making the kink point of F (·) under bad initial health farther away from ε. The calibrated
production function implies that for bad health individuals, it is important to alleviate thesickness through medical expenditures, whereas for good health individuals, there is more
scope for forgoing treatment or doing over-investment.
Lastly, ι (B) implies that bad health is associated with a utility loss of about 60% ofconsumption, which is within the range of those in Low and Pistaferri (2015).22 We further confirm the validity of ι(B) in Section 5.2 by comparing the model-implied value of astatistical injury with empirical estimates from the literature.
Table 6 shows that our model generates reasonable fits on the target moments reported
in Table 3. For example, for the uninsured workers with bad initial health, the model
Table 5: Parameters Calibrated in the Model
Parameter Description
Health production
1 − α (x, ε)Baseline probability

Values

Bad
Good

λ (x)
Scale: Bad; Goodγ (x)Concavity: Bad; Goods (x)Min. inv. share: Bad; Good
Worker Utility
ι (x)Marginal utility: Bad; Good

ε0
0.244
0.658

ε1
ε2
ε3
0.193 0.142 0.107
0.587 0.532 0.524
2.411; 0.839
0.167; 0.757
0.467; 0.797

ε4
0.107
0.523

-0.931; 0 (normalization)

22

Low and Pistaferri (2015) estimates disutility effects from health and employment. Their estimates
imply between 36% and 66% loss in utility depending on the employment and health statuses.

27

predicted share of zero medical utilization is 0.27 versus 0.28 in the data.23 On medical
expenditure side, the model-predicted patterns of expenditures across worker characteristics
are qualitatively consistent with those of the data: conditional on health (insurance) statuses,
uninsured (good health) workers’ average expenditures are lower than those of insured (badhealth) workers. Figure 5 plots the future good health probabilities by initial health status,by insurance status, by sickness shock. We see that the model predictions (◦) track the datatargets (×) fairly well.24
Table 6: Model Fit on Targeted Moments

Average Medical Expenditures(positive only)
Share of Individuals
without medical utilizations

InsuredModel
Data$3,134$3,297$2,155$2,246
0.07
0.07
0.12
0.10

Bad
Good
Bad
Good

Uninsured
Model
Data
$1,802$1,755$1,545$1,294
0.27
0.28
0.34
0.34

Figure 5: Model Fit on Good Health Probability
Bad Initial HealthGood Initial Health(a) Insured(b) Uninsured(c) Insured(d) Uninsured
0.5

0.5

0.9

0.9

0.4

0.4

0.8

0.8

0.3

0.3

0.7

0.7

0.2

0.2
Model

0.6

Data

Model

0.1

Model

0.1
0

5.2

1

2

3

4

0.6

Data

Data

Model

0.5
0

1

2

3

4

Data

0.5
0

1

2

3

4

0

1

2

3

4

Validation of the Model

Having established the model’s good fit with targeted moments, we now test the empiricalvalidity of the calibrated model by comparing its predictions on the value of health andworkers’ health investment decisions with the corresponding untargeted data moments.
Value of Health We first aim to confirm whether the value of the calibrated parameter
ι(B), the utility loss from bad health, is plausible. Motivated by Hall and Jones (2007), who
23

It is the sum of the probability of not being sick (i.e. ε0 = 0) and the share of endogenously chosenzero treatment (H ∗ = 0 < ε).
24
Given the workers’ choices and coinsurance rates, the actuarially fair health insurance premium in theequilibrium is $2,260, close to the exogenously set premium of $1,889 (Table 4) from the MEPS data. In
counterfactual analyses, we use transfers to ensure budget neutrality of the government, incorporating the
gap between the health insurance premium and endogenously determined medical expenditures.

28

use the estimates of value of a statistical life (VSL) to calibrate the flow utility parameter intheir model, we compare our model’s prediction of value of a statistical injury (VSI) to theempirical estimates. We combine the CPS data with the BLS data on non-fatal injuries, andfind that a 1% increase in the industry injury risk is associated with a 0.37% reduction in
the workers’ probability of self-reported good health, conditional on worker characteristics.
The empirical estimate of VSI obtained from our data is around 3.3 times the average wage,or $153,000, which is comparable to those in the literature; e.g., Biddle and Zarkin (1988)
report VSI of 3.7 times the average wage and the corresponding estimate in Hersch andViscusi (1990) ranges between 3.3 and 5.4. Meanwhile, our model-predicted VSI is 3.8 times
the mean wage, or $176,000, given the conditional correlation between self-reported healthand injury risk discussed above. This prediction is similar to our estimate and within therange of the literature’s estimates.25
Income Elasticity of Health Investment We compare the model-predicted income
elasticity of health investment with the estimates from previous empirical studies. To doso, we use our model to simulate a temporary increase in income and evaluate their effects
on health investment. The average elasticity in our model is 0.47, in line with the rangeof estimates from previous studies (e.g. Acemoglu et al., 2013) of 0.3 to 1.1.26 Thus, theworkers’ quantitative responsiveness of health investment in response to income changes in
the model is in line with empirical studies.
Prevalence of Under -Investment An important model prediction is that workers may
endogenously choose to under-invest (partially treat or forego their sickness) in health. To
measure the prevalence of under-investment in the data, we utilize survey questions from the
NHIS data in 2011-2012 that ask whether the respondent missed or reduced medical care or
medicine doses due to cost.27 If an individual’s answer to any of these questions is “Yes,”
our indicator variable for under-investment in health turns on the value of one. We obtainthat, among the working-age adults (18-64) in the U.S., 18.6% under-invest in health. In
25

See also Viscusi and Aldy (2003) for estimates. The detailed description is contained in Appendix D.3.
Acemoglu et al. (2013) obtains the range of 0.3-1.1 for the income elasticity of hospital expenditure at the
U.S. Economic Subregion level, by instrumenting local income by global oil price and ESR-level importanceof oil in the economy. Other papers that estimate the elasticity are Moscone and Tosetti (2010),Baltagi andMoscone (2010), and Baltagi et al. (2017) and their estimates vary between 0.35 and 0.9.
27
These questions are not available for earlier years, and we stop in 2012 because the ACA went into
effect in 2014. We use questions that ask whether, due to affordability, the person restricted medical care
(PNMED12M), prescription medicine (AHCAFYR1), a specialist visit (AHCAFYR5), follow-up care (AHCAFYR6), skipped medication (ARXPR1), or took less medicine (ARXPR2).
26

29

comparison, our model predicted share of under-investment (those with ε > 0 and H ∗ < ε)is 18.9% in the pre-China economy, close to the empirical share from the NHIS.
Magnitude of Over -Investment The model also predicts that workers may endogenously choose to over-invest in health, in the amount of max {H ∗ − ε, 0}. From the data, it
is difficult to disentangle non-medical expenditures that help improve health (e.g., healthy
foods) from ordinary consumption expenditures. As a result, we compute the total nonmedical consumption of c + max {0, H ∗ − ε} in the model, which would be measured as thetotal consumption expenditures net of medical expenditures in the data. Using the recent
surveys of the PSID (1999-2013) that include consumption data, we show that among theemployed, the ratio of non-medical consumption to income is 70% for those with bad healthand 60% for those with good health.28 In the model, these ratios are 83% and 73%, respectively for bad and good health individuals, both in line with the data in terms of levels andthe differences across health statuses. That is, our model generates a reasonable non-medical
consumption to income ratio, even though this ratio is not directly targeted.
In summary, our model can replicate several untargeted moments about the value of
health and health investment. We provide additional validation for the post-China economy
in Section 6, but before doing so, we discuss the key features of our model.

5.3

Key Model Features

Our main model mechanisms revolve around the optimal health investment, H ∗ , which
consists of both medical expenditures, min {H ∗ , ε}, and non-medical expenditures beyond
the treatment of sickness, or over-investment, max {H ∗ − ε, 0}. We illustrate the key modelfeatures using Figures 6(a) through 6(d), which summarize health investment choices for
employed workers by health and insurance statuses.29 In the plot, we demonstrate, for eachsickness shock, the size of the sickness shock ε, the average medical expenditures min{H ∗ , ε},and the average health investment H ∗ . The unit of the vertical axis is $10K.
Over -Investment as a Channel for Self-Insurance In our model, bad health individuals experience a direct utility loss (ι(B)), lower probabilities of employment (1 − δ(l, B)),and lower wages (ν(B)). As a result, workers have incentives to self-insure against the future
28

As the PSID data records consumption at the household level, we use equivalent scale (0.7 for an
additional adult and 0.5 for an additional child) to adjust for family size. Our sample includes those who areemployed with positive labor income and we drop those with ratios in top and bottom 1% of the distribution.
29
We relegate the discussion of unemployed workers to Appendix D.2 as they are qualitatively similar.

30

Figure 6: Health Investment of Employed Workers
Bad Initial Health(a) Insured
10.8(b) Uninsured

Bad,Emp,Ins

Bad,Emp,Unins

1

Med.Exp
Investment

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

Med.Exp
Investment

0
0

1

2

3

4

0

Good Initial Health(c) Insured

1.5

2

3

4

(d) Uninsured

Good,Emp,Ins

2

1

Good,Emp,Unins

2

Med.Exp
Investment

1.5

1

1

0.5

0.5

0

Med.Exp
Investment

0
0

1

2

3

4

0

1

2

3

4

risk of landing in a bad-health state. Individuals with good initial health do so by investingin health beyond the full treatment of sicknesses (over -investment), which is the first novel
feature of our model relative to the literature. As illustrated in Figures 6(c) and 6(d), theaverage health investment exceeds the size of the sickness shock (H ∗ − ε > 0) regardless ofsickness severity and regardless of insurance status.
The quantitative magnitude of the over-investment depends on their marginal benefits.
As seen in Figure 4, the marginal benefit of health investment for good-health individuals
remains substantial even when the investment is large. As a result, the average amount ofover-investment in Figures 6(c) and 6(d) is typically large, exceeding $5K, except for theuninsured workers with the most severe sickness of ε4 . For individuals with bad health, theshocks of severe sickness are especially large (Table 4). As a result, the bad-health workers
are incentivized to over-invest when they are not sick or when they have mild sickness, as
illustrated in Figures 6(a) and (b). However, the amount of the average over-investment31

is much smaller than for good-health workers, because the marginal benefits to investment
decrease sharply in the health production function for bad-health workers.
Under -Investment and the Role of Health Insurance Another novel feature of ourmodel relative to the literature is that workers may choose to under-invest in health relative
to sickness, sacrificing treatment for consumption, especially when the cost of treatment ishigh. In our model, the cost of treatment is closely related to health insurance status andminimum investment for health.
First, health insurance has no direct effect on health in our model. Instead, it lowers themarginal cost of medical expenditures, allowing covered workers to leverage more resources
for treatment. Figures 6(a) and 6(b) illustrate this channel by showing the bad-healthworkers’ optimal choices of medical spending. The insured (Figure 6(a)) tends to fully treat
their sicknesses (average medical expenditure is very similar to the sickness shock), while
the uninsured (Figure 6(b)) under-invests (H ∗ < ε). The amount of the average underinvestment is modest, but becomes large for the most severe sickness ε4 , approaching $6K.
In addition, the health production function in our model has a flat segment, which saysthat a minimum investment is required before the benefits of health investment materialize.
For the good-health individuals, the minimum health investment is large relative to sickness(Table 5), and so many of them choose not to invest in health at all (Table 6). Figure 6(d)illustrates this channel for the uninsured workers when they face the severe sickness of ε4 .
We see that the average medical expenditure is lower than ε, because many choose zerotreatment (H ∗ = 0), due to the lack of resources and high minimum investment.
In summary, the flexibly parameterized health production function is a unique elementof our model, and it generates the novel features of over-investment and under-investment
in health relative to sickness, providing an additional channel for self-insurance. These features also help our model match the health dynamics, shares of individuals without medical
utilization, and average medical expenditures, as summarized in Empirical Facts 1 and 2.

6

Quantitative Analysis

In the previous section, we discussed the fit and key features of our calibrated model in the
pre-China shock economy. Now, we use the model as a laboratory to quantify the effectsof the China shock on workers’ health through the optimal health investment mechanism,
to compute the effects of the China shock on workers’ welfare, taking this mechanism into32

account, and to evaluate the effectiveness of potential policy responses.

6.1

The Post-China Economy

As discussed in Section 4.4, we simulate two versions of the China shock. In the first, wage
adjusts to clear the labor market in response to the China shock, and in the second, bothwage and job destruction rates adjust. Table 7 describes the main aggregate outcomes ofthe post-China economies in the manufacturing sector.
The first panel of Table 7 recaps the wage, employment rate, and export-GNE ratio of the
pre-China economy. The second panel shows that in our first simulation, the model predicts
a 5.78% drop in the wage rate of manufacturing workers. This is because the increase inimport competition from the China shock reduces demand for manufacturing labor, as canbe seen from Equation (12). The magnitude of the wage decline falls within the range of theestimates from Autor et al. (2014), 2.3% to 7.2%. We also see that the export-GNE ratio for
the U.S. manufacturing sector increases from 0.057 to 0.068. as the lower manufacturing wage
reduces the production cost of the domestic input. The value of the post-China export-GNE
ratio is comparable to the mean value for the years of 2010-2012 in the data, 0.077.
The last panel of Table 7 shows the results of our second simulation. We fix the wage
drop at 2.3%, the lower end of the estimates in Autor et al. (2014), and find that an increaseof 1.12pp in the job destruction rate balances the labor market clearing condition of (12).
Relative to the pre-China economy, the manufacturing sector employment rate drops by
2.8pp. With the manufacturing sector employment share of 15%, this implies that the ratioof manufacturing employment to population declines by 0.42pp, accounting for a substantial
portion of the effect of the China shock, 0.88pp, as reported by Autor et al. (2013).
Overall, the macroeconomic predictions of our model for the effects of the China shock areconsistent with both data and estimates from previous studies. These results provide further
validation of our model on post-China economy simulations and therefore, its suitability as
Table 7: Manufacturing Sector Outcomes in the Post-China Economy
Pre-China economy
Post-China I: Wage ⇓Change from Pre-China
Post-China II: Wage ⇓ & Job destruction ⇑Change from Pre-China

33

Wage
$50,211$47,308-5.78%$49,056-2.30%

Employment
72.5%
72.2%
-0.30pp69.8%-2.76pp

Export-GNE
0.057
0.068
+19.65%0.061+7.28%

a laboratory for analyzing its effects.

6.2

Mechanism: The China Shock and Health Investment

We now discuss the health effects of the China shock as predicted by our model. We start withthe aggregate effects and uncover the heterogeneity in its effects across worker characteristics.
6.2.1

Aggregate Effects

Table 8 summarizes the aggregate effects of the China shock. The second column summarizes
the key metrics about health and health investment in the pre-China economy, and the next
two columns show how these metrics change in the simulated post-China economies.
The top panel of Table 8 focuses on changes in the shares of workers with good health.
We see that, in the first post-China simulation, the good health share decreases by 1.2pp.
This means that the model-predicted elasticity of good-health share with respect to importpenetration per worker (IPW) is -0.0203. In Section 3.1, we have shown that the empiricalestimate of this elasticity is -0.054. That is, the mechanism of optimal health investment,
the only mechanism at work in our stylized model, accounts for around 38% of the estimatedempirical elasticity. In the second post-China simulation, the model-predicted elasticity islarger in magnitude, at -0.0282, accounting for 52.2% of the empirical estimate. These results
imply that the optimal health investment mechanism is economically significant in explaining
the health effect of the China shock, and that it might be important for understanding thehealth effects of other negative economic shocks. In comparison, the models that abstract
away from health or treat health transition as exogenous would be unable to shed light on
the health effect of the China shock (or other economic shocks in general).
The second panel of Table 8 clarifies the economic intuition of the results in the first
Table 8: The Effects of the China Shock on Health and Health Investment

Good health share
Implied elasticity(% of empirical elasticity, -0.054)
Total health investment, H ∗Medical expenditure, min {H ∗ , ε}Partial treatment share
No treatment share
Over-investment, max {H ∗ − ε, 0}

Pre-China
58.9%$5,140$2,35912.7%
6.2%$3,02434∆ from Pre-China Economy
Post-China I
Post-China II-1.2pp-1.7pp-0.0203-0.0282(37.6%)(52.2%)-6.8%-9.5%-11.6%-11.8%-0.0pp+0.9pp+1.3pp+0.9pp-10.6%-14.9%

panel, by showing the workers’ choices regarding the optimal health investment in the preChina economy, and how these choices change in the post-China simulations. We see that theamount of total investment, H ∗ drops significantly, by 6.8% and 9.5%, because both medical
expenditures and non-medical (over-) investment decrease substantially.30 The decrease of
medical expenditures, in turn, is closely related to the increase in the share of workers whochoose to under-invest relative to their sickness (H ∗ < ε). In particular, more sick workers
choose to forego all treatment (H ∗ = 0), increasing its share by 1.3pp and 0.9pp. Intuitively,
due to the minimum health investment, more workers who are on the fence between H ∗ ofzero and a slightly higher value than Hmin in the pre-China economy are pushed into choosing
H ∗ = 0 when the China shock hits. As a result, these workers’ medical expenditures change
substantially, from higher than Hmin to 0, contributing to the decrease in overall medical
expenditures. Additionally, over-investment in health decreases considerably, as the workers
who have fewer economic resources after the China shock cut back on the amount of nonmedical health investment.
We now place the aggregate health effect of our model into context. In the first postChina economy, the share of workers with good health decreases from 58.9% to 57.7%. Thistranslates into nearly half a million, or 460,000 individuals, being pushed into bad health,assuming that the manufacturing sector accounts for 15% of the U.S. population (251.6
million) in 1990-1992. According to MEPS, individuals with bad health have more frequent
visits to the emergency room (ER) than their good health counterparts—0.44 per person peryear versus 0.21—and also longer hospital stays—0.67 inpatient days per person per year,
versus 0.26. As a result, our model predicts that, in response to the China shock, the U.S.
manufacturing workers experience 103,000 more ER visits and spend 189,000 more inpatientdays in hospitals per year, causing economically significant aggregate health impacts.
6.2.2

Individual Heterogeneity

The aggregate effect analysis above masks substantial heterogeneity in individuals’ responses
to the China shock, which we discuss now. Given the qualitatively similar patterns in thetwo post-China simulations, we focus on the first simulation in the remaining analyses.
In Table 9, we show the change in good-health probabilities between the pre- and the30

Although the wage drop is mild in the second post-China simulation, the increase in the probability of
unemployment implies that the loss of overall economic resources is substantial.

35

post-China economy by worker characteristics.31 The left panel of Table 9 shows that thehealth effects of the China shock are more pronounced for workers with good initial health,both overall and within employment status. For example, employed workers with goodinitial health suffer a drop of 1.33% in good health transition probabilities, but those with
bad initial health suffer a drop of only one-third as much, about 0.46%. As seen in Figure
6, those with good initial health often choose to over-invest in health as self-insurance, andthey have a larger margin of response to the China shock. These predictions suggest thatthe decrease in the mean non-medical investment in Table 8 is largely driven by workers
with good initial health. This feature is also qualitatively consistent with our empiricalfinding from Table 1, where the coefficient estimate for the effect of the China shock is large
in magnitude and statistically significant for workers with good initial health, but small inmagnitude and statistically insignificant for those with bad initial health.
The right panel of Table 9 shows that the health effects of the China shock are more
pronounced for those who experience severe sickness, and conditional on sickness, those
who are uninsured. For example, while those with the severe sickness of ε4 see their goodhealth probability decrease by 2.22% on average, those who are sickness-free (ε0 ) experiencea mild decline of 1.48%. Among the former group, the decrease in good-health probability
is larger for the uninsured than the insured, 2.94% versus 2.04%. Intuitively, in our model,
the workers may optimally choose to over-invest in health relative to their sickness, andsuch over-investment decreases in response to the China shock. Thus, even the sickness-freeworkers (ε0 ) face a lower probability of good health. In addition, the drop in over-investment
is higher for those with severe sicknesses and for those without health insurance.
Table 9: Heterogeneity in Health Effects of the China Shock% Change in Transition to Good Health (from Pre-China)
By Initial Health and Employment
By Sickness Shock and Insurance
HealthAll Unemployed Employed Sickness All Uninsured Insured
All
-2.03
-2.04
-1.92
All
-2.03
-2.30
-1.95
Bad
-0.47
-0.49
-0.46
ε0
-1.48
-1.46
-1.48
Good -1.47
-1.93
-1.33
ε1
-1.87
-2.22
-1.78
ε2
-2.11
-2.07
-2.22
ε3
-2.15
-2.45
-2.06
ε4
-2.22
-2.94
-2.04
31

D
With πmof 0.71 and 0.85 in pre- and post-China economies, the elasticity is the percent change in good
health share divided by 93. The aggregate health effects in Table 8 reflect the intensive-margin effect fromgroup-specific elasticities, ∆Pr (G; s), and the extensive-margin effect from compositional changes, ∆µ (s).

36

6.3

Welfare: The China Shock and Welfare Cost

Having established the health effects of the China shock, we discuss the steady-state welfare
effects. We first present the benchmark welfare cost, where we compare the pre-China
economy with the first post-China simulation. Then, we present the welfare costs from twocounterfactuals, the exogenous health economy and the no-health economy, to understandand quantify the role of health investment and health in forming the welfare costs.
In the second column of Table 10, we summarize the benchmark welfare cost of the China
shock as a compensating consumption equivalent, the amount of consumption such that theworker’s lifetime utility in the post-China economy is the same as that in the pre-China
economy. The steady-state welfare loss amounts to 8.4% of average annual consumption in
the pre-China economy, or $1,721. There is also heterogeneity by worker characteristics. As
the China shock directly impacts the wages of employed workers, the welfare loss is higher
for the employed, at $1,989 of annual consumption, whereas for the unemployed, the welfare
loss is $966. Within employment status, the welfare loss is similar across health status.
The benchmark welfare cost captures both health and health investment featured in ourmodel. Health matters because the state of bad health carries both direct utility losses andeconomic consequences such as lower probability of employment and lower earnings whenemployed. Meanwhile, health investment serves as an additional channel for consumption
smoothing; e.g. sick workers who are already in bad health may have an incentive to sacrificesickness treatment for consumption.
To further understand the roles of these two model features in shaping the welfare effects, we first consider the counterfactual economy in which the workers are not allowed tochoose their health investment. We refer to this counterfactual as the “exogenous health
Table 10: Welfare Cost of the China Shock

Aggregate
Unemployed
Bad healthGood health
Employed
Bad healthGood health

BenchmarkEconomy$1,721
$966
$919
$974
$1,989$1,818$1,978Counterfactual Economy, Change from BM Cost
Exogenous Health Economy
No Health Economy
USD (% of BM Cost)
USD (% of BM Cost)+$173 (10%)-$452 (24%)+$196 (20%)-$205 (18%)+$281 (30%)+$138 (14%)+$157 (8%)-$512 (24%)+$298 (16%)+$181 (9%)-

37

Figure 7: The “Value” of Health Investment Channel (USD) by Worker Characteristics

economy.” To be specific, we assume that all workers experiencing a sickness shock of ε areforced to spend ε. That is, sickness shocks are equivalent to income shocks in the form of
medical expenses. This assumption implies that the exogenous health economy is consistent
with models with exogenous health evolution. We further assume that the workers’ healthtransition probabilities are equal to the model-predicted values in the pre-China economy.
The welfare effects from the exogenous health economy are summarized in the thirdcolumn of Table 10, expressed as changes from the benchmark welfare effects in the previous
column. In the aggregate, the welfare cost of the China shock is equivalent to an annual
loss in consumption of $1,895, which is $173 higher than the benchmark welfare cost. Thatis, because we have deprived the workers of a consumption-smoothing channel when facing
a negative economic shock, the welfare losses are higher, and this difference is about 10%of the benchmark welfare cost. Table 10 also shows that the additional welfare loss inthe exogenous health economy varies substantially across workers. For example, it is $281,
or 30% of the benchmark welfare loss, for the unemployed with bad health, over twice ashigh as the additional loss of $138, or 14%, for the unemployed with good health. These
additional welfare losses gauge how much the workers in our benchmark model value theconsumption-smoothing channel via endogenous health investment.
Figure 7 further highlights the heterogeneity in this value of health investment by plotting
the additional welfare costs in dollar values by health, employment, and insurance statuses.
It shows that the additional welfare losses are positive for all worker groups, implying that for
all the workers in our benchmark model, endogenous health investment provides an important38

buffer in the face of an adverse shock, even for employed and insured individuals. Figure
7 also shows that the value of endogenous health investment is especially high for workers
with bad health, as they have relatively fewer resources. As a result, abstracting away fromendogenous health investment would likely overstate the welfare losses, especially for workers
with bad health or with scarce resources. Overall, the results for the counterfactual of theexogenous health economy suggest that modeling endogenous health investment is significant
for measuring the welfare effects of the China shock, and may also be useful for studying
negative economic shocks in general.
We now move on to clarify how the second model feature, health itself, contributes tothe welfare losses from the China shock. To do so, we consider the counterfactual economy
in which health does not have any roles, the “no health economy.” To be specific, we set thelabor income and job transition rates to be averages across health status, and set the utility
loss from bad health and probability of sickness shocks to zero.
The results for the no health economy are presented in the fourth column of Table 10. In
the aggregate, the welfare cost of the China shock would be $1,270, substantially lower thanthe benchmark cost of $1,721, by 24%. For the unemployed workers, the no-health economy
underestimates the welfare loss by $205, or 18% of the benchmark loss, and for the employedworkers, the underestimation is $512, or 24%. The welfare losses are lower in the no-healtheconomy because the model does not capture the direct utility loss and the adverse labormarket outcomes associated with bad health. Therefore, abstracting away from health islikely to substantially underestimate the welfare losses from the China shock and potentiallyfrom other economic shocks.

6.4

Policy: Universal Health Insurance

In this section, we highlight the policy implications of our model. Specifically, we simulate apost-China economy in which all individuals are covered by health insurance with premiumand coinsurance rates specified in Table 4.32 This is a pertinent counterfactual to consider, as
the increase in import penetration from China was most pronounced between 1990 and 2007,
before the implementation of the major provisions of the ACA that subsequently expanded
insurance coverage. We report the results in the last column of Table 11, as changes relative
to the pre-China economy. The rest of Table 11 recap the results from Table 8, to place the32

We also impose budget neutrality, i.e., individuals receive lump-sum transfers so that the government’s
aggregate expenditure in the counterfactual economy is equal to that in the benchmark post-China economy.

39

results of the counterfactual into context.
In the aggregate, the population share of good-health workers would increase by 1.1pp
with universal health insurance (UHI), in contrast to the 1.2pp drop under the benchmark
post-China economy, i.e., UHI would fully remedy the adverse health effect of the China
shock. The economic intuition of this result is as follows. First, medical expenditure would
only drop by 0.2% under UHI, in sharp contrast to the 11.6% drop under the benchmark.
This reversal, in turn, is closely related to the large decrease in the share of workers choosing
no treatment, because for the workers who switch out of no treatment, medical expenditures
increase sharply, from 0 to above the minimum investment of Hmin . This effect throughmedical expenditures enhances the efficacy of UHI. On the other hand, the drop in the averageover-investment is similar to that in the benchmark at around 10%, as health insurance does
not cover non-medical investments in our model. This effect through non-medical investment
in health diminishes the efficacy of UHI. In the aggregate, with a relatively modest 5.8%
decrease in the wage, the first effect dominates making UHI an effective policy for mediating
adverse health effects.
Summarizing, we see that, because health insurance affects health through the investment
choice of workers, the overall efficacy of UHI is nuanced, and hinges upon the importanceof the loss in non-medical investments due to wage losses and the extent to which healthinsurance can compensate for such losses. To further clarify this, we study how the efficacyof UHI varies across commuting zones experiencing different exposures to the China shock.
We start by multiplying the percentiles of the distribution of the change in import penetration per worker, ∆IPW (e.g. $4,500 per worker, or 4.5 units, at the 75th percentile) by
the estimate of 2.14% per unit of ∆IPW (Table 9 of Autor et al., 2013), to obtain the percentiles of the distribution of empirically estimated wage changes (e.g. 4.5 × 2.14% = 9.7%
at the 75th percentile). We list these percentiles and wage changes in the first two columns
Table 11: Effects of Universal Health Insurance

Good health share
Total health investment
Medical expenditurePartial treatment share
No treatment share
Over-investment

Pre-China
58.9%$5,140$2,35912.7%
6.2%$3,024Post-China, ∆ from Pre-China Economy
Benchmark Economy Universal Insurance-1.2pp+1.1pp-6.8%-1.2%-11.6%-0.2%-0.0pp-0.51pp+1.3pp-4.0pp-10.6%-10.0%

40

Table 12: Effects of Universal Health Insurance by IPW Exposure∆IPW Percentile
5th
10th
25th
50th
Mean (53rd )
75th
90th
95th

Wage Drop (%)
0.2
0.4
2
5.5
7.3
9.7
15.8
21.7

% Population with Good Health(pp change from Pre-China)
Benchmark Insurance Universal Insurance
58.9 (-0.00)
60.2 (+1.26)
58.8 (-0.05)
60.1 (+1.21)
58.6 (-0.35)
59.8 (+0.90)
57.8 (-1.13)
59.2 (+0.24)
57.4 (-1.53)
58.8 (-0.11)
56.9 (-2.00)
58.3 (-0.60)
55.6 (-3.31)
57.1 (-1.85)
54.3 (-4.58)
55.9 (-3.07)

of Table 12. We interpret each percentile as a single commuting zone and simulate the effectof the China shock by feeding in the commuting zone specific wage drops exogenously. We
report the results of these simulations in the third column of Table 12 and perform the same
counterfactual UHI and present the results of these counterfactuals in the last column.
From Table 12, we see that the commuting zones with large drops in wages experiencelarge deterioration of health. For example, although the median commuting zone experiencesa drop of 1.1pp in the population share of good health, the 95th percentile commuting zone
has a sharp decline of 4.6pp, more than 8%. We also see that while UHI helps mitigate thesenegative health effects, the efficacy of the mitigation varies substantially across commuting
zones. For a commuting zone with a small wage decline (e.g. those below the median), UHI
delivers higher population shares with good health than the pre-China economy, more thanfully reversing the adverse health effect of the China shock. In contrast, for the commuting zone at the 95th percentile, even with UHI, the good health share would still drop by
3.1pp. This means that UHI would only remedy around 33% ((4.6-3.1)/4.6) of the healthdeterioration from the China shock. The intuition of these results is similar to that for Table
11. Relative to the benchmark post-China economy, UHI has little effect on the change inover-investment, but increases medical expenditure substantially. When the wage decline issmall, the increase in medical expenditure dominates. With large wage declines, however,the drop in over-investment dominates, limiting the overall efficacy of UHI.
In Figure 8, we investigate how the efficacy of UHI would vary by sickness shock. Figure8(a) plots the change in the good health probability relative to the pre-China economy
under benchmark insurance and under UHI by percentiles of ∆IPW among those with the41

Change in Transition to Good Health (pp)
-4
-2
0
2

Change in Transition to Good Health (pp)
-4
-2
0
2

Figure 8: Effects of Universal Health Insurance by IPW Exposure and Sickness(a) Moderate Sickness Shocks (ε2 )(b) Severe Sickness Shocks (ε4 )

th

5

th

10

th

th

th

25
50
Mean
75
Percentiles of ∆IPW Distribution∆ from Pre-China to Post-China with BM Insurance∆ from Pre-China to Post-China with Insurance for All-6-6∆ from Pre-China to Post-China with BM Insurance∆ from Pre-China to Post-China with Insurance for All
th

90

th

th

95

5

th

10

th

th

th

25
50
Mean
75
Percentiles of ∆IPW Distribution

th

90

th

95

moderate sickness of ε2 , and Figure 8(b) plots this change for the severe sickness of ε4 .33 In
both plots, the gap between the two bars measures the effectiveness of UHI. We see from
Figure 8(a), that among those mildly sick, the gap between the bars is small across the∆IPW distribution, in contrast to those with severe sicknesses in Figure 8(b). In otherwords, Figure 8 shows that for severely (mildly) sick individuals, UHI is (not) very effectivein mitigating the adverse health effects of the China shock.

7

Conclusion

In this paper, we develop a model with endogenous health dynamics to study the mechanism,
welfare consequences, and policy implications of the impacts of economic shocks on health.
A key innovation of our model is that workers may optimally choose to partially treat orforego treatment (under -invest), or invest beyond the full treatment of sickness itself (over invest). We use the China shock as our application and estimate its causal effect on workers’
probabilities of being in good health using micro-level panel data. Our estimates show thatthe elasticity of future good health probability with respect to IPW is around −0.05. We
then embed our worker-level model of health transition dynamics into a sector-level modelof international trade.
Our simulation shows that the health investment mechanism is quantitatively important,capturing about 40% of our empirical elasticity estimates. It generates an economicallysignificant aggregate health effect, pushing nearly half a million manufacturing workers into
bad health. In addition, the health effects of the China shock are heterogeneous across33

The graphs for ε0 and ε1 are similar to Figure 8(a), and the graph for ε3 is similar to Figure 8(b).

42worker characteristics, with larger effects among those with good initial health, consistent
with our empirical estimates.
In terms of welfare, our simulations suggest that the average worker’s loss is equivalent to a drop in annual consumption of $1,721. Importantly, the welfare losses would beover-estimated in an economy with exogenous health dynamics, and under-estimated in an
economy that abstracts away from health. Our evaluations show the significance of capturing both endogenous health investment and health itself in measuring the welfare costs fromnegative economic shocks.
Moving on to policy implications, we find that universal health insurance, if implemented
after the China shock, would provide a useful remedy for the adverse health effects, primarily
through the substantial reduction in the under-investment of health. However, since healthinsurance does not cover over-investment (non-medical expenditures in health), the efficacy
of universal health insurance would be fairly limited for workers with large exposure to the
China shock who suffer large wage losses, with the silver lining that it would still be highly
effective for the individuals with the most severe sicknesses. Our results speak to the recent
discussions about whether some form of universal health insurance would be beneficial for
the U.S. (e.g. Baicker et al., 2023; Einav and Finkelstein, 2023; Chen et al., 2024). These
analyses may also be relevant for the second China shock on the horizon, as the impacts ofChina’s excess industrial capacity may be felt around the globe, including in many middleincome countries with evolving healthcare systems.34
Finally, for future research, our modeling framework is more general than our applicationof the China shock, and so it is useful for studying other economic questions. For example, it
may be interesting to explore whether under-investment and over-investment in health may
contribute to the evolution of health inequalities and earnings, complementing recent works
by Hosseini et al. (2024) and De Nardi et al. (2023).

References
Acemoglu, Daron, Amy Finkelstein, and Matthew Notowidigdo, “Income and
Health Spending: Evidence from Oil Price Shocks,” The Review of Economics and Statistics, 2013, 95 (4), 1079–1095.
34

Quoting Janet Yellen, the U.S. Treasury Secretary, “China’s industrial policy may seem remote as we
sit here in this room, but if we do not respond strategically and in a united way, the viability of businesses
in both our countries and around the world could be at risk.” (Lawder, 2024)

43

Adda, Jerome and Yarine Fawaz, “The Health Toll of Import Competition,” The Economic Journal, 2020, 130, 1501–1540.
Aizawa, Naoki and Hanming Fang, “Equilibrium Labor Market Search and Health
Insurance Reform,” Journal of Political Economy, 2020, 128 (11), 4258–4336.
Autor, David, David Dorn, and Gordon Hanson, “The China Syndrome: Local Labor
Market Effects of Import Competition in the United States,” American Economic Review,
2013, 103 (6), 2121–68.
, , , and Jae Song, “Trade Adjustment: Worker-Level Evidence,” Quarterly Journalof Economics, 2014, 129 (4), 1799–1860.
Baicker, Katherine, Amitabh Chandra, and Mark Shepard, “Achieving Universal
Health Insurance Coverage in the United States: Addressing Market Failures or Providing
a Social Floor?,” Journal of Economic Perspectives, 2023, 37 (2), 99–122.
Baltagi, Badi and Francesco Moscone, “Health care expenditure and income in theOECD reconsidered: Evidence from panel data,” Economic Modelling, 2010, 27 (4), 804–
811. Special Issue on Health Econometrics.
Baltagi, Badi H., Raffaele Lagravinese, Francesco Moscone, and Elisa Tosetti,“Health Care Expenditure and Income: A Global Perspective,” Health Economics, 2017,26 (7), 863–874.
Biddle, Jeff and Gary A. Zarkin, “Worker Preferences and Market Compensation for
Job Risk,” The Review of Economics and Statistics, 1988, 70, 660–67.
Caliendo, Lorenzo, Maximiliano Dvorkin, and Fernando Parro, “Trade and Labor
Market Dynamics: General Equilibrium Analysis of the China Trade Shock,” Econometrica, 2019, 87 (3), 741–835.
Carroll, Daniel and Sewon Hur, “On the Heterogeneous Welfare Gains and Losses from
Trade,” Journal of Monetary Economics, 2020, 109, 1–16.
Chen, Charon, Zhigang Feng, and Jiaying Gu, “Health, Health Insurance, and Inequality,” International Economic Review, 2024.
Cole, Harold L., Soojin Kim, and Dirk Krueger, “Analyzing the Effects of Insuring Health Risks: On the Tradeoff between Short Run Insurance Benefits vs. Long Run
Incentive Costs,” The Review of Economic Studies, 2019, 86, 1123–1169.
Costinot, Arnaud and Andres Rodriguez-Clare, “Chapter 4. Trade Theory with Numbers: Quantifying the Consequences of Globalization,” in G. Gopinath, E. Helpman, and
K. Rogoff, eds., Handbook of International Economics, Vol. 4, Elsevier, 2014.
Currie, Janet and Brigitte C. Madrian, “Chapter 50 Health, Health Insurance and theLabor Market,” in “Handbook of Labor Economics,” Vol. 3, Elsevier, 1999, pp. 3309–3416.
Davis, Karen and Jeromie Ballreich, “Equitable Access to Care–How the United States
Ranks Internationally,” New England Journal of Medicine, 2014, 371 (17), 1567–70.
De Nardi, Mariacristina, Svetlana Pashchenko, and Ponpoje Porapakkarm, “The
Lifetime Costs of Bad Health,” NBER Working Paper No. 23963, 2023.
Einav, Liran and Amy Finkelstein, We’ve Got You Covered, Penguin Random House,
2023.
Ferriere, Axelle, Gaston Navarro, and Ricardo Reyes-Heroles, “Escaping the Losses
from Trade: The Impact of Heterogeneity and Skill Acquisition,” Working Paper, 2021.

44

Fonseca, Raquel, Titus Galama, Pierre-Carl Michaud, and Arie Kapteyn, “Accounting for the Rise of Health Spending and Longevity,” Journal of the European Economic Association, 2021, 19, 536–579.
Hall, Robert and Charles Jones, “The Value of Life and the Rise in Health Spending,”
The Quarterly Journal of Economics, 2007, 122 (1), 39–72.
Hersch, Joni and Kip W. Viscusi, “Cigarette Smoking, Seatbelt Use, and Differences inWage Risk Trade-offs,,” The Journal of Human Resources, 1990, 25 (2), 202–227.
Hosseini, Roozbeh, Karen Kopecky, and Kai Zhao, “How Important is Health Inequality for Lifetime Earnings Inequality?,” Working Paper, 2024.
Hummels, David, Jakob Munch, and Chong Xiang, “No Pain, No Gain: Work Demand, Work Effort, and Worker Health,” The Review of Economics and Statistics, 2023.
Kim, Soojin and Serena Rhee, “Understnading the Aggregate Effects of Disability Insurance,” Review of Economic Dynamics, 2022, 46, 328–364.
Lawder, David, “Yellen pushes for joint G7 response to China’s industrial overcapacity,”
Reuters, 21 May 2024.
Low, Hamish and Luigi Pistaferri, “Disability Insurance and the Dynamics of the
Incentive-Insurance Tradeoff,” American Economic Review, 2015, 105 (10), 2986–3029.
Lukas, Mahler and Minchul Yum, “Lifecycle Behaviors and Wealth-Health Gaps inGermany,” Econometrica, 2024, 92 (5), 1697–1733.
Lyon, Spencer and Michael Waugh, “Redistributing the gains from trade through progressive taxation,” Journal of International Economics, 2018, 115, 185–202.
Maccini, Sharon and Dean Yang, “Under the Weather: Health, Schooling, and Economic
Consequences of Early-Life Rainfall,” American Economic Review, 2009, 99 (3), 1006–26.
Moscone, Francesco and Elisa Tosetti, “Health expenditure and income in the UnitedStates,” Health Economics, 2010, 19 (12), 1385–1403.
Nielsen, Torben Heien, “The Relationship Between Self-Rated Health and Hospital
Records,” Health Economics, 2016, pp. 497–512.
Pierce, Justin and Peter Schott, “Trade Liberalization and Mortality: Evidence from
US Counties,” American Economic Review: Insights, 2020, 2 (1), 47–64.
Ruhm, Christopher J., “Are Recessions Good for Your Health?,” Quarterly Journal of
Economics, 2000, 115 (2), 617–650.
Schaller, Jessamyn and Ann Huff Stevens, “Short-run Effects of Job Loss on Health
Conditions, Health Insurance, and Health Care Utilization,” Journal of Health Eocnomcis,
2015, 43, 190–203.
Simonovska, Ina and Michael E. Waugh, “The elasticity of trade: Estimates andevidence,” Journal of International Economics, 2014, 92 (1), 34–50.
Sullivan, Daniel and Till von Wachter, “Job Displacement and Mortality: An Analysis
Using Administrative Data,” The Quarterly Journal of Economics, 2009, 124 (3), 1265–
1306.
Tauchen, George, “Finite State Markov-Chain Approximations to Univariate and Vector
Autoregressions,” Economics Letters, 1986, 20 (2), 177–181.
Viscusi, Kip and Joseph Aldy, “The Value of a Statistical Life: A Critical Review ofMarket Estimates Throughout the World,” Journal of Risk and Uncertainty, 2003, 27,
5–76.

45