debt market responses to longevity shocks

Debt Market Responses to Longevity Shocks

Zhanhui Chen Vidhan K. Goyal† Pingyi Lou‡ Wenjun Zhu§

August 3, 2021

Abstract

Unexpected increases in life expectancy induce life insurers to extend the durationof their assets, which results in significant purchases of long-term corporate bonds.We show that this variation in life insurer demand for bonds of specific maturities hasreal-economy consequences for corporate sector financing and investment policies. Aslongevity increases, long-term bond yields fall and the corporate sector absorbs suchshocks by issuing more long-term bonds, while simultaneously increasing investmentsin long-term assets. The effects are particularly marked where life insurers are theprimary holders of a firm’s debt. The response is also more pronounced for firms thatrely on long-term financing, and financially unconstrained firms.

JEL classification: G12, G22, G32, J11

Keywords: debt maturity, longevity risk, life insurers, bond yields, duration

Zhanhui Chen, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong [email protected]

†Vidhan K. Goyal, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, HongKong. [email protected]

‡Pingyi Lou, Fudan University. [email protected]§Wenjun Zhu, Nanyang Technological University, Singapore. [email protected]

1 Introduction

Although life expectancy is increasing worldwide, shocks to longevity are not always positive

or predictable. In the United States, life expectancy increased annually by 0.15 years on

average from 1974-2018. Yet the country experienced substantial year-to-year variation.

For example, life expectancy grew 0.47 years in 1975 and fell 0.18 years in 1993, while

the annual standard deviation of longevity shocks was 0.14 years.1 Longevity shocks affect

life insurance liabilities, as such liabilities arise from the sale of life-related and long-dated

products. Longevity increases, for example, extend claim periods for annuity holders that,

if unhedged, result in a duration mismatch. Thus, life insurers seek to shift to long-dated

assets to match the increasing duration of their liabilities.2

Corporate bonds constituted about 56% of life insurers’ invested assets in 2018. Ac-

cording to the Financial Accounts of the United States (Z.1), life insurers held, on average,

about 46% of all domestic nonfinancial corporate bonds outstanding during 1990-2018

(see Appendix B). Thus, we expect life insurers to primarily adjust the maturity of their

corporate bond portfolios in response to longevity shocks.3

This paper explores two questions: (1) how much longevity shocks affect pricing and

issuance of corporate bonds of specific maturities; and (2) how the corporate sector absorbs

these shocks. Given that life insurers are the largest holders of corporate bonds, we expect

1Unexpected longevity changes could be due to a confluence of factors affecting human life expectancy,including socioeconomic, environmental, health care, lifestyle, biological, and institutional factors (see,for example, Fuchs (2004), Shaw, Horrace, and Vogel (2005), OECD (2010), Mackenbach et al. (2008),Moreno-Serra and Smith (2015), and Chiu and Pain (2018)).

2Matching of asset-liability duration is also a regulatory mandate since unexpected changes in life ex-pectancy affect the duration risk of insurance liabilities. See NAIC (2017) and requirements under the “RiskManagement and Own Risk and Solvency Assessment Model Act.” The S&P risk-based capital (RBC) modelalso considers duration mismatch risk in its ratings.

3Life insurers could also respond to longevity shocks by adjusting their holdings in equities and treasuries(Chen, Lou, and Zhu (2020)).

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the insurance sector to be the primary channel through which longevity shocks affect

corporate bond markets. In particular, we are interested in examining whether life insurers’

maturity adjustments affect corporate term spreads and the duration of new corporate

debt issues. We are also interested in examining whether longevity-induced responses

in corporate bond markets determine long-term corporate investments and the overall

maturity of assets on corporate balance sheets.

We begin by empirically confirming that life insurers hedge duration mismatches from

longevity shocks by adjusting the duration of their corporate bond portfolios. We find strik-

ing comovements between the average duration of life insurers’ corporate bond portfolios

and changes in US life expectancy (see Figure 1). Further tests confirm that life insurers

increase duration of their bond portfolio by about 0.7 to 0.8 years for every one-year

increase in life expectancy. We also confirm duration adjustment results from active trades,

with life insurers significantly increasing purchases of long-term investment-grade bonds in

response to life expectancy increases.

The challenge in making a causal claim is the difficulty of isolating adjustment to bond

portfolios due to changes in life expectancy independent of credit market conditions and

macroeconomic variables. To overcome this challenge, we exploit the significant geographic

dispersion in longevity shocks. States differ in exposure to factors driving life expectancy,

with substantial geographic variation observable in pollution, changing weather patterns,

natural disasters, and even drug overdoses. Focusing on bond trades of “local” (state-level)

insurers, we find these trades respond to local longevity shocks rather than nationwide

economic conditions.

We next examine whether longevity shocks affect pricing and issuance of corporate

bonds of specific maturities. With limited arbitrage capital and the high cost of arbitrage

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across bonds with different maturities, a shift in life insurer demand for long-term corporate

bonds affects bond yields (Greenwood, Hanson, and Stein, 2010; Badoer and James, 2016).

Consequently, long-term financing becomes less costly when longevity increases. Corporate

issuers then “fill the gap” by issuing longer-dated bonds.

Here, we present three key results. First, we find yield spreads between long-term

and short-term bonds move inversely with changes in life expectancy. The decline in

corporate term spreads during a period of increasing life expectancy results in a substantial

aggregate response in the duration of new bond issues while positive longevity shocks bring

a significant increase in the weighted average duration of new corporate bond issues.

Second, we show that firms issue more long-term debt when life expectancy increases.

We also find that longevity risk is mainly conveyed to the corporate sector via the insurance

sector. Firms whose bonds are primarily held by life insurers exhibit significantly pronounced

supply elasticity. Furthermore, the response is mainly from investment-grade issuers

consistent with life insurers’ demand for highly rated bonds to comply with regulatory

requirements.

Finally, results confirm expectations that longevity shocks disproportionately affect

credit availability for firms more dependent on long-term debt; and that financially uncon-

strained firms have the flexibility to absorb demand shocks in the long-term segment of the

corporate debt market. We also show that these firms invest relatively more in research

and development, increase capital expenditures, and exhibit higher property, plant, and

equipment growth. In short, we find that longevity shocks improve credit availability for

firms with two real consequences. Firms that can more readily supply macro liquidity to

long-term corporate debt market issue more long-term bonds and deploy the proceeds to

fund long-term assets. And longevity shocks disproportionately increase the maturity of

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assets at firms with a preference for long-term debt and those with fewer constraints in

accessing debt markets.

As such, the evidence in this paper collectively supports the view that longevity risks

have significant consequences for corporations’ financing and investment policies, with

the insurance sector, traditionally a considerable buyer of corporate bonds, as the primary

channel. Overall, we show longevity shocks increase demand for long-term corporate debt,

significantly impacting the real economy by reducing long-term debt financing costs and

stimulating long-term investment.

Our paper makes several contributions to the literature. We provide new evidence on

the effect of longevity shocks that propagate to corporate debt markets via the life insurance

sector. Thus, we contribute to the literature that examines corporate debt maturity choices

when bond market returns have some predictability in partially segmented bond markets

with limited arbitrage. Greenwood, Hanson, and Stein (2010) articulate the “gap-filling”

theory of corporate debt maturity choice and show that firms act as macro liquidity providers

to absorb the supply shocks resulting from changes in the maturity structure of government

debt. Badoer and James (2016) examine debt issuances demonstrating changes in the

supply of long-term government debt affect corporate issuances of long-term debt. Other

papers focus on market segmentation and the effect of changes in the supply of Treasury

securities on corporate borrowing costs (Greenwood and Vayanos, 2010; Krishnamurthy

and Vissing-Jorgensen, 2011; Vayanos and Vila, 2020).4 Although the mechanism exploring

how these shocks transmit to the corporate sector is similar to Greenwood, Hanson, and

Stein (2010), we focus on a demand shock that arises from regulatory requirements that

4There is also a broader literature examining the effect of the investors’ demand on asset prices (Koijenand Yogo, 2019; Koijen, Richmond, and Yogo, 2020; Bretscher et al., 2020). Chaderina, Weiss, and Zechner(2021) consider dynamic corporate debt maturity and leverage choices with a time-varying market price ofrisk. They show firms with long-term debt are riskier.

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life insurers minimize their duration risks, demonstrating the importance of this insurance

sector in transmission of exogenous shifts in life expectancy to the financing and asset mix

of the corporate sector.

We also complement the existing literature on factors determining the composition of

life insurers’ bond portfolios. Several recent papers show life insurers tilt their corporate

bond portfolio toward longer-dated bonds in a low-interest-rate environment (Domanski,

Shin, and Sushko, 2017; Yu, 2020; Ozdagli and Wang, 2020). Similarly, Becker and Ivashina

(2015) find insurers invest more in riskier bonds within a credit rating category, especially

during economic expansions. The literature also indicates regulatory constraints affect life

insurers’ bond holdings. Ellul, Jotikasthira, and Lundblad (2011) show relatively more

constrained life insurers engage in fire-sales of downgraded bonds because of regulatory

constraints leading to price pressure. Ge and Weisbach (2020) show property and casualty

insurers invest in safe bonds following losses. Sen and Sharma (2020) demonstrate insurers

increased holdings of illiquid bonds during and after the financial crisis. In contrast to this

literature, we show regulatory constraints increase demand for long-term debt when life

expectancy increases, offering new evidence on the effects of longevity shocks on term

spreads and long-term bond issues.

Finally, we add to studies examining implications of demographic shifts on asset prices

(Bakshi and Chen, 1994; Poterba, 2001; Goyal, 2004; Ang and Maddaloni, 2005; Geanakop-

los, Magill, and Quinzii, 2004; Favero, Gozluklu, and Tamoni, 2011; Chen and Yang, 2019),

and sensitivities to those shifts (DellaVigna and Pollet, 2007, 2013; Koijen, Philipson, and

Uhlig, 2016; Koijen, Nieuwerburgh, and Yogo, 2016; Maurer, 2018), by providing new

evidence on how demographic changes determine the duration of insurers’ bond portfolios

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and affect corporate bond markets. We also study bond maturity choices while previous

studies usually assume long-lived assets.

2 Data and Variables

Our empirical analyses rely on data from several sources. We obtain the detailed mortality

and population data from the Human Mortality Database and United States Mortality

Database.5 The data on credit market conditions and macroeconomic variables are from

the Federal Reserve Economic Data (FRED) website. We obtain life insurer data from the

National Association of Insurance Commissioners (NAIC) filings from 1995-2019. From

NAIC “Schedule D” fillings, we obtain insurers’ bond holdings, including the issuer’s name,

bond characteristics, and holding size. Schedule D transaction data provide us with date-

stamped trades along with trading prices, the size of transaction, and direction of trade.

Information on new corporate debt issues by US nonfinancial firms is from the Mergent Fixed

Income Securities Database (FISD). Financial data on bond issuers are from Compustat.

We merge Compustat to FISD using issuer CUSIPs and company names.

We use the Human Mortality Database (HMD) to estimate longevity risks for the US

population from 1974-2018. First, we obtain the average of a population’s period life

expectancy (Et) in year t, weighted by corresponding exposure, as follows:

Et =

∑99x=0(x + ex ,t)Ex ,t∑99

x=0 Ex ,t

, (1)

5Human mortality data is available at https://www.mortality.org. See Mila (2019) for more details.United States mortality data are available at https://usa.mortality.org.

6

https://www.mortality.org

https://usa.mortality.org

where ex ,t is the remaining period life expectancy for a person aged x in year t, and Ex ,t is

the corresponding exposure of cohort x . We restrict the age range to 0-99 years as data for

ages over 100 are not as reliable.6

Second, we estimate longevity risk (LongevityRisk) as the change in weighted average

of period life expectancy, i.e., Et - Et−1. We similarly construct state-level longevity shocks

(LocalLongevityRisk) using state-level mortality data over the 1989-2018 period from the

United States Mortality Database. Both LongevityRisk and LocalLongevityRisk are easily

interpretable, model-free measure of longevity shocks across all ages over time.7

Longevity shocks are economically large. Summary statistics reported in Table 1, Panel A

show that nationwide longevity shocks have a mean of 0.15 years annually over 1974-2018,

with a standard deviation of 0.14 years per year. State-level longevity shocks average about

0.10 years per year, and are substantially more volatile (a standard deviation of 0.21).

— Table 1 about here —

Panel B shows aggregate bond market variables over 1990-2019, with credit spread

(CreditSpread) measuring the spread between percentage yields of Moody’s Seasoned Baa

Corporate Bond Index and 20-year Treasury securities (mean=2.07%). Changes in one-year

Treasury yields (∆Treasury-1Y) average -0.21%, reflecting the overall low-interest-rate

environment over this period. The term spread (TermSpread) is the spread between the

percentage yields of 10- and one-year Treasury securities (mean=1.42%). We also use the

orthogonalized term spread (Term spread⊥), estimated as residuals from a regression of

6The results were not materially different if we restricted our sample to working ages of 20-65 years.7Lee and Carter (1992) present an alternative measure of the latent mortality index. The Lee-Carter

measure and the one we use are highly correlated and yield qualitatively identical results.

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term spread on longevity risk. Term spread⊥ has a mean of 0.57%. Excess bond premium

(EBP), which captures bond market sentiment, has a mean of 0.11%.8

Average annual changes in the yield spread between long- and short-term bonds

(∆CorpTermSpread) is 0.03%, where long-term (short-term) bonds are defined as bonds

with maturities over 10 years (under three years). On average, the amount of long-term

bond issues are about 5.2 times greater than new short-term bond issues (LTtoSTDebt). The

mean change in the weighted average duration of new bond issues (∆NewBondDuration)

is about 0.04 years.9

Panel C focuses on life insurer characteristics, showing life insurers are large (mean

assets = $6.66 billion; median = $338 million), highly levered (average total liabilities-to-

assets ratio, InsLeverage, of 0.73), and profitable (return on assets, InsROA, of 2%), with

an average risk-based capital (InsRBC) ratio of 17.57.10 Almost 55% of bonds held by life

insurers had a NAIC 1 designation (the highest quality), 27% were NAIC 2, while the rest

were NAIC 3 or higher, indicating life insurers mostly invest in investment-grade bonds.11

The average bond portfolio duration change (∆InsDuration) was 0.04 years.

8For more details on EBP, see Gilchrist and Zakrajšek (2012) and López-Salido, Stein, and Zakrajšek(2017). The data are available at www.federalreserve.gov/econresdata/notes/feds-notes/2016/files/ebp_csv.csv.

9We weigh the duration of new bonds by issue size. In estimating the Macaulay duration of bonds, weignore bond features such as callability and convertibility. While it introduces noise, it also biases our resultstowards zero.

10According to NAIC Risk-Based Capital Guidelines, risk-based capital (RBC) is the ratio of total availableregulatory capital (Assets - Liabilities) to total required capital. We obtain the required capital by multiplyingthe book value of a bond holding with the appropriate risk weight, depending on the bond’s credit rating.The RBC ratio is a key metric used by state regulators to determine an insurer’s capital adequacy.

11NAIC Securities Valuation Office assigns NAIC designations to bonds on a scale of 1 to 6 based on creditratings by approved agencies (see Appendix C). Higher NAIC designation bonds are of lower credit quality.Hence, according to RBC requirements, an insurer must hold more capital to cover expected losses on thatsecurity. To maintain capital adequacy, insurers primarily invest in investment-grade bonds (i.e., bondsdesignated NAIC 1 or 2). See Ellul, Jotikasthira, and Lundblad (2011) and Murray and Nikolova (2021).

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www.federalreserve.gov/econresdata/notes/feds-notes/2016/files/ebp_csv.csv


Panel D shows that bond issuers are large, with mean Assets of $6.67 billion (me-

dian $906 million). Average growth in long-term debt (LTDebtGrowth) is 8%, with R&D

(R&DIntensity) and capital expenditure (CAPEX) representing 2% and 9% of total assets,

respectively. Average growth rate of plant, property, and equipment (PPEGrowth) is 3%.

Firms have an average ROA of 16%, Tobin’s q of 1.63, and tangibility of 46%. Average

long-term debt dependence (LTDebtDep), measured as the ratio of debt with maturities

over five years to total debt, is 52%.

3 Insurer bond duration adjustments

3.1 Life insurers’ response to longevity shocks

If increases in life expectancy extend the duration of insurer liabilities, life insurers need to

purchase longer-dated securities to match their extended liabilities. We expect much of the

adjustment to be in corporate bonds since these bonds constitute a significant fraction of

life insurers’ assets. Figure 1 plots time-series changes in the average duration of corporate

bonds on life insurers’ balance sheets and changes in weighted life expectancy of the US

population over 1995-2019 (ensuring changes in weighted life expectancy lag the changes

in bond duration by at least two quarters). This reveals a striking positive comovement

between the two series (ρ=0.32), consistent with a strong bond duration response to

longevity shocks.

— Figure 1 about here —

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However, as Figure 1 compares changes in the two series over time and does not control

for insurer characteristics, credit market conditions, and other macroeconomic factors, we

also estimate the following panel regression:

∆InsDurationi,t = β · Longevi t yRiskt−1 +X′

i,t ·λ+ Z′

t · γ+ ζInsurer + εi,t , (2)

where ∆InsDuration is the change in duration of corporate bond portfolio of life insurer

i in year t; Xi,t is a vector of insurer characteristics; Zt is a vector of macroeconomic

variables; ζInsurer are insurer fixed effects; and εi,t is an idiosyncratic error. Vector Xi,t

includes: the natural log of insurer assets (Ln(InsAssets)); leverage (InsLeverage); risk-

based capital ratio (InsRBC); profitability (InsROA); and growth of net premium written

(InsNPWGrowth). Vector Zt includes the following state-level and aggregate economic

indicators: inflation measured by the growth of the Consumer Price Index (CPIGrowth);

US GDP growth (GDPGrowth); state GDP growth (StateGDPGrowth); state population

growth (StatePopGrowth); credit spread (CreditSpread); changes in one-year Treasury

yield (∆Treasury1Y); and term spread (TermSpread). We include these controls given

that macroeconomic variables and credit market conditions could affect bond duration

choices, and may also be correlated with changes in life expectancy (Cutler, Deaton, and

Lleras-Muney, 2006; Acemoglu and Johnson, 2007).


Table 2 reports the results. Column (1) shows that life insurers increase the duration of

their bond portfolio by about 0.69 years for every one-year increase in nationwide longevity

(p<0.01). As longevity risks affect term spreads, we use orthogonalized term spread in

column (2) to separate the effects of term spreads from longevity risks on bond portfolio

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duration. We find life insurers increase the duration of their bond portfolio by about 0.78

years for every one-year increase in longevity. In either case, the response is large and

relatively quick, confirming life insurers hedge longevity-induced shocks to the duration of

their liabilities.12

Given our expectation that more constrained insurers would find it relatively more

costly to adjust their duration structure as they face a steep capital supply curve in adjusting

their asset portfolio, we test whether small insurers (likely to be more constrained) exhibit

a more muted response to changes in life expectancy. We perform annual sorts of insurers

based on median assets and then separately estimate Equation (2) for large insurers in

column (3) of Table 2 and for small insurers in column (4). As predicted, results show large

insurers increase bond portfolio duration by almost 0.91 years for a one-year increase in life

expectancy, while the corresponding response for small insurers is 0.47 years, suggesting

large insurers are considerably more responsive to longevity shocks.

Insurers also differ in the composition of their liabilities. This matters because life

insurance and annuities naturally hedge each other and attenuate the effects of longevity

risks on insurers’ balance sheets (Cox and Lin, 2007). To address whether insurers with

product portfolios offering natural hedges react less to longevity risks, we first estimate the

ratio of direct premium written (DPW) of the life insurance business to premiums collected

from both life insurance and annuities. We then simulate the variance of insurer liabilities

to longevity shocks over the whole range of premium share between life insurance and

annuity businesses. Appendix D provides the details. Findings indicate liability portfolio

12In Appendix E, we show the results hold when we examine various subperiods. They are also robust toadditional controls for business cycle effects, and other institutional investors’ holdings of corporate bonds.Specifically, Appendix E.1 presents results for the subperiods 1995-2005 and 2006-2019. Appendix E.2controls for business cycle effects. Appendix E.3 controls for corporate bond holdings by other institutionalinvestors.

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variance is minimized when the share of premiums collected from life insurance is 81.9%.

However, the typical insurer’s average is 31.6% in our sample, i.e., far from naturally

hedged.

We define deviation as the absolute difference between an insurer’s life insurance

premium share and the natural-hedge share estimated from the simulation. Insurers with

above-median deviation are more exposed to longevity shocks, while those with below-

median deviation are less exposed. Columns (5) and (6) of Tables 2 show that more exposed

insurers make significantly larger adjustments to changes in life expectancy, with duration

increasing by 0.88 years for a one-year increase in life expectancy. By contrast, more

hedged, less exposed insurers adjust duration by only 0.47 years, a statistically significant

difference at the 1% level.

Thus, these results overall support the view that longevity increases induce life insurers

to increase the duration of their corporate bond portfolios, and that longevity risks produce

more extensive bond duration adjustments from less constrained and more exposed insurers.

3.2 Life insurer trades in corporate bond markets

The analysis so far suggests that the duration of bonds on life insurers’ balance sheets moves

almost one-to-one with changes in life expectancy. To examine if insurers accomplish this

through active trades of bonds of specific maturities, we focus on changes in net purchases

of both long and short-term bonds. We define NetBuyLTBonds as purchases (net of sales) of

long-term bonds (10 years or more) scaled by the market value of insurer’s bond portfolio.

Similarly, we define NetBuySTBonds as purchases (net of sales) of short-term bonds (three

years or less). As insurers primarily hold investment-grade bonds because of risk-based

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capital requirements, we further separate trades by NAIC rating designations. Hence, we

expect insurer trades to concentrate on NAIC 1 and 2, the investment-grade categories.


Table 3, Panel A presents results from regressions where the dependent variable is

∆NetBuyLTBonds. Column (1) shows a one-year increase in life expectancy increases net

purchases of long-term bonds by 8.7% (p<0.01). In columns (2) to (7), we dis-aggregate

bond purchases by NAIC rating and examine the duration response by rating category.

Here, the dependent variable is each NAIC designation’s contribution to net purchases of

long-term corporate bonds. Although we find a significant trading response to longevity

risks in all rating designations, the evidence strongly suggests that much of the effect is

concentrated in investment-grade bonds. A one-year increase in longevity increases net

purchases of long-term bonds rated NAIC 1 and 2 by 2.4% and 2.2%, respectively, while

the same increase in longevity increases net purchases of long-term bonds rated NAIC 6

by only 0.3%. In Panel B, we report results for net purchases of short-term bonds (with a

duration of less than three years). We find no clear pattern in trades of short-term bonds. If

anything, there is weak evidence that insurers sell high-quality short-term bonds in response

to increases in life expectancy.

Overall, results show that insurers actively hedge duration risk by purchasing long-term

bonds when longevity increases, with their duration adjustment concentrated on highly

rated bonds.

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3.3 Local longevity shocks and insurer trades

While our tests controlled for both macroeconomic variables and credit market conditions,

it remained possible that unobservables might be affecting results rather than longevity

shocks. For example, insurers might be trading bonds due to yield expectations instead of

longevity shocks.

To address these concerns, we exploit the substantial geographic dispersion in longevity

shocks across the US. Figure 2 provides snapshots of state-level longevity risks at four

different points corresponding to the year at the end of each decade. Each map displays

the extent to which life expectancy increased or fell in a state in that year. Darker shading

indicates more significant increases in life expectancy, while lighter shading represents

more significant declines.


The maps indicate substantial cross-sectional variation in shocks to longevity at the state

level, consistent with extensive literature documenting significant geographic disparities in

mortality within the US (Ezzati et al., 2008; Dwyer-Lindgren et al., 2017; Li and Hyndman,

2021). States differ in how demographic, economic, political, and legislative processes

evolve, and these perhaps contribute to differences in mortality outcomes. They also

differ in exposure to factors that drive life expectancy. In particular, we observe significant

geographic variation in pollution, changing weather patterns, natural disasters, and drug

overdoses across states.13 Unreported tests suggest local measures of these environmental13There is extensive evidence that these factors affect mortality. Bunker et al. (2016) found elevated

temperature-induced risks for the elderly, including cerebrovascular, cardiovascular, and respiratory outcomes.The World Health Organization and International Actuarial Association estimate significantly higher mortalitybecause of climate change. Other research documents higher death rates in certain US states due to frequentand severe extreme natural hazards. According to Hedegaard, Miniño, and Warner (2018), drug overdose isa significant contributor to the decline in life expectancy in the US.

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variables are significantly correlated with state-level mortality risk.14 More importantly,

changes in life expectancy are positively correlated in some states and negatively in others.

For example, longevity risks in Florida and Georgia are most correlated (ρ = 0.88), while

Massachusetts and Alaska exhibit the lowest correlation (ρ = -0.27).

Variation in longevity risks correlations across states enables test that explore whether

life insurers trade because they anticipate yield changes or need to hedge changes in liability

duration caused by local longevity shocks. If life insurers responded to anticipated yield

changes, they would react similarly to macroeconomic factors since bonds are traded in

national markets. However, if they adjust bond durations to hedge longevity-induced

duration mismatches, those trades would respond to the direction of state-level longevity

shocks. Thus, we examine whether two life insurers located in two states with negatively

correlated longevity shocks trade the same bonds in the same direction, as they would

if responding to nationwide economic variables. Or, if they make opposite trades due to

negatively correlated local longevity shocks.

First, we establish many life insurers are geographically concentrated and derive much

of their revenues from their headquarter state, classifying insurers generating at least 80%

of their revenue from a given state as local life insurers. Second, we establish life insurers

respond to local longevity shocks (see Appendix E.4). If longevity risks affect how insurers

trade bonds, life insurers located in states with opposite longevity shocks should trade a

given bond in opposite directions. However, if anticipated yield changes drive bond trades,

life insurers would trade the same bond in the same direction regardless of state-level

14For example, the PM2.5 measure of pollution has a correlation of -0.33 with increases in life expectancy.Similarly, state-level deaths from a drug overdose per 100,000 population have a -0.40 correlation withlongevity shocks.

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longevity shocks. We test this prediction by examining the trading directions of two life

insurers over a bond and report the results in Table 4.


The dependent variable is a trading direction indicator that equals one if two local life

insurers trade the same bond in the opposite direction and 0 otherwise. The key variable

of interest in column (1) is the correlation of these two life insurers’ local longevity risks

(LongevityCorri, j). In column (2), we use a dummy variable (SimilarLongevityRiski, j), which

equals one if two states have longevity shocks either above or below the sample median

simultaneously in a year, and 0 otherwise. The tests control for credit market conditions

(Credit spread, ∆Treasury1Y, Term spread), state characteristics (state GDP growth, state

population growth), and life insurer characteristics (risk-based capital ratio (InsRBC),

leverage (InsLeverage), return on assets (InsROA), growth rate of net premium written

(InsN PW Growth), and size (Ln(InsAssets)). Columns (3) and (4) further control for year

fixed effects.

Table 4, column (1) shows the coefficient on LongevityCorri, j is negative and statistically

significant (p<0.01), suggesting local life insurers make opposite trades when faced with

negatively correlated local longevity shocks. In column (2), a metric that captures the

similarity of longevity shocks across states again finds a negative and statistically significant

coefficient on SimilarLongevityRiski, j, confirming life insurers make opposite trades when

the states where they are located have dissimilar longevity shocks. Substituting time-varying

macroeconomic variables with year fixed effects yields almost identical results.

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Overall, we conclude life insurers’ bond trades respond to local longevity shocks and

insurers trade the same bond in the opposite direction when faced with negatively correlated

local longevity shocks.

4 Effect of longevity risks on bond markets

As noted earlier, life insurers are significant holders of corporate bonds. Although maturity

is an important determinant of bond yields, corporate bond term spreads flatten as life

insurers shift their demand for long-term bonds in response to increases in longevity and

arbitrageurs with limited capital are unable to bridge markets across different maturities.

(Greenwood and Vayanos, 2010; Vayanos and Vila, 2020).15 In deciding whether to issue

at short or long-maturity, corporations consider differences in financing costs. If yields on

long-term debt fall relative to yields on short-term debt, corporations respond by issuing

more long-term debt, provided the cost of deviating from their maturity target is modest.

Corporate issuers thus vary the maturity of the debt issued to absorb shocks resulting from

life insurers’ hedging needs. Our questions in this section are: if changes in life expectancy

cause shifts in demand for bonds of specific maturities, whether corporate bond term

spreads decline as longevity increases; and whether issuers absorb these demand shifts by

issuing more long-term debt.

4.1 Aggregate evidence

First, we examine the aggregate time-series behavior of corporate bond term spreads to

see whether yields on long-term bonds fall relative to yields on short-term bonds during

15See Huang and Shi (2021) for a recent review on the determinants of corporate bond returns.

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periods of increasing life expectancy. Figure 3 plots changes in yield spreads between

newly-issued long and short-term bonds against longevity risk over 1990-2019, indicating

the two series move opposite to each other.16 They correlate -0.23, consistent with longevity

risks propagating to bond markets and affecting bond yields. The most plausible mechanism

for the negative correlation is increases in life expectancy result in life insurers increasing

their demand for long-term bonds, as shown in Table 3. As a result, yields on long-term

bonds decline relative to those on short-term bonds.


We next examine if this negative relation holds once we control for relevant macroeco-

nomic and bond market variables, in particular inflation (CPIGrowth), economic growth

(GDPGrowth), risk premiums in bond markets (CreditSpread), interest rate changes (∆Treasury1Y),

treasury term-spread (TermSpread), and a measure of bond market sentiment (excess bond

premium EBP).17 The results in Table 5, column (1) show changes in term spread between

long and short-term corporate bonds decline with longevity risk, while other control vari-

ables are insignificant.18 Overall, the results indicate changes in life expectancy lower

corporate bond term spreads.

— Table 5 about here —16We define a bond as long-term if it has a maturity of 10 years or more and short-term if it has a maturity

of three years or less.17Bai, Bali, and Wen (2019) show downside risk, credit risk, and liquidity risk strongly predict future

bond returns. EBP measures credit spreads over estimated default risk. Gilchrist and Zakrajšek (2012) andLópez-Salido, Stein, and Zakrajšek (2017) argue it could affect credit market conditions and predict economicactivities.

18The insignificant coefficient on the term-spread variable in column (1) reflects the strong multicollinearitybetween longevity risk and term spreads. In unreported tests, we note the term spread, orthogonal tolongevity risk, has a significantly positive coefficient in regression specifications.

18

We then analyze if the maturity of new bond offerings tilts towards longer-dated bonds

as life expectancy increases. We obtain data on new domestic corporate bond issues from

FISD and estimate the average duration, weighted by issue size, and examine if new

domestic bond issues respond to changes in life expectancy. We first plot changes in the

aggregate-weighted duration of new corporate bond issues and changes in life expectancy

over 1990-2019 in Figure 4. The plot shows the two are strongly positively correlated

(ρ=0.46), suggesting that firms provide liquidity to the long-term corporate debt market

when expected yields on long-term bonds decline.


Table 5, column (2) further examines this relationship. As before, we control for

inflation (CPIGrowth), economic growth (GDPGrowth), risk premiums in bond markets

(CreditSpread), interest rate changes (∆Treasury1Y), treasury term-spread (TermSpread),

and a measure of bond market sentiment (excess bond premium or EBP). The dependent

variable in column (2) is the change in weighted average duration of new bond issues in a

given year. The key variable of interest is LongevityRisk. Results show the average duration

of new bond issues increases significantly in response to increases in life expectancy, with

the coefficient estimate on LongevityRisk being large and statistically significant (p<0.01).

The evidence is consistent with the gap-filling view of debt maturity choice. The coefficient

on ∆Treasury-1Y is negative (p<0.10), suggesting long-term bonds are preferred by life

insurers when the short-term interest rate is low (Domanski, Shin, and Sushko, 2017; Yu,

2020; Ozdagli and Wang, 2020). Meanwhile, EBP is insignificant, suggesting credit market

sentiment has little impact on maturities of new bond issues, after controlling for other

factors.

19

Next, we consider the relative issue size of long and short-term bonds in column (3). The

dependent variable is the first difference of the natural logarithm of the ratio of long-term

bonds issued to short-term bonds during the year to examine whether corporate issuers

shift issuances from short-term to long-term as life expectancy increases. Results confirm

that aggregate long-term bond issues increase relative to aggregate short-term bond issues

in response to increases in life expectancy.

Overall, Table 5 confirms that longevity increases lead to lower term spread of corporate

bonds and more long-term bond issuances. This is consistent with the literature (Guedes

and Opler, 1996; Barclay and Smith, 1995; Stohs and Mauer, 1996; Baker, Greenwood, and

Wurgler, 2003) that debt maturity is negatively related to term spreads and firms borrow

more long-term when long-term bond yields are low.

4.2 Firm-level evidence

In analyzing firm-level evidence on corporate supply response to longevity risks, we first

look at whether increases in life expectancy improve the availability of long-term financing

for firms. We expect firms to issue more long-term bonds to exploit differences in yields

between short and long-term bonds.19 We also expect a more pronounced supply response

for issuers whose bonds are primarily held by life insurers and those with investment-grade

credit ratings.

We expect gap filling to be more prevalent at the long end of the term structure. Hence,

we use issuance data to sort debt issues into four maturity buckets: short-term debt with

maturities in (0,3) years, medium-term debt with maturities in [3,10) years, long-term debt

19Baker, Greenwood, and Wurgler (2003) show that time series variation in debt maturity choice reflectspredictability in excess long-term bond returns.

20

with maturities in [10,20) years, and very long-term debt with maturities in [20,...) years

range. We then estimate the following multinomial logit model to relate the likelihood of

debt issuances in various segments of the term structure to longevity risks:

Issue ji,t = β Longevi t yRiskt−1 +X

′

i,t−1 ·λ+ γIssuer + νPeriod + εi,t (3)

where Issue ji,t is a dummy variable, which equals one if firm i issues bonds in maturity

bucket j during year t, and zero otherwise. We select the [3,10) year segment as the base

year as it closely matches life insurers’ average asset duration. The estimated coefficients

are thus interpreted relative to this base category. Macro control variables address concerns

that the estimated β reflects the effects of shifts in credit market conditions or the overall

macroeconomic environment facing firms. Hence, we control for CPIGrowth, GDPGrowth,

CreditSpread, ∆Treasury1Y, and TermSpread. We also control for firm-specific variables

that may affect the propensity to issue long-term debt, including ROA, Ln(Assets), TobinsQ,

Leverage, Age, Cash, EquityIssues, NIGrowth, and Tangibility. In addition, we include

indicator variables corresponding to five-year intervals to control for time-series variation

in demand for bonds of specific maturities. Firm fixed effects control for time-invariant

heterogeneity across issuers. Standard errors are clustered at the firm level.


Table 6 presents the estimates of the multinomial logit model. The coefficient estimate

of longevity risk is negative and significant at the 1% level for maturities of (0,3) years

relative to the base category, but notably, turns positive for longer maturities. It is positive

and statistically significant at the 5% level for maturities of [10,20) years and positive and

more than two times as large for very long-term debt issuances [20,...) years compared to

21

the [10,20) years range estimate. The evidence suggests that the likelihood of firms issuing

long-term debt and especially very long-term debt is highly sensitive to longevity risks. The

results also indicate the increases in longevity reduce the likelihood of issuing short-term

debt relative to the assumed base case. Column (3) provides estimates for maturities

in the [20,...) year range indicating that a one-standard-deviation increase in longevity

risk leads to an increase of 43% in the likelihood ratio of issuing very long-term bonds

relative to issuing medium-term bonds. Overall, firm-level evidence shows an increase in

life expectancy results in firms substituting short-term bonds with longer-dated bonds.

We then examine whether the supply elasticity is more significant for firms whose bonds

are primarily held by life insurers. If firms differ in the extent to which life insurers hold

their bonds, those with a bond market “relationship” with life insurers should exhibit the

greatest supply response. This leverages the idea that if life insurers have previously bought

a firm’s bonds, they would likely add to those holdings because of fixed costs associated

with screening and monitoring bond issuers, which make starting a new relationship with

an issuer more costly. Zhu (2021) makes a similar argument in the context of mutual funds

and shows substantial “stickiness” in investment decisions of mutual funds. We expected

the same stickiness for life insurers, predicting if longevity risk is mainly conveyed via

life insurers, firms whose bonds are primarily held by insurers will be more sensitive to

longevity shocks.

For each issuer in our sample, we first compute the share of its bonds held by life insurers.

We then define insurer-dependent (non-insurer-dependent) firms as those with life insurer

shares above (below) the cross-sectional median, and run multinomial logit regressions

separately for insurer-dependent firms and non-insurer-dependent firms. Results in Table

7 again show that when longevity increases, insurer-dependent firms issue more long-

22

term bonds and fewer short-term bonds. By contrast, non-insurer-dependent firms do not

respond to longevity shocks.


Issuers also differ in credit ratings. Our results in Table 3 suggest life insurers primarily

respond to longevity shocks mainly by increasing their holdings of investment-grade bonds

(NAIC 1 and 2). Consequently, we expect much of the corporate response to be concentrated

among investment-grade firms.

We test whether investment-grade firms exhibit a larger response to longevity shocks by

estimating the multinomial logit regressions in Equation (3) separately for investment-grade

and non-investment-grade firms. Table 7, Panel B presents the results. Columns (1) to (3)

show investment-grade firms issue more long-term bonds and fewer short-term bonds after

unexpected longevity increases, similar to those reported in Table 6. By contrast, columns

(4) to (6) suggest noninvestment-grade firms are insensitive to longevity shocks. Overall,

we see that investment-grade firms are more responsive to longevity shocks.

5 Long-Term investments and asset maturity

Finally, we turn to the effects of longevity shocks on corporate investments. In particular,

contracting cost theories predict that firms attempt to match the duration of their assets and

liabilities (Myers, 1977; Hart and Moore, 1994). When longevity increases, firms with the

ability to respond to mispricing in corporate bond markets will increase their investments

in long-term projects and lengthen the maturity of their assets. We test two predictions that

long-term debt supply response will be greater for firms with greater financial flexibility,

23

and for those with a stronger preference for issuing longer-term debt. We also expect these

firms to make larger increases in long-term investments. We test these predictions using

Compustat data over 1975-2019.

Table 8 examines if the corporate response is more pronounced for firms with a pref-

erence for long-term debt. Following Foley-Fisher, Ramcharan, and Yu (2016), we use

the lagged ratio of long-term debt to total debt as a measure of a firm’s long-term debt

dependence. The key variable of interest is the interaction between longevity risk and the

firm’s long-term debt dependence. The dependent variable in column (1) is the growth of

outstanding long-term debt (with a maturity of more than five years). If longevity risks

disproportionately increase long-term debt growth at firms more reliant on long-term debt,

then the coefficient on the interaction term will be positive. We include the usual firm

controls. Firm fixed effects absorb firm-level time-invariant heterogeneity, while year fixed

effects control for macro effects. We also cluster standard errors by firm. Column (1) shows

firms that depend more on long-term debt issue exhibit higher long-term debt growth when

longevity increases. These results are consistent with earlier tests in Table 6, based on new

bond issues.


Next, we study the effects of longevity risk on long-term investments using three

variables: R&D intensity in column (2) (R&D scaled by lagged total assets), the growth rate

of plant, property, and equipment in column (3) (PPEGrowth), and capital expenditures in

column (4) (CAPEX scaled by lagged total assets). The key variable of interest is again

the interaction between longevity risk and long-term debt dependence measure. The

coefficient on the interaction term between longevity risk and long-term debt dependence

24

is positive and significant at the 5% level in columns (2) to (4). Results show that firms

more dependent on longer-term financing exhibit larger growth in long-term investment,

invest more in R&D, have higher growth in PPE, and larger CAPEX.

In column (5), we investigate how longevity risk affects asset maturity. Following Stohs

and Mauer (1996), we compute asset maturity as (ACT/(ACT+PPENT))*(ACT/COGS)+

(PPENT/(ACT+PPENT))*(PPENT/DP), where ACT is current assets total, PPENT is net

property, plant, and equipment, COGS is cost of goods sold, and DP is depreciation and

amortization. Results show firms with a dependence on long-term debt increase asset

maturities when longevity increases.


In Table 9, we examine if financially unconstrained firms are more responsive to longevity

shocks. A firm is considered financially constrained if the Whited-Wu index (Whited and

Wu, 2006) is above the sample median, and zero otherwise (WhitedWu). We then interact

the longevity risk with the WhitedWu measure. Column (1) shows the interaction term is

negative (p < 0.05), consistent with financial constraints limiting the ability of firms to

respond to longevity risks, thus indicating financially unconstrained firms issue more long-

term debt when longevity increases. Columns (2) to (4) show that financially unconstrained

firms exhibit a larger increase in long-term investments, except for R&D investment. In

column (5), we find that financially unconstrained firms show larger increases in asset

maturity. Overall, the results suggest that financially unconstrained firms show a much

larger increase in long-term borrowings during periods of higher life expectancy. Financially

unconstrained firms also invest more in fixed assets and increase their asset maturity.

25

6 Conclusion

This paper examines how demand shocks from life insurers, among the most influential

investors, affect corporate bond markets. Life insurers respond to unexpected changes in

longevity by varying the duration of their assets, for example, adjusting their holdings of

bonds with various maturities. Such demand shocks influence corporate bond markets and

issuing firms in areas including debt maturity structure, financing costs, and long-term

investment. Our results are important in several ways. First, we show the sizable impacts

of demand shocks on corporate bonds and highlight the economic effects of the insurance

sector on the corporate sector. Second, we illustrate a plausible channel through which

longevity shocks transmit to the real sector via the insurance sector and bond markets.

Last, results suggest the positive impacts of longevity increases on the real economy via

the financial markets, helping to reduce long-term financing costs and stimulate long-term

investments.

26

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https://www.mortality.org/hmd/USA/InputDB/USAcom.pdf

https://www.mortality.org/hmd/USA/InputDB/USAcom.pdf

http://content.naic.org/publications

http://content.naic.org/publications

−.1

0.1

.2.3

.4L

on

gev

ity

ris

k (

yea

rs)

−1

−.5

0.5

1∆

Bo

nd

du

rati

on

(y

ears

)

1995 1999 2003 2007 2011 2015 2019Year

∆Bond duration Longevity risk

Figure 1: Changes in bond duration of life insurers and longevity risk

The blue solid line shows changes in average duration of life insurers’ bond holdings, whilethe red dashed line indicates longevity risk, measured as the first-order difference of theweighted average period life expectancy. Life insurers’ data are from NAIC.

31

−0.4

−0.2

0.0

0.2

0.4

0.6

Longevity shocks

Longevity Shocks in Each State (1990)

State−level Longevity Risk

(a) State-level longevity risk (1990)

−0.4

−0.2

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0.4

0.6

Longevity shocks



(b) State-level longevity risk (2000)

−0.4

−0.2

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Longevity shocks



(c) State-level longevity risk (2010)

−0.4

−0.2

0.0

0.2

0.4

0.6

Longevity shocks



(d) State-level longevity risk (2018)

Figure 2: State-level longevity risk

Snapshots of the state-level longevity shocks in 1990, 2000, 2010, and 2018, respectively.

32

−.2

0.2

.4L

on

gev

ity

ris

k (

yea

rs)

−4

−2

02

46

∆C

orp

Ter

mS

pre

ad (

%)

1990 1994 1998 2002 2006 2010 2014 2018Year

∆CorpTermSpread Longevity risk

Figure 3: Changes in corporate bond term spread and longevity risk

This blue solid line shows the changes in term spreads of corporate bonds, while the reddashed line indicates longevity risk, measured as the first-order difference of the weightedaverage period life expectancy. Spread is the yield difference between long-term bonds(maturity above 10 years) and short-term bonds (maturity under three years).

33

−.2

0.2

.4L

ongev

ity r

isk (

yea

rs)

−2

−1

01

∆D

ura

tion (

yea

rs)

1990 1994 1998 2002 2006 2010 2014 2018Year

∆Duration (years) Longevity risk

Figure 4: Changes in average duration of new bond issues and longevity risk

The blue solid line shows changes in average duration of new bond issues, while the reddashed line indicates longevity risk measured as the first-order difference of the weightedaverage period life expectancy. The average duration of new bond issues is computed fromFISD, weighted by issue size.

34

Table 1: Summary statistics

This table summarizes the descriptive statistics of key variables: Panel A reports longevityrisk, across 1974-2018 nationwide and 1989-2018 for local (state) level longevity risk,based on HMD and USMD data; Panel B reports bond market characteristics, across 1990-2019, based on FISD data; Panel C shows life insurer characteristics across 1995-2019,based on NAIC data; Panel D reports firm characteristics, across 1975–2019 based onCompustat data. Appendix A describes the variables.

Distribution

N Mean Std. Dev. Min P25 Median P75 Max

Panel A: Longevity risk

LongevityRisk 45 0.15 0.14 -0.18 0.06 0.12 0.22 0.47LocalLongevityRisk 1,530 0.10 0.21 -0.60 -0.03 0.10 0.24 1.10

Panel B: Bond market characteristics

CreditSpread 30 2.07 0.86 1.11 1.49 1.95 2.38 5.25∆Treasury1Y 30 -0.21 1.39 -3.38 -0.77 -0.09 0.44 3.53TermSpread 30 1.42 1.13 -0.38 0.40 1.56 2.58 3.22TermSpread⊥ 30 0.57 0.51 -0.23 0.20 0.49 0.94 1.70EBP 30 0.11 0.74 -0.75 -0.33 -0.10 0.40 3.03∆CorpTermSpread 30 0.03 1.91 -3.05 -0.98 -0.24 1.14 4.89LTtoSTDebt 30 5.20 4.10 0.43 1.72 4.23 7.91 16.51∆NewBondDuration 30 0.04 0.91 -2.06 -0.50 0.25 0.77 1.22

Panel C: Life insurer characteristics

InsAssets (MM$) 15,523 6,663 23,996 0.3 45 338 2,413 326,382∆InsDuration 15,523 0.04 1.12 -3.84 -0.47 -0.04 0.44 4.69InsLeverage 15,523 0.73 0.25 0.03 0.59 0.83 0.91 0.98InsRBC 15,523 17.57 30.62 1.94 6.09 8.89 14.75 231.86InsROA 15,523 0.02 0.05 -0.17 0.00 0.01 0.03 0.21InsNPWGrowth 15,523 0.11 1.24 -3.17 -0.14 -0.01 0.11 9.64NAIC1 10,250 0.55 0.11 0.06 0.48 0.54 0.61 1.00NAIC2 10,250 0.27 0.10 0.00 0.21 0.26 0.32 0.74NAIC3 10,250 0.07 0.04 0.00 0.04 0.06 0.08 0.58NAIC4 10,250 0.07 0.04 0.00 0.04 0.07 0.09 0.62NAIC5 10,250 0.02 0.02 0.00 0.01 0.02 0.04 0.33NAIC6 10,250 0.02 0.02 0.00 0.00 0.01 0.03 0.42

35

Table 1: Continued

Distribution

N Mean Std. Dev. Min P25 Median P75 Max

Panel D: Firm characteristics

Assets (MM$) 48,131 6,669 24,314 3 213 906 4,058 847,409LTDebtGrowth 48,131 0.08 0.50 -0.86 -0.10 -0.02 0.11 3.34R&DIntensity 48,131 0.02 0.03 0.00 0.00 0.00 0.01 0.24PPEGrowth 48,131 0.03 0.09 -0.19 -0.01 0.01 0.05 0.56CAPEX 48,131 0.09 0.08 0.00 0.04 0.06 0.11 0.45AssetMat 48,131 7.24 7.60 0.55 2.46 4.24 8.83 40.14ROA 48,131 0.16 0.07 -0.25 0.11 0.15 0.20 0.38TobinsQ 48,131 1.63 1.07 0.52 1.00 1.29 1.88 7.80Leverage 48,131 0.28 0.15 0.00 0.17 0.28 0.38 0.91Age 48,131 17.14 12.54 0.00 7.00 15.00 24.00 60.00Cash 48,131 0.08 0.10 0.00 0.02 0.05 0.11 0.62EquityIssue 48,131 0.01 0.07 -0.15 -0.00 0.00 0.01 0.53NIGrowth 48,131 0.06 0.72 -2.69 -0.17 0.08 0.31 2.55Tangibility 48,131 0.46 0.28 0.02 0.23 0.40 0.67 1.30LTDebtDep 48,131 0.52 0.28 0.00 0.31 0.52 0.73 1.00

36

Table 2: Life insurers’ responses to longevity shocks

The dependent variable is the changes in a life insurer’s bond portfolio duration(∆InsDuration). We control for macroeconomic indicators, credit market conditions, andinsurer characteristics. Column (1) uses treasuries’ term spread (TermSpread). Column(2) uses treasuries’ term spread orthogonal to longevity shocks (TermSpread⊥). Columns(3) and (4) differentiate large and small insurers, which are classified by median assets.Columns (5) and (6) examine insurers with high or low exposure to longevity risks dueto different product mix of annuities and life insurances. Appendix A provides detailedvariable definitions. Standard errors are clustered by insurer, and t-statistics are reportedin parentheses. ∗∗∗, ∗∗, and ∗ indicate 1%, 5%, and 10% two-tailed statistical significance,respectively. The sample period is from 1995-2019.

Insurer Size Exposure

Large Small High Low(1) (2) (3) (4) (5) (6)

LongevityRisk 0.687∗∗∗ 0.782∗∗∗ 0.907∗∗∗ 0.471∗∗∗ 0.884∗∗∗ 0.471∗∗∗

(7.7) (8.8) (8.7) (3.2) (5.3) (4.1)

TermSpread 0.091∗∗∗ 0.101∗∗∗ 0.072∗∗∗ 0.096∗∗∗ 0.084∗∗∗

(9.3) (8.2) (4.6) (4.6) (6.8)

TermSpread⊥ 0.155∗∗∗

(7.1)

∆Treasury1Y -0.036∗∗∗ -0.029∗∗∗ -0.045∗∗∗ -0.028∗ -0.057∗∗∗ -0.031∗∗

(-3.6) (-2.7) (-3.9) (-1.7) (-3.4) (-2.3)

CreditSpread 0.085∗∗∗ 0.077∗∗∗ 0.016 0.141∗∗∗ 0.099∗∗ 0.111∗∗∗

(3.8) (3.4) (0.6) (3.8) (2.3) (3.9)

CPIGrowth -0.028∗∗ -0.036∗∗∗ -0.055∗∗∗ -0.003 -0.057∗∗∗ -0.014(-2.4) (-3.0) (-4.6) (-0.1) (-2.9) (-0.9)

GDPGrowth 0.102∗∗∗ 0.088∗∗∗ 0.080∗∗∗ 0.114∗∗∗ 0.127∗∗∗ 0.114∗∗∗

(8.8) (7.9) (5.8) (6.1) (6.0) (7.7)

StateGDPGrowth 2.044∗∗∗ 1.547∗∗∗ 2.406∗∗∗ 2.043∗∗ 0.580 2.624∗∗∗

(3.8) (2.9) (3.4) (2.6) (0.6) (3.8)

StatePopGrowth -9.279∗∗∗ -9.738∗∗∗ -6.269 -10.714∗∗ -11.709∗ -11.435∗∗

(-2.6) (-2.7) (-1.6) (-2.1) (-1.7) (-2.5)

37

Table 2 Continued

Insurer Size Exposure

Large Small High Low(1) (2) (3) (4) (5) (6)

Ln(InsAssets) -0.010 -0.003 0.006 0.030 -0.082∗ 0.008(-0.5) (-0.2) (0.2) (0.7) (-1.7) (0.3)

InsLeverage 0.103 0.078 0.169 -0.036 0.424 0.071(0.8) (0.6) (0.8) (-0.2) (1.1) (0.5)

RBCRatio -0.001 -0.001 -0.003 -0.001 -0.001 -0.001(-1.1) (-1.0) (-1.0) (-1.1) (-0.6) (-0.9)

InsROA -0.162 -0.178 -0.013 -0.181 -0.001 -0.136(-0.5) (-0.6) (-0.0) (-0.5) (-0.0) (-0.4)

NPWGrowth 0.022∗∗ 0.021∗∗ 0.011 0.038∗∗ 0.031∗∗ 0.012(2.4) (2.2) (1.0) (2.4) (2.1) (0.9)

Insurer FE Yes Yes Yes Yes Yes Yes

R2 0.071 0.069 0.091 0.077 0.108 0.077

Observations 15,523 15,523 7,746 7,741 4,026 9,531

38

Table 3: Longevity shocks and life insurer bond trades

This table examines changes in net purchases of long-term (Panel A) and short-term bonds(Panel B) by insurers in response to changes in life expectancy. The net purchases are scaledby market value of an insurer’s bond portfolio. Long-term bonds have a duration of 10years or more. Short-term bonds have a duration of three years or less. Column (1) reportsestimates of all bond purchases, while Columns (2) to (7) report estimates of bond purchasesby bond ratings, based on six NAIC rating designations. We control for macroeconomicindicators, credit market conditions, and insurer characteristics (see variables in Table2, column (1)). Appendix A provides detailed variable definitions. Standard errors areclustered by insurer, and t-statistics are reported in parentheses. ∗∗∗, ∗∗, and ∗ indicate1%, 5%, and 10% two-tailed statistical significance, respectively. The sample period is1995-2019.

(1) (2) (3) (4) (5) (6) (7)

Bonds with NAIC Designation

All bonds 1 2 3 4 5 6

Panel A: Net Purchases of Long-term Bonds by Insurers

LongevityRisk 0.087∗∗∗ 0.024∗∗ 0.022∗∗∗ 0.007∗∗∗ 0.008∗∗∗ 0.004∗∗∗ 0.003∗∗∗

(3.6) (2.2) (4.0) (4.5) (4.2) (3.5) (2.8)

Macro controls Yes Yes Yes Yes Yes Yes YesBond market controls Yes Yes Yes Yes Yes Yes YesInsurer controls Yes Yes Yes Yes Yes Yes YesInsurer fixed effects Yes Yes Yes Yes Yes Yes Yes

R2 0.043 0.035 0.034 0.020 0.020 0.018 0.018

N 14,262 14,002 14,002 14,002 14,002 14,002 14,002

Panel B: Net Purchases of Short-term Bonds by Insurers

LongevityRisk -0.015 -0.014∗ 0.002 -0.001 0.003∗∗ 0.000 0.000(-1.4) (-1.8) (0.5) (-0.9) (2.5) (0.7) (1.2)

Macro controls Yes Yes Yes Yes Yes Yes YesBond market controls Yes Yes Yes Yes Yes Yes YesInsurer controls Yes Yes Yes Yes Yes Yes YesInsurer fixed effects Yes Yes Yes Yes Yes Yes Yes

R2 0.027 0.028 0.017 0.010 0.016 0.009 0.011

N 14,262 14,002 14,002 14,002 14,002 14,002 14,002

39

Table 4: Local longevity shocks and local insurer bond tradesWe run panel regressions of trading directions of two local life insurers against the corre-lation between local longevity shocks. The dependent variable is a dummy, which equalsone if two local life insurers (i and j) trade the same bond in the opposite directionsand 0 otherwise. Local life insurers are insurers with at least 80% of revenues from astate. Local longevity risk represents state-level longevity shocks. Column (1) uses thecorrelation coefficient of local longevity shocks faced by insurers (LongevityCorri, j). Column(2) uses a dummy variable (SimilarLongevityRiski, j), which equals one if two states havelongevity shocks above or below their sample medians simultaneously, and 0 otherwise.Columns (3) and (4) further control for year fixed effects. In all regressions, we control formacroeconomic indicators, credit market conditions, and insurer characteristics. AppendixA describes the variables and data sources. Standard errors are clustered by states ofinsureri, and insurer j, and t-statistics are in parentheses. ∗∗∗, ∗∗, and ∗ indicate 1%, 5%,and 10% two-tailed statistical significance, respectively. The sample period is 1995-2019.

(1) (2) (3) (4)

LongevityCorri, j -0.024∗∗∗ -0.024∗∗∗

(-5.3) (-5.3)SimilarLongevityRisk -0.009∗∗∗ -0.007∗∗∗

(-5.7) (-3.4)CPIGrowth -0.002 -0.006∗∗

(-0.6) (-2.2)GDPGrowth 0.014∗∗∗ 0.013∗∗∗

(4.0) (3.5)CreditSpread 0.028∗∗∗ 0.022∗∗∗

(4.1) (3.3)∆Treasury1Y -0.003 -0.003

(-1.2) (-1.4)TermSpread 0.009∗∗ 0.006∗

(2.7) (1.9)StateGDPGrowthi 0.178 0.193 -0.071 -0.078

(0.7) (0.8) (-1.0) (-1.0)StatePopGrowthi -1.251∗∗∗ -1.065∗∗ -0.223 -0.266

(-2.7) (-2.4) (-1.3) (-1.4)InsRBCi -0.000 -0.000 -0.000 -0.000

(-0.6) (-0.4) (-1.0) (-0.8)InsLeveragei 0.001 0.000 -0.004 -0.008

(0.0) (0.0) (-0.2) (-0.4)

40

Table 4 Continued

(1) (2) (3) (4)

InsROAi 0.027 0.024 0.043 0.044(0.6) (0.5) (1.1) (1.1)

InsNPWGrowthi 0.000 0.000 -0.000 -0.000(0.6) (0.5) (-0.1) (-0.3)

Ln(InsAsset)i -0.009∗∗∗ -0.009∗∗ -0.008∗∗∗ -0.007∗∗

(-2.9) (-2.4) (-2.9) (-2.2)StatePopGrowth j 0.429∗∗ 0.452∗ 0.095 0.101

(2.0) (2.0) (0.9) (0.9)StatePopGrowth j -1.147∗∗ -0.993∗∗ -0.258 -0.334

(-2.6) (-2.4) (-1.4) (-1.5)InsRBC j 0.000 0.000 -0.000 -0.000

(1.5) (1.3) (-0.3) (-0.4)InsLeverage j 0.012 0.008 0.002 -0.006

(0.8) (0.5) (0.2) (-0.4)InsROA j -0.002 0.017 0.004 0.021

(-0.1) (0.5) (0.1) (0.7)InsNPWGrowth j 0.001 0.001 0.000 0.000

(1.3) (1.3) (0.2) (0.6)Ln(InsAsset) j -0.005 -0.006∗ -0.005 -0.004

(-1.5) (-1.8) (-1.7) (-1.4)

Insureri FE Yes Yes Yes YesInsurer j FE Yes Yes Yes YesYear FE No No Yes YesR2 0.010 0.010 0.017 0.018Observations 778246 744576 778246 744576

41

Table 5: Longevity risk and new bonds issues

This table reports results from regressions of new bond characteristics against longevityrisk. Columns (1) examines changes of term spread between long-term and short-termcorporate bonds. Column (2) looks at changes of average duration of new bond issues, withthe average computed from FISD, weighted by issue size. Column (3) examines changes ofrelative issue size of long-term bonds to short-term bonds. In all regressions, we controlfor macroeconomic and credit market conditions. Appendix A provides detailed variabledefinitions. t-statistics, shown in parentheses, are computed from standard errors usingNewey-West corrections of two lags.∗∗∗, ∗∗, and ∗ indicate 1%, 5%, and 10% two-tailedstatistical significance, respectively. The sample period is 1990-2019.

(1) (2) (3)∆Corporate ∆NewBondDuration ∆Ln(Long termterm spread /Short term)

LongevityRisk -6.358∗∗∗ 2.904∗∗∗ 2.227∗∗∗

(-3.0) (3.0) (3.6)

CPIGrowth 0.282 -0.141 -0.001(0.9) (-1.0) (-0.0)

GDPGrowth 0.129 0.006 -0.120(0.3) (0.0) (-1.5)

CreditSpread -0.050 -0.093 -0.139(-0.1) (-0.3) (-0.9)

∆Treasury1Y -0.221 -0.256∗ -0.206∗

(-1.0) (-2.0) (-1.8)

TermSpread 0.691 -0.032 0.058(1.4) (-0.2) (0.7)

EBP -0.015 -0.085 -0.085(-0.0) (-0.5) (-1.0)

Constant -1.077 0.194 0.200(-0.5) (0.2) (0.4)

R2 0.260 0.366 0.561

Observations 30 30 30

42

Table 6: Corporate responses to longevity shocks: Bond maturity choicesThis table reports results from multinomial logit regressions of bond maturity choice againstlongevity risk. We classify bonds into four categories: short-term bonds (with a maturityless than 3 years), medium-term bonds (with a maturity between 3 and 10 years), long-termbonds (with a maturity between 10 and 20 years), and extra long-term bonds (with amaturity above 20 years). We use medium-term bonds (with a maturity between 3 and 10years) as the base category. In all regressions, we control for macroeconomic indicators,credit market conditions, and firm characteristics. Appendix A describes the variables andour data sources. Standard errors are clustered by firm, and t-statistics are in parentheses.∗∗∗, ∗∗, and ∗ indicate 1%, 5%, and 10% two-tailed statistical significance, respectively. Thesample period is 1990-2019.

Bond issues with maturities< 3 years [10, 20) years ≥ 20 years

(1) (2) (3)

LongevityRisk -6.330∗∗∗ 1.143∗∗ 2.556∗∗∗

(-2.8) (2.2) (4.5)

CPIGrowth 0.794∗∗∗ 0.024 0.010(2.6) (0.5) (0.2)

GDPGrowth 1.002∗∗∗ -0.073 -0.092(3.4) (-1.4) (-1.5)

CreditSpread -0.169 -0.037 -0.267∗∗∗

(-0.4) (-0.4) (-2.8)

∆Treasury1Y -0.590∗∗ 0.091∗ 0.070(-2.3) (1.7) (1.2)

TermSpread -0.010 0.095∗ 0.070(-0.0) (1.8) (1.2)

ROA -5.459 -0.384 -1.110(-1.3) (-0.4) (-0.9)

Ln(Assets) 1.013∗∗∗ 0.162∗∗∗ 0.718∗∗∗

(6.1) (4.0) (12.6)

TobinsQ 0.325∗ 0.035 0.080(1.9) (0.5) (1.0)

Leverage -0.610 -1.331∗∗∗ -2.156∗∗∗

(-0.5) (-3.4) (-4.6)

Age 0.013 0.002 0.022∗∗∗

(1.2) (0.8) (5.2)

43

Table 6 Continued

Bond issues with maturities< 3 years [10, 20) years ≥ 20 years

(1) (2) (3)

Cash -0.655 -0.793 -0.444(-0.2) (-1.1) (-0.5)

EquityIssue -3.932 0.317 -1.939∗

(-0.8) (0.4) (-1.8)

NIGrowth -0.038 -0.014 0.062(-0.1) (-0.2) (1.0)

Tangibility 0.257 -0.016 1.210∗∗∗

(0.4) (-0.1) (5.7)

Year 1995-1999 -0.900 -0.198 0.710∗∗∗

(-1.0) (-0.9) (3.0)

Year 2000-2004 -0.777 0.020 0.386(-0.8) (0.1) (1.6)

Year 2005-2009 -0.412 0.157 -0.677∗∗∗

(-0.6) (1.0) (-3.5)

Year 2010-2014 -0.819 -0.135 -0.545∗∗∗

(-1.1) (-0.9) (-3.1)

Constant -16.069∗∗∗ -0.362 -6.146∗∗∗

(-5.9) (-0.6) (-8.5)

R2 0.108Observations 4197

44

Table 7: Maturity choices: HeterogeneityThis table reports results from multinomial logit regressions of bond maturity choice againstlongevity risk for firms sorted by insurer dependence (Panel A) and debt rating (Panel B).Medium-term bonds (with a maturity between three and 10 years) are the base category.Insurer-dependent (non-insurer-dependent) firms are those with life insurer shares above(below) the cross-sectional median. Investment grade firms are designated NAIC 1 or 2.Both panels use the same controls as in Table 6. Appendix A describes the variables andour data sources. Standard errors are clustered by firm, and t-statistics are in parentheses.∗∗∗, ∗∗, and ∗ indicate 1%, 5%, and 10% two-tailed statistical significance, respectively. Thesample period is 1995-2019.

Panel A: Sorted by insurer dependence

Insurer-dependent firms Non-insurer-dependent firmsBond issues with maturities Bond issues with maturities

< 3 years [10,20) years ≥ 20 years < 3 years [10,20) years ≥ 20 years(1) (2) (3) (4) (5) (6)

LongevityRisk -11.975∗∗ 1.904∗ 2.778∗∗∗ -5.126 0.614 0.501(-2.2) (1.8) (2.7) (-1.6) (0.8) (0.5)

Macro Controls Yes Yes Yes Yes Yes YesCredit Conditions Yes Yes Yes Yes Yes YesInsurer Controls Yes Yes Yes Yes Yes YesPeriod Indicators Yes Yes Yes Yes Yes YesR2 0.111 0.132Observations 1608 2153

Panel B: Sorted by debt rating

Investment-grade firms Noninvestment-grade firmsBond issues with maturities Bond issues with maturities

< 3 years [10,20) years ≥ 20 years < 3 years [10,20) years ≥ 20 years(1) (2) (3) (4) (5) (6)

LongevityRisk -8.028∗∗∗ 1.599∗∗ 2.971∗∗∗ -3.691 0.798 1.561(-2.6) (2.4) (4.5) (-0.9) (1.1) (1.3)

Macro Controls Yes Yes Yes Yes Yes YesCredit Conditions Yes Yes Yes Yes Yes YesInsurer Controls Yes Yes Yes Yes Yes YesPeriod Indicators Yes Yes Yes Yes Yes YesR2 0.081 0.169Observations 2924 1273

45

Table 8: Corporate responses to longevity shocks: Long-term debt dependenceThis table runs panel regressions to examine the impacts of longevity risk on corporatelong-term debt and long-term investment, with firms differentiated by long-term debtdependence. Long-term debt dependence is the ratio of debt with maturities in excessof five years. Column (1) regresses long-term debt growth against the interaction termof longevity risk and long-term debt dependence. Columns (2) to (4) use long-terminvestment, measured as R&D expenditure (scaled by lagged total assets), growth rateof plant, property, and equipment (PPEGrowth), and capital expenditures (CAPEX scaledby lagged total assets). Column (5) uses asset maturity. In all regressions, we controlfor various firm characteristics. Appendix A describes the variables and our data sources.Standard errors are clustered by firm, and t-statistics are in parentheses. ∗∗∗, ∗∗, and ∗

indicate 1%, 5%, and 10% two-tailed statistical significance, respectively. The sampleperiod is 1975-2019.

(1) Long-term investment (5)Long-term (2) (3) (4) Asset

debt growth R&D PPEGrowth CAPEX maturity

LongevityRisk × LTDebtDep 0.132∗∗ 0.005∗∗∗ 0.022∗∗ 0.021∗∗∗ 1.886∗∗∗

(2.0) (2.8) (2.0) (3.1) (4.8)

LTDebtDep -0.488∗∗∗ -0.001 0.003 0.001 0.301∗∗∗

(-26.7) (-1.3) (1.0) (0.6) (2.7)

ROA 0.187∗∗ 0.009∗∗∗ 0.109∗∗∗ 0.122∗∗∗ -8.521∗∗∗

(2.4) (3.0) (7.5) (11.2) (-11.8)

Ln(Assets) -0.064∗∗∗ -0.002∗∗∗ -0.030∗∗∗ -0.016∗∗∗ 0.267∗∗∗

(-8.9) (-5.7) (-18.3) (-14.8) (3.3)

TobinsQ 0.025∗∗∗ 0.001∗∗∗ 0.016∗∗∗ 0.008∗∗∗ -0.007(4.0) (4.6) (14.3) (10.8) (-0.1)

Leverage -1.149∗∗∗ -0.012∗∗∗ -0.074∗∗∗ -0.061∗∗∗ 0.145(-27.0) (-7.6) (-10.3) (-13.1) (0.4)

Age 0.001 -0.000 0.001∗∗∗ 0.000∗∗∗ -0.003(1.1) (-0.0) (3.0) (3.0) (-0.2)

Cash -0.170∗∗∗ -0.005∗∗ 0.052∗∗∗ -0.003 1.654∗∗∗

(-2.9) (-2.2) (5.7) (-0.6) (4.2)

46

Table 8 Continued



EquityIssue 0.148∗∗ -0.013∗∗∗ 0.055∗∗∗ 0.023∗∗∗ -1.304∗∗∗

(2.2) (-6.7) (4.7) (3.2) (-3.6)

NIGrowth 0.003 -0.000 0.004∗∗∗ 0.002∗∗∗ 0.156∗∗∗

(0.8) (-0.7) (6.3) (5.6) (7.7)

Tangibility 0.022 0.000 -0.042∗∗∗ 0.051∗∗∗ 8.643∗∗∗

(0.8) (0.0) (-6.0) (11.0) (19.7)

Firm FE Yes Yes Yes Yes YesYear FE Yes Yes Yes Yes YesR2 0.233 0.895 0.333 0.652 0.885Observations 48131 48131 48131 48131 48131

47

Table 9: Corporate responses to longevity shocks: Financial constraintsThis table runs panel regressions to examine the impacts of longevity risk on corporatelong-term debt and long-term investments with firms differentiated by financial constraints.Long-term debt is defined as debt with maturities over five years. Column (1) regresseslong-term debt growth against the interaction term of longevity risk and a measure offinancial constraints (WhitedWu). Columns (2) to (4) use long-term investment, measuredas R&D expenditure (scaled by lagged total assets), the growth rate of plant, property andequipment (PPEGrowth), and capital expenditures (CAPEX scaled by lagged total assets),respectively. Column (5) uses asset maturity. In all regressions, we control for variousfirm characteristics as in Table 8. Appendix A describes the variables and data sources.Standard errors are clustered by firm, and t-statistics are in parentheses. ∗∗∗, ∗∗, and ∗

indicate 1%, 5%, and 10% two-tailed statistical significance, respectively. The sampleperiod is 1975-2019.



LongevityRisk -0.072∗∗ 0.001 -0.020∗∗∗ -0.018∗∗∗ -0.893∗∗∗

× WhitedWu (-2.1) (0.8) (-3.2) (-4.5) (-3.9)

WhitedWu -0.008 0.000 0.001 0.002 0.085(-0.7) (0.3) (0.5) (1.4) (1.0)

Firm controls Yes Yes Yes Yes Yes

Firm FE Yes Yes Yes Yes Yes

Year FE Yes Yes Yes Yes Yes

R2 0.199 0.895 0.334 0.652 0.886

Observations 47602 47602 47602 47602 47602

48

Appendices

A Variable Definitions and Data Sources

Panel A: Longevity Risk

LongevityRisk The first difference of average period life expectancy of the U.S. population.The average period life expectancy is computed from the period remaining lifeexpectancy and the corresponding exposure. We collect data of mortality rates,deaths and the corresponding exposure from the Human Mortality Database (HMD).The data is available at https://www.mortality.org. See Mila (2019) for moredetails. The sample period is 1974-2018.

LocalLongevityRisk State-level longevity is estimated from state-level human mortalitydata. The data is from the Human Mortality Database (HMD), which is available athttps://usa.mortality.org. The sample period is 1989-2018.

LongevityCorri, j The time-series correlation of longevity risks between the states of insur-ers i and j.

SimilarLongevityRiski, j A dummy variable that equals one if the longevity risks in stateswhere insurers i and j are located are both above or below sample median in a year,and zero otherwise.

Panel B: Macro Variables and Credit Market Conditions

CPIGrowth US CPI growth rate. Source: Federal Reserve Economic Data (item CPIAUCSL),1990-2019.

GDPGrowth US GDP growth rate. Federal Reserve Economic Data (item GDPC1), 1990-2019.

StateGDPGrowth State GDP growth rate. US Bureau of Economic Analysis (item SAGDP1),1990-2019.

StatePopGrowth State population growth rate. US Bureau of Economic Analysis (itemSAINC51), 1990-2019.

IndProdGrowth Industrial production growth rate. Federal Reserve Economic Data (itemINDPRO), 1990-2019.

CreditSpread The yield difference between Moody’s Baa and 20-year Treasury bonds.Federal Reserve Economic Data (item GS20), 1990-2019.

∆Treasury1Y Changes in 1-year Treasury yield. Federal Reserve Economic Data (itemGS1), 1990-2019.

49

https://www.mortality.org

https://usa.mortality.org

TermSpread The yield difference between 10-year and 1-year Treasuries. Data of 10-yearand 1-year treasuries yields are from Federal Reserve Economic Data (item GS10 andGS1), 1990-2019.

TermSpread⊥ Orthogonalized term spread obtained as residuals from a regression of termspread (the yield difference between 10-year and 1-year treasuries) on longevity risk.Data of 10-year and 1-year treasuries yields are from Federal Reserve Economic Data(item GS10 and GS1), 1990-2019.

EBP Excess bond premium as in Gilchrist and Zakrajšek (2012).Source: www.federalreserve.gov/econresdata/notes/feds-notes/2016/files/ebp_csv.csv.

∆PensionShare Changes in the market share of corporate bonds held by pensions. FederalReserve Economic Data (item BOGZ1FL593063045Q), 1995-2019.

∆MFShare Changes in the market share of corporate bonds held by mutual funds. FederalReserve Economic Data (item BOGZ1FL653063043Q), 1995-2019.

Panel C: Bond Characteristics

∆CorpTermSpread The first difference of the yield difference between long- and short-term corporate bonds. Long-term (short-term) bonds are defined as bonds withmaturities above 10 (below 3) years. Source: Mergent FISD, 1990-2019.

∆Ln(Long term/Short term) The first difference of the natural logarithm of the ratioof issue amount of long-term to short-term domestic corporate bonds. Long-term(short-term) bonds are defined as bonds with maturities above 10 (below 3) years.Source: Mergent FISD, 1990-2019

∆NewBondDuration The first difference of duration of new domestic corporate bonds.We compute Macaulay duration, using data of coupon rate, maturity, and bond pricesfrom Mergent FISD, 1990-2019

Panel D: Life Insurer Characteristics

∆InsDuration The first difference of the duration of a life insurer’s corporate bond portfolio.We compute Macaulay duration using data of coupon rate, maturity, and bond prices.Source: NAIC, 1995-2019

NetBuyLTBond Net purchase of long-term bonds of a life insurer, scaled by the marketvalue of this insurer’s bond portfolio. Long-term bonds are bonds with durations often years or more. Source: NAIC, 1995-2019

50



NetBuySTBond Net purchase of short-term bonds of a life insurer, scaled by the marketvalue of this insurer’s bond portfolio. Short-term bonds are bonds with durations ofthree years or less. Source: NAIC, 1995-2019

InsRBC Risk-based capital ratio, computed as the ratio of total adjusted capital to risk-based capital. A lower RBC ratio indicates lower capital adequacy. Source: NAIC,1995-2019

InsNPWGrowth Growth rate of net premium written. Source: NAIC, 1995-2019

InsROA Profitability of an insurer estimated as net income scaled by the average totalassets in the current and previous years. Source: NAIC, 1995-2019

Ln(InsAssets) Size of an insurer measured as the natural logarithm of total assets. Source:NAIC, 1995-2019

InsLeverage The ratio of total liabilities to total assets of an insurer. Source: NAIC, 1995-2019

Deviation Deviation measured as the distance of the share of life insurances of a life insurerto the industry-level natural-hedging share. The share of life insurances of a lifeinsurer is calculated as the direct premium written (DPW) of life insurances scaledby the sum of DPW collected from life insurance and annuities. The industry-levelnatural-hedging share is computed in Appendix D.

Panel E: Firm Characteristics

InsurerDepFirm For each firm, we first compute the share of its bonds held by life insurersupon issuance. Next, we compute the average life insurer share for each firm. Insurer-dependent (Non-insurer-dependent) firms are those with life insurer shares above(below) the cross-sectional median. Source: Mergent FISD, 1990-2019

ROA Firm profitability measured as operating income before depreciation (oidbp) scaledby the average total assets (at) in the current and previous years. Source: Compustat,1975-2019

Ln(Assets) Firm size, the natural logarithm of total assets. Source: Compustat, 1975-2019

Leverage The ratio of total debts (dltt+dlc) to total assets. Source: Compustat, 1975-2019

TobinsQ Market-to-book ratio estimated as the book value of assets plus the market valueof common stock (prcc_f × csho) less the sum of the book value of common stock(ceq) and balance sheet deferred taxes (txdb), divided by the book value of assets.Source: Compustat, 1975-2019

51

Age Firm age measured as years from the IPO date. If Compustat variable “ipodate” ismissing, it is measured as years from the first date in CRSP. Source: Compustat,1975-2019

Cash Ratio of cash and cash equivalents (che) to total assets. Source: Compustat, 1975-2019

EquityIssues Sale of equity (sstk) minus purchases of equity (prstkc), divided by laggedassets. Source: Compustat, 1975-2019

NetIncomeGrowth Net income growth measured as log growth rate of net income (ni).Source: Compustat, 1975-2019

Tangibility The value of net plant, property and equipment (ppent), scaled by lagged totalassets. Source: Compustat, 1975-2019

LTDebtGrowth The first difference of the value of long-term debts, scaled by lagged totalassets. Long-term debt is defined as debt with maturities in excess of five years(dltt-dd1-dd2-dd3-dd4-dd5). Source: Compustat, 1975-2019

R&D R&D intensity measured as R&D expenditure (xrd) scaled by lagged total assets.Source: Compustat, 1975-2019

PPEGrowth The difference in the value of plant, property and equipment (ppent), scaledby lagged total assets. Source: Compustat, 1975-2019

CAPEX capital expenditures (capex) scaled by lagged total assets. Source: Compustat,1975-2019.

AssetMat Asset maturity is (act/(act+ppent)) × (act/cogs) + (ppent/(act+ppent)) ×(ppent/dp), where act is current asset, ppent is net property, plant and equipment,cogs is cost of goods sold, and dp is depreciation and amortization (Stohs and Mauer,1996). Source: Compustat, 1975-2019

LTDebtDep The ratio of debt with maturities in excess of five years (dltt-dd1-dd2-dd3-dd4-dd5) in total debts (dltt+dlc). Source: Compustat, 1975-2019

WhitedWu Indicator variable that takes a value of one for financially constrained firmsidentified as those with Whited-Wu index (Whited and Wu, 2006) above the medianfor the sample. It takes a value of zero otherwise.

52

B Corporate bond markets and life insurers

Figure B plots the market shares of domestic nonfinancial corporate bonds held by life

insurers, mutual funds, and pensions over 1990-2018, using data from the Financial

Accounts of the United States (Z.1). Life insurers are the most prominent investors, holding

more than 50% of nonfinancial corporate bonds in earlier years. While their market share

has decreased after the financial crisis, they continue to be significant holders of corporate

bonds (holding 35% of the nonfinancial corporate market in 2018). On average, life

insurers held about 46% of corporate bonds over 1990-2018.

0.2

.4.6

Shar

e of

Aggre

gat

e C

orp

ora

te B

ond M

arket

1990 1995 2000 2005 2010 2015 2020Year

Life Insurers Pensions Mutual Funds

Figure B: Corporate bond market shares of institutional investors

This plot shows the market shares of domestic nonfinancial corporate bonds held by lifeinsurers, mutual funds, and pensions over 1990-2018. Data are from Financial Accounts ofthe United States (Z.1).

53

C NAIC Designation and Risk-based Capital Requirement of Bonds

This table reports the NAIC designations of bonds, based on S&P ratings, and the corre-sponding risk-based capital (RBC) requirement for life insurers in 2018. See more detailsat https://www.naic.org/.

S&P ratings RBC

NAIC Designation 1 AAA/AA+/AA/AA-/A+/A/A- 0.39%

NAIC Designation 2 BBB+/BBB/BBB- 1.26%

NAIC Designation 3 BB+/BB/BB- 4.46%

NAIC Designation 4 B+/B/B- 9.70%

NAIC Designation 5 CCC+/CCC/CCC- 22.31%

NAIC Designation 6 CC/C/D 30.00%

54

https://www.naic.org/

D Natural Hedging Share of Life Insurances

To derive the natural hedging share of life insurances, we need to assume a mortality

process. We follow the seminal Lee-Carter model (Lee and Carter, 1992). Lee-Carter model

assumes that the logarithm of mx ,t , the mortality rate for age x in year t, could be described

by the following linear relationship:

log�

mx ,t

�

= αx + βxκt , (D.1)

where αx is a static age function specifying the general shape of mortality by age; βxκt

captures the age-period effect, with κt reflecting overall mortality trend (period-related

effect) and βx modulating its effect across ages (age-related effect). In particular, κt is

commonly known as the mortality index, which captures the overall level of mortality

improvement.20

Based on the Lee-Carter model, the probability that an individual aged x dies during

year t, qx ,t , can be computed from mx ,t through the approximation qx ,t ≈ 1−exp(−mx ,t).21

Let Sx ,t(T ) be the ex post probability that an individual aged x at time t would have survived

to time t + T , then

Sx ,t(T ) =T∏

s=1

�

1− qx+s−1,t+s

�

. (D.3)

20The Lee-Carter model is only identifiable up to a transformation. As a result, in the literature, it isconventional to impose the following parameter constraints to circumvent the identification problem:

∑

t

κt = 0,∑

x

βx = 1. (D.2)

21This approximation implicitly assumes a stationary population and that the force of mortality over eachyear of integer age and over each calendar year is constant.

55

Let Ft be the filtration up to and including time t. Then qx ,t is unknown prior to t and

Sx ,t(T ) is known prior to time t + T . We further define the expected survival probability as

px ,u

�

T,κt

�

= E�

Sx ,u(T )|Ft

�

= E�

Sx ,u(T )|κt

�

. (D.4)

When u = t, we call px ,u

�

T,κt

�

a spot survival probability, while when u > t, we call it a

forward survival probability.

Let us assume that the life insurer has an annuity portfolio for cohorts from the same

population aged x1, x2, . . . , xk at time 0. The annuity pays each annuitant $1 at the end of

each year until death. Hence the annuity plan’s future liability per survival annuitant at

time t is calculated as

F LAt =

1k

xk∑

x=x1

∞∑

s=1

(1+ r)−spx ,t(s,κt), (D.5)

where r is the annual interest rate, and a superscript of A denotes an annuity business line.

Now let us consider the life insurance business. Similar to Sx ,t(T ), we can also define

Dx ,t(T ) as the ex post probability that an individual aged x at time t would have survived

to time t + T − 1 and died in year t + T , then we have

Dx ,t(T ) =T−1∏

s=1

�

1− qx+s−1,t+s

�

· qx+T−1,t+T . (D.6)

Given Dx ,t(T ), we can define the expected death probability as

qx ,u

�

T,κt

�

= E�

Dx ,u(T )|Ft

�

= E�

Dx ,u(T )|κt

�

. (D.7)

56

Assume that the life insurer provides life insurance for the same cohort from the same

population. Then the insurance’s future liability per death at time t can be expressed as

F L Lt =

1k

xk∑

x=x1

∞∑

s=1

(1+ r)−sqx ,t(s,κt), (D.8)

where a superscript of L denotes a life insurance business line.

The natural hedge simulation is based on the following assumptions:

1. The insurer provides both annuity and life insurance to cohorts who are aged x1 =

35, x2 = 36, . . . , xk = 80 at time 0. The mortality experience of these individuals is

identical to that of the US total population.

2. The annuity plan pays each individual $1 at the end of each year until death or year

20, whichever the earliest.

3. The 20-year term life insurance pays $1 upon death.

4. Interest rate is assumed to be r = 1% per annum. The interest rate remains constant

over time.

5. The US mortality index is estimated using all the available mortality data from the

HMD, with the sample period from 1933 to 2018 and the age range of 0 - 99.

6. To match the endpoint of the sample period, time 0 is set at the end of 2018.

7. We evaluate the effectiveness of natural hedge based on N = 10,000 rounds of

simulation generated from the Lee-Carter model in Equation (D.1).

Suppose the insurer’s portfolio contains X shares of annuities and let θX be the number

of shares of life insurances in the portfolio. Then the insurer’s total liability at time 0 is

57

F L0 = (F LA0 + θ F L L

0)X . To achieve a natural hedge, the insurer wishes to minimize the

variance of its portfolio’s liability, that is

minθ

Var(F L0), (D.9)

where F L0 = (F LA0 + θ F L L

0)X .

Let PA and P L be the total premiums collected from the annuity and life insurances,

respectively, then the proportion of premiums collected from life insurance business is

calculated as

P L

PA+ P L=

θE(F L L0)

E(F LA0) + θE(F L L

0). (D.10)

The optimal ratio ( P L

PA+P L ) is 81.9%, in our simulation. That is, a portfolio of 81.9% of

life insurance is naturally hedged against longevity risk. This result is robust to different

cohort sets, other annuity and term life insurance horizons. However, the average industry

share of life insurance is 31.6% over 1995-2019. That is, life insurers are far away from

the natural hedging ratio.

58

E Robustness Checks

E.1 Subperiod Analyses

While life insurers are the largest investors in corporate bond markets, their market share has

decreased since 2005. To check if our results hold after this date, we repeated our analyses

over subperiods 1995-2005 and 2006-2019. Table E, columns (1) and (2) report regression

results for these subperiods. While the earlier subperiod has more robust responses to

longevity shocks (coefficient of 1.209), the later subperiod still shows significant responses

to longevity shocks (coefficient of 0.720 and p < 0.01).

E.2 Business Cycles

Confounding impacts of business cycles may influence longevity risk if, for example, eco-

nomic conditions affect health status and hence life expectancy (see, e.g., Cutler, Deaton,

and Lleras-Muney (2006) and Acemoglu and Johnson (2007)). We thus need to differ-

entiate effects of longevity risk from other economic shocks. While already controlling

for aggregate and state-level economic indicators, including GDP growth and CPI growth,

we further consider longevity shocks orthogonal to business cycles to directly address this

concern. We measure business cycles as the cyclical component of industrial production

growth, computed from the Hodrick–Prescott filter. We then regress longevity risk against

the cyclical component of industrial production growth and use residuals as the orthogo-

nalized longevity risk (Longevity risk⊥) to repeat the previous analyses. Table E, column

(3) reports the results, showing they are similar to those reported in Table 2, including

magnitudes.

59

E.3 Other institutional investors

Other significant investors in corporate bond markets could also affect bond markets, for

example, pensions and mutual funds. As shown in Figure B, the market share of mutual

funds increases over time. Similar to life insurers, pensions also face longevity shocks,

though responses of mutual funds remain unclear. To further control for institutional

investor impacts, we add changes in the market share of corporate bonds held by pensions

(∆ PensionShare) and mutual funds (∆ MFShare) to the regression. Table E, column

(4) shows longevity risk remains significantly positive, with magnitudes similar to those

reported in Table 2.

E.4 Local (state-level) longevity risk

We examine local life insurers’ responses to local longevity shocks in Table E, column (5).

Local life insurers are firms with at least 80% of revenues from one state. We use state-level

US Mortality Data to estimate the longevity risks in each state. Cross-state variations of

longevity risk provide greater testing capability. Column (5) regresses the changes in local

life insurers’ bond portfolio duration to local longevity shocks. The state-level tests confirm

life insurers adjust their bond portfolio duration according to local longevity shocks.

60

Table E: Life insurers’ responses to longevity shocks: Robustness checksThe dependent variable is the changes in a life insurer’s bond portfolio duration(∆InsDuration). We control for macroeconomic indicators, credit market conditions, andinsurer characteristics. Columns (1) and (2) consider subperiods 1995-2005 and 2006-2019. Column (3) uses longevity shocks orthogonal to business cycles, with the lattermeasured as the cyclical component of industrial production growth, computed from theHodrick–Prescott filter. Column (4) controls for other institutional investors, i.e., changes inthe market share of corporate bonds held by pensions (∆PensionShare) and mutual funds(∆M FShare). Column (5) considers responses of local life insurers (with at least 80%of revenue from one state) to local (state-level) longevity shocks (Local Longevi t yRisk).Appendix A provides detailed variable definitions. Standard errors are clustered by in-surer, and t-statistics are reported in parentheses. ∗∗∗, ∗∗, and ∗ indicate 1%, 5%, and 10%two-tailed statistical significance, respectively. The sample period is 1995-2019.

Subperiods Business Other Local1995-2005 2006-2019 cycles institutions longevity

(1) (2) (3) (4) (5)

LongevityRisk 1.209∗∗∗ 0.720∗∗∗ 0.681∗∗∗

(5.1) (4.0) (7.3)Longevity risk⊥ 0.771∗∗∗

(8.6)∆PensionShare 5.004∗∗∗

(2.8)∆MFShare -10.494∗∗∗

(-7.9)LocalLongevityRisk 0.408∗∗∗

(4.1)TermSpread 0.172∗∗∗ 0.022 0.100∗∗∗ 0.122∗∗∗ 0.065∗∗∗

(9.5) (1.5) (10.2) (11.6) (4.3)∆Treasury1Y -0.085∗ -0.011 -0.029∗∗∗ -0.059∗∗∗ -0.054∗∗

(-1.8) (-0.4) (-2.9) (-4.2) (-2.6)CreditSpread 0.046 0.225∗∗∗ 0.074∗∗∗ -0.064∗∗ 0.090∗

(0.8) (5.5) (3.3) (-2.1) (1.7)CPIGrowth 0.118 -0.024 -0.027∗∗ -0.060∗∗∗ -0.037

(1.6) (-1.2) (-2.3) (-4.8) (-1.6)GDPGrowth 0.132∗∗∗ 0.183∗∗∗ 0.101∗∗∗ 0.077∗∗∗ 0.104∗∗∗

(4.6) (7.4) (8.7) (6.5) (3.8)

61

Table E Continued

Subperiods Business Other Local1995-2005 2006-2019 cycles institutions longevity

(1) (2) (3) (4) (5)

StateGDPGrowth -1.466∗ 2.336∗∗∗ 1.973∗∗∗ 1.153∗∗ 2.305(-1.7) (3.0) (3.7) (2.1) (1.2)

StatePopGrowth 10.852 -5.663 -9.482∗∗∗ -6.462∗ -11.575∗∗∗

(1.6) (-1.2) (-2.7) (-1.8) (-2.8)Ln(InsAssets) 0.080∗ -0.122∗∗∗ -0.010 -0.015 -0.010

(1.8) (-3.2) (-0.5) (-0.8) (-0.4)InsLeverage 0.380∗ 0.176 0.101 0.106 -0.246

(1.8) (0.7) (0.8) (0.9) (-1.2)RBCRatio 0.001 -0.002 -0.001 -0.001 -0.002∗∗∗

(1.2) (-1.3) (-1.1) (-1.2) (-3.6)InsROA 0.564 -0.249 -0.167 -0.163 -0.357

(1.2) (-0.5) (-0.6) (-0.6) (-0.5)NPWGrowth 0.006 0.036∗∗ 0.022∗∗ 0.022∗∗ 0.021

(0.5) (2.5) (2.4) (2.3) (1.3)

Insurer FE Yes Yes Yes Yes YesR2 0.156 0.094 0.072 0.076 0.067Observations 7060 8391 15523 15523 5689

62

debt market responses to longevity shocks

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