debt market responses to longevity shocks
TRANSCRIPT
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)).
1
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
2
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
3
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.
4
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
5
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
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.
7
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).
8
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 —
9
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 about here —
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
10
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.
11
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
12
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 about here —
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.
13
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.
— Figure 2 about here —
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.
14
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.
15
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.
— Table 4 about here —
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.
16
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.
17
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.
— Figure 3 about here —
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.
— Figure 4 about here —
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 about here —
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.
— Table 7 about here —
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.
— Table 8 about here —
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.
— Table 9 about here —
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
References
Acemoglu, D., and S. Johnson. 2007. Disease and development: The effect of life expectancyon economic growth. Journal of Political Economy 115:925–85.
Ang, A., and A. Maddaloni. 2005. Do demographic changes affect risk premiums? Evidencefrom international data. Journal of Business 78:341–79.
Badoer, D., and C. James. 2016. The determinants of long-term corporate debt issuances.Journal of Finance 71:457–92.
Bai, J., T. G. Bali, and Q. Wen. 2019. Common risk factors in the cross-section of corporatebond returns. Journal of Financial Economics 131:619–42.
Baker, M., R. Greenwood, and J. Wurgler. 2003. The maturity of debt issues and predictablevariation in bond returns. Journal of Financial Economics 70:261–91.
Bakshi, G., and Z. Chen. 1994. Baby boom, population aging, and capital markets. Journalof Business 67:165–202.
Barclay, M., and C. Smith. 1995. The maturity structure of corporate debt. Journal ofFinance 50:609–31.
Becker, B., and V. Ivashina. 2015. Reaching for yield in the bond market. Journal of Finance70:1863–901.
Bretscher, L., L. Schmid, I. Sen, and V. Sharma. 2020. Institutional corporate bond demand.Working Paper, Harvard Business School, London Business School, and USC Marshall.
Bunker, A., J. Wildenhain, N. Henschke, J. Rocklöv, S. Hajat, and R. Sauerborn. 2016.Effects of air temperature on climate-sensitive mortality and morbidity outcomes in theelderly: A systematic review and meta-analysis of epidemiological evidence. EBioMedicine6:258–68.
Chaderina, M., P. Weiss, and J. Zechner. 2021. The maturity premium. Journal of FinancialEconomics Forthcoming.
Chen, Z., P. Lou, and W. Zhu. 2020. Duration-hedging trades, return momentum andreversal. Working paper, Hong Kong University of Science and Technology.
Chen, Z., and B. Yang. 2019. In search of preference shock risks: Evidence from longevityrisk and momentum profits. Journal of Financial Economics 133:225–40.
Chiu, Y., and D. Pain. 2018. Mortality improvement: Understanding the past and framingthe future. Report, Swiss Re Institute.
Cox, S., and Y. Lin. 2007. Natural hedging of life and annuity mortality risks. NorthAmerican Actuarial Journal 11:1–15.
27
Cutler, D., A. Deaton, and A. Lleras-Muney. 2006. The determinants of mortality. Journalof Economic Perspectives 20:97–120.
DellaVigna, S., and J. Pollet. 2007. Demographics and industry returns. American EconomicReview 97:1667–702.
DellaVigna, S., and J. M. Pollet. 2013. Capital budgeting versus market timing: Anevaluation using demographics. Journal of Finance 68:237–70.
Domanski, D., H. Shin, and V. Sushko. 2017. The hunt for duration: Not waving butdrowning? Working Paper, Bank for International Settlements.
Dwyer-Lindgren, L., A. Bertozzi-Villa, R. Stubbs, C. Morozoff, J. Mackenbach, F. van Lenthe,A. Mokdad, and C. Murray. 2017. Inequalities in life expectancy among US counties,1980 to 2014: Temporal trends and key drivers. JAMA Internal Medicine 177:1003–11.
Ellul, A., C. Jotikasthira, and C. Lundblad. 2011. Regulatory pressure and fire sales in thecorporate bond market. Journal of Financial Economics 101:596–620.
Ezzati, M., A. Friedman, S. Kulkarni, and C. Murray. 2008. The reversal of fortunes: Trendsin county mortality and cross-county mortality disparities in the United States. PLoS Med5:557–68.
Favero, C., A. Gozluklu, and A. Tamoni. 2011. Demographic trends, the dividend-priceratio, and the predictability of long-run stock market returns. Journal of Financial andQuantitative Analysis 46:1493–520.
Foley-Fisher, N., R. Ramcharan, and E. Yu. 2016. The impact of unconventional monetarypolicy on firm financing constraints: Evidence from the maturity extension program.Journal of Financial Economics 122:409–29.
Fuchs, V. 2004. Reflections on the socio-economic correlates of health. Journal of HealthEconomics 23:653–61.
Ge, S., and M. Weisbach. 2020. The role of financial conditions in portfolio choices: Thecase of insurers. Journal of Financial Economics forthcoming.
Geanakoplos, J., M. Magill, and M. Quinzii. 2004. Demography and the long-run pre-dictability of the stock market. Brookings Papers on Economic Activity 2004:241–325.
Gilchrist, S., and E. Zakrajšek. 2012. Credit spreads and business cycle fluctuations.American economic review 102:1692–720.
Goyal, A. 2004. Demographics, stock market flows, and stock returns. Journal of Financialand Quantitative Analysis 39:115–42.
Greenwood, R., S. Hanson, and J. Stein. 2010. A gap-filling theory of corporate debtmaturity choice. Journal of Finance 65:993–1028.
28
Greenwood, R., and D. Vayanos. 2010. Price pressure in the government bond market.American Economic Review 100:585–90.
Guedes, J., and T. Opler. 1996. The determinants of the maturity of corporate debt issues.Journal of Finance 51:1809–33.
Hart, O., and J. Moore. 1994. A theory of debt based on the inalienability of human capital.Quarterly Journal of Economics 109:841–79.
Hedegaard, H., A. Miniño, and M. Warner. 2018. Drug overdose deaths in the UnitedStates, 1990-2017. NCHS Data Brief No. 329. Hyatsville, MD: National Center for HealthStatistics.
Huang, J.-Z., and Z. Shi. 2021. What do we know about corporate bond returns? AnnualReview of Financial Economics forthcoming.
Koijen, R., S. Nieuwerburgh, and M. Yogo. 2016. Health and mortality delta: Assessing thewelfare cost of household insurance choice. Journal of Finance 71:957–1010.
Koijen, R., T. Philipson, and H. Uhlig. 2016. Financial health economics. Econometrica84:195–242.
Koijen, R., R. Richmond, and M. Yogo. 2020. Which investors matter for equity valuationsand expected returns? Working Paper, University of Chicago.
Koijen, R., and M. Yogo. 2019. A demand system approach to asset pricing. Journal ofPolitical Economy 127:1475–515.
Krishnamurthy, A., and A. Vissing-Jorgensen. 2011. The effects of quantitative easing oninterest rates: Channels and implications for policy. Brookings Papers on Economic ActivityFall:215–87.
Lee, R., and L. Carter. 1992. Modeling and forecasting U.S. mortality. Journal of theAmerican Statistical Association 87:659–71.
Li, H., and R. Hyndman. 2021. Assessing mortality inequality in the US: What can be saidabout the future? Insurance: Mathematics and Economics forthcoming.
López-Salido, D., J. Stein, and E. Zakrajšek. 2017. Credit-market sentiment and the businesscycle. Quarterly Journal of Economics 132:1373–426.
Mackenbach, J., I. Stirbu, A.-J. Roskam, M. Schaap, G. Menvielle, M. Leinsalu, and A. Kunst.2008. Socioeconomic inequalities in health in 22 European countries. New EnglandJournal of Medicine 358:2468–81.
Maurer, T. 2018. Asset pricing implications of demographic change. Working Paper,Washington University in St. Louis.
29
Mila, A. 2019. About mortality data for United States. https://www.mortality.org/hmd/USA/InputDB/USAcom.pdf. Accessed: 2021-1-16.
Moreno-Serra, R., and P. Smith. 2015. Broader health coverage is good for the nation’shealth: Evidence from country level panel data. Journal of the Royal Statistical Society.Series A, (Statistics in Society) 178:101–24.
Murray, S., and S. Nikolova. 2021. The bond pricing implications of rating-based capitalrequirements. Journal of Financial and Quantitative Analysis forthcoming.
Myers, S. 1977. Determinants of corporate borrowing. Journal of Financial Economics5:147–75.
NAIC. 2017. NAIC own risk and solvency assessment (ORSA) Guidance Manual. http://content.naic.org/publications.
OECD. 2010. Health care systems: Efficiency and policy settings. Working Paper, OECD.
Ozdagli, A., and K. Wang. 2020. Interest rates and insurance company investment behavior.Working Paper, Federal Reserve Bank of Dallas.
Poterba, J. 2001. Demographic structure and asset returns. Review of Economics andStatistics 83:565–84.
Sen, I., and V. Sharma. 2020. Internal models, make believe prices, and bond marketcornering. Working Paper, Harvard University.
Shaw, J., W. Horrace, and R. Vogel. 2005. The determinants of life expectancy: An analysisof the OECD health data. Southern Economic Journal 71:768–83.
Stohs, M., and D. Mauer. 1996. The determinants of corporate debt maturity structure.Journal of Business 69:279–312.
Vayanos, D., and J.-L. Vila. 2020. A preferred-habitat model of the term structure of interestrates. Econometrica Forthcoming.
Whited, T., and G. Wu. 2006. Financial constraints risk. Review of Financial Studies19:531–59.
Yu, Y. 2020. Hunt-for-duration in the corporate bond market. Working paper, PrincetonUniversity.
Zhu, Q. 2021. Capital supply and corporate bond issuances: Evidence from mutual fundflows. Journal of Financial Economics Forthcoming.
30
−.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
0.0
0.2
0.4
0.6
Longevity shocks
Longevity Shocks in Each State (2000)
State−level Longevity Risk
(b) State-level longevity risk (2000)
−0.4
−0.2
0.0
0.2
0.4
0.6
Longevity shocks
Longevity Shocks in Each State (2010)
State−level Longevity Risk
(c) State-level longevity risk (2010)
−0.4
−0.2
0.0
0.2
0.4
0.6
Longevity shocks
Longevity Shocks in Each State (2018)
State−level Longevity Risk
(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
(1) Long-term investment (5)Long-term (2) (3) (4) Asset
debt growth R&D PPEGrowth CAPEX maturity
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.
(1) Long-term investment (5)Long-term (2) (3) (4) Asset
debt growth R&D PPEGrowth CAPEX maturity
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
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
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