Stock Market Wealth and the Real Economy: A Local Labor Market Approach (NBER Working Paper 25959)

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NBER Working Paper No. 25959, "Stock Market Wealth and the Real Economy: A Local Labor Market Approach," by Gabriel Chodorow-Reich, Plamen T. Nenov and Alp Simsek, dated June 2019 and revised February 2020. The abstract says the authors provide evidence of the stock market wealth effect on consumption using a local labor market analysis and regional heterogeneity in stock market wealth. It states that an increase in local stock wealth driven by aggregate stock prices increases local employment and payroll in nontradable industries and in total, with no effect on employment in tradable industries. The authors report a marginal propensity to consume out of a dollar of stock wealth of 3.2 cents per year.

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NBER WORKING PAPER SERIES

STOCK MARKET WEALTH AND THE REAL ECONOMY:
A LOCAL LABOR MARKET APPROACH

Gabriel Chodorow-Reich
Plamen T. Nenov
Alp Simsek

Working Paper 25959
http://www.nber.org/papers/w25959

NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
June 2019, Revised February 2020

We would like to thank George-Marios Angeletos, Ricardo Caballero, Anthony DeFusco
(discussant), Paul Goldsmith-Pinkham, Annette Vissing-Jorgensen, Kairong Xiao, and numerous
seminar participants for helpful comments. Joel Flynn and Katherine Silva provided excellent
research assistance. Chodorow-Reich acknowledges support from the Molly and Dominic
Ferrante Economics Research Fund. Nenov would like to thank Harvard University and the
NBER for their hospitality during the initial stages of the project. Simsek acknowledges support
from the National Science Foundation (NSF) under Grant Number SES-1455319. Any opinions,
findings, conclusions or recommendations expressed in this material are those of the author(s)
and do not necessarily reflect the views of the NSF or the National Bureau of Economic
Research.

NBER working papers are circulated for discussion and comment purposes. They have not been
peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies
official NBER publications.

© 2019 by Gabriel Chodorow-Reich, Plamen T. Nenov, and Alp Simsek. All rights reserved.
Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission
provided that full credit, including © notice, is given to the source.
Stock Market Wealth and the Real Economy: A Local Labor Market Approach
Gabriel Chodorow-Reich, Plamen T. Nenov, and Alp Simsek
NBER Working Paper No. 25959
June 2019, Revised February 2020
JEL No. E21,E32,E44

ABSTRACT

We provide evidence of the stock market wealth effect on consumption by using a local labor
market analysis and regional heterogeneity in stock market wealth. An increase in local stock
wealth driven by aggregate stock prices increases local employment and payroll in nontradable
industries and in total, while having no effect on employment in tradable industries. In a model
with consumption wealth effects and geographic heterogeneity, these responses imply a marginal
propensity to consume out of a dollar of stock wealth of 3.2 cents per year. We also use the model
to quantify the aggregate effects of a stock market wealth shock when monetary policy is passive.
A 20% increase in stock valuations, unless countered by monetary policy, increases the aggregate
labor bill by at least 1.7% and aggregate hours by at least 0.75% two years after the shock.

Gabriel Chodorow-Reich Alp Simsek
Department of Economics Department of Economics, E52-552
Harvard University MIT
1805 Littauer Center 50 Memorial Drive
Cambridge, MA 02138 Cambridge, MA 02142
and NBER and NBER
chodorowreich@fas.harvard.edu asimsek@mit.edu

Plamen T. Nenov
Norwegian Business School (BI)
Nydalsveien 37 0484 Oslo, Norway
plamen.nenov@bi.no

A online appendix is available at http://www.nber.org/data-appendix/w25959
A Dynamic link to the most recent draft: is available at https://www.dropbox.com/s/7q1zzxkkr184rjy/crns_stock
1 Introduction
According to a recent textual analysis of FOMC transcripts by Cieslak and Vissing-Jorgensen
(2017), many U.S. policymakers believe that stock market fluctuations affect the labor market
through a consumption wealth effect. In this view, a decline in stock prices reduces the wealth
of stock-owning households, causing a reduction in spending and hence in employment. While
apparently an important driver of U.S. monetary policy, this channel has proved difficult to
establish empirically. The main challenge arises because stock prices are forward-looking.
Therefore, an anticipated decline in future economic fundamentals could also lead to both a
negative stock return and a subsequent decline in household spending and employment.
We use a local labor market analysis to address this empirical challenge and provide
quantitative evidence on the stock market consumption wealth effect. Our empirical strategy
combines regional heterogeneity in stock market wealth with aggregate movements in stock
prices to identify the causal effect of stock wealth changes on regional labor market outcomes.
We then present a model that relates the regional outcomes to the household-level propensity
to consume out of stock wealth as well as to the aggregate labor market effects of stock wealth
changes. Our empirical estimates map into a household-level annual marginal consumption
propensity of 3.2 cents per dollar of stock wealth and imply that annual aggregate payroll
increases by 1.7% following a yearly standard deviation increase in the stock market, unless
countered by monetary policy.
To frame the regional analysis, it helps to begin by describing the consumption wealth
effect in our model setting. The environment features a continuum of areas, a tradable
good and a nontradable good, and two factors of production, capital and labor. The only
heterogeneity across regions is in their ownership of capital, which also equates to stock
wealth. The aggregate price of capital is endogenous and fluctuates due to changes in
households’ beliefs about the expected future productivity of capital. An increase in stock
wealth increases local spending on nontradable goods, and more so in areas with greater
capital ownership. Higher spending drives up the labor bill and increases employment in the
nontradable sector and in total. Local wages increase (weakly) more in high wealth areas,
which induces a (weak) fall in tradable employment.
In the data, we measure changes in county-level stock market wealth in three steps. In
the first step, we capitalize dividend income reported on tax returns aggregated to the county
level to arrive at a county-level measure of taxable stock wealth. Our capitalization method
improves on existing work such as in Saez and Zucman (2016) by allowing for heterogeneity
in dividend yields by wealth, which we obtain using a sample of account-level portfolio
holdings from a large discount broker. In the second step, we adjust this measure of taxable

1
stock wealth to account for non-taxable (e.g., retirement) stock wealth, using information
on the relationship between taxable and total stock wealth and demographics in the Survey
of Consumer Finances. In the final step, we multiply the total county stock wealth with
the return on the market (CRSP value-weighted) portfolio and a county-specific portfolio
beta constructed from county demographic information and variation in betas across the age
distribution in the data from the discount broker. This provides a measure of the change
in county stock wealth driven by the aggregate stock return. Motivated by our theoretical
analysis, we then divide this change by the county labor bill to arrive at our main regressor.
Our empirical specification identifies the effect of changes in stock wealth on local labor
market outcomes by exploiting the substantial variation in the aggregate stock return that
occurs independent of other macroeconomic variables. In particular, we allow high wealth
areas to exhibit greater sensitivity to changes in aggregate bond wealth, aggregate housing
wealth, and aggregate labor income and non-corporate business income, and also control for
county fixed effects, state-by-quarter fixed effects, and a Bartik-type industry employment
shift-share. Our identifying assumption is that, conditional on these controls, areas with
high stock market wealth do not experience unusually rapid employment or payroll growth
following a positive aggregate stock return for reasons other than the stock market wealth
effect on local spending.
An increase in local stock wealth induced by a positive stock return increases total local
employment and payroll. Seven quarters after an increase in stock market wealth equivalent
to 1% of local labor market income, local employment is 0.77 basis points higher and local
payroll is 2.18 basis points higher. Because stock returns are nearly i.i.d., these responses
reflect the short-run effect of a permanent change in stock market wealth. Motivated by the
theory, we also investigate the effect on employment and the labor bill in the nontradable and
tradable industries, following the sectoral classifications in Mian and Sufi (2014). Consistent
with the theory, the employment response in nontradable industries exceeds the overall
response, while employment in tradable industries does not increase. We also report a large
response in the residential construction sector, consistent with a household demand channel.
The main threat to a causal interpretation of these findings is that high wealth ar-
eas respond differently to other aggregate variables that co-move with the stock market.
This concern motivates the variables included in our baseline specification. The absence of
“pre-trend” differences in outcomes in the quarters before a positive stock return and the
non-response of employment in the tradable sector support a causal interpretation of our
findings. We report additional robustness along a number of dimensions, including: using
a more parsimonious specification that excludes the parametric controls; including interac-
tions of stock market wealth with TFP growth to allow wealthier counties to have different

2
loadings on this variable; controlling for local house prices; using only within commuting
zone variation in stock market wealth; subsample analysis including dropping the wealthi-
est counties and the quarters with the most volatile stock returns; and not weighting the
regression. A decomposition along the lines of Andrews et al. (2017) shows that no single
state drives the results. We also report a quantitatively similar response using cross-state
variation and state-level consumption expenditure from the Bureau of Economic Analysis.
We combine our empirical results with the theoretical model to calibrate two key pa-
rameters: the strength of the household-level stock wealth effect and the degree of local
wage adjustment. To calibrate the stock wealth effect, we provide a separation result from
our model that decomposes the empirical coefficient on the nontradable labor bill into the
product of three terms: the partial equilibrium marginal propensity to consume out of stock
market wealth, the local Keynesian multiplier (equivalent to the multiplier on local govern-
ment spending), and the labor share of income.1 This decomposition applies to more general
changes in local consumption demand and therefore may be of use outside our particular
setting. We use standard values from previous literature to calibrate the labor share of
income and the local Keynesian multiplier. Given these values, the empirical response of
the nontradable labor bill implies that in partial equilibrium a one dollar increase in stock-
market wealth increases annual consumption expenditure by about 3.2 cents two years after
the shock. For the degree of wage adjustment, comparing the response of total employment
with the response of the total labor bill suggests that a 1 percent increase in labor (total
hours worked) is associated with a 0.9 percent increase in wages at a two year horizon.
Finally, we use the model to quantify the aggregate effects that stock price shocks would
generate if monetary policy (or other demand-stabilization policies) did not respond to the
shock. We first show that a one dollar increase in stock market wealth has the same propor-
tional effect on the local nontradable and aggregate total labor bills, up to an adjustment for
the difference in the local and aggregate spending multipliers. Homothetic preferences and
production across sectors underlies this theoretical result, and we provide evidence of such
homotheticity in the data. Next, we show how the local response of wages informs about
the aggregate wage Phillips curve in our model. Since labor markets are local, the aggregate
wage response is similar to the local wage response, with an adjustment due to the fact that
demand shocks impact aggregate inflation and local inflation differently. We then consider
a 20% positive shock to stock valuations—approximately the yearly standard deviation of
stock returns. Using our empirical estimate for the nontradable labor bill, and applying a
1
In general, there may be an additional term reflecting the response of output in the tradable sector
when relative prices change across areas. This term disappears in our benchmark calibration, which features
Cobb-Douglas preferences across tradable goods produced in different regions. Allowing for a non-unitary
elasticity of substitution across regions does not meaningfully change our conclusions.

3
bounding argument for moving from local to aggregate effects similar to that in Chodorow-
Reich (2019), this shock would increase the aggregate labor bill by at least 1.7% two years
after the shock. Combining this effect with the degree of aggregate wage adjustment implied
by our local estimates, the shock would also increase aggregate hours by at least 0.75%.
The rest of the paper is organized as follows. After discussing the related literature,
we start by presenting the empirical analysis. Section 2 describes the data sets and the
construction of our main variables. Section 3 presents the baseline empirical specification
and discusses conditions for causal inference. Section 4 contains the empirical results. We
then turn to the theoretical analysis and the structural interpretation. Section 5 describes
our model. Section 6 uses the empirical results to calibrate the model and derive the partial
equilibrium wealth effect. Section 7 calculates the implied aggregate wealth effects, and
Section 8 concludes.

Related literature. Our paper contributes to a large literature that investigates the re-
lationship between stock market wealth, consumption, and the real economy. A major
challenge is to disentangle whether the stock market has an effect on consumption over a rel-
atively short horizon (the direct wealth effect), or whether it simply predicts future changes
in productivity, income, and consumption (the leading indicator effect). The challenge is
compounded by the scarcity of data sets that contain information on household consump-
tion and financial wealth. The recent literature has tried to address these challenges in
various ways (see Poterba (2000) for a survey of the earlier literature).
The literature using aggregate time series data finds mixed evidence (see e.g. Poterba
and Samwick, 1995; Davis and Palumbo, 2001; Lettau et al., 2002; Lettau and Ludvigson,
2004; Carroll et al., 2011). Davis and Palumbo (2001) and Carroll et al. (2011) estimate
a wealth effect of up to around 6 cents. On the other hand, Lettau and Ludvigson (2004)
argue for more limited wealth effects. However, an aggregate time series approach introduces
two complications: First, in an environment in which monetary policy effectively stabilizes
aggregate demand fluctuations, as in our model, there can be strong wealth effects and yet no
relationship between asset price shocks and aggregate consumption. Second, stock market
fluctuations may affect aggregate demand via an investment channel (see Cooper and Dynan
(2016) for other issues with using aggregate time series in this context).
Another strand of the literature uses household level data and exploits the heterogeneity
in household wealth to isolate the stock wealth effect. Dynan and Maki (2001) use Consumer
Expenditure Survey (CE) data to compare the consumption response of stockholders with
non-stockholders. They find a relatively large marginal propensity to consume (MPC) out of
stock wealth—around 5 to 15 cents per dollar per year. However, Dynan (2010) re-examines

4
the evidence by extending the CE sample to 2008 and finds weaker effects. More recently,
Di Maggio et al. (forthcoming) use detailed individual-level administrative wealth data for
Sweden to identify the stock wealth effect from variation in individual-level portfolio returns.
They find substantial effects: the top 50% of the income distribution, who own most of the
stocks, have an estimated MPC of around 5 cents per dollar per year.2
We complement these studies by focusing on regional heterogeneity in stock wealth. We
show how the regional empirical analysis can be combined with a model to estimate the
household-level stock wealth effect. The MPC implied by our analysis (3.2 cents per dollar
per year) is close to estimates from the recent literature. An important advantage of our
approach is that it directly estimates the local general equilibrium effect. In particular,
by examining the labor market response, we provide direct evidence on the margin most
important to monetary policymakers.
Case et al. (2005) and Zhou and Carroll (2012) also use regional variation to estimate
financial wealth effects. Case et al. (2005) overcome the absence of geographic data on
financial wealth by using state-level mutual fund holdings data from the Investment Company
Institute (ICI) and measure state consumption using retail sales data from the Regional
Financial Associates. Zhou and Carroll (2012) criticize the data construction and empirical
specification in Case et al. (2005) and construct their own data set using proprietary data on
state-level financial wealth and retail sales taxes as a proxy for consumption. Both papers
find negligible stock wealth effects and a sizable housing wealth effect. Relative to these
papers, we exploit the much greater variation in financial wealth across counties than across
states and provide evidence on the labor market margin directly. Other recent papers use
regional variation but focus only on estimating housing wealth effects (Mian et al., 2013;
Mian and Sufi, 2014; Guren et al., 2018).3
Our focus on the consumption wealth channel complements research on the investment
channel of the stock market that dates to Tobin (1969) and Hayashi (1982). Under the
identifying assumptions we articulate below, our local labor market analysis absorbs the
effects of changes in Tobin’s Q or the cost of equity financing on investment into a time fixed
effect, allowing us to isolate the consumption wealth channel.
Our theoretical framework builds upon the model in Mian and Sufi (2014) by incor-
2
See also Bostic et al. (2009) and Paiella and Pistaferri (2017) for similar analyses of stock wealth effects
in different contexts.
3
See also Case et al.(2005; 2011), Campbell and Cocco (2007), Mian and Sufi (2011), Carroll et al. (2011),
and Browning et al. (2013), among others. In terms of comparison of wealth effects from stock wealth versus
housing wealth, Guren et al. (2018) estimate an MPC out of housing wealth of around 2.7 cents during
1978-2017, which is comparable in magnitude to our estimate of the stock wealth effect. This is substantially
lower than the estimates in Mian et al. (2013) and Mian and Sufi (2014), which are in the range of 7 cents.
See Guren et al. (2018) for a discussion of the possible drivers of these differences.

5
porating several features important for a structural interpretation of the results, including
endogenous changes in wealth, monetary policy, partial wage adjustment, and imperfectly
substitutable tradable goods. Our framework also shares features with models of small open
economies with nominal rigidities (e.g. Gali and Monacelli, 2005) adapted to the analysis
of monetary unions by Nakamura and Steinsson (2014) and Farhi and Werning (2016), but
differs from these papers by including a fully nontradable sector. This feature facilitates the
structural interpretation and aggregation of the estimated local general equilibrium effects.
Our structural interpretation and aggregation results represent methodological contribu-
tions that apply beyond our particular model. First, and similar to the approach in Guren
et al. (2018) and formalized in Guren et al. (2020), we illustrate how the estimated local
general equilibrium effects can be combined with external estimates of the local income
multiplier (e.g., estimates from local government spending shocks) to obtain the partial
equilibrium spending effect.4 Our decomposition differs from theirs in that it applies to the
coefficient for the nontradable labor bill—a variable that is easily observable at the regional
level—and therefore includes an adjustment for the labor share of income. Second, we show
how, under standard assumptions, the response of the local labor bill in the nontradable sec-
tor provides a direct and transparent bound for the response of the aggregate effect across
all sectors when monetary policy does not react.

2 Data
In this section we explain how we measure the key objects in our empirical analysis: the ratio
of geographic stock market wealth to labor income, the stock market return, employment,
and payroll. Our geographical unit is a U.S. county. This level of aggregation leaves ample
variation in stock market wealth while being large enough to encompass a substantial share
of spending by local residents. The U.S. contains 3,142 counties using current delineations.

2.1 Stock Market Wealth
We denote our main regressor as Sa,t−1 Ra,t−1,t , where Sa,t−1 is stock market wealth in county
a in period t − 1 normalized by the period t − 1 labor bill and Ra,t−1,t is the portfolio return
between t − 1 and t. In Section 5, we show that regressions of log changes in local labor
market outcomes on this variable yield coefficients tightly related to the key parameters of
our model.
4
In contemporaneous work, Wolf (2019) formally establishes (in a closed economy setting) conditions
under which the multiplier effects from private spending are exactly the same as the multiplier effects from
public spending.

6
We construct local stock market wealth by capitalizing taxable dividend income and then
adjusting for stock wealth held in non-taxable accounts. We summarize our methodology
here and provide additional detail of the data, sample construction, and adjustments in
Appendix A.1. Our capitalization method involves multiplying observed taxable dividend
income by a price-dividend ratio to arrive at stock wealth held in taxable accounts.5 We
start with IRS Statistics of Income (SOI) data containing county aggregates of annual divi-
dend income reported on individual tax returns, over the period 1989-2015. Dividend income
as reported on form 1040 includes any distribution from a C-corporation. It excludes dis-
tributions from partnerships, S-corporations, or trusts, except in rare circumstances where
S-corporations that converted from C-corporations distribute earnings from before their con-
version. While we cannot separate distributions from publicly-traded and privately-held C-
corporations, we show in Appendix A.1.4 that equity in privately-held C-corporations is too
small (less than 7% of total equity of C-corporations) to meaningfully affect our results.
We construct a county-specific capitalization factor as the product of the price-dividend
ratio on the value-weighted CRSP portfolio and a time-varying county-specific adjustment.
The CRSP portfolio contains all primary listings on the NYSE, NYSE MKT, NASDAQ, and
Arca exchanges and, therefore, covers essentially the entire U.S. equity market. The county-
specific adjustment recognizes that older individuals both have higher average wealth and
hold higher dividend-yield stocks, as first conjectured in Miller and Modigliani (1961) and
documented in Graham and Kumar (2006). We believe we are the first to apply such an
adjustment in capitalizing equity wealth. To do so, we follow Graham and Kumar (2006)
and use the Barber and Odean (2000) data set of individual account-level stock holdings
from a large discount broker over the period 1991-1996.6 Specifically, as we describe in more
detail in Appendix A.1.2, we merge the Barber and Odean (2000) data set with CRSP stock
5
The literature has proposed other income measures and capitalization factors. Mian et al. (2013) and
Mian and Sufi (2014) group dividends, interest, and other non-wage income together and use the ratio of
total household financial wealth in the Financial Accounts of the United States (FAUS) to the national
aggregate of this combined income measure as a single capitalization factor for all financial wealth. Saez and
Zucman (2016) and Smith et al. (In progress) use both dividends and capital gains to allocate directly held
corporate equities in the FAUS, with Smith et al. arguing forcefully for a low weight on the capital gains
component because realized capital gains include many transactions other than sales of corporate equity.
Relative to these alternatives, capitalizing dividends using a price-dividend ratio isolates the income stream
most closely related to corporate equity wealth and facilitates the adjustment for heterogeneous dividend
yields described below.
6
The data are a random sample of accounts at the brokerage and have been used extensively to study
individual trading behavior (Barber and Odean, 2000, 2001; Graham and Kumar, 2006; Barber and Odean,
2007; Mitton and Vorkink, 2007; Kumar, 2009; Seasholes and Zhu, 2010; Kent et al., 2019). Graham and
Kumar (2006) compare the data with the 1992 and 1995 waves of the SCF and show that the stock holdings
of investors in the brokerage data are fairly representative of the overall population of retail investors. We
consider taxable accounts with at least one dividend-paying stock to mimic the dividends observed in the
IRS data.

7
and mutual fund data and compute average dividend yields for five age groups, separately
for each Census Region. The dividend yield slopes upward with age, with individuals 65
and over holding stocks with a dividend yield about 10% (not p.p.) higher than the market
average and individuals 35 and younger holding stocks with a dividend yield about 10%
lower than the market average. Importantly, variation by age accounts for essentially all
of the variation in dividend yields across the wealth distribution, as shown in Figure A.1
and Table A.1. We combine the age-specific dividend yields with county-level demographic
information and wealth by age group from the Survey of Consumer Finances (SCF). We then
adjust the CRSP dividend yield in each county-year by the age-wealth-weighted average of
the age-specific dividend yields.
We next adjust county taxable stock market wealth to account for wealth held in non-
taxable accounts, primarily in defined contribution pension plans.7 We do not include wealth
in defined benefit pension plans, since household claims on that wealth do not fluctuate di-
rectly with the value of the stock market. Roughly one-third of total household stock market
wealth is held in non-taxable accounts (see Figure A.4). In Appendix A.1.3, we estimate the
relationship at the household level between total stock market wealth, taxable stock market
wealth, and household demographic characteristics, using the SCF. Total and taxable stock
market wealth vary almost one-to-one, reflecting statutory limits on contributions to non-
taxable accounts that make non-taxable wealth much more evenly distributed than taxable
wealth. The variables also explain total wealth well, with an R2 above 0.9. We combine
the coefficients on taxable wealth and demographic characteristics from the SCF with our
county-level measure of taxable stock wealth and county-level demographic characteristics
to produce our final measure of total county stock market wealth. Finally, we divide this
measure by SOI (annual) county labor income to arrive at our measure of local stock market
wealth relative to labor income, Sa,t .
Figure 1a shows the variation in this measure across U.S. counties in 1990. Figure 1b
and Figure 1c show the variation in 1990 and 2015, respectively, after removing state-specific
means. The within-state differences are persistent over time, with a within-state correlation
between Sa,1990 and Sa,2015 of 0.81. Table A.4 reports summary statistics for Sa,t and other
variables used in the analysis.

2.2 Stock Market Return
We write the stock market return in county a as Ra,t−1,t ∗
= αa + Rt−1,tf m
+ ba,t × (Rt−1,t −
f
Rt−1,t ) + ea,t−1,t , where Rt−1,t
f
is the risk-free rate in period t, Rt−1,t
m
is the market return, ba,t
7
This adjustment is appropriate if the marginal propensities to consume out of taxable and non-taxable
stock wealth are the same. We revisit this assumption at the end of our analysis (see Footnote 44.)

8
Figure 1: Stock Market Wealth Relative to Labor Income Across U.S. Counties.
(a) 1990

(0.94,12.38] (0.70,0.94] (0.56,0.70] (0.45,0.56] (0.34,0.45] (0.24,0.34] [0.00,0.24] No data

(b) 1990, within state

(0.28,11.82] (0.08,0.28] (-0.04,0.08] (-0.13,-0.04] (-0.22,-0.13] (-0.33,-0.22] [-1.28,-0.33] No data

(0.45,25.51] (0.13,0.45] (-0.07,0.13] (-0.22,-0.07] (-0.36,-0.22] (-0.56,-0.36] [-2.13,-0.56] No data

9
is a county-specific portfolio beta, and ea,t−1,t is an idiosyncratic component of the return.
We do not observe Ra,t−1,t
∗
. Instead, we define the variable Ra,t−1,t that enters into our main
regressor as Ra,t−1,t = Rt−1,t + ba,t × (Rt−1,t
f m f
− Rt−1,t ). To operationalize Ra,t−1,t , we equate
the risk-free rate Rt−1,t
f
with the interest rate on a 3-month Treasury bill, the market return
Rt−1,t with the total return on the value-weighted CRSP portfolio, and construct the county-
m

specific portfolio beta ba,t using the relationship between market beta and age in the Barber
and Odean (2000) data set and our measure of the county age-wealth distribution. This
adjustment incorporates the tendency for older, wealthier households to hold stocks with
lower betas, a pattern we document in Figure A.6 of the online appendix. Ignoring it would
result in systematic over-counting of changes in wealth in high wealth areas when the stock
market changes, leading to an under-estimate of the consumption wealth effect, although
this effect turns out to be small in practice as the ba,t all lie between 0.97 and 1.03.
We now discuss the differences between the true county return Ra,t−1,t∗
and the measured
return Ra,t−1,t and why these differences do not affect the validity of our empirical analysis.
Three possible differences exist. First, the true county return includes a county-specific αa ,
reflecting differences in portfolio characteristics and the possibility that high wealth areas
have systematically better portfolios, as suggested by Fagereng et al. (2016). Our empirical
specification will include county fixed effects to absorb this type of heterogeneity. Second,
high wealth areas could have systematically riskier or less risky stock portfolios beyond
the correlation due to age, in which case we would systematically mis-measure ba,t . While
previous work has documented that wealthy households have portfolios tilted toward riskier
asset classes than the general population (Carroll, 2000; Calvet and Sodini, 2014), here what
matters is risk-taking within stock portfolios. Figure A.6 shows this correlation using the
Barber and Odean (2000) data set. Except for the bottom wealth decile, who typically hold
only one or two securities and have very low beta portfolios, there is a nearly flat relationship
between beta and wealth decile within age bins. Therefore, this source of heterogeneity does
not appear important in practice. Third, the true return Ra,t−1,t ∗
contains an idiosyncratic
component ea,t−1,t , reflecting differences in portfolio allocation arising, for example, from
home bias as documented in Coval and Moskowitz (1999) or from differences in market beta
uncorrelated with wealth. This component has no impact on our empirical results because it
gives rise to idiosyncratic changes in wealth that are uncorrelated with our main regressor.
This statement remains true even if the idiosyncratic part of the return correlates with local
economic activity, as might occur due to home bias in portfolio allocation.8
8
Formally, assume the true structural model is ya = β (Sa Ra∗ ) + a and Ra∗ = Ra + ea , where ya is an
outcome, ea is a mean-zero component of the return independent of wealth Sa or the measured part of the
return Ra , and the structural residual a is independent of the measured change in wealth Sa Ra . (We have
dropped time subscripts and ignored the component αa to simplify notation and without loss of generality).

10
Figure 2: Attributes of Quarterly Stock Returns

(a) Serial correlation of returns (b) Cumulative return response
8 1.084
3
c =
5 7)
= 2
& ~~ 1.045
o B
: 5
4
3 8 1.02:
ig :
=
fs)
j 1.00 1 ; 1 1 ; 1 1 1 1 1 1
4 5 6 1012 3 4 5 6 7 8 9 10
Return horizon Return horizon

Correlation (Rj, #10+nY)

Correlation horizon

Mewes A Bond @HPI

Notes: Panel (a) reports the coefficients (7, from estimating the regression Ri+p,_-1.447 = Qn+BnRi_-iiten at
each ws: Banal (p) repo h shown on the ae axis, where Revhoute n is the total return on te ides tect an at

CRSP portfolio between quarters t+h—1andt+h. Panel (b) reports the transformation Il _, (1+ Bror)
at each quarterly horizon 7 shown on the lower axis, where og is the standard deviation of the CRSP return.
Panel (c) reports the correlation coefficients of Ry1,4 and y~1,44n at each quarterly horizon h shown on the
lower axis, where 71,44 is the log change in aggregate labor compensation, the holding return on the 5
year Treasury, or the change in aggregate house prices between t — 1 and t +h.

Substituting, we have ya = 8(SaRa) + Ua, where Ua = BSaea + €a is a composite residual. Therefore, the
coefficient B from regressing yq on S,R, asymptotes to 6, since Cov (Saea, SaRa) = Cov (€a, SaRa) = 0 by
the independence assumptions on eg and €,. Alternatively, one can think of S¢4-1R:~-1,4 as the excluded
instrument and Sqz-1R7 4-14 as the endogenous variable in an instrumental variables design. Under the
assumption of purely idiosyncratic heterogeneity, the first stage regression of Sat-1 Ro 4-14 on So4—-1Ri-1,
would yield a coefficient of 1, in which case the IV coefficient coincides with the reduced form coefficient
that we estimate. Importantly, this argument extends straightforwardly to mis-measurement of 5,4 due
to heterogeneity in the price-dividend ratio uncorrelated with true wealth. Finally, the argument makes
no assumption on the correlation between the idiosyncratic component of the return e, and the structural
residual €,, as might occur in the context of home bias in portfolio allocation. Hyslop and Imbens (2001)
provide a more general discussion of measurement error that does not lead to biased estimation.

11
Figure 2a shows the serial correlation in the quarterly return on the CRSP portfolio and
Figure 2b the cumulative return following a one standard deviation increase in the stock
market during our sample period. As is well known, stock returns are nearly i.i.d., a result
confirmed by the almost complete absence of serial correlation in Figure 2a. This pattern
facilitates interpretation of our empirical results since it implies that a stock return in period
t has a roughly permanent effect on wealth, and we mostly ignore the small momentum and
subsequent reversal shown in Figure 2b in what follows. Figure 2c shows the correlation of
the period t stock return with the changes in other macroeconomic aggregate variables over
the horizon t − 1 to t + h. In our sample, the stock market return is positively correlated
with aggregate labor income and house prices, and negatively correlated with fixed income
returns. However, the correlation coefficients are all well below one, reflecting the substantial
movement in stock prices independent of these other factors (Shiller, 1981; Cochrane, 2011;
Campbell, 2014).

2.3 Outcome Variables
Our main outcome variables are log employment and payroll from the Bureau of Labor
Statistics Quarterly Census of Wages and Employment (QCEW). The source data for the
QCEW are quarterly reports filed with state employment security agencies by all employers
covered by unemployment insurance (UI) laws. The QCEW covers roughly 95% of total
employment and payroll, making the data set a near universe of administrative employment
records. We use the NAICS-based version of the data, which start in 1990, and seasonally
adjust the published county-level data by sequentially applying Henderson filters using the
algorithm contained in the Census Bureau’s X-11 procedure.9
An important element of our analysis is to distinguish between responses in sectors af-
fected by local demand shocks, which we refer to as “nontradable” sectors, and “tradable”
sectors unlikely to be affected by local demand shocks. We follow Mian and Sufi (2014)
and label NAICS codes 44-45 (retail trade) and 72 (accommodation and food services) as
nontradable and NAICS codes 11 (agriculture, forestry, fishing and hunting), 21 (mining,
quarrying, and oil and gas extraction), and 31-33 (manufacturing) as tradable.10 The re-
9
The NAICS version of the QCEW contains a number of transcription errors prior to 2001. We follow
Chodorow-Reich and Wieland (Forthcoming, Appendix F) and hand-correct these errors before applying the
seasonal adjustment procedure.
10
Mian and Sufi (2014) exclude NAICS 721 (accommodation) from their definition of nontradable indus-
tries. We leave this industry in our measure to avoid complications arising from the much higher frequency
of suppressed data in NAICS 3 than NAICS 2 digit industries in the QCEW data. The national share of
nontradable employment and payroll in NAICS 721 are both less than 8% and we have verified using coun-
ties with non-suppressed data that including this sector does not affect the nontradable responses reported
below.

12
tail trade sector includes a wide variety of establishments that cover essential (e.g. grocery
stores, drug stores) and luxury (e.g. specialty food stores, jewelry stores) expenditure and
everything in between (e.g. auto dealers, furniture stores, clothing stores). Nonetheless,
this classification is conservative in the sense that it leaves a large amount of employment
unclassified. This is in line with our model calibration, which depends only on having a
subset of industries that produce truly nontradable goods. On the other hand, even most
manufacturing shipments occur within the same zip code (Hillberry and Hummels, 2008),
which suggests local consumption demand could impact our measure of tradables. We re-
port robustness to using a classification scheme based on the geographic concentration of

employment in an industry.

3 Econometric Methodology

This section provides a formal discussion of causal identification, presents our baseline spec-

ification, and discusses the main threats to identification.

3.1 Framework

Motivated by the model in Section 5, we assume a true data generating process of the form:

Aa t-1t+hy = Pr{Sat—1Rat-1,t] +P), Xat—1 + €at—1t-th: (1)

where Agi—it+hY = Yatth — Yat—1 iS the change in variable y in area a between t — 1 and
t+h, Saz—1 is stock market wealth in area a in period t—1 relative to labor market income in
the area, Rat—i4 = bat Re ay +(1- bat) RL, is the measured return on the stock portfolio,
Xaz-1 collects included covariates determined (from the perspective of a local area) as of
time t — 1, 6, and Ty are coefficients (with the latter possibly vector-valued), and €a2—-11+h
contains un-modeled determinants of the outcome variable.

Let Br and T), denote the coefficients from treating €.4-144n as unobserved and Eq. (1)
as a Jorda (2005) local projection to be estimated by OLS. Because the local portfolio
betas {baz} all lie close to 1 and Rha, is much less volatile than R;",,, we can use the
approximation SqiiRatit © Sat-1bae Ri, in Eq. (1).17 In that case, Eq. (1) has an

approximate shift-share structure with a single national shifter given by the market return

"That is, for any (de-meaned) variable va, E[Sa,2-1Ra,t—-14Vat] = E[Sat—1ba eR” 1 Vat] + E[Sae—-11 —
bat) RE 1 vast] = E[Sat-1bae Re 1 4Va,t], where the term E[S,4-1(1 — bat) RE 4 (Vast is negligible because
1— baz © 0 and Var(Ri_, 4) << Var(R/",,). In fact, our results below change imperceptibly whether or

not we include the term S4-1(1 — bat) RE 4:

13
R14, and the identifying assumption for plim6;, = 6), takes the form:

E [RM au] =, (2)

where pup = E'[Sa2-10at€at—1,+h| iS a time t cross-area average of the product of the beta-
adjusted stock wealth—to—income b,45a4-1 and the unobserved component €at—Ltthe In-
tuitively, this condition will not hold if the outcome variable (e.g., employment or payroll)
grows faster for unmodeled reasons (€¢,:-144n > 0) in high wealth areas (= 4; > 0) in periods
when the stock return is positive, and vice versa when the stock return is negative.

The econometrics of shift-share designs have recently received renewed attention in
Goldsmith-Pinkham et al. (2018) and Borusyak et al. (2018). Condition (2) coincides with
the exogeneity condition in Borusyak et al. (2018) in the case of a single national observed
shock and multiple (asymptotically infinite) areas and time periods. As in their framework,
the condition recasts the identifying assumption from a panel regression into a single time
series moment by defining the cross-area average /;. Borusyak et al. (2018) defend the valid-
ity of shift-share instruments when the shifter is exogenous, a seemingly natural assumption
in our setting given that stock market returns are nearly i.i.d. Nonetheless, since stock mar-
ket returns are equilibrium outcomes (as most shifters are), identification of 3), also requires
that other aggregate variables correlated with R/",, and not controlled for in X impact areas
with high and low stock market wealth uniformly. Importantly, we do not require that stock
market wealth be distributed randomly, and show in Table A.5 that 5,4 correlates with the
share of a county’s population with a college education and the median age, among other
variables. Instead, as illustrated by Eq. (2), we require that high and low wealth areas not
be heterogeneously affected by other aggregate variables that co-move with stock returns.

This insight motivates our baseline specification and the robustness analysis below.

3.2. Baseline Specification

Our baseline specification implements Eq. (1) at the county level and at quarterly frequency,
with outcome y either log employment or log quarterly payroll. We include the following

controls in Xq+4~-1: a county fixed effect, a state x quarter fixed effect, and eight lags of the

12To derive this condition, let Y denote the AT x 1 vector of Aat—1,t+hy stacked over A areas and T
time periods, S the AT x T matrix containing the vector (b1,291,¢-1 Lee batSat—1). in rows A(t—1)+1
to At of column ¢ and zeros elsewhere, R the T x 1 vector of stock market returns, X the AT x K
matrix of K covariates stacked over areas and time periods, and € the AT’ x 1 stacked vector of €¢1-1,4n-
Then we can rewrite Eq. (1) in matrix form as Y = 8,SR-+ XT, +. It follows that plimBn = By if
0 = limaryo0 (SR) € = lima ro R’S'€ = lima ryo0 ; Ri-1.t oy bat Sat—1€0,t-1,t+h = E[Re-14pe] -
Note that this identification condition presumes a homogenous treatment effect. We explore treatment
heterogeneity explicitly in Section 4.4.

14
“shock” variable {Sat—j-1Rat—j-i1t—j}5=1- We also include interactions of 5,41 with changes
in other forms of aggregate wealth: the holding return on a 5 year Treasury bond, the log
growth of national house prices between t — 1 and t, and the log change in national labor
income and non-corporate business income from t—1 to the cumulative total over the next 12
quarters (to capture human capital and private business wealth).' Finally, we also include a
Bartik (1991) shift-share measure of predicted employment growth at horizon h based only on
industry composition, A, +—144,e.4 We weight regressions by 2010 population and report
standard errors two-way clustered by time and county. Clustering by county accounts for
any residual serial correlation in stock market returns and has a small effect on the standard
errors in practice. Clustering by time allows for areas with high or low stock market wealth
to experience other common shocks and accords with the recommendation of Adao et al.
(2019) in the special case of a single national shifter. Finally, we exclude from our baseline
sample counties in the top 5% of the share of employees working at large (500+) firms, as

these firms can have direct exposure to the stock market.

3.3. Threats to Identification and Motivation for Covariates

Our identifying assumption is that following a positive stock return, areas with high stock
market wealth relative to labor income do not experience unusually rapid employment or
payroll growth—relative to their own mean and to other counties in the same state, and
conditional on the included covariates—for reasons other than the wealth effect on local

consumption expenditure. As emphasized by Goldsmith-Pinkham et al. (2018), this require-

13Specifically, we interact S_4—-1 with (i) the holding return on a 5 year zero coupon Treasury bond using
the updated Giirkaynak et al. (2006) data set, (ii) the log change in the Case-Shiller national house price

series, and (iii,iv) In (Sho RIAs) —In A;_; for A;=aggregate labor compensation (NIPA code A4002C)
or aggregate non-corporate business income (nonfarm sole proprietor income and partnership income, NIPA
code A041RC) and a quarterly discount factor R = 1.03!/4. To see the rationale for the last two controls, let
Arp = Yio R~4Az4; denote the discounted stream of labor (or private business) income A;. The revision

Fe ~ In Ey [AP] — n Bs [AP].
Relative to this definition, our control (i) truncates the horizon at T = 11 (truncating at longer horizons gives
similar results); (ii) replaces E; |H?'] with its perfect-forecast counterpart H}1 (under rational expectations,
this provides an unbiased measure of expected wealth); and (iii) replaces E,_1 [H?!] with income in the last
period, A;_1. Under the efficient market hypothesis, this last step does not matter because both Ey_1 [HP°]
and A;—; are determined in period t — 1 and therefore should be orthogonal to the stock return R7” , ;.
The Bartik (1991) industry shift-share predicted employment growth between t — 1 and t+ h is defined

B_ Ea,it—1 Exttn—Fijt-1 . sana tag
= Vienarcs 3 ( at ) ( Ean , where F,,;,4 denotes the (seasonally unadjusted)

to human capital (or private business) wealth in period t is

as Aat—1,t+he
level of employment in NAICS 3-digit industry 7 in county a and period t, E,4 is total employment in county
a, and Ej, is seasonally-adjusted total national employment in industry 7.

'5Data on payroll by firm size come from the Census Bureau’s Quarterly Work Force Indicators. Because
this data set has less historical coverage than our baseline sample, we use the time series mean share for each
county. This step contains little loss of information because the large payroll share is extremely persistent
at the county level, with an R? of 0.85 from a regression of the quarterly share on county fixed effects.

15
ment mirrors the parallel trends assumption in a continuous difference-in-difference design
with multiple treatments. Two main threats to identification exist.
The first threat occurs because stock prices are forward-looking, so fluctuations in the
stock market may reflect news about deeper economic forces such as productivity growth
that independently affect consumption and investment. This “leading indicator” channel
confounds interpretation of the relationship between consumption and the stock market in
aggregate time series data. Our cross-sectional research design requires only the weaker con-
dition that areas with high and low stock wealth to labor income ratios not load differently
on other aggregate variables that co-move with the stock market. Conceptually, such dif-
ferential loading could occur if stock wealth correlates with other forms of wealth and the
return on the stock market correlates with the returns on other forms of wealth. Inclusion in
Xa,t−1 of interactions of Sa,t−1 with other aggregate variables directly addresses the possible
heterogeneity in exposure to changes in four other types of wealth: human capital wealth,
non-corporate business wealth, fixed income wealth, and housing wealth.16 For example,
controlling for the interaction of Sa,t−1 and aggregate earnings addresses the possibility of
high wealth areas having different exposure to aggregate earnings risk. Similarly, the Bartik
variable controls for the possibility of high wealth counties concentrating in industries with
higher stock market betas than those in low wealth counties or in industries that drive overall
market returns, and the state-quarter fixed effects control non-parametrically for aggregate
shocks that have heterogeneous impacts on different states. Finally, inclusion of the lags of
Sa,t−1 Rt−1,t controls for the small serial correlation in stock returns shown in Figure 2a.
The second threat to identification concerns the separation of a consumption wealth ef-
fect from firm investment or hiring responding directly to the change in the cost of equity
financing. Indeed, the response of total national employment to an increase in the stock
16
For non-corporate business wealth, fixed income wealth, and housing wealth, we could alternatively try
to control directly for changes in the local values of these variables. This alternative has two deficiencies.
First, these variables may endogenously respond to local stock market wealth, making them an over-control.
Second, measuring local business wealth and fixed income wealth poses a more formidable challenge than
measuring local stock market wealth, because of the much larger variation in capitalization factors for the
income streams generated by these variables and the particular sensitivity of fixed income wealth to the
capitalization factor at interest rates near zero (Kopczuk, 2015; Smith et al., In progress). While this
difficulty precludes estimation of the local labor market effects of changes in these other types of wealth,
including interactions with the aggregate values of other wealth is still sufficient for identifying the stock
market wealth effect. The reason is that heterogeneity in holdings of other wealth matters for our purpose
o o
only insofar as returns on such wealth correlate with our main regressor. Formally, denoting by Sa,t−1 Rt−1,t
o o o o,⊥ o
the change in some other type of wealth o, we can write Sa,t−1 Rt−1,t = γSa,t−1 Rt−1,t + Sa,t−1 Rt−1,t , where
o o,⊥
γSa,t−1 is the fitted value from a regression of Sa,t−1 on Sa,t−1 and so by construction Sa,t−1 is orthogonal
o,⊥ o
to Sa,t−1 . Therefore, omitting the part Sa,t−1 Rt−1,t from the change in wealth of type o has no impact on
the remaining variables in the regression (and note that we do not need to separately identify the parameter
γ). As an example, interacting the Treasury return with stock wealth directly amounts to allowing for an
arbitrary correlation between the levels of stock wealth and fixed income wealth across counties.

16
market cannot separately identify these two channels. Our local labor market analysis ab-
sorbs changes in the cost of issuing equity common across areas into the time fixed effect.
Nonetheless, firms in high stock wealth areas may have a cost of capital more sensitive to
the value of the stock market. Two aspects of our research design make such a correlation an
unlikely driver of our results: (i) we find an employment response in nontradable but not in
tradable industries, so differential access to capital markets would have to occur within areas
and align with the tradable/nontradable sectoral distinction, and (ii) our baseline sample
excludes counties in the top 5% of the share of employees working at large (500+) employee
firms that might have greater access to public capital markets.

4 Results
4.1 Baseline Results
In this section we report our baseline results: (i) an increase in the stock market causes
faster employment and payroll growth in counties with higher stock market wealth, (ii)
the response is pronounced in industries that produce nontradable goods and in residential
construction, and (iii) there is no increase in employment in industries that mostly produce
tradable goods.
Figure 3 reports the time paths of responses of quarterly employment and payroll to an
increase in stock market wealth; formally, the coefficients β̂h from estimating Eq. (1). Table 1
reports the corresponding coefficients and standard errors for h = 7, where the stock market
return occurs in period 0. Because the stock market is close to a random walk (Figure 2b),
these time paths should be interpreted as the dynamic responses to a permanent change in
stock market wealth. Panel A of Figure 3 shows no pre-trends in either total employment
or payroll, consistent with the parallel trends assumption. Both series start increasing in
period 1. Payroll responds more than employment, reflecting either rising hours per employee
or rising compensation per hour. The point estimates indicate that a rise in stock market
wealth in quarter t equivalent to 1% of labor income increases employment by 0.0077 log
point (i.e. an approximately 0.69 basis point increase) and payroll by 0.0218 log point in
quarter t + 7. The increases appear persistent.
Panels B and C examine the responses in industries classified as producing nontradable
or tradable output, respectively. Employment and payroll in nontradable industries rise
by more than the total effect. In contrast, the responses in tradable industries are flat
following a positive stock market return. The horizon 7 differences between the tradable
and nontradable employment and payroll coefficients are both significant at the 1% level.

17
Table 1: Baseline Results

All Non-traded Traded
Emp. W&S Emp. W&S Emp. W&S
(1) (2) (3) (4) (5) (6)
Right hand side variables:

Sa,t−1 Ra,t−1,t 0.77∗ 2.18∗∗ 2.02∗ 3.24∗∗ −0.11 0.71
(0.36) (0.63) (0.80) (1.01) (0.64) (0.74)
Horizon h Q7 Q7 Q7 Q7 Q7 Q7
Pop. weighted Yes Yes Yes Yes Yes Yes
County FE Yes Yes Yes Yes Yes Yes
State × time FE Yes Yes Yes Yes Yes Yes
Shock lags Yes Yes Yes Yes Yes Yes
R2 0.66 0.64 0.39 0.48 0.35 0.36
Counties 2,901 2,901 2,896 2,896 2,877 2,877
Periods 92 92 92 92 92 92
Observations 265,837 265,837 263,210 263,210 252,928 252,928

Notes: The table reports coefficients and standard errors from estimating Eq. (1) for h = 7. Columns
(1) and (2) include all covered employment and payroll; columns (3) and (4) include employment and
payroll in NAICS 44-45 (retail trade) and 72 (accommodation and food services); columns (5) and (6)
include employment and payroll in NAICS 11 (agriculture, forestry, fishing and hunting), NAICS 21 (mining,
quarrying, and oil and gas extraction), and NAICS 31-33 (manufacturing). The shock occurs in period 0 and
is an increase in stock market wealth equivalent to 1% of annual labor income. All columns also include eight
lags {Sa,t−j−1 Ra,t−j−1,t−j }8j=1 , interactions of Sa,t−1 with the log change in national labor income and with
non-corporate business income from t − 1 to the cumulative total over the next 12 quarters, the interaction
of Sa,t−1 and the holding return on a 5 year Treasury bond, the interaction of Sa,t−1 and the log growth of
national house prices between t − 1 and t, and a Bartik (1991) shift-share measure of predicted employment
growth. For readability, the table reports coefficients in basis points. Standard errors in parentheses and
double-clustered by county and quarter. * denotes significance at the 5% level, and ** denotes significance
at the 1% level.

These patterns accord with the predictions of the theoretical model presented in the next
section. They also militate against a leading indicator or cost-of-capital explanation since
such confounding forces would have to apply only to the nontradable sector.
Figure 4 shows a large response of employment and payroll in the residential building
construction sector (NAICS 2361). We show this sector separately because, while it also
produces output consumed locally, the magnitude does not easily translate into our theo-
retical model since the sector produces a capital good (housing) that provides a service flow
over many years. Thus, a desire by local residents to increase their consumption of housing
services following a positive wealth shock will result in a front-loaded response of employ-

18
Figure 3: Baseline Results
Panel A: All Industries
Employment Payroll

Difference from t-1 (basis points) Difference from t-1 (basis points)
4 4

3 3

2 2

1 1

0 0

-1 -1

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Panel B: Nontradable Industries
Employment Payroll

Difference from t-1 (basis points) Difference from t-1 (basis points)
4
4
3
3
2
2
1
1
0 0
-1 -1

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Panel C: Tradable Industries
Employment Payroll

Difference from t-1 (basis points) Difference from t-1 (basis points)
4 4

3 3

2 2

1
1
0
0
-1
-1

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Notes: The figure reports the coefficients βh from estimating Eq. (1) for quarterly employment (left panel)
and wages (right panel) at each quarterly horizon h shown on the lower axis. Panel A includes all covered
employment and payroll; Panel B includes employment and payroll in NAICS 44-45 (retail trade) and 72
(accommodation and food services); Panel C includes employment and payroll in NAICS 11 (agriculture,
forestry, fishing and hunting), NAICS 21 (mining, quarrying, and oil and gas extraction), and NAICS 31-33
(manufacturing). The shock occurs in period 0 and is an increase in stock market wealth equivalent to 1%
of annual labor income. The dashed lines show the 95% confidence bands based on standard errors two-way
clustered by county and quarter.

19
Figure 4: Response of Residential Construction
Employment Payroll

Difference from t-1 (basis points) Difference from t-1 (basis points)
8
6 8

4 6
4
2
2
0
0
-2 -2
-4 -4
-6 -6
-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Notes: The figure reports the coefficients βh from estimating Eq. (1) for residential building construction
(NAICS 2361) employment and payroll at each quarterly horizon h shown on the lower axis. The shock
occurs in period 0 and is an increase in stock market wealth equivalent to 1% of annual labor income. The
dashed lines show the 95% confidence interval bands.

ment in the construction sector. Nonetheless, the large response of residential construction
provides additional evidence of a local demand channel at work. We find no corresponding
response in construction sectors unrelated to residential building.17
Figure 5 reports the response of population. The magnitude lies well below the response
of total employment and the data cannot reject no population response at the horizon we
examine.18

4.2 Robustness
Tables 2 and 3 report results from a number of robustness exercises for the horizon h = 7
overall, nontradable, and tradable responses of employment and payroll. The first row of
each table reproduces the baseline specification.
Table 2 shows robustness to subtracting or adding covariates to the baseline specification.
Rows 2 expands the variation used to identify the response by removing the interactions of
Sa,t−1 with changes in aggregate labor income, non-corporate income, bond wealth, and
house prices, and the Bartik control. The results are similar to the baseline specification.
The insensitivity reflects a combination of two forces: (i) the loadings on the other aggregate
variables do not vary too much with stock wealth, and (ii) as illustrated in Figure 2c, while
17
In unreported results, we find smaller but statistically significant positive responses in specialty trade
contractors (NAICS 238), a category that includes a number of sectors (electrical contractors, plumbers, etc.)
involved in the construction of residential buildings. In sharp contrast, there is a flat or slightly negative
response in heavy and civil engineering construction (NAICS 237). We also find a large and statistically
significant response of new building permits using the Census Bureau residential building permits survey.
18
The population data by county come from the Census Bureau. The Census reports population as of
July 1 of each year. We linearly interpolate these data to obtain a quarterly series.

20
Figure 5: Response of Population

Difference from t-1 (basis points)
4

-1

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Notes: The figure reports the coefficients βh from estimating Eq. (1) for total county population at each
quarterly horizon h shown on the lower axis. The shock occurs in period 0 and is an increase in stock market
wealth equivalent to 1% of annual labor income. The dashed lines show the 95% confidence interval bands.

stock prices are not strictly exogenous, much of the volatility in the stock market and hence
the variation in our main regressor occurs for reasons unrelated to these other aggregate
factors.
The remaining rows add additional control variables to the baseline specification to ad-
dress particular concerns. While our baseline specification already includes a linear interac-
tion of stock wealth/income and aggregate labor earnings, previous work has found especially
high sensitivity among very high earners (Guvenen et al., 2014). To address this concern,
row 3 includes an indicator for being in the top 5% of counties by share of returns with
greater than $200,000 in adjusted gross income, interacted with time fixed effects. This
row illustrates that controlling flexibly for cyclical patterns of counties with a large share of
high earners has a small impact on the coefficients. Motivated by theories of news-driven
business cycles (Beaudry and Portier, 2006), row 4 adds an interaction of Sa,t−1 with the
Fernald (2012) measure of TFP growth between t − 1 and t + 7, again with little effect. Row
5 adds contemporaneous and 12 lags of local house prices. While our baseline specification
controls for the sensitivity of wealthier areas to the aggregate housing cycle, adding the local
controls allows this sensitivity to vary with the performance of the stock market.19 Row
6 controls for the share of payroll in a county at establishments belonging to large (500+
employee) firms interacted with the stock market return. Large firms are more likely to have
publicly traded equity and thus experience a direct reduction in their cost of capital when
the stock market rises; the stability of coefficients indicates that our results do not reflect an
19
We use the Federal Housing Finance Agency (FHFA) annual county-level repeat sales house price index
and interpolate to obtain a quarterly series. In unreported results, we also find the response of residential
construction remains quantitatively robust to controlling for contemporaneous and lags of house price growth
so that the construction response does not merely reflect a run-up in local house prices in high wealth areas
before the stock market rises.

21
Table 2: Robustness to Covariates

Dependent variable: Total Nontradable Tradable
Emp. Payroll Emp. Payroll Emp. Payroll
Specification:

1. Baseline 0.77∗ 2.18∗∗ 2.02∗ 3.23∗∗ −0.12 0.71
(0.36) (0.63) (0.80) (1.01) (0.64) (0.74)
2. Only county & stateXquarter FE 1.04∗ 2.82∗∗ 1.21 2.92∗∗ 0.02 1.55
(0.40) (0.74) (1.06) (1.06) (0.87) (1.04)
3. Control high earners 0.58 1.64∗∗ 1.90∗ 2.83∗∗ −0.06 0.30
(0.35) (0.58) (0.80) (0.94) (0.65) (0.70)
4. Aggregate TFP sensitivity 0.66∗ 2.06∗∗ 1.85∗ 3.03∗∗ −0.09 0.75
(0.31) (0.62) (0.76) (0.95) (0.59) (0.71)
5. Control local house prices 0.70+ 2.15∗∗ 1.50∗ 2.82∗∗ −0.45 0.35
(0.37) (0.65) (0.64) (0.92) (0.62) (0.70)
6. Control large firm share 0.70∗ 2.05∗∗ 1.93∗ 3.09∗∗ −0.18 0.67
(0.34) (0.59) (0.76) (0.95) (0.61) (0.70)
7. Control lagged outcomes 0.75∗ 2.17∗∗ 2.10∗ 3.19∗∗ −0.19 0.75
(0.36) (0.63) (0.80) (0.99) (0.70) (0.73)
8. CzoneXtime FE 1.09∗∗ 2.24∗∗ 2.41∗ 3.68∗∗ −0.37 0.24
(0.38) (0.67) (0.96) (1.11) (0.64) (0.86)

Notes: The table reports alternative specifications to the baseline for h = 7. The shock occurs in period 0.
Each cell reports the coefficient and standard error from a separate regression with the dependent variable
indicated in the table header and the specification described in the left-most column. For readability, the
table reports coefficients in basis points. Standard errors in parentheses and double-clustered by county and
quarter. + denotes significance at the 10% level, * denotes significance at the 5% level, and ** denotes
significance at the 1% level.

investment response by such firms. Row 7 includes lagged outcomes to control directly for
any pre-trends.20 Row 8 replaces the state-by-quarter fixed effects with commuting zone-by-
quarter fixed effects. In this specification, identification comes from comparing the responses
of high and low wealth counties within the same commuting zone. Adding these controls has
a minor effect on the point estimates.
Table 3 collects other robustness exercises. Rows 2 and 3 show that the quarters with
the most extreme stock returns and the counties with the largest and smallest values of
Sa,t do not drive the results, although excluding these quarters and counties increases the
standard errors. Rows 4 excludes counties in which at least one S&P 500 constituent firm
20
We include both a county fixed effect and lags of the dependent variable because of the large time
dimension (roughly 100 quarters) of the data (Alvarez and Arellano, 2003).

22
has its headquarters, while row 4 excludes counties headquartering a firm on the Forbes list
of the largest private companies. The coefficients remain qualitatively similar, although the
payroll responses drop somewhat when excluding S&P 500 headquarter counties. We suggest
caution in interpreting these results, however, because these 130 counties account for more
than half of total stock wealth and payroll, so that excluding them substantially alters the
characteristics of the sample. Rows 5 and 6 show robustness to not weighting the regressions
and to trimming at the 1st and 99th percentile of county population.
The next three rows alter the shock variable. Row 8 uses only the price component of the
S&P 500 return with similar results. Row 9 instruments Sa,t−1 Ra,t−1,t with Sa,t−8 Ra,t−1,t and
row 10 uses the within-county mean ratio of dividend income to labor income interacted with
the time-varying price-dividend ratio and return as an instrument. Because the dividend-
labor income ratio changes little over time, instrumenting with the lagged wealth variable
or fixing this ratio has a small effect on the results.
Row 11 uses an alternative classification of industries into tradable and nontradable
based on their geographic concentration. Intuitively, if preferences for output of different
industries are similar across locations, then industries with concentrated production must
sell to buyers in other regions. This idea traces back at least to Krugman (1991, p. 55)
and has been pursued in Ellison and Glaeser (1997), Jensen and Kletzer (2005), and Mian
and Sufi (2014), among others. We follow these authors and define a tradability index for
industry i as Gi = a (sa,i − xa )2 , where sa,i denotes the share of employment in industry
P

i located in county a and xa denotes the share of total employment located in county a,
and classify industries in the bottom quartile of this index as nontradable and industries in
the top quartile as tradable. We obtain responses very similar to those using our baseline
categorization.21
The last row returns to the baseline specification but expands the geographic unit to
a Core Based Statistical Area (CBSA).22 The point estimates change little except in the
21
We construct the index at the NAICS 3 digit level and group industries such that the share of to-
tal employment in each quartile is the same. The classification has substantial overlap with our baseline
categorization: 7 of the 12 least-concentrated industries are in NAICS 44-45 or 72, and 27 of the 45 most-
concentrated industries are in NAICS 11, 21, or 31-33 (the concentrated industries are smaller on average).
Even at the 3 digit level, disclosure limitations affect the number of industries reporting employment and
payroll in each period. We restrict to county-quarters with the same number of industries reporting non-
missing employment and wages in periods t − 1 and t + 7, resulting in a final sample about one-half as large
as our baseline and explaining why we prefer the simpler 2 digit-based classification for our baseline.
22
The Office of Management and Budget (OMB) defines CBSAs as areas “containing a large population
nucleus and adjacent communities that have a high degree of integration with that nucleus” and has des-
ignated 917 CBSAs of which 381 (covering 1,166 counties) are Metropolitan Statistical Areas (MSAs) and
the remainder (covering 641 counties) are Micropolitan Statistical Areas (MiSAs). An MSA is a CBSA
with an urban core of at least 50,000 people. The remaining counties not affiliated with a CBSA are rural
and excluded from the estimation. Because CBSA’s may contain counties from multiple states (e.g. the

23
Table 3: Other Robustness

Dependent variable: Total Nontradable Tradable
Emp. Payroll Emp. Payroll Emp. Payroll
Specification:

1. Baseline 0.77∗ 2.18∗∗ 2.02∗ 3.23∗∗ −0.12 0.71
(0.36) (0.63) (0.80) (1.01) (0.64) (0.74)
2. Keep if Rt−1,t ∈ [P 5, P 95] 1.14∗ 2.98∗∗ 3.52∗∗ 5.12∗∗ 0.27 1.84
(0.46) (0.93) (1.01) (1.25) (0.97) (1.23)
3. Trim top/bottom 1% of Sa,t 1.02∗ 2.93∗∗ 2.65∗ 4.56∗∗ 0.52 1.33
(0.51) (0.91) (1.15) (1.40) (1.06) (1.11)
4. Drop S&P 500 HQs 0.30 0.69+ 1.68∗ 1.98∗∗ 0.02 0.72
(0.21) (0.39) (0.66) (0.68) (0.82) (0.88)
5. Drop Forbes Top Private HQs 0.40 0.89∗ 1.88∗ 2.66∗∗ 0.29 0.75
(0.25) (0.42) (0.75) (0.84) (0.78) (0.85)
6. Unweighted 0.47 0.84∗ 2.98∗ 2.86∗∗ 0.11 0.56
(0.31) (0.42) (1.19) (1.03) (0.84) (1.05)
7. Trim by population 0.82∗∗ 1.84∗∗ 2.15∗∗ 3.04∗∗ 0.51 1.52
(0.31) (0.56) (0.78) (0.91) (0.74) (0.94)
8. Price component only 0.74∗ 2.11∗∗ 1.93∗ 3.11∗∗ −0.15 0.65
(0.36) (0.62) (0.78) (0.99) (0.62) (0.72)
9. IV with lagged wealth 0.76∗ 1.91∗∗ 1.60∗ 2.61∗∗ −0.23 0.42
(0.37) (0.60) (0.76) (0.96) (0.58) (0.72)
10. IV with fixed dividends/income 0.89∗∗ 2.61∗∗ 1.63∗∗ 2.89∗∗ 0.21 1.20∗
(0.12) (0.18) (0.21) (0.25) (0.42) (0.51)
11. Concentration-based T/NT 0.77∗ 2.18∗∗ 2.13∗∗ 4.26∗∗ −0.72 0.62
(0.36) (0.63) (0.62) (1.00) (0.98) (1.61)
12. Across CBSAs 0.44 1.80+ 2.56+ 3.00+ 0.68 1.95
(0.47) (1.03) (1.53) (1.63) (1.61) (1.73)

24
tradable sectors where they rise slightly, while the standard errors increase substantially.
The larger standard errors reflect the decrease in wealth variation after averaging across
counties within a CBSA and the smaller sample size. The larger coefficients in the tradable
sector could reflect spending on tradable goods produced outside of a resident’s county but
within the CBSA; however, the data do not reject equality of the coefficients in the county
and CBSA specifications.

4.3 Decomposing Variation
In this section we provide evidence on whether certain areas “drive” the results in the sense
of Andrews et al. (2017). Consider the specification reported in row 2 of Table 2 in which
Xa,t includes only a county fixed effect and state-by-quarter fixed effect. In this case, letting
z̃a,t denote Sa,t−1 Rt−1,t demeaned by county and state-by-quarter, ∆a,t ỹ the outcome after
demeaning with respect to county and state-by-quarter (where for notational simplicity we
have suppressed the dependence of ∆ on the horizon h), πa the 2010 population in county
a, and s index states, we can decompose the OLS coefficient as follows:
X
β= ws βs
s
!−1
XX XX
where βs ≡ 2
πa z̃a,t πa z̃a,t ∆a,t ỹ,
a∈s t a∈s t
!−1 !
XX XX
ws ≡ πa0 z̃a20 ,t 2
πa z̃a,t .
a0 t a∈s t

Here, βs is the regression coefficient obtained by using only observations from state s and
the weight ws is the contribution to the total (residual) variation in the regressor from state
s.23 The weights {ws } are all positive and sum to one.
Table 4 reports the ten states with the largest weight in the regression. Not surprisingly,
since the regression weights by population, California, Texas, and Florida rank among the
states with the highest weights. More surprisingly, Florida, with 6% of the 2010 population,
has a weight in the regression above 30%. This high share reflects the large variation across
Florida counties in stock market wealth. On the other hand, Florida does not drive the
Boston-Cambridge-Newton MSA contains five counties in MA and two counties in NH), the specification in
this row replaces the state×quarter fixed effects with quarter fixed effects.
23
We could have done this decomposition for the baseline specification after partialing out the interactions
of Sa,t−1 with other aggregate variables and the Bartik employment variable. In that case, the coefficient
βs would no longer equate to the coefficient from estimating the regression in state s only because the
coefficient on these additional controls would differ across states. The alternative of re-estimating the baseline
specification while dropping one state at a time yields conclusions similar to those obtained from Table 4.

25
Table 4: Ten States with Largest Weight

βs , nontradable wage
State Population share Weight
bill
Florida 0.061 0.313 0.30
California 0.121 0.081 5.01
Virginia 0.026 0.050 2.36
Texas 0.081 0.039 1.98
Ohio 0.037 0.034 1.90
North Carolina 0.031 0.032 3.14
Missouri 0.019 0.031 3.23
Illinois 0.042 0.027 7.88
Washington 0.022 0.027 8.46
Maryland 0.019 0.026 5.46

finding of a positive regression coefficient, as the Florida-only nontradable labor bill coeffi-
cient is smaller than the overall coefficient. Hence excluding Florida from the sample would
raise the estimated coefficient. Virginia also receives a larger weight in the regression than
its population share, reflecting the contrast in the state between wealthier northern suburbs
of D.C. and poorer southern counties. Notably, all 10 of the states with the largest weight
have βs > 0. Thus, no one or two states drive the overall result.

4.4 Heterogeneity
This section reports heterogeneity of the response along the dimensions of whether the stock
return is positive or negative, the sample period, and wealth level. For each dimension, we
augment Eq. (1) by replacing βh [Sa,t−1 Ra,t−1,t ] with M m
P
m=1 βh × I{oa,t ∈ m} × [Sa,t−1 Ra,t−1,t ],
where I{oa,t ∈ m} is an indicator for observation oa,t belonging to set m. Figure 6 reports
results for the coefficient on nontradable payroll, the variable most directly used in our
theoretical analysis.
The left bars show a similar response of nontradable payroll to a negative or positive
stock return. Nearly 75% of quarters in our sample contain a positive return, explaining
the higher precision around the coefficient on positive returns. The middle bars show the
response split before and after the end of the NASDAQ bust. The response is slightly larger
in the more recent period, but not statistically significantly different.24
24
Not shown, this pattern holds across other outcomes except total employment, which responds much
more strongly in the latter period. Our theory can rationalize a larger response of employment if the more
recent period featured greater wage rigidity.

26
Figure 6: Heterogeneity

10.0

8.0

Regression coefficient
6.0

4.0

2.0

0.0

R<0 R>0 To 2003:Q1 2003:Q2-end T1 T2 T3
Return asymmetry Sample period State wealth tercile

Notes: The figure reports the coefficients βhm from estimating Eq. (1) for the nontradable wage bill at
horizon h = 7, where m indexes positive versus negative stock return (left bars), before or after 2003:Q2
(middle bars), or tercile of the state’s per capita wealth distribution (right bars). The whiskers show the
95% confidence intervals.

Finally, many theories of consumption predict higher MPCs for less wealthy households.
In the context of stock market wealth, Di Maggio et al. (forthcoming) find a higher MPC in
Sweden among households in the lower half of the wealth distribution. In our regional con-
text, such heterogeneity could also arise from local general equilibrium amplication declining
in wealth (since, all else equal, a smaller MPC also leads to a smaller multiplier effect). The
right bars show that the coefficient indeed declines in tercile of state wealth, although the
differences are not statistically significant.25 This insensitivity may partly reflect that in
practice stock wealth heterogeneity is substantially greater within than across counties, and
our cross-county analysis already reflects the wealth-weighted MPC within a typical county.

4.5 Labor Income versus Consumption Expenditure
Our analysis so far has focused on the impact on labor market variables. Shortly, we will use
economic theory to relate the response of payroll in the nontradable sector to the marginal
propensity to consume out of stock market wealth. Before turning to that analysis, we
25
We split states by tercile of their time-averaged real (deflated by the price index for personal consumption
expenditure) dividends per capita. Splitting by state wealth level maintains the identification of each coeffi-
cient as coming only from within-state variation. The terciles are: Alabama, Arkansas, Delaware, Georgia,
Idaho, Indiana, Kentucky, Louisiana, Mississippi, New Mexico, North Carolina, North Dakota, Oklahoma,
Tennessee, Texas, Utah, West Virginia (tercile 1); Alaska, Arizona, California, Hawaii, Iowa, Maine, Michi-
gan, Montana, Nebraska, New York, Ohio, Oregon, Rhode Island, South Carolina, South Dakota, Wisconsin,
Wyoming (tercile 2); Colorado, Connecticut, Florida, Illinois, Kansas, Maryland, Massachusetts, Minnesota,
Missouri, Nevada, New Hampshire, New Jersey, Pennsylvania, Vermont, Virginia, Washington (tercile 3).

27
Figure 7: Nontradable Payroll, Consumption Expenditure, and Total Payroll
Nontradable payroll versus consumption Nontradable versus other payroll
45 25.0
40

BEA consumption expenditure
20.0

8 quarter log point change
35
15.0
30
25 10.0

20 5.0
15
0.0
10
-5.0
5 Nontradable
Other
0 -10.0
-5 0 5 10 15 20 25 30 35 40 1992 1996 2000 2004 2008 2012 2016
QCEW nontradable wage and salary growth

Notes: The left panel presents a scatter plot of five-year log changes in state-level QCEW nontradable wages
and salaries and state-level BEA personal consumption expenditure, for each five-year period corresponding
to processed quinquennial Economics Censuses (1997-2002, 2002-2007, 2007-2012). The right panel shows 8
quarter log changes in national QCEW wages and salaries in the nontradable sector (NAICS 44-45 and 72)
and all other sectors.

present empirical evidence of the relationship between nontradable payroll and consumption
expenditure, nontradable sectors and the rest of the economy, and direct evidence of a
response of consumption expenditure.
We first show a tight relationship between nontradable payroll and consumption expendi-
ture growth at the state level. The left panel of Figure 7 presents a scatter plot of five-year log
changes in state-level QCEW nontradable wages and salaries and state-level BEA personal
consumption expenditure (the lowest level of aggregation at which BEA reports consumption
expenditure), for each five-year period corresponding to processed quinquennial Economics
Censuses (1997-2002, 2002-2007, 2007-2012). We restrict attention to these five-year inter-
vals in which consumption expenditure derives essentially entirely from actual sales data
(Awuku-Budu et al., 2016). The two series exhibit a strong positive relationship.
Next, our theoretical analysis in Section 7 will require an assumption of homotheticity
across nontradable and other sectors. The right panel of Figure 7 shows evidence of this
relationship by plotting 8 quarter log changes of national nontradable payroll and total
payroll in all other sectors in the QCEW. At the local level, these two series exhibit different
responses to increases in stock wealth, with nontradable payroll rising more sharply. At the
national level these series co-move uniformly over time, with a regression coefficient of 0.96
(Newey-West standard error 0.077) and R2 of 0.79. The similarities in the mean growth
rates and high frequency movements of these two series signify homotheticity across locally-
nontradable spending and other categories. Intuitively, if the national economy is nearly

28
closed, then all sectors are nontradable nationally and will co-move if homotheticity holds.
Appendix A.5 provides further evidence of preference homotheticity across nontradable
and other sectors by extending the Dynan and Maki (2001) analysis of securities-owning
households in the Consumer Expenditure Survey. We estimate the effect of the stock market
on these households’ consumption, separately for their retail expenditure and other expen-
diture. Consistent with homotheticity, we find similar (cumulative) effects across the two
types of expenditure.
Finally, we provide direct evidence of the response of consumption expenditure to stock
wealth in Table 5, using the BEA state-level data. These data start in 1997 and have
an annual frequency, resulting in a very large reduction in both the cross-section (roughly
3000 counties to 50 states) and time (93 quarters to 18 years) dimensions relative to our
baseline, county-quarter specification. Guided by the theoretical model in the next section,
we also modify Eq. (1) by replacing Sa,t−1 with Sa,t−1
C
, defined as the ratio of stock wealth
to consumption expenditure in state a and year t − 1.
We estimate a cross-state coefficient of 4.8. As we will see, this magnitude accords ex-
tremely well with the coefficient on nontradable payroll of 3.2 estimated in our baseline
specification, providing additional support for the homotheticity assumption and the theo-
retical mapping of our baseline specification into the MPC out of stock wealth in the next
section. From an econometric identification standpoint, this coincidence is remarkable, as
our baseline specification uses only within-state variation while Table 5 uses only cross-state
variation for identification. However, the coefficient is estimated less precisely than in our
baseline, reflecting the large reduction in sample size. Moreover, since we have few clusters
in the time dimension (18 years), the conventional clustered standard errors reported in
column (2) might be biased. We address this issue by reporting in column (3) the standard
error using the “LZ2” bias-reduction adjustment recommended by Imbens and Kolesár (2016)
for samples with relatively few clusters and in column (4) the Imbens and Kolesár (2016)
suggested degrees of freedom for the t-distribution implied by columns (1) and (3).

5 Theoretical Model
This section develops a stylized theoretical model to interpret the empirical analysis. We
present the main equations and results in the main text and relegate additional details to
Appendix B. We use the model to illustrate the cross-sectional effects of changes in aggregate
stock prices and to validate our empirical specification. In subsequent sections, we calibrate
the model and structurally interpret our empirical findings.
We start with a brief overview of the model. There is a continuum of areas denoted by

29
Table 5: Cross-state Expenditure Results

Conventional LZ2 two-way BM deerees of
Coefficient two-way clustered clustered standard 6
freedom
standard error error
4.82 1.97 2.85 4.50

The table reports results from estimating Ag t—1,14ny = Bn [SO Rat-1,t] +14, Xat—-1 + €a,t—1,t+h, Where y
is total consumption expenditure in state a, h = 2 years, So 4-1 is the ratio of stock wealth to consumption
expenditure in state a in period t—1, and the remaining variables are analogous to our baseline specification.
The first column reports the regression coefficient. The second column reports the standard error clustered
by state and year using the conventional degrees of freedom adjustment. Column (3) reports the standard
error using the “LZ2” adjustment recommended by Imbens and Kolesér (2016) for samples with relatively
few clusters. Column (4) reports the Imbens and Kolesar (2016) suggested degrees of freedom for the
t-distribution implied by columns (1) and (3).

subscript a and two time periods denoted by subscripts 0 and 1. We interpret period 1 as
the long-run, in which prices adjust and macroeconomic outcomes are determined solely by
productivity. In contrast, period 0 is the short-run in which aggregate demand can matter.
Hence, a period in the model may correspond to several years. There are two factors of
production, labor and capital. Labor is specific to the area in period 0, which ensures
that wages and employment in the short run are influenced by local demand. Capital is
mobile across areas (in either period), which simplifies the analysis by ensuring that capital
has a single price. The price of capital in period 0 is endogenous and can change due
to fluctuations in its expected productivity in period 1. Importantly, capital ownership is
heterogeneous across areas. We analyze how changes in the price of capital affect local labor
market outcomes. We also separately model nontradable and tradable goods, which yields

additional predictions and will play an important role in the calibration.

5.1 Environment and Equilibrium

In each period t € {0,1} and area a, a representative household divides its consumption

C,4 between a tradable good that can be transported costlessly across areas, C/,, and a

a,t?
nontradable good that must be consumed in the area where it is produced, C%,

at according

to the preferences:
Cot = (Cai/n)" (Chi (Ln).

Competitive firms produce the nontradable good using labor LY

az and capital KN, and

the Cobb-Douglas technology:

YN = (KN Ja) (LN, (1-0)

30
Here, 1 — a® denotes the share of labor in the nontradable sector.
There are two technologies for producing the tradable consumption good. The first
technology uses tradable inputs produced in each area using local labor Die and capital K, a. 1

and the Cobb-Douglas technology:

where Yo = (KP, /a") “ (L2,/ (1 — at)

The elasticity of substitution ¢ > 0 governs the effect of unit costs in an area on the exports
from that area. The term 1 — a? captures the share of labor in the tradable sector.

The second technology uses only capital Kr :
y,- = Di" Ki.

The productivity parameter D, determines the rental rate of capital. This technology does
not play an important role beyond the asset pricing side of the model. Specifically, we
will obtain changes in stock prices in period 0 by varying the future productivity of this

technology, D,. The normalizing power 1 — a7

simplifies the expressions.

Areas are identical except for their initial capital wealth. The representative household in
area a enters period 0 owning 1+ %q,9 units of capital, where J, Lada = 0. We let Qo denote
the (cum-dividend) price of capital at the beginning of period 0 and normalize the aggregate
capital supply to one. Therefore, (1+ 4,9) Qo denotes the value of capital and, hence, the
stock market wealth held by households in area a at the start of period 0. Consequently,
the distribution of capital ownership, {va}, determines the cross sectional heterogeneity
of stock wealth.

The representative household in each area separates its consumption and labor choices as
follows. At the beginning of period 0, the household splits into a consumer and a continuum

of workers.“° The consumer makes a consumption-savings decision to maximize a time-

separable log utility function subject to an intertemporal budget constraint:

cmax log Cao + 910g Cat (3)

26We choose to model consumption and labor decisions separately for two reasons. First, assuming workers
choose labor according to Greenwood et al. (1988) (GHH) preferences allows us to ignore the wealth effects
of labor supply. Second, we can endow consumers with standard time-separable preferences. In addition to
simplifying the subsequent expressions, this setup accords with the fact that workers hold relatively little
stock market wealth. At the same time, we sidestep some consequences of GHH preferences, such as leading
to unplausibly large fiscal and monetary multipliers (Auclert and Rognlie, 2017).

ol
PaaCaa WarsLas
s.t. PaoCao + RF a0Lao + (1+ 2a) Qo + Rr (4)

Here, P,, denotes the price level in period ¢ in area a, W,, the wage level, L,; labor supply,
and R/ the risk-free rate. The elasticity of intertemporal substitution (EIS) of one simplifies
the analysis and is empirically plausible (see Appendix B.9 for a discussion of how a more
general EIS affects our analysis).

In period 1 (the long run) labor is exogenous, La, = [1, for all a, and the nominal wage
is constant, Wa, = W. We model period 0 labor supply to incorporate both some degree of
wage stickiness and disutility of labor. Specifically, a worker of type v supplies specialized
labor services Lao(v) subject to a constant elasticity labor demand curve—determined by
the aggregate demand for labor in the area as well as the elasticity of substitution between
specialized labor types.?’ A fraction of the labor types (the sticky workers) supply labor at
the preset wage W (the same wage as in the long-run). The remainder (the flexible workers)

set a wage W,0(v) to maximize:

log (Cas — Lao (v)'*? iv) ,

1+¢ Jo
where y denotes the inverse of the Frisch elasticity of labor supply. Thus, the worker chooses
labor according to Greenwood et al. (1988) preferences, which omit a wealth effect on labor
supply.

In Online Appendix B.1, we derive the optimal wage set by flexible workers and combine
it with the wage of the sticky workers to obtain a labor supply curve (c.f. Eq. (B.17)). We
linearize the resulting equation around a benchmark in which all areas have common wealth

to derive the log-linear labor supply curve (c.f. Eq. (B.57)):

W., 0 P, 0 La :)
log —— = A { log — + vlog = }. 5
8 ( Bp tele s (5)
Here, Pj and Lp denote the price level and labor that would obtain if all areas had the same
wealth, and \ € [0,1] is a meta-parameter that is an inverse meausure of wage stickiness.
When A = 0, wages are fully sticky. When A = 1, wages are fully flexible and the equation

reduces to a neoclassical labor supply relationship between labor and the real wage.”8

ey
27Formally, the worker faces the labor demand curve Lao (v) = (Spe) Lao, where Wao =
1/(l-ew) 1 ew-l au
0 and Lao = (J, Lao (v) = dv) . Here, Lao denotes the aggregate de-
mand for labor in area a that obtains in equilibrium.

8Letting A, denote the fraction of flexible workers that reset wages in period 0, A = aoe:

(0 Wao (v)'& dv)

32
Finally, at the end of period 0 the household recombines and makes a portfolio decision
to allocate savings between capital (stock wealth) and a risk-free asset. The risk-free asset
is in zero net supply and generates a gross nominal return in period 1 denoted by Rf . The
monetary policy sets Rf to keep labor supply equal to its frictionless level on average.29
Specifically, it ensures a La,0 da = L0 , where L0 denotes the labor supply that would obtain
R

if all areas had the same stock wealth and there were no wage rigidities. Appendix B.1
completes the description of the setup and defines the equilibrium.

5.2 Consumption Wealth Effect
In Appendix B.2, we characterize the equilibrium and establish the key mechanism behind
our results: the consumption wealth effect. Specifically, in view of the preferences in (3), the
time-zero consumption expenditure in area a satisfies:

1
Pa,0 Ca,0 = (Ha,0 + (1 + xa,0 ) Q0 ) . (6)
1+δ

Here, Ha,0 denotes human capital wealth, the present discounted value of labor income.
Hence, we have the standard result with log utility that consumption expenditure is a fraction
of lifetime wealth.
We now solve for the endogenous variables, first in a benchmark case in which areas have
common wealth and then by linearizing the equilibrium equations around that benchmark.
We use the common wealth benchmark to illustrate the source of stock price fluctuations,
and we use the log-linearized equilibrium to describe the empirical predictions regarding the
cross-sectional effects of these fluctuations.

5.3 Common Wealth Benchmark and Stock Price Fluctuations
First suppose all areas have the same stock wealth, xa,0 = 0 for each a. In this case, the
equilibrium allocations and prices are the same across areas, so we drop the subscript a.
We solve for the equilibrium in Appendix B.3. We make a parametric assumption on D0 to
ensure that firms are indifferent to using the capital-only technology in period 0 (but they do
use it in period 1).30 In this case, the equilibrium is particularly simple. To state the result,
29
In practice, monetary policy affects the nominal interest rate by changing the money supply, in an
environment where money provides liquidity services and the interest rate reflects the “price” of liquidity.
To simplify the exposition, we do not explicitly model money or its liquidity services. These features can be
added to the model without changing anything substantive (see Woodford (1998) for further discussion).
30
For simplicity, we assume the capital-only technology can be used to produce tradables but not nontrad-
ables. This provides a potential source of nonhomotheticity across sectors. The assumption on D0 ensures
that production remains homothetic in period 0, which is important for some of our results.

33
we define the weighted average capital share across the nontradable and tradable sectors,

α = ηαN + (1 − η) αT . (7)

The equilibrium with common wealth is then given by:

W0 = W , L0 = L0 where L0 solves (B.38) , (8)
1 − αN 1 − αT
LN
0 /L 0 = η and L T
0 /L0 = (1 − η) .
1−α 1−α
1 L1 + D1
Rf = Rf,∗ = ,
δ L0 + D0
D1 D1
Q0 /W = D0 + f = D0 + δ L0 + D0 ,
R L1 + D1
L1 L1
H0 /W = L0 + f = L0 + δ L0 + D0 .
R L1 + D1

The first line shows that the nominal wage is equal to its long-run level and labor supply
is given by its frictionless level (see the appendix for a characterization). The second line
shows that the share of labor employed in each sector is determined by the sectoral shares
in household spending, adjusted by the differences in labor shares across sectors. The third
line characterizes the interest rate that brings about this outcome (“rstar”).
The last two lines characterize the prices of physical and human capital. An increase in
the future productivity of capital, D1 , increases the equilibrium price of capital Q0 . Monetary
policy responds to this change by raising Rf ; however, the equilibrium price of capital
increases even after incorporating the monetary policy response.31
We focus on the comparative statics of a change in the future productivity of capital
from some D1old to D1new . By Eq. (8), the price of capital changes from Qold 0 to some Q0 ,
new

while leaving the aggregate labor market outcomes unchanged, L0 = L0 , W0 = W . We
next investigate how this change affects local labor market outcomes when stock wealth
is heterogeneously distributed across areas. In Appendix B.8, we generalize the model to
incorporate uncertainty over D1 and show that our analysis is robust to other sources of
fluctuations in Q0 , such as changes in the level of uncertainty or changes in risk aversion.32
dQ0 δW (L0 +D0 )D1 f d(Q0 +H0 )
31
Specifically, we have dD = > 0 and dR
2
1
dD1 = δ (L0 +D0 ) > 0. We also have dD1 = 0:
1 (L1 +D1 )
that is, the interest rate response stabilizes the total wealth, Q0 + H0 . This ensures that aggregate spending
and thus aggregate employment remains unchanged.
32
Specifically, we show that a reduction in households’ perceived uncertainty about D1 increases Q0 and
f,∗
R . After extending the analysis to more general Epstein-Zin preferences, we also establish that a decrease
in households’ relative risk aversion parameter increases Q0 and Rf,∗ (see Proposition 3). Finally, we show
that, conditional on generating the same increase in Q0 , the decline in risk or risk aversion has the same

34
5.4 Heterogeneous Wealth and Cross-Sectional Predictions

We now derive cross-sectional predictions for the empirically-relevant case of a heterogeneous
distribution of stock wealth. We also highlight the properties of the coefficients that will
inform our calibration exercise.

We first log-linearize the equations that characterize the equilibrium around the com-
mon wealth benchmark for a given D;. Specifically, we let wao = log (Wa0/W) »Pao =
log (Pi,o/Po) and lao = log (Lao/Lo) denote the log-deviations of nominal wages, nominal
prices, and total labor for each area. We define 1 and Ino similarly for the nontradable and
tradable sectors. In Appendix B.4 we present closed-form solutions for pao, Wao, la,0; Io: IX
for a given level of Dy.

In particular, we express local prices in terms of local wages,

Pao = 7) @ — a) Wa,0: (9)
Combining this with Eq. (5), we obtain a reduced-form labor supply equation:

Ap
1—\n(1—ad)’

Wao = Klao, where Kk = (10)
Here, « is a composite wage adjustment parameter that combines the effect of inverse wage
stickiness, A, and the inverse labor supply elasticity, y. The parameter also depends on
the share of nontradables, 7, and the share of labor in nontradables, 1 — a, because these
parameters determine the extent to which a change in local nominal wages affects local prices
and therefore local real wages.

Our key predictions correspond to the comparative statics as D?’4 changes to Di’. Since
the benchmark we log-linearize around does not change, the first-order effect on local labor
market outcomes is characterized by changes in log-deviations. We solve for these changes

as follows (see Appendix B.5):

1 + K 1 La oAQo
A (Wa a0) = 1— a) ,7— =, 11
(Wao + lao) Teac! | a) 15 Lo (11)
1
Algo = To (Wao + lao) ’ (12)
1 _, Lap AQ

A (wao + lito) = Mz | -@) Tr, +(1-a7)(L-n)A(waotlio)|, (13)
A (wao + loo) = —(€-— 1) (1-07) Away, (14)

quantitative effects on local labor market outcomes as in our baseline model.

39
1

wnere A Ta nf 1 8)
ond ¢=14(e- 2) a

Here, Ay = y"*” — y®4 denotes the change in equilibrium variable y. In particular, AQo =

new __

6 ed denotes the dollar change in the aggregate stock wealth. Thus, x20AQp denotes

the change in stock wealth in area a relative to other areas. The equations describe how the

xoAQo
WLo

(relative) stock wealth change normalized by the labor bill, , affects the (relative) local
labor market outcomes in the area.

These equations are intuitive. Eq. (11) shows that an increase in stock wealth in an
area increases the total labor bill. To understand the coefficient, note that one more dollar
of stock wealth in an area leads to 1/(1+ 6) dollars of additional total spending (cf. Eq.
(6)), of which 7/ (1+) is spent on nontradable goods produced locally. The increase in
spending, in turn, increases the local labor bill by (1 — a) n/ (1+ 6) dollars. This direct

effect gets amplified by the local Keynesian income multiplier, denoted by M. The remaining

1+4
> 14K0?

areas. Specifically, an increase in local wages makes the areas’s goods more expensive, which
reduces (resp. increases) the tradable labor bill (and thus the total labor bill) when tradable

inputs are gross substitutes, ¢ > 1 (resp. gross complements, ¢ < 1).

term reflects potential adjustments to the labor bill due to changes in exports to other

Eq. (12) is a rearrangement of the reduced-form labor supply equation in (10), which
relates changes in labor to changes in the labor bill according to the wage adjustment pa-
rameter, «. In particular, how much employment responds relative to the total labor bill
(given a change in stock wealth) will discipline « in our calibration exercise.

Eqs. (13) and (14) characterize the effects on the labor bill separately for the nontradable
and tradable sectors. These equations are particularly simple when tradable inputs have unit
elasticity, ¢ = 1. In this case, the effect on the tradable labor bill is zero, A (wWa,o + Ir 0) = 0.
The coefficient multiplying the wealth change for the nontradable labor bill can be decom-
posed into three terms: the partial equilibrium MPC out of stock market wealth 1/(1+ 4),
the weighted average labor share of income 1 — @, and the local multiplier M. In Section 6
we use this decomposition to recover the partial equilibrium MPC given externally calibrated
1—aand M. Notably, the expression does not require information on the share of nontrad-

ables in spending, 7, or the share of labor in the nontradable sector, 1 — a%

(see Section 6
for the intuition).

When ¢ # 1, the decomposition for the nontradable sector does not hold exactly. In this
case, as illustrated by Eq. (14), the stock wealth shock can affect the tradable labor bill if

it has an effect on wages. As illustrated by Eq. (13), this affects local households’ income

36
and, therefore, creates knock-on effects in the nontradable sector (captured by the additional
term in brackets). However, if wages do not adjust much, then the tradable adjustment has
a small impact on the analysis even when ε is somewhat different from 1.

5.5 Summary and Mapping into the Empirical Analysis
According to Eqs. (11) to (14), an increase in national stock prices driven by, e.g., changes
in expected future productivity of capital or in risk aversion, increases the current total
labor bill and nontradable labor bill by more in areas with greater stock market wealth. The
effect on the tradable labor bill is ambiguous and depends on whether tradable inputs are
gross substitutes or complements. In Appendix B.4, we derive the additional predictions
that nontradable employment, total employment, and wages weakly increase, and tradable
employment weakly falls. All of these predictions accord with our empirical results.
The model also explains the functional form of our empirical regressions. In particular,
define Sa,0 ≡ xW
a,0 Q0
L0
as area a’s (relative) stock wealth divided by its labor bill and R0 ≡ ∆Q
Q0
0

as the stock return. Then, we have:

xa,0 ∆Q0
Sa,0 R0 = . (15)
W L0

This variable corresponds to our main regressor, the change in the stock wealth of the area
normalized by the local labor bill. Eqs. (11) to (14) illustrate that the empirical coefficients
using this regressor have a tight mapping into the key parameters of the model.33 We next
exploit this mapping and provide a structural interpretation of our empirical findings.34

6 Calibration and Structural Interpretation
In this section, we use our empirical results from Section 4 to calibrate two key parameters
of the model: the strength of the direct stock wealth effect, 1+δ1
, and the degree of wage
adjustment, κ. We only need two model equations to recover these parameters. Therefore,
33
In the model, there is only one type of capital so all areas are associated with the same stock return,
Ra,0 = R0 for each a. In the empirical exercise, we allow areas to have heterogenous risky portfolios and
thus heterogeneous stock returns, Ra,0 . Eqs. (11) to (14) would naturally generalize to a richer setting that
features multiple risky assets and heterogeneous portfolios.
34
As emphasized by Dynan and Maki (2001), such “dollar-dollar” specifications arise naturally in
consumption-wealth models. An alternative approach would be to estimate an elasticity and to convert
back into a dollar-dollar coefficient using the sample average ratio of stock market wealth to labor income
(or consumption). This alternative has the drawback that the actual ratio varies substantially over time
as the stock market booms and busts, a problem noted in the very different context of fiscal multipliers by
Ramey and Zubairy (2018).

37
our calibration also applies in richer models as long as these equations hold. Throughout, we
choose the coefficients reported in Table 1 as our calibration targets. As shown in Figure 3,
the first few quarters of the impulse response feature sluggish adjustment for reasons outside
the model, due e.g. to adjustment costs, consumer habit, or delayed recognition of the stock
wealth changes, as found in Brunnermeier and Nagel (2008) and Alvarez et al. (2012). By
quarter 7 adjustment is complete and the effect is relatively stable thereafter.

6.1 Direct Stock Wealth Effect
To determine the stock wealth effect parameter, we consider the nontradable labor bill in
the special case with ε = 1. To facilitate interpretation, we rewrite Eq. (13) as:

N
= M (1 − α) ρ × Sa,0 R0 , (16)

∆ wa,0 + la,0
1 1 xa,0 Q0 ∆Q0
where ρ = and Sa,0 = , R0 = .
T1+δ W L0 /T Q0

Here, we have introduced the change of variables 1+δ 1
= ρT, where we interpret ρ as the stock
market wealth effect per year and T as the length of period 0 in years. Thus, the denominator
of Sa,0 , WTL0 , equals the labor bill per year as in the empirical implementation, and the
empirical coefficient maps into the stock wealth effect per year. In particular, the empirical
coefficient can be decomposed into the product of three terms: ρ, the partial equilibrium
MPC out of stock market wealth, the weighted-average labor share of income 1 − α, and the
local Keynesian multiplier M—equivalent to the multiplier on local government spending.
We set the weighted-average labor share to a value standard in the literature, 1 − α = 2/3,
and adjust other parameters to achieve a multiplier M =1.5, in line with empirical estimates
(Nakamura and Steinsson, 2014; Chodorow-Reich, 2019).35 We then calculate ρ by combining
Eq. (16) with the empirical coefficient for the nontradable labor bill.
Specifically, using the coefficient from Table 1, we obtain:

∆ wa,0 + la,0
M (1 − α) ρ = = 3.23%. (17)
Sa,0 R0
35
To see how we calibrate the multiplier, note that the change of variables in (16) creates one free parameter,
T. This parameter is not very meaningful since our model has stylized time periods (it has only two periods).
The parameter affects the analysis mainly through its impact on the local multiplier, which is given by:
1 1
M= = .
1 − (1 − αN ) η/ (1 + δ) 1 − (1 − αN ) ηρT

Therefore, we use T to calibrate the local multiplier as M = 1.5 given all other parameters. We avoid a
literal interpretation of T and view it as a stand in for other features, such as borrowing constraints, which
would affect M in richer models (see Appendix B.6 for intuition about why T affects M in our model).

38
Substituting 1 — @ = 2/3 and M =1.5, yields
p = 3.23%.

Hence, our estimates suggest that a one dollar increase in stock wealth increases household
spending by about 3.23 cents per year (at a horizon of two years). The implied magnitude
is in line with the yearly discount rates typically assumed in the literature. It is also close to
the estimates of the stock wealth effect on consumption for wealthy households in Sweden
estimated in Di Maggio et al. (forthcoming).

We make four remarks on this approach. First, it does not depend on the labor supply
block of the model. Second, we do not have to parameterize the spending share of nontrad-
ables, 7, or the labor share in the nontradable sector, 1 — a. To understand why, rewrite
Eq. (16) as:

A (WoL, /T) WEN Wy _,l-o%
Waokeo!T) W Ey _ pay (1 —a") 9 (rq0AQs) where W22 = ple
WL /tT TT Who ts

(18)

This expression illustrates that the effect of stock market wealth on the nontradable labor bill
in dollars, A (W.o0L2)/T), does depend on both 7 and 1 — a%. However, with homothetic

wyN
: WL —aN :
preferences and production across sectors, we have 7>* = na —: that is, the nontradable
3 =

labor bill as a fraction of the total labor bill reflects the nontradable spending share as well

as the sectoral differences in labor share. Therefore, since Eq. (16) normalizes the stock
wealth change with the total labor bill, 7 and 1 — a drop out of the equation. Intuitively,
with homothetic preferences these sectors’ average share of the labor bill proxies for their
marginal share of changes in the labor bill. As a consequence, the decomposition in (16) is
robust to the nontradable spending share as well as the sectoral differences in labor share.*©
Moreover, since the decomposition does not depend on 77, we can use it as long as we observe
the response in a subset of nontradable sectors.

Third, when ¢ 4 1, Eq. (16) applies up to an adjustment (see Eq. (13)). The adjustment
reflects the possibility that the change in the tradable labor bill—due to the change in local
wages—affects local households’ income and creates knock-on effects on the nontradable

labor bill. If wages are sufficiently rigid, then the tradable adjustment does not change the

36 Eq. (18) suggests the decomposition is also robust to (certain types of) cross-county heterogeneity in
labor shares. For instance, suppose that areas with high stock wealth (%a,9 > 0) feature greater labor share
in nontradables (1 — a > 1—a%)—perhaps because they spend more on high-quality goods that are more
labor intensive as recently shown by Jaimovich et al. (2019). Then, the average labor bill of nontradables in

these areas is also greater than average (WL. y > WL, ). As long as the average labor bill is proportional

awyN
to the labor share, a = nie, Eq. (18) would still give the decomposition in (16).

39
analysis by much even if ε is somewhat different from 1. In practice, the value we obtain for
κ (described next) implies that there is little loss of generality in ignoring this adjustment
for empirically reasonable levels of ε, consistent with the small and statistically insignificant
response of tradable payroll we estimate in the data. Therefore, we adopt ε = 1 as our
baseline calibration in the main text and relegate the more general case to the appendix.37
Fourth, we can compare the ρ of 3.23 obtained from Eq. (17) to the ρ implied by the
estimation using state-level consumption data. Following similar steps as in the derivation
of Eq. (17), we obtain (see Eq. (B.67) in the appendix)

C
∆ (pa,0 + ca,0 ) = Mρ × Sa,0 R0 . (19)

Here, pa,0 + ca,0 denotes log nominal consumption expenditure and Sa,0
C
= xPa,0 Q0
0 C0
denotes the
ratio of area a’s (relative) stock wealth to its consumption expenditure. Notably, the labor
share does not enter into Eq. (19). Using M = 1.5 and the coefficient from Table 5, we
obtain a nearly identical ρ of 4.82/1.5 = 3.21.

6.2 Wage Adjustment
We use Eq. (12) to determine the wage adjustment parameter κ,

1
∆la,0 = ∆ (wa,0 + la,0 ) . (20)
1+κ

Recall that κ is a composite parameter that combines inverse wage stickiness and inverse
labor supply elasticity [cf. Eq. (10)]. Therefore, it captures wage adjustment over the
estimation horizon. One caveat is that, while the model makes predictions for total labor
supply including changes in hours per worker, in the data we only observe employment. A
long literature dating to Okun (1962) finds an elasticity of total hours to employment of 1.5.
Applying this adjustment and using the coefficients for total employment and the total labor
bill from Table 1 yields:

∆la,0
= 1.5 × 0.77%
Sa,0 R0
∆ (wa,0 + la,0 )
= 2.18%.
Sa,0 R0
37
Specifically, in Appendix B.6.2 we consider alternative calibrations with ε = 0.5 and ε = 1.5. In these
cases, since trade adjustment affects the analysis, the implied ρ also depends on the share of tradables, η.
We allow this parameter to vary over a relatively large range, η ∈ [0.5, 0.8], and show that the implied ρ
remains within 5% of its baseline level. As expected, the greatest deviations from the baseline occur when
η is low (that is, when the area is more open).

40
Combining these with Eq. (20), we obtain:

κ = 0.9. (21)

Thus, a one percent change in labor is associated with a 0.9% change in wages at a horizon
of two years.38

7 Aggregation when Monetary Policy is Passive
We next describe the effect of stock market changes on aggregate outcomes. In our model so
far, these effects appear only in the interest rate (“rstar”) because monetary policy adjusts
to ensure aggregate employment remains at the frictionless level. We now consider an alter-
native scenario in which monetary policy is passive and leaves the interest rate unchanged in
response to changes in stock prices. In this case, stock wealth changes affect aggregate labor
market outcomes. These aggregate responses are of direct interest to monetary policymakers
considering whether or not to accommodate a change in the stock market.
Our aggregation result for the labor bill is straightforward and relies on two observations.
First, given homothetic preferences and production across sectors, a one dollar increase in
stock market wealth has the same proportional effect on the aggregate total labor bill and
the local nontradable labor bill, up to an adjustment for the difference in the aggregate and
local spending multipliers. Second, since the aggregate spending multiplier is greater than
the local multiplier, we can bound the aggregate effect from below. Therefore, our empirical
estimate of the effect on the local nontradable labor bill is a lower bound for the effect on
the aggregate total labor bill.
Our aggregation result for labor combines this finding with a third observation: since
labor markets are local, the structural labor supply equation (5) remains unchanged as we
switch from local to aggregate analysis (as emphasized by Beraja et al. (2016)). The reduced
form labor supply equation in (10) changes slightly because shocks impact aggregate inflation
and local inflation differently.
To establish these results formally, consider the model from Section 5, but assume that
f
monetary policy keeps the nominal interest rate at a constant level, Rf = R .39 Appendix
38
We can also estimate κ from the response of tradable employment [cf. Eq. (B.66)]. Intuitively, tradable
employment declines only insofar as local wages and prices rise, so the response of lT provides information
about κ. Auclert et al. (2019) implement this approach in a different empirical setting. We prefer not to
rely on this relationship because in practice (unlike in our model) even tradable goods may be influenced
by local demand due to home bias, non-zero transportation costs, and supply chains. Nonetheless, the flat
response of employment in the industries we classify as tradable in the data accords with a low value of κ.
39
As before, monetary policy stabilizes the long-run wage level at the constant level, W .

41
B.7 extends our theoretical analysis to this case. The aggregate equilibrium with a fixed
interest rate is described by the tuple, (Q0 , L0 , W0 , P0 ), that solves four equations provided
in Appendix B.7. These equations illustrate that changes in the expected productivity of
capital, D1 , affect not only the price of capital—as in the baseline model—but also aggregate
income, employment, wages, and prices.
To characterize these effects further and to compare them with their local equilibrium
counterparts, we log-linearize the equilibrium around the frictionless benchmark. Specifically,
f
we let D1 denote the level of capital productivity such that R = Rf,∗ given D1 . Considering
the equilibrium variables as a function of D1 , and log-linearizing around D1 = D1 , we obtain
the following equations for the aggregate labor bill and labor:

1 ∆QA
∆ (w0 + l0 ) = MA (1 − α) 0
, (22)
1 + δ W L0
1
∆l0 = ∆ (w0 + l0 ) , (23)
1 + κA
1 1 + κA
where MA ≡
1 − 1/ (1 + δ) 1 − α + κA
λϕ
and κA ≡ .
1−λ

Here, l0 = log L0 /L0 and w0 = log W0 /W denote log deviations of aggregate employment

and wages from the frictionless benchmark. The variable QA 0 is the log-linear approximation
to the exogenous part of stock wealth, f . As before, ∆y ≡ y new −y old denotes the change
W D1 40
R
in equilibrium variable y when expected future dividends change. Hence, Eqs. (22) and (23)
describe the effect of a change in stock wealth on aggregate labor market outcomes. The
parameter MA captures the aggregate multiplier. The parameter κA captures the degree of
aggregate wage adjustment.
Eq. (22) shows that the effect on the aggregate labor bill closely parallels its local
counterpart (Eq. (12)), with three differences. First, the direct spending effect is greater
(1−αN )η
in the aggregate than at the local level, 1−α
1−δ
> 1−δ
. Intuitively, some spending falls on
goods that are tradable across local areas but nontradable in the aggregate. Second, the
aggregate labor bill does not feature the export adjustment term 1+κζ 1+κ
. Third, the aggregate
multiplier is greater than the local multiplier, M > M, because spending on tradables (as
A

40
The stock price satisfies Q0 = W0 D0 + W Df 1 . In this setting, a one dollar increase in W Df 1 increases the
R R
equilibrium stock price, Q0 , by more than one dollar. This is because the increase in aggregate demand and
output in period 0 also increases the rental rate of capital, W0 D0 . We focus on the comparative statics for a
one dollar change in the exogenous component of the stock wealth (as opposed to actual stock wealth) as the
appropriate counterfactual scenario for what would happen if monetary policy did not react to an observed
stock price shock in an environment where it usually stabilizes the demand effects of these shocks.

42
well as the mobile factor, capital) diminish the local but not the aggregate multiplier.*4
Likewise, Eq. (23) shows that the reduced-form labor supply equation closely parallels
its local counterpart (cf. Eqs. (12) and (10)). In fact, since labor markets are local, the
structural labor supply equation (5) that features prices and labor does not change as we
switch from local to aggregate analysis. However, while the aggregate price level moves
one-for-one with wages, po = Wo, the price level for local consumption does not, since the
prices of tradable goods and capital are determined nationally, pao = Wao @ —a% ) cf.
Eq. (9)|. Therefore, the real wage w — p responds locally but not in the aggregate. The real
wage response generates a neoclassical local labor supply response, with strength determined
by the magnitude of the Frish elasticity 1/y, that does not extend to the aggregate level.
Rewriting the expressions for & and «4 to eliminate the wage stickiness parameter, \, we

obtain:

5 =o (=n (10%) +. (24)

This expression illustrates that the local labor response, , combines a neoclassical response

to higher real wages, 5 @ —n @ — a’)), that only occurs locally, and a term due to wage

stickiness that extends to the aggregate, +.

We now use our estimates for the local effects to quantify the aggregate effects on the

labor market. We first use Eq. (22) to quantify the effect on the aggregate labor bill. Using

the change of variables = pT, we rewrite this equation as follows:

> T+
A (wo +l) = M4(1-a)px SARA (25)
A A
where Sj) = = and Ri = AGe
W Lo/T Q

We define $4 as the ratio of aggregate stock wealth to the aggregate yearly labor bill, and
R4 as the shock to stock valuations. Hence, S{'Ré is the aggregate analog of S,oRo from
the local analysis.

The coefficient in Eq. (25) is the same as its local counterpart in Eq. (16) for the local
nontradable labor bill, up to an adjustment for the differences in the local and aggregate

spending multipliers. Hence, we can combine our estimate for the local nontradable labor

“lThe aggregate spending multiplier is captured by the term M4 which exceeds the local

_ 1
= 1-1/(1+6)?
multiplier M = aca Fs) In our setting, there is also a second multiplier effect in the aggregate,

144
1-a4+K4
model are absorbed by labor only. We refer to F4 as the factor-share multiplier. The composite multiplier,
M4 = F4MA4, combines the standard spending multiplier with the factor-share multiplier. Our model
is too stylized to provide an exact mapping between the local and aggregate multipliers. The inequality

Me > 1is a robust feature of settings with constrained monetary policy (Chodorow-Reich, 2019).

captured by the term F4 =

> 1. This effect emerges because demand-driven fluctuations in our

43
A
bill (for quarter 7) with the inequality M
M
≥ 1 to bound the coefficient from below:

MA
MA (1 − α) ρ = 3.23% ≥ 3.23%.
M

Therefore, if not countered by monetary policy, a one dollar increase in stock valuations
increases the aggregate labor bill per year by at least 3.23 cents. Why does the effect on
the local nontradable labor bill provide information about the implied effect on the aggregate
total labor bill? With homothetic preferences and production technologies (and ignoring
trade effects, ε = 1), a given amount of spending generates the same proportional change on
the labor bill in all sectors. In particular, the proportional change of the labor bill in the
nontradable sectors—which we estimate with our local labor market approach—is the same
as the proportional change of the labor bill in the tradable sectors, which we cannot estimate
directly due to demand slippage to other regions. Importantly, while clearly convenient for
aggregation, the homotheticity assumption also has empirical grounding, as we demonstrated
in Section 4.5.
We next quantify the effect on aggregate labor. Using Eqs. (21) and (24) and setting
the Frisch elasticity ϕ−1 to 0.5 (Chetty et al., 2012), the nontradable labor share 1 − αN to
2/3 (a conservative value), and the nontradable share η to 0.5 (a conservative value), yields
κA = 1.3.42 Then, Eqs. (23) and (25) imply:

1 1
∆l0 = A
∆ (w0 + l0 ) = A
MA (1 − α) ρ × S0A R0A . (26)
1+κ 1+κ

Substituting in the value of κA and the response of the labor bill, we obtain:

1 A 3.23% MA
M (1 − α) ρ ≥ ≥ 1.4%.
1 + κA 1 + 1.3 M

Therefore, a one dollar increase in stock valuations increases aggregate labor (total hours
worked) by the equivalent of at least 1.4 cents (i.e. the labor bill for the additional hours
worked is at least 1.4 cents) if monetary policy does not respond.
We can combine these estimates with the ratio of aggregate stock wealth to the aggregate
yearly labor bill, S0A , to obtain the responses to a stock return, R0A . Using data from 2015
(weighting counties by their income), we obtain S A = 2.67.43 Substituting this value into
42
As we have emphasized, the nontradable share of consumption expenditure η is a difficult parameter to
calibrate given available regional data. Dupor et al. (2019) use the Commodity Flow Survey to estimate that
two-thirds of shipments remain within a metropolitan area and 61% remain within a county. This estimate
excludes the services component of consumption, which likely has a higher nontradable share. On the other
hand, it may include some shipments within a local supply chain that eventually produces a tradable good.
43
This value coincides almost exactly with the corresponding ratio of 2.63 obtained using C-corporation

44
Eqs. (25) and (26), we obtain:

MA
∆ (w0 + l0 ) = 3.23% × 2.67 × R0A ≥ 8.6% × R0A ,
M
MA
∆l0 ≥ 1.4% × 2.67 × R0A ≥ 3.73% × R0A .
M

Therefore, if not countered by monetary policy, a 20% stock return—approximately the
yearly standard deviation of the return on the market portfolio—would increase the aggregate
labor bill by at least 1.7%, and aggregate hours by at least 0.75%, at a horizon of two years.44

8 Conclusion
We estimate the effect of stock market wealth on labor market outcomes by exploiting
regional heterogeneity in stock wealth across U.S. counties. An increase in stock wealth in a
county increases local employment and the labor bill, especially in nontradable industries but
also in total, but does not increase employment in tradable industries. We use a theoretical
model to convert the estimated local general equilibrium effect into a household-level MPC
out of stock market wealth of around 3.2 cents per year. We also calculate the aggregate
general equilibrium effects of the stock wealth consumption channel on the labor market: a
20% change in stock valuations, unless countered by monetary policy, affects the aggregate
labor bill by at least 1.7% and aggregate hours by at least 0.75% two years after the shock.
Our estimate for the household-level MPC out of stock market wealth is broadly in line
with the quantitative predictions from frictionless models such as the permanent income
hypothesis, but considerably smaller than the estimated MPCs out of liquid income found
in the recent literature (Parker et al., 2013), even among higher income households (Kueng,
2018; Fagereng et al., 2019). One interpretation is that households that hold stock wealth
are affected relatively less by borrowing constraints or by behavioral frictions that increase
MPCs. Another possibility is that these households are subject to similar frictions as other
households, but stock wealth is associated with more severe transaction costs (such as tax
frictions or information frictions) that lead to lower MPCs than other types of liquid income.
The latter view is consistent with recent evidence from Di Maggio, Kermani and Majlesi
equity wealth in the FAUS and total wages and salaries in NIPA. This value has increased to 2.89 in 2018.
44
The magnitude of this calculation changes slightly if we instead assume consumption only responds
to changes in taxable stock wealth. In that case, we would recover a larger marginal effect on payroll
(intuitively, a larger consumption response would be required to rationalize the same cross-county changes
in labor income given smaller wealth), but we would multiply that response by a smaller change in wealth
given a 20% change in the stock market. Combining these changes, we would find that a 20% stock return
increases the aggregate labor bill by at least 1.3%.

45
(forthcoming), who argue that Swedish households respond to capital gains significantly less
than they respond to dividend payouts.
Our regional analysis complements household-level studies of the stock wealth effect by
providing direct evidence of stock market affecting labor market outcomes—a key concern
for monetary policymakers. Our findings support “the Fed put”—the central banks’ tendency
to cut interest rates after stock market declines unrelated to productivity (see e.g., Rigobon
and Sack (2003); Bjørnland and Leitemo (2009); Cieslak and Vissing-Jorgensen (2017)).
Our estimates and aggregation results can be used to calibrate the appropriate interest rate
response. If the interest rate is constrained, e.g., due to the zero lower bound or fixed
exchange rates, then our analysis implies that stock price declines would induce a sizeable
reduction in aggregate labor bill and employment (see Caballero and Simsek (forthcoming)
for a related dynamic setup that illustrates the downturn would be further amplified by
feedbacks between output and asset prices).
An important question for policymakers concerns the speed at which stock wealth changes
affect the economy. We find evidence of sluggish adjustment, with the effect on labor markets
starting after 1 to 2 quarters and stabilizing between quarters 4 and 8. This pattern suggests
that large stock price declines that quickly reverse course—such as the stock market crash
of 1987 or the Flash crash of 2010—are unlikely to impact labor markets, whereas more
persistent price changes—such as the NASDAQ boom in the late 1990s or the stock market
boom of recent years—have more sizeable effects.
On the other hand, our focus on the consumption channel and our empirical design omit
factors that could further increase the effect of stock market wealth changes on aggregate
labor markets. First, as discussed by Chodorow-Reich (2019), the Keynesian multiplier
effects are likely greater at the aggregate level (when monetary policy is passive) than at
the local level. Second, other channels, such as the response of investment, also create a
positive relationship between stock prices and aggregate demand (see Caballero and Simsek,
forthcoming). Relatedly, while our industry-level analysis mostly focuses on sectors that
produce nondurable goods and services, we also find that stock price changes have a large
effect on the construction sector. The construction response provides further qualitative
evidence that stock wealth affects the economy by changing local demand and inducing an
accelerator-type effect on housing investment (see Rognlie et al., 2018; Howard, 2017). We
leave a quantitative assessment of these additional factors for future work.

46
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