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Federal Reserve Bank
of Chicago
Third Quarter 2009
rtcSFARCn l'BRAK\
Festal Reserve Bank
of St. Louis

DEC« 3 2009

Economic___

perspectives

2

Investing over the life cycle with long-run labor
income risk
Luca Benzoni and Olena Chyruk

17

Preannounced tax cuts and their potential influence
on the 2001 recession
R. Andrew Butters and Marcelo Veracierto

Economic.

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Contents

Third Quarter 2009, Volume XXXIII, Issue 3

2

Investing over the life cycle with long-run labor income risk
Luca Benzoni and Olena Chyruk
Many financial advisors and much of the academic literature often argue that young people should
place most of their savings in stocks. In contrast, a significant fraction of U.S. households do not
hold stocks. Investors typically hold very little in stocks when they are young, progressively increase
their holdings as they age, and decrease their exposure to stock market risk when they approach
retirement. The authors show how long-run labor income risk helps explain this evidence. Moreover,
they discuss the effect of long-run labor income risk on the valuation of pension plan obligations,
their funding, and the allocation of pension assets across different investment classes.

17

Preannounced tax cuts and their potential influence
on the 2001 recession
R. Andrew Butters and Marcelo Veracierto
The authors present a model in which anticipated future tax cuts, like those promised during the
2000 U.S. presidential campaign, generate a contraction in economic activity with some of the
atypical features observed during the 2001 recession (such as its relatively strong consumption
and home investment).

Investing over the life cycle with long-run labor income risk
Luca Benzoni and Olena Chyruk

Introduction and summary
Throughout life, people make saving and spending
decisions. Moreover, they choose how to allocate their
savings among assets that have predictable but low
returns, like bonds, and assets that are riskier but could
yield higher returns, like stocks. Choices that are made
when individuals are relatively young will have large
implications for their standard of living in retirement,
when much of their income is likely to come from
savings. Private pension plans and the Social Security
system face similar decisions about how best to invest
assets for their clients.
Financial advisors and much of the academic literature often argue that it is optimal for young investors
to place most of their savings in stocks, which historically have paid a high risk premium relative to low-risk
bonds like Treasuries, and to switch their holdings to
less risky securities as they age. For instance, Malkiel
(1996) recommends that investors place (100 – age)%
of their financial wealth in a well-diversified portfolio
of stocks. In contrast, empirical evidence shows that a
significant fraction of U.S. households do not hold stocks.
Moreover, life-cycle stock holdings are “hump-shaped”:
Investors typically hold very little in stocks when they
are young, progressively increase their holdings as they
age, and decrease their exposure to stock market risk
when they approach retirement (for example, Ameriks
and Zeldes, 2004; and Campbell, 2006). This empirical
evidence is commonly referred to as the “limited stock
market participation” puzzle.
In this article, which draws on work by Benzoni,
Collin-Dufresne, and Goldstein (2007), we discuss
how long-run labor income risk helps to explain the
limited stock market participation puzzle. We argue
that the correlation in labor income flows and stock
market returns is a positive function of the investment
horizon. At long horizons, labor income and stock
market returns are likely to move together, mirroring



changes in the broader economy. However, at shorter
horizons idiosyncratic events lower the correlation
between labor income flows and stock returns. When
a worker is young and has her entire career ahead of
her, the first effect prevails. Thus, she prefers to buy
risk-free bonds rather than risky stocks to compensate
for the risk of possible long-run fluctuations in her labor
income. This outcome is consistent with empirical observation: As mentioned previously, there is little participation in the stock market among young American
households.
To better convey the intuition for this result, it is
useful to introduce the notion of “human capital,” which
is broadly defined as the set of knowledge, skills, health,
and values that contribute to making workers productive (for example, Becker, 1964; and Rosen, 2008).
A measure of a worker’s human capital is the present
value of her future labor income flows. When the worker
is young, human capital dwarfs financial wealth on hand.
Thus, the properties of human capital wealth will have
a significant impact on her investment decisions.
At the beginning of her career, a worker is highly
exposed to long-run labor income risk. Because of this
effect, a significant fraction of her human capital is implicitly tied up in the stock market; that is, the present
value of future labor income flows acquires “stock-like”
properties. The worker cannot get rid of this forced
investment in stocks, since any contract written against
future labor services is not strictly enforceable (labor
income is a nontraded asset). Thus, the young worker

Luca Benzoni is a senior financial economist and Olena
Chyruk is a senior associate economist in the Economic
Research Department at the Federal Reserve Bank of
Chicago. The authors are grateful to Gene Amromin,
Phil Doctor, Bob Goldstein, Anna Paulson, Rich Rosen,
and seminar participants at the Federal Reserve Bank
of Chicago for helpful comments and suggestions.

3Q/2009, Economic Perspectives

finds herself overexposed to stock market risk. To compensate for this effect, she places her financial wealth
in a risk-free bond, rather than buying stocks.
When the worker ages, she is less exposed to longrun labor income risk. As a result, the fraction of her
human capital implicitly tied up in the stock market
declines; that is, the stock-like properties of human
capital are attenuated. This effect reduces the worker’s
overall exposure to stock market risk. Thus, she finds
it optimal to place a larger fraction of her financial
wealth in stocks, resulting in the upward sloping part
of the life-cycle portfolio holding profile.
Finally, as the worker grows older, two counteracting effects are at play. Since the investment horizon
is short, long-run labor income risk fades away. As
such, the worker’s human capital attains “bond-like”
properties, in turn increasing the demand for stocks.
However, the number of years left to work goes down,
and human capital shrinks, which pushes the ratio of
human capital to financial wealth to zero. When that
happens, labor income no longer affects portfolio choice
and the demand for stocks goes down. As the worker
approaches retirement, the second effect dominates,
resulting in the downward sloping portion of the lifecycle profile.
The rest of the article proceeds as follows. We
first present stylized evidence on the relation between
stock holdings and age. In the next two sections we
outline the Benzoni, Collin-Dufresne, and Goldstein
(2007) labor income model and compare it with other
specifications previously considered in the literature.
The following section gives intuition for the model
and its implications for a worker’s life-cycle investment decisions. Next, we discuss the role of long-run
labor income risk in other applications that are at the
center of a heated debate among financial, political,
and academic circles: the valuation of pension plan
obligations, their funding, and the allocation of pension assets across different investment classes. We
conclude the article with some ideas for future work.
The limited stock market
participation puzzle
Over the years, participation in the stock market
by Americans has increased considerably. Still, a vast
number of U.S. households do not hold stocks, either
directly (for example, through direct holdings of publicly
traded stocks) or indirectly (for example, through investment in mutual funds; individual retirement accounts,
or IRAs; or other retirement accounts). Figure 1 illustrates this claim using data from the Federal Reserve
Board’s Survey of Consumer Finances (SCF), while
the appendix provides a brief description of the data.

Federal Reserve Bank of Chicago

The plots show that a very small fraction of young
investors have been holding stocks in the past decade.
The participation rate is higher for middle-age households and declines for older investors.
Moreover, the share of financial assets placed in
stocks is typically low when investors are young, it
increases with age, and then it decreases when individuals approach retirement. This pattern is illustrated in
figure 2 for the years 1998, 2001, 2004, and 2007. The
plots show the median share of stock holdings, computed as a fraction of financial assets, for U.S. households in different age brackets. They are in stark contrast
to the recommendations of many financial advisers
who suggest investors should place (100 – age)% in
stocks (also shown in figure 2).
There may be a legitimate concern that this evidence is biased by the financial decisions of less affluent investors, who own little financial assets and
therefore prefer to keep their limited savings in lowrisk securities. However, figure 3 (p. 6) shows that the
share of financial assets invested in stocks for households participating in the stock market remains low.
Moreover, figure 4 (p. 7) depicts stock market participation rates and stock holdings for 2007, broken down
by groups of investors holding different amounts of
financial assets. The plots show that even the richest
households are reluctant to participate in the stock market when they are young (panel A) and their stock
holdings are very low (panel B).
Of course, other factors affect individuals’ investment decisions besides age and financial wealth. We
do not pursue a more formal analysis here and instead
point the interested reader to the vast empirical literature that has studied life-cycle investment decisions
(see Ameriks and Zeldes, 2004; Campbell, 2006; Faig
and Shum, 2002; Haliassos and Bertaut, 1995; Heaton
and Lucas, 2000; Poterba and Samwick, 2001; Wachter
and Yogo, 2009; and many others). It is difficult to
reconcile the findings of all these studies because of
differences in sample period, data sources, and assumptions.1 The main conclusions of these papers are, however, largely consistent with the stylized evidence
presented here. For instance, Campbell (2006) documents a great deal of stock market nonparticipation,
even among rich households, and finds hump-shaped
life-cycle stock holdings, with a peak when the agent
is in her late fifties.
A model of long-run labor income risk
A vast literature has examined the empirical
properties of labor income using household-level
data—for example, Carroll and Samwick (1997);
Cocco, Gomes, and Maenhout (2005); Gomes and



figure 1

U.S. households holding stocks: Empirical evidence
A. 1998
percentage of households holding stocks

B. 2001
percentage of households holding stocks

100

100

80

80

60

60

40

40

20

20

0

20

40

age

60

80

0

20

40

age

60

C. 2004
percentage of households holding stocks

D. 2007
percentage of households holding stocks

100

100

80

80

60

60

40

40

20

20

0

20

40

age

60

80

0

20

40

age

80

60

80

Note: The plots show the percentage of U.S. households holding stocks, either directly or indirectly.
Source: Authors’ calculations based on data from the Board of Governors of the Federal Reserve System, 1998, 2001, 2004, and 2007 Surveys
of Consumer Finances.

Michaelides (2005); Gourinchas and Parker (2002);
and Jagannathan and Kocherlakota (1996). These
studies generally agree that the flow of labor income
has three salient components. First, there is an aggregate stochastic component that captures the effect of
economy-wide shocks on total workers’ compensation.
Second, there is an idiosyncratic stochastic component
subject to individual-specific shocks. Third, there is
an idiosyncratic deterministic component due to lifecycle predictability in wages.
More specifically, this literature concurs that the
(logarithmic) household-level labor income, ℓ, is well
approximated by the sum of an aggregate and an idiosyncratic term,
1)	 ℓ = ℓ1 + ℓ2.



The idiosyncratic term ℓ2 embeds both stochastic
and deterministic components. The idiosyncratic shocks
have both transient and persistent features, and the persistent shocks are well characterized by a unit-root
process. Moreover, there is compelling evidence that the
deterministic life-cycle labor income profile is humpshaped; that is, on average, labor income is low when a
worker is young, increases as she advances in her career,
and tends to decrease as she approaches retirement.
In contrast, the properties of the aggregate labor
income term ℓ1 are more controversial. There is an
ongoing debate regarding the linkage between the
performance of the stock and labor markets. Contemporaneous correlations between aggregate labor income
shocks and stock market returns are typically found
to be low or zero. Prior studies have examined the
implications of this property for life-cycle portfolio

3Q/2009, Economic Perspectives

figure 2

Life-cycle stock holdings: Empirical evidence
A. 1998
percentage of financial assets in stocks

B. 2001
percentage of financial assets in stocks

100

100

80

80

60

60

40

40

20

20

0

0
20

40

age

60

20

80

40

age

60

C. 2004
percentage of financial assets in stocks

D. 2007
percentage of financial assets in stocks

100

100

80

80

60

60

40

40

20

20

0

80

0
20

40

age

60

80

(100 − age)%

20

40

age

60

80

Survey of Consumer Finances data

Notes: The blue lines show the median percentage of stock holdings, computed as a share of financial assets, for U.S. households.
The black lines show the life-cycle stock holdings for a strategy that invests (100 – age)% of financial assets in stocks.
Source: Authors’ calculations based on data from the Board of Governors of the Federal Reserve System, 1998, 2001, 2004, and
2007 Surveys of Consumer Finances.

choice—for example, Campbell et al. (2001); Cocco,
Gomes, and Maenhout (2005); Davis and Willen
(2000); Gomes and Michaelides (2005); Haliassos
and Michaelides (2003); and Viceira (2001). This
literature concurs that, in spite of labor income risk,
a young investor should place much of her financial
wealth in the risky asset. This result holds because in
these models labor income shocks are assumed to be
(nearly) independent from stock market return innovations. Thus, a young investor chooses to diversify
away her human capital risk by holding a high fraction
of her liquid wealth invested in a well-diversified
portfolio of stocks.

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These models, however, also restrict long-run correlations between aggregate labor income and stock
market shocks to be low or zero. This restriction is controversial. For instance, it is natural to conjecture that
a sustained period of high economic growth will result
in strong stock and labor market performance over
the long run. Along these lines, Baxter and Jermann
(1997) argue that aggregate labor income and economic
growth, measured as gross domestic product (GDP)
growth, are co-integrated, while Benzoni, CollinDufresne, and Goldstein (2007) provide evidence that
aggregate labor income and dividends on the stock
market portfolio are co-integrated.



figure 3

Life-cycle stock holdings for stockholders: Empirical evidence
A. 1998
percentage of financial assets in stocks

B. 2001
percentage of financial assets in stocks

100

100

80

80

60

60

40

40

20

20
0

0
20

40

age

60

80

20

40

age

60

C. 2004
percentage of financial assets in stocks

D. 2007
percentage of financial assets in stocks

100

100

80

80

60

60

40

40

20

20

80

0

0
20

40

age

60

80

(100 − age)%

20

40

age

60

80

Survey of Consumer Finances data

Notes: The blue lines show the median percentage of stock holdings, computed as a share of financial assets, for U.S. households holding
stocks. The black lines show the life-cycle stock holdings for a strategy that invests (100 – age)% of financial assets in stocks.
Source: Authors’ calculations based on data from the Board of Governors of the Federal Reserve System, 1998, 2001, 2004, and 2007
Surveys of Consumer Finances.

Here we focus on the Benzoni, Collin-Dufresne,
and Goldstein (2007) model. We specify the dividend
process D(t) on the stock market portfolio to follow a
geometric Brownian motion,
2)	 dD = g D dt + σdz3 .
D
Ito’s lemma gives the dynamics for the logarithmic
∧
dividend process d (t ) ≡ log [ D(t ) ] ,
3)



∧

σ2 
dd (t ) =  g D −  dt + σdz3 .
2 


Assuming that the pricing kernel has a constant drift
equal to the risk-free rate and a constant market price
for risk, the return on the investment strategy S(t) that
reinvests all proceeds (dividends and capital gains)
in the stock market portfolio is:

σ2 
4) ds =  µ −  dt + σdz3 ,
2 

where s(t) ≡ log[S(t)] and μ is the total expected rate
of return of the investment strategy.
In this simple model, the dividend growth rate
volatility σ is identical to the stock return volatility.
This is counterfactual (stock returns fluctuate more

3Q/2009, Economic Perspectives

5)

figure 4

Stock holdings and financial assets:
Empirical evidence

where the constant d is the longrun logarithmic ratio of aggregate
labor income to dividends. They
assume that y(t) is a mean-reverting
process,

A. Percentage of U.S. households holding stocks

percentage of households
holding stocks

100
80

6) 	 dy (t) = –қy (t) dt + ν1 dz1 (t)
			
  – ν3 dz3 (t),

60
40
20
0
4
3
2
financial assets
quartiles

1

20

30

50
40
age

60

70

B. Median percentage of financial assets in stocks
  for U.S. households

100

percentage of financial
assets in stocks

∧

y (t ) ≡ �1 (t ) − d (t ) − �d ,

80
60
40
20
0
4
3
2
financial assets
quartiles

1

20

30

50
40 age

60

70

where z1 is a standard Brownian
motion independent from z3. The
coefficient қ measures the speed
of mean reversion for the process
y. Benzoni, Collin-Dufresne, and
Goldstein (2007) provide evidence
that қ > 0; that is, y is stationary,
^
so that ℓ1 and d are co-integrated.
Moreover, consistent with
the findings of Carroll and Samwick
(1997); Cocco, Gomes, and Maenhout
(2005); Gomes and Michaelides
(2005); and Gourinchas and Parker
(2002), Benzoni, Collin-Dufresne,
and Goldstein (2007) assume that the
idiosyncratic labor income component is subject to permanent shocks:

ν2 
7) d  2 (t ) =  α(t ) − 2  dt
2 

+ ν 2 dz2,i (t ) ,

where z2,i is a standard Brownian
motion independent from both z1
and z3. The subscript i emphasizes
that this shock pertains to the i-th
agent process, in contrast to the
aggregate shocks z1 and z3. Further,
the time-dependent drift term α(t)
captures the findings in the literature that the conditional mean of an individual’s labor income is a function of her age. Specifically, when

Note: The plots show the percentage of households holding stocks (panel A)
and life-cycle stock holdings (panel B) for different groups of U.S. households,
categorized by financial assets holdings.
Source: Authors’ calculations based on data from the Board of Governors of the
Federal Reserve System, 2007 Survey of Consumer Finances.

than dividends), but inconsequential for life-cycle
portfolio decisions as long as σ is calibrated to match
historical stock return volatility.
To capture the notion of long-run dependence
between aggregate labor income flow and dividends,
Benzoni, Collin-Dufresne, and Goldstein (2007) introduce a variable y that measures the (logarithmic)
difference between these two variables,

Federal Reserve Bank of Chicago

8) 	 α(t) = α0 + α1t,	
the coefficients α0 and α1 are calibrated to match the
hump shape of earnings over the life cycle (for example, Cocco, Gomes, and Maenhout, 2005).



Taken together, equations 3 and 5–7 yield the
following dynamics for the total labor income process ℓ = ℓ1 + ℓ2:

9)


ν2 
σ2
d (t ) =  − κy (t ) + g D −
+ α(t ) − 2  dt
2
2 


+ ν1 dz1 (t ) + ν 2 dz2,i (t ) +  σ − ν 3  dz3 (t ) .

Since z1 and z2,i are orthogonal to the stock return
shock z3, equations 4 and 9 imply that the contemporaneous correlation between stock market and labor
income shocks is
10)

corr(ds, d ) =

(σ − ν 3 )
ν + ν 22 + (σ − ν 3 ) 2
2
1

.

Thus, labor income is contemporaneously uncorrelated
with the stock market return when (σ – ν3) = 0, consistent with empirical evidence. Yet, co-integration
generates nonzero long-run correlations between
labor income and risky asset returns.
A comparison with the extant literature
In previous studies, most authors have specified
the labor income process in levels rather than in changes.
Furthermore, it is common to write the model in
discrete time rather than continuous time. To clarify
how the approach in Benzoni, Collin-Dufresne, and
Goldstein (2007) relates to the extant literature, here
we compare their specifications for the stock price
and labor income processes (equations 4 and 9) to
those considered in related studies. In particular, we
show that in the limit қ→0, these specifications are
nearly identical to the standard model.
For example, Campbell et al. (2001) assume that
the labor income of an investor i at age t, Yi,t , is exogenously given by
11)	 log(Yi,t) = f (t, Zi,t) + νi,t + εi,t,
where f (t, Zi,t) is a deterministic function of age and
other individual characteristics Zi,t, εi,t is an idiosyncratic temporary shock uncorrelated across households and distributed as N (0, σε2 ), and νi,t is given by
12)	 νi,t = νi,t–1 + ui,t.
Here, ui,t is distributed as N (0, σu2 ) and is uncorrelated
with εi,t. Moreover, ui,t is decomposed into an aggregate



component ξt and an idiosyncratic component ωi,t,
uncorrelated across households:
13) 	 ui,t = ξt + ωi,t.
Further, similar to equation 4, Campbell et al. (2001)
assume that the excess return on the risky asset is
given by
14)

Rt +1 − R f = µ + ηt +1 ,

where the innovations ηt are independent and identically
distributed over time and distributed as N (0, ση2 ).
Campbell et al. (2001) allow for correlation between
the aggregate component of labor income shocks, ξt,
and innovations to stock returns, ηt; they denote the
correlation coefficient ρη,ξ.
Using equation 11 at date t and date (t + Δt) and
then using equation 12, we can write the change in
labor income as
15) log(Yi ,t +∆t ) − log(Yi ,t )
=  f (t , Z i ,t +∆t ) − f (t , Z i ,t )  +  ν i ,t + ∆t − ν i ,t 




+  εi ,t +∆t − εi ,t 




=  f (t , Z i ,t +∆t ) − f (t , Z i ,t )  + ui ,t +∆t
+  εi ,t +∆t − εi ,t 




=  f (t , Z i ,t +∆t ) − f (t , Z i ,t )  + ωi ,t +∆t
+ξt + ∆t +  εi ,t +∆t − εi ,t  .




After some relabeling and minor changes, this
labor income specification closely matches the specification of Benzoni, Collin-Dufresne, and Goldstein
(2007) reproduced in equation 9. Let us ignore for
now the temporary shock term [εi,t+Δt – εi,t]. We do this
for two reasons. First, it is not feasible to capture this
temporary shock in continuous time in the way that
Campbell et al. (2001) do without introducing another
state variable, which would significantly increase the
difficulty of solving the model numerically. Instead,
Benzoni, Collin-Dufresne, and Goldstein (2007) capture
the notion of temporary shocks by placing them into
the wealth dynamics rather than the labor income dynamics. Second, and more importantly, both Campbell
et al. (2001) and Benzoni, Collin-Dufresne, and
Goldstein (2007) find this term to have a negligible
effect on optimal portfolio decisions. We then relabel
Δℓ(t) ≡ log (Yi,t+Δt) – log (Yi,t), ωi,t + Δt­ ≡ ν2 Δz2,i (t) and

3Q/2009, Economic Perspectives

(

2

)

 f (t , Z i ,t +∆t ) − f (t , Z i ,t )  ≡ g D − σ2 + α ( κ = 0 ) (t ) − ν22 .
Finally, since Campbell et al. (2001) allow aggregate
labor income shocks ξ to correlate with innovations
in market returns η, we decompose ξ into two terms
ξ┴ ≡ ν1Δz1 and ξ║≡ (σ − ν3) Δz3, which are “orthogonal”
and “parallel” to stock market shocks ηt, respectively.
Thus, we write ξt ≡ ξ┴ + ξ║= ν1 Δz1 + (σ − ν3) Δz3. With
this relabeling and the dropping of the temporary
component term, the labor income dynamics in the
Campbell et al. (2001) and Benzoni, Collin-Dufresne,
and Goldstein (2007) models can be written as
2


ν2 
σ2
16) ∆CCGM =  g D −
+ α ( κ = 0 ) (t ) − 2  ∆t
2
2 


+ ν1 ∆z1 + ν 2 ∆z2,i +  σ − ν 3  ∆z3 ,

17)


ν2 
σ2
∆ BCDG =  − κy + g D −
+ α κ (t ) − 2  ∆t
2
2 


+ ν1 ∆z1 + ν 2 ∆z2,i +  σ − ν 3  ∆z3 .

Here, the superscript in αқ(t) emphasizes that α(t) is
calibrated for a given қ to match the labor income profile of Cocco, Gomes, and Maenhout (2005). Clearly,
the two models differ only in the conditional drift, and
are identical in the limit where the mean reversion
parameter қ→0. Even though these two models are
extremely difficult to distinguish econometrically for
“small” values of қ, Benzoni, Collin-Dufresne, and
Goldstein (2007) show that they have substantially
different predictions for the optimal portfolio choice
of young agents.
This analysis is also useful to clarify the link with
the labor income models considered in recent work
by Lynch and Tan (2008) and Storesletten, Telmer, and
Yaron (2004, 2007). Storesletten, Telmer, and Yaron
(2004) estimate that idiosyncratic risk is strongly countercyclical, with a conditional standard deviation that
increases by 75 percent (from 0.12 to 0.21) as the macroeconomy moves from peak to trough. In the context
of our framework, fluctuations in the ν2 coefficients
over the business cycle would capture this feature.
Storesletten, Telmer, and Yaron (2007) show that when
idiosyncratic shocks become more volatile during economic contractions, human capital acquires stock-like
features. In a realistic calibration of their model they
also obtain a hump-shaped life-cycle investment profile.
Lynch and Tan (2008) extend the work by Storesletten, Telmer, and Yaron (2004, 2007) by showing
that the conditional mean of the labor income flow

Federal Reserve Bank of Chicago

also fluctuates at business cycle frequencies. They
use the dividend yield to predict aggregate labor income growth and find that mean labor income growth
is procyclical. They refer to this feature as the statedependent mean channel. Combined with the statedependent volatility channel of Storesletten, Telmer,
and Yaron (2004, 2007), this effect generates realistic
portfolio holdings over the life cycle. The Lynch and
Tan (2008) state-dependent mean channel is cast
within our framework by replacing the state variable
that drives the conditional mean of labor income flow
in equation 17. In Benzoni, Collin-Dufresne, and
Goldstein (2007), the predictive variable is y, the logarithmic difference between aggregate labor income
and dividends, which underlies the co-integration relation. In Lynch and Tan (2008), the predictive variable
is the dividend yield. While the condition explored by
Lynch and Tan (2008) is weaker than the co-integration relation, it is still sufficiently powerful to have a
first-order effect on the agent’s investment decision.
Specifically, Lynch and Tan (2008) find the correlation between the growth rate in labor income and the
lagged dividend yield to be approximately 3 percent.
As they note in their paper, the magnitude may seem
small, but the effect on portfolio allocations could be
large, much in the same way that return predictability
regressions with a low R2 coefficient can still induce
large hedging demands for stock.
Other previous studies have also considered specifications consistent with the notion that labor income
flow and stock returns correlate highly over the long
run. For example, Campbell (1996) assumes that labor
income follows an autoregressive AR(1) process with
low contemporaneous correlation with stock dividends.
He finds a highly time-varying discount factor for
security prices, and assumes that this same discount
factor is appropriate for discounting labor income. This
assumption generates a high correlation for stock returns and returns to human capital. Moreover, Santos
and Veronesi (2006) consider a model in which labor
income and dividends are co-integrated. They show that,
consistent with the model’s predictions, the lagged ratio
of labor income to consumption predicts stock returns.
Yet not all the literature concurs that the long-run
correlation of shocks to labor income and stock returns
is positive and high. For instance, Lustig and Van
Nieuwerburgh (2008) attribute the component of consumption growth innovations that cannot be explained
by their model to news about expected future returns on
human wealth. They back out the implied human wealth
and market return process and conclude that innovations in human wealth and financial asset returns are
negatively correlated. This conclusion, however, would



figure 5

figure 6

Life-cycle stock holdings:
Model predictions

Life-cycle stock holdings:
Exposure to long-run risk

percentage of financial assets in stocks

percentage of financial assets in stocks
100

100
80

80

60

60

40

40

20

20

0
20

25

30

35

40 45
age

50

55

60

65

(100 − age)%
Stocks share with long-run risk
Notes: The blue line shows the life-cycle stock holdings for
a worker subject to long-run labor income risk. The black line
shows the life-cycle stock holdings for a strategy that invests
(100 – age)% of financial assets in stocks.
Source: Benzoni, Collin-Dufresne, and Goldstein (2007),
figure 3, panel B, p. 2149.

deepen the limited stock market participation puzzle:
Under this condition the young agent would want to
invest even more in risky assets, since human capital
would become a hedge to stock market holdings.
Nontradable labor income and
life-cycle asset allocation
Benzoni, Collin-Dufresne, and Goldstein (2007)
solve the life-cycle portfolio choice problem of an agent
who maximizes time-separable constant relative risk
aversion (CRRA) utility when the stock return and
labor income dynamics are those in equations 4 and 9.
They use a 1929–2004 sample of data on total aftertax U.S. employee compensation and dividends on a
well-diversified portfolio of U.S. stocks to estimate
the coefficients of the co-integration relation in equation 6. Moreover, they calibrate the idiosyncratic labor
income dynamics in equation 7 to match the evidence
in prior papers that have studied the properties of labor
income using household-level data. In their baseline
case, they assume an equity premium of 6 percent and
a CRRA coefficient of 5. Further, they impose shortselling constraints on the stock and the bond. They do
not impose any entry cost to participate in the stock
market. Figure 5 illustrates the life-cycle portfolio holdings predicted by this model calibration, and contrasts
it to the recommendation of many financial advisers

10

0

20

25

30

35

40

45
age

50

55

60

65

κ = 0.10
κ = 0.15 (baseline)
κ = 0.20
Note: The plots show life-cycle stock holdings for workers
subject to different degrees of exposure to long-run labor
income risk (measured by the model coefficient κ).
Source: Benzoni, Collin-Dufresne, and Goldstein (2007),
figure 6, p. 2154.

to invest (100 – age)% of financial assets in stocks.
Consistent with empirical evidence, the optimal portfolio share is hump-shaped.
The intuition for this finding is as follows. When
the investor is young, there is sufficient time for the
co-integration effect to act. Thus, the young agent’s
human capital displays a high level of co-movement with
the stock market due to long-run labor income risk; that
is, human capital has stock-like features. Since much of
a young investor’s wealth is tied up in her human capital
(financial wealth is relatively small when she is young),
she finds herself overexposed to stock market risk and
therefore chooses to invest her financial wealth in the
risk-free asset. As the investor grows older, co-integration has less time to act so that idiosyncratic shocks
become the prevalent source of human capital risk.
Since these latter shocks are orthogonal to stock market
fluctuations, the investor has an incentive to diversify
them away via a larger position in stocks. This effect
generates the increasing part of the portfolio holding
profile. When the agent approaches retirement, human
capital has mainly bond-like features. However, the
present value of future labor income flows shrinks to
zero, since there are few remaining years of employment. Thus, the agent reduces her position in the
stock market to buy more of the risk-free asset.

3Q/2009, Economic Perspectives

figure 7

figure 8

Life-cycle stock holdings:
Equity risk premium

Life-cycle stock holdings:
Risk aversion

percentage of financial assets in stocks

percentage of financial assets in stocks

0.7

100

0.6

80

0.5

60

0.4
0.3

40

0.2
20

0.1
0
20

25

30

35

40

45
age

50

55

60

65

µ – r = 4%; κ = 0.05
µ – r = 4%; κ = 0.10
µ – r = 4%; κ = 0.15
µ – r = 6%; κ = 0.15 (baseline)
Note: The plots show life-cycle stock holdings for different
values of the equity risk premium (measured by the expected
stock return minus the risk-free rate, µ – r) and different
degrees of exposure to long-run labor income risk (measured
by the model coefficient κ).
Source: Benzoni, Collin-Dufresne, and Goldstein (2007),
figure 7, p. 2155.

The hump-shaped life-cycle profile is robust to a
wide range of model calibrations. The most important
model coefficient is қ, which measures the time scale of
the co-integration relation in equation 6. Larger values
of қ determine faster reversion of the variable y toward
its long-run mean, which tends to increase the long-run
correlation between labor income and stock returns. As
a result, the worker invests more conservatively; that is,
she reduces her stock holdings throughout the life cycle
(figure 6). In contrast, when қ is smaller the worker invests more aggressively in stocks. When қ is zero the
effect of long-run labor income risk vanishes (as shown
in the previous section). In this case the effect of idiosyncratic shocks prevails, and the worker invests most
of her financial assets in stocks. But even for an estimate of қ as low as 0.05, which implies a time scale
of 0.105 = 20 years, and a risk premium of 4 percent (the
same risk premium assumed by, for example, Campbell
et al., 2001; Cocco, Gomes, and Maenhout, 2005; and
Gomes and Michaelides, 2005), it is optimal for the
young agent not to invest in the risky market portfolio
(figure 7). This is important, since such a low value of
қ makes co-integration hardly detectable in the data.
Yet, the effect on her risky asset holding is significant.
Increasing the variance of the permanent idiosyncratic shocks increases the diversification motive, inducing

Federal Reserve Bank of Chicago

0

20

25

30

35

40 45
age

50

55

60

65

γ=3
γ=4
γ = 5 (baseline)
Notes: The plots show life-cycle stock holdings for workers
with different levels of risk tolerance. For most workers,
the risk aversion measure γ is positive. Values of γ  below
10 are considered to be common.
Source: Benzoni, Collin-Dufresne, and Goldstein (2007),
figure 10, p. 2158.

an investor to buy more stocks. This effect, however,
does not fully offset the long-run aggregate risk component when the investor is young. Consistent with the
findings of the prior literature, transient labor income
shocks do not have a significant impact on portfolio holdings. Finally, the hump shape of the portfolio profile holds
even when we account for stock return predictability.
This last result is important, since several recent studies
have documented that the expected future stock returns
are high when current returns are low. Thus, when returns are predictable an investment in the stock market
creates its own hedge, which makes stock ownership
even more appealing than when returns are uncorrelated.
In Benzoni, Collin-Dufresne, and Goldstein
(2007), the results are quite sensitive to the agent’s attitude toward risk. In their baseline case, they fix the
CRRA coefficient at 5, a value well below the upper
bound CRRA=10, which most economists find to be
reasonable. Of course, higher values of risk aversion
reinforce the long-run labor income risk effect and
make the agent hold even less of her portfolio in stocks.
However, as the agent becomes more risk tolerant,
for example, CRRA=3, the diversification motive due
to idiosyncratic shocks prevails, and a young investor
places most of her financial wealth in stocks (figure 8).
This is a nice feature of the model. The literature has

11

documented a great deal of heterogeneity in stock
market participation, and this property is useful to explain the equity premium puzzle (for example, Basak
and Cuoco, 1998; and Mankiw and Zeldes, 1991).
Heterogeneity in risk aversion (possibly combined
with different degrees of exposure to economy-wide
and idiosyncratic shocks across agents) is a possible
explanation for this evidence.
The valuation of pension plan obligations,
their funding, and the optimal allocation
of pension assets
The ideas set forth in the literature that studies
life-cycle asset allocation find direct application in
other fundamental problems. For instance, long-run
labor income risk strongly affects the valuation of
pension plan obligations, their funding, and the allocation of pension assets across different investment
classes. In this section, we discuss recent research
that has addressed these issues, focusing in particular
on the work by Lucas and Zeldes (2006) on defined
benefit (DB) pension plans and Geanakoplos and
Zeldes (2007) on Social Security.
Lucas and Zeldes (2006) study the valuation and
hedging of DB plans. A DB plan awards the employee
deferred compensation in the form of future payments
(typically a retirement annuity) linked to the length of
her tenure with the firm and the salary received during
the final year(s) of employment. In spite of much recent growth in defined contribution (DC) plans, a
number of firms still offer DB plans as an important
part of the retirement package for their employees.
Uncertainty about future wages, the date of the
worker’s separation from the firm, and the size and
composition of the pool of existing and future employees
complicates the analysis of DB plans. These factors
affect the measure of the firm’s liability (for example,
Lucas and Zeldes, 2006). On one extreme, the firm
can focus on a narrow measure of the DB plan’s liabilities that accounts only for accrued benefit obligations (ABOs) toward former and current workers,
computed based on current years of employment and
wages. On the opposite extreme is a broad measure of
the firm’s obligations that also accounts for liabilities
toward all employees (former, current, and expected
future workers), computed based on past and projected future years of employment and wages. Lucas and
Zeldes refer to this latter measure as an “all-inclusive”
projected benefit obligation (PBO).
This distinction is important in the analysis of the
problem. First, different measures of DB pension
liabilities are relevant in various contexts because of
institutional restrictions. For instance, the ABO is a

12

legal obligation that the firm can avoid only through
bankruptcy. Related, the ABO measure serves as a
basis to compute minimum funding requirements by
which firms are legally required to abide. Moreover,
insurance by the Pension Benefit Guaranty Corporation
(PBGC) makes the ABO an essentially safe asset, up
to a certain cap. In addition, the valuation and hedging
of various measures of DB pension liabilities differ
depending on the uncertainty associated with such
obligations. For instance, since ABOs are a firm’s
obligations of a known amount, they should be discounted accordingly when one computes their present
value. Moreover, to fund these obligations the firm
should invest the assets in its pension plan entirely in
bonds that match the cash flows of the current ABOs
(for example, Bodie, 1990, 2006). However, the valuation and funding of PBOs should reflect the risk associated with these uncertain future payments.
The choice of how to optimally fund such obligations is complicated by multiple factors, including
taxes, the effect of PBGC guarantees, accounting and
tax regulations, corporate liquidity needs (funds tied
up in the pension plan may not be easily redirected to
other corporate needs), and other labor contracting
considerations. Abstracting from some of these issues,
Lucas and Zeldes (2006) focus on the problem of
hedging PBOs. They argue that, while the hedging of
ABOs is best accomplished with a portfolio of bonds,
the hedge portfolio for PBOs should contain a mix of
stocks and bonds, with a share of stocks versus bonds
that depends on firm and worker characteristics—for
example, the probability of bankruptcy, worker separation, and mortality. This result is robust to taking into
account the possible reduction of future wages by the
value of current pension accruals (for example, Bulow,
1982). Moreover, the rate at which to discount uncertain PBOs is a function of similar macroeconomic,
firm, and worker characteristics.
The intuition for these results is as follows. If
wage growth correlates positively with stock returns
over the long run, then future pension liabilities will
also correlate positively with the performance of the
stock market. Thus, stocks should be part of the hedge
portfolio, and firms with a higher percentage of active
workers should invest more heavily in stocks. Moreover, firms should discount their projected PBOs at a
rate that increases with the share of active workers relative to separated and retired employees. Similar to
Benzoni, Collin-Dufresne, and Goldstein (2007),
these results are driven by long-run labor income risk:
Because of the long-run correlation between labor
income flows and stock returns, human capital has a
stock-like component, and this component is higher for

3Q/2009, Economic Perspectives

younger workers. Thus, the PBO of a firm with a higher
fraction of active (that is, younger) workers also has
stock-like properties. This feature determines a higher
hedge position in stocks, increases the rate at which to
discount the PBO, and reduces the PBO’s present value.
Lucas and Zeldes (2006) provide evidence consistent, at least in part, with the predictions of their model.
Companies with relatively few retirees and separated
workers hold more stocks in their pension plans. However, the hedging demand for long-run labor income
risk cannot explain why some firms that have a high
proportion of retirees and separated workers still invest much of their pension fund assets in stocks.
Similar issues arise when we study the valuation of
Social Security obligations. A key input to this problem
is the rate at which to discount future liabilities. The
traditional actuarial approach uses a risk-free rate to
discount future expected cash flows. Geanakoplos and
Zeldes (2007) argue that this approach underestimates
the riskiness of such obligations. Social Security benefits
depend on the realization of the future economy-wide
wage level. If future wages and stock market performance correlate positively over the long run, then the
appropriate discount rate for Social Security obligations
toward active workers should exceed the risk-free rate.
This risk adjustment reduces the present value of the
obligation, which is relevant to assessing the projected
burden of Social Security on the taxpayer. Moreover,
there is much debate on the costs and benefits associated
with investing a fraction of the Social Security fund in
stocks (for example, Abel, 2001). This problem resembles
optimal allocation of the assets that fund private DB
pension plans. Thus, the results derived in Lucas and
Zeldes (2006) apply to this setting, too. Specifically, the
portfolio that hedges projected Social Security obligations contains a share of stocks that depends on macroeconomic conditions and worker characteristics.
Finally, there is a heated debate in the U.S. about
the opportunity to replace part of the existing DB
Social Security system with a system of DC personal
accounts. If such a reform were to occur, it is possible
that the private sector would take over some of the
obligations that are currently guaranteed by Social
Security. For instance, Geanakoplos and Zeldes (2008)
advocate a system of progressive personal accounts
with two main features. First, accruals in the personal
accounts would be in a new kind of derivative security
that pays its holder one inflation-adjusted dollar during
every year of life after her statutory retirement date,
multiplied by the economy-wide average wage at
retirement date. They call this derivative a personal
annuitized average wage security (PAAW). Second,
households would buy their new PAAWs each year

Federal Reserve Bank of Chicago

with their Social Security contributions, augmented
or reduced by a government match. Some of these
securities, which effectively define benefits for the
future retiree, could be pooled together and sold to
financial markets.2 In this event, how would investors
price them? Geanakoplos and Zeldes (2007) show
that accounting for long-run labor income risk is a
key ingredient in a model to value these claims.
Conclusion
The recent literature has offered various alternative explanations for the limited stock market participation puzzle. The discussion here, focused on the work
of Benzoni, Collin-Dufresne, and Goldstein (2007),
shows that long-run labor income risk has a first-order
effect on optimal life-cycle asset allocation. We make
no attempt to discuss the other numerous important
contributions, which are reviewed in the excellent
articles by, for example, Campbell (2006) and Curcuru
et al. (2004). We do not view the explanation discussed
here as a substitute for these previous theories, but
rather as a complement.
The importance of long-run labor income risk is
further underscored in the recent work by, for example,
Lucas and Zeldes (2006) and Geanakoplos and Zeldes
(2007, 2008). In particular, these studies show that longrun labor income risk is an important conduit through
which macroeconomic uncertainty affects the valuation
of DB pension plans, their funding, and the allocation
of pension assets across different investment classes.
The ideas developed in Benzoni, Collin-Dufresne,
and Goldstein (2007) are also potentially useful to shed
light on other important topics. For instance, heterogeneity in risk aversion combined with different degrees of exposure to long-run labor income risk can
generate limited stock market participation. Thus, an
extended version of the model with two different agent
groups that endogenously choose whether to buy stocks
may provide a general equilibrium foundation for the
setting considered by, for example, Basak and Cuoco
(1998) and Mankiw and Zeldes (1991), who show
that limited stock market participation helps explain
the equity premium puzzle.
Finally, it is natural to conjecture that, similar to
labor income, real estate ownership is an important conduit for macroeconomic uncertainty. For instance, Quan
and Titman (1997) argue that the housing and stock markets are co-integrated. Since real estate has a significant
share in the portfolio of most households, a model that
accounts for the long-run correlation between real estate
and stock market returns would prescribe that an investor should be even more cautious about bearing
stock market risk.

13

NOTES
For instance, it is impossible to separately identify three effects on
life-cycle asset allocation: the investor’s age, the investor’s birth
cohort, and the time of observation (Ameriks and Zeldes, 2004).
This is because the investor’s age is given by the difference between
the date at the time of observation and her birth date. As a result,
researchers typically focus on two of the three effects and set the
third one (typically the cohort effect) to zero.
1

Geanakoplos and Zeldes (2008) advocate a system of regulations
to ensure that firms purchasing these securities fully collateralize
their obligations. While Social Security obligations are guaranteed
by the federal government, a privatized system would not have
such a guarantee.
2

Appendix: The Survey of Consumer Finances

We use data from the 1998, 2001, 2004, and 2007
Surveys of Consumer Finances to construct the plots in
figures 1–4 (pp. 4–7). The SCF is an interview survey of
U.S. households sponsored by the Board of Governors of
the Federal Reserve System. The survey contains information on household balance sheets, income, labor force
participation, and demographic characteristics.
It has been conducted every three years since 1983; the
most recent available data were collected in 2007, when
4,422 households were interviewed.
We downloaded the SCF data from the SCF website
at www.federalreserve.gov/pubs/oss/oss2/scfindex.html,
and we produce core variables using the SCF macro posted
at www.federalreserve.gov/pubs/oss/oss2/bulletin.macro.txt.
In our analysis, we mainly focus on four variables produced by the macro: the age of the head of the household
(denoted by AGE in the macro), financial assets (FIN),
financial assets invested in stocks (EQUITY), and sample
weights (WGT).
We use the AGE variable to create a new categorical variable that splits the population into seven age
groups: 18–25, 26–30, 31–40, 41–50, 51–60, 61–65, and
66 and above. In figures 1–4, the horizontal axis values

14

of the points that make up the plots are the midpoints of
these age intervals. Financial assets (FIN) include checking, savings, money market, and call accounts; certificates
of deposit; mutual funds; stocks; bonds; IRAs; cash value
of life insurance; business assets; and other managed
assets. Financial assets invested in stocks (EQUITY)
include directly held stocks, stock mutual funds, IRAs/
Keoghs invested in stock, other managed assets with
equity interest (annuities, trusts, and managed investment accounts), and thrift type retirement accounts invested in stock. The SCF’s sample design consists of
two parts: a standard geographically based random sample and a special oversample of relatively wealthy families. Thus, we use the weights (WGT) provided in the
survey to combine information from the two samples
and make estimates for the full population.
To create the subsample of stockholders we use the
variable HEQUITY, which equals one if EQUITY is greater
than zero. The percentage of households holding stocks
is given by the mean of the HEQUITY variable. Our
measure of the share of stocks in the portfolio of financial
assets is the ratio of the variables EQUITY and FIN when
FIN is strictly positive, and is zero when FIN is zero.

3Q/2009, Economic Perspectives

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Federal Reserve Bank of Chicago

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Ogura, Toshiaki Tachibanaki, and David A. Wise (eds.),
Chicago: University of Chicago Press, pp. 65–104.

16

Quan, Daniel C., and Sheridan Titman, 1997,
“Commercial real estate prices and stock market returns:
An international analysis,” Financial Analysts Journal,
Vol. 53, No. 3, May/June, pp. 21–34.
Rosen, Sherwin, 2008, “Human capital,” in The
New Palgrave Dictionary of Economics, Steven N.
Durlauf and Lawrence E. Blume (eds.), 2nd ed.,
8 vols., Houndmills, Basingstoke, UK, and New York:
Palgrave Macmillan.
Santos, Tano, and Pietro Veronesi, 2006, “Labor
income and predictable stock returns,” Review of
Financial Studies, Vol. 19, No. 1, Spring, pp. 1–44.
Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron,
2007, “Asset pricing with idiosyncratic risk and overlapping generations,” Review of Economic Dynamics,
Vol. 10, No. 4, October, pp. 519–548.
__________, 2004, “Cyclical dynamics in idiosyncratic
labor market risk,” Journal of Political Economy,
Vol. 112, No. 3, June, pp. 695–717.
Viceira, Luis M., 2001, “Optimal portfolio choice
for long-horizon investors with nontradable labor
income,” Journal of Finance, Vol. 56, No. 2, April,
pp. 433–470.
Wachter, Jessica A., and Motohiro Yogo, 2009,
“Why do household portfolio shares rise in wealth?,”
University of Pennsylvania, Wharton School, working
paper, February.

3Q/2009, Economic Perspectives

Preannounced tax cuts and their potential influence
on the 2001 recession
R. Andrew Butters and Marcelo Veracierto

Introduction and summary
The 2001 recession differed from previous recessions
in several ways. First, it was quite mild in terms of
its associated contractions in output and consumption.
Also, since total hours worked fell sharply, labor productivity remained relatively high. Furthermore, while
business fixed investment plummeted (actually, much
more than in a typical recession), residential investment
and purchases of durable goods remained surprisingly
strong. This is highly unusual: Typically, residential
investment and purchases of durable goods collapse
during recessions, often leading the general contraction in economic activity by several quarters.
Another distinctive feature of the 2001 recession
was that it was preceded by a presidential election dominated by tax cut discussions. The proposals of the two
major candidates differed in crucial ways. While the
Democratic candidate, Al Gore, promised cuts that would
leave statutory income tax rates essentially unchanged
(most cuts would come in the form of tax credits for
particular economic activities), the Republican candidate, George W. Bush, announced a plan that would
significantly reduce income tax rates across all income
brackets. Thus, the outcome of the 2000 presidential
election promised to have a large impact on the tax rates
that households and businesses would face in the future.
A basic hypothesis in this article is that the two sets
of facts—the unusual features of the 2001 recession
and the tax cuts promised during the 2000 presidential
election—could be related. The rationale for this view
is that people and firms are forward-looking: Expectations about the future may have a significant effect on
the decisions that they make today. For instance, the
anticipation of higher demand may lead a producer to
expand his production capacity, or the anticipation of
higher wages in a particular occupation may induce a
worker to acquire specific skills. Anticipated tax cuts
are no exception. If tax rates are expected to decrease

Federal Reserve Bank of Chicago

in one year, the current year becomes a relatively bad
year for working and investing.1 Forward-looking households and businesses may thus decide to devote less
time to market activities, cutting back on time worked
in the market and increasing time worked at home
and substituting business investment for home investment. These contractionary effects of anticipated tax
cuts could have played an important role in the patterns of activity observed during the 2001 recession.
Of course, the anticipated tax cuts were not the
only factor potentially influencing economic activity
during the 2001 recession. A number of other important shocks and policy responses also occurred in 2000
and 2001. For starters, market participants apparently
began to reevaluate the profitability of many investment projects in the high-tech sector. This and other
factors were reflected in a sharp decline in equity prices
starting the spring of 2000. In addition, in 2001 there
were the terrorist attacks on September 11, followed
by the revelation of the Enron scandal later that fall.
Moreover, the Federal Reserve lowered its policy rate
substantially over the course of 2001, which influenced
costs underlying household and business decisions
regarding the purchase of durables and capital goods.
In order to determine the possible effects of anticipated tax cuts, we construct and analyze a theoretical
model that abstracts from these other influences on the
economy. The model will thus tell us if the anticipated tax
effects can plausibly reproduce some of the patterns observed in the data. However, it is important to point out
that since the other factors are excluded, we cannot use

R. Andrew Butters is an associate economist and Marcelo
Veracierto is a senior economist in the Economic Research
Department at the Federal Reserve Bank of Chicago. They
thank Jeff Campbell, Spencer Krane, Anna Paulson, and
Dan Sullivan for their comments.

17

the analysis to rank the relative importance of taxes and
these other influences on the economy over this period.
The model we use is a version of the Greenwood
and Hercowitz (1991) home production model. In this
model, the economy is populated by a representative
household that values consumption of a market good
and consumption of a home good. The home good is
produced using home capital and time spent at home.
The market good is produced using business capital
and time worked in the market. Output of the market
good can be consumed, invested in business capital,
invested in home capital, or consumed by the government. The government finances its expenditures by
taxing capital and labor income. Moreover, the government is assumed to balance its budget every period.
Admittedly, the model is quite simple. However, it
captures important decision margins, and therefore,
we consider it a useful starting point for the analysis.
Selecting model parameters to reproduce salient
features of the U.S. economy, we find that, while immediate tax cuts generate a boom in economic activity,
delayed tax cuts initially generate a recession. Our
analysis underscores the importance of taking forwardlooking behavior on the part of households and businesses into account in considering the impact of policy
alternatives. In particular, taking this behavior into
account can help us understand some of the patterns
in activity observed during the 2001 recession.
There are a number of papers that have previously
analyzed the effects of anticipated changes to the
economic environment (for example, Jaimovich and
Rebelo, 2008, 2009; and Beaudry and Portier, 2007).
However, the most closely related is the one by House
and Shapiro (2006). Their paper also evaluates the
effects of the 2001 tax reform. However, they focus
on the effects of phased-in tax cuts from the time that
the reform was signed into law, and they consider a
model in which business capital is the only form of
capital. Contrary to House and Shapiro (2006), we
emphasize the anticipatory effects of the reform before
it was signed into law, and introduce home capital into
the analysis. Both extensions allow us to analyze the
start of the 2001 recession and to evaluate whether the
model is able to generate the unusual strength in home
investment that was observed during that recession.
In the next section, we present the salient observations from the 2001 recession. Then, we describe
the tax reforms that were promised during the 2000
presidential campaigns, as well as the tax reform that
was actually implemented. Next, we explain the model economy. We describe the competitive equilibrium
to be analyzed and how the model’s parameters are
selected. Finally, we present our results.

18

The 2001 recession
On November 26, 2001, the National Bureau of
Economic Research (NBER) issued a statement announcing that the U.S. economy had reached a peak
in business activity in March 2001 and had moved
into a recessionary period.2 The NBER report cited
falling industrial production as the most significant
piece of evidence to suggest the economy had slowed.
Poor real sales and employment also provided evidence
supporting the decision to announce a recession. While
employment peaked in March, in parallel with the
NBER peak date, both industrial production and sales
had peaked six and seven months before that date,
respectively. The NBER committee mentioned in its
statement that earlier dates had been considered to
reflect the “divergent paths” of manufacturing and
employment, but these dates were dismissed because
of the lower emphasis placed on the manufacturing
and goods-producing sectors of the economy.3
On July 17, 2003, the NBER reported that the economy had reached a trough in November of 2001, ending
the recession.4 The strength of both real gross domestic product (GDP) and real personal income relative to
levels before the recession allowed the NBER committee
to conclude that any future downturn in the economy
would in fact be a separate recession and not a continuation of the 2001 recession. Nevertheless, industrial production and employment showed no sign of recovery.
To gain a more detailed understanding of the
2001 recession, figure 1 reports the paths of output,
consumption, hours worked, business investment, and
home investment leading up to and during the 2001
recession. For comparison, it also reports the average
of those paths before and during the previous six recessions.5 For consistency with the model used later
on, residential investment and personal consumption
expenditures on durables goods are combined into a
single measure denoted home investment. In turn, business investment is defined as private nonresidential
fixed investment plus changes in inventories, and consumption is restricted to consumption of nondurables and
services. Because our model economy will be closed,
output is defined as GDP minus net exports (that is,
gross domestic purchases).6 All of these variables are
reported in real terms. For hours worked, we focus on
a broad measure constructed by Prescott, Ueberfeldt,
and Cociuba (2009), which includes military personnel.
Because our model will have no growth component,
we detrend each series using a deterministic trend.7
A quick glance at figure 1 indicates that, relative
to the standard recession, the 2001 recession was highly
atypical in several respects. Output and consumption
(panels A and B) fell during 2001, but not as much as

3Q/2009, Economic Perspectives

figure 1

2001 recession versus average recession
A. Output
index

B. Consumption
index

101

101

100
100
99

98
–5

–4

–3

–2 –1 0
1
2
quarters since peak

3

4

5

99
–5 –4

–3

–2

–1

0

1

2

3

4

5

3

4

5

quarters since peak

C. Hours worked
index

D. Business investment
index

102

106
102

100
98
98
94
96
–5

–4

–3

–2

–1

0

1

2

3

4

5

quarters since peak

90
–5 –4

–3

–2

–1

0

1

2

quarters since peak

E. Home investment
index
105

100

95
–5

–4

–3

–2

–1

0

1

2

3

4

5

quarters since peak

	

	

                           Average recession       

   2001 recession

	
Notes: All variables are normalized (indexed) to 100 at the recession peaks. Time 0 indicates the recession peak quarter. The average 	
recession is based on those that occurred in 1960–61, 1969–70, 1973–75, 1980, 1981–82, and 1990–91, according to the National 	
Bureau of Economic Research.
Source: Authors’ calculations based on data from the U.S. Bureau of Economic Analysis, National Income and Product Accounts of the
United States, from Haver Analytics.

Federal Reserve Bank of Chicago

19

in the average recession.8 Once the 2001 recession started,
hours worked (panel C) behaved similarly to the average
recession. However, during the three quarters leading up
to the 2001 recession, there was a steady decline in hours
worked compared with the constant levels leading up to
the average recession. For the 2001 recession, the decline
in business investment (panel D) was much sharper and
started much earlier. Perhaps most notably, the 2001
downturn had minimal effects on home investment
(panel E). On average, home investment’s decline leads
an upcoming recession, while there were no noticeable
effects both before and during the 2001 recession.
Later on, we will show that the anticipation of future
tax cuts could have contributed to some of these atypical features of the 2001 recession (for example, the
relatively strong consumption and home investment).
In order to do this, we must first identify reasonable
estimates for two critical elements of the analysis:
1) when economic agents began anticipating the future
tax cuts and 2) what was the particular tax cut schedule
that economic agents were anticipating. We will examine the 2000 presidential campaigns and election,
as well as the implementation of the Economic Growth
and Tax Relief Reconciliation Act of 2001 (EGTRRA),
to determine these two elements.
The presidential campaigns and
the 2000 election
On March 14, 2000, both George W. Bush and
Al Gore won their respective party’s nomination to
become the 43rd President of the United States. Over
the next eight months, both candidates campaigned
and presented the American public with their own
proposals to stimulate the economy.9
The Republican candidate, George W. Bush, ran on
a platform with across-the-board marginal rate tax cuts
as one of its foundations. Leading up to the election, the
total cost of the cuts was estimated at $1.3 trillion over
the nine-year period 2002–10. In the plan, the 28 percent
and 31 percent tax brackets would both be dropped to
25 percent. The 15 percent bracket would be dropped to
10 percent, and both the 36 percent and the 39.6 percent
tax brackets would be reduced to 33 percent.10 All of
these cuts were proposed to be “phased in” starting in
2002, with a further reduction in 2004, and with all of
the effects being implemented by 2006.
Al Gore, the Democratic candidate and incumbent
Vice President, proposed a tax plan more conservative
in cost (estimated at $500 billion) and more geared to
the low- and middle-income classes. His tax reform
included raising the standard deduction, with tax breaks
and deductions for savings accounts, child care, college
tuition, and long-term caregivers. A tax credit for new

20

retirement savings accounts was the most substantial
of these proposals.
Although both candidates promised significant
tax cuts, their proposals differed in a fundamental way.
While the Republican candidate promised reductions
in marginal tax rates, the Democratic candidate promised cuts in inframarginal taxes. This is an important
distinction, since reductions in marginal tax rates tend
to increase labor supply, while reductions in lump-sum
taxes have the opposite effect. These differences made
it difficult for economic agents to adjust their behavior
to the prospective tax cuts. The reason is that adjusting to one type of reform would have produced large
errors had the alternative reform been implemented.
It would be extremely difficult to determine at
each point in time the economic agents’ beliefs about
the likelihood of either type of reform being implemented and, therefore, the future taxes they were anticipating. However, it is convenient for the purposes of
this article to make a number of not entirely implausible
assumptions. First, since the election was so tight and
the Florida recount actually postponed its outcome
for almost a month after election day (November 7),
it seems reasonable to assume that until the end of
2000, economic agents were putting a 50/50 chance
on either type of reform being eventually implemented.
Second, since adjusting to each type of reform required
such drastically different types of labor supply responses,
it is not implausible to assume that agents waited until
the election outcome before making any changes to
their behavior. Third, we assume that, once George W.
Bush was declared the new President of the United
States, economic agents immediately shifted their
expectations about future tax cuts to what had been
promised during his campaign. Fourth, we assume
that once a slightly different reform was later implemented, economic agents adjusted their expectations
accordingly. In the next section, we describe the reform
that was actually implemented.
The implementation of the 2001 tax cuts
The Economic Growth and Tax Relief Reconciliation Act was signed into law by George W. Bush on
June 7, 2001. As proposed in Bush’s campaign for the
presidency, the law’s most substantial changes involved
an across-the-board reduction in the marginal tax rates.
A 0.5 percentage point cut in the marginal rates for all
tax brackets above the 15 percent rate became effective
immediately. The law stipulated subsequent cuts in 2002,
2004, and 2006 of 0.5 percentage points, 1 percentage
point, and 1 percentage point, respectively, for each tax
bracket (the only exception being a cut of 2.6 percentage
points for the highest bracket in 2006). This schedule

3Q/2009, Economic Perspectives

Table 1

Statutory and effective marginal tax rates: Proposed and enacted
	

Income tax brackets 	   Effective marginal tax rates

	 	
Date 	

$45,200 to 	
$109,250 	

	
A.	Pre-EGTRRA 	
	 Before 2001:Q1	

( - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - percent - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - )
28 	

$109,250 to 	
$166,340 	

$166,340 to 	
$297,300

31 	

36 	

$297,300
and above 	

39.6 	

Labor tax 	
rate (τn) 	

36.20 	

Capital tax
rate (τk)

37.43  

B.	Campaign proposal 						
	 2001:Q1–2001:Q4 	
28 	
31 	
36 	
39.6 	
36.20 	
	 2002:Q1–2003:Q4a 	
—	
—	
—	
—	
35.39 	
	 2004:Q1–2005:Q4a 	
—	
—	
—	
—	
34.58 	
	 2006:Q1 and beyond 	
25 	
25 	
33 	
33 	
33.77 	

37.43
36.98
36.52
36.07

C.	EGTRRA 						
	 2001:Q3–2001:Q4 	
27.5 	
30.5 	
35.5 	
39.1 	
35.92 	
	 2002:Q1–2003:Q4 	
27 	
30 	
35 	
38.6 	
35.64 	
	 2004:Q1–2005:Q4 	
26 	
29 	
34 	
37.6 	
35.08 	
	 2006:Q1–2010:Q4 	
25	
28 	
33 	
35 	
34.40 	
	 2011:Q1 and beyond 	
28 	
31 	
36 	
39.6 	
36.20 	

37.27  
37.11  
36.80  
36.41  
37.43

a
The campaign proposal by George W. Bush did not explicitly state the tax reduction schedule that would be implemented in 2002 and 2004.
Notes: EGTRRA means the Economic Growth and Tax Relief Reconciliation Act of 2001. This table shows the tax rates for the brackets above the 	
15 percent rate. The schedule for the effective marginal tax rates on both labor and capital is taken from House and Shapiro (2006). By using 	
the same weighting procedure used by House and Shapiro (2006), we interpolate the effective marginal tax rates if George W. Bush’s proposed
tax schedule (panel B) had been enacted.

Sources: Authors’ calculations based on data from House and Shapiro (2006) and Congressional Budget Office (2001).

would remain in effect until 2011, when the tax rates
would revert, or “sunset,” to their pre-EGTRRA rates.
In addition, the law phased out the estate tax and
sent a tax rebate check of $300 to each individual.
An increase in the child credit from $500 to $1,000
and relief from the alternative minimum tax (AMT)
and the marriage penalty rounded out the bill. Although
the rebate checks were highly visible in 2001, they
did very little to affect marginal tax rates (House and
Shapiro, 2006).11 The effects of the other provisions on
marginal tax rates will be discussed shortly.
Relative to the tax cuts that George W. Bush had
proposed during his campaign, EGTRRA differed in
several ways. First, the initial cuts to marginal rates of
EGTRRA became effective immediately (in June 2001)
and were retroactive to the beginning of the year. In
proposals during the campaign, the Bush tax cuts were
not to take place until 2002. Next, as seen in table 1,
the ultimate percentage cuts for some tax brackets signed
into law were slightly smaller than what had been proposed to Congress. For the 31 percent and 39.6 percent
tax brackets (panel A), proposed cuts of 6 percentage
points and 6.6 percentage points, respectively (panel B),
were scaled back to 3 percentage points and 4.6 percentage points (panel C). In addition, an explicit “sunset”
date of January 2011 was put on all marginal tax rate
changes (Brumbaugh et al., 2002).

Federal Reserve Bank of Chicago

A study administered by the Congressional Budget
Office (2001, p. 34, boxes 2–3), or CBO, estimated the
effective marginal tax rates (for both labor and capital
income) before and after EGTRRA. Effective marginal
tax rates depend on other features of tax law beyond
the statutory rate, including the earned income tax credit,
the child tax credit, and the AMT, among others. The
analysis by the CBO attempted to take these other provisions into account when determining the estimated
change due to EGTRRA.12
The CBO’s estimates of effective marginal tax
rates of labor and capital income are reported in table 1
(the last two columns of data). We see that, according
to the CBO, the effective marginal tax rate on labor fell
from a pre-EGTRRA level of 36.20 percent (panel A)
to 34.40 percent (fourth row of panel C) and that the
effective marginal tax rate on capital fell from 37.43
percent to 36.41 percent, once EGTRRA was fully
phased in (in 2006).13 A more formal discussion on
the taxation of capital can be found in the appendix.
The effective marginal tax rates estimated by the
CBO for the years 2000 and 2006 can be interpolated
to all other years by using the corresponding tax rates
for the different income brackets (the first through fourth
columns of panel C in table 1).14 The results are shown in
the last two columns of panel C. This procedure can
also be used to construct the implicit effective marginal

21

tax rates that were proposed by George W. Bush during
the presidential campaign. These tax rates are reported
in the last two columns of panel B. The effective marginal tax rates in panels B and C are the ones that will be
used to determine economic agents’ expectations at each
point in time. In particular, we will assume that starting
in 2001:Q1 agents were anticipating the effective marginal tax rates provided in panel B, but that in 2001:Q3 (that
is, after the passage of EGTRRA) they switched their
expectations to the effective marginal tax rates listed
in panel C. These expectations will play an important
role in the model economy to be described next.
The model
The model economy consists of three sectors: a
household sector, a firms sector, and a government
sector. The household sector is composed of a large
number of identical individuals that supply labor and
business capital to the firms. In addition, they produce
a home good, using time and home capital. The firms
sector is constituted by a large number of identical
firms that produce the market good, using business
capital and labor. The market good is sold to the households, which use it for consumption and investment.
The government needs to purchase a certain amount
of the market good every period. These expenditures
are financed with a combination of capital income,
labor income, and lump-sum taxes.15 In what follows
we describe the model in detail.
The household sector
The representative household has preferences
described by the following utility function:
1)	

∞

∑β
t =0

t 


ψ ln ct + (1 − ψ ) ln ht  ,

where itk is gross business investment, itd is gross home
investment, 0 < δk < 1 is the depreciation rate of business
capital, and 0 < δd < 1 is the depreciation rate of home
capital. At the beginning of date 0, the stock of business
capital k0 and the stock of home capital d0 are given.
The home good is produced according to the
following production function:
4)	 ht = dtα (1 − nt )1− α,
where nt is the amount of time spent in market activities,
and 0 < α < 1. Observe that since the time endowment
is equal to one, 1 − nt is the amount of time that the
household spends in home activities.
The household’s budget constraint is given as
follows:
5)
	

ct + itk + itd + Tt ≤ 1 − τtn  wt nt

	

+ 1 − τtk  rt kt + τtk δ k kt ,

where wt is the wage rate, rt is the rental rate on capital, τtn is the tax rate on labor income, τtk is the tax
rate on capital income, and Tt is the lump-sum taxes.
Observe that the household receives a tax depreciation
allowance given by τtk δ k kt . Also observe that the household uses its after-tax labor and capital income to consume, to invest in business capital, to invest in home
capital, and to pay lump-sum taxes. The household
takes the lump-sum taxes Tt , the tax rates τ tn  and  τ tk,
and the prices wt and rt as given.
The household’s problem is to maximize the utility
function (equation 1) subject to equations 4 and 5.
The firms sector
The representative firm produces the market
good using the following production function:

where ct is consumption of a market-produced good, ht is
consumption of a home-produced good, 0 < β < 1 is the
subjective time discount factor, and 0 < ψ < 1. The representative household is endowed with one unit of time.
At the beginning of period t, the household owns
kt units of business capital and dt units of home capital.
Both types of capital can be accumulated using a
standard linear technology. In particular,

where yt is output, Kt is business capital, Nt is labor,
and 0 < θ < 1.
The firm solves the following static profit maximization problem:

2)	 kt +1 = 1 − δ k  kt + itk 	

7) 	 max {yt – rt Kt – wt Nt },

and

subject to equation 6. That is, the firm maximizes the
difference between the revenues that it receives from
selling its output and the total rental payments on capital
and labor. The firm takes the rental rate of capital rt
and the wage rate wt as given.

3)	 dt +1 = 1 − δ d  dt + itd,

22

6)	 yt = K tθ N t1− θ ,

3Q/2009, Economic Perspectives

The government sector
The government needs to make a sequence of ex∞
penditures { gt } t = 0. These expenditures are exogenous—
that is, they are determined outside the model.16 However,
the following government budget constraint must be
satisfied:

That is, the rental markets for capital and labor must
clear.18

with private nonresidential fixed investment plus government gross investment (from the NIPAs).
Using annual data from 1967 through 2007 published in the NIPAs, we find that the corresponding
average annual investment rates id/d and ik/k are equal
to 9.1 percent and 8.5 percent, respectively, and that
the average investment–output ratios ik/y and id/y are
equal to 14.9 percent and 12.7 percent, respectively.19
This provides four target observations.
Two additional target observations are the share
of labor in national income (equal to 70 percent) and
the average fraction of time spent working by the total
civilian noninstitutional population aged 16–64 and
military personnel (equal to 27 percent).20 The first
observation, which is standard in the macroeconomics
literature, is obtained from the NIPAs. The second
observation, which corresponds to the period 1967–
2007, is from Prescott, Ueberfeldt, and Cociuba (2009).
The last three observations that we use are associated with the government sector. The first of these
observations is a government expenditures ratio g/y
equal to 16 percent, which is the average over the period 1967–2007 in the NIPAs. The other two observations
are the pre-EGTRRA effective marginal tax rates on
labor and capital that were described in table 1 (p. 21).
Table 2 lists the parameter values that generate
these nine observations when the model’s time period
is set to one quarter.

Selection of parameter values

Results

gt = τtn wt nt + τtk rt kt − τtk δ k kt + Tt .
That is, government expenditures must be financed
with tax revenues.17
Market clearing
At equilibrium all markets must clear. In particular,
8)	 ct + itk + itd + gt = yt .
That is, consumption of the market good ct plus total
investment itk + itd plus government expenditures gt
must be equal to output yt.
Also,
Kt = kt,
and
Nt = nt.

With constant government expenditures and tax
rates, the model economy eventually settles into a steady
state where consumption, business capital, home capital, output, hours worked, and all prices are constant
over time. In what follows, model parameters are chosen
so that this steady state reproduces key observations
about the U.S. economy. Since there are nine parameters
to choose, we target nine observations. The parameters
to be selected are β, ψ, α, θ, δd, δk, g, τn, and τk.
Before proceeding we need to identify empirical
counterparts for the different types of capital. In what
follows we identify the stock of home capital d with
the sum of residential structures and consumer durable
goods. As a consequence, we associate home investment id with gross private residential fixed investment
plus personal consumption expenditures on durable
goods (from the U.S. Bureau of Economic Analysis’s
national income and product accounts, or NIPAs). In
turn, we identify the stock of business capital k with
total fixed assets minus residential structures. That is,
k includes private business structures, equipment, and
software, as well as all forms of government capital.
As a consequence, we associate business investment ik

Federal Reserve Bank of Chicago

In this section, we analyze the effects of introducing
different types of tax reforms to the economy calibrated
in the previous section. The purpose of the exercises
is twofold: to compare the effects of anticipated tax
cuts with those of unanticipated tax cuts and to explore
whether anticipated tax cuts may have contributed to
generating some of the atypical features of the 2001
recession. In all cases we will assume that in 2000:Q4,
the economy was at the steady state calibrated in the
previous section.
The effects of immediate tax cuts
The first experiment is to evaluate the effects of immediate tax cuts—that is, a tax cut reform that introduces
no delays between the time of its announcement and the
time of its implementation. The experiment’s purpose is to
illustrate how the model works and to facilitate comparisons with a delayed reform later on. The particular tax
cuts considered are the total tax cuts promised by George
W. Bush during the presidential campaign. In particular,
we assume that in 2001:Q1 economic agents learn that
their marginal tax rate on capital (τk) is immediately and
permanently reduced from its pre-EGTRRA rate of
37.43 percent to 36.07 percent. Similarly, we assume that

23

the marginal tax rate on labor (τn) is immediately and
permanently reduced from 36.20 percent to 33.77
percent (see first and last rows of panel B in table 1,
p. 21). We want to emphasize that this exercise is
purely illustrative: As was described previously,
George W. Bush did not promise that these tax cuts
would take place immediately but that they would be
phased in over a period of several years.
Figure 2 shows the evolution of the economy after this reform. We see that, in the model, the reform
generates a boom in economic activity. The lower income tax rates increase the returns to working in the
market and to investing in business capital. As a consequence, hours worked (panel C) and business investment (panel E) increase during the first period of the
reform. Also, the lower reliance on distortionary taxes makes households feel richer, and they respond by
increasing their consumption (panel B). Observe that
during the first period of the reform there is a sharp
drop in home investment (panel F). The reason is that
the lower tax rate on business capital changes the desired mix of capital. In particular, households want to
hold more business capital and less home capital.
During the second period of the reform, business
investment drops and home investment increases. The
reason is that once the correct capital mix is achieved
during the first period of the reform, both types of capital
start growing at a more balanced pace. As business
capital increases during the subsequent periods, output (panel D) and consumption continue to grow and
hours worked start to decrease.
The effects of delayed tax cuts
In the previous section, we considered a scenario
in which the total tax cuts promised by George W. Bush
during his presidential campaign were immediately implemented. The scenario was highly unrealistic: In actuality, his promise was to gradually reduce tax rates
in 2002, 2004, and 2006, with the total tax cuts taking
full effect only by 2006. Here we consider the scenario
in which not only the total tax cuts but their pace of reduction are the ones promised during the campaign. In
particular, the sequence of tax rates τtk and τtn introduced
are those given by the last two columns of panel B in
table 1 (p. 21). The purpose of this experiment is twofold: First, it illustrates the effects of preannouncing
tax cuts instead of implementing them as surprises; second, it evaluates the effects that might have been obtained had the tax reform promised by George W. Bush
during his campaign been implemented.
Figure 3 shows the evolution of the economy
starting in 2001:Q1, when economic agents first learn
that tax rates will be reduced in the future. We see that
in the model economy the delayed reform generates a

24

		

Table 2

Parameter values
Parameter 	
	
	
	
	
	
	
	
	
	

β	
ψ	
α	
θ	
dd	
dk 	
g	
τn	
τk	

Value
0.9868
0.286
0.143  
0.30  
0.02274
0.02112
0.16 × y
0.362
0.3743

Note: The government-expenditures-to-output ratio (g/y) is 	
equal to 0.16.

recession during 2001. The reason is that the anticipated
tax reduction makes 2001 a relatively bad year for
working and investing. Economic agents essentially
take a break from market activities, substituting time
worked in the market for time worked at home and substituting business investment for home investment. Most
of the investment adjustment takes place in 2001:Q1,
when there is a sharp decline in business investment
(panel E) and a sharp increase in home investment
(panel F). Also observe that consumption (panel B)
immediately jumps to a permanently higher level
because the lower future tax rates make the representative household richer. Later, in 2001:Q4, agents know
that taxes are going to be cut the following quarter, so
they prepare for this by increasing business investment
and decreasing home investment. This leaves agents
at the start of 2002:Q1 with a higher stock of business
capital and a lower stock of home capital, which are
appropriate for the sharp substitution in time worked
at home for time worked in the market (panel C) and
for the increase in output (panel D) that subsequently
takes place.
The effects of EGTRRA
The “delayed tax reform” scenario of the previous
section seems to be a plausible description of how prospective tax cuts may have affected the economy through
2001:Q2. There are two reasons for this. First, although
George W. Bush was already announcing his intentions
of cutting marginal tax rates during his 2000 presidential
campaign, it seems unlikely that this may have had significant effects on economic decisions before 2001:Q1. If
economic agents had changed their behavior in anticipation of George W. Bush winning the election (and marginal tax rates being reduced), they would have regretted
it later on had Al Gore become the new president (and
marginal tax rates had remained unchanged). Given the
high uncertainty about the election outcome and given

3Q/2009, Economic Perspectives

figure 2

Effects of immediate tax cuts
A. Tax rates

B. Consumption

rate
0.38

index
103

0.37

102

Tax on capital
0.36

101
0.35
100

Tax on labor

0.34

99

0.33
2000:Q3

’01:Q1

’01:Q3

’02:Q1

C. Hours worked

2000:Q3

’01:Q1

’01:Q3

’02:Q1

’01:Q1

’01:Q3

’02:Q1

D. Output

index

index

104

104

102

102

100

100

98

98
96

96
2000:Q3

’01:Q1

’01:Q3

’02:Q1

E. Business investment

2000:Q3

F. Home investment

index
200

150

150

100

100

50

index

50

0
2000:Q3

’01:Q1

’01:Q3

’02:Q1

2000:Q3

’01:Q1

’01:Q3

’02:Q1

Note: Panels B through F are normalized (indexed) to 100 at 2000:Q4.

the risk of erring in either direction, it seems reasonable
to assume (as a first approximation) that economic agents
waited until the election outcome before changing their
behavior. Second, it seems plausible to think that once
forward-looking economic agents learned by the end
of 2000:Q4 that George W. Bush would become the

Federal Reserve Bank of Chicago

new president, they started to adjust their behavior in
anticipation of the tax cuts announced during his
presidential campaign.
While being a plausible description of the effects of
prospective tax cuts through 2001:Q2, the “delayed tax
reform” scenario of the previous section does not apply

25

figure 3

Effects of delayed tax cuts
A. Tax rates

rate
0.38

B. Consumption

index
103

Tax on capital

0.37

102

Tax on labor
0.36

101
0.35
100

0.34
0.33

99
2000:Q3

’01:Q1

’01:Q3

’02:Q1

2000:Q3

C. Hours worked

D. Output

index

index

104

104

102

102

100

100

98

98

96

’01:Q1

’01:Q3

’02:Q1

’01:Q1

’01:Q3

’02:Q1

’01:Q1

’01:Q3

’02:Q1

96
2000:Q3

’01:Q1

’01:Q3

’02:Q1

E. Business investment

2000:Q3

F. Home investment

index
200

index
150

150

100

100

50

0

50
2000:Q3

’01:Q1

’01:Q3

’02:Q1

2000:Q3

Note: Panels B through F are normalized (indexed) to 100 at 2000:Q4.

after 2001:Q2. The reason is that the actual tax reform
passed by Congress and signed into law in June 2001,
EGTRRA, differed in significant ways from the tax
reform that George W. Bush had announced during the
campaign: 1) The total tax cuts were smaller (although
they would still take full effect by 2006), 2) a “sunset”

26

provision was incorporated, and 3) small tax cuts were
already given for the year 2001 (retroactively to the beginning of the year). So, in a third scenario that follows,
we will assume that economic agents are surprised by
the actual passage of EGTRRA and that they revise their
expectations accordingly. In particular, we will assume

3Q/2009, Economic Perspectives

that in 2001:Q3 economic agents start to believe that the
n
future sequence of tax rates τtk and τt will be given by
the last two columns of panel C in table 1 (p. 21).
Figure 4 shows the complete evolution of the
economy. By construction, the path that the economy
follows through 2001:Q2 is identical to that of the
“delayed tax reform” scenario. However, starting in
2001:Q3, the path is significantly different. Since now
households find out that some tax cuts already take
place in 2001, they immediately shift hours worked at
home to hours worked in the market (panel C) and increase the amount of output produced (panel D). Because of the substitution toward market activities, we
also see that in 2001:Q3 there is an increase in business
investment (panel E) and a drop in home investment
(panel F). Consumption (panel B) drops, however, because agents learn that they are not as rich as they initially believed: EGTRRA now incorporates a “sunset”
provision. In anticipation of further tax cuts that will
take place in 2002:Q1, business investment remains relatively high in 2001:Q4 and home investment remains
relatively low. Once the tax rates are reduced in 2002:Q1,
there is an additional increase in hours worked and output, while business investment and home investment
stabilize around their pre-EGTRRA levels.
Adjustment costs
We saw in the previous section that in the model
economy, the expectations of future tax cuts during the
early part of 2001, followed by the actual implementation of EGTRRA, generate a short-lived recession during
2001 in which hours worked and output fall, while consumption remains relatively strong. These are features observed in the actual 2001 recession (see figure 1, p. 19).
However, home investment is extremely strong during
the early part of the year and extremely weak during
the second half of the year (panel F in figure 4). The
opposite is true with business investment (panel E in
figure 4). These large swings in investment are highly
counterfactual (see figure 1, p. 19).
In order to improve the performance, we introduce
adjustment costs to the model economy. In particular,
we assume that it is costly to change both types of investments from their levels in the previous period. Under
this assumption, the household’s budget constraint
(equation 5) becomes
φk  k k  2 φd  d d  2
 it − it −1  +
 it − it −1  + Tt ≤


2 
2 
n
k 
k k


1 − τt  wt nt + 1 − τt  rt kt + τt δ kt ,





ct + itk + itd +

and the market-clearing condition (equation 8) becomes

Federal Reserve Bank of Chicago

ct + itk + itd +

φk  k k  2 φd  d d  2
 it − it −1  +
 it − it −1  + g t = yt ,


2 
2 

where φk ≥ 0 and φd ≥ 0.
In what follows, we will assume that φk = 0.01
and φd = 0.01. These adjustment costs are quite small.
To see this, consider starting from the steady state
calibrated previously and doubling the amount of
business investment ik and home investment id. As a
fraction of total output, the associated adjustment
costs turn out to be
2

 k 
φk  i 
= 0.007%
2 y

and
2

 d 
φd  i 
= 0.005%,
2 y

respectively, which are small numbers indeed.21
Figure 5 reproduces the experiment that we performed in the previous section to measure the effects of
EGTRRA, but subject to the small adjustment costs
described here. We see that the behavior of the model
economy resembles the broad features described in
figure 4, but without the large swings in the investment
components.22 We conclude that the model with adjustment costs broadly reproduces some of the activity patterns observed during the 2001 recession. During the first
year after the initial steady state, the model economy goes
into a recession with low levels of hours worked, output,
and business investment (panels C, D, and E) but
with relatively strong consumption and home investment
(panels B and F). The recovery starting in the second
half of 2001 seems to be too strong, though. However,
this is not surprising, since the model abstracts from
important subsequent shocks to the economy, such as
the Enron accounting scandal and September 11 terrorist
attacks, and the cyclical propagation of earlier shocks,
such as the high-tech bust and the associated stock
market decline of 2000.
The 2008 presidential election
So far we have focused on the effects of anticipated
tax cuts following the 2000 presidential election. In this
section, we consider the mirror image: the aftermath of
the 2008 presidential election. During the 2008 presidential campaigns, the Republican candidate, John McCain,
promised to make permanent the tax cuts that were implemented by the George W. Bush administration. Contrary
to that campaign proposal, the Democratic candidate,
Barack Obama, made it clear that, at least for high-income

27

figure 4

Effects of EGTRRA
A. Tax rates

B. Consumption

0.38

Tax on capital

103

Tax on labor

102

rate

index

0.37
0.36

101
0.35
100

0.34
0.33

99
2000:Q3

’01:Q1

’01:Q3

’02:Q1

2000:Q3

C. Hours worked

D. Output

index

index

104

104

102

102

100

100

98

98

96

’01:Q1

’01:Q3

’02:Q1

’01:Q1

’01:Q3

’02:Q1

’01:Q1

’01:Q3

’02:Q1

96
2000:Q3

’01:Q1

’01:Q3

’02:Q1

2000:Q3

E. Business investment

F. Home investment

200

150

150

100

100

50

index

index

50

0
2000:Q3

’01:Q1

’01:Q3

’02:Q1

2000:Q3

Notes: EGTRRA means the Economic Growth and Tax Relief Reconciliation Act of 2001. Panels B through F are normalized (indexed) 	
to 100 at 2000:Q4.

individuals, he would let those tax cuts expire with
the existing “sunset” provision. With Barack Obama
winning the presidency in 2008 and his party retaining control of Congress, economic agents are likely
to have concluded that tax rates would partly revert
in 2011 to their pre-EGTRRA levels.

28

In what follows, we illustrate the effects of this
type of anticipated tax increase. Since it is extremely
difficult to determine what tax increases might eventually be implemented and what impact they might
have on effective marginal tax rates, we make an extremely simplistic assumption: That all tax rates will

3Q/2009, Economic Perspectives

figure 5

Effects of EGTRRA with adjustment costs
B. Consumption

A. Tax rates

rate
0.38

index
103

Tax on capital

0.37

102

Tax on labor
0.36

101
0.35
100

0.34

99

0.33
2000:Q3

’01:Q1

’01:Q3

’02:Q1

C. Hours worked

2000:Q3

’01:Q1

’01:Q3

’02:Q1

’01:Q1

’01:Q3

’02:Q1

’01:Q1

’01:Q3

’02:Q1

D. Output

index
104

index
104

102

102

100

100

98

98
96

96
2000:Q3

’01:Q1

’01:Q3

’02:Q1

2000:Q3

F. Home investment

E. Business investment
200

index
150

150

100

100

50

index

50

0
2000:Q3

’01:Q1

’01:Q3

’02:Q1

2000:Q3

Notes: EGTRRA means the Economic Growth and Tax Relief Reconciliation Act of 2001. Panels B through F are normalized (indexed) 	
to 100 at 2000:Q4.

revert to their pre-EGTRRA levels by 2011 and that all
economic agents believe that this will be the case.
While this is a highly unrealistic assumption, it will
suffice for our illustrational purposes.
Specifically, we assume that in 2008:Q4 the economy was at the steady state corresponding to the low

Federal Reserve Bank of Chicago

marginal tax rate on capital (τk) of 36.41 percent and
on labor (τn) of 34.40 percent introduced by the George
W. Bush administration (see fourth row of panel C in
table 1, p. 21). We also assume that in 2009:Q1 economic agents find out that marginal tax rates on capital
(τk) and labor (τn) will be permanently increased to their

29

figure 6

Effects of reverting to pre-EGTRRA tax rates
A. Tax rates

B. Consumption

0.38

103

rate

0.37

index

Tax on capital

102

0.36
101
0.35

Tax on labor
100

0.34
0.33
2008:Q3 ’09:Q1

’10:Q1

’11:Q1

’12:Q1

99
2008:Q3 ’09:Q1

C. Hours worked

D. Output

index

index

104

104

102

102

100

100

98

98

96
2008:Q3 ’09:Q1

’10:Q1

’11:Q1

’12:Q1

96
2008:Q3 ’09:Q1

E. Business investment

F. Home investment

200

150

150

100

100

50

index

’10:Q1

’11:Q1

’12:Q1

’10:Q1

’11:Q1

’12:Q1

’10:Q1

’11:Q1

’12:Q1

index

50
2008:Q3 ’09:Q1

’10:Q1

’11:Q1

’12:Q1

0
2008:Q3 ’09:Q1

Notes: EGTRRA means the Economic Growth and Tax Relief Reconciliation Act of 2001. Panels B through F are normalized (indexed) 	
to 100 at 2008:Q4.

pre-EGTRRA levels of 37.43 percent and 36.20 percent,
respectively, starting in 2011:Q1. For comparability,
we introduce the same adjustment costs considered
in the previous section.
Figure 6 presents the results. We see that during 2009
and 2010 the model economy experiences a marked boost
in economic activity, with hours worked and output

30

increasing monotonically over time (panels C and D).
Business investment (panel E) is strong during 2009 but
weak during 2010. The opposite is true for home investment (panel F). Consumption (panel B) drops immediately because economic agents feel poorer from the higher
expected tax rates. The reason for the early economic
boom is that agents realize that the period before the tax

3Q/2009, Economic Perspectives

increase is relatively attractive for working and investing.
Once the tax increase takes place in 2011:Q1, there is
a sharp drop in hours worked and output.
So, according to the model, the current recession
would have been even worse in terms of hours worked
and output had there not been expectations of future
tax increases. However, these expectations might be
contributing to the weakness in consumption and residential investment that we currently see. The model
expects a further downward influence on economic
activity in 2011 once tax rates are increased.
Conclusion
In this article, we used a stylized model economy
to investigate the hypothesis that some of the unusual

features of the 2001 recession may have been influenced by the tax cuts promised during the 2000 presidential campaigns. We found that the model is consistent
with this hypothesis: In the model economy, anticipated
tax cuts generate a mild recession with relatively strong
consumption and home investment, but with weak hours
worked and business investment. Because the 2008
presidential election also had a significant impact on
future tax rates, but in reverse, we also used our model
to illustrate the possible effects on the economy of
anticipated future tax increases. Both of these applications illustrate a more basic result in economic theory:
That anticipated future changes in economic policy
might have large effects on current economic activity.

NOTES
The argument that expected tax cuts one year down the road decrease investment during the current year is based on the assumption that investment affects the stock of capital rather quickly (say,
within one quarter). If there were long gestation lags in building
capital, anticipated tax cuts in one year may actually increase investment during the current year. The assumption that capital is
quickly built will be maintained throughout this article.

1

See www.nber.org/cycles/november2001/.

2

The NBER looks at more than gross domestic product (GDP) in
determining when a recession starts, so that the timing can differ
from that of declines in GDP. According to revised estimates, the
annualized growth rates in GDP were +2.1 percent, –0.5 percent,
+1.2 percent, and –1.4 percent in 2000:Q4, 2001:Q1, 2001:Q2, and
2001:Q3, respectively. However, at the time that the NBER declared
that the recession had started, these numbers were +1.9 percent,
+1.3 percent, +0.3 percent, and –0.4 percent, respectively.

3

See www.nber.org/cycles/july2003.html.

4

The six previous recessions had occurred in 1960–61, 1969–70,
1973–75, 1980, 1981–82, and 1990–91, according to the National
Bureau of Economic Research.

5

6
The source of all data unless otherwise specified is the U.S. Bureau
of Economic Analysis’s National Income and Product Accounts of
the United States (NIPAs) from Haver Analytics.

The deterministic trends are determined by regressing the log of
the different variables against time.

7

8
Output started to decline a few quarters before the start of the 2001
recession, as it did before some previous recessions. However, once
the 2001 recession started, output did not fall as much as during
the average recession.
9
Prior to the campaigns, two pieces of legislation defined the existing
tax structure: the Omnibus Budget Reconciliation Act of 1993 and
the Taxpayer Relief Act of 1997. While the latter only had effects on
capital gains taxes, the former created the 36 percent and 39.6 percent
income tax brackets and set the statutory rates at the levels seen in
table 1, panel A (p. 21).
10

Bush (2001).

According to House and Shapiro (2006), only households with
taxable income below $12,000 actually experienced any reduction
in their marginal tax rate as a result of the new 10 percent bracket.
Though this change can be expected to have had large effects on
average tax liabilities, marginal rates remained relatively unaffected.

11

The CBO simulated income tax liability for each return in a
sample of all tax returns filed in the United States. The analysis

12

Federal Reserve Bank of Chicago

then calculated marginal tax rates by adding $1,000 to the earnings
on each return and recomputing the amount of income tax owed.
The difference between the two tax liabilities, divided by $1,000,
equals the effective marginal tax rate.
13
Our effective marginal tax rates on capital are roughly twice as large
as the CBO’s estimates, since our notion of capital does not include
residential structures, while the CBO’s does. See the appendix for a
brief discussion regarding the treatment of housing capital.

Among other things, this implicitly assumes that the AMT is changing
in a similar way.

14

By allowing for lump-sum taxes, the optimal tax system is to set
the capital and labor income taxes to zero and rely exclusively on
lump-sum taxes. However, the focus of our analysis is not on optimal taxation but on the effects of actual tax rates.

15

Although the 2000 election outcome may have had implications for
prospective government expenditures, we abstract from these.

16

Observe that we are assuming that government expenditures are
unproductive. However, this could be modified without altering the
analysis by assuming that government expenditures enter the utility
function in a separable way.

17

Observe that there is no rental market for home capital: All home
capital is directly owned by the household sector. This is a limitation
of the model economy. In practice, a significant fraction of residential
structures are rented, and the income generated is subject to taxes.
Another limitation of the model is that the stock of home capital is
not taxed at all, although in the U.S. economy, housing is subject to
property taxes.

18

Since ours is a closed economy, the measure of output that we use
is GDP minus net exports.

19

The implied Frisch elasticity of labor supply is equal to 2.7. This
is somewhat lower than the Frisch elasticity of labor supply used
by Prescott (2004) in his cross-country analysis of labor income
taxes but much higher than econometric estimates based on microeconomic data. However, recent research has shown that the large
elasticity of labor supply used by the macro literature can be reconciled with the micro evidence through heterogeneity in labor supply (for example, Chang and Kim, 2006; Rogerson and Wallenius,
2009; and Gourio and Noual, 2007).

20

21
We make no claim that these adjustment costs are empirically plausible. However, they improve the model’s performance quite significantly.

The investment measures reported in figure 5 (p. 29) include the
adjustment costs. However, in practice this does not matter because
the adjustment costs are extremely small.

22

31

APPENDIX: Calibration of the tax rate on capital (tk)

When the Congressional Budget Office (2001) estimates
the effects of EGTRRA on effective marginal tax rates for
labor and capital income, it includes residential structures
in its notion of capital. Because owner-occupants of residential structures “exclude their implicit gross receipts
(i.e., the rental value of the home) from taxable income ...
[and may] deduct mortgage interest and property tax payments if they itemize their deductions,” the CBO concluded
that owner-occupied housing capital is subsidized (Congressional Budget Office, 2005). Since this subsidy is
not given to tenant-occupied housing capital, the CBO
concluded that this form of capital is taxed. Using the
CBO’s estimates of the effective tax rates on both tenantoccupied (18.2 percent) and owner-occupied (–5.1 percent)
housing capital income, as well as the proportion of each
type of capital in total housing capital, we obtain that the
h
“housing capital income tax rate” τ is given as follows:1
h
τ = (% Tenant-occupied housing) × (0.182)
		 + (% Owner-occupied housing) × (–0.051)
	 = (0.20) × (0.182) + (0.80) × (–0.051)
	 = –0.0044 ≅ 0.

Since the services from consumer durables are not
h
taxed and τ ≅ 0, we have that the effective marginal tax
rate on capital income estimated by the CBO is equal to:
k
τCBO
=

k
d
× τk +
× 0,
k+d
k+d

where k represents business capital and d represents
home capital.
Using the average ratio (k + d) / k over the period
1998–2003, we have that the tax rate on business capital
income is then given by:
k+d 
k
τk ≅ τCBO
×

 d 
≅ (0.182) × (2.0456)
≅ 0.3743.
The fractions of each type of housing capital are obtained from
Congressional Budget Office (2005), p. 19, table A-1.

1

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3Q/2009, Economic Perspectives