WHY HAS THE U.S. ECONOMY STAGNATED SINCE THE GREAT RECESSION?

Yunjong Eo and James Morley*

Abstract—Since the Great Recession in 2007–2009, NOI. real GDP has
failed to return to its previously projected path, a phenomenon widely asso-
ciated with secular stagnation. We investigate whether this stagnation was
due to hysteresis effects from the Great Recession, a persistent negative
output gap following the recession, or slower trend growth for other rea-
sons. To do so, we develop a new Markov-switching time series model of
output growth that accommodates two different types of recessions: quelli
that permanently alter the level of real GDP and those with only temporary
effects. We also account for structural change in trend growth. Estimates
from our model suggest that the Great Recession generated a large, persis-
tent negative output gap rather than any substantial hysteresis effects, con
the economy eventually recovering to a lower trend path that appears to be
due to a reduction in productivity growth that began prior to the onset of
the Great Recession.

IO.

introduzione

THE slow growth of the U.S. economy in the wake of

the Great Recession in 2007–2009 has led to a revival
of earlier notions of secular stagnation (Hansen, 1939) E
hysteresis (Blanchard & Summers, 1986). There are differ-
ent theories of secular stagnation, but Summers (2014, 2015)
emphasizes the role of inadequate demand. According to his
view, the global financial crisis in 2008 saw an unwinding of
a financial bubble that had propped up the world economy. In
its absence and in the face of the zero-lower-bound that pre-
vented a further lowering of interest rates, inadequate demand
caused the economy to grow at a slower rate than otherwise.
This theory is related to the idea that inadequate demand re-
sulting from the Great Recession may have produced hystere-
sis or even “super-hysteresis” effects (Ball, 2014; Guerron-
Quintana & Jinnai, 2019) that have permanently lowered both
the level and growth path of economic activity. Using data
from 23 countries, Blanchard, Cerutti, and Summers (2015)
document that many recessions have led to such effects, al-
though they acknowledge that the causality could reflect sup-
ply shocks and financial crises producing both a recession
and subsequent stagnation. Cerra and Saxena (2017) argue
that recessions always have negative permanent effects on

Received for publication June 24, 2019. Revision accepted for publication

Giugno 3, 2020. Editor: Olivier Coibion.

∗Eo: Korea University; Morley: University of Sydney.
We thank James Bullard, Ana Galvao, Nicolas Groshenny, Yu-Fan Huang,
Susumu Imai, Ryo Jinnai, Chang-Jin Kim, Ian King, Mengheng Li, Charles
Nelson, Masao Ogaki, Jeremy Piger, Ben Wang, and conference and semi-
nar participants at the 2018 Norges Bank Workshop on Nonlinear Models
in Macroeconomics and Finance, 2018 SNDE meetings in Tokyo, IL 2018
International Symposium on Econometric Theory and Applications in Syd-
ney, IL 2018 IAAE conference in Montreal, IL 2019 Renmin Univer sity
of China School of Finance Workshop, the Bank of Japan, University of
Adelaide, Hitotsubashi University, Hokkaido University, Keio University,
Macquarie University, Monash University, Sun-Yat Sen University, Uni-
versitat Pompeu Fabra, University of Queensland, and University of Tech-
nology Sydney for helpful comments and suggestions. This research was
supported by ARC DP190100202 and Korea University grant K2003321.
The usual disclaimers apply.

the level of aggregate output and question the relevance of
the concept of an output gap in the first place, including in
explaining weak economic activity and sluggish growth fol-
lowing the global financial crisis.

A contrasting view of secular stagnation, emphasized by
Gordon (2015, 2016), is that it reflects supply-side forces such
as slower productivity growth and demographic changes that
started before the Great Recession. Notably, Fernald et al.
(2017) use a growth accounting decomposition and find that,
once allowing for cyclical effects, the slow growth in the U.S.
economy since the Great Recession can be related to slow
growth of total factor productivity and a decline in labor force
participation, with both phenomena starting prior to the onset
of the recession and not obviously connected to the financial
crisis. Supporting this view, a few recent empirical studies
have estimated a structural break in U.S. trend growth in the
mid-2000s prior to the Great Recession, including Grant and
Chan (2017), Antolin-Diaz, Drechsel, and Petrella (2017),
and Kamber, Morley, and Wong (2018). Tuttavia, an ability
to reject that the slowdown actually occurred during the Great
Recession, rather than before, is unclear from this literature.
in questo documento, we develop a flexible new nonlinear time se-
ries model that allows us to examine the empirical support
for competing views surrounding why U.S. real GDP did not
return to its projected path prior to the Great Recession. In par-
ticular, we investigate whether the stagnation of the economy
was due to level and growth hysteresis effects from the Great
Recession, a persistent negative output gap following the re-
cession, or slower trend growth for other reasons. Building on
Hamilton (1989), Kim and Nelson (1999UN), Kim, Morley, E
Piger (2005), and Eo and Kim (2016), our univariate Markov-
switching model of real GDP growth allows a given recession
to either permanently alter the level of aggregate output (an
L-shaped recession) or only have a temporary effect (a U-
shaped recession).1 We also account for structural change in
trend growth. In particular, using the testing procedures from
Qu and Perron (2007), we find an estimated reduction in the
long-run growth rate of U.S. real GDP in 2006Q1. When al-
lowing for this break in our Markov-switching model, we find
that the Great Recession was U shaped, generating a nega-
tive and persistent output gap rather than any substantial level
hysteresis effects, with the economy eventually recovering to
a lower-growth trend path. Tuttavia, our finding about the na-
ture of the Great Recession is robust to the reduction in trend
growth occurring earlier, allowing for more complicated

1The univariate approach often taken in the literature on nonlinear out-
put growth dynamics makes the implicit oversimplifying assumption of a
common propagation for all underlying symmetric shocks to aggregate out-
put, regardless of their source. Tuttavia, it has the benefit of allowing for
a tightly parameterized but still sophisticated specification of dynamics for
asymmetric shocks, in our case allowing for different dynamics for two
types of recessions.

The Review of Economics and Statistics, Marzo 2022, 104(2): 246–258
© 2020 The President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative Commons Attribution 4.0
Internazionale (CC BY 4.0) licenza.
https://doi.org/10.1162/rest_a_00957

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WHY HAS THE U.S. ECONOMY STAGNATED SINCE THE GREAT RECESSION?

247

patterns of structural change, or even assuming no structural
change at all, although the model without a break in trend
growth produces persistently downward-biased forecast er-
rors after the Great Recession. Compared to the analysis using
Qu and Perron (2007) procedures, the precision of our infer-
ence that the break occurred before the Great Recession is
sharpened considerably by taking into account nonlinear dy-
namics with our Markov-switching model. Notably, we are
able to formally reject that the slowdown in trend growth
occurred after 2006Q2, and therefore does not appear to be
due to the Great Recession. Inoltre, we find that the
apparent timing of the slowdown is more consistent with a
reduction in productivity growth than demographic factors.
Our analysis is related to Huang, Luo, and Startz (2016),
who also consider a univariate time series model with two dif-
ferent types of recessions but determine the prevailing regime
using NBER dates and assume a given recession is predeter-
mined as being either L or U shaped. Our Markov-switching
model is more directly an extension of Hamilton (1989), Kim
and Nelson (1999UN), and Kim, Morley, and Piger (2005) to al-
lowing two different types of recessions by modeling regimes
as being stochastic. We believe this is a more natural assump-
tion given that the exact timing and nature of recessions are
not predetermined in practice. This also leads to a different
result than that of Huang, Luo, and Startz (2016) in terms
of categorizing the Great Recession as being U shaped rather
than L shaped. Our model is also somewhat related to Kim and
Murray (2002), Kim and Piger (2002), and Kim, Piger, E
Startz (2006), who consider multivariate unobserved compo-
nents models with Markov switching in both the trends and
cycles of panels of macroeconomic time series, thus allow-
ing for L- and U-shaped recessions. Tuttavia, those models
make assumptions about the correlations between permanent
and transitory movements, which implicitly place strong re-
strictions on the variance of the stochastic trend in aggregate
output that do not appear to be supported by the data (Morley,
Nelson, & Zivot, 2003).

The rest of this paper proceeds as follows. In section II, we
provide background evidence for nonlinearity and structural
breaks in U.S. real GDP. In section III, we present the details
of our new Markov-switching model and show how it can
generate both L- and U-shaped recessions. In section IV, we
report estimates for a benchmark version of our model and
examine implications for why real GDP has stagnated since
the Great Recession. In section V, we consider alternatives to
our benchmark model in order to investigate the robustness
and interpretation of our results. Section VI concludes.

II. Background

There is some existing evidence for Markov-switching
nonlinear dynamics in U.S. real GDP growth. Specifically,
Morley and Piger (2012) test for nonlinearity using the pro-
cedure developed in Carrasco, Eh, and Ploberger (2014) E
find support for the Markov-switching model in Kim et al.
(2005) that captures U-shaped recessions, but not for the

model in Hamilton (1989) that captures L-shaped recessions.
Tuttavia, the tests are applied using data over the sample
period of 1947–2006 and so do not include the Great Reces-
sion. More recently, Morley and Panovska (2019) conduct
tests for nonlinearity using data for a number of countries
and find similar results to Morley and Piger (2012) of greater
support for a Markov-switching model with U-shaped reces-
sions than L-shaped recessions. For the U.S. dati, they find
support for nonlinearity when allowing for an estimated slow-
down in trend growth in 2000Q2 based on Bai and Perron’s
(1998, 2003) testing procedures.2 While it is not straightfor-
ward to apply the Carrasco et al. (2014) testing procedure to
our model, we note that Eo and Kim (2016) are able to reject
simpler models with only one type of recession in favor of
more heterogeneity in business cycle regimes using Bayesian
metodi, thus providing a strong motivation for allowing dif-
ferent types of recessions. Inoltre, we are able to show
that the estimated nonlinear dynamics capturing recessions
for our model hold up well with more years of data, including
enough observations after the end of the Great Recession to
discriminate among competing hypotheses about its long-run
consequences.

Before presenting the details of our new Markov-switching
modello, we follow Morley and Panovska (2019) by first con-
sidering possible structural breaks in trend growth. We do so
by applying Qu and Perron’s (2007) testing procedures for
multiple structural breaks in mean or variance of quarterly
NOI. real GDP growth for the sample period of 1947Q2 to
2018Q4 with 10% trimming at the beginning and the end
of the sample and between breakdates.3 Based on a likeli-
hood ratio test, we find evidence of two breaks, which are
estimated to have occurred in 1984Q2 and 2006Q1, respec-
tively, as reported in table 1. These breakdates align with the
timing of the Great Moderation widely reported in the liter-
ature (Kim & Nelson, 1999B; McConnell & Perez-Quiros,
2000) and the breakdate for the slowdown in trend growth
that was also found in Kamber et al. (2018).4 The structural
breaks are significant at the 5% level, and there is no sup-
port for an additional break even at a 10% level. Related to

2Given the sample period of 1947–2016 and a minimum-length trimming
restriction for subsamples of 15% of the total sample when testing for
structural breaks, we note that Morley and Panovska (2019) did not consider
whether the estimated breakdate corresponds to the Great Recession, while
we are able to do so given the availability of a few extra years of data and
our different choice of 10% trimming. Also, Bai and Perron’s (1998, 2003)
procedures allow for a break only in mean, but not variance, unlike the Qu
and Perron (2007) procedures considered in our analysis. Note that reporting
the breakdate in Morley and Panovska (2019) as 2000Q2 corresponds to the
convention of a breakdate being the last period of the previous structural
regime.

3The raw data for seasonally adjusted quarterly U.S. real GDP and all
other series considered in this paper were obtained from the St. Louis Fed
database (FRED), and quarterly growth rates were calculated as 100 times
the first differences of the natural logarithms of the levels data.

4A break in 2006Q1 was also found in Luo and Startz (2014) for Bayesian
estimation of an unobserved components model of U.S. real GDP. How-
ever, Kim and Chon (2020) show that the results for such a model are
more favorable for gradual structural change when the posterior sampler
for Bayesian estimation correctly takes correlation between movements in
trend and cycle into account.

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248

THE REVIEW OF ECONOMICS AND STATISTICS

TABLE 1.—STRUCTURAL BREAKS IN OUTPUT GROWTH

(UN) Sequential Break Tests

# of Breaks Test Statistic 5% Critical Value

Estimated Breakdate(S)

1
2
3

72.87
18.76
8.77

12.80
13.96
14.84

1984Q2
1984Q2, 2006Q1
1984Q2, 2000Q2, 2009Q2

(B) Mean and Standard Deviation given Two Breaks
in 1984Q2 and 2006Q1

Subsample

Mean

Std. Dev.

1
2
3

0.89
0.80
0.41

1.16
0.49
0.59

95% Confidence Set
for Breakdate

[1982Q1, 1987Q1]
[1991Q3, 2011Q3]

Five percent critical values are from Qu and Perron (2007). Ninety-five percent confidence sets are based

on the inverted likelihood ratio approach in Eo and Morley (2015).

the Great Moderation and our Markov-switching model, we
note that a larger variance for output growth before 1984Q2
could potentially be related to a more frequent realization of
recessions before the mid-1980s. In particular, the postwar
NOI. economy experienced eight recessions between 1947
E 1984 (37 years), but only three recessions between 1985
E 2018 (34 years). Così, we will be able to use our Markov-
switching model to check whether this estimated structural
break is due to the less frequent realization of recessions since
1984 or a reduction in residual volatility.

Tavolo 1 also reports estimates for the mean and standard
deviation of output growth based on the estimated breakdates,
along with the confidence sets for the breakdates. The con-
fidence set for the first breakdate covers a reasonably short
interval of 1982Q1 to 1987Q1, while the confidence set for
the second breakdate is wider and ranges from 1991Q3 to
2011Q3, where the latter date represents the last possible
breakdate given 10% trimming. The estimated breakdate of
2006Q1 is consistent with the date for the growth slowdown
in Fernald et al. (2017), and they argue that it reflects slow
growth of total factor productivity and a decline in labor force
participation that are unrelated to the financial crisis and the
Great Recession.

For the first estimated break in 1984Q2, a likelihood ra-
tio test of no change in mean suggests that the break corre-
sponded to a change in variance only, with the sample stan-
dard deviation of output growth dropping by more than 50%.
The average growth rates before and after the first estimated
breakdate of 1984Q2 are very close to each other at 0.89
E 0.80, rispettivamente, in contrast to the average growth rate
Di 0.41 after the second breakdate of 2006Q1. We note that
the decline in average growth since 2006Q1 could be related
to the realization of a particularly severe recession between
2007 E 2009. Così, we will also use our Markov-switching
model to check whether this estimated structural break is due
to the Great Recession or a more sustained decline in trend
growth. We will also determine whether explicitly account-
ing for nonlinear dynamics affects the precision of inferences
about the timing of structural breaks.

III. Model

We develop a new univariate Markov-switching model of
real GDP growth that accommodates two different types of
recessions. In particular, the model builds on the Markov-
switching models in Hamilton (1989) and Kim et al. (2005),
which assume all recessions have the same dynamics by
allowing for two distinct contractionary regimes: (UN) an L-
shaped regime with permanent effects on the level of output,
as in Hamilton (1989), E (B) a U-shaped regime with tem-
porary effects, corresponding to a restricted version of the
model in Kim et al. (2005) that is related to Kim and Nelson
(1999UN). The idea of allowing for different contractionary
regimes is strongly motivated by Eo and Kim (2016), who
find a Markov-switching model with time-varying, regime-
dependent mean growth rates that depend on each other
across booms and recessions fits the U.S. data better than
the simpler Markov-switching models in Hamilton (1989)
and Kim et al. (2005).

Extending the specification in Kim et al. (2005), we assume
that output growth, (cid:2)yt , has the following time-varying mean
based on three regimes.

(cid:2)yt = μ0 + μ1 × 1(St = 1) + μ2 × 1(St = 2)

+ λ2 ×

M(cid:2)

k=1

1(St−k = 2) + et ,

(1)

Dove 1(·) is an indicator function, St is a latent Markov-
switching state variable that takes on discrete values such that
St = 0 for the expansionary regime, St = 1 for the L-shaped
contractionary regime, and St = 2 for the U-shaped contrac-
tionary regime according to transition probabilities Pr[St =
j|St−1 = i] = pi j for i, j = 0, 1, 2, and et ∼ N (0, σ2). For
simplicity and following the empirical results in Hamilton
(1989), Kim et al. (2005), Morley and Piger (2012), and Eo
and Kim (2016), we abstract from autoregressive dynamics
in linear shocks by assuming that et is serially uncorrelated.5
To identify the contractionary regimes as corresponding to
two different types of recessions, we assume that the econ-
omy does not switch between contractionary regimes without
going through an expansionary regime first. This sequencing
of regimes is imposed using the following restrictions on the
regime transition probabilities: p12 = 0 and p21 = 0. Mean-
while, the λ2 parameter is the key distinctive feature of the
U-shaped contractionary regime in equation (1) because it
allows for a bounceback effect that generates an asymmetric
output gap, as in Morley and Piger (2012) and Morley and
Panovska (2019).6 To clearly identify this regime as distinct
from the L-shaped regime that only has permanent effects on

5Specifically, these earlier papers find that linear autoregressive dynamics
in the residual are not particularly important, once allowing for a Markov-
switching mean. Tuttavia, it is important to note that the statistical evidence
for Markov-switching nonlinearity discussed in section II allows for AR(2)
dynamics in output growth under the null of linearity.

6Possible sources of an asymmetric output gap are capacity constraints,
monopoly power, asymmetric wage and price adjustments, collateral

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WHY HAS THE U.S. ECONOMY STAGNATED SINCE THE GREAT RECESSION?

249

FIGURE 1.—ILLUSTRATION OF DIFFERENT TYPES OF RECESSIONS

The shaded area denotes the contractionary regime.

the level of output by construction, we impose the restriction
μ2 + m × λ2 = 0.7 This restriction implies that following the
realization of St = 2, the bounceback effect m × λ2 exactly
cancels out the contractionary effect from μ2 such that the
U-shaped regime has only temporary effects on the level of
produzione, as in the Markov-switching model in Kim and Nel-
figlio (1999UN) but distinct from the model in Kim et al. (2005),
which does not impose this restriction.8

Figura 1 illustrates how the two contractionary regimes
create different types of recessions in terms of their long-
run effects on the level of output. In particular, we plot the
path of output implied by the model in equation (1) before,
during, and after the occurrence of a contractionary regime.
Motivated by the estimates for our benchmark model pre-
sented in the next section, we set the length of the postre-
cession bounceback effect to m = 5 quarters and the model
parameters to be μ0 = 0.91 for the expansionary regime,
μ1 = −1.32 for the L-shaped regime, and μ2 = −2.10 for
the U-shaped regime (thus implying λ2 = 0.42). For clarity
in seeing the relative impact of the two different regimes,
we abstract from the linear et shocks when calculating the
path of output. We assume that the economy enters a con-
tractionary regime at time t = 0 that lasts for four quarters
for the L-shaped regime and five quarters for the U-shaped
regime. The longer duration for the U-shaped regime is moti-
vated by a higher continuation probability in the next section.

Tuttavia, because the bounceback effect takes hold as the U-
shaped regime persists and flattens out the path of output,
there is only an outright recession in the level of output for
four quarters in both cases. After the flat path for output for
the one additional quarter of the U-shaped regime, the econ-
omy grows quickly and eventually recovers to its prerecession
sentiero. In this sense, the recession has no permanent effect on
the level of output, and its path traces out what looks like a
tilted and elongated U. By contrast, for the L-shaped regime,
the absence of a bounceback effect means that the economy
contracts sharply in the recession and never recovers to its
prerecession path, growing only at the usual expansionary
rate when the recession is over. Così, this recession has a
permanent effect on the level of output, and its path traces
out what looks like a tilted L.

IV. Benchmark Results

Estimation is conducted via maximum likelihood, Dove
the conditional likelihood function given the length of the
postrecession bounceback effect m is evaluated based on the
filter presented in Hamilton (1989) keeping track of 3m+1
states in each period. The estimate of the discrete-value pa-
rameter m is also chosen to maximize the likelihood by con-
sidering the profile likelihood for m across a set of differ-
ent possible values (capped, for computational feasibility, at
m = 7, corresponding to 6,561 possible states to keep track of
in estimation). Because the estimates of the other parameters
are calculated using the conditional likelihood function, Rif-
ported standard errors based on numerical second derivatives
do not reflect sampling uncertainty about ˆm.

To incorporate the possible structural breaks found in sec-
tion II into the benchmark version of our model, we modify
the basic model in equation (1) come segue:

(cid:2)yt = μ0 + δ × 1(t > τ) + μ1 × 1(St = 1) + μ2

× 1(St = 2) + λ2 ×

M(cid:2)

k=1

1(St−k = 2) + et ,

(2)

constraints, aggregation of microeconomic shocks, and underlying asym-
metric shocks. See Friedman (1964, 1993); DeLong and Summers (1988);
Auroba, Bocola, and Schorfheide (2013); Guerrieri and Iacoviello (2016);
Baqaee and Farhi (2019); and Dupraz, Nakamura, and Steinsson (2019),
among many others, for more information on these theories of business
cycle asymmetry. Also see Morley (2009, 2019) for surveys of the broader
literature on business cycle asymmetry.

7Typically with Markov-switching models, it is necessary to place label-
ing restrictions such as μ1 < 0 and μ2 < 0 to identify the model. However, (cid:4)= 2, the U-shaped contrac- because there is no bounceback effect when St tionary regime turns out to be uniquely identified given only the restriction on λ2 and the restrictions on the transition probabilities. Thus, we place no restrictions on the other parameters in equation (1). 8In addition to our consideration of a latent Markov-switching state vari- able instead of predetermined NBER dates, this restriction on the bounce- back effect is another key distinction from Huang et al. (2016), who al- low for possible permanent effects with their U-shaped regime, as in Kim et al. (2005), in addition to assuming permanent effects with their L-shaped regime. = σ2 v0 t ), with σ2 × 1(t ≤ τv ) + σ2 v1 where et ∼ N (0, σ2 × t 1(t > τv ). Based on the findings in section II, we assume the
breakdates τ = 2006Q1 for trend growth and τv = 1984Q2
for residual volatility in our benchmark model. If the breaks
found in section II actually reflected the severe recession in
2007–2009 and the less frequent realization of recessions in
the second half of the sample period, then the estimate for
δ should be small and σ2
v0. How-
ever, incorporating these structural breaks allows for a per-
manent trend growth slowdown and a reduction in the volatil-
ity of linear shocks in the second half of the sample period if
these phenomena remain relevant even when accounting for
Markov-switching dynamics.

v1 should be similar to σ2

Tavolo 2 reports maximum likelihood estimates for the
benchmark model. The implied growth rates are ˆμ0 + ˆμ1 < 0 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 2 2 4 6 1 9 9 6 4 0 3 / r e s t _ a _ 0 0 9 5 7 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 250 THE REVIEW OF ECONOMICS AND STATISTICS TABLE 2.—PARAMETER ESTIMATES FOR THE BENCHMARK MODEL FIGURE 2.—MEAN GROWTH AND PROJECTED OUTPUT Parameter p01 p02 p11 p22 μ0 μ1 μ2 λ2 δ σv0 σv1 m log-lik Estimate 0.03 0.02 0.66 0.73 0.91 −1.32 −2.10 0.42 −0.41 0.90 0.42 5 −317.35 Standard Error 0.01 0.01 0.17 0.13 0.05 0.27 0.29 0.06 0.08 0.07 0.03 The benchmark model is given by equation (2) with τ = 2006Q1, and τv = 1984Q2. Estimates are reported for both μ2 and λ2 even though they are jointly estimated using the restriction μ2 + m × λ2 = 0. for the L-shaped regime and ˆμ0 + ˆμ2 < 0 for the U-shaped regime, indicating that both regimes are indeed contrac- tionary, even though this was not imposed in estimation. The estimated transition probabilities suggest that expansions are much more persistent than either type of recession, like the NBER reference cycle. In particular, the implied continua- tion probability of the expansionary regime 1 − ˆp01 − ˆp02 is 0.96, with an expected duration of 23 quarters, while the expected duration is three quarters for the L-shaped regime and four quarters for the U-shaped regime. Residual volatility is estimated to have dropped by more than half in 1984Q2, suggesting the Great Moderation was not simply due to less frequent realization of recessions. Meanwhile, the estimated reduction in trend growth in 2006Q1 of −0.41 is very close to the reduction of −0.39 found with the Qu and Perron (2007) analysis in section II, suggesting that lower average growth since 2006 was also not simply due to the realization of a severe recession. The estimated length of the postrecession bounceback effect is five quarters, although we note that other parameter estimates are very similar for m = 6, which was the length considered in Kim et al. (2005).9 Figure 2 plots the implied time-varying mean from the benchmark model using the filtered estimate E [μt |(cid:3)t ], where μt ≡ (cid:2)yt − et and (cid:3)t ≡ ((cid:2)y1, (cid:2)y2, . . . , (cid:2)yt ). Closely tracking realized real GDP growth and reflecting ˆδ = −0.41, the time-varying mean declines abruptly after 2006Q1, with this slowdown in trend growth explaining the weak recovery of the U.S. economy following the Great Recession.10 It is also clear that not accounting for a break in trend growth in 2006Q1 would have resulted in persis- 9For comparison, the log-likelihood values for m = 4, 6, 7 are −318.59, −317.65, and −318.68, respectively. 10The top panel of figure 2 looks similar to the estimated time-varying mean in Eo and Kim (2016) for a Markov-switching model with time- varying, regime-dependent mean growth rates that depend on each other across booms and recessions and also allowing for possible structural change in trend growth. Our relatively simple model captures differences in mean growth for each recession and expansion based on whether the contractionary regime is L or U shaped, with mean growth in a recession related to mean growth in the subsequent expansion. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 2 2 4 6 1 9 9 6 4 0 3 / r e s t _ a _ 0 0 9 5 7 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 The shaded areas denote NBER recession dates. tently downward-biased forecast errors even after the Great Recession. To help illustrate the magnitude of the trend break in 2006Q1, figure 2 also plots projections from t = 2006Q1 for future log output E [yt+h|(cid:3)t ], h > 0, both accounting for
and not accounting for the structural break. The dotted line
shows the projection of log output without accounting for
the structural break, which diverges markedly from realized
log output (solid line) even before the Great Recession. IL
dashed line shows the projection accounting for the structural
break and clearly supports the idea that the decline in trend
growth began in 2006 prior to the onset of the Great Reces-
sion. Notably, given the natural log scale, the difference by
the end of the Great Recession corresponds to more than 5%
of the level of real GDP in 2006Q1.

Figura 3 reports the smoothed probabilities of being in a
contractionary regime at time t. The top panel plots the prob-
ability of being in one or the other regime, calculated from
the sum of the probabilities of being in the L-shaped regime
and the U-shaped regime using Pr[t = contraction|(cid:3)T ] ≡
Pr[St = 1|(cid:3)T ] + Pr[St = 2|(cid:3)T ]. This probability closely
matches the timing of NBER recessions. In particular, for nine
of the eleven NBER recessions in the sample, the smoothed
probability is well above 50% for most of a given recession.
The bottom panel of figure 3 plots the underlying smoothed
probabilities of the L-shaped and U-shaped regimes sepa-
rately. Considering their relative contribution to the overall

WHY HAS THE U.S. ECONOMY STAGNATED SINCE THE GREAT RECESSION?

251

FIGURE 3.—PROBABILITIES OF CONTRACTIONARY REGIMES

FIGURE 4.—OUTPUT GAP AND TREND

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The shaded areas denote NBER recession dates.

The shaded areas denote NBER recession dates.

probability of a contractionary regime, these probabilities
suggest that the 1973–1975, 1990–1991, E 2001 recessions
in particular can be classified as L shaped, while the 2007–
2009 recession can be largely classified as U shaped, con
only the small probability of an L-shaped regime at the be-
ginning of the recession implying any level hysteresis effects.
The less definitive classification of the other recessions sug-
gests they may exhibit more of a partial recovery, as found
for the estimated bounceback model in Kim et al. (2005).

It might seem surprising that the Great Recession is clas-
sified as being U shaped given the conventional view that
recessions associated with financial crises have large perma-
nent effects on the level of economic activity.11 Also, mean
growth in figure 2 does not display the same surge after the
Great Recession as occurred following other recessions with
a sizable probability of being U shaped. The econometric ex-
planation for this finding is that the probability corresponding
to a U-shaped regime in figure 3 remains elevated for a sub-
stantial period of time after the trough date established by the
NBER for the Great Recession.12 This could be related to a
prolonged weak labor market (“jobless recovery”) following
the recession. Also, the zero-lower-bound on interest rates

11Vedere, Per esempio, Cerra and Saxena (2008), Reinhart and Rogoff (2009),

and Jordà, Schularick, and Taylor (2017).

12As illustrated in figure 1, a U-shaped regime can imply flat growth after
the end of a recession if the regime persists long enough before the eventual
recovery to the prerecession path.

restricted the ability of monetary policy to help stimulate a
strong recovery immediately after the recession. Così, IL
relatively restrained mean growth following the Great Re-
cession could be related to a large, persistent negative output
gap that dissipates very slowly.

To estimate the output gap implied by our model, we adopt
the regime-dependent steady-state (RDSS) generalization of
the Beveridge and Nelson (1981) decomposition for Markov-
switching processes developed in Morley and Piger (2008).
This approach involves constructing long-horizon forecasts
conditional on sequences of regimes and then marginaliz-
ing over the distribution of the unknown regimes. Unlike the
traditional Beveridge-Nelson decomposition, there is no im-
plicit assumption that the cycle is unconditionally mean zero,
and we choose the expansionary regime as having a mean-
zero transitory component.13

Figura 4 plots the estimated output gap from the RDSS
decomposition implied by the benchmark model. The large,
negative movements in the output gap closely match up with
some of the NBER-dated recessions. Tuttavia, because an
L-shaped contractionary regime is assumed to only affect
the trend, the large, negative movements in the output gap

13See Morley and Piger (2008) for a full discussion of this choice and
Morley and Piger (2012) for a justification of choosing the expansionary
regime as having a mean-zero transitory component.

252

THE REVIEW OF ECONOMICS AND STATISTICS

correspond primarily to the recessions with a high probabil-
ity of being U shaped. In terms of the Great Recession, IL
negative output gap opens up later than the NBER peak date of
2007Q4, corresponding to when the probability of U-shaped
regime spikes up in figures 3. As the bottom panel of figure 2
makes clear, the reason for this different timing is that the
level of real GDP does not decline sharply until the second
half of 2008, although real GDP did not grow at its usual ex-
pansionary rate in the first half of 2008, even accounting for
the structural break in trend growth. This delayed timing of
the severe contraction for the Great Recession is distinct from
the behavior of real GDP in previous recessions and could
perhaps reflect a misattribution by the NBER of a particu-
larly lackluster manifestation of weak trend growth during
the first half of 2008 as being part of the recession phase.14
Nel frattempo, the output gap remains persistently negative long
after the NBER trough date, corresponding to only a very slow
recovery in the level of output.

Figura 4 also plots log output and the estimated trend path
from the RDSS decomposition around the Great Recession.
The magnitude and persistence of the output gap following
the recession are clear from this plot. In particular, the implied
negative output gap is not estimated to fully close until around
2012. Because the closure of the output gap is so slow, there
is no apparent surge in output growth following the recession
in the top panel of figure 2. Tuttavia, it is important to note
that this estimated dynamic of a persistent negative output
gap is clearly distinctly identified from an L-shaped reces-
sion that only alters the level of trend output. If we consider a
modification of our model to impose that the Great Recession
was L shaped and not U shaped, such as was found in Huang
et al. (2016) using NBER dates for the regimes, the fit of the
model noticeably deteriorates, with the log likelihood drop-
ping to −319.61 from −317.35 for our benchmark model.15
The deterioration of fit appears to be due to a failure to cap-
ture the rounded U shape of the recession as it approaches its
trough and an eventual gradual recovery of output to a trend
path that are both evident in the bottom panel of figure 4.

V. Robustness

In this section, we consider some alternatives to our bench-
mark model in order to investigate the robustness and inter-
pretation of our results. Primo, we estimate two models that
allow us to consider whether there are really different types of
recessions in terms of their permanent effects on the level of
produzione. Secondo, we estimate a model using output per capita
and examine the possible role of demographic factors in driv-
ing our results. Third, we directly estimate breakdates for the

14Invece, the weak growth may be related to a typical end-of-expansion
overhiring phenomenon (Gordon, 2003) that lowered productivity prior to
the sharp contraction in the second half of 2008.

15To estimate a restricted model that imposes the Great Recession is an
L-shaped regime, we set the parameters for the expansionary and U-shaped
regimes to temporarily take on implausible values for the duration of the
NBER dates corresponding to the Great Recession.

structural breaks in trend growth and residual volatility as ad-
ditional parameters in the model rather than assuming the es-
timated breakdates from section II. Fourth, we check whether
our inferences about the Great Recession are robust to alter-
native assumptions about the nature of structural change in
trend growth and the length of the postrecession bounceback
effect.

UN. Are There Really Different Types of Recessions?

To consider whether there are actually different types of re-
cessions, we estimate two alternative models. The first model
is more general than our benchmark specification in that it
allows for a possible bounceback effect in the first contrac-
tionary regime in addition to the assumed full recovery in the
second contractionary regime,

(cid:2)yt = μ0 + δ × 1(t > τ)

+ μ1 × 1(St = 1) + λ1 ×

+ μ2 × 1(St = 2) + λ2 ×

M(cid:2)

k=1
M(cid:2)

k=1

1(St−k = 1)

1(St−k = 2) + et , (3)

where the possibility that λ1 (cid:4)= 0 makes the model more gen-
eral than equation (2). Unlike λ2, which is constrained such
that μ2 + m × λ2 = 0, we leave λ1 unrestricted in estima-
zione. Così, the general model nests our benchmark model if
ˆλ1 = 0. In principle, it also nests the possibility that there are
only U-shaped recessions with full recoveries if ˆμ1 = ˆμ2 and
ˆλ1 = ˆλ2, although the regime transition probabilities would
not be identified in such a case. The second model is a re-
stricted version of the general model in equation (3) con
only one contractionary regime and corresponds to the orig-
inal bounceback model in Kim et al. (2005):

(cid:2)yt = μ0 + δ × 1(t > τ) + μ1 × 1(St = 1)

+ λ1 ×

M(cid:2)

k=1

1(St−k = 1) + et ,

(4)

Dove, Ancora, we leave λ1 unrestricted in estimation and only
need to estimate regime transition parameters p01 and p11.
This restricted model nests the possibility that there are only
L-shaped recessions if ˆλ1 = 0. For both alternative models,
et ∼ N (0, σ2
T ) is specified as in equation (2) to allow for a
structural break in residual volatility. The breakdates are also
the same as in the benchmark model: τ= 2006Q1 and τv =
1984Q2. For direct comparability to our benchmark model,
we set m = 5 rather than estimate it.

Tavolo 3 reports maximum likelihood estimates for the two
alternative models in equations (3) E (4). For the general
modello, the estimate for the additional parameter is ˆλ1 < 0, implying prolonged slow growth following an L-shaped l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 2 2 4 6 1 9 9 6 4 0 3 / r e s t _ a _ 0 0 9 5 7 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 WHY HAS THE U.S. ECONOMY STAGNATED SINCE THE GREAT RECESSION? 253 TABLE 3.—PARAMETER ESTIMATES FOR ALTERNATIVE MODELS AND FOR OUTPUT GROWTH PER CAPITA General Model Restricted Model Per Capita Parameter p01 p02 p11 p22 μ0 μ1 μ2 λ1 λ2 δ σv0 σv1 log-lik Estimate 0.03 0.02 0.68 0.73 0.94 −1.02 −2.08 −0.10 0.42 −0.39 0.90 0.41 −315.74 S.E. 0.02 0.01 0.14 0.13 0.05 0.22 0.28 0.05 0.06 0.08 0.07 0.03 Estimate 0.05 0.80 0.94 −1.24 0.12 −0.48 1.00 0.43 −323.87 S.E. 0.02 0.07 0.05 0.15 0.04 0.08 0.07 0.03 Estimate 0.03 0.02 0.75 0.67 0.64 −1.29 −2.09 0.42 −0.40 0.87 0.40 −313.69 S.E. 0.01 0.01 0.09 0.13 0.04 0.13 0.22 0.04 0.07 0.06 0.03 The general model is given by equation (3), the restricted model is given by equation (4), and the model specification for output growth per capita is the same as the benchmark case in equation (2), with τ = 2006Q1, τv = 1984Q2, and m = 5 in all three cases. Estimates are reported for both μ2 and λ2 even though they are jointly estimated using the restriction μ2 + m × λ2 = 0. Model-implied trend growth Average growth TABLE 4.—TREND GROWTH DECOMPOSITIONS Pre-2006 Post-2006 Reduction Pre-2006 Post-2006 Reduction (cid:2) ln Yt 0.91 0.50 −0.41 0.86 0.41 −0.45 (cid:2) ln(Yt /Nt ) (cid:2) ln(Yt /Et ) (cid:2) ln(Et /Nt ) (cid:2) ln Nt 0.64 0.24 −0.40 0.52 0.16 −0.36 0.45 0.23 −0.22 0.47 0.23 −0.24 0.13 0.03 −0.10 0.05 −0.08 −0.12 0.34 0.25 −0.09 Yt , Nt , and Et denote output, population, and employment, respectively. Model-implied trend growth rates correspond to estimated growth in the expansionary regime in equation (2). Unlike average growth rates, they do not necessarily add up exactly according to accounting relationships due to differences in estimated regimes for the different variables. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 2 2 4 6 1 9 9 6 4 0 3 / r e s t _ a _ 0 0 9 5 7 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 recession rather than any bounceback effect. Given an off- setting smaller magnitude for ˆμ1 and other parameters sim- ilar to those in table 2, the implied dynamic effects of the two types of recessions are close to those in the benchmark model.16 Meanwhile, for the restricted model, the estimates imply only a partial recovery for all recessions given that ˆλ1 < − ˆμ1/5. The estimated expected partial recovery looks like an averaging of the estimated effects of the two contrac- tionary regimes for the general model. Notably, the fit of the restricted model is considerably worse, although a likelihood ratio test of the two models would not have a standard distri- bution. Taken together, though, these results, combined with the different smoothed probabilities for the two regimes in the bottom panel of figure 3, support the existence of different types of recessions in the U.S. economy. B. What Role Do Demographic Factors Play in the Growth Slowdown? We apply our benchmark model specification with two dif- ferent types of recessions to output growth per capita instead of overall output growth in order to isolate the effects of pop- ulation growth on overall trend output growth. Table 3 also reports the estimates for this case. The estimates are strik- ingly similar to those for output growth presented in table 2. One particularly notable similarity is that the slowdown in 16Note that if we constrain λ1 ≥ 0, the maximum likelihood estimate is exactly ˆλ1 = 0. trend growth per capita is estimated to be ˆδ = −0.40, which is very close to ˆδ = −0.41 for the benchmark model. This di- rectly implies that population growth is not responsible for the slowdown in overall trend output growth since 2006 but in- stead suggests possible roles for productivity and labor force participation (Stock & Watson, 2012; Fernald et al., 2017). Table 4 reports trend growth decompositions based on basic accounting relationships between the growth rates of output, output per capita, output per employed worker, the employment-population ratio, and population for both before and after a breakdate of 2006Q1.17 We consider the estimated growth in an expansionary regime implied by our model es- timated for the various growth rate series, as well as subsam- ple averages for comparison. Corresponding to the results reported in tables 2 and 3, a lot of the slowdown in overall trend growth can be explained by a reduction in the growth rate of output per capita rather than population growth. In- deed, in terms of estimates for our benchmark model, almost all of the slowdown is accounted for by a reduction in trend growth for output per capita. In terms of the estimates based on subsample averages, most of the slowdown is accounted for in the same way, although we note that the Great Re- cession has considerable influence on average growth rates since 2006 that is controlled for in our model-based estimates 17The accounting relationships that inform our trend growth decompo- sitions are (cid:2) ln Yt ≡ (cid:2) ln(Yt /Nt ) + (cid:2) ln Nt , and (cid:2) ln Yt ≡ (cid:2) ln(Yt /Et ) + (cid:2) ln(Et /Nt ) + (cid:2) ln Nt , where Yt , Nt , and Et denote output, population, and employment, respectively. 254 THE REVIEW OF ECONOMICS AND STATISTICS FIGURE 5.—PROFILE LIKELIHOODS FOR BREAKDATES The solid lines plot log-likelihood values for different possible breakdates, conditioning on τ = 2000Q2 for τv and τv = 1982Q2 for τ. The dashed horizontal lines correspond to cutoffs for 95% confidence sets based on inverted likelihood ratio tests for a breakdate from Eo and Morley (2015). of trend growth. For output per capita growth, more of the slowdown can be explained by a reduction in the growth of output per employed worker than by a reduction in the growth of the employment-population ratio. Thus, these results sug- gest that productivity played a bigger role than demographic factors in explaining the slowdown in overall trend growth. C. What Does Our Model Imply about Timing of Structural Breaks? In section II, we estimated breakdates of 1984Q2 and 2006Q1 for output volatility and trend growth, respectively, using Qu and Perron (2007) testing procedures. Based on this result, we assumed these breakdates as known parameters τv and τ when estimating the benchmark model in section IV. Here, we examine whether inferences about structural breaks are robust to estimating their timing under the assumption that our Markov-switching model captures the dynamics of output growth. Figure 5 plots profile likelihoods for the breakdates based on the Markov-switching model in equation (2). In particu- lar, the top panel shows the results for the residual volatility breakdate τv , and the bottom panel shows the results for the trend growth breakdate τ.18 The maximum likelihood esti- 18The profile likelihoods are calculated as log-likelihood values for differ- ent possible breakdates, conditioning on the maximum likelihood estimate mate for the structural break in residual volatility is 1982Q2, which is close to the breakdate of 1984Q2 assumed in our benchmark model. The log-likelihood value for the volatil- ity breakdate of 1982Q2 is −315.28 compared to the value of −317.35 for the benchmark model with the breakdate in 1984Q2. The difference is less than the cutoff value used for constructing a 95% confidence set for a breakdate in Eo and Morley (2015). Therefore, the confidence set for the volatility breakdate includes the benchmark assumption of 1984Q2 obtained from Qu and Perron (2007) procedures in section II. The maximum likelihood estimate for the struc- tural break in trend growth of 2000Q2 is the same breakdate as found in Morley and Panovska (2019) using Bai and Perron (1998, 2003) testing procedures for a shorter sample period. However, 2006Q1 is a local mode for the profile likelihood and cannot be rejected using the cutoff value for construct- ing a 95% confidence set for a breakdate in Eo and Morley (2015). Furthermore, the last date in the 95% confidence set is 2006Q2, and we find no support for an additional struc- tural break in trend growth. Thus, compared to the results for the Qu and Perron (2007) procedures, our Markov-switching model sharpens inferences about the timing of a structural break in trend growth and allows us to formally reject that the trend growth slowdown occurred either during or after the Great Recession. If the structural break in trend growth actually occurred in 2000Q2, as implied by the highest mode in the bottom panel of figure 5, it is even clearer than with an estimate in 2006Q1 that it is unrelated to the Great Recession or the forces that led to the financial crisis. At the same time, it is possible that the spike in the likelihood in 2000Q2 is somehow re- lated to in-sample overfitting of the slow growth right before and during the 2001 recession. Looking back at figure 2, it is possible to see how a trend growth slowdown could cap- ture the weak output growth between 2000 and 2002 without having to capture the 2001 recession as being due to a con- tractionary regime shift. However, a trend growth slowdown in 2000Q2 would also appear to imply a positive bias in fore- cast errors for the model in the mid-2000s before the shift back down in mean growth in 2006Q1. Next, we further in- vestigate the possibility of overfitting, as well as robustness of our inferences about the Great Recession to different as- sumptions about structural change, including that a break in trend growth may have occurred in 2000Q2. of a trend growth break in 2000Q2 in the case of τv and the maximum likelihood estimate of a residual volatility break in 1982Q2 in the case of τ and maximizing the other parameters out of the likelihood for each pos- sible breakdate. We condition on the maximum likelihood estimate for the other breakdate for computational simplicity, although we have confirmed these are maximum likelihood estimates by calculating the likelihood for a grid of possible breakdates in residual volatility between 1979Q3 and 1987Q1 and breakdates in trend growth between 1997Q2 and 2012Q2. The profile likelihoods that maximize all other parameters including the other breakdate out of the likelihood (and assuming the conditional maximum likelihood estimate of the other breakdate is always in the included range) are almost identical to the profile likelihoods presented in figure 5 for the ranges covered by the grid. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 2 2 4 6 1 9 9 6 4 0 3 / r e s t _ a _ 0 0 9 5 7 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 WHY HAS THE U.S. ECONOMY STAGNATED SINCE THE GREAT RECESSION? 255 TABLE 5.—PARAMETER ESTIMATES UNDER DIFFERENT ASSUMPTIONS ABOUT STRUCTURAL CHANGE No Break Break in 2000Q2 Dynamic Demeaning Parameter Estimate p01 p02 p11 p22 μ0 μ1 μ2 λ2 δ σv0 σv1 log-lik 0.02 0.02 0.65 0.73 0.77 −1.48 −2.03 0.41 0.93 0.46 −329.10 S.E. 0.01 0.01 0.21 0.12 0.04 0.29 0.28 0.06 0.07 0.03 Estimate 0.02 0.02 0.67 0.72 0.94 −1.55 −2.10 0.42 −0.39 0.90 0.42 −315.05 S.E. 0.01 0.01 0.15 0.13 0.05 0.21 0.29 0.06 0.07 0.07 0.03 Estimate 0.03 0.02 0.74 0.73 0.09 −1.19 −2.11 0.42 0.87 0.43 −321.21 S.E. 0.02 0.01 0.10 0.12 0.04 0.15 0.27 0.05 0.06 0.03 The model specification is the same as the benchmark case in equation (2) with τv = 1984Q2 and m = 5, but with the following assumptions for trend growth: (a) no break; (b) τ = 2000Q2; and (c) structural change is gradual and can be captured by a backward-looking rolling forty-quarter average growth rate. Estimates are reported for both μ2 and λ2 even though they are jointly estimated using the restriction μ2 + m × λ2 = 0. D. How Robust Are Inferences about the Great Recession? To the extent that there is uncertainty about the timing of an apparent structural break in trend growth or whether it is even best characterized by a single abrupt break (Stock & Watson, 2012; Eo & Kim, 2016; Antolin-Diaz et al., 2017; Kim & Chon, 2020), it is important to investigate the robust- ness of our inferences regarding the nature of the Great Re- cession to different assumptions about structural change. To do so, we consider the following alternative cases for trend growth: no break; a break in 2000Q2; gradual change ad- dressed by dynamically demeaning output growth rate using a backward-looking rolling 40-quarter average growth rate, as in Kamber et al. (2018); and gradual change addressed by using weighted-average inferences based on the relative profile likelihood value over all of the possible breakdates, as discussed in more detail below. Table 5 reports the parameter estimates for our Markov- switching model under the first three assumptions for trend growth of no break, a break in 2000Q2, and gradual change addressed by dynamic demeaning.19 Notably, for all three of these alternative assumptions, the parameter estimates related to the effects of recessions are highly robust and similar to the estimates for the benchmark model in table 2. Meanwhile, looking at the log-likelihood values, the fit for dynamic de- meaning and especially the no break case is worse than in the benchmark case or when allowing for a break in 2000Q2.20 19Following Kamber et al. (2018), dynamic demeaning involves calcu- lating deviations from a slowly moving, time-varying unconditional mean as follows: (cid:2) ˜yt ≡ (cid:2)yt − 1 (cid:2)yt− j. We then estimate our Markov- 40 switching model in equation (2) using the dynamically demeaned data (cid:2) ˜yt and setting δ = 0, with the residual volatility breakdate still fixed at τv = 1984Q2 and m = 5 for direct comparison to the benchmark case. 39 j=0 (cid:3) 20Another way to look at model fit is to consider whether the filtered estimates of the residuals display serial correlation. Interestingly, over the subsample from 1984Q3 to 2018Q4, we find that the benchmark model with a break in 2006Q1 has the smallest Ljung-Box Q-statistics of 0.00 (1 lag) and 2.80 (4 lags). The model with a break in 2000Q2 has Q-statistics of 0.09 (1 lag) and 4.16 (4 lags), with the worse fit possibly reflecting a positive bias in forecast errors in the mid-2000s, although we note that consistent with the log likelihood, the model with a break in 2000Q2 has the smallest Q statistics (but very similar to those for the benchmark model) when considering the For weighted-average inferences to capture possible grad- ual change, we calculate probabilistic weights over different possible breakdates in trend growth. In particular, using the profile likelihood value for each breakdate, the probabilistic weight for a breakdate τ is calculated as ˆw(τ) ≡ (cid:3) f (y| ˆθτ; τ) t∈[0.1T,0.9T ] f (y| ˆθt ; t ) , (5) (cid:3) where f (y| ˆθτ; τ) is the likelihood value for the trend growth breakdate τ given the model in equation (2) with maxi- mum likelihood estimates ˆθτ for the other parameters con- ditional on τ, τv = 1984Q2, and m = 5. By construction, the sum of the weights over the possible breakdates will τ ˆw(τ) = 1. Then, for example, the weighted- equal 1, average smoothed probability of the regime j at time t τ ˆw(τ) × Pr[St = j|(cid:3)T , τ], where given these weights is Pr[St = j|(cid:3)T , τ] is the smoothed probability of the regime j at time t given the breakdate of τ. Weighted-average in- ferences inherently lose precision compared to knowing the exact breakdate, but they are potentially robust to multiple breaks in trend growth. (cid:3) Figure 6 plots smoothed probabilities of the two contrac- tionary regimes for the weighted-average approach, as well as for the different assumptions about structural change re- ported in table 5. The classification of certain recessions dif- fers across the various cases and sometimes in comparison to the benchmark results in figure 3. For example, it is clear that considering the trend growth break in 2000Q2 means that the 2001 recession would no longer be classified as a contractionary regime, supporting the idea that this timing for the structural break is overfitting the temporary effects of full sample. The model with dynamic demeaning performs similar to the model with a break in 2000Q2 with Q-statistics of 0.30 (1 lag) and 3.60 (4 lags). Meanwhile, the model with no break has much larger Q-statistics of 2.14 (1 lag) and 12.20 (4 lags), the latter of which is significant at a 5% level. The significant deterioration of fit presumably reflects negative bias in forecast errors since at least 2006Q1 by failing to account for a structural break in trend growth. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / / / / 1 0 4 2 2 4 6 1 9 9 6 4 0 3 / r e s t _ a _ 0 0 9 5 7 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 256 THE REVIEW OF ECONOMICS AND STATISTICS FIGURE 6.—PROBABILITIES OF L- AND U-SHAPED REGIMES FOR DIFFERENT CASES l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / The shaded areas denote NBER recession dates. the recession on growth rates.21 However, despite different inferences about some of the recessions, the Great Reces- sion is always classified as being U shaped. Thus, we can be confident that our inferences about the nature of the Great Recession in particular are robust to different assumptions about structural change in trend growth. As was the case for our benchmark model, the smoothed probabilities in figure 6 directly imply that the Great Re- cession corresponded to a large, persistent negative output gap. However, the exact persistence of the implied output gap varies considerably across the different alternatives and, in some cases, would suggest that the economy was back at trend even when the unemployment rate remained quite el- evated. There is a literature documenting time variation in Okun’s law, especially after the Great Recession (Owyang & Sekhposyan, 2012; Grant, 2018). Yet it is important to consider whether the implied persistence of the output gap following the Great Recession is in some way constrained by the structure of our Markov-switching model. To consider how the structure of our Markov-switching model interacts with inferences about the persistence of the output gap following the Great Recession, we extend the benchmark model in equation (2) to allow for a structural break in the length of the postrecession bounceback effect to 21The behavior of other variables such as the unemployment rate provides a strong signal that there actually was a recession in 2001. FIGURE 7.—ESTIMATED OUTPUT GAP FOR ALTERNATIVE LENGTHS OF BOUNCEBACK EFFECT FOR THE GREAT RECESSION / / / 1 0 4 2 2 4 6 1 9 9 6 4 0 3 / r e s t _ a _ 0 0 9 5 7 p d . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 The shaded areas denote NBER recession dates. m(cid:9) = 3, 4, 6, 7 with the Great Recession instead of m = 5 for previous recessions. Figure 7 plots the estimated output for different values of m(cid:9). For m(cid:9) = 3, 4, the estimated output gap is more persistent than in the benchmark case of m(cid:9) = m = 5 and does not close until around 2015. For m(cid:9) = 6, 7, the esti- mated output gap is less persistent and closes soon after the end of the Great Recession.22 22To understand this counterintuitive result econometrically, note that given a similar estimated negative negative effect of the U-shaped regime ˆμ2 across models with different m(cid:9), a smaller m(cid:9) directly implies a larger quarter-by-quarter bounceback effect ˆλ(cid:9) 2. Because the recovery from the Great Recession was only gradual, this implied strong bounceback is offset WHY HAS THE U.S. ECONOMY STAGNATED SINCE THE GREAT RECESSION? 257 In terms of which m(cid:9) to choose, we note that the likelihood values for the models with different m(cid:9) are all very similar to that of the benchmark model, ranging only from −317.35 to −317.34. However, the relative robustness of the infer- ence about the persistence of the output gap for m(cid:9) = 3, 4 compared to the higher values of m(cid:9) suggests that the higher values mechanically impose constraints on the estimated per- sistence of the output gap that the lower values do not.23 Furthermore, the external consideration of the elevated un- employment rate in the United States above 6% until the middle of 2014 would also seem to support the models with m(cid:9) = 3, 4. The key point, though, is that the inference about the Great Recession being U-shaped is completely robust to different possible values of m(cid:9).24 VI. Conclusion We have developed a new Markov-switching model of real GDP growth that accommodates two different types of reces- sions and allows for structural change in trend growth. Apply- ing our model to U.S. data, we find that, perhaps surprisingly, that the Great Recession was U shaped and did not appear to have any substantial hysteresis effects. Instead, the Great Re- cession generated a large, persistent negative output gap, with the economy eventually recovering to a lower-growth trend path that, consistent with Fernald et al. (2017), appears to be due to a reduction in productivity growth that began no later than 2006. We highlight that our inferences about the timing of the output growth slowdown are sharpened by our con- sideration of a time series model that accounts for nonlinear dynamics of recessions. Meanwhile, our inferences about the nature of the Great Recession as generating a persistent neg- ative output gap rather than large hysteresis effects is highly robust to different assumptions regarding the nature of struc- tural change in trend growth. Our analysis is univariate, and we leave consideration of the implications of our findings for a multivariate setting to future research. However, we note that, similar to the con- clusions in Huang and Luo (2018), our estimated output gap can clearly help explain weak inflation in the years imme- diately after the Great Recession. Our results also suggest that the slow growth of the U.S. economy is likely to per- by the model attributing a high probability that the U-shaped regime per- sisted well beyond the end of the recession. By contrast, when m(cid:9) = 6, 7, the quarter-by-quarter bounceback effect ˆλ(cid:9) 2 is smaller and insufficient to offset ˆμ2 in capturing positive but weak growth in real GDP immediately following the recession, but before the full recovery. Thus, in these cases, the model attributes a very low probability that the U-shaped regime persisted beyond the end of the Great Recession. 23The likely offsetting benefit of the higher values of m(cid:9) is that they can capture a smaller quarter-by-quarter bounceback effect. 24Because the low probability of an L-shaped regime in the Great Reces- sion could be due to the smaller estimated contractionary effect ˆμ1 com- pared to ˆμ2 that is evident in figure 1 and table 2, we also considered a model with a structural break in μ1 to μ(cid:9) 1 with the Great Recession. The es- timated ˆμ(cid:9) = −1.92 does increase the probability that the Great Recession 1 was L shaped, but the probability of U-shaped regime is still higher, with the implied output gap very similar to that for m(cid:9) = 7. sist even when the recession related to the COVID-19 crisis ends and interest rates eventually move back above the zero- lower-bound again. 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