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Economic Quarterly— Volume 99, Number 3— Third Quarter 2013— Pages 163–192
Characterizing the Unusual
Path of U.S. Output During
and After the Great
Recession
Jonathon Lecznar, Pierre-Daniel Sarte, and Robert Sharp
T
he growth of the U.S. economy coming out of the 2007–09 Great
Recession has been relatively muted when compared to other
economic recoveries over the postwar period. Four and a half
years into the current recovery, the unemployment rate remains elevated at 6.6 percent, while per capita gross domestic product (GDP)
growth has consistently fallen short of its historical average. One interpretation of current economic conditions is that the U.S. economy
continues to operate below potential, and that one may soon expect a
return to normal conditions driven by increases in cyclical forces like
productivity and employment. Another view is that the tepid recovery
following the Great Recession has been driven by slower moving forces,
and that a notable pick-up in economic activity hinges on variables
that tend to change more slowly over time. This article investigates
these two perspectives empirically and …nds evidence for the latter interpretation.
The focus of the article will be on U.S. per capita GDP, where population is measured as the civilian non-institutional population (i.e.,
non-military, non-inmates at institutions, 16 years of age and over).
As others have noted, the fall in per capita GDP that began in the
We wish to thank Marianna
for their comments. We also
expressed in this article are
those of the Federal Reserve
errors are our own. E-mail:
Kudlyak, Steven Sabol, Zhu Wang, and Alex Wolman
thank Mark Watson for helpful discussions. The views
those of the authors and do not necessarily represent
Bank of Richmond or the Federal Reserve System. All
pierre.sarte@rich.frb.org; robert.sharp@rich.frb.org.
164
Federal Reserve Bank of Richmond Economic Quarterly
fourth quarter of 2007 was unprecedented in U.S. postwar history.1 In
addition, the higher-than-trend growth rates that typically characterize U.S. economic recoveries were notably absent following the Great
Recession: In fact, this was the only recession of the postwar period
for which, 16 quarters after its end, per capita GDP had yet to reach
its pre-recession peak.
To examine these observations objectively, we …rst perform some
statistical analysis on the per capita GDP time series. Using a range
of structural break tests and univariate representations of the process
governing U.S. GDP, we present evidence that the Great Recession
may have left a scar on the U.S. economy in the form of a long-lasting
decline in the level of GDP. Moreover, while we cannot conclusively
establish that U.S. per capita GDP growth has shifted to a lower trend,
we provide calculations that estimate the likelihood of realized growth
rates since the end of the Great Recession to be only 21 percent. To the
extent that the Great Recession was driven in part by …nancial factors,
these …ndings are consistent with work by Reinhart and Rogo¤ (2014)
that highlights the long-lasting e¤ects of …nancially driven recessions.
Finally, we show that unlike every other recession in the postwar period,
the fall in and subsequent slow recovery of output during and after the
Great Recession cannot easily be explained by shocks typical of the
history up to that recession. In this respect, the Great Recession is
statistically unique among postwar recessions.
The next part of our analysis focuses on a decomposition of per
capita GDP. Since the de…nition of population used in this article represents the potential workforce of the U.S. economy, our per capita GDP
series may be decomposed into the following labor market components:
labor productivity, the ratio of employment to the labor force, and
the labor force participation rate.2 The time series behavior of these
components can then be further decomposed into di¤erent frequencies,
highlighting how their contributions to per capita GDP evolve more or
less slowly over time. These decompositions lead us to several observations. First, labor productivity and the employment rate tend to move
with the business cycle, and although they experienced unusually large
negative shocks during the Great Recession, their behavior during and
after this recession was not qualitatively di¤erent from other postwar
recessions in that they soon began to recover. In contrast, the labor
force participation rate moves considerably slower over time, and its
1
For a detailed account that disentangles the various channels underlying the 2007–
09 recession, see Stock and Watson (2012).
2
At times, for convenience given our decomposition, we refer to the ratio of employment to the labor force as the employment rate, although this di¤ers from the more
conventional use of the term to denote the ratio of employment to population.
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 165
Figure 1 U.S. Per Capita GDP, Logged
behavior during and after the 2007–09 recession di¤ers markedly from
that in previous recessions. In this sense, consistent with Stock and
Watson (2012), these simple decompositions show that nearly all of
the slow recovery in output coming out of the Great Recession stems
from a secular decline in the labor force participation rate. Remarkably, in terms of deviations from slow-moving trends, the behavior of
per capita GDP and its components in the 2007–09 recession were not
unlike that of the other postwar recessions.
This article is organized as follows. Section 1 examines several different univariate characterizations of per capita GDP over the postwar
period and conducts a series of exercises that help put the 2007–09
recession and subsequent recovery in the context of previous business
cycles. Section 2 decomposes per capita GDP into subcomponents in
order to further explore key drivers of its behavior over time. Section
3 concludes.
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Federal Reserve Bank of Richmond Economic Quarterly
Table 1 1948:Q1{2013:Q4
Before Split
On and After Split
Before Split y
On and After Split y
2
(2)
2008:Q1
3.853
3.118
1.904
0.558
*137.32
Split Date
2008:Q4
2009:Q2
3.852
3.850
-3.455
3.527
1.899
1.892
1.085
1.198
*180.87
*123.46
Notes: y in annualized growth rates; Critical
1.
2
2009:Q3
3.849
3.513
1.888
1.175
*111.04
(2) value: 1% 9.21*.
UNIVARIATE CHARACTERIZATIONS OF PER
CAPITA GDP
Figure 1A illustrates the behavior of the natural logarithm of per capita
GDP over the postwar period, from 1948:Q1 to 2014:Q1, where recessions are highlighted by vertical bars. Figure 1B zooms in on the Great
Moderation period, 1984:Q1 to 2014:Q1, which we will consider separately since the nature of business cycles appears to be di¤erent during
this period.3 The most recent recession clearly stands out as unique
in postwar data, both because of the size of the fall in the level of
GDP during the recession and because of the tepid growth rate that
characterizes the subsequent recovery. We will begin our analysis by
using two simple statistical characterizations of the process driving per
capita GDP growth to examine the extent to which the recent behavior
of per capita output appears unusual in the context of recessions in the
postwar era.
Deterministic Trend Model
From looking at Figure 1, a simple linear trend model appears to provide a reasonable …rst-pass description of the process generating per
capita GDP prior to the beginning of the Great Recession in 2007:Q4,
yt =
+ t + "t ;
(1)
where yt denotes the natural logarithm of per capita GDP and "t is a
mean-zero error term. In Figure 1A, the logarithm of per capita GDP
indeed generally appears to have ‡uctuated around a constant slope
over the postwar period. In (1), then represents the growth rate of
3
Aside from changes in volatility of key macroeconomic aggregates, see Gordon
(2010) on shifts in various properties of U.S. business cycles over the Great Moderation
period.
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 167
Table 2 1984:Q1{2013:Q4
Before Split
On and After Split
Before Split y
On and After Split y
2
(2)
2008:Q1
3.188
2.917
1.977
0.558
*218.21
Split Date
2008:Q4
2009:Q2
3.185
3.182
3.066
3.098
1.946
1.905
1.085
1.198
*219.58
*78.33
Notes: y in annualized growth rates; Critical
2
2009:Q3
3.180
3.092
1.882
1.175
*54.84
(2) value: 1% 9.21*.
per capita GDP while captures its log level at some initial date, in
this case 1948:Q1.
The dashed lines in Figures 1A and 1B are the best-…t trend lines
given by the ordinary least squares (OLS) estimates of and both
before and after the end of the Great Recession (2009:Q3). Tables 1
and 2 present …ndings from standard Chow tests that consider the hypothesis that the Great Recession may have been associated with joint
changes in
and . Structural break tests for changes in
and
separately were also carried out. The results (not shown) were similar
to those we report in Tables 1 and 2. Table 1 considers the full sample
while Table 2 considers only the Great Moderation period. In each
table, the Chow tests are carried out using di¤erent break dates, from
the beginning to the end of the recession as de…ned by the National
Bureau of Economic Research (NBER). The tests allow for autocorrelation and heteroskedasticity in the residuals "t and are reported as 2
statistics. Regardless of the assumed break date, and over both sample
periods, the tests unambiguously reject the null hypothesis of no change
in and . Observe that up to a given split date, the growth rate in
per capita GDP, , averages around 1:9 percent (annualized) but falls
considerably lower, to well under 1:2 percent, after the assumed break
date.
It is important to note that this same method also suggests structural breaks (at the 1 percent level) for both joint and separate changes
in and in more than half of the other postwar recessions. However, in the 2007–09 recession, the p-values for all tests are less than
10 7 . Only the 1973 recession matches this level of signi…cance, and,
in this case, the change in is actually positive. In fact, in all other
postwar recessions, either the p-values for the results of the Chow test
are several orders of magnitude larger than those associated with the
2007–09 recession, or the change in is positive rather than negative.
Thus, while Chow-type structural breaks were observed in many of the
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Federal Reserve Bank of Richmond Economic Quarterly
postwar recessions, the downward shift in coupled with extremely
small p-values make the structural break of the 2007–09 recession somewhat unique.
Stochastic Trend Model
Findings from the simple structural break tests in the previous subsection rely on (1) representing a reasonable data generating process for
per capita GDP. The 2 statistics shown in Tables 1 and 2 also rely on
derivations that hold asymptotically rather than in …nite samples. A
popular alternative model of per capita GDP instead characterizes the
series as having a stochastic trend,
yt = yt
1
+
+ "t :
(2)
Under this approach, the growth rate of per capita GDP, yt yt 1 =
yt , is seen as ‡uctuating around a constant, as described by +
"t , where "t is assumed to be independently and identically (i.i.d.)
distributed with mean zero. Importantly, in contrast to equation (1),
this stochastic process is such that disturbances, "t , have permanent
e¤ects on the level of GDP. Nelson and Plosser (1982) argued that many
economic series are in fact better described as processes that allow
shocks to have permanent e¤ects rather than e¤ects that gradually
subside over time. In practice, with …nite samples, Stock (1990) and
Blough (1992) argue that the question of whether per capita GDP is
more accurately characterized as having a deterministic time trend as
in (1) or a stochastic trend as in (2) is inherently unanswerable, so that
both approaches are worth considering.
Regardless of the assumptions on the data generating process governing per capita GDP, it remains the case that the Great Recession
appears unprecedented both in terms of its severity and its slow recovery. To help formalize the notion of the “uniqueness” of the 2007–09
recession, we ask two questions: First, given the set of shocks observed
in the postwar period, how likely was the realization of the path characterizing per capita GDP from 2007:Q4 onward? Second, how does
this likelihood compare with that of previous recessions in U.S. postwar
history? In particular, were recessions preceding the most recent downturn somewhat more plausible considering the history of disturbances
incurred up to that recession?
To answer these questions, in contrast to the previous subsection,
we explicitly take into account the fact that observations of per capita
GDP growth since the 2007–09 recession constitute a …nite sample.
Thus, let us think of a given date around the start of the Great Recession, denoted date s, from which we are trying to gauge the likely
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 169
Figure 2 Residuals from Stochastic Trend Model (2)
path forward for per capita GDP. If date T represents the last date for
which we have an observation for per capita GDP, the exercise aims to
give us a sense of the likelihood of having observed the realized path
(ys ; ys+1 ; :::; yT ), relative to all other possible paths for per capita GDP,
(ys ; ys+1 ; :::; yT ), given the history of shocks up to date s under the null
hypothesis that data is generated by (2). Note that there will be a distribution of paths (ys ; ys+1 ; :::; yT ), and that the actual observed path
(ys ; ys+1 ; :::; yT ) will generally fall somewhere within that distribution.
To make matters concrete, let s denote 2009:Q3, the start of the recovery. It is then possible to construct estimates of the paths (ys ; ys+1 ;
:::; yT ) by way of bootstrapping, where the observed residuals (b
"1 ; :::;
b
"s 1 ) from the model (2) are used to represent the unobserved distribution ("1 ; :::; "s 1 ) under the bootstrap procedure. The sample of
observed residuals, b
"t , t = 1; :::; s 1, is obtained as b
"t = yt b ,
where the OLS estimate b is simply the mean of yt . In this case, as
indicated in Table 1, b is approximately 1:9 percent. Figures 2A and
2B illustrate the properties of the estimated residual, b
"t , from which
we are sampling, and which appear close to i.i.d. as assumed. To the
170
Federal Reserve Bank of Richmond Economic Quarterly
extent that some small degree of serial correlation characterizes b
"t , we
consider a slightly di¤erent variant of (2) later in the article.
The bootstrap algorithm proceeds as follows:
1. Let (b
"s ; b
"s+1 ; :::; b
"T ) represent a uniformly resampled version
of (b
"1 ; :::; b
"s 1 ); where b
"t = yt b; t = 1; :::; s 1, and b is treated as
true in the bootstrap world.
2. Construct the estimated sample path (b
ys ; ybs+1 ; :::; ybT ) using
the stochastic trend model, ybt = ybt 1 + b +b
"t , where the starting value
ybs 1 is set to the observed value ys 1 .
3. Repeat Steps 1 and 2 many times to obtain a distribution
of estimated paths, (b
ys ; ybs+1 ; :::; ybT ).
Figure 3 illustrates examples of four sample paths for (b
ys ; ybs+1 ; ::; ybT ),
starting in 2009:Q3, generated by drawing disturbances from the period 1948:Q1 to 2009:Q2. Results reported in this section are ultimately
based on sample paths calculated from 50,000 Monte Carlo trials. Figure 4A then gives 95 percent con…dence intervals for the path of per
capita GDP starting in 2009:Q3, given the history of observed shocks
and an estimated trend growth rate of roughly 1:9 percent under the
null. Two observations are worth noting. First, under the null hypothesis of postwar average trend growth, it is unlikely that today’s level
of GDP would be back in line with that predicted by the pre-Great
Recession trend. This …nding holds even when we take into account
that, over 50,000 Monte Carlo trials, some sample paths include some
of the largest positive shocks to per capita GDP in the postwar period experienced in succession. Second, since 2009:Q3, the observed
per capita GDP path has consistently grown below the historical trend
growth rate given by the slope of the median (50th percentile) path
predicted by the bootstrap simulations.
What if we had set s to be 2008:Q1, the …rst period of decline in
the Great Recession? Using (2), we can write per capita GDP at the
end of the recession, yT , as
yT = ys
1
+ (T
s + 1) +
T
X
"j ;
(3)
j=s
so that P
conditioning on ys 1 and , yT is explained by the sequence of
shocks Tj=s "j .
The 95 percent con…dence intervals in Figure 4B indicate that the
fall in the level of per capita GDP experienced during the Great Recession, together with the subsequent recovery, cannot plausibly be
explained by a sequence of bad shocks representative of historical data.
As mentioned earlier, recall that the 95 percent con…dence intervals
illustrated in Figure 4B obtained from a large number of Monte Carlo
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 171
Figure 3 Sample Paths Versus Realized GDP Per Capita
after 2009:Q3 Split
trials contain sample paths that include some of the worst shocks in
postwar data experienced in succession.
One way to highlight the sense in which the Great Recession was
unique relative to other postwar recessions is to consider previous recessions in the context of the bootstrapping exercise we have just carried out. Thus, Figure 5 illustrates the results obtained from carrying
out analogous exercises with respect to the four most recent recessions
prior to 2007. On the whole, all previous recessions fall within a 95
percent con…dence interval generated by a resampling of shocks up to
that recession. Only the 1980–81 recession stands as somewhat of an
exception to these …ndings, but this is only because this recession is
followed very soon after by another one, and even in this case, Figure
5 shows that per capita GDP returns to the 95 percent con…dence interval as soon as the second recession ends. Statistically, therefore, the
Great Recession stands as somewhat unique in the postwar era in that,
compared to previous recessions, its severity cannot easily be explained
by shocks incurred over the postwar period.
Figure 4 also shows that throughout the recovery period following
the 2007–09 recession, per capita GDP has consistently deviated from
the median path generated by (2) estimated up to 2007:Q4. Since
2009:Q3, the average per capita GDP growth rate has hovered more
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Federal Reserve Bank of Richmond Economic Quarterly
Figure 4 Con dence Intervals from Monte Carlo Trials
than 0.75 percent below the average growth rate prior to the Great
Recession. One point of view regarding this is that although GDP
continues to evolve below trend, it should be expected to revert back
to its historical trajectory at some future date. Another interpretation
is that the trend growth rate of GDP has decreased. A test of the
latter hypothesis depends on two key considerations: First, the greater
the distance between the observed growth rate and the growth rate
under the null, the more likely the null will be rejected. In this case,
the observed growth rate during the recovery period that started in
2009:Q3 is approximately 1:14 percent while the growth rate under the
null was 1:9 percent. Second, the longer the sample period over which
the new growth rate is calculated, the more con…dent we are of its
estimate. In the case of the Great Recession, we are roughly 4.75 years
into the recovery, or 19 quarters.
As an example, suppose that four quarters have elapsed since the
end of the Great Recession, and we now …nd ourselves in the midst of
a weak recovery in 2010:Q3. We want to know whether the observed
weakness is enough to reject the null of a growth rate at least as high
as 1:9 percent given the stochastic trend model (2) and the history
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 173
Figure 5 Con dence Intervals for Past Recessions
of observed shocks up to the beginning of the recovery. To address
this question, we generate a distribution of estimated growth rates, b ,
computed from 50,000 Monte Carlo trials of averages over samples of
size 4, (b
ys ; ybs+1 ; ybs+2 ; ybs+3 ), generated by the bootstrap algorithm described above with s = 2009:Q3. The resulting distribution is shown
in the top left-hand panel of Figure 6. The left p-value associated with
a growth rate of 1.14 percent is roughly 35 percent under the null. In
other words, our …ndings indicate a 35 percent probability of experiencing an average growth rate at least as far below the pre-recession
growth rate as 1.14 percent over four quarters. Given standard critical
values, we cannot reject the null of a growth rate at least as high as 1:9
percent during the recovery. A 95 percent con…dence interval in this
case ranges from 2.15 percent to 5.91 percent.
That said, it’s now been 19 quarters since the end of the recession.
Therefore, the top right-hand panel of Figure 6 illustrates the distribution of estimated growth rates analogous to our previous scenario.
With more observations over which growth rates are calculated under
the null hypothesis, the distribution of b tightens and the left p-value
associated with a 1.14 percent average growth rate falls to 21 percent.
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Federal Reserve Bank of Richmond Economic Quarterly
Figure 6 Distributions of Estimated Growth Rates from
Monte Carlo Trials
In other words, there is now only a 21 percent chance of observing a
growth rate of 1.14 percent or below given historical data. The associated 95 percent con…dence interval now shrinks to (:011; 3:764): The
bottom two panels in Figure 6 show the distributions, along with the
corresponding sample sizes, needed to generate left p-values of 5 percent and 1 percent given a growth rate of 1.14. At the 5 percent critical
level, the weak recovery now characterizing the U.S. economy and its
disappointing growth rate would have to persist for roughly 20 years
before we could unambiguously conclude that we had indeed switched
to a new lower trend growth rate.
Initially, it appears that the current weak recovery would have to
last for quite a while before we could unambiguously conclude that
there has been a change in the trend growth rate. However, the relationship between p-values and sample size is generally convex, which
suggests that when the sample size is small, a few more observations
can dramatically lower the left p-value of this test. In contrast, the
size of the sample under consideration has a relatively small impact
when there are many observations. Thus, for example, if the current
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 175
situation were to extend three and a half more years, there would be
only a 15 percent chance of observing such weak circumstances under
the null. While not conclusive evidence of a change in trend growth,
these calculations nevertheless suggest a relatively low likelihood of
having observed the realized path of per capita GDP since 2009:Q3.
So far, we have examined the extreme cases of a pure deterministic
trend and a pure stochastic trend model. To the degree that Figure 2B
indicates a small degree of serial correlation in the error term of equation (2), a more ‡exible representation of the data-generating process
is given by
yt = yt
1
+
yt
1
+
+ "t ; y0 given:
(4)
In this case,
yt 1 in (4) can be thought of as an error correction term
that introduces smoothness in how GDP growth reverts back to trend
following a shock, and thus also addresses leftover serial correlation in
"t in the simpler stochastic trend representation (2). The properties of
the estimated errors under this more ‡exible representation will more
closely resemble those of white noise. Repeating the bootstrap exercises
described in this section under the more ‡exible model (4) does not
substantively alter our conclusions.
2.
DECOMPOSING PER CAPITA GDP
The analysis thus far has provided simple calculations that illustrate
how the Great Recession stands as relatively unique in the postwar
landscape and suggest that a rapid improvement of the current situation to levels expected from pre-recession trend is questionable. A
gradual increase in per capita GDP growth back toward historical trend
appears more plausible. However, even in the latter case, every new
quarter characterized by below trend growth adds weight to the argument that the U.S. economy has switched to a lower trend growth
rate.
To provide further insight into per capita GDP over the postwar
period, and in particular its unusual behavior throughout the Great
Recession and the subdued recovery that followed, we now decompose
per capita GDP into several components and examine the behavior of
each of these components individually. Thus, throughout this section,
we will work with the following decomposition of per capita GDP:
y
p
| t {z }t
Per Capita GDP
=
(yt et )
| {z }
Labor Productivity
+
+
(et lt )
| {z }
Ratio of Employment to Labor Force
(lt pt );
| {z }
Labor Force Participation Rate
(5)
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Federal Reserve Bank of Richmond Economic Quarterly
Figure 7 Decomposition of Per Capita GDP
where yt is real per capita GDP, pt is the civilian non-institutional population (i.e., non-military, non-inmates at institutions, 16 years of age
and over), et is employment, and lt is the labor force, all in logarithm
form.4 We may think of the decomposition in (5) as (roughly) capturing
di¤erent forces in the economic environment, namely technological considerations that a¤ect primarily labor productivity, demographic and
other structural labor market considerations that have a direct bearing
on labor force participation, and other labor market factors that a¤ect
the unemployment rate.5 Our objective will be in part to assess how
the di¤erent components in (5) have contributed to per capita GDP
growth during the recessions and recoveries of the postwar period.
In any decomposition of the type in (5), one issue is that the
di¤erent components making up the series of interest may move at
4
This decomposition, which lies at the core of our analysis, is a natural one but
is by no means the only potentially useful decomposition of GDP. Other non-structural
decompositions that can shed insight into the Great Recession might include a breakdown by GDP components in a VAR, a breakdown by regions highlighting the role of
housing, or a separation into nominal GDP and in‡ation.
5
Note that et lt is simply one minus the unemployment rate.
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 177
Figure 8 Changes in Log Variables, 1953 and 1960 Recessions
di¤erent rates, each potentially having di¤erent implications for the
series’short- and medium-run forecasts. Thus, let each of the components making up per capita GDP follow a univariate stochastic process,
yt et = (L)"ye;t , et lt = (L)"el;t , and lt pt = (L)"lp;t , where the
"t s represent identically and independently distributed disturbances to
the individual component series. We then have that
yt
pt =
(L)"ye;t +
(L)"el;t +
(L)"lp;t ;
(6)
where GDP per capita at any date t re‡ects the realization of current, and potentially past, disturbances to the individual component
series. Suppose now that labor force participation, (L)"lp;t , moves
relatively slowly over time while the ratio of employment to the labor
force, (L)"el;t , moves more rapidly. Then a fall in per capita GDP
induced by a large shock to labor force participation might imply a relatively slow adjustment back to historical conditions when compared
to the case in which the fall in GDP is caused by a shock to the unemployment rate.
Figure 7 illustrates the decomposition of per capita GDP depicted
in (5) along with the recession periods indicated by vertical lines. Several observations stand out. First, the slope (or growth rate) of log per
178
Federal Reserve Bank of Richmond Economic Quarterly
Figure 9 Changes in Log Variables, 1981 and 1990 Recessions
capita GDP generally appears to mimic the slope of log labor productivity. Second, there are nevertheless notable variations in GDP growth
over particular periods that are evidently in‡uenced by variations in
the unemployment and labor force participation rates. Third, of the
latter two variables, the unemployment rate appears to ‡uctuate with
the business cycle, while variations in the labor force participation rate
tend to occur more slowly over time.
Taken together, these observations suggest important variations in
the way per capita GDP has behaved historically. Thus, in a recent
e¤ort to construct long-horizon forecasts of average growth using a univariate framework, Müller and Watson (2013) allow for ‡exibility in the
univariate process governing per capita GDP by allowing the data to
be generated by a mix of empirical representations capturing di¤erent
aspects of its slow moving components. This assumption, in e¤ect, may
be thought of as capturing the idea that di¤erent components of per
capita GDP, which behave noticeably di¤erent from each other, play
roles of varying importance at di¤erent times.
Figures 8 through 10 illustrate the decomposition in (5) during
select recessions and recoveries of the U.S. postwar period, using the
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 179
Figure 10 Changes in Log Variables, 2001 and 2007 Recessions
starting quarter of each recession to normalize the component series.6
On the whole, the fall in per capita GDP during recessions tends to be
re‡ected mostly in a fall in the ratio of employment to the labor force.
In contrast, recoveries are generally associated with a pickup in labor
productivity. In fact, labor productivity tends not to fall dramatically
even during recessions, re‡ecting the fact that technology is almost
always improving. Therefore, the decomposition in (5) reveals that,
during most downturns, falling per capita GDP can be accounted for
primarily by decreases in et lt and not the other components.
More recently, however, this pattern has changed. The 2001 and
2007–09 recessions are the only recessions of the postwar period in
which the labor force participation rate fell noticeably during both the
recessions and subsequent recoveries, dragging down GDP per capita
even after the recessions ended. Moreover, the 2007–09 recession and
subsequent recovery is the only episode in the postwar period in which,
four years after the end of the recession, GDP per capita had yet to
6
To economize on space, we do not illustrate these decompositions for every postwar recession but the observations we highlight tend to hold across all business cycles.
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Federal Reserve Bank of Richmond Economic Quarterly
Figure 11 Trend Components of Per Capita GDP
Decomposition
reach its pre-recession peak. However, the behavior of labor productivity in the last two recessions does not di¤er markedly from the other
postwar recessions.
Trends and Cycles
As mentioned earlier, the various components in our decomposition of
per capita GDP contribute di¤erently to the aggregate series. Labor
productivity, for instance, mostly contributes a steady increase over
time, or an upward “trend,” to GDP per capita. That said, the term
“trend” is somewhat charged and can mean very di¤erent things in
di¤erent contexts.
For the purposes of this article, we will mainly take the approach
of thinking in terms of particular frequencies of a series of interest.
Following the literature on business cycles and NBER practice, the
business cycle component of a series will be de…ned as the component
made up of cyclical frequencies corresponding to periods less than eight
years. The remaining slower moving components, made up of cycles
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 181
Figure 12 Cyclical Components of Per Capita GDP
Decomposition
with periods greater than eight years, may be thought of as one de…nition of “trend.”Since the period, p, of a cycle is given by 2! , where !
is its frequency, and eight years represents 32 quarters, business cycle
frequencies are then given by ! 2 [ =16; ] when using quarterly data.
Conversely, “trend” frequencies are given by ! 2 [0; =16).
De…nition 1 The trend of per capita GDP corresponds to its component cycles with frequencies ! 2 [0; =16).
The motivation underlying this approach is in part that slower moving cycles are thought to be generally determined by forces outside
policymaking, such as ongoing technological progress or changes in demographics. From Figure 7, it is likely the case that the bulk of the
contributions of labor productivity to per capita GDP occur at frequencies lower than business cycle frequencies. Contributions of labor
productivity to the business cycle component of per capita GDP, relative to those of the other two components, however, may nevertheless
be signi…cant.
182
Federal Reserve Bank of Richmond Economic Quarterly
Balanced Growth
In considering the decomposition (5), it is useful to think about balanced growth implications. In particular, we can think of balanced
growth theory as providing long-run relationships that should broadly
hold between the variables depicted in (5). Thus, suppose that output,
Yt , is produced by way of the technology
Yt = At Kt (Zt Et )1
; 0<
< 1;
where At denotes multifactor productivity, Kt is the capital stock, Et
is labor input, and Zt represents a composition e¤ect that increases the
productivity of labor. Further, let Lt and Pt denote the labor force and
population respectively, and let the growth rate of a given variable, xt ,
be given by gx . Then, along a balanced growth path, where ratios of
variables are constant, we have that
gY = gA + gK + (1
)(gZ + gE ):
But, along a balanced growth path, gY = gK , so the above equation
simpli…es to
1
gY =
gA + (gZ + gE ):
1
In the long run, it must also be the case that
gE = gP = gL :
From (5), we have that
1
|
1
gA + (gZ + gE )
{z
Per Capita GDP growth
+
gP =
1
} |
1
gA + (gZ + gE )
{z
Labor Productivity growth
(gE gL )
| {z }
gE
}
Employment Rate growth
+
(g
g )
| L {z P }
Labor Force Participation Rate growth
or, using the balanced growth relationships,
1
|
1
gA + gZ =
{z
}
1
|
1
gA + gZ :
{z
}
(7)
Per Capita GDP growth Labor Productivity growth
Ultimately, therefore, per capita GDP growth follows labor productivity growth, and both are determined by technological parameters.
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 183
Figure 13 Changes in Trend and Cyclical Log Variables, 1953
Recession
Beyond this observation, it is also important to recognize that balanced
growth calculations, where we may think of 1 1 gA + gZ as an alternate de…nition of trend, are only informative in terms of long-run
relationships. This represents a single frequency in the frequency domain, frequency zero, among all of the periodic variations that make
up per capita GDP. Put another way, the mean growth rate is (in a
sense) a single cycle of in…nite period among all of the cycles that make
up per capita GDP growth.
De…nition 2 The trend of per capita GDP is
1
1
gA + gZ .
In practice, we tend to be concerned with more than the long run,
and there may be a range of slow-moving variations in per capita GDP
outside frequency zero on which policy may nevertheless have very little
e¤ect. Demographic changes underlying changes in labor force participation might be an example of such variations. It is in this sense that
the de…nition of trend in terms of frequencies corresponding to periods
longer than eight years is potentially useful. In particular, a “gap”
184
Federal Reserve Bank of Richmond Economic Quarterly
Figure 14 Changes in Trend and Cyclical Log Variables, 1960
Recession
h
i
between yt pt and + 1 1 gA + gZ t, for some constant , may
be one that is expected to close very slowly or more rapidly depending
on the source of the shock and the frequency at which it moves. So, if
the labor force participation rate, lt pt , experiences
a negative
h
i shock,
1
we might expect yt pt to fall short of + 1
gA + gZ t for a
relatively long period, with policy having very little ability to quicken
the closing of this gap.
Finally, there is an alternative de…nition of “gap” that is more
model-based, de…ned as the deviations of sticky price allocations from
‡exible price allocations in a setting with nominal rigidities. To work
with this de…nition, one must take a stance on the degree of price stickiness and the nature of the shocks a¤ecting the economy at a given time.
Comparisons with this more formal notion of trend, while important,
are beyond the scope of this article.
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 185
Figure 15 Changes in Trend and Cyclical Log Variables, 1981
Recession
Trends and Cycles in the Decomposition of
GDP
Figures 11 and 12 illustrate the trend and cyclical components of the
di¤erent per capita GDP components in (5). The decomposition into
trend and business cycle components is carried out using a HodrickPrescott (HP) …lter with smoothing parameter of 1,600, given the
quarterly data. Note that, because of the linearity of the HP …lter,
the trends of each of the per capita GDP components add up to trend
per capita GDP, and likewise for the cyclical components.7 The …gures
suggest that most of the variation in labor productivity and the labor
force participation rate is driven by slow-moving cycles (with periods
greater than eight years), while variations in the unemployment rate
are more frequent. This is particularly evident in Figure 12, where
7
Because the HP …lter is a two-sided …lter, estimation of the trend is biased toward
the end of the sample. Depending on the nature of the data-generating mechanism, it
takes roughly two years for estimation of the trend to settle.
186
Federal Reserve Bank of Richmond Economic Quarterly
Figure 16 Changes in Trend and Cyclical Log Variables, 1990
Recession
the deviations from trend in the labor force participation rate indeed
appear small.
Figures 13 through 17 illustrate the same decomposition as those in
Figures 8 through 10, but are presented in terms of cycles and trends.
Annualized growth rates for each of the series in Figures 8 through 10
are now broken down into contributions from “cyclical” and “trend”
components. Examination of Figure 13, which illustrates the 1953 recession, reveals that the trend behavior of the series shown in the lefthand panel matches well with textbook balanced growth calculations
described in the previous subsection. Trend log per capita GDP and
log labor productivity have the same slope (i.e., grow at the same rate),
while the trend unemployment and labor force participation rates stay
relatively constant. This observation also applies to the 1957, 1960,
1980, 1981, 1990, and 2001 recessions. The slopes of labor productivity
vary somewhat, ranging from 1:6 percent in the 2001 recession to 2:7
percent in the 1960 recession. However, the recessions of the 1970s, and
especially that of 2007 shown in Figure 17, present a di¤erent story.
In the most recent recession in particular, while labor productivity has
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 187
Figure 17 Changes in Trend and Cyclical Log Variables, 2007
Recession
steadily trended upward in a way typical of the postwar period, the
labor force participation rate has clearly trended downward, noticeably dragging the growth rate of per capita GDP down from that of
labor productivity. Remarkably, the behavior of the series’ cyclical
components, depicted in the right-hand panel of Figure 17, appears
relatively similar to that of other postwar recessions. Put another way,
at business cycle frequencies, the Great Recession is not so dissimilar
to other postwar recessions. Its “uniqueness” resides almost entirely
in slow-moving components of per capita GDP, in this case mostly the
labor force participation rate. For the current recovery period, a small
negative output gap relative to trend still persists.
While the trend labor force participation rate has fallen signi…cantly
since the start of the last recession, thereby mitigating the strength of
the subsequent recovery in per capita GDP, a word of caution is in
order. As mentioned earlier, the HP …lter-based decomposition of a
given series into business cycle and trend components tends to be biased toward the end of the sample, and it typically takes two years or
more for the trend decomposition to settle. Because of this, one still
188
Federal Reserve Bank of Richmond Economic Quarterly
Figure 18 Labor Force Participation Rate, Actual Versus
Counterfactual
might suspect that the large decline in the labor force participation
rate can, in fact, be explained to a degree by cyclical factors related
to the recession. If this were the case, our suggestion that the unusual
behavior of output can be explained by secular changes in its components would be tenuous. However, the HP …lter-based trends of the
labor force participation rate, de…ned as component cycles with periods greater than eight years, are very similar to those calculated by
Kudlyak (2013) using demographic information including age, gender,
and cohort e¤ects. In other words, a considerable portion of low frequency variations in the labor force participation rate are essentially
explained by demographic factors; for example, one might attribute
part of the recent low frequency decline in the labor force participation
rate to the slow movement into retirement of the baby boomers.8 If, as
Kudlyak’s article indicates, demographic factors are driving the decline
in labor force participation, one might expect the recovery of labor force
8
See Fujita (2014) for a detailed explanation of the causes underlying declines in
the labor force participation rate.
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 189
Figure 19 A Counterfactual Exercise
participation— and therefore per capita GDP— to be protracted, with
little room for improvement from policymakers.9
Counterfactual Labor Force Participation
Rates
This subsection further investigates the extent to which the recent
decline in the trend labor force participation rate has potentially contributed to the tepid recovery of per capita GDP following the Great
Recession. Speci…cally, we carry out a counterfactual exercise in which,
similar to Erceg and Levin (2013), the trend labor force participation
rate ‡attens out after 2007:Q4. In this exercise, the counterfactual
9
The decomposition we study, being an identity, is not necessarily inconsistent with
the notion of …nancial factors having played a key role in the way the Great Recession
played out. However, one expects that the productivity subcomponent of this decomposition, among all three subcomponents, might have been most in‡uced by such factors,
rather than the labor force participation rate where demographics clearly have a role.
Indeed, productivity and employment experienced a more pronounced decline relative
to other recessions, but these components appear to have recovered at a pace not too
di¤erent from that of other recessions.
190
Federal Reserve Bank of Richmond Economic Quarterly
trend labor force participation rate is de…ned relative to low frequency
variations isolated by the HP …lter. A comparison of this counterfactual labor force participation rate series to the actual one is shown in
Figure 18.
In any counterfactual calculation of this type, changing the labor
force series, LFt , to re‡ect a di¤erent trend path for the labor force participation rate means that we must also change either the employment
series, Et , the unemployment series, Ut , or both, so that the identity
LFt = Et + Ut continues to hold under the counterfactual.10 We consider two polar cases: an “optimistic”case in which all of the additional
labor force participation is matched by an increase in employment, and
a “pessimistic” case in which the extra labor force participation is re‡ected by increased unemployment. Thus, the pessimistic case might
be interpreted as one in which the distinction between being out of the
labor force and being unemployed is not substantive for the counterfactual increase in labor force participation. In contrast, the optimistic
case might be interpreted as one in which the counterfactual increased
labor force participation assumes away any labor market mismatch
issues or other forces that could potentially produce mismatched or
discouraged workers who then leave the labor force.
The resulting implications for (HP …lter-based) trend GDP per
capita are shown in Figure 19.11 In the pessimistic case, as expected,
when the counterfactual increase in the labor force participation series
is simply matched by increased unemployment, the path of per capita
GDP is una¤ected, but the ratio of employment to the labor force falls.
In the optimistic case, a ‡attening out of the trend labor force
participation rate after 2007:Q4 results in a gain of roughly 0:8 percent
in per capita GDP growth during the recovery beginning in 2009:Q3. In
a sense, this …gure represents an upper bound on what a ‡attening out
of the labor force participation rate after the Great Recession might
have implied for per capita GDP growth. At the same time, to the
degree that the current recovery in per capita GDP has fallen short of
historical trend growth by roughly 1 percent, a considerable portion of
that di¤erence may be accounted for by the behavior of the trend labor
force participation rate. In principle, the implications of a ‡attening of
the trend labor force participation rate lie somewhere between the two
cases depicted in Figure 19.
10
Here, the behavior of population is taken as given so that a counterfactual labor
force series is easily constructed by multiplying the counterfactual labor force participation rate by population.
11
In these calculations, trend labor productivity is assumed to be unchanged.
Lecznar, Sarte, and Sharp: U.S. Output and the Great Recession 191
3.
CONCLUDING REMARKS
A simple decomposition of per capita GDP traces the unusual behavior
of output during and after the Great Recession to a large and steady
decline in the labor force participation rate. The magnitude and persistence of this decline are unprecedented in U.S. postwar history, much
as the fall in per capita GDP that accompanied the Great Recession
was unprecedented. Moreover, the fact that the labor force participation rate moves slowly over time, at frequencies much lower than
those characterizing business cycles, presaged a muted recovery from
the 2007–09 recession relative to other recoveries throughout the postwar period. The persistently slow recovery of per capita GDP might
continue to cause concern and potentially warrants further inquiries
into the factors— particularly demographic ones— that drive ‡uctuations in the labor force participation rate. Such inquiries could help
determine whether government policy can and should be used to raise
the rate of economic growth in the years ahead.
REFERENCES
Blough, Stephen R. 1992. “The Relationship between Power and
Level for Generic Unit Root Tests in Finite Samples.” Journal of
Applied Econometrics 7 (July–September): 295–308.
Erceg, Christopher, and Andrew Levin. 2013. “Labor Force
Participation and Monetary Policy in the Wake of the Great
Recession.” International Monetary Fund Working Paper
WP/13/245 (July).
Fujita, Shigeru. 2014. “On the Causes of Declines in the Labor Force
Participation Rate.” Federal Reserve Bank of Philadelphia
Research Rap Special Report (February).
Gordon, Robert J. 2010. “Okun’s Law and Productivity Innovations.”
American Economic Review 100 (May): 11–15.
Kudlyak, Marianna. 2013. “A Cohort Model of Labor Force
Participation.” Federal Reserve Bank of Richmond Economic
Quarterly 99 (First Quarter): 25–43.
Müller, Ulrich, and Mark Watson. 2013. “Measuring Uncertainty
about Long-Run Predictions.” Mimeo, Princeton University.
192
Federal Reserve Bank of Richmond Economic Quarterly
Nelson, Charles, and Charles Plosser. 1982. “Trends and Random
Walks in Macroeconomic Time Series: Some Evidence and
Implications.” Journal of Monetary Economics 10: 139–62.
Reinhart, Carmen, and Kenneth Rogo¤. 2014. “Recovery from
Financial Crises: Evidence from 100 Episodes.” American
Economic Review 104 (May): 50–5.
Stock, James H. 1990. “‘Unit Roots in Real GNP: Do We Know and
Do We Care?’A Comment.” Carnegie-Rochester Conference
Series on Public Policy 32 (January): 63–82.
Stock, James H., and Mark W. Watson. 2012. “Disentangling the
Channels of the 2007–09 Recession.” Brooking Papers on
Economic Activity 44 (Spring): 81–156.
Economic Quarterly— Volume 99, Number 3— Third Quarter 2013— Pages 193–227
MBS Real Estate Investment
Trusts: A Primer
Sabrina R. Pellerin, Steven J. Sabol, and John R. Walter
R
eal estate investment trusts (REITs) have played a signi…cant
role …nancing U.S. real estate going back to at least the late
1800s. However, those REITs that invest predominantly in
mortgage-backed securities (MBS), the focus of this article, have a
much shorter history, dating to the mid-1980s.1 MBS-focused REITs (mREITs) grew quite rapidly after 2008— so much so that some
observers have expressed concerns that the largest might pose systemic
risks for the broader economy, which has led to speculation that they
may be subjected to heightened supervisory oversight (Solomon 2013).
The two largest mREITs, which account for 54 percent of all mREIT
assets, have been the focus of special attention from policymakers and
the press.2;3;4 Currently, mREITs are not as tightly supervised as other
…nancial entities that are thought to pose systemic risks, such as large
commercial or investment banks.
Observers have raised concerns along the following three dimensions: 1) mREITs invest in fairly long-term assets but fund themselves
with short-term liabilities, implying that they are sensitive to interest
The authors would like to thank Huberto Ennis, Roisin McCord, Nicholas Trachter,
and John Weinberg for comments on an earlier draft and Elizabeth Marshall for validating our data. The views expressed in this article are those of the authors and do
not necessarily re‡ect those of the Federal Reserve Bank of Richmond or the Federal
Reserve System. E-mail: sabrina.pellerin@rich.frb.org; john.walter@rich.frb.org.
1
See Pellerin, Sabol, and Walter (2013, 3–10) for a detailed review of the history
of REITs, mREITs, and MBS.
2
While some observers de…ne mREITs as those REITs that invest in mortgages or
MBS, we use the abbreviation “mREIT” to refer only to REITs that invest in MBS.
Additionally, we include in our de…nition of mREITs only those that …nance their assets
predominantly with repurchase agreements (or other short-term debt, such as commercial
paper).
3
As of 2012:Q4. Please see Table 5 for data on other mREITs.
4
For example, see Adrian, Ashcraft, and Cetorelli (2013), International Monetary
Fund (2013), and Stein (2013).
194
Federal Reserve Bank of Richmond Economic Quarterly
rate and liquidity risks; 2) they hold large portfolios of one type of
asset, such that if mREITs become troubled and are forced to liquidate holdings, MBS prices might be driven down; and 3) the assets
that they hold, predominantly government agency-backed MBS, play
an important role in the operation of the home mortgage market, implying that if policymakers become concerned that mREITs might fail,
these policymakers could feel compelled to intervene to prevent such
failures.
Typical discussions of these risks often provide only sparse information from which one can evaluate them. Therefore, this article sheds
light on how mREITs operate, in what ways they are regulated, and
how their regulation compares to that of other similar types of …rms.
It also explains factors contributing to their recent growth, provides
some analysis of the risks they face, how they manage these risks, and
the potential dangers for the broader …nancial system.
1.
HOW mREITS OPERATE
mREITs are investment vehicles that hold MBS and …nance these holdings with equity and debt. Currently, mREITs predominantly hold
agency MBS— meaning those MBS issued by Fannie Mae, Freddie Mac,
and Ginnie Mae— which enjoy implicit or explicit government backing
and therefore have no credit risk. mREIT investors, i.e., the holders of
mREIT equity, typically receive greater earnings than they might by
simply buying MBS, because mREITs use short-term debt and leverage to magnify returns such that, on average, mREIT assets are 7.4
times equity (Table 1).
Because MBS have fairly long maturities, one might imagine that
mREITs would tend to fund themselves with equity and long-term
debt.
Instead, mREITs typically are funded with short-term
instruments— largely repurchase agreements (repos). Indeed, because
short-term debt instruments typically pay a lower rate of interest than
long-term instruments, borrowing short-term and holding long-term
assets has tended to earn mREITs a signi…cant spread that accounts
for much of their income. The combination of a high degree of leverage with an asset-liability mix that emphasizes funding long-term assets with short-term liabilities (such an asset-liability structure is often
termed maturity transformation) carries signi…cant risks, leading them
to engage in hedging activities (discussed in Section 4).
Five Largest mREITS
Annaly Capital Mgmt Inc.
American Capital Agency Corp.
Hatteras Financial Corp.
CYS Investments
ARMOUR Residential REIT Inc.
Total (includes all
other mREITs)
Average (includes all
other mREITS)
Source: SNL Financial.
Total Assets
2012Y
Agency
Securities
2012Y
Repurchase
Agreements
2012Y
Total Equity
2012Y
133,452,295
100,453,000
26,404,118
21,057,496
20,878,878
127,724,851
85,245,000
24,057,589
20,842,142
19,096,562
102,785,697
74,478,000
22,866,429
13,981,307
18,366,095
15,924,444
10,896,000
3,072,864
2,402,662
2,307,775
434,421,733
359,902,940
319,384,054
58,888,023
14,980,060
12,410,446
11,013,243
2,030,621
Leverage
Multiple
(Assets-toEquity)
8.4
9.2
8.6
8.8
9.0
7.4
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 195
Table 1 Financial Highlights for all mREITS and the Five
Largest
196
Federal Reserve Bank of Richmond Economic Quarterly
Figure 1 mREIT Repo Borrowing and Broker-Dealer
Lending
Sources: Federal Reserve Bank of New York FR2004 Form, SNL Financial, and
Richmond Fed.
Because repos play such a signi…cant part in how mREITs operate,
it is fundamental to understand the broader functioning of the repo
market. A repo is the sale of an asset, by the borrower, with an accompanying promise by the borrower to buy back the same (or like) asset
upon maturity.5 In fact, they typically are thought of as simply a collateralized loan, with the asset acting as the collateral. In the tri-party
repo market, the predominant assets backing repos are MBS issued by
Fannie Mae, Freddie Mac, or Ginnie Mae (36 percent of all tri-party
repo collateral), securities issued by the U.S. Treasury (35 percent),6
and debt securities issued by Fannie Mae or Freddie Mac (6 percent).
Interest rates on repo borrowing are among the lowest in the funding
markets because repos are typically fairly short-term borrowings, repos are collateralized, and repo borrowing receives especially bene…cial
treatment in bankruptcy.
5
6
Ennis (2011, 389–92) provides background on the repo market.
Percentage …gures from Federal Reserve Bank of New York (2012).
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 197
Figure 2 Broker-Dealer Agency MBS Financing and
Tri-Party Repo
Sources: Federal Reserve Bank of New York FR 2004 Form, Tri-party Repo Task
Force, Richmond Fed, Haver Analytics.
A review of the …nancial statements of several of the largest mREITs indicates that most of their repo funding comes from broker-dealers.7
Brokers receive agency MBS as collateral in bilateral repo transactions
with the mREITs and then subsequently use this high-quality collateral
to borrow from other …nancial …rms (e.g., money market mutual funds)
via the tri-party repo market.8 As illustrated in Figure 1, over the last
several years the amount of the increase in MBS-backed broker-dealer
lending (approximately $300 billion between June 2010 and December
2012) is almost exactly equivalent to the amount of the increase in
mREIT borrowing. In turn, as can be seen in Figure 2, the amount
of agency MBS collateral posted to the tri-party market by brokerdealers— the dotted line— increased by about this same $300 billion
between June 2010 and December 2012. The total value of agency
7
For mREITs that disclose details on their repo borrowings, broker-dealers appear to be the predominant source of repo …nancing. See, for instance, the second
quarter 2013 10-Qs of the following mREITs: Bimini Capital Management Inc., p.
15; Invesco Mortgage Capital Inc., page 21; CYS Investments, p. 41; or page 11 of
Armour Residential REIT, Inc., “Company Update,” December 19, 2013 (available at
www.armourreit.com/updates/ARR_Company_Update_Dec_19_2013.pdf).
8
A bilateral repo transaction is one in which there are only two parties to the
transaction. In contrast, a tri-party repo transaction is one in which the two counterparties use a custodian bank or clearing organization (the third party) to act as an
intermediary, and typically the holder of the collateral, to settle the transaction. For
more information on the tri-party repo market, see Ennis (2011, 389–92), Copeland et
al. (2012), and Adrian et al. (2013, 4–6).
198
Federal Reserve Bank of Richmond Economic Quarterly
MBS collateral in the tri-party repo market— the solid line— appears
to mirror movements in the dotted line, and both increase by about
$300 billion over the same period. Therefore, taken together, Figures
1 and 2 suggest that the agency MBS that mREITs have pledged for
most of their recent borrowing has ‡owed through to the tri-party market via broker-dealers and accounts for much of the growth over the last
several years in that market.
Broker-dealers bene…t in two ways by performing an intermediary
role between mREITs and the tri-party repo market. First, brokerdealers earn a spread between the interest rate paid to them by mREITs
and what they must pay to …nance these loans. For example, in 2012
the largest mREIT by assets, Annaly, paid a weighted average repo
rate for its borrowings with maturities of two to 59 days of 45 to 50
basis points (Annaly 2012, F-19), whereas, the average 30-day MBSbacked repo rate in the tri-party market was 25 basis points in 2012
(Bloomberg 2014). Beyond the spread, broker-dealers also face lower
“haircuts”on their repo borrowings than do mREITs.9 A haircut is the
di¤erence between the current market value of the collateral and the
amount the creditor will lend, and it is typically stated as a percentage
of the value of the collateral. It provides a bu¤er to protect the lender
if the market value of the collateral declines. The lower the haircut a
…rm faces, the more it can borrow and re-invest for a given amount of
collateral.
While mREITs face no regulatory leverage limits, the haircut itself
places a limit on the amount they can lever up, meaning haircuts limit
how large an mREIT can grow, given its equity. For example, if an
mREIT starts with $10 million in equity from shareholders and faces
a 5 percent haircut, then the maximum amount it can grow without
raising more capital is $200 million. Here is how the process for this
mREIT would proceed: 1) starting with the $10 million in new equity,
the mREIT buys $10 million worth of MBS; 2) it then uses the $10
million in MBS as collateral for a repo loan of $9.5 million because
the lender requires a 5 percent haircut; 3) it buys an additional $9.5
million in MBS and repos it out to receive $9.025 million in a second
loan; and 4) it buys an additional $9.025 million in MBS. This buying
and “repoing out” (meaning borrowing in the repo market) of MBS
could go on until the …rm has MBS holdings equal to one divided by
1
) times the original equity ($10 million), or
the haircut (in this case :05
9
For instance, Annaly’s (2012, 69) average repo collateral haircut in 2012 was 5
percent, while the median repo haircut for cash investors in agency MBS in the triparty market was only 2 percent (see Federal Reserve Bank of New York [2012], Cash
Investor Margin Levels, Agency MBS).
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 199
20 times the original equity (meaning $200 million). However, mREITs’
leverage ratios are not typically this high— as of December 31, 2012,
their assets (mostly MBS) were on average 7.4 times their equity (see
Table 1).
The borrower not only must provide the lender with extra collateral to cover the haircut percentage at the time the loan is initially
entered into, but also must ensure that the lender’s haircut is maintained throughout the life of the loan (Choudhry 2010, 151–3). If the
value of the posted collateral falls more than a speci…ed amount, the
lender will issue a margin call requiring the borrower to send the lender
additional collateral to reestablish the haircut percentage.10 The possibility that the value of MBS collateral might fall— for example, when
market interest rates increase— provides one explanation of why mREITs do not lever up as much as haircuts might allow. Instead, they
must maintain a portfolio of unencumbered assets— that is, assets not
used to back loans— in order to be prepared to respond to any margin calls.11 For example, as of the end of 2012, Annaly (2012, F-3)
had unencumbered MBS in its portfolio equal to 16 percent of its repo
borrowings.
Beyond these market-imposed limitations, an mREIT’s payouts, investments, and management and ownership structures must meet a set
of requirements found in the federal tax code (see Table 2) in order to
ensure that its income is not taxed.12 Given that one of these requirements is that an mREIT must pass 90 percent of its taxable income to
investors in the form of dividends (rather than retaining earnings), it
must fund its growth by acquiring new debt or equity …nancing.
2.
HOW mREITS ARE REGULATED
Currently, mREITs face very limited regulatory oversight. In addition
to complying with the rules associated with maintaining REIT tax
treatment, the mREITs reviewed in this article are registered with the
U.S. Securities and Exchange Commission (SEC) and publicly traded
and therefore must comply with SEC disclosure and reporting requirements and the rules of the exchange on which they trade (e.g., NYSE or
10
Speci…cally, mREITs are subject to two types of margin calls: valuation and factor calls. Valuation calls occur when the value of the collateral falls, whereas factor calls
occur when prepayment frequencies (prepayment factors) change, based on prepayment
tables published by Fannie Mae and Freddie Mac.
11
Unencumbered assets can include cash, MBS, and other securities.
12
Note that mREIT distributions are taxable income for their investors.
200
Federal Reserve Bank of Richmond Economic Quarterly
Table 2 REITs Requirements to Maintain REIT Status
1. Distribute at least 90 percent of each year’s income to shareholders.
2. Earn at least 75 percent of its gross income from real estate investments,
speci…cally from a) rents on real property; b) interest earned on obligations
secured by mortgages on real property; c) gains from the sale or other
disposition of real property or mortgages; d) distributions from other REITs
or gains from the sale of shares in other REITs; and e) other real estate-related
activities.
3. Earn at least 95 percent of its gross income from: dividends; interest; rents
on real property; gains from the sale or other disposition of stock, securities,
and real property; and other real estate-related activities.
4. Less than 30 percent of its gross income is derived from the sale or other
disposition of: stock or securities held for less than six months; and real
property held for less than four years.
5. At least 75 percent of the value of its total assets is represented by real
estate assets (which includes interests in mortgages), cash and cash items,
and government securities; and not more than 25 percent of the value of its
total assets is represented by non-mortgage or non-government securities.
6. The entity issues transferable shares owned by at least 100 persons.
7. The entity is managed by one or more trustees or directors.
Notes: Government Printing O¢ ce (2010). The Cigar Excise Tax Extension Act
of 1960 (Public Law 86-779) amended Subchapter M such that tax protection was
given to REITs.
NASDAQ).13 However, all SEC-registered and publicly traded …nancial
companies are subject to these rules.
One feature that makes the mREIT unique among its non-REIT
competitors is that its business model relies heavily on an exception
contained in the Investment Company Act of 1940 (the “1940 Act”)
that excludes, from the de…nition of investment company (and therefore from the Act’s rules), certain companies involved in “purchasing
or otherwise acquiring mortgages and other liens on and interest in
real estate.”14 The rationale behind this exception is to di¤erentiate
companies exclusively engaged in the mortgage banking business from
those in the investment company business and allow the former to bene…t from less regulatory oversight since their activities are providing
important liquidity into the housing market (National Association of
13
Publicly listed companies must satisfy rules related to corporate governance (including having a majority of independent directors), liquidity, earnings, share price,
and an internal audit function. For the rule manuals of the NYSE and NASDAQ, see
http://nysemanual.nyse.com/lcm/ and http://nasdaq.cchwallstreet.com/, respectively.
14
The 1940 Act is the primary law that governs investment companies. See Section 3(a)(1) of the Investment Company Act, p. 18, for a de…nition of an investment
company. The exclusion is contained in Section 3(c)(5)(C) of the 1940 Act.
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 201
Real Estate Investment Trusts 2011; Securities and Exchange Commission 2011; Securities Industry and Financial Markets Association
2011). To qualify for this exception, the SEC requires that the exempt
company invest at least 55 percent of its assets in mortgages and other
liens on and interest in real estate (or “qualifying real estate assets”)
and at least 80 percent of its assets in the more broadly de…ned “real
estate-related assets.”15
Traditional REITs that predominantly hold mortgages clearly …t
the mortgage banking exemption contained in the 1940 Act (Securities and Exchange Commission 2011, 55,301). However, mREITs, the
…rst of which appeared in 1985 (based on our de…nition of an mREIT),
have relied on SEC sta¤ interpretations of the 1940 Act, which identify
“whole pool”agency and non-agency residential mortgage-backed securities (RMBS) as being functionally equivalent to mortgage loans, and
therefore “qualifying real estate assets.”16;17 Thus, most mREITs hold
at least 55 percent of their assets in whole pool agency MBS and treat
any “partial pool”agency MBS as satisfying the broader requirements
of a real-estate related asset.18
In 2011, the SEC released a proposal for comment expressing their
concerns that certain types of mortgage-focused companies that exist
today, such as mREITs, may not be the type of company originally
intended to be exempt from the rules of the 1940 Act (Securities and
Exchange Commission 2011). Moreover, while traditional REITs engage in activities that are clearly tied to the mortgage banking business,
the SEC questions whether the mREIT business model is more similar to that of an investment company and should therefore face the
same regulatory oversight as one. For instance, both mREITs and investment companies pool investor assets to purchase securities, provide
professional asset management services, publicly o¤er their securities to
retail and institutional investors, and most avoid paying corporate income taxes (Securities and Exchange Commission 2011, 55,303). While
15
These thresholds are based on SEC sta¤ no-action letters and other interpretations (Securities and Exchange Commission 2011, 55,305) and are broadly recognized
by mREITs as indicated in their 10-K …nancial statements (see, e.g., Annaly [2012, 49]
and CYS Investments Inc. [2012]).
16
From Annaly’s (2012, 49) Annual Report: “This interpretation was promulgated
by the SEC sta¤ in a no-action letter over 30 years ago, was rea¢ rmed by the SEC in
1992 and has been commonly relied on by mortgage REITs.”
17
A “whole-pool” certi…cate is a security that represents all of the ownership interest in a speci…c mortgage pool. From CYS Investments Inc. (2012): “We treat Fannie
Mae, Freddie Mac and Ginnie Mae whole-pool residential mortgage pass-through securities issued with respect to an underlying pool of mortgage loans in which we hold all
of the certi…cates issued by the pool as qualifying real estate assets.”
18
A partial pool certi…cate is a security that represents partial ownership interest
in a speci…c mortgage pool.
202
Federal Reserve Bank of Richmond Economic Quarterly
mREITs generally have a higher concentration of their assets in real
estate, many other investment companies invest in some of the same
kinds of assets.19 Nonetheless, according to a congressional statement
associated with the Investment Company Act Amendments of 1970,
mortgage REITs are excluded from the 1940 Act’s coverage “because
they do not come within the generally understood concept of a conventional investment company investing in stocks and bonds of corporate
issuers.”So it seems likely that mREITs would meet this congressional
intent.20
If mREITs became subject to the 1940 Act, they would face stricter
regulation. Most importantly, the 1940 Act places limits on investment
companies’use of leverage. The Act also gives the SEC the authority
to monitor the companies’activities to ensure that, for instance, they
are accurately computing the value of their assets and are not engaging
in activities with a¢ liates that bene…t insiders at the cost of investors
(Securities and Exchange Commission 2011, 55,303).21 In addition,
it restricts a¢ liate transactions between the investment company and
any a¢ liate that holds at least 5 percent ownership interest in the
company.22
These additional restrictions could be very costly for mREITs, especially the leverage requirements. Unlike their investment company
competitors, mREITs are able to rely more heavily on debt …nancing
because they have no statutory leverage limits.23 In other words, they
can purchase more assets for a given amount of capital compared to
their competitors. Imposing additional restrictions would eliminate any
advantage they might have compared to investment companies that are
subject to greater regulatory oversight. Beyond investment companies,
mREITs also compete with other …nancial entities, which face even
greater regulatory oversight, such as banks, investment banks, insurance companies, and other lenders. This comparatively light regulatory
oversight is likely one of the contributing factors to the growth of the
mREIT sector.
19
Securities and Exchange Commission 2011, p. 55,303, fn. 27, p. 55,300, fn. 3.
U.S. House Investment Company Act Amendments of 1970. House Report 911382 (August 7, 1970), at 17.
21
From ICI (2013) Factbook in reference to leverage limitations: “these limitations
greatly minimize the possibility that a fund’s liabilities will exceed the value of its assets.” See Section 2(a)(41) of the 1940 Act to see how registered investment companies
are required to value their assets.
22
See Section 17 of the 1940 Act for prohibitions related to registered investment
companies engaging in certain transactions with their a¢ liates.
23
Note that repurchase agreements have restrictive covenants that may also put
restrictions on leverage.
20
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 203
Figure 3 Total Assets, Repos, and Securities of mREIT
Industry
Sources: SNL Financial and Richmond Fed.
3.
GROWTH OF mREITS
mREIT assets have grown eight-fold over the last decade (Figure 3).
They increased fairly signi…cantly from 2003 until the time of the …nancial crisis and then grew especially rapidly beginning in 2009. mREITs’
share of agency MBS (and agency debt) has also increased considerably (Figure 4). While their share remains fairly small, mREITs have
grown to be important suppliers of agency MBS collateral. As of September 2013, mREITs supplied, through broker-dealers, 54 percent of
the agency MBS collateral used in the tri-party repo market.24 Clearly,
an important reason for their growth is their strong returns. As seen in
Figure 5, their dividend yield over the last …ve years has consistently
been around 15 percent, considerably higher than equity REITs. One
reason for mREITs’strong performance is the favorable tax treatment
that they receive compared to many of their competitors. Of course
this cannot be the only explanation given that, at least recently, mREITs have produced much stronger returns than equity REITs, which
also enjoy this tax advantage.
24
SNL Financial and Federal Reserve Bank of New York (2013).
204
Federal Reserve Bank of Richmond Economic Quarterly
Figure 4 Holders of Agency MBS and Agency Debt in 2008
and 2013
Notes: “Other” includes non…nancial corporations, households, U.S. government,
and credit unions; “Nonbanks” include security brokers and dealers, ABS issuers,
holding companies, and money market mutual funds; as of the second quarter of
2013, total agency MBS and agency debt equals $7.6 trillion, according to Z.1
data. Of this total, $5.8 trillion is agency MBS, according to Securities Industry
and Financial Markets Association data.
Source: Z.1 Federal Reserve Board of Governors’Financial Accounts of the United
States, Table L.210, 2013:Q2.
Other factors that may have contributed to their strong growth
and high returns include a lack of regulatory restrictions on mREITs’
use of leverage, federal policies supporting the agency MBS market
(and therefore mREITs’ main asset), and advantages associated with
using repo (their main liability) as a primary method of …nancing.
mREITs’ability to produce rapid growth has been dependent on these
factors taken together, as well as various external factors, including the
growth of securitization and of the repo market, and the interest rate
environment.
By investing predominantly in agency MBS, not only do mREITs
avoid credit risk, but they are also reliant on a sector that has bene…ted
from a large amount of government support. As a result of the recent
…nancial crisis, the Treasury and the Federal Reserve took actions that
stabilized the market for mortgage-related securities (see Table 3 for
a list of policy actions that have supported MBS). For instance, in
an e¤ort to stimulate the economy, the Federal Reserve purchased a
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 205
Figure 5 Dividend Yield for Agency mREITs and Equity
REITs
Sources: SNL Financial and Richmond Fed.
signi…cant amount of MBS (holdings total $1.3 trillion as of September
30, 2013) as part of its large-scale asset purchase program.25
While many sectors were contracting during the …nancial crisis,
existing mREITs continued to grow and new ones were formed. Of
the 42 mortgage REITs (both listed and unlisted) existing today, 19 of
them were formed between 2008 and 2012 (see Figure 6).26 One of the
recently formed mREITs— Five Oaks Investment Corporation— notes
that the government policies that support the MBS market created
an attractive investment opportunity for mREITs. In its registration
statement, it indicates that if such policies were to change, they could
experience signi…cant …nancial hardship.27 Even though some of this
support has dwindled, the MBS market has remained liquid and these
securities have consistently been relied on as high-quality collateral
in repo transactions with broker-dealers. Additionally, the fact that
25
While Fed purchases of MBS could certainly be viewed as making agency MBS
more attractive (enhancing liquidity and, therefore, safety), they have also driven up
agency MBS prices to some extent, which tends to make agency MBS somewhat less
attractive. Data for Federal Reserve MBS holdings from the Board of Governors (2013).
26
Note that these …gures include both listed and non-listed mortgage REITs. As
of December 31, 2012, 24 of these are publicly traded mREITs (per our de…nition).
27
From the Five Oaks Investment Corporation (2012, 32–3).
206
Federal Reserve Bank of Richmond Economic Quarterly
Table 3 Policy Interventions
issuance of non-agency MBS dried up following the crisis (see Figure 7)
provides further evidence that government support in the agency MBS
market was fundamental to the survival (and growth) of mREITs.
As can be seen in Figure 6, mREITs’ total assets (predominantly
MBS) grew following a period in which MBS issuance had risen signi…cantly and mREIT assets have increasingly been funded by repos (also
see Figure 8), indicating that MBS and repo growth may have contributed importantly to mREIT growth. The repo market is part of
the so-called “shadow banking system,” which has grown signi…cantly
over the last several decades.28 The ratio of private securitization to
28
Shadow banking “comprises a diverse set of institutions and markets that, collectively, carry out traditional banking functions— but do so outside, or in ways only
loosely linked to, the traditional system of regulated depository institutions. Examples
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 207
Figure 6 mREITs in Existence, Issuance of Securitized
Mortgages, Repo, Assets, and Major Federal
Policies
Sources: SNL Financial, SIFMA, Flow of Funds, and Richmond Fed.
total bank loans grew from zero in the early 1980s to over 60 percent
prior to the …nancial crisis (Gorton and Metrick 2010, 265). The overall
growth in repo usage and MBS issuance over the last two decades has
been attributed to the reduced competitive advantage held by banks
for deposits (due to certain innovations and regulations) and the rise
in “securitization and the use of repo as a money-like instrument”
(Gorton and Metrick 2010, 266). As institutional investors, pension
funds, mutual funds, states and municipalities, and non…nancial …rms
had a growing demand for nonbank alternatives for deposit-like products, they turned to the repo market, which allowed nonbank …nancial entities such as mREITs to acquire …nancing for their activities
of important components of the shadow banking system include securitization vehicles,
asset-backed commercial paper conduits, money market mutual funds, markets for repurchase agreements, investment banks, and mortgage companies” (Bernanke 2012). Also
see Pozsar et al. (2013) for a thorough discussion of shadow banking.
208
Federal Reserve Bank of Richmond Economic Quarterly
Figure 7 MBS, CMBS, and CMO Issuance from 1985 to 2012
Source: Fannie Mae, Federal Reserve, Freddie Mac, Ginnie Mae, HUD, FHFA;
data compiled by SIFMA.
in return for collateral.29 The growth in securitization meant that an
increasing amount of collateral was available for repo …nancing.
Additionally, bankruptcy’s favorable treatment of repos, which limits counterparty risk, may be another factor contributing to mREIT
growth. In a repo transaction, if the borrower defaults, the lender is
not subject to the automatic stay provisions of the code (whereby creditors of a bankrupt …rm are prevented, or “stayed,” from making any
attempts to collect what they are owed) and can take possession and
immediately liquidate the assets pledged as collateral under the repurchase agreement. Financial contracts that receive this special treatment
in bankruptcy (exemption from the stay) are called quali…ed …nancial
contracts (QFCs) and include repurchase agreements, commodity contracts, forward contracts, swap agreements, and securities contracts.
While special treatment for certain …nancial contracts has existed since
1978, only in 2005 was the de…nition of a QFC expanded to include
29
“In 2003, total world assets of commercial banks amounted to USD $49 trillion,
compared to USD $47 trillion of assets under management by institutional investors”
(Bank for International Settlements 2007, 1, fn. 2).
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 209
Figure 8 Repurchase Agreements as a Percentage of Total
mREIT Liabilities
Notes: Quarterly observations of repo liabilities as a percentage of total liabilities
for mREITs.
Sources: SNL Financial and Richmond Fed.
repos backed by MBS (Government Accountability O¢ ce 2011, 14).30
Because the risk to mREIT counterparties is greatly reduced, mREITs
receive repo …nancing on favorable terms (fees and haircuts), and counterparties may be more willing to be heavily exposed to mREITs. As
a result, repos’special treatment in bankruptcy could be a signi…cant
factor in mREITs’ growth.31 Notably, the vast majority of mREIT
asset growth took place after the MBS repo exemption and, as seen
in Figure 8, repos have accounted for an increasing share of mREIT
liabilities since 2005. Importantly, mREITs rely, almost exclusively, on
the use of repo …nancing to attain leverage.
mREITs’ ability to lever up without regulatory restriction seems
to be a critical part of their ability to produce high returns and grow
rapidly. According to Annaly, the largest mREIT, if leverage limits
30
For the types of contracts currently exempt from the stay, see the following sections of the Bankruptcy Code: 11 U.S.C. § 362(b)(6), (b)(7), (b)(17), 546, 556, 559,
560.
31
For a discussion of potential ine¢ ciencies that might arise because of exemption
of QFCs (e.g., repos) from the stay, see Roe (2011).
210
Federal Reserve Bank of Richmond Economic Quarterly
Figure 9 Formation and Failures of mREITs and the Yield
Curve
Notes: “Historical” refers to MBS REITs that were founded but are currently no
longer in existence. “Current” refers to MBS REITs that are still in existence.
Asset data only for listed mREITs.
Sources: SNL Financial, FRED, and Richmond Fed.
were imposed its business model would have to be changed in a way
that would have a material adverse impact (Annaly 2012, 49).
While equity REITs also use leverage, their returns over the last six
years have been considerably lower than returns produced by mREITs
(Figure 5). An important di¤erentiating feature that could account for
this earnings di¤erence is that mREITs lever up using short-term debt.
This ability to lever up with short-term debt (repo) is particularly advantageous during periods in which short-term interest rates are low
relative to long-term rates, for example over the last six years. During
such periods, mREITs bene…t from holding long-term assets (MBS) at
favorable spreads over their funding (repo) costs and utilize leverage
to amplify returns. Figure 9 shows that when the yield curve environment is favorable (when the spread between 10-year and three-month
Treasury securities is greatest), mREITs’asset growth and formations
increased.
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 211
The E ect of the Recent Increase in Interest
Rates
In late 2012, long-term interest rates increased slightly and then signi…cantly in mid-2013, producing a less favorable environment for mREIT
earnings and growth. In the third quarter of 2012, mREIT assets
peaked at $449 billion (see Figure 3) and declined afterward in response
to this increase in interest rates.
The sello¤ of mREIT assets as rates increased could be explained
by three things. First, to the extent that investors shifted into mREITs
when interest rates were low and falling to “reach for yield,”when interest rates started increasing these same investors may have started shifting back to less risky investments. Second, mREIT managers themselves may have developed concerns about the adverse e¤ect that increasing interest rates would have on their MBS portfolio and therefore
reduced leverage to an extent (by 1.4 percent to 7.2 percent over a period of nine months) by selling assets and repaying debt.32 Third, repo
counterparties could have become concerned about increased mREIT
risks and the risks of holding MBS collateral in a rising rate environment and therefore may have become less willing to roll over MBS-based
repo funding or may have increased funding-related costs (e.g., interest
rates, haircuts, and fees).
Although recently mREIT assets have decreased somewhat, their
business model has generally remained favorable— meaning they continued to provide investors with high dividend yields (Figure 5)— even
in 2014. However, mREITs carry some signi…cant risks. In the following section, we will look more closely at the risks inherent in their
business model and how they manage them.
4.
mREIT RISKS AND RISK MANAGEMENT
mREITs are exposed to: 1) interest rate risk, 2) prepayment risk, 3)
credit risk to the extent that mREITs hold assets other than governmentguaranteed MBS, and 4) liquidity risk. To mitigate these risks, mREITs engage in measures such as hedging and taking steps to reduce the
fragility of their funding structure.
32
Leverage here is assets divided by equity (data from SNL Financial). The leverage calculations here are not weighted by mREIT assets, as they were in Table 1.
212
Federal Reserve Bank of Richmond Economic Quarterly
Interest Rate Risk
Because of the maturity mismatch between mREITs’assets and liabilities, interest rate movements can a¤ect their earnings and, indeed, their
solvency. As of December 31, 2012, mREITs’ repo maturities were,
on average, about 48 days,33 while their average MBS maturity was
4.5 years.34 This maturity mismatch implies that when interest rates
increase, mREITs’ earnings will decline because their repos re-price
quickly while the yield on their MBS remains unchanged or increases
slowly.
If interest rates increase rapidly, the value of MBS holdings could
decline enough to threaten mREIT solvency. The way in which this
could happen is as follows. An interest rate-driven decline in the value
of an mREIT’s MBS holdings will lead its creditors to issue margin
calls, requiring the mREIT to use its unencumbered assets to post additional collateral to secure their repo funding. If interest rates increase
enough, all of the mREIT’s unencumbered assets will be expended, and
the mREIT will be unable to meet additional margin calls.
Prepayment Risk
Prepayment risk exists because most mortgage contracts allow the borrower the option to prepay, meaning pay back their mortgage prior to
maturity. Because 82 percent of mREITs’assets are agency MBS (as of
December 31, 2012), mREITs are highly exposed to prepayment risk.
The prepayment option can produce losses for mREITs when interest
rates fall or rise. When interest rates fall, homeowners are more likely
to re…nance their mortgages, meaning they will prepay. As a result,
MBS holders are repaid more quickly than they would be if there were
no prepayment option, and they are likely to su¤er losses when their
funds are returned to them and must be reinvested at the prevailing
lower market yields. When interest rates rise, homeowners are less
likely to re…nance their mortgages, meaning MBS maturities (or, alternatively, durations35 ) are extended. Therefore, the value of the MBS
declines in response to this rise more than it would for a “plain vanilla”
33
Figures are for the 26 …rms that …t our mREIT de…nition and are as of December
31, 2012. See Table 5.
34
We don’t have a …gure for the average maturity of all mREITs’ MBS holdings.
This …gure (4.5 years) is the weighted average maturity of Annaly (2012, F-16) and
American Capital Agency Corporation (2012, 44) only.
35
From Vickery and Wright (2013): “Duration is a measure of the maturity of
a …xed-rate security or, equivalently, its sensitivity to movements in interest rates. A
duration of four years implies that a 1 percent change in yields is associated with a 4
percent change in price. Note that this market rule-of-thumb estimate of MBS duration
is approximate— because future prepayment rates are unknown, the expected duration
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 213
bond (one without any call or prepayment features). This is because
the increase in interest rates extends the maturity or duration of the
MBS— due to the embedded prepayment option in mortgages— thereby
producing more losses.
Credit Risk
Agency MBS has come to dominate mREIT holdings as non-agency
MBS issuance declined to just a few billion per year starting in 2008
(see Figure 7).36 Therefore, today’s mREITs face little credit risk—
the danger that the issuer of the security (the borrowing …rm) will be
unable to repay all of the principal or interest promised in the security
contract, leading to a loss for the security holder. However, mREITs
have historically held a mix of mortgage-related securities, including
non-agency MBS and therefore at times have been exposed to credit
risk (Figure 10). If the non-agency MBS market recovers, mREITs
may, once again, increase their holdings of non-agencies, thus making
credit risk a greater concern.
Liquidity Risk
Liquidity risk arises for mREITs because of their reliance on shortterm funding. If an mREIT’s counterparties grew concerned about its
…nancial health, these counterparties could become unwilling to roll
over their repo funding. Because mREITs are highly dependent on
short-term funding, such unwillingness could quickly cause mREITs
to go out of business. For instance, the mREIT Thornburg Mortgage (Thornburg) …nanced $29 billion of non-agency MBS it owned
in the second quarter of 2007 with repurchase agreements and assetbacked commercial paper. Between the second and third quarter of
2007, Thornburg began having trouble rolling over its repos and eventually had to repay $14.2 billion37 of its repo borrowings, in part by
selling assets.38;39 Ultimately, Thornburg defaulted on JPMorgan when
of an MBS will ‡uctuate over time because of variation in market conditions and the
term structure of interest rates.”
36
www.sifma.org/research/statistics.aspx, “U.S. Mortgage-Related Issuance and
Outstanding.”
37
Figure from the di¤erence in repo holdings between 2007:Q3 and 2007:Q4 from
Thornburg’s 10-Qs.
38
See Kingsbury and Wei (2007).
39
From class action complaint: Case 1:07-cv-00815-JB-WDS Document 68 Filed
05/27/2008, UNITED STATES DISTRICT COURT, DISTRICT OF NEW MEXICO,
IN RE THORNBURG MORTGAGE, INC Case No. 07-815 JB/WDS, SECURITIES
LITIGATION.
214
Federal Reserve Bank of Richmond Economic Quarterly
Figure 10 Non-Agency and Agency Holdings for All mREITs
Notes: Quarterly holdings of non-agency MBS and agency MBS as a percentage
of total assets of mREITs. Data from mREITs listed in Table 5.
Sources: SNL Financial and Richmond Fed.
they failed to meet a margin call on a repo agreement.40;41 This default
triggered “cross-default provisions”— a feature that is common to the
repo market— whereby the default on one repo contract automatically
puts the borrower in default on other repo contracts. These provisions
can exacerbate liquidity risk because they create the possibility that all
of an mREIT’s repo creditors may instantly demand their money back
regardless of the maturity of repo contracts.
While for Thornburg the losses occurred because of its non-agency
MBS holdings, today’s mREITs invest predominantly in agency MBS.
Excluding other problems at an agency-MBS-focused mREIT, one would
imagine that liquidity risk would be a fairly minor problem given that
repos backed by agency MBS could easily be rolled over because they
enjoy an implicit government guarantee. However, if lenders were to
become unwilling to accept agency MBS collateral, mREITs could experience trouble rolling over their repos. Figure 11 suggests that during
the …nancial crisis repo lenders did become less willing to accept agency
40
See Bogoslaw (2008), Mildenberg (2008), and Thornburg (2008).
Thornburg ultimately declared bankruptcy on April 1, 2009, at which point any
remaining repo contracts would have been terminated and may have been immediately
liquidated. See McCarty (2009).
41
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 215
Figure 11 Spread between Agency MBS Term Repo Rate and
Treasury Term Repo Rate
Notes: Five-day centered moving average of spread between 60-day agency MBS
repo and 60-day Treasury repo, in basis points.
Sources: ICAP/Bloomberg and Richmond Fed.
MBS as collateral, at least relative to U.S. Treasury securities, as evidenced by the widened spread between MBS-backed and Treasurybacked repo rates (Figure 11). As some observers have claimed, there
was a ‡ight to the highest quality securities, i.e., Treasury securities,
during the …nancial crisis, which could be one explanation for the
widened spread.42
Risk Management
mREITs engage in several forms of risk management in order to limit
some of the risks we have just outlined. Because the fundamental
feature of mREITs is that they engage in maturity transformation,
most of their risk management e¤orts are focused on addressing interest rate risk, but some e¤orts simultaneously address liquidity risk and
42
p. 18.
http://research.stlouisfed.org/publications/regional/10/07/treasury_securities.pdf,
216
Federal Reserve Bank of Richmond Economic Quarterly
prepayment risk. One such activity that addresses both interest rate
risk and liquidity risk is laddering— spreading out the maturities of
their …nancing so that all of their liabilities do not come due at once.
Beyond laddering, mREITs also hedge using simple and complex
derivative-based strategies to address interest rate risk and the risks
associated with the prepayment option embedded in MBS.43 Currently,
mREITs are less concerned with managing credit risk since their portfolios are comprised largely of agency MBS.
Figure 12 illustrates the magnitude of the asset-liability mismatch
of one of the largest mREITs (AGNC) and the extent to which it
hedges. The size of the “bubbles” indicates the amount of either the
notional values of swaps and swaptions or market values of agency
MBS and repos. The vertical axis represents the interest rates earned
on assets (positive numbers), repo rates paid (positive numbers), and
net swap rates on hedges (…xed pay less ‡oating receive rate).44 The
horizontal axis represents the maturity (in days) of assets, liabilities, or
derivative contracts. From the …gure, it is clear that AGNC’s MBS have
a much greater average maturity (and yield) than their repo liabilities,
but some of this mismatch is o¤set by the swaps and swaptions, albeit
at a cost.
Laddering
Repo …nancing is typically thought of as being very short term— having
an overnight maturity.45 If all mREIT repo …nancing was overnight,
they would be exposed to bank-like runs, since all of their liabilities
would mature daily. In other words, it is possible that all mREIT
creditors could, on a given day, refuse to roll over their repo …nancing;
just like all depositors of a bank could demand their funds on a given
day— producing a run. mREITs typically will arrange their repo funding such that their contracts have various terms to maturity, which can
mitigate the possibility of bank-like runs.
43
One might imagine that mREITs would need to address prepayment risk associated with declining interest rates (the chance that falling interest rates will cause
mortgage borrowers to re…nance, and therefore repay their mortgages, forcing mREITs
to need to reinvest these received funds at the new lower interest rate) because MBS
contains such risk. However, because mREITs’ have longer-term assets than liabilities,
a decline in interest rates would reduce their funding costs, tending to o¤set any losses
produced by prepayments.
44
Interest payments on repos are expressed as a positive number, rather than a negative number, to allow readers to more easily visualize the net interest margin (spread).
45
Investopedia de…nes a repo contract as “a form of short-term borrowing for
dealers in government securities. The dealer sells the government securities to investors, usually on an overnight basis, and buys them back the following day”
(www.investopedia.com/terms/r/repurchaseagreement.asp).
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 217
Figure 12 AGNC's Balance Sheet and Hedges
Notes: For swaps and swaptions, the “yield” is the receive rate minus the pay
rate; the size of the bubble refers to the notional dollar amount. For agency MBS
the value is their fair value, the yield is the current yield, and the life is the estimated average life. For repos, notional is the size and yield rate is the repo rate.
The term until maturity for ARMS was their average number of days until reset.
TBAs are net notionals, rate is dollar roll, implied …nancing rate, and maturity
is 60 days. The 30-year TBA bubble lies behind the 15-year TBA bubble and is
of similar size, so it is obscured. All dollar amounts are in millions.
Sources: Richmond Fed and AGNC 2013:Q1 10Q.
While over the last couple of decades the majority of mREITs’repo
contracts have had maturities of fewer than 30 days, a large portion of
their repo …nancing has still been for greater than 30 days, particularly
in periods when interest rates were expected to rise.46 As seen in
Figure 13, mREITs increased the proportion of repos with maturities
greater than 30 days beginning in 2002 and again in 2009, periods
during which it seemed clear that interest rates could only increase.
Creditors may have greater concerns about the health of …rms, such
46
The decline in the use of repos with maturities greater than 30 days during the
2007–09 …nancial crisis could have been, in part, due to broker-dealers’ e¤orts to shorten
the maturities of their repo loans.
218
Federal Reserve Bank of Richmond Economic Quarterly
Figure 13 mREITs Share of Repo Borrowing by Maturity and
Federal Funds Rate
Sources: SNL Financial, Haver Analytics, and Richmond Fed.
as mREITs, which have signi…cant maturity mismatch, when rising
interest rates are expected to produce losses.
In addition to protecting them somewhat from liquidity risk, lengthening repo maturities also reduces interest rate risk to a limited extent
because it reduces the maturity gap between their assets and liabilities.
Despite their use of laddering, as seen in Figure 12, their liabilities (orange bubbles) still have signi…cantly shorter maturities than most of
their assets (red bubbles). Thus, while laddering can mitigate some of
the rollover risk mREITs face, it still leaves them exposed to interest
rate risk.
Fixed-for-‡oating interest rate swaps
Of all their risk management activities, mREITs rely most heavily on
interest rate swaps to manage interest rate risk. In fact, the notional
value of their swaps at the end of 2012 totaled $160 billion (equal to
37 percent of all mREIT assets) (Table 5). Because mREITs’funding
costs (determined by repo rates) adjust more quickly than the interest earnings on their MBS portfolio, when interest rates rise, their net
income declines. To compensate for the increased funding costs, mREITs enter into …xed-for-‡oating rate swap contracts that pay o¤ when
interest rates rise. Fixed-for-‡oating swaps, in this case, will pay the
mREIT’s swap counterparty a …xed rate while the mREIT receives a
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 219
Figure 14 Annaly and AGNC's Swap Ratio
Notes: Swap ratio is de…ned as the notional amount of swaps divided by the repo
borrowings outstanding.
Sources: AGNC and NLY 10K/10Qs, Richmond Fed.
‡oating rate tied to some short-term market interest rate index, such
as the London Interbank O¤ered Rate (LIBOR). Since short-term interest rates tend to move together, the income that an mREIT receives
on its contract will increase at the same time that their repo costs are
increasing.
The average swap ratio for all mREITs— total notional value of
swaps divided by total repos— was only 50 percent as of December 31,
2012 (Table 5). This means that approximately 50 percent of any rise in
mREITs’repo funding costs resulting from an increase in market rates
will be o¤set by the income received on these swap contracts. However,
given that the two largest mREITs have recently added, rather aggressively, to the amount of their interest swaps, this …gure is larger than
it was in recent years and appears to continue to trend upward. Combined, these mREITs increased the notional amount of their swaps by
$68 billion from 2010 to the second quarter of 2013, providing evidence
that they were expecting interest rates to rise (Figure 14).
220
Federal Reserve Bank of Richmond Economic Quarterly
Other commonly used hedging activities
Beyond laddering and entering into interest rate swaps, mREITs engage in a number of other activities to hedge interest rate risk caused
by their maturity mismatch. mREITs use the measure duration to estimate the size of their maturity mismatch. Speci…cally, mREITs control
their duration gap (duration of assets minus duration of liabilities) by
engaging in hedging activities such as swaptions, options, futures, and
short sales.47 Table 4 shows the market values and durations of all of
AGNC’s assets, liabilities, and hedges as of the …rst quarter of 2013
and the resulting net duration gap. A positive duration gap, such as
AGNC’s, means that a …rm will experience losses when interest rates
rise. The larger the positive duration gap, the larger the losses.
Some observers argue that there exists a feedback between hedging
and the volatility of market interest rates. Hedging, therefore, is seen
as one way mREITs potentially pose risks for the broader …nancial
system (Financial Stability Oversight Council 2013, 88–9).
5.
RISKS mREITS POSE (SYSTEMIC RISKS)
While mREITs’ holdings of MBS are only a small share of all MBS
outstanding (see Figure 4), a number of observers have raised concerns
about the potential systemic impact of mREIT problems. A sudden
rise in interest rates, a decline in MBS prices caused by other market
forces, or any event that causes mREITs to lose a signi…cant portion of
their funding, could lead to rapid deleveraging by mREITs and possibly
declines in MBS prices broadly and problems for other …nancial …rms.48
For example, one observer argues that a 50-basis-point sudden increase in interest rates could lead to a decline in the values of mREITs’MBS portfolios and signi…cant mREITs sales, and generate “temporary dislocations in MBS markets” (International Monetary Fund
2013, 10).49 More speci…cally, the idea seems to be that an initial increase in market interest rates could produce mREIT actions— sales of
MBS— that could amplify the initial interest rate movement, thereby
producing large enough increases in mortgage rates to slow the growth
of home sales.
47
mREITs may also modify their portfolio holdings as a means of controlling their
duration gap.
48
These concerns are raised in the following: Financial Stability Board (2013, 38–
9), Financial Stability Oversight Council (2013, 7 and 87–90), International Monetary
Fund (2013, 9–14), and O¢ ce of Financial Research (2013, 16–8).
49
See the Financial Stability Board (2013, 39) and the O¢ ce of Financial Research
(2013, 16) for a discussion of similar concerns.
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 221
Table 4 AGNC Balance Sheet and Hedges
Assets
Fixed
ARM
CMO
TBA
Cash
Total
Liabilities and Hedges
Liabilities
Liabilities (Other)
Swaps
Preferred
Swaptions
Treasury/Futures
Total
Net Duration Gap
Market Value
74.8
0.8
0.7
27.3
3.3
106.9
Market Value/Notional
66.3
0.9
51.3
0.2
22.9
13.6
Duration
4.2
1.8
6.7
4.4
0.0
4.1
Duration
0.3
7.0
4.5
8.4
1.9
6.8
3.6
0.5
Notes: CMO balance includes interest-only, inverse interest-only, and principalonly securities; “Liabilities (Other)” represents other debt in connection with the
consolidation of structured transactions under generally accepted accounting principles; the “Net Duration Gap” is derived from the weighted duration of assets
and liabilities and is not calculated by simply summing the various durations
listed here.
Source: American Capital Agency Group, Investor Presentation, June 12, 2013,
p. 24.
Observers have also noted that mREITs are important suppliers of
MBS collateral to the tri-party repo market, and that rapid mREIT
sales of MBS could have negative e¤ects on this market (O¢ ce of Financial Research 2013, 16). Presumably, the concern here is that the
withdrawal of this collateral from the market could impede the smooth
functioning of the tri-party market and perhaps reduce the ability of
other tri-party-dependent borrowers to raise funds in the tri-party market. Still, this could only be a problem if the buyers of the MBS that
are being sold by mREITs tend to hold these MBS in portfolio, rather
than themselves returning them to the tri-party market in repo loan
transactions.50
50
Some observers refer to this as a reduction in “collateral velocity.” See Singh
(2011) for more information on collateral velocity.
Sources: Respective 2012 10K/10Qs, Richmond Fed.
Federal Reserve Bank of Richmond Economic Quarterly
Notes: As of December 31, 2012. Short-term leverage is de…ned as the amount of repurchase agreement liabilities
as a ratio of equity. Leverage ratios below 6 are in blue. Swap ratios above 50 percent are in blue with the red
text and below 50 percent is in pink with light blue text. NIM are from the SNL Financial (Financial Highlights)
for 2012:Q4. Year-end measures are used instead of 2012:Q4 if no 2012:Q4 estimate is provided.
222
Table 5 mREITS|Financial Highlights
Pellerin, Sabol, and Walter: MBS Real Estate Investment Trusts 223
Regardless of such systemic concerns, and the various risks faced
by mREITs (interest rate, prepayment, credit, and liquidity risks), the
mREIT industry seems to have weathered recent stresses reasonably
well. During the crisis of 2007 and 2008 only two mREITs failed, both
of which invested primarily in non-agency MBS, and the industry as a
whole produced fairly consistent earnings through the crisis (see Figure
5). In the years following the crisis, short- and long-term interest rates
had been consistently falling or ‡at until long-term rates bottomed out
in mid-2012 and then, beginning in May 2013 increased rapidly through
the summer (10-year Treasury rate increased from 1.70 percent in May
to 2.92 percent in September). One might expect that such an increase
would lead to signi…cant MBS sales by mREITs, and that such sales
could have an impact on MBS interest rates. Indeed mREITs did sell
following the rate increase and interest rates on MBS rose over this
period. However, it is not clear that mREIT sales ampli…ed interest
rate increases. Surprisingly, given mREITs’heavy reliance on leverage
and signi…cant maturity mismatch, mREITs don’t seem to have reacted
as strongly to rising interest rates as some other players. As illustrated
in Figure 1, mREITs’ repo borrowings only account for about onequarter of the decline of dealer-provided MBS repo funding, indicating
that other parties reduced their MBS repo funding even more, and
likely sold even more MBS.
6.
CONCLUSION
Policymakers, the press, and other observers have raised concerns about
possible systemic risks that may ‡ow from mREITs, especially given
the speed with which they have grown over the last …ve years. mREITs
invest heavily in MBS, a long-term asset, and fund these investments
largely with term repo, a fairly short-term liability.
Clearly investors in mREITs have reason to be concerned given
that this asset-liability mix leaves mREITs critically exposed to interest
rate risk. In fact, recent interest rate increases have caused mREITs to
shrink and have produced signi…cant declines in mREIT stock prices.
Still, the danger to the …nancial system more broadly is less clear.
For one thing, interest rates would need to increase signi…cantly and
rapidly to cause widespread mREIT insolvencies. Additionally, mREITs’share of all MBS outstanding, while not insigni…cant, is only about
6 percent as of December 31, 2012 (Securities Industry and Financial
Markets Association 2011; Table 5), so that any problems at mREITs
would have to be magni…ed by counterparty actions in order to produce
system-wide problems.
224
Federal Reserve Bank of Richmond Economic Quarterly
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Economic Quarterly— Volume 99, Number 3— Third Quarter 2013— Pages 229–250
Does Intra-Firm Bargaining
Matter for Business Cycle
Dynamics?
Michael U. Krause and Thomas A. Lubik
W
e analyze the aggregate implications of intra-…rm bargaining
in a fully ‡edged, yet simple, general equilibrium business
cycle model with search and matching frictions in the labor
market. The notion and relevance of intra-…rm wage bargaining in such
a setting was introduced to the labor economics literature in a classic
article by Stole and Zwiebel (1996).1 The central idea is that a …rm
is a web of bargaining relationships between its factors of production,
or more narrowly and speci…cally, between the owners of the …rm and
the workers it employs. Under the assumption that labor contracts
are nonbinding, that is, workers can quit any time and …rms can lay
o¤ workers at will, wage determination can therefore be understood
as an ongoing bargaining process within the …rm. Before production
takes place, and within a time period, both workers and the …rm can
revisit an existing wage negotiation. As Stole and Zwiebel (1996) have
demonstrated, this intra-…rm bargaining has implications for allocations whenever the scale of the …rm changes non-linearly with its labor
input. In this case, marginal revenue depends explicitly on the number of workers employed, which changes the incentives for a …rm in a
noncooperative bargaining setting. In particular, it leads to over-hiring
We are grateful for useful comments by Marios Karabarbounis, Christian Matthes,
and Robert Sharp. The views expressed in this article are those of the authors
and should not necessarily be interpreted as those of the Federal Reserve Bank of
Richmond or the Federal Reserve System. E-mail: michael.krause@wiso.uni-koeln.de;
thomas.lubik@rich.frb.org.
1
Their article takes inspiration from and shares many features with the seminal
article by Jensen and Meckling (1976) on the theory of the …rm from an organizational
design perspective.
230
Federal Reserve Bank of Richmond Economic Quarterly
compared to an environment where intra-…rm bargaining does not play
a role.
This idea has bearing for macroeconomic models that incorporate
search and matching frictions in the labor market. Intra-…rm bargaining is not an issue in the standard search and matching model of Shimer
(2005), which uses the assumption of one-worker one-…rm matches such
that the scale of the …rm is independent of the labor input. However, in
frameworks that incorporate concave production and downward-sloping
demand,2 such as in the New Keynesian search and matching model of
Krause and Lubik (2007), intra-…rm bargaining would have to be taken
into account through its e¤ect on steady-state allocations and business
cycle dynamics.
In this article, we thus demonstrate by means of a simple search
and matching model how intra-…rm bargaining implies a feedback effect in the bargaining process from a …rm’s marginal product to wage
setting. The …rm has an incentive to increase production in order to
decrease the marginal product, and thus the wages of existing employees, in order to capture higher rents. In e¤ect, the …rm reduces the
bargaining position of the marginal worker by over-hiring. This partial
equilibrium scenario, however, implies a general equilibrium feedback
e¤ect in that it leads to an expansion in production and thus a higher
surplus to be shared among more workers. With a tighter labor market,
the additional hiring of …rms improves the outside options of workers
and thus raises their wage in general equilibrium.
The main contribution of this article lies in the analysis of business cycle dynamics in addition to the above steady-state e¤ects. It is
motivated by the observation that these feedback e¤ects are not taken
into account in many business cycle models that incorporate search
and matching frictions, which may raise concerns as to the robustness
of their results. When compared to a speci…cation that neglects intra…rm bargaining, we …nd that the dynamic response of the economy to a
productivity shock is barely a¤ected. The response of unemployment is
slightly magni…ed, depending on the degree of returns to scale and the
elasticity of demand. Similarly, employment and vacancies rise slightly
more than without taking intra-…rm bargaining e¤ects into account. In
this respect, intra-…rm bargaining plays a role as the bargaining position of workers improves by less than is mandated by the rise in labor
market tightness. However, intra-…rm bargaining does not a¤ect the
2
Intra-…rm bargaining under concave production has previously been studied by
Smith (1999), Cahuc and Wasmer (2001), Cahuc, Marque, and Wasmer (2008), and
Rotemberg (2008). The implications of downward-sloping demand schedules have been
analyzed by Ebell and Haefke (2003) and also Rotemberg (2008).
M. U. Krause and T. A. Lubik: Intra-Firm Bargaining
231
qualitative response of the economy and an overall e¤ect on output is
virtually nonexistent.
We interpret our …ndings to the e¤ect that, in many circumstances,
researchers may safely ignore intra-…rm bargaining even when analyzing business cycle models with large …rms that face decreasing returns
or downward-sloping demand. This is not meant to imply that there
may not be important and interesting e¤ects on the steady state of
a model. This has been explored, for example, by Ebell and Haefke
(2003). However, if we falsely calibrate a model without this strategic feedback on wages to actual data where it is present, the mistake
we make is likely to be small. We therefore conclude that intra-…rm
bargaining is not the driving force of signi…cant cyclical dynamics.
The article closest to ours conceptually is Rotemberg (2008), who
incorporates intra-…rm bargaining issues in a New Keynesian model
with search and matching frictions. While he conducts a quantitative
analysis, it is based on comparative statics around the steady state. In
contrast, we perform a full calibration-based business cycle analysis,
where we attempt to match the key labor market stylized facts. Cahuc
and Wasmer (2001) and Cahuc, Marque, and Wasmer (2008) are similar
in spirit in that they work out in detail qualitatively how the partial
equilibrium e¤ects of intra-…rm bargaining have general equilibrium
feedback. They work with a continuous-time framework, whereas we
use a discrete-time setting that is common in business cycle literature.
More recently, Hertweck (2013) provides independent quantitative and
qualitative evidence in a model with strategic wage bargaining that
intra-…rm bargaining e¤ects are negligible for aggregate dynamics.
In the rest of the article we proceed as follows. We …rst provide a
simple static example to develop some intuition about the implications
of intra-…rm bargaining. The subsequent section outlines the model
under the assumption of decreasing returns to labor and matching frictions in the labor market. This allows us to disentangle the relevant
e¤ect without much complexity. We then add general equilibrium constraints, calibrate the model, and proceed to analyze the steady state
and business cycle implications graphically and numerically. In Section
5, we discuss the similarities of the results to the case of monopolistic
competition, and show the robustness of our …ndings to its inclusion
alongside decreasing returns. The …nal section concludes and highlights
some further connections to the literature.
232
1.
Federal Reserve Bank of Richmond Economic Quarterly
THE SIMPLE INTUITION OF
INTRA-FIRM BARGAINING
The gist of our analysis can be illustrated by means of a simple static
example that abstracts from search and matching frictions. Consider
a simple bargaining problem of a large …rm that negotiates with each
worker individually. Employed workers bargain over the wage w, with
their outside option being unemployment that generates bene…ts b.
The …rm’s bargaining position is given by the surplus that an additional
worker generates, net of its outside option, which is the value of leaving
the job un…lled. This outside option is zero.
Let the …rm’s price be p and its output y. The …rm pays wage w
and employs n workers. Its value is given by its revenue minus cost,
which consists of the wage bill and the hiring cost:
V = py
wn:
(1)
Consider value maximization with respect to employment:
@p
@y
@V
=
y+p
@n
@y
@n
|
{z
}
mr
@w
n+w ;
@n
|
{z
}
(2)
mc
where we allow for the price to depend on output, which in turn depends
on labor input. This covers the cases of downward-sloping demand and
concave production. Moreover, we take into account that the wage
schedule depends on the level of employment, which is the source of
the intra-…rm bargaining problem. The …rst term in the brackets on
the right-hand side would not be present if the …rm were a price taker
in the product market; without concavity in the production function,
the partial derivative @y=@n would be independent of employment. If
the …rm were a price taker in the labor market, the …rst term in the
second brackets would be absent. It would equal zero when …rms can
only hire one worker, or when the …rm does not internalize the feedback from its employment choice to the wage schedule. The value of a
marginal worker is therefore the di¤erence between marginal revenue
and marginal cost, mr(n) mc(n), which we indicate as depending on
the level of employment.
In a standard search and matching framework, wages are typically
determined using the Nash bargaining solution, which maximizes the
weighted product of the involved parties’surpluses. Given a worker’s
bargaining weight , the solution would be
w
b=
1
[mr(n)
mc(n)] .
(3)
M. U. Krause and T. A. Lubik: Intra-Firm Bargaining
233
Inserting the marginal cost term and taking account of the dependence
of the wage on employment yields
@w(n)
w(n) =
mr(n)
n + (1
)b:
(4)
@n
The wage is a weighted average of the …rm’s marginal revenue and
the worker’s outside option. The second term in brackets captures
the e¤ect from intra-…rm bargaining. Marginal revenue is adjusted for
the feedback of the employment choice on the wage, which in turn
a¤ects the optimal number of employees.3 Stole and Zwiebel (1996)
have shown that this prompts the …rm to over-hire. This feedback
e¤ect crucially relies on the assumption that the …rm’s marginal revenue
function is not independent of employment. Otherwise, as in the basic
one-worker one-…rm setup of Pissarides (2000) or Shimer (2005), the
wage would not depend on n as mr(n) = p, for all n, and the …rm would
have no incentive to strategically adjust its marginal revenue schedule
since hiring an additional worker would have no e¤ect (Smith 1999).
2.
A BUSINESS CYCLE MODEL WITH SEARCH
FRICTIONS AND INTRA-FIRM BARGAINING
We now embed the above mechanism in a simple model in which production is characterized by decreasing returns to labor and …rms are
large in the sense that they employ multiple workers. This contrasts
with the standard search and matching framework in which production
originates in one-worker one-…rm pairs. We assume an economy with
a continuum of …rms that use labor as the only input in production.
The production function of a typical …rm is given by
y t = At n t ;
(5)
where 0 <
1, and At is a stochastic productivity process common to
all …rms; nt is the measure of workers employed by the …rm. We assume
that all …rms behave symmetrically, and consequently suppress …rmspeci…c indices. With the total labor force normalized to one, aggregate
employment is identical to …rm-level employment. Unemployment is
de…ned as
u t = 1 nt :
(6)
The labor market is characterized by search and matching frictions encapsulated in the matching function m(ut ; vt ) = mut vt1 . It
3
This expression is a partial di¤erential equation that we can solve under parameteric assumptions for the marginal revenue function. We will demonstrate that the
solution implies a wage schedule that in equilibrium scales the marginal revenue component of the wage schedule.
234
Federal Reserve Bank of Richmond Economic Quarterly
describes the outcome of search behavior of …rms and workers in that
unemployed job seekers ut are matched with vacancies vt at rate m(ut ; vt )
to produce new employment relationships. 0 < < 1 is the match
elasticity of the unemployed, and m > 0 describes the e¢ ciency of
the match process. Using the de…nition of labor market tightness
t = vt =ut , the aggregate probability of …lling a vacancy (taken parameterically by the …rms) is q( t ) = m(ut ; vt )=vt . The evolution of
employment is then
nt+1 = (1
)[nt + vt q( t )]:
(7)
0 < < 1 is the (constant) separation rate that measures in‡ows into
unemployment.
Firms maximize pro…ts by choosing employment next period and
vacancies to be posted, subject to the …rm-level employment constraint.
This job creation comes at a ‡ow cost c > 0. The Bellman equation is
V(nt ) = max fAt nt
nt+1 ;vt
w(nt )nt
cvt + Et t V(nt+1 )g :
(8)
V( ) is the value of the …rm, t is the time-varying discount factor,
and w(nt ) is the wage schedule, which will be determined below. The
notation indicates that the wage of the marginal worker potentially
depends on the existing number of workers in the …rm. The …rst-order
conditions are
)q( t );
c =
t (1
0
t = Et t V (nt+1 );
(9)
(10)
where t is the Lagrange-multiplier on the employment constraint (7).
The corresponding envelope condition is
@nt+1
@w(nt )
nt + Et t V 0 (nt+1 )
: (11)
@nt
@nt
The presence of the derivative of the wage schedule re‡ects the impact
of intra-…rm wage bargaining. When choosing employment, …rms take
into account how an additional worker a¤ects their bargaining position
and thus wage setting.
We de…ne the value of the marginal job J(nt ) = V 0 (nt ), and rewrite
the envelope condition using @nt+1 =@nt = (1 ) from the law of motion
(7):
V 0 (nt ) = At nt
1
w(nt )
@w(nt )
nt + (1
)Et t J(nt+1 ): (12)
@nt
With constant returns to scale, = 1, the marginal product of labor
is At (the “one-worker one-…rm”case), and the wage is independent of
the …rm’s current employment level. The equation then reduces to the
one in Pissarides (2000).
J(nt ) = At nt
1
w(nt )
M. U. Krause and T. A. Lubik: Intra-Firm Bargaining
235
Combining this with the …rst-order conditions results in a vacancyposting, or job creation, condition:
c
= (1
q( t )
)Et t J(nt+1 );
(13)
which can alternatively be written as
c
= (1
q( t )
c
@w(nt+1 )
nt+1 +
:
@nt+1
q( t+1 )
(14)
To gain some intuition, suppose …rms anticipate an increase in productivity At+1 . This raises the present value of pro…ts and thereby the
marginal bene…t of hiring more workers at given marginal cost c=q( t ).
Other things being equal, more vacancies are posted, and nt+1 is expected to be higher, which, in turn, reduces expected marginal product
of labor until equality is restored.
This adjustment is a¤ected by two additional channels. The …rst
takes place within the …rm, hence the label intra-…rm bargaining.
Adding a worker reduces the e¤ective bargaining power of current workers and thus their wage. Assuming Et @w(nt+1 )=@nt+1 < 0, which we
will show below to be true, this ampli…es the incentive to post vacancies
and employment increases further. In order to determine the quantitative signi…cance of this e¤ect, we need to solve for the equilibrium
wage schedule w(nt ); which is done below. The other channel is a feedback e¤ect that arises in general equilibrium. As all …rms post more
vacancies, aggregate vacancies increase, the labor market tightens, and
it becomes more costly to recruit additional workers with the rise in
c=q( t ). Therefore, employment in each …rm increases by less than it
would if t were constant.
)Et
t
At+1 nt+11
w(nt+1 )
Determining the Wage Schedule
Wages are determined based on the Nash bargaining solution: Surpluses accruing to the matched parties are split according to a rule
that maximizes the weighted average of the respective surpluses. Denoting the workers’weight in the bargaining process as 2 [0; 1], this
implies the sharing rule
Wt
Ut =
1
Jt ;
(15)
236
Federal Reserve Bank of Richmond Economic Quarterly
where Wt is the asset value of employment, Ut is the value of being
unemployed, and Jt is, as before, the value of the marginal worker to
the …rm.4
The value of employment to a worker is described by the following
Bellman equation:
Wt = wt + Et t [(1
)Wt+1 + Ut+1 ]:
(16)
Workers receive the wage wt , and transition into unemployment next
period with probability . The value of searching for a job, when
currently unemployed, is
Ut = b + Et t [ft (1
)Wt+1 + (1
ft (1
))Ut+1 ]:
(17)
An unemployed searcher receives bene…ts b and transitions into employment with probability ft (1
). The job …nding rate ft is de…ned
as f ( t ) = t q( t ) = m(ut ; vt )=ut ; which is increasing in tightness t . It
is adjusted for the probability that a completed match gets dissolved
before production begins next period.
We substitute these equations into the sharing rule (15) and, after
some algebra, …nd the wage equation
w(nt ) =
A t nt
@w(nt )
nt + c
@nt
1
+ (1
t
)b:
(18)
Because of the presence of the derivative of the wage schedule on account of intra-…rm bargaining, this is a …rst-order di¤erential equation,
the solution of which is
w(nt ) =
1
(1
)
At nt
1
+ c
t
+ (1
)b:
(19)
The derivative with respect to employment is given by
@w(nt )
=
@nt
(1
1
)
(1
)
At n t
2
< 0;
(20)
which, when inserted into (18), veri…es the validity of the solution.
For given employment, intra-…rm bargaining increases the wage by
virtue of the scale factor 1= [1
(1
)] > 1. The addition of a
worker to the workforce implies a higher value to the …rm as it lowers
the marginal product of all incumbent workers. A new worker has
therefore a higher value to the …rm than just his marginal product
because he contributes to lowering the …rm’s wage bill. By the logic of
bargaining, the surplus is split, and workers get their share in terms of a
higher wage. However, for the very reason that adding workers reduces
4
In models with one-worker …rms, the net surplus of a …rm is usually given by
Jt Vt ; with Vt the value of a vacant job. By free entry, Vt is then assumed to be
driven down to zero.
M. U. Krause and T. A. Lubik: Intra-Firm Bargaining
237
the wage bill, …rms post more vacancies to increase employment. This
lowers the marginal impact of adding workers, which falls in nt . Thus,
workers’ marginal product declines with employment and hence their
wage. Equation (19) gives the overall e¤ect of the declining marginal
product on the wage, corrected for intra-…rm bargaining.5
The wage schedule can be used in the job creation condition (14)
to yield
"
#
(1 )
1
A
n
c
c
t+1
t+1
t+1
= (1
)Et t 1 (1 )
:
(21)
c
(1
)b + q( t+1
q( t )
)
1
The e¤ects of intra-…rm bargaining are captured by the term [1 (1
)] ;
which re‡ects the …rm’s internalization of the feedback from employment on the wage. It exerts a level e¤ect in that the marginal bene…t
from adding workers is perceived to be higher. This induces more job
creation. For the case of constant returns,
= 1, the equation collapses to the usual form, and intra-…rm bargaining is irrelevant. However, our argument has so far relied on partial equilibrium reasoning
from the perspective of the …rm. We will analyze the general equilibrium feedbacks both on the steady-state allocation and on the model’s
adjustment dynamics below.
Wage Determination without
Intra-Firm Bargaining
We assume from the outset that …rms internalize the dependence of the
wage schedule on employment (see [8] and [11]). This allows them to
act strategically and extract rents from workers. Alternatively, assume
that …rms behave myopically by taking the wage of their incumbent
workforce as given when choosing employment. This amounts to setting
@wt =@nt = 0 in the …rms’problem. In this case, the value function of
the …rm is
J(nt ) = At nt
1
wt + (1
)Et t J(nt+1 ):
(22)
Following the same steps as outlined above, we …nd the corresponding
wage equation
wt =
At nt
1
+ c
t
+ (1
)b;
(23)
5
In a sense, this setup can be interpreted from the perspective of insider-outsider
theory: Firms are willing to expand employment and incur vacancy costs in order to
reduce the bargaining power of insiders. What is crucial is that incumbents’ wages are
not protected by long-term contracts but are constantly renegotiated. The term “bargaining power” is of course used loosely in the sense that the Nash bargaining parameter
is …xed.
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Federal Reserve Bank of Richmond Economic Quarterly
and the job creation condition
c
= (1
q( t )
)Et
t
(1
) At+1 nt+11
c
t
(1
)b +
c
q(
t+1 )
:
(24)
When comparing the two job creation conditions, the only algebraic
di¤erence is the term multiplying the marginal product of labor, namely
(1 ) < (1 )=[1 (1
)]. Intra-…rm bargaining scales the marginal
product of labor and thereby introduces an additional incentive for
vacancy posting. The wage equations and job creation conditions under
both scenarios will be the reference points from which we evaluate the
general equilibrium e¤ects of intra-…rm bargaining.
Closing the Model
We assume that all workers belong to a representative household that
insures its members perfectly against income risk implied by the two
states of employment and unemployment. By means of a complete
internal asset market, incomes are pooled in such a way that all households choose the same level of consumption.6 Assuming a CRRA-utility
function for the household, we can thus construct an implied stochastic
discount factor
t
=
ct+1
ct
;
(25)
which …rms use to evaluate future revenue streams. 0 < < 1 is the
household’s subjective discount factor, and > 0 is the intertemporal elasticity of substitution; ct is the household’s consumption, which
draws from production as described by the social resource constraint
ct = yt
cvt :
(26)
Total hiring costs cvt are subtracted from gross production as resources
are lost in the search process.
3.
THE GENERAL EQUILIBRIUM EFFECTS OF
INTRA-FIRM BARGAINING
This simple search and matching model with concave production provides a laboratory for analyzing the qualitative and quantitative e¤ects
of intra-…rm bargaining. We proceed in two steps. We …rst compute
6
This assumption is standard in the literature following Merz (1995) and
Andolfatto (1996). Note that the unemployed enjoy a higher level of utility than the
working since they do not su¤er the disutility of working.
M. U. Krause and T. A. Lubik: Intra-Firm Bargaining
239
the model’s steady state and compare allocations across the two wagesetting assumptions. This discussion parallels the results in Cahuc and
Wasmer (2001). In the second step, we study the dynamic behavior of
the model and the implications for business cycle statistics.
In order to …x a baseline for the model’s quantitative analysis, we
calibrate the parameters to typical values found in the literature.7 We
set the discount factor = 0:98 and choose = 1. The mean of the
technology process At is normalized to one. We assume that the input
elasticity
= 32 , which is roughly the labor share in U.S. aggregate
income. The separation rate is …xed at a value of = 0:1, which is
a midpoint of the range of values used in the literature. The match
elasticity is calibrated at 0:4 based on the empirical estimates in
Blanchard and Diamond (1989), while the match e¢ ciency parameter
m = 0:4 is chosen to generate an unemployment rate of roughly 8
percent to 10 percent for the di¤erent model speci…cations. To be
consistent with this, we …x vacancy creation costs c at 0:1. The bene…t
parameter b, which captures the outside option of the worker, is set to
0:4 as in Shimer (2005). Finally, the Nash bargaining parameter is set
at = 0:5.8
Steady-State E ects
The model’s …rst-order conditions can be reduced to a two-equation
system in unemployment u and vacancies v. The …rst equation is the
Beveridge curve, and is derived from the employment accumulation
equation (7) in steady state, after substituting the expression for the
…rm-matching rate q( ) and unemployment n = 1 u. After rearranging, this results in a relationship between v and u:
v=
(1
(1
u)
)mu
1
1
u:
(27)
It is straightforward to show that this relationship is downward-sloping
and concave in v-u space.
The second steady-state relationship is derived from the job creation condition (21). Substitution and rearrangement results in the
7
A more detailed discussion of the calibration of a closely related model can be
found in Krause and Lubik (2007).
8
Note that this violates the e¢ ciency condition in Hosios (1990). We do not regard
this as restrictive for our purposes since, as Cahuc and Wasmer (2001) have shown, the
e¢ ciency condition is modi…ed under intra-…rm wage bargaining. Moreover, we are not
explicitly concerned with welfare considerations. Tripier (2011) discusses the implications
of intra-…rm bargaining on e¢ ciency grounds in a model with hiring and training costs.
He …nds that intra-…rm bargaining internalizes the thus created externalities.
240
Federal Reserve Bank of Richmond Economic Quarterly
Figure 1 The Steady-State E ects of Intra-Firm Bargaining
following expression:
1 (1
) c v
(1
)
=
A (1
(1
)
m u
1
(1
)
u)
1
c
v
u
(1
)b;
(28)
for which no closed-form solution in terms of v is available. We note,
however, that this equation de…nes the steady-state value of = v=u,
so that this is a linear function in v-u space, namely v =
u. Consequently, the two curves intersect once, so that the model delivers a
unique steady-state equilibrium. We solve the steady-state job creation
condition numerically for our baseline calibration.9 The two curves determining the steady state are depicted in Figure 1. The graph also
contains the job creation curve that neglects the feedback from intra…rm bargaining, which is derived from (24).
Steady-state equilibrium is at the intersection of both curves, which
yields an unemployment rate of 8:5 percent. Without intra-…rm bargaining, the job creation schedule is ‡atter and tilts downward,
9
See Lubik (2013) for further discussion of the simple analytics of the search and
matching model.
M. U. Krause and T. A. Lubik: Intra-Firm Bargaining
241
Figure 2 Wage Determination in Steady State
resulting in steady-state unemployment of 10 percent. This con…rms
the result by Stole and Zwiebel (1996), subsequently re…ned by Cahuc
and Wasmer (2001), Ebell and Haefke (2003), and Cahuc, Marque, and
Wasmer (2008), that intra-…rm bargaining leads to over-hiring. Firms
have an incentive to add more employees since the wage paid to all
workers is declining in employment. This e¤ect is mitigated by the
feedback that hiring has on unemployment, as it raises labor market
tightness and thus marginal hiring costs c=q( ). Overall, the levels
of vacancies and employment are higher in the intra-…rm bargaining
case since …rms can generate higher surplus by diluting the e¤ective
bargaining power of their workers.10
The same reasoning can be illustrated with an alternative description of the steady state. We use the Beveridge curve to substitute
out n in the wage equation (19), from which we derive a relationship
10
The underlying mechanism is not a labor supply e¤ect in the traditional sense,
which would require increases in the wage in order to attract additional workers. More
searchers …nd employment since the increase in vacancy postings increases labor market
tightness, and thus increases the job-…nding rate, which is enough to compensate the
marginal unemployed worker for the lower wage rate.
242
Federal Reserve Bank of Richmond Economic Quarterly
between w and , labeled the “wage curve.” The job creation condition can be rewritten in a similar way. Both schedules are depicted
in Figure 2. We also plot the two schedules for the speci…cation in
which intra-…rm bargaining is neglected. The graph shows that both
wage and tightness are lower compared to the baseline with intra-…rm
bargaining.11 Recall that, for given labor market tightness , higher
employment allows a …rm to reduce wages paid to workers and to increase overall pro…ts. However, when all …rms act in this manner, labor
market tightness rises both due to more vacancy postings and a decline
in unemployment. The overall e¤ect on the wage is positive, so that
intra-…rm bargaining raises wages in general equilibrium, which Figure
2 illustrates.
Adjustment Dynamics and Business Cycle Statistics
We now turn to an analysis of the e¤ects of intra-…rm bargaining on
the dynamic properties of the model. In order to do so, we linearize
both the baseline speci…cation and the model that neglects intra-…rm
bargaining around their respective steady states. Strictly speaking,
this analysis con‡ates two e¤ects: the di¤erences in steady state, and
the di¤erences in the coe¢ cients in the dynamic model. It is quite
conceivable that models with identical steady states can have di¤erent dynamic properties. Similarly, di¤erences in responses (which are
themselves measured in percentage deviations from the steady state)
have to be interpreted with care as they are relative to di¤erent steady
states. This implied error in our framework is likely to be small since
the di¤erences in steady states are small.12
The resulting linear rational expectations models are solved using
standard techniques. We …rst compare dynamic adjustment paths toward the steady state after a productivity disturbance. Second, we
contrast their predictions for business cycle statistics based on simulated data. In order to describe the stochastic properties of the
model we have to calibrate the technology process. We assume that
11
Since both schedules are a¤ected under the di¤erent speci…cations, it may be
conceivable that, say, the wage increased or decreased. Analytically, the schedules with
and without IFB di¤er by a factor of 1= [1
(1
)] that multiplies the marginal product of labor An 1 . The schedules thus shift both in the same direction. It is only
for very small values of
that such a reversal can occur.
12
The conceptual background we have in mind is that a researcher might ask how
much of an error he commits when neglecting intra-…rm bargaining. The reason for this
neglect might be di¢ culty in solving di¤erential equations of the type (18), and the
possibly burdensome underlying …rst-order conditions. Alternatively, a researcher may
be interested in exploring the implications of myopic behavior by …rms that ignores the
strategic incentives to expand employment.
M. U. Krause and T. A. Lubik: Intra-Firm Bargaining
243
Figure 3 The Dynamic E ects of Intra-Firm Bargaining
Notes: Impulse responses to a 1 percent productivity shock. Solid lines refer to
the baseline, and dashed lines refer to the model without intra-…rm bargaining.
productivity At follows an AR(1) process with autoregressive coe¢ cient
A = 0:90, and that it is driven by a zero mean innovation "t with variance 2" = 0:0072 . This value is chosen to replicate the observed U.S.
gross domestic product (GDP) standard deviation of 1:62 percent.
The impulse response functions for both speci…cations are depicted
in Figure 3. Two observations stand out immediately. First, the model
exhibits an almost complete lack of internal propagation. The behavior
of GDP follows virtually in its entirety the adjustment path of the productivity process. This observation has been emphasized by Krause
and Lubik (2007) and is a corollary to the Shimer (2005) argument
that the standard search and matching model is unable to replicate
the volatility of unemployment and vacancies. Second, and more importantly for our discussion, the responses are remarkably similar in
terms of shape, size, and direction. A persistent 1 percent increase in
productivity raises current production and future marginal products
of labor. This raises the value of jobs, and thus vacancies posted, per
244
Federal Reserve Bank of Richmond Economic Quarterly
Table 1 Business Cycle Statistics
u
Intra-Firm Bargaining
Neglecting Intra-Firm Bargaining
U.S. Data
Standard Deviations
v
w
0.78
0.68
6.90
0.95
0.84
8.27
u
1.00
v
0.58
1.00
1.55
1.36
14.96
y
0.98
1.02
0.69
1.62
1.62
1.62
w
0.84
0.92
0.99
1.00
y
0.86
0.91
0.99
0.99
1.00
Correlations
u
v
w
y
0.85
0.91
1.00
the job creation condition (21). This leads to increased employment
in the following period (see equation [7]). Workers experience a rise in
wages on account of higher productivity and labor market tightness.
However, wages rise by less than productivity because of the strategic
hiring decisions by …rms. Thus, intra-…rm bargaining does not change
the basic dynamics of search and matching, but it (slightly) modi…es
its strength.
We also compare business cycle statistics computed from simulations of the two model speci…cations. The results are reported in Table
1. The baseline model is calibrated so as to replicate the standard deviation of U.S. GDP; the standard deviations of all other variables are
then measured relative to this value. The overall impression is that the
cyclical properties of the model with and without intra-…rm bargaining
are virtually identical. There is no di¤erence in the behavior of output,
which has already been apparent from the impulse response functions.
However, when intra-…rm bargaining is neglected, unemployment, vacancies, and tightness are roughly 10 percent less volatile than in the
baseline case. When compared to the corresponding business cycle
facts for the U.S. economy, both models fall woefully short: The latter
statistics are o¤ by a factor of 10, and the wage is 50 percent more
volatile than in the data.
In terms of contemporaneous correlations, both speci…cations
produce identical results. The models are reasonably successful in
matching unemployment correlations. A benchmark statistic is the
correlation between unemployment and vacancies. The model-implied
value of 0:58 is not too far away from the value in U.S. data of 0:95.
However, the models produce perfect correlation between the wage, ,
M. U. Krause and T. A. Lubik: Intra-Firm Bargaining
245
and output, which is inconsistent with the data. Overall, these results support the impression that a model with intra-…rm bargaining
is essentially observationally equivalent to one without. An empirical,
likelihood-based test of both speci…cations would …nd it very di¢ cult
to distinguish between the two alternatives as they exhibit identical comovement and only minor di¤erences between variable-speci…c volatilities. While intra-…rm bargaining is a conceptually compelling idea,
and quite conceivably relevant at the …rm level, we conclude that it
does not have a signi…cant e¤ect on aggregate dynamics.
4.
MONOPOLISTIC COMPETITION AND
INTRA-FIRM BARGAINING
An alternative source of declining marginal revenue is downward-sloping
demand in an environment with monopolistically competitive …rms.
Even with linear production, …rms would feel compelled to expand hiring since they can capture rents by moving down the demand curve.
The assumption of price-setting monopolistic competitors has been
used, for instance, in New Keynesian models of output and in‡ation
dynamics with search and matching in the labor market. Key examples
are Krause and Lubik (2007) and Trigari (2009).
We assume that output of a representative monopolistically competitive …rm is linear in labor, yt = At nt , and that each …rm faces a
downward-sloping demand function for the product variety it produces,
yt = (pt =pt ) Yt , where Yt is aggregate demand, and pt is the aggregate price level, both taken as given by the …rm; > 1 is the elasticity
of substitution between competing varieties, and pt is the individual
…rm’s price. The …rm’s real revenue is then given by
pt
pt
1
y t = At
1
Yt nt
1
:
(29)
The asset equation for the value of a marginal job can be derived following the same steps as before:
J(nt ) =
1
1
At
1
1
1
Yt nt
w(nt )
@w(nt )
nt + (1
@nt
)Et t J(nt+1 ):
(30)
Note that despite linear production, marginal revenue responds to
changes in employment, which opens the possibility of intra-…rm
bargaining.
The asset equation for workers remains unchanged, and so does the
sharing rule. We can consequently derive a wage equation as before:
w(nt ) =
1
1
At
1
Yt nt
1
@w(nt )
nt + c
@nt
t
+ (1
)b:
(31)
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Federal Reserve Bank of Richmond Economic Quarterly
The solution to this di¤erential equation is
1
w(nt ) =
1
1
1
(1
)
At
1
1
Yt nt
+ c
t
+ (1
)b:
(32)
It is straightforward to verify that this expression corresponds to the
1
.
wage equation (19), derived under concave production, if
=
However, this neglects the general equilibrium feedback e¤ect from the
aggregate demand condition, captured by Yt , which both parties in the
bargaining process take as given. Substituting Yt = yt = At nt , i.e.,
assuming a symmetric equilibrium, results in
1
wt =
1
=
At + c
t
+ (1
)b:
(33)
The aggregate wage equation is now independent of employment (on
account of constant returns in production), but the feedback e¤ect from
intra-…rm bargaining modi…es the productivity coe¢ cient. If intra-…rm
1
bargaining is neglected, this coe¢ cient is 1 < 1 = .
This wage equation can be used to derive the job creation condition,
which closely parallels (21):
"
#
(1
) 1
c
c
= (1
)Et t
At+1
c t+1 (1
)b +
:
q( t )
1
=
q( t+1 )
(34)
Since the employment equation (7) is una¤ected by the presence of
monopolistic competition, we can describe the steady-state solution by
references to Figures 1 and 2. In the former graph, the shape of the
curves is una¤ected, there is a unique equilibrium, and intra-…rm bargaining results in over-hiring as the job creation curve tilts downward
when intra-…rm bargaining is neglected. Similarly, the steady-state relationships depicted in Figure 2 remain the same qualitatively. In the
literature, the substitution elasticity is often calibrated with a value
of 11, which implies a steady-state markup of 10 percent. Given our
baseline speci…cation with = 0:5, the intra-…rm bargaining feedback
coe¢ cent is 1=(1
= )
1:05, which is negligible with respect to
steady-state values and dynamics.
5.
A FINAL GENERALIZATION
Concave production and downward-sloping demand do not produce
substantial e¤ects of intra-…rm bargaining on their own for plausible
calibrations. We therefore combine both elements from before in the
simple search and matching framework. Following the steps outlined
earlier, the wage equation that takes into account the feedback from
M. U. Krause and T. A. Lubik: Intra-Firm Bargaining
247
Table 2 Intra-Firm Bargaining: Robustness
= 0:5
= 2=3
" = 11
1.25
0.92
Scale Factor
Employment w/ IFB
Percent Increase due to IFB
Employment
Wage
Standard Deviation of
Relative to Output
Percent Increase due to IFB
= 0:9
= 2=3
"=2
1.50
0.88
= 2=3
"=2
2.50
0.73
= 1=2
"=2
3.08
0.72
3.7
30.6
6.0
48.4
35.2
137
41.2
167
1.60
16.8
1.90
35.7
0.55
52.8
0.53
60.6
intra-…rm bargaining is
1
wt =
1
1
1
At nt
1
+ c
t
+ (1
The job creation condition is
2
1
(1 )
1
c
c
1 At+1 nt+1
1
1
(
)
= (1
)Et t 4
c
q( t )
(1
)b + q( t+1
)
)b:
t+1
3
5:
(35)
(36)
The speci…cation without intra-…rm bargaining results in the same
equations, the di¤erence being the denominator of the term
pre-multiplying the marginal product of labor. The scale factor that
measures the feedback from intra-…rm bargaining is now 1 1 1 1 .
)
(
This factor is increasing in , decreasing in , and decreasing in ".
In other words, intra-…rm bargaining a¤ects steady-state allocations
and business cycle dynamics more in economies in which workers enjoy
higher bargaining power (large ), the labor share of income is small
(low ), and markets are not very competitive (low ").13
We illustrate the role of intra-…rm bargaining in the extended model
by a few numerical examples, which are reported in Table 2. We compute various model statistics for variations of the parameters a¤ecting
the scale factor. In particular, we contrast our baseline calibration
with a high worker bargaining parameter ( = 0:9), a lower labor share
( = 0:5), and inelastic demand (" = 2). We …rst note that for an
extreme parameterization, shown in the right-most column, the scale
13
This reasoning underlies Ebell and Haefke’s (2003) …nding that product market
deregulation can have substantial employment and welfare e¤ects. In fact, their implied
values for the substitution elasticity is " = 3.
248
Federal Reserve Bank of Richmond Economic Quarterly
factor goes up to 3, compared to a baseline of 1:25. That this implies
stronger e¤ects of intra-…rm bargaining is con…rmed by the percentage
increase of steady-state employment and wage over the case when intra…rm bargaining is neglected, as the percentage change is monotonically
related to the scale factor. For baseline bargaining power, the change in
employment is, however, fairly small, but more substantial for wages.
With higher worker bargaining power, these numbers increase dramatically. What the percentages hide, however, are the actual steady-state
levels. The second row in the table shows that employment actually
falls with increases in the scale factor.
An increase in the scale factor also has a monotonic e¤ect on the
percentage change in the standard deviation of labor market tightness.
For a given parameterization, the inclusion of intra-…rm bargaining improves the predictive power of the model as far as the volatility of key
labor market variables is concerned. However, this scale e¤ect again
masks the fact that with high and low " the standard deviation of
is implausibly low. We conclude that the combination of concave production and downward-sloping demand can increase the strength of the
feedback e¤ect of intra-…rm bargaining. From a pure calibration perspective, there is, however, a tradeo¤ between “maximizing”the intra…rm bargaining e¤ect and the plausibility of key model predictions. For
empirically relevant parameter values, the intra-…rm bargaining e¤ect
still remains negligible as far as business cycle dynamics are concerned.
6.
CONCLUSIONS
Intra-…rm bargaining yields a strategic incentive for …rms to expand
employment in order to weaken their workers’bargaining position. This
increases employment and raises wages in general equilibrium because
lower unemployment and higher vacancies raise workers’ outside options, thereby o¤setting the partial equilibrium e¤ect. While this is a
conceptually compelling story of hiring behavior at a microeconomic
level, we have shown in this article that the aggregate e¤ects of intra…rm bargaining are negligible in a standard search and matching framework with concave production and downward-sloping product demand.
The results in this article should not be taken to imply that we regard intra-…rm bargaining as irrelevant per se. The speci…cation that
combines both sources of declining marginal revenue product shows
that somewhat extreme, but still plausible calibrations can imply large
e¤ects. This raises a few questions for further research. Given aggregate data, do the restrictions implied by intra-…rm bargaining help
with parameter speci…cation? Speci…cally, the bargaining parameter
is di¢ cult to pin down. Furthermore, it is often di¢ cult to …t the
M. U. Krause and T. A. Lubik: Intra-Firm Bargaining
249
behavior of the marginal product of labor, which might be ameliorated
by the inclusion of the scale factor. A related question is to what extent
it is possible to distinguish between the two speci…cations in aggregate
data. Hertweck (2013) contains some e¤ort in this direction using a
structural VAR. A second line of research delves deeper into the production side. Cahuc, Marque, and Wasmer (2008) show that intra-…rm
bargaining has di¤erent e¤ects with capital and heterogenous labor.
Depending on the bargaining power of workers, it may actually lead to
underemployment. Their analysis, however, is restricted to the steady
state only.
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