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Federal Reserve Bank of Chicago

Is the United States an optimum currency
area? An empirical analysis of regional
business cycles

By: Michael A. Kouparitsas

WP 2001-22

Is the United States an optimum currency area?
An empirical analysis of regional business cycles
Michael A. Kouparitsas∗
Federal Reserve Bank of Chicago
P.O. Box 834
Chicago IL 60690-0834
mkoup@frbchi.org
December 2001
Abstract
This paper develops a statistical model to study the business cycles of the eight U.S. BEA
regions. By combining unobserved component and VAR techniques I identify not only common
and idiosyncratic sources of innovation, but also common and idiosyncratic responses to common
shocks. Using this model, I show, at the usual levels of statistical significance, that U.S. regions
deviate significantly from Mundell’s notion of an optimum currency area. I identify five core
regions that have similar sources of disturbances and responses to disturbances (New England,
Mideast, Great Lakes, Rocky Mountains and Far West) and three non-core regions that differ
significantly from the core in their sources of disturbances and/or responses to disturbances
(Southeast, Plains and Southwest), at business cycle frequencies.
JEL Classification: E32; E52; R11.
Key Words: VAR; Unobserved Components; Monetary Union;.

∗

I would like to thank Charles Evans for helpful discussions and Carrie Jankowski for excellent research
assistance. All errors and omissions are mine. The views expressed herein are those of the author and not
necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve System.

Introduction
There was a great deal of doubt over the long-run viability of the U.S. Federal Reserve System

in 1913, largely because it followed two previously unsuccessful attempts at establishing a U.S.
central bank.1 Similarly, there is widespread skepticism today surrounding the long-run viability
of the EMU. Although, the debate over the viability of the EMU is more focused than the earlier
FRS debate. This is due in large part to seminal work on currency areas by Mundell (1961).
Mundell argued that the survival of a currency union depends on how close it comes to the notion
of an optimum currency area (OCA). According to this theory, if a monetary union is not an
OCA, then some of its members will incur macroeconomic costs (persistent high unemployment
and low output) that will outweigh the microeconomic benefits of a single currency (lower
transaction and hedging costs), forcing them to abandon the union. Many commentators argue
that common monetary policy actions will be damaging to some member countries because the
EMU is a long way from an OCA.2
Since Mundell’s work, economists have basically agreed that four criteria must be met for a
group of regions/countries to constitute an optimal currency area: (i) regions should be exposed to
similar sources of economic disturbance (common shocks); (ii) the relative importance of these
shocks across regions should be similar (symmetric shocks); (iii) regions should have similar
responses to common shocks (common responses); and (iv) if regions are subject to regionspecific economic disturbances (idiosyncratic shocks), they need to be capable of quick
adjustment. The basic idea is that regions satisfying (i)-(iv) will have similar business cycles, so a
common monetary policy response would be optimal.

The First Bank of the United States was disbanded in 1811, and the national charter of the Second Bank
of the United States expired in 1836 after its renewal was vetoed four years earlier by President Andrew
Jackson.
2
See, for example, “Euro brief: The merits of one money” The Economist, October 28, 1998, pp. 85-86.
1

How far the EMU is from an OCA is an open question for research. At first glance, the data
seem to support the skeptics’ view that the EMU is not an OCA. First, EMU countries have
experienced frequent and often large idiosyncratic shocks over recent years. A well-known
example is German reunification. Second, persistent high unemployment rates throughout Europe
suggest that EMU economies are slow to adjust to all economic disturbances.
These observations have spawned a small, but growing body of formal empirical research that
assesses the long-run viability of potential European currency unions. These papers typically
approach the issue of whether a region will be a viable monetary union by comparing the region
with a well-functioning monetary union (the U.S.) along OCA criteria.3 The basic idea is that if
the monetary union is as close as the U.S. is to an OCA, then there can be no presumption that the
monetary union will not be viable in the long run. Alternatively, if the monetary union is less like
an OCA than the U.S., then there is some doubt about the long-run viability of the monetary
union. Implicit in this hypothesis is the critical joint assumption that satisfying OCA criteria is
sufficient for a monetary union to be viable and that the U.S. is an OCA. This paper examines the
usefulness of this research to the EMU debate by formally investigating whether the U.S. is an
OCA.
I do so, by estimating a quarterly structural vector autoregression (VAR) that allows me to
examine whether the eight U.S. Bureau of Economic Analysis (BEA) regions satisfy (i)-(iv). The
VAR includes the growth rates of real personal income in the BEA regions, the relative price of
oil, and a monetary policy variable (federal funds rate). The estimation period is 1969:Q1 to
2002:Q1. Model based forecast error decompositions suggest that U.S. regions are largely subject
to common sources of innovation. The relative importance of common shocks differs somewhat
across regions. However, the main influence on regional activity appears to be a common shock

See for example Eichengreen (1992), Eichengreen and Bayoumi (1993), and Kouparitsas (1999).
2

to income that is not explained by shocks to the relative price of oil or monetary policy. Impulse
responses functions estimated from the VAR suggest that, with the exception of the Plain and
Southwest regions, U.S. regions have similar responses to common shocks. Variance
decompositions suggest that there is a great deal of variation in the share of income fluctuations
explained by region specific shocks. While, the model’s impulse response functions suggests that
regions adjust quickly to region specific disturbances, with most of the adjustment to these shocks
occurring in the first year after the shock.
The remainder of the paper is organized as follows. Section 2 introduces the data by way of
the second-moment properties of the business cycle components of U.S. regional income. Section
3 describes in detail the structural VAR and estimation strategy. The empirical findings of the
paper (details of forecast error decompositions, variance decompositions and impulse response
functions) are reported in section 4. Section 5 concludes by summarizing the paper’s main
findings.

Business cycle properties of U.S. regional income
A simple and direct way of making a preliminary assessment of whether the U.S. is an OCA is

to calculate the correlation between U.S. regional business cycles. A high correlation implies
common sources of disturbances and similar responses to disturbances across U.S. regions, while
a low correlation indicates differences in the sources of disturbances and/or different responses to
disturbances across U.S. regions. Regional cyclical fluctuations are estimated by applying a
Baxter and King (1999) business cycle band-pass filter to U.S. Department of Commerce, Bureau

of Economic Analysis (BEA) quarterly state personal income from 1969:Q1 to 2001:Q1, deflated
by the national consumer price index.4,5
Estimates reported in first column of the upper panel of Table 1 indicate a high level of
comovement across U.S. regions, with the contemporaneous correlation between regional and
aggregate U.S. income ranging from 0.77 for the Southwest to 0.99 for the Southeast. A similar
picture emerges for the interregional correlation statistics. Regions that are geographically close
tend to have correlation coefficients that are higher than regions that are not geographically close.
For example, the correlation of New England and Mideast business cycle fluctuations is 0.94,
while the correlation between New England and Southwest business cycle fluctuations is 0.52.
The lower panel of Table 1 reports the correlation coefficients for leads and lags of regional
income. The main diagonal describes the persistence of regional fluctuations. Regional cycles are
roughly as persistent as the aggregate cycle, with own-lag-correlation coefficients of between
0.92 and 0.95. The remaining cells of this panel do not indicate a strong lead/lag relationship for
U.S. regional business cycles at one quarter: there are only a few cases where the lead/lag
correlation exceeds the contemporaneous correlation and the differences are not statistically
significant. The lead/lag relationship is considerably weaker at longer horizons of two to four
quarters.
Overall, these results suggest that U.S. regions have common sources of innovation and
common responses to these disturbances. On the basis of these findings the U.S. can not be ruled
out as an OCA. An obvious weakness of this simple approach is that it does not allow for a
comparison of the sources of disturbances or responses to disturbances across regions.

Gross state product (GSP) is an alternative measure of regional activity. The main drawback of GSP is
that it is collected annually, which makes it less able to pick business cycle turning points with any
precision.
5
The Baxter-King business cycle filter isolates frequencies of the data that occur at 18 months to 8 years. I
use this filter in large part because these frequencies are arguably of more interest to policymakers.
4

Empirical method
One way of overcoming the limitations of the simple correlation analysis is to use a structural

vector auto regression (VAR). With appropriate parameter restrictions a VAR can identify
common and idiosyncratic sources of innovation, and identify the shape of common and
idiosyncratic responses to common shock.
3.1

The model
I approach the problem of identifying shocks and responses to shocks by classifying them as

either being common or idiosyncratic. Common shocks affect all regions, while idiosyncratic
shocks only affect one region. Similarly, a common response is a response to common shock that
is the same across regions, while an idiosyncratic response is a response to a common shock that
is region specific.
Working toward that end, I assume that the log-first-difference of real regional income in
region i at time t, yit , is the sum of two unobserved components, a common component of
regional output xt and an idiosyncratic (or region specific) component xit . I permit regions to have
different sensitivity to the common component governed by a parameter γ i , so that,

yit = γ i xt + xit ,

(1)

for all i = 1,...,8 .
In this setting, if U.S. regions had no idiosyncratic component xit , then regional income

yit would simply be proportional to the common component xt , their business cycles would be
perfectly correlated and they would easily satisfy the OCA criteria, (i)-(iv).
I follow the literature on regional business cycles by allowing for two other sources of
economic disturbance to affect real regional income. In addition to shocks to the common and

region-specific income components, regions are affected shocks to monetary policy and energy
prices. Following many others, I use the first-difference of the level of the federal funds rate as
my explicit indicator of monetary policy. While, energy prices are measured as the log-first
difference of the price of oil relative to the CPI.
From here I divide the time series into common and idiosyncratic variables. The common
variables include xt , the monetary policy indicator mt , and the relative price of energy pt , while
the idiosyncratic components are the xit ’s . I identify shocks to the common variables by
following the approach of the VAR literature on identifying shocks to U.S macroeconomic
variables. I do so by treating the common regional income component in the same way
macroeconomic studies treat aggregate U.S. income. My approach is most closely related to
Christiano, Eichenbaum and Evans (1994) in their work on identifying and measuring the
aggregate effects of U.S. monetary policy shocks.
To be more specific the common components block of the model focuses on the dynamic
behavior of a 3 × 1 vector,

Z t = [ pt , xt , mt ]’
The dynamics of Zt are represented by a VAR,

AZ t = B( L) Z t −1 + et

(2)

where A is a 3 × 3 matrix of coefficients describing the contemporaneous correlation among the
variables; B ( L) is a 3 × 3 matrix of polynomials in the lag operator L ; and et = [ε pt , ε xt , ε mt ] is a

3 × 1 vector of orthogonal structural disturbances.
Additional structure must be placed on A to identify the elements of et . Following
Christiano, et al. I restrict A to be a unique lower triangular matrix with ones along the diagonal.

The implications of that assumption are that: innovations to pt have a contemporaneous effect on

xt and mt ; innovations to xt have a contemporaneous effect on mt and a lagged effect on pt ;
and innovations to mt have a lagged effect on pt and xt . The underlying assumption is that in
setting policy the U.S. Federal Reserve both reacts to and affects the economy. This is
implemented by assuming that the monetary authorities feedback rule can be written as a linear
function, Ψ , defined over a vector, Ωt , of variables observed at or before date t, so that
monetary policy is completely described by,

mt = Ψ (Ωt ) + A33ε mt ,

(3)

where Ψ (Ωt ) is described by the third row of B ( L) and A33 is the (3,3) element of the matrix A .
I model Ωt as containing lagged values (date t-1 and earlier) of all variables in the common
component block, as well as time t values of those variables that the monetary authority looks at
contemporaneously in setting policy (energy prices and the common income component). In
accordance the assumptions of the feedback rule, an exogenous shock to monetary
policy ε mt cannot contemporaneously affect time t values of the elements of Ωt . However, lagged
values of ε mt can affect variables in Ωt .
The idiosyncratic block of the model focuses on the dynamic behavior of a 8 × 1 vector of
idiosyncratic components of regional income,

X t = [ x1t , x2t ,..., x8t ]’
I assume that the relative price of energy and monetary policy affect the idiosyncratic component
of regional income in a similar way in which they affect the common component. In particular, I
assume that innovations to pt have a contemporaneous effect on xit , while innovations to mt
have a lagged effect on xit . In contrast to the common income component, innovations to the
7

idiosyncratic component are assumed to have no effect on oil prices or monetary policy, either
contemporaneously or lagged. Underlying this assumption is the idea that aggregate energy prices
only respond to aggregate income shocks, while the Federal Reserve only reacts to common
income fluctuations. I also assume for parsimony that innovations to xit do not affect x jt for

i ≠ j , either contemporaneously or with a lag.
Under these assumptions the dynamics of region i’s idiosyncratic component is explained by,

xit = Di ( L) xit −1 + Ei ( L)Wt + ε it ,

(4)

for all i, where Di ( L) is a scalar polynomial in the lag operator L ; Ei ( L) is a 1× 2 matrix of
polynomials in the lag operator L ; Wt = [ pt , mt ]’; and ε it is an orthogonal structural disturbance
(that is, ε it ⊥ ε jt for all i ≠ j ).
Following from this, the dynamics of the idiosyncratic component vector X t are represented
by,

X t = D( L) X t −1 + E ( L)Wt + vt

(5)

0
0
0 
 D1 ( L)
 E1 ( L) 
 ε1t 
 0

ε 


D2 ( L) L
0 
E2 ( L) 
2t


where D ( L) =
, E ( L) =
, vt =   and et ⊥ vt .
 M
M 
 M 
0 
M
O


 


0
0 D8 ( L) 
 0
ε 8t 
 E8 ( L) 
With this model in hand, I assess the similarity of U.S. regional business cycles along two
dimensions. First, by studying the sources of regional economic disturbances I can determine the
extent to which fluctuations are caused by common and region-specific shocks. Common shocks
include unanticipated changes to energy prices ε pt , unanticipated shocks to monetary policy
variable ε mt and unanticipated shocks to the residual common income shock ε xt that captures
innovations to common output not captured by the other common shocks. Idiosyncratic shocks
8

include unanticipated fluctuations in region i’s income ε it . The relative importance of the various
sources of disturbance is revealed by ratios of the standard deviations of innovations and the
model’s one-step ahead forecast error decompositions.
Second, by studying the model’s impulse response functions, I can assess whether regions
have similar responses to common shocks and determine the time it takes a region to adjust to
idiosyncratic shocks.
3.2

Previous approaches to modeling regional income fluctuations
The most closely related study is Carlino and Defina (1998), hereafter (CD).6 They use a

structural VAR to estimate the effects of U.S. monetary policy on the eight BEA regions. My
approach to identifying shocks and responses to shocks differs from CD in three significant ways.
First, they assume that there is no common income component across the eight BEA regions. In
their model common shocks to the relative price of energy and monetary policy affect regional
output with a one period lag, while the residual shocks to regional incomes are region specific.
This is a major shortcoming of their study since my analysis suggests that a large share of the
variation regional income across the eight BEA regions is explained by innovations in the
common income component.
Second, following their earlier paper Carlino and Defina (1995) they allow region specific
income shocks to spillover to other regions. However, the approaches of the two studies are quite
different. The earlier paper controls for common shocks by removing a common component from
regional income growth equal growth rate of aggregate income. This is similar to my approach,
with the main difference being that I allow for the common component to be estimated in the
model. The stated objective of allowing for spillovers in the later paper is so that there is an

Carlino and DeFina (1998) provide an extensive literature review of empirical studies of regional business
cycles.
9

aggregate income shock affecting regional income in the model. In other words, this is meant to
capture common income fluctuations across regions. CD estimate their model using first
differences of the log of regional output. While there is a very strong correlation between current
and lagged regional incomes at business cycle frequencies (see Table 1) the correlation
coefficients are significantly lower for first-difference data, which means that lagged aggregate
regional output fails to capture the contemporaneous comovement of regional income across BEA
regions. My model does not allow for spillovers of region specific shocks, since the impulse
responses of region specific shocks from other regions were found to be not significantly different
from zero.
Finally, CD allow region-specific shocks to affect the monetary policy variable
contemporaneously, while my model only allows the common income shock to affect the
monetary policy variable contemporaneously. My approach is arguably more appropriate, since it
says that central banks do not respond to idiosyncratic shocks, which is the point of the debate
surrounding the ECB monetary policy.
Using this approach CD find that unanticipated shocks to U.S. monetary policy have very
different effects on the income of the eight BEA regions. They identify a core group of regions
including New England, Mideast, Plains, Southeast and Far West and a non-core group including
the Great Lakes, Southwest and Rocky Mountains. Regions in the core group have very similar
responses to monetary policy shocks, while regions in the non-core have very different responses
to monetary policy shocks. Their analysis implies that the U.S. is not an OCA, since it fails to
meet the common response criteria due to the very different responses of the non-core regions.
One of the drawbacks of their analysis is that they do not provide a formal statistical test of the
hypothesis that the responses of regional income incomes to monetary policy vary significantly,

so it remains an open question for research to test if regions respond differently to monetary
policy shocks.
3.3

Data

I estimate the model using quarterly data from 1969:Q1 to 2001:Q1. Regional income is
measured by real personal income across eight BEA regions. Real incomes are calculated by
deflating each region’s nominal income with the national consumer price index (CPI). The
relative price of energy is the International Monetary Fund’s U.S. dollar world crude oil price
index deflated by the U.S. CPI. Following the wealth of empirical research on identifying
monetary policy, I use the federal funds rate as my indicator of monetary policy.
I use maximum likelihood to estimate the model’s parameters, so the variables used in the
estimation must be stationary. Table 2 reports the results of Augmented Dickey-Fuller unit root
tests applied to the log-levels and log-first-differences of real regional income and the relative oil
price, and the levels and first-difference of the federal funds rate. The null of a unit root cannot be
rejected for any of the log-level data series at the 5 percent level of significance. However, the
null of a unit root is rejected for the log-first-difference data at the same level of significance. In
light of this, I specify and estimate the model using the log-first-differences of real regional
income and the relative oil price, and the first-difference of the federal funds rate. Finally, I
multiply the log-first-difference data is by 100 so that standard deviations of disturbances and
impulse response functions are expressed as percentages of regional income.
3.4

Estimation strategy

The model described by (1)-(5) is a variant of Watson and Engle’s (1983) general dynamic
multiple indicator-multiple cause (DYMIMIC) model. This framework allows unobserved
variables to be dynamic in nature as well as be associated with observed variables. This latter

feature is an important part of the present study, since one the goals is to see how much of the
variation in the common income component is explained by shocks to observed variables
(monetary policy and energy prices).
DYMIMIC models are estimated using maximum likelihood. Likelihood functions are
evaluated by using the Kalman filter on the model’s state space representation. In my case the
state space representation of the model is described by the following: measurement equation,

 I8×8

02×8

0   Yt   08×10   Yt −1   I8×8
=
+
A Wt  0


 2×8 B( L)  Wt −1  02×8

08×1 
Γ 



 X t +  ε pt 

C ( L) 
 ε mt 

(6)

and transition equation,

0 
 D( L)
 E ( L) 
v 

Xt = 
X t −1 + 
Wt +  t 


Dx ( L) 
 0
 Ex ( L) 
ε xt 

(7)

( L) is an 2 × 2 matrix of
A is an 2 × 2 lower triangular matrix; B
where Yt = [ y1t , y2t ,..., y8t ]’;
( L) is an 2 × 1 matrix of polynomials in
polynomials in the lag operator L; Γ = [γ 1 , γ 2 ,..., γ 8 ]’; C
the lag operator L;
X t = [ X t ’, xt ]’; Dx ( L) is a scalar polynomial in the lag operator L; Ex ( L) is
an 1× 2 matrix of polynomials in the lag operator L. These parameter matrices map into the
model specified in (1)-(5) in the following way,

 1
0

A =  Ex (0)11
1

C (0)12
 A21

( L)
( L)
B
0
C
11
11


0  , while B( L) =  Ex ( L)11 Dx ( L)
B

1 
 ( L)21 C ( L) 21

( L) 
B
12

Ex ( L)12  for all L ≥ 1
( L) 
B
22 

Identifying the parameters that govern the common income component, idiosyncratic
responses and structural disturbances requires additional normalization restrictions. The variance
of the common income component’s structural disturbance is identified by normalizing γ i to

unity for one of the eight regions. The idiosyncratic responses of regional income to unanticipated
shocks to the relative oil price and monetary policy are identified by normalizing one region’s
idiosyncratic responses to be the same as the common income component’s responses. In other
words, the idiosyncratic responses are identified by restricting Ei ( L) = 0 for one of the eight
regions. I use the Southeast as the normalizing region since it is has the highest correlation with
aggregate U.S. income and it has virtually the same amplitude as aggregate U.S. income, at
business cycle frequencies.
The lag length of the model is determined by changes in the value of the likelihood function.
The number of lags of all variables was increased up to the point where the likelihood ratio
statistic could not reject the null that the additional parameters were jointly equal to zero. Using
this criterion the model was restricted to two lags in all variables.
I estimate the DYMIMIC model using the recursive EM algorithm described in Watson and
Engle (1983). To avoid local optimization problems I examined a wide range of starting values
and impose severe convergence criteria on the parameter space of 1× 10−7 . Standard errors of the
parameters are estimated using a standard gradient search algorithm to evaluate the matrix of
second derivatives of the likelihood function at the EM parameter estimates.
3.5

Variance decompositions at business cycle frequencies

A goal of this paper is to decompose the variance of regional income at business cycle
frequencies according to the various common and idiosyncratic sources of innovation. I do this by
way of a linear filter G ( L) that allows me to map from the covariance of the first-difference of the
regional income to the covariance of the business cycle components of regional income. The
precise form of the filter is, G ( L) =

BP6,32 ( L)
1− L

, where BP6,32 ( L) is the Baxter-King approximate

band-pass filter for quarterly data; and L is the lag operator. The mapping of covariance of the

first-difference data to covariance of the business cycle frequency data is carried using standard
spectral/Fourier analysis tools.

Empirical results

With estimates of the model in hand, I assess the similarity of U.S. regional business cycles along
two dimensions. First, by studying the sources of regional economic disturbances I determine the
extent to which fluctuations are caused by common and region-specific shocks. Second, by
studying the model’s impulse response functions, I assess whether regions have similar responses
to common shocks and determine the time it takes a region to adjust to idiosyncratic shocks.
4.1

Sources of variation

The upper panel of Table 3 describes the level of the estimated standard deviation of the model’s
eleven structural disturbances, while the lower panel of Table 3 describes the relative volatility of
region-specific shocks, using the Southeast as the normalizing region.
Focusing on the upper panel, we see that innovations to the common income component are
estimated to have a standard deviation that is more than more than twice as large are the standard
deviation of region specific shock to the Southeast. This implies that common shocks are an
important source of variation in the Southeast. While, the lower panel reveals that there is a great
deal of statistically significant variation in the relative size of the standard deviations of regionspecific shocks. Estimates range from 1.29 for the Great Lakes up to 2.85 for the Plains, which,
holding other things constant, suggests that region specific shocks are more important source of
income variation in the Plains than in the Great Lakes.
Decompositions of the forecast errors of regional income reported in Table 4, provide a more
complete picture of the relative importance of disturbances. These decompositions indicate the
share of the forecast error attributable to a particular disturbance for a given horizon. The one-

step-ahead errors are informative about the similarity of the sources of disturbances across
regions, while step lengths of greater than one contain joint information about the similarity of
disturbances and responses to disturbances.
Table 4 reveals that a large share of the disturbance to U.S. regions is due to common shocks
(that is, unanticipated shocks to oil prices, monetary policy, and common income component).
For example, common disturbances explain a large share of the Southeast’s one-step-ahead
forecast error, 87 percent. The Plains appear to have the largest region-specific influences, with
only 47 percent of the variation in their one-step-ahead forecast error explained by common
disturbances. The six other regions fall in between, with common disturbances explaining roughly
58 to 76 percent of the variation in their one-step-ahead forecast errors. The relative importance
of different common disturbances is similar across regions. Shocks to the common income
component are considerably more important than shocks to oil prices and monetary policy at all
forecast horizons. With the exception of the Southeast and Plains, these results suggest that U.S.
regions have similar sources of economic disturbances.
Table 4 also provides some indication of the similarity of responses to disturbances. Looking
at horizons of greater than one quarter, the relative importance of common and idiosyncratic
disturbances is similar across regions. This suggests that responses to common and idiosyncratic
shocks are similar. A common finding is that unanticipated shocks to the common income
component are less important at longer horizons.
4.2

Impulse response functions
Figures 1 to 6 describe in detail the cumulative responses of the log-first-difference of income

of the eight BEA regions to common shocks. These impulse response functions describe the way
that the level of regional income responds over time to a permanent one-standard deviation shock
to the relative price of oil, the federal funds rate, and common component of income. The

responses are presented in two ways. First, I plot the regional responses against each other to
establish differences across the regions. Next, I plot the individual responses with their 95 percent
confidence interval.7
Figure 1 shows that an unanticipated rise in the relative price of oil has a negative effect on
income in all eight regions. Regions can be broken up into three groups. The Plains response is
much larger than in the Southeast, while the responses in the Southwest, Rocky Mountains and
Far West are much weaker than in the Southeast. Responses of the remaining regions are similar
to those of the Southeast. Figure 2 reveals that with the exception of the weak response group, the
response functions of the regions are all significantly different from zero.
Figure 3 reveals that an unanticipated shock to monetary policy (an unexpected rise in the
federal funds rate) also has a negative effect on regional income in all eight regions. Regions fall
into two groups. New England, Mideast, Southwest and Far West have weaker responses than the
Southeast, while the Great Lakes, Plains and Rocky Mountains have responses that are stronger
than the Southeast. The responses are shown in Figure 4 to be significantly different from zero
across all regions two to three quarters after the shock, which reflects the well known lagged
effect of monetary policy.
Responses to an unanticipated increase in the common income component are described in
Figure 5. Regions fall into three groups. The Plains, Southwest, and Rocky Mountains have
stronger responses than the Southeast, while the Mideast has a weaker response than the
Southeast. New England, Great Lakes and Far West have responses that are similar to the
Southeast. Figure 6 reveals that these responses are all significantly different from zero at all lags.

Confidence intervals are calculated by Monte Carlo methods. Following Hamilton (1994) section 11.7, I
randomly draw from the estimated distribution of the model’s parameters. For each draw of parameters I
generate an impulse response function. I repeat this process 10,000 times. At each lag I calculate the 2500th
lowest and 9750th highest value across all 10,000 simulated response functions. The boundaries of the
confidence intervals in the figures correspond to these values.
16

Overall, the response functions suggest that regions respond to common sources of
disturbance in a similar way. However, there is some variation across regions in the sensitivity of
the responses to these common disturbances. The objective of the next two sections is test if the
differences in response functions are statistically significant. I do this by breaking down the
responses into their common and idiosyncratic components
4.3

Common responses
Differences in common responses to common shocks across regions merely reflect differences

in the sensitivity to the common component measured by γ i . Regions with a γ i > 1 have greater
sensitivity to fluctuations of the common component, while regions with γ i < 1 are less sensitive
to fluctuations of the common component. Table 5 reports the maximum likelihood estimates of
these parameters along with their standard errors and t-statistics for the null hypothesis that

γ i = 1 . These statistics suggest that the null of a common response to the common component
across all regions cannot be rejected at the 5 percent level of significance. At the 10 percent level,
the null is rejected for the Plains and Far West.
4.4

Idiosyncratic responses
The model developed in the previous section is flexible enough to allow for different regional

responses to common shocks. These so-called idiosyncratic responses capture the difference
between the region’s total and common response to a common shock.
Figure 7 shows that the idiosyncratic responses of regional income to an unanticipated rise in
the relative price of oil is not significantly different from zero in New England, the Mideast and
Great Lakes. The idiosyncratic response functions of the Southwest, Rocky Mountains and Far
West are significantly greater than zero, while the response function of the Plains is significantly
less than zero. This reflects the fact that the Southwest, Rocky Mountains and Far West are oil

producing and distribution regions. The Plains, on the other hand, has a large agriculture sector,
which is highly sensitive to oil price fluctuations.
Idiosyncratic responses to unanticipated shocks to monetary policy are plotted in Figure 8.
They reveal that idiosyncratic responses to monetary policy shocks are not statistically different
from zero in all eight BEA regions. This finding stands in contrast to the general conclusion of
Carlino and Defina (1998) that monetary policy has a greater effect on the income of more
manufacturing oriented regions, such as the Great Lakes. There is, however, some evidence in
support of their conclusion that the Southwest is less sensitive to monetary policy. This is
revealed by the fact that the idiosyncratic response of the Southwest is very close to being
statistically different from zero at the 5 percent level.
Figure 9 reveals the effects of an unanticipated shock to the common income component on
the idiosyncratic components of regional income. Shocks to the common component of income
affect the idiosyncratic component through the lagged responses of oil prices and monetary
policy. With the exception of the Southwest, the idiosyncratic responses to common income
shock are not statistically different to zero. This reflects the fact that positive shocks to the
common income component have a positive effect on oil prices and the federal funds rate, to
which the South has a significant positive idiosyncratic response.
Responses to unanticipated region-specific shocks are reported in Figure 10. All eight regions
have significant responses to their region-specific shocks. Regions generally complete their adjust
to a region specific disturbance within a year of the shock. However, adjustment is slower in New
England, Southwest and Far West, with adjustment lags of almost two years. In most cases the
cumulative effect exceeds the impact effect. The main exceptions to this rule are Southeast and
Plains. The main implication of this observation is that the relative importance of region-specific

disturbances is relatively smaller at longer horizons in the Southeast and Plains, when compared
to New England, Southwest and Far West (see Table 4).
4.5

Variance decomposition at business cycle frequencies
Panel A of Table 5 ties together the sources of disturbances and responses by decomposing the

variance of regional output at business cycle frequencies. Each column breaks down the variance
of regional income by source of shock. For example, the first element of the first column reveals
that innovations to oil prices explain 16 percent of the business cycle fluctuations in Southeast
income. The next entry reveals that a similar percentage is explained by monetary policy shocks,
while common income shocks explain 64 percent of the variation in Southeast income. Moving
on down the column, we see that common shocks explain 96 percent of the variation in Southeast
income, with the remaining 4 percent of the variation in Southeast income explained by region
specific shocks.
The remaining columns of the upper panel reveal that a large share of the business cycle
fluctuations of U.S. regions is due to common shocks. Regions fall into three groups. At the upper
end of the range common shocks explain more than 86 percent of the variation in regional income
of the Southeast and Great Lakes, while at the lower end common shocks account for 56 and 63
percent of the income variation in New England and Southwest regions, respectively. The other
regions fall in between with common shocks accounting for 68 to 74 percent of income
fluctuations in the Mideast, Plains, Rocky Mountains and Far West.
Panel B highlights differences in the idiosyncratic responses of regions by breaking down the
relative importance of the common sources of variation. The residual common-incomecomponent shock is the most important source of disturbance explaining on average 70 percent of
the variation explained by all three common shocks. While, monetary policy and relative oil price
shocks account on average for 15 percent of the variation in regional income explained by

common shocks. The variation across regions is greatest for oil price shocks, with oil price
shocks explaining 4-5 percent of the variation in the Southwest, Rocky Mountains and Far West
on up to 32 percent in the Plains. This reflects the relatively weaker responses in the former
regions and the relatively strong response in the latter region. The relative importance of
monetary policy shocks is more uniform across regions, with the main outlier being the
Southwest, where shocks to monetary policy account for 8 percent of the variation explained by
common shocks.
I assess the overall similarity of the regional business cycles by a simple distance measure that
compares the variance decomposition of each region with the average across all regions. These
statistics are reported at the bottom of Panel A (they are distributed as a χ 2 with 3 degrees of
freedom). At the 5 percent level of significance I can reject the null of common sources of
innovation and/or responses to innovations at business cycle frequencies in the Southeast, Plains
and Southwest. This implies the U.S. regions can be divided into a core group of New England,
Mideast, Great Lakes, Rocky Mountains and Far West, that meet Mundell’s OCA criteria
described by (i)-(iv), and a non-core group of the Southeast, Plains and Southwest that fail to
meet this criteria.8
In the case of the Plains and Southeast these findings largely reflect differences in the relative
volatility of region-specific disturbances when compared to the core group. In particular, regionspecific disturbances account for a relatively small share of the business cycle volatility of
Southeast income and a relatively large of the business cycle volatility of Plains income. On the
other hand, these findings reflect the fact that the Southwest has very different responses to both
common and idiosyncratic shocks, when compared to the core group.

Relaxing the level of significance to the 1 percent level expands the optimum currency area to include the
Southeast and Southwest.
20

Conclusion

This paper develops a statistical model to study the business cycles of the eight U.S. BEA
regions. By combining unobserved component and VAR techniques I identify not only common
and idiosyncratic sources of innovation, but also common and idiosyncratic responses to common
shocks. I use formal statistical tests to show that the eight U.S. BEA regions deviate from
Mundell’s ideal of an optimum currency area, at typical levels of significance. Based on these
results, I identify five core regions that have similar sources of economic disturbance and similar
responses to these disturbances (New England, Mideast, Great Lakes, Rocky Mountains and Far
West) and three non-core regions that differ significantly from the core in their sources of
disturbance (Southeast and Plains) and responses to disturbances (Southwest), at business cycle
frequencies.

References
Baxter, M. and R.G. King, 1999, Measuring business cycles: Approximate band pass filters for
economic time series, Review of Economics and Statistics, Vol. 81, pp. 575-593.
Carlino, G.A. and R. Defina, 1995, Regional income dynamics, Journal of Urban Economics, Vol
27, pp. 88-106.
Carlino, G.A. and R. Defina, 1998, The differential regional effects of monetary policy, The
Review of Economics and Statistics, Vol. 80, pp. 572-587.
Christiano, L.J., M. Eichenbaum and C.L. Evans, 1994, Identification and the effects of monetary
policy shocks, Federal Reserve Bank of Chicago, working paper, No. 94-7.
Eichengreen, B.J., 1992, Is Europe an optimum currency area?, reprinted in European Monetary
Unification: Theory, Practice, and Analysis, B.J. Eichengreen (ed.), Cambridge: MIT Press,
pp. 51-71.
21

Eichengreen, B.J., and T. Bayoumi, 1993, Shocking aspects of European monetary unification,
reprinted in European Monetary Unification: Theory, Practice, and Analysis, B.J. Eichengreen
(ed.), Cambridge: MIT Press, pp. 73-109.
Hamilton, J.D., 1994, Time Series Analysis, Princeton: Princeton University Press.
Kouparitsas, M.A., 1999, Is the EMU a viable common currency area? A VAR analysis of
regional business cycles, Federal Reserve Bank of Chicago, Economic Perspectives, Vol 23,
pp. 2-20.
Mundell, R.A., 1961, A theory of optimum currency areas, American Economic Review, Vol. 51,
pp. 657-665.
Sims, C., 1972, Money, income, and causality, American Economic Review, Vol. 62, pp. 540552.
Watson, M.W., and R.F. Engle, 1983, Alternative algorithms for the estimation of dynamic
factor, MIMIC and varying coefficient models, Journal of Econometrics, Vol. 23, pp. 385-400.

Table 1: Regional business cycle comovement and persistence
A. Contemporaneous correlation
Income at time t
United States
Southeast
New England
Mideast
Great Lakes
Plains
Southwest
Rocky Mountains
Far West

US
1.00
0.99
0.89
0.94
0.97
0.90
0.77
0.85
0.91

SE
0.99
1.00
0.89
0.92
0.96
0.89
0.76
0.88
0.86

NE
0.89
0.89
1.00
0.94
0.84
0.70
0.52
0.62
0.81

ME
0.94
0.92
0.94
1.00
0.88
0.77
0.59
0.71
0.87

Income at time t
GL
PL
0.97
0.90
0.96
0.89
0.84
0.70
0.88
0.77
1.00
0.88
0.88
1.00
0.72
0.76
0.83
0.86
0.86
0.74

SW
0.77
0.76
0.52
0.59
0.72
0.76
1.00
0.87
0.65

RM
0.85
0.88
0.62
0.71
0.83
0.86
0.87
1.00
0.69

FW
0.91
0.86
0.81
0.87
0.86
0.74
0.65
0.69
1.00

US
0.94
0.92
0.87
0.94
0.92
0.81
0.68
0.78
0.84

SE
0.94
0.94
0.87
0.92
0.91
0.83
0.68
0.81
0.79

NE
0.82
0.81
0.95
0.91
0.78
0.63
0.43
0.55
0.72

Income at time t+1
ME
GL
PL
0.84
0.92
0.86
0.81
0.90
0.85
0.88
0.82
0.70
0.95
0.89
0.81
0.79
0.95
0.84
0.65
0.80
0.91
0.49
0.65
0.69
0.60
0.76
0.80
0.75
0.79
0.70

SW
0.75
0.74
0.53
0.62
0.70
0.72
0.92
0.82
0.63

RM
0.83
0.84
0.62
0.73
0.80
0.81
0.80
0.94
0.65

FW
0.89
0.83
0.82
0.89
0.84
0.69
0.59
0.65
0.94

B. Lead/lag correlation
Income at time t
United States
Southeast
New England
Mideast
Great Lakes
Plains
Southwest
Rocky Mountains
Far West

Notes: US=United States, SE=Southeast, NE=New England, ME=Mideast, GL=Great Lakes, PL=Plains, SW=Southwest, RM=Rocky Mountains, and
FW=FarWest. Regional and aggregate income data filtered using the quarterly business cycle band-pass filter described in Baxter and King (1999).
Sources: Author’s calcuations using data from the Bureau of Economic Analysis.

Table 2: Unit root tests
Variable
Southeast income
New England income
Mideast income
Great Lakes income
Plains income
Southwest Income
Rocky Mountains income
Far West income
Relative price of oil
Federal funds rate

Log level
-3.27
-2.67
-2.31
-1.90
-2.96
-2.26
-2.07
-2.72
-2.78
-2.80

Log first difference
-3.85
-3.19
-3.03
-3.81
-3.52
-2.90
-3.19
-3.23
-4.04
-4.21

Notes: With exception of funds rate all tests of unit roots in log-levels include include an
intercept term and time trend, funds rate test only has an intercept. Unit root tests of log-firstdifferences include an intercept term.
Source: Author’s calculations using regional income data from Bureau of Economic Analysis,
oil price data from the International Monetary Fund and federal funds rate data from the Board
of Governors of the Federal Reserve System.

Table 3: Estimated volatility of structural disturbances
Structural disturbance
Common
Oil price
Common income
Monetary policy
Region specific
Southeast
New England
Mideast
Great Lakes
Plains
Southwest
Rocky Mountains
Far West
Structural disturbance
Region specific
Southeast
New England
Mideast
Great Lakes
Plains
Southwest
Rocky Mountains
Far West

Standard deviation

Standard error

t-statistic (σi=0)

17.03
0.73
0.99

1.00
0.05
0.06

17.02
13.95
16.20

0.32
0.49
0.55
0.42
0.92
0.48
0.64
0.42
Relative standard
deviation

0.03

12.67

Standard error

t-statistic (σi/σ1=1)

1.00
1.53
1.70
1.29
2.85
1.48
1.99
1.31

0.14
0.15
0.12
0.23
0.13
0.18
0.12

3.86
4.53
2.32
8.19
3.63
5.49
2.59

Table 4: Sensitivity to common shock
Region
Southeast
New England
Mideast
Great Lakes
Plains
Southwest
Rocky Mountains
Far West

Coefficient (γi)
1.00
0.89
0.87
1.04
1.20
1.01
1.10
0.88

Standard error

t-statistic (γi=1)

0.07
0.08
0.06
0.10
0.07
0.09
0.06

-1.45
-1.59
0.69
1.92
0.13
1.03
-1.93

Table 5: Variance decomposition of U.S. regional income at business cycle frequencies
A. All sources of innovation
Source of innovation:
Relative oil prices
Monetary policy
Common income
Total common
Region-specific income
Total all shocks
Chi squared test (sources are common)
B. Common sources of innovation
Source of innovation:
Relative oil prices
Monetary policy
Common income
Total common

SE
16
16
64
96
4
100
10.67

Percentage of total variation due to innovation
NE
ME
GL
PL
SW
RM
8
14
18
23
2
3
7
12
14
9
5
14
41
46
54
42
56
53
56
72
86
74
63
69
44
28
14
26
37
31
100
100
100
100
100
100
4.99
1.51
4.82
13.44
8.62
5.70

FW
4
10
54
68
32
100
4.30

Average
11
11
51
73
27
100

SE
17
17
66
100

Percentage of common variation due to innovation
NE
ME
GL
PL
SW
RM
15
20
21
32
4
4
12
16
16
12
8
20
73
64
63
57
88
77
100
100
100
100
100
100

FW
5
14
80
100

Average
15
14
71
100

Notes: SE=Southeast, NE=New England, ME=Mideast, GL=Great Lakes, PL=Plains, SW=Southwest, RM=Rocky Mountains, and FW=FarWest.

Figure 1: Cummulative impulse response of
regional income to oil price shock
0.0

Cummulative % change

-0.2

-0.4

-0.6

-0.8

-1.0

-1.2
0

Number of quarters after shock
Southeast

New England

Mideast

Great Lakes

Plains

0.0

Cummulative % change

-0.2

-0.4

-0.6

-0.8

-1.0

-1.2
0

Number of quarters after shock
Southeast

Southwest

Rocky Mountains

Far West

Figure 2: Cummulative impulse response of regional income to oil price shock
(with 95 percent confidence interval)
Southeast

New England
0.4

Cummulative % change

0.4
0.0
-0.4
-0.8
-1.2
-1.6

0.0
-0.4
-0.8
-1.2
-1.6

Number of quarters after shock

Mideast

Cummulative % change

0.0
-0.4
-0.8
-1.2

0.0
-0.4
-0.8
-1.2
-1.6

Number of quarters after shock

Southwest

Plains
0.4

0.8

Cummulative % change

0.4

-1.6

0.0
-0.4
-0.8
-1.2
-1.6

0.4
0.0
-0.4
-0.8
-1.2
-1.6

-2.0
0

Number of quarters after shock

Rocky Mountains

Far West

0.4

Cummulative % change

Great Lakes

0.4

Cummulative % change

Number of quarters after shock

0.0
-0.4
-0.8
-1.2
-1.6

Number of quarters after shock

Figure 3: Cummulative impulse response of
regional income to monetary policy shock

Cummulative % change

0.0

-0.2

-0.4

-0.6
0

Number of quarters after shock
Southeast

New England

Mideast

Great Lakes

Plains

Cummulative % change

0.0

-0.2

-0.4

-0.6
0

Number of quarters after shock
Southeast

Southwest

Rocky Mountains

Far West

Figure 4: Cummulative impulse response of regional income to monetary policy shock (with
95 percent confidence interval)
Southeast

New England
0.2

Cummulative % change

0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2

0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2

Number of quarters after shock

Mideast

Cummulative % change

0.0
-0.2
-0.4
-0.6
-0.8
-1.0

0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2

Number of quarters after shock

Southwest

Plains
0.2

Cummulative % change

0.2

Cummulative % change

0.2

-1.2

0.0
-0.2
-0.4
-0.6
-0.8
-1.0

0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2

-1.2
0

Number of quarters after shock

Rocky Mountains

Far West

0.2

Cummulative % change

Great Lakes

0.2

Cummulative % change

Number of quarters after shock

0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2

Number of quarters after shock

Figure 5: Cummulative impulse response of
regional income to common income shock

Cummulative % change

1.4

1.2

1.0

0.8

0.6
0

Number of quarters after shock
Southeast

New England

Mideast

Great Lakes

Plains

Cummulative % change

1.4

1.2

1.0

0.8

0.6
0

Number of quarters after shock
Southeast

Southwest

Rocky Mountains

Far West

Figure 6: Cummulative impulse response of regional income to common income shock (with
95 percent confidence interval)
Southeast

New England
2.0

Cummulative % change

2.0

1.6

1.2

0.8

0.4

1.6

1.2

0.8

0.4
0

Number of quarters after shock

Mideast

Cummulative % change

Great Lakes

1.6

1.2

0.8

0.4

1.6

1.2

0.8

0.4
0

Number of quarters after shock

Southwest

Plains
2.0

2.0

Cummulative % change

2.0

1.6

1.2

0.8

1.6

1.2

0.8

0.4

0.4
0

Number of quarters after shock

Rocky Mountains

Far West

2.0

Cummulative % change

Number of quarters after shock

1.6

1.2

0.8

0.4

1.6

1.2

0.8

0.4
0

Number of quarters after shock

Figure 7: Cummulative impulse response of idiosyncratic regional income to oil price shock
Southeast

New England
1.0

Cummulative % change

1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6

0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6

Number of quarters after shock

Mideast
1.0

1.0

0.8

0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6

0.6
0.4
0.2
0.0
-0.2
-0.4

Number of quarters after shock

Southwest

Plains
1.0

1.0

0.8

Cummulative % change

-0.6
0

0.6
0.4
0.2
0.0
-0.2
-0.4

0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6

-0.6
0

Number of quarters after shock

Rocky Mountains

Far West

1.0

0.8

Cummulative % change

Great Lakes

Cummulative % change

Number of quarters after shock

0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6

Number of quarters after shock

Figure 8: Cummulative impulse response of idiosyncratic regional income to monetary
policy shock
Southeast

New England
0.6

Cummulative % change

0.6

0.4

0.2

0.0

-0.2

0.4

0.2

0.0

-0.2
0

Number of quarters after shock

Mideast

Cummulative % change

0.4

0.2

0.0

0.4

0.2

0.0

-0.2
0

Number of quarters after shock

Southwest

Plains
0.6

Cummulative % change

0.6

Cummulative % change

Great Lakes

-0.2

0.4

0.2

0.0

0.4

0.2

0.0

-0.2

-0.2
0

Number of quarters after shock

Rocky Mountains

Far West

0.6

Cummulative % change

0.6

Cummulative % change

Number of quarters after shock

0.4

0.2

0.0

-0.2

0.4

0.2

0.0

-0.2
0

Number of quarters after shock

Figure 9: Cummulative impulse response of idiosyncratic regional income to aggregate
output shock
Southeast

New England
0.6

Cummulative % change

0.6

0.4

0.2

0.0

-0.2

0.4

0.2

0.0

-0.2
0

Number of quarters after shock

Mideast

Cummulative % change

0.4

0.2

0.0

0.4

0.2

0.0

-0.2
0

Number of quarters after shock

Southwest

Plains
0.6

0.6

Cummulative % change

Great Lakes

-0.2

0.4

0.2

0.0

0.4

0.2

0.0

-0.2

-0.2
0

Number of quarters after shock

Rocky Mountains

Far West

0.6

Cummulative % change

0.6

Cummulative % change

Number of quarters after shock

0.4

0.2

0.0

-0.2

0.4

0.2

0.0

-0.2
0

Number of quarters after shock

Figure 10: Cummulative impulse response of idiosyncratic regional income to region-specific
output shock
Southeast

New England
2.5

Cummulative % change

0.6

0.4

0.2

0.0

-0.2

2.0
1.5
1.0
0.5
0.0

Number of quarters after shock

Mideast
Cummulative % change

Cummulative % change

0.8

1.0
0.8
0.6
0.4
0.2
0.0

0.6

0.4

0.2

0.0
0

Number of quarters after shock

Southwest

Plains
2.0

Cummulative % change

1.2

Cummulative % change

Great Lakes

1.2

1.0
0.8
0.6
0.4
0.2

1.5

1.0

0.5

0.0

0.0
0

Number of quarters after shock

Rocky Mountains

Far West

1.6

Cummulative % change

Number of quarters after shock

1.2

0.8

0.4

0.0

1.2

0.8

0.4

0.0
0

Number of quarters after shock

Full text of Working Papers (Federal Reserve Bank of Chicago) : Is the United States an Optimum Currency Area? : An Empirical Analysis of Regional Business Cycles, Working Paper 2001-22

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