Common trends and cycles and the structure of Florida’s economy
Edgar Parker
Such changes in the structure of a regional economy
have implications for economic forecasters, policymakers,
businesses, and the general public. The ultimate effects of
economic shocks on a region depend on the ways different
parts of that region are linked to each other and to external
areas, as well as the region’s relative degree of homogeneity.
A particular economic policy or shock may have a
completely different effect on a highly homogeneous region
than it would on a more heterogeneous one.
This article uses multiple cointegration and common
cycles analysis to study the evolution of the relationships
among some major Florida cities’ labor
markets. (See the glossary on page 66 for short discussions
of the technical terms.) Cointegration analysis is used to
examine the degree and type of long-run relationships that
exist in these labor markets. This analysis is extended with
the introduction of the common cycle methodology (of
Vahid and Engle 1993) to illustrate the short-run dynamics
of the tabor markets studied.
Cointegration
Cointegration analysis deals with long-run equilibrium
relationships among economic variables. When a group of
variables move together in a common way over time they
may be cointegrated–that
is, influenced by a common (random) trend. This
comovement can be caused by economic links that tie the
variables together in a long-term bond. Economic theory is
used to suggest variables to test for cointegration.
Examples may include strongly linked variables such as
consumption and income or the levels of total payroll
employment among metropolitan statistical areas in a
homogeneous, well-integrated state economy. Once
economic theory suggests a list of variables that may be
cointegrated, statistical tests such as the Engle-Granger
(1987) test and the Johansen (1995) test can be used to
determine formally if a group of variables is cointegrated.
This article suggests that the labor markets within six
Florida metropolitan statistical areas (MSAs) may share a
cointegrating relationship.
Cointegration analysis can also reveal the response of
particular labor markets to shocks in other labor markets.
For example, changes in labor demand and supply in one
MSA can be transmitted to another. Such information, by
helping determine which MSAs are more independent of
one another (weakly exogenous) and which react strongly
to disturbances in surrounding markets (endogenous), can
be valuable for clarifying how the effects of state level
policy changes as well as economic shocks are transmitted
among individual MSAs.
The Florida MSAs studied are the six largest: Fort
Lauderdale, Jacksonville, Miami, Orlando, Tampa, and
West Palm Beach. The study of their labor markets began
with collecting the seasonally adjusted monthly levels of
total nonagricultural payroll employment from January
1970 to June 1996. The data were tested over the entire
time period for a cointegrating (or long-run equilibrium)
relationship among the MSAs. The hypothesis of a
cointegrating relationship over this time period is not
rejected.
Even when they are governed by the same basic
factors, however, economic relationships change over time.
For this reason, the stability of the relationships over the
entire sample period was examined using a rolling
regression. The results are presented in the first panel of
Chart 1. The number 1 on the vertical axis represents the 5
percent level of significance. At points above this line the
hypothesis that the equilibrium relationship of the entire
time period studied is the same as the subperiods (or the
cointegrating vectors of the full sample are the same as
those of the subsample) is rejected.
[Chart 1 ILLUSTRATION OMITTED]
The first panel of Chart 1 shows that the full sample
can be divided into three subperiods. The first, 1970 to
1980:06, is a period of rejection of the hypothesis that the
full-sample cointegrating vectors are those of the
subsample. Next appears a subsample that suggests
increasing acceptance of the stability of the coefficients of
the cointegrating vectors over the period from
1980:07 to 1987:12. Finally, there is a period of high
acceptance of the null hypothesis, from 1988:1 to 1996:06.
The stability tests suggest that the relationships among the
labor markets of the MSAs change over time.
Next, tests are applied to these subperiods. First, the
sample of the period from 1970:01 to 1980:06 is studied to
determine which MSAs are included in the long-run
equilibrium and which are weakly exogenous. Then an
observation is dropped and the cointegrating relationship is
examined again. This process was continued for a three-year
period. It was found that a stable period in the
cointegrating relationships from 1970:01 to 1978.08 (with
all cities included in the cointegrating relationship test and
with Miami, Tampa, and West Palm Beach found to be
weakly exogenous) was interrupted by a period of
transition beginning around 1978:09.
The data show that the point of division indicated by
the stability test is a time period of relatively dramatic
change that begins one to two years before the actual
dividing date of 1980:06. An appropriate end date to use in
sampling the first period should therefore be shortly before
this transition period. August 1978 was chosen because it
is the month just before changes in weak exogeneity among
the MSAs occur. The same rolling regression technique
used in the original sample was used to test this subperiod.
The second panel of Chart 1 shows that the hypothesis
that the cointegrating relationship for the period from
January 1970 to August 1978 is the same over subperiods
of this sample is accepted over most of the time period.
The results of tests of long-run exclusion and weak
exogeneity for this subperiod are shown in Table 1; all
MSAs are included in the long-run equilibrium relation, as
the hypothesis of exclusion is rejected. The table also
shows that Miami, Tampa, and West Palm Beach are
weakly exogenous.
TABLE 1
Chi-Square Tests, Labor Market Data for Six Florida MSAs,
January 1970-August 1978
West Fort West Fort
Critical Value Miami Orlando Palm Beach Lauderdale
Long-Run Exclusion
5.99 9.16 14.39 17.74 12.21
Weak Exogeneity
5.99 0.70 17.54 1.32 9.30
Critical Value Tampa Jacksonville
Long-Run Exclusion
5.99 19.53 20.95
Weak Exogeneity
5.99 1.48 8.09
Next, moving past the unstable 1980:06-1987:12
transition period indicated in the first panel of Chart 1, the
months spanning the last time period are examined. As
indicated in the chart, this is the region of high acceptance
of the original cointegrating relationship. The dividing date
appears to be early 1988, and thus the sample period is
from January 1988 to June 1996. As before, tests of the
robustness of the cointegrating relationships
are performed by sampling around the transition point.
The results of this period are much less robust than in
the first era, perhaps because of increased linkages of all
Florida MSAs to regions outside the state and less homogeneity
(more specialization) among the MSAs. Miami is
always excluded from the cointegrating relationship.
Orlando is excluded in most of the time periods around
the transition. These findings support the thesis that
Florida’s economy has become less integrated, apparently
beginning around 1988.
There is strong evidence that Miami and Orlando
are excluded from the long-run equilibrium relationship,
as shown in Table 2. There is also strong evidence
that these two MSAs and Fort Lauderdale are weakly
exogenous. This condition indicates that these three
MSAs not only do not move with the others over the
1988:01-1996:06 period but they are also insulated from
short-run shocks in the rest of the state. Just as before,
the stability of the cointegrating relationship is tested
over this period using the rolling regression and chi-square
tests. The third panel of Chart 1 shows that the
observed long-run relationship is stable over most of the
last sample period.
TABLE2
Chi-Square Tests, Labor Market Data for Six Florida MSAs,
January 1970-August 1978
West Fort West Fort
Critical Value Miami Orlando Palm Beach Lauderdale
Long-Run Exclusion
9.49 8.48 8.59 17.72 10.45
Critical Value Tampa Jacksonville
Long-Run Exclusion
5.99 22.78 14.10
The above analysis suggests that for some reason
the relationship between the MSAs changed over the
sample period. Initially the levels of total payroll
employment in the cities grew together in a cointegrated
relationship. The nature of this relationship then
changed, and the MSAs became less bound by the long-run
equilibrium relationship. What could have caused
this apparent change in behavior?
The concepts of temporary cointegration and sudden
change as introduced by Siklos and Granger (1996)
and Krugman (1991, 26), respectively, may help shed
fight on the observed relationships. Siklos and Granger
use the concept of temporary cointegration to describe
data for which the underlying series need not be cointegrated
at all times. The relationship shown over one time
span may be different from that of another period. This
change in the long-run equilibrium relationship might
be expected if there are changes in the makeup of particular
MSAs over time, leading to possible differences in
the demand for and supply of labor in each MSA.
The concept of sudden change offers another possible
explanation for why the relationships between the
MSAs became less cointegrated. Krugman (1991, 26)
describes sudden change as the result of a gradual and
unnoticed change in the underlying conditions that
leads to an explosive apparent change. A likely explanation
is that the gradual transitions of Florida MSAs,
Miami and Orlando in particular, as they became
increasingly linked to economic regions outside Florida
and internally more heterogeneous, fragmented the
state’s economic integration. The growth of tourism in
Orlando and foreign trade in Miami have driven the significant
changes in these labor markets.
In testing for the gradual changes in the MSAs that
may have created the new relationships, location quotients
are useful. Location quotients indicate the relative
concentration of a particular industry in a region.
In this study location quotients are constructed using
total payroll earnings. They are computed by dividing
the percentage of total payroll earnings generated by a
particular industry in an MSA by the percentage of the
industry’s total payroll earnings at the state level. A
location quotient equal to 1 indicates that total payroll
earnings in this industry are as concentrated in the
studied MSA as they are in the state as a whole. If
greater than 1 the location quotient shows greater concentration
in the MSA than at the state level, and if less
than 1, less relative concentration. The location quotients
are consistent with the hypothesis that increased
specialization in tourism in Orlando and trade in Miami
have led to the breakup of the cointegrating relationship
that held the MSAs together. The location quotients
identify some gradual changes in the underlying
economic structure that may have resulted in sudden
change. Growth in import and export activity through
the port of Miami are taken to reflect growth in international
trade links. For the Orlando area (Orange
County) the hotel and service sector is a proxy for
tourism-related activities.
The water transportation location quotient for the
Miami area (Dade County) from 1969 to 1994 depicted
in Chart 2, shows the rise from an above-average concentration
of water transportation in 1969 to the
extremely high level of about three times that of the
state at the end of the period. The increasing concentration
of water transportation in Miami’s economy
clearly shows Miami’s emerging trade links with the rest
of the world gradually growing and helping pull Miami
out of its cointegrating relationship with the rest of the
state. Miami is now the seventh-busiest container port
in the United States as well as the number-one cruise
port in the world.
[Chart 2 ILLUSTRATION OMITTED]
The location quotients of Orlando’s service sector,
measured by sector payroll earnings, tell a similar story
about tourism-related growth in that area in Chart 3. In
1969 Orlando was similar to the state in concentration of
its service sector. This situation changes over the sample
period as this concentration gradually grows to nearly
twice the level in the state. Nationally, Orlando is second
only to Las Vegas when ranked by the relative percentage
of service-sector employment in its economy.
[Chart 3 ILLUSTRATION OMITTED]
Location quotients of hotel total payroll earnings
were calculated to further examine the emergence of
tourism-related activities in the Orlando area. Although
these data are incomplete (the data for hotel payroll
earnings exist only from 1985 to 1987 and 1993 to 1994),
in Chart 4 it can be seen that the Orlando area already
had a high concentration of hotel payroll earnings in
1985 relative to the rest of the state. This concentration
continued to grow to more than five times the state’s
level by 1994. It seems reasonable to assume that the
concentration of hotel earnings in Orlando was much
lower in 1970.
[Chart 4 ILLUSTRATION OMITTED]
These dramatic rises in service and hotel-related
total payroll earnings indicate the growing importance
of tourism in the Orlando area, linking its economy to
areas outside of Florida as well as differentiating it from
the rest of the state. This emerging link helped remove
Orlando from the cointegrating relationship of the early
time period.
The changing level of stability in cointegrating
relationships reveals periods of economic structural
change in the labor forces of the Florida MSAs studied.
What began as a high degree of cointegration began to
lessen by the last period as Orlando and Miami became
excluded. As Siklos; and Granger state, “It seems realistic
to assume that some series are cointegrated only
during some periods and not at others. The reason is
that events or important changes in some of the
institutional features of an economy can interrupt an
underlying equilibrium-type relationship possibly for an
extended period of time” (1996, 8). Examining cointegrating
relationships over different periods of time helps
illuminate the evolution of those relationships.
Common Cycles
The remaining discussion explores the short-run dynamics
of the Florida MSAs’ labor markets. This analysis will
reveal some of the similarities and differences in the
reactions of the MSAs to short-run economic shocks. The
short-run behavior of the MSAs can be strikingly different.
One MSA may be able to expand employment above its
long-run trend while another may be left below its long-ran
trend.
The concepts of common trends and common cycles,
as introduced in Vahid and Engle (1993), extend the
previous cointegration analysis. Their technique can in
some cases be used to separate the long- and
short-run behavior of an economic series. If one can
demonstrate that a specific set of mathematical conditions
is met, then it is possible to decompose data series such as
employment in Florida MSAs into their trend (long-run)
and cyclical (short-run) components.
As the appendix shows, the prerequisites of the Vahid-Engle
decomposition are met in data for the Florida MSAs,
so the series can be decomposed into their long-term and
short-term components. Chart 5 depicts the actual series
and estimated employment trends (which incorporate other
macroeconomic effects and are therefore not straight lines)
for the six MSAs from 1970 to 1996. In Chart 6 the
cyclical components of the trends are plotted by
themselves. These lines correspond to the distance
between the actual series and the estimated trend in Chart
5.
[Charts 5-6 ILLUSTRATION OMITTED]
These charts show that for each MSA there are
several periods when the actual series is either above or
below the estimated trend. These deviations from the
long-term trend are generated by short-run economic
shocks to the growth of total payroll employment.
Positive shocks such as a temporary increase in demand for
a locally produced product (for example, a defense contract
for a local firm) would lead local businesses temporarily to
hire more workers than they otherwise would have. While
they were employing more workers, the charts of the
actual series and trend would show the actual number of
employees exceeding the long-term trend. On the cyclical
graphs this gap would correspond to an upswing above the
horizontal axis. Shocks in one area may also spill over into
others through demand for or supply of labor. Further, two
or more areas may be subject to the same outside shocks or
to shocks propagating across areas.
Comparing cycles shown by this series of charts
reveals both common and differential effects of short-term
shocks on the MSA’s employment. For example, Miami’s
and Orlando’s deviations from their long-run trends appear
in the Charts 5 and 6. Over the sample period the short-run
behavior of these two MSAs is very different. In fact, they
appear to be on opposite paths, with Miami hitting the
height of its cycle in 1980 at a time when Orlando is near
its lowest point.
Looking at all of the MSAs, it can be seen that during
most of the expansion of the 1980s, Miami, Fort
Lauderdale, Tampa, and West Palm Beach are all above
their long-run trend. However, Jacksonville’s level of total
payroll employment, similar to Orlando’s, is below its
trend. Viewing Miami and Orlando as the driving forces
behind Florida’s economy could help explain the apparent
division of the state into a countercyclical northern half and
a procyclical southern one in terms of total payroll
employment during this time period.
Further examination of Chart 6 reveals that the MSAs
can be grouped into three pairs of similar dynamics–Miami
and Fort Lauderdale, Orlando and Jacksonville, and West
Palm Beach and Tampa. Miami and Fort Lauderdale are
the first to rise above their long-run trends in the 1980s’
expansion. They are followed by West Palm Beach and
Tampa. Orlando and Jacksonville remained below their
long-run trend during most of this period. It is interesting
to note that West Palm Beach, although geographically
closer to Miami, displays short-run dynamics more similar
to Tampa’s in terms of the timing of its cyclical upswing.
Conclusion
Cointegration techniques developed by Johansen
(1995) and the common trends and common cycles
analysis developed by Vahid and Engle (1993) have aided
in studying the long- and short-run interrelationships in the
behavior of total payroll employment in six Florida MSAs
over the past quarter-century. The analysis showed that
these MSAs have shared a long-run comovement in their
labor markets. However, there are indications that these
relationships have changed as the economic structures of
the MSAs have evolved. Further, the cyclical dynamics
displayed by these cities suggest that the labor markets of
the northern half of the state behave differently from those
in the southern half in response to short-run economic
shocks.
This analysis helps underline the growing diversity of
influences on the growth trends of Florida MSAs. It also
suggests that these MSAs react differently to short-run
shocks. Both of these dynamics are important in gauging
the differing effects of policy or economic shocks on the
state in parts and as a whole.
Glossary
Cointegration between economic variables may exist if
these variables tend to move together in a common way
over time. Economic theory may suggest which variables to
test for cointegration–for example, strongly linked
variables such as consumption and income or the levels of
total payroll employment among MSAs in a homogenous.
well-integrated state economy.
Common cycles refers to the short-run dynamics of the
time series. In this article the decomposition of the levels
of total nonagricultural payroll employment reveals the
effects of short-run shocks to the group of MSAs.
Common trends refers to the long-run behavior of the
levels of total nonagricultural employment in the MSAs.
This long-run behavior is revealed by the Vahid-Engle
decomposition, which removes the short-run effects of
shocks and leaves the long-run trends associated with the
time series.
Endogenous metropolitan statistical areas, in the
context of this article, are the cities whose labor markets
are dependent on and react to demand and supply shocks
from other metropolitan areas.
Location quotients are used to determine the relative
concentration of a particular industry in a region. If the
location quotient is equal to 1 then the particular industry is as
concentrated in the MSA as in the state as a whole. The
relative concentration of the industry in the MSA is greater
than that of the state if the location quotient is greater than
1 and the reverse if less than 1.
Rolling regressions, in this article, make use of a
statistical test (chi-square) to determine whether the
cointegrating relationship of the full sample is the same as
that of subsamples of the full time period. Starting with a
subsample that begins at the start of the original sample,
the Chisquare test is performed over and over again adding
one more month of data after each test until all the data are
included and tested.
Sudden change is introduced by Krugman as the result of
“a gradual change in the underlying (economic) conditions
(that) can at times lead to explosive … change” (1991,26).
Temporary cointegration is described by Siklos and
Granger (1996) as a change in the long-run relationships
between variables that could lead to the underlying series
not being cointegrated at all times.
Weakly exogenous metropolitan statistical areas
transmit internal supply and demand shocks to other less
independent metropolitan areas.
APPENDIX
Decomposing the Series into
Given r cointegrating vectors defined as the n x r
matrix [[Alpha]] and s cofeature vectors defined a,, the n x s matrix
[[Beta]], stack the vectors in one matrix A:[MATHEMATICAL EXPRESSION NOBLE IN ASCII]
Calculate A-inverse a [[[Alpha].sup.-][[Beta].sup.-]].
Partition A-inverse into the s x
n matrix [[[Beta].sup.-]] and r x n matrix [[[Alpha].sup.-]].
This calculation allows the decomposition into permanent (P) and cyclical
(C) components such that Y(t) = P + C. It follows, then,
that P = [[Beta].sup.-][Beta]Y(t) eliminates the cycles and leaves the
trend or permanent component; C = [[Alpha].sup.-][Alpha]Y(t) eliminates
the trend and leaves the cyclical or temporary component.
Using the maximum eigenvalue test results presented
in Table A, it was found that the time series has four
cointegrating vectors. Next, to find the number of cofeature
vectors, a test of canonical correlations between the series
and certain other variables as explained in Vahid and Engle
(1993) was used. This test (see Table B) shows that
Florida’s MSAs share two cofeature vectors, satisfying
the condition of the Vahid-Engle decomposition that the
sum of the two groups of vectors add up to the number of
variables in the system.
Table A
Test of the Number of Cointegrating Vectors
Test Statistic
Critical Value r Test Statistic
50.30 0 24.63
31.77 1 20.90
27.45 2 17.15
15.65 3 13.39
6.79 4 10.60
0.13 5 2.71
The test of the null hypothesis that the number of the
cointegrating vectors is equal to r results in four
cointegrating vectors.
Table B
Test of the Number of Cofeature Vectors
Row Appox F Numerator DF Denominator DF Pr > F
1 2.7092 168 1644.062 0.0001
2 1.9561 135 1381.116 0.0001
3 1.7113 104 1113.348 0.0001
4 1.4652 75 840.884 0.0080
5 1.2902 48 564 0.0968
6 1.0946 23 283 0.3502
The F-Test of the null hypothesis that the canonical
correlations in the current row and all that follow
are zero results in two cofeature vectors. The
number of cofeature vectors is equal to the
statistically zero canonical correlations (see Vahid
and Engle 1993 for detailed explanations). The sum
of the number of cointegrating vectors and
cofeature vectors equals the number of variables
in the system, and the Vahid-Engle decomposition can
be used.
REFERENCES
Engle, Robert F., and Clive W.J. Granger. 1987.
“Co-integration and Error Correction:
Representation, Estimation, and Testing.”
Econometrica 55:251-76.
Johansen, Soren. 1995. Likelihood-Based Inference
in Cointegrated Vector Autoregressive Models. Oxford:
Oxford University Press.
Krugman, Paul. 1991. Geography and Trade.
Cambridge, Mass.: MIT Press.
Siklos, Pierre L., and Clive W.J. Granger. 1996.
“Temporary Cointegration with an Application Interest Rate
Parity.” University of California at San Diego, Discussion
Paper 96-11.
Vahid, Farshid, and Robert F. Engle. 1993.
“Common Trends and Common Cycles.” Journal of
Applied Econometrics 8:341-60.
EDGAR PARKER
The author is an analyst in the regional section of the
Atlanta Fed’s research department He thanks David
Avery, Zsolt Becsi, Tom Cunningham, Robert Eisenbeis,
hunk King, Whitney Mancuso, William Roberds, Gus
Uceda, and Tao Zha for helpful conversations and
comments on earlier drafts.
COPYRIGHT 1997 Federal Reserve Bank of Atlanta
COPYRIGHT 2004 Gale Group