Federal Reserve Bank of Atlanta

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