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Economic Review
Federal Reserve Bank of Dallas
May 1984

Industrial Diversification,
Exchange Rate Shocks,
and the Texas-Mexico Border
Alberto E. Davila, Ronald H. Schmidt,
and Gary M. Ziegler

Comparisons across border cities show retail and
wholesale trade employment to be more sensitive
than manufacturing employment to changes in
exchange rates . This result suggests that these
cities can become less sensitive to future peso shocks
by developing their industrial infrastructure.
Consequently, adverse employment effects of
exchange rate shocks, such as those following
the 1982 peso devaluations, are likely to be
reduced by attracting maquiladoras and other
manufacturing firms to border cities .

Time Series Forecasting Models
of the Texas Economy: A Comparison
James G. Hoehn, William C. Gruben,
and Thomas B. Fomby

Different approaches to time series forecasting
for Texas suggest that less complicated univariate
techniques often work at least as well as more
sophisticated procedures. Only over longer
forecast horizons do multivariate vector
autoregression models predict better, and then
only in some cases . Otherwise, simpler univariate
methods forecast as well. Multivariate time
series models for Texas variables also require
more effort to construct than has sometimes been
claimed for other such regional models.

This publication was digitized and made available by the Federal Reserve Bank of Dallas' Historical Library (FedHistory@dal.frb.org)

I ndustrial Diversification,
Exchange Rate Shocks,
and the Texas-Mexico Border
By Alberto E. Davila, Ronald H. Schmidt, and Cary M. Ziegler*

Unemployment surged along the Texas-Mexico
border following the February and August 1982 peso
devaluations. The higher unemployment rates can
be attributed to other factors also- the recessions
in both Mexico and the United States, falling oil
prices, a glutted natural gas market, and a bad year
for agriculture- but clearly the devaluations had a
major impact.
Comparisons across border cities, however,
demonstrate that there were significant differences
in the degree to which the major border cities were
affected by the devaluations. Laredo's unemployment rate increased from 9.8 percent in January
1982 to 23.7 percent in September 1982. By con-

* Alberto E. Davila and Ronald H. Schmidt are
economists and Gary M. Ziegler is an assistant
economist at the Federal Reserve Bank of Dallas.
The views expressed are those of the authors and
do not necessarily reflect the positions of the
Federal Reserve Bank of Dallas or the Federal
Reserve System. The authors would like to thank
William C. Gruben and Leroy O. Laney for their
helpful comments.
Economic Review/May 1984

trast, EI Paso's rate rose from 8.8 percent to 12.2
percent in this period.
Empirical results presented in this article suggest
that the unemployment impact of the peso devaluations was related to the relative share of manufacturing employment in some border cities. After controlling for nondevaluation employment effects
through multiple regression analysis, manufacturing
employment was found to be less sensitive than
wholesale and retail trade employment to exchange
rate movements. The evidence also demonstrates
how the uneven impact of the devaluations on
border cities was related to the different degrees of
dependence on the Mexican economy. Manufacturing and trade employment in Laredo exhibited
stronger ties to the Mexican economy than to the
Texas economy. By contrast, Brownsville and, to
some extent, McAllen and EI Paso were more
closely linked to the Texas economy.
The resu Its of this study suggest that TexasMexico border cities can become less sensitive to
future peso shocks by developing their industrial infrastructure. Cities along the border can attract
labor-intensive firms that are drawn by the relatively
low wages of workers there, as well as firms that
use either Mexican inputs or raw materials found in

the border region.
Texas border cities can also take advantage of the
expanding number of maquiladoras in neighboring
Mexican cities. (See the accompanying box.) Maquiladora employment results in spillover effects on
twin-plant operations on the U.S. side. Furthermore,
because maquiladora workers produce goods for
U.s. consumption, increases in maquiladora employment can potentially reduce the sensitivity of
border cities to exchange rate fluctuations.
I n the past, cities along the border have not been
equally successful in attracting manufacturing firms
or maquiladoras. This can be seen by comparing the
manufacturing bases of EI Paso and Laredo. Continuation of these trends may lead, therefore, to a
greater degree of heterogeneity with respect to the
impact of future peso devaluations on unemployment along the border.

Chart 1

Peso/Dollar Exchange Rate
MEXICAN PESOS PER U.S. DOLLAR
140
(QUARTERLY AVERAGES)
120
100
80
60
40
20

1970

1972

1974 1976

1978 1980

1982

SOURCE OF PRIMARY DATA: Board of Covernors, Federal Reserve System.

Problems with a pegged exchange rate
The peso has experienced three abrupt devaluations
against the dollar over the past decade, once in
1976 and twice in 1982 (Chart 1). These large,
discrete jumps reflected the inability of the Mexican
government to maintain a pegged exchange rate as
the peso became increasingly overvalued with
respect to the dollar. A truly floating peso would
have resulted in a slower, more continuous pattern
of change.
Several factors are usually cited in the literature
as contributing to the underlying equilibrium value
of a currency, ranging from differences in current
account balances to real interest rate gaps between
countries. I n the long run, however, the exchange
rate should reflect differences in price levels between countries. This article concentrates on the
overvaluation of the peso as reflected by differences in inflation rates between Mexico and the
United States. These differences had a direct bearing on the allocation of resources in Texas-Mexico
border cities and were, therefore, responsible for
much of the impact of the peso shocks on these
cities.
Inflation rates differed considerably between
Mexico and the United States in the periods
preceding each of the most recent peso devaluations. From 1970 through August 1976, the consumer
price index for Mexico grew an average of S.8 percent faster than the consumer price index for the
United States. Between 1977 and 1981, the index
2

grew an average of 10.3 percent faster than its U.S.
counterpart. 1
I n the 1970-76 and 1977-81 periods, however, the
peso/dollar exchange rate showed little change. (In
fact, in the 1970-76 period, there was no change in
the exchange rate.) As a result, the peso became increasingly overvalued with respect to the dollar.2
Because Mexican consumers were able to trade
with U.S. merchants at the official exchange rate,
overvaluation of the peso allowed them to purchase
more U.S. goods and services than would have been
possible at levels determined by freely floating exchange rates. This overvaluation "subsidy" to Mexican consumers encouraged border cities to increase
their reliance on retail trade with Mexico.

1. The natural logarithm of the ratio of the Mexican consumer
price index to the U.S. consumer price index was regressed
against time for each of the two periods. The coefficients
represent the difference between growth rates of the Mexican
and U.S. price indexes.
2. A measure of purchasing power parity (PPP) was used to obtain
an estimate of what the peso/dollar exchange rate would have
been under floating exchange rates. The PPP takes into account changes in price levels between the United States and
Mexico. Values of PPP from 1970 through August 1976 and
from late 1977 through January 1982 (before the first 1982
devaluation) indicate that pressure on the peso was rising in
these intervals.

Federal Reserve Bank of Dallas

Table 1

BORDER AREA EMPLOYMENT, BY SElECTED SECTORS
Total

Manufacturing
Durable
goods

EI Paso
Percent of total

38,700
20.3

12,150
6.4

26,550
13.9

8,150
4.3

10,150
5.3

Laredo
Percent of total

1,950
4.8

600
1.5

1,350
3.3

1,850
4.5

McAllen'
Percent of total .

9,300
8.4

1,800
1.6

7,500
6.8

10,700
12.4

5,350
6.2

Standard
metropol itan

statistical area

Brownsville' .
Percent of total

Contract
Trade
construcNondurable
Retail
Wholesale
tion
goods
Annual averages for 1982 employment

S.ervices

Government

31,350
16.5

27,150
14.3

33,500
17.6

1,800
4.4

10,350
25.2

5,100
12.4

6,700
16.3

5,950
5.4

9,150
8.3

17,850
16.2

10,150
9.2

20,000
18.1

4,050
4.7

4,200
4.9

14,150
16.5

10,400
12.1

12,300
14.3

1 McAllen-Pharr-Edinburg.
2. Brownsville-Harlingen-San Benito.
SOURCE OF PRIMARY DATA Texas Employment Commission

Because of the price and income effects on the
Mexican side of the border, Mexican firms and consumers drastically reduced their purchases in U.S.
border city markets. This decline in sales to Mexico
led to significant layoffs by border merchants.
Absence of more frequent changes in the exchange rate, therefore, exacerbated the employment
effects of exchange rate changes by providing additional short-run incentives for US firms in border
cities to focus on retail trade with Mexico. In times
of devaluation, those are the firms most affected by
the loss of purchasing power on the Mexican side of
the border.
Manufacturing activity in the border cities was
less vulnerable to peso shocks because the linkage
to the Mexican economy was not as direct. Consequently, the elimination of the subsidy by official
devaluations of the peso had a much smaller impact
on cities that concentrated more extensively on
manufacturing than on international trade with
Mexico.
Differential employment effects
The four major Texas cities along the border-EI
Paso, Laredo, McAllen, and Brownsville-were all
affected differently by the peso devaluations (Chart
2). In particular, Laredo and McAllen experienced
larger increases in unemployment than did
Brownsvi lie and EI Paso.
Economic Review/May 1984

These differential effects of exchange rate
changes on the four border cities reflect fundamental differences in their underlying economic structures. As shown in Table 1, EI Paso and Brownsville,
the two cities least affected by the devaluations,
had the largest manufacturing employment shares in
1982 -20.3 percent and 12.4 percent, respectively.
Laredo, which had the largest increase in unemployment following the devaluations, had only 4.8 percent of its employment in manufacturing.
To help untangle the effects of exchange rates on
different types of employment, a set of regression
equations was constructed for each city. I n addition
to exchange rates, both of the major categories of
employment-trade (wholesale and retail) and
manufacturing-were also hypothesized to be influenced by industrial production in Texas and
Mexico, oil and natural gas prices, and the number
of maquiladora workers employed in the Mexican
city adjacent to each of the four border cities.'
I ndustrial production indexes for Texas and Mexico were included in an attempt to control for the

3. Additional variables describing the economic infrastructure
and capital investment in each city would provide considerable power in explaining the employment patterns more
precisely. Unfortunately, monthly series on such variables are
not currently available for these cities.

Chart 2

Unemployment Rates in Major Texas Border Areas and the United States
PERCENT UNEMPLOYED
30
(SEASONALLY ADJUSTED)

;::

....::>

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>

0
~

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I

.... 1'

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',I .., I\

I I
I Ir'
II • \" 1

1983

I "

1979

(SEASONALLY ADJUSTED)

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>
0

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::>

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::>
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\;/11

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I

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15
BROWNSVILLE-HARLINGENSAN BENITO

..... .,;

....

«
>
w
Cl

0
~
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::>

::>

1982

1983

,,,

I,
I

/ '/\'\ / ......V / I

10
UNITED STATES

,,
,
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,\,
, I,

1981

u..

McALLEN-PHARR- ~
EDINBURG
/'

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>«
::>

w
0-

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::>
""w

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>

1983

1982

1981

1980

«
>

PERCENT UNEMPLOYED

,..II I

'I I
'
"

II
" I

1982

LAREDO

1981

>::>,

u..

...

(' '.. .1

II I ~
,I I
,
I,
~

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II
II

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>-

PERCENT UNEMPLOYED
30
(SEASONALLY ADJUSTED)

(I
I. ,,:

1980

«
>

><I)
::>

w
u..

1979

«
>

....

""'"

;::

::>

z
0
;::
«

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::>

;::

PERCENT UNEMPLOYED
30
(SEASONALLY ADJUSTED)

I" \

I
\-,1

1980

1982

1983

i
I

SOURCES OF PRIMARY DATA: Texas Employment Commission.
U.S. Department of Labor, Bureau of labor Stdtistics.

I
~

Federal Reserve Bank of Dallas

The Maquiladora Program
Maquiladoras are assembly plants, mostly in northern
Mexico, that are an outgrowth of the border industrialization program initiated in 1965.' Originally intended to industrialize the northern states of Mexico,
the maquiladora program has also increased the
manufacturing base of U.S. border cities through the
creation of U.S. "twin plants" As part of the program,
a U.S. firm locating a plant in Mexico also builds a
plant on the U.S. side of the border. This twin plant
is usually a distribution center for the Mexican
maquiladora plant, although some twin plants do additional assembly work.
American firms have found the Maquiladora pro-

1. For discussions of the border industrialization program,
see Anna-Stina Ericson, "An Analysis of Mexico's Border
Industrialization Program," Monthly Labor Review, May
1970,33-40, and Donald W. Baerresen, "Mexico's Assembly Program: Implications for the United States," Texas
Business Review, November-December 1981,253-57.

effects of cyclical changes in business conditions on
employment along the border. Positive coefficients
indicate that border cities tend to be influenced by
the same factors that affect the overall Texas and
Mexican economies. Oil and natural gas prices
reflect the employment and wealth effects corresponding to changes in energy markets' Higher
natural gas prices, for example, increase the income
of owners of gas wells and lead to increases in the
drilling industry. Higher natural gas prices also increase spending in areas that have significant
deposits of natural gas. The number of maquiladora
workers was included to capture the effect of the
growth of twin plants in the cities.
Regression results using monthly data from July
1978 to April 1983 are reported in Table 2.5 In each
of the four cities, the coefficient on the exchange
rate was negative and significant for employment in
the trade sector. Furthermore, looking across equations, the coefficients were larger for Laredo and
McAllen and considerably smaller for EI Paso and
Brownsville.
Manufacturing employment was also negatively
affected by devaluations in all cities except
Economic ReviewlMay 1984

gram attractive for several reasons. Tariff codes in
both Mexico and the United States permit American
firms to ship raw materials and assembled goods between the two countries at lower duties. An American
firm is allowed to ship raw materials to Mexico dutyfree, use them to produce a good in its maquiladora,
and import the assembled product into the United
States, paying duties only on the value added to the
good in Mexico.
The maquiladora program provides significant cost
advantages because of Mexico's proximity to U.S.
distribution centers and because of the low cost of
Mexican labor. Low transportation costs from Mexico
make other low-wage countries in the Far East, South
America, and the Caribbean relatively less attractive
to U.S. firms. Furthermore, the fact that wages of
Mexican workers are less than those of U.S. workers
has created incentives for labor-intensive firms to
locate assembly plants in Mexico rather than in the
United States.

McAllen. For McAllen, this coefficient was insignificantly different from zero. The exchange rate
coefficients in the manufacturing employment equations, however, were consistently smaller than those
in the trade employment equations. 6 Changes in the
value of the peso have an immediate impact on the

4. The regressions reported in Table 2 use nominal prices for oil
and natural gas. Regressions that used real oil and natural gas
prices (nominal prices deflated by the U.S. consumer price
index) in place of the nominal prices had no effect on the
signs, significance, or relative magnitudes of the coefficients in
Table 2.
5. The results of the simple linear regressions reported in Table 2
were insensitive to alternative, more complicated formulations.
The use of lag structures, nonlinearities, and multiple-equation
estimation techniques had little effect on the relationship between exchange rate coefficients in the manufacturing and
trade employment equations.
6. The hypothesis that the coefficients on exchange rates in the
trade and manufacturing employment equations were insignificantly different from each other was tested for each city
individually. The hypothesis was rejected at the 90-percent
confidence level for all cities except Brownsville.

Table 2
INFLUENCES ON BORDER AREA EMPLOYMENT, JULY 1978-APRIL 1983
Area,
employment

sector

EI Paso
Manufacturing.
Trade.
Laredo
Manufacturing.
Trade.
McAllen'
Manufacturing.
Trade.
Brownsville 2
Manufacturing
Trade.

Texas

Mexican
produc-

rate

industrial
production
index

index

Natural
gas
price

Oil
price

Maquiladora
employment

Rho

9,397.93
(2.1)*
32,961.06
(11.2)*

-16.85
(-1.9)
-18.31
(-3.3)*

38.53
(18)
-1.21
(-.1 )

21.18
(1.9)
7.59
(.9)

1.38
(6)
4.26
(3.2)*

5.82
(22)*
-.84
(-.5)

.21
(21 )*
.07
(1.0)

-.81
(-10.4)*
-.65
(-6.6)*

.74

739.52
(12)
4,592.66
(1.7)

-2.21
(-1.8)
-30.95
( -5.7)*

2.85
(1.2)
7.70

3.33
(2.3)*
19.75
(2.8)*

-.41
(-1.4)
304
(2.4)*

.63
(21 )*
1.53
(1.2)

-.03
(-2)
-1.09
(-16)

-.75
(-85)*
-.63
(-61)*

.53

-22,345.96
(-2.3)*
15,836.74
(39)*

6.12
(.4)
-30.86
(-4.5)*

147.18
(28)*
3.12
(.2)

6.43
(.2)
-8.54
(-8)

-3.91
(-8)
6.41
(29)*

.82
(.2)
-1.90
(-1.0)

-.38
(-.9)
.80
(38)*

.10
(.8)
-.472
(-41)*

.49

5,230.30
(2.5)*
7,288.88
(4.3)*

-18.13
(-5.6)*
-21.83
(-86)*

18.18
(20)*
21.09
(26)*

13.74
(25)*
3.76
(.7)

-1.50
(-1.9)
4.39
(7.1 )*

.51
(.5)
-1.02
(-1.3)

.01
(.1)
.07
(11 )

-.53
(-48)*
-.32
(-27)*

.85

Regression
intercept

Peso!
dollar
exchange

(7)

tlon

.68

.83

.92

.95

1 McAllen-Pharr-Edinburg.
2. Brownsville-Harlingen-San Benito
NOTE: Trade employment covers both wholesale and retail trade
Figures in parentheses are t statistics; * indicates significance of the independent variable at the 5-percent level
All estimates except those for manufacturing employment in the McAllen area were corrected for first-order autocorrelation
Rho is the estimated autocorrelation coefficient.
SOURCES OF PRIMARY DATA Banco de Mexico.
Board of Governors, Federal Reserve System
Federal Reserve Bank of Dallas.

Secretarla de Programacion y Presupuesto.
Texas Employment Commission.
U.S. Department of Labor, Bureau of Labor Statistics.

retail trade portion of a city's economy because of
the reduction in purchasing power on the Mexican
side of the border,
Aside from the exchange rate results, the other
coefficients in Table 2 help to explain the differential employment effects of the devaluations across
cities, One of the more interesting results is the
relative effect of the Texas industrial production
index (TIPI) and the Mexican production index (MPI)
on the different cities. Both trade and manufacturing employment in Laredo demonstrated greater
responsiveness to MPI than to TI PI. By contrast, the
6

coefficients on TI PI and MPI for the other cities
generally indicate a closer link to the Texas
economy.
This result reflects the long-term development
patterns and geography of the different cities,
McAllen is located a few miles from the border,
with one of its major products being citrus fruit
targeted toward the U.S. market. EI Paso, with its
copper smelters and garment manufacturing, and
Brownsville, with its seafood processing, both produce commodities bound for the U,S. market.
Laredo, on the other hand, developed on one of the
Federal Reserve Bank of Dallas

major rail lines connecting Mexico and the United
States. The stronger impact of devaluations on
Laredo, therefore, is to a large extent a result of its
historical role as a trade center between the two
countries.
To say that Texas cities with closer ties to Mexico
are more affected by peso devaluations is almost
tautological, of course. It could be argued that if
the border cities were to cease trading with Mexico,
they would not be affected by fluctuations in the
peso. Such an argument, however, ignores the fact
that cities typically develop along the border to
take advantage of foreign trade with Mexico. Consequently, although the cities would be less influenced by changes in the peso if they were to turn
away from the Mexican market toward the U.s.
market, they would probably be worse off. Trade,
especially trade with factor mobility, can be shown
to lead to greater production for both countries
involved.

Factors influencing the growth
of manufacturing along the border
The evidence in Table 2 suggests a link between the
share of manufacturing employment and the effect
of an exchange rate shock on unemployment rates
along the border. The extent to which cities alter
the composition of their industrial structures over
time, therefore, may change the relative sensitivity
of their economies to future devaluations. Results
from this study suggest border cities that develop
their manufacturing base tend to be less vulnerable
to devaluations.
Several factors have influenced and continue to
influence the pattern of industrial development in
border cities? One important factor is the low wage
paid to border workers relative to the U.s. average.
According to the 1980 Census, workers along the
border earned 39 percent less than their counterparts in the interior of Texas' Consequently, laborintensive firms have incentives to relocate to the
border. For example, a large number of apparel
manufacturing plants have moved to the border
cities, especially to EI Paso.
Region-specific natural resources can also affect
the pattern of manufacturing along the TexasMexico border. Because of its proximity to the Culf
of Mexico, Brownsville has a large proportion of
manufacturing employment in seafood processing.
McAllen has a considerable number of frozen fruit
Economic Review/May 1984

and vegetable plants, reflecting Hidalgo County's
leading role in citrus production, and EI Paso has
several copper smelters and mines.
In all these cases, firms have sought to combine
the advantages of proximity to natural resources
with the lower-than-average wages to establish
labor-intensive manufacturing plants. The existing
wage gap between Texas border cities and the U.s.
interior, in particular, could be used by border cities
to encourage further movement of capital to the
border.

Contribution of maquiladoras
The newest and potentially most dynamic development influencing diversification patterns across
border cities is the maquiladora program. The
maquiladora program has grown rapidly in recent
years. Between July 1978 and April 1983, total
employment in maquiladora plants in Ciudad
Juarez, Nuevo Laredo, Reynosa, and Matamoros
rose 48.3 percent, from 50,066 workers to 74,239. As
shown in Table 3, Reynosa (across from McAllen)
has had the fastest maquiladora employment
growth rate over the past five years, while
Matamoros (across from Brownsville) has had the
slowest growth rate.
This program can be hypothesized to have two
effects on decreasing the sensitivity of the border
cities to exchange rate shocks. First, the twin-plant
concept is targeted toward labor-intensive manufacturing industries that can best take advantage of the
low wages on the Mexican side of the border. As a
result, the maquiladora program can be expected to
increase the manufacturing base of the border
cities. The creation of an assembly plant on the

7. For some discussions of the manufacturing characteristics of
Texas-Mexico border cities, see the following articles in the
Texas Business Review: Charles P. Ziatkovich and Carol T. F.
Bennett, "EI Paso Economic Profile," January 1977,4-7;
Charles P. Ziatkovich and Carol T. F. Bennett, "The Lower Rio
Grande Valley: An Area of Rapid Growth," September 1977,
204-9; and Niles Hansen, "Development of the Southwest
Borderlands," November-December 1981, 247-52.
8. This estimate is based on annual wages and salaries of
householders as defined by the Public Use Sample of the 1980
Census. For more on the border-interior wage differential, see
Alberto E. Davila, "Sources of Depressed Earnings Along the
Texas-Mexico Border," Economic Review, Federal Reserve
Bank of Dallas, November 1982,13-19.

Mexican side is likely to generate incentives for
firms to move other divisions of their manufacturing
firms to the border, especially given the relatively
low wages that also exist on the u.s. side of the
border.
Second, even in cases where the u.S. firm chooses
to establish a distribution center, rather than a
manufacturing center, on the u.S. side of the
border, sensitivity to peso devaluations is reduced.
In such cases, output of the maquiladora firms
tends to be targeted toward the general u.S. market.
As a result, the maquiladora-related portion of the
trade sector on the u.S. side and the maquiladora
portion on the Mexican side are less influenced by
changes in the Mexican economy than by changes
in the u.S. economy. This aspect of the maquiladora
program is especially attractive because the
economies of both the u.S. border city and the Mexican twin city have less dependence of employment
on the value of the peso.
Some evidence of the influence of maquiladoras
on employment in the border cities can be seen in
the regression results reported in Table 2. In both
the manufacturing employment equation for EI Paso
and the trade employment equation for McAllen,
the coefficient on maquiladora employment was
positive and significant. Coefficients in the other
equations, however, turned up insignificant at the
5-percent level.
The significance of the coefficients for EI Paso
and McAllen, as well as the lack of significance for
the other cities, may be the result of the uneven implementation of the maquiladora program across
cities. EI Paso and McAllen had the fastest growth
rates of the four border cities in maquiladora
employment on the Mexican side of the border
(Table 3). Furthermore, Ciudad Juarez, which is
across from EI Paso, is the city along the border
with the most maquiladora workers.
The difference in employment effects between
EI Paso and McAllen, with the positive effect on
manufacturing employment in EI Paso and on trade
employment in McAllen, may be the result of differences in existing economic infrastructures. As
shown in Table 1, EI Paso has a larger manufacturing sector than McAllen. Proximity to existing
manufacturing is often an added incentive for firms
to move manufacturing facil ities to the border,
rather than setting up a distribution center.
The effects of maquiladora employment
8

Table 3

MAQUILADORA EMPLOYMENT
IN BORDER CITIES
Annual
growth
rate,

Mexican city (Texas city)

Ciudad Juarez (E I Paso)

April
1983
level

48,039

July 1978April 1983
(Percent)

Nuevo Laredo (Laredo)

2,383

3.6

Reynosa (McAllen)

9,277

22.8

14,540

Matamoros (Brownsville) .
SOURCE OF PRIMARY DATA
Secretdfl a

de Programacion y Presupuesto

demonstrated in Table 2 tend to support the
hypothesis that border cities are better insulated
from exchange rate shocks through the program.
The results, however, are far from conclusive.
Several problems warranting further study should be
pointed out in interpreting the effects of the maquiladora program.
First, the data used in this article, which have not
been used previously, do not allow inference about
a direct link for either the trade sector or the
manufacturing sector of employment in the border
cities. No data are currently available that would
make it possible to determine directly the type of
employment created in U.S. border cities by the
establishment of a maquiladora plant on the Mexican side of the border. The positive effects that
emerge for the trade sector in McAllen and the
manufacturing sector in EI Paso reflect a "spillover"
from income gains in Mexico from maquiladora
employment. This income effect, of course, is also
an insulating factor for the border cities, because
jobs in maquiladora plants are not as responsive as
jobs in other firms in Mexico to changes in the
Mexican economy.
Second, the use of maquiladora employment data
for the city directly across from the U.S. city as a
proxy for U.S. twin-plant development has some
limitations. Maquiladoras have begun to move from
the border into the interior of Mexico. 9 Although
these plants have twin plants in U.S. border cities, it
Federal Reserve Bank of Dallas

is difficult to identify the location of a twin plant's
maquiladora from available maquiladora data. ' °
Establishing a clear relationship between the
maquiladora program and the insulation of the
border cities from future peso devaluations,
therefore, cannot be accompl ished without further
study. Nonetheless, the results of this preliminary
research provide some support for the hypothesis
that maquiladoras, through developing the manufacturing industry on both sides of the border and
through increasing the share of the trade sector
dedicated to a wider U.S. market, could lead to less
dependence of U.S. border employment on the
value of the peso.

Implications
If the peso becomes seriously misaligned again,
future abrupt movements in the exchange rate are a
possibility. The Mexican government has made recent attempts to change the official exchange rate
between the peso and the dollar more systematically, but there is no guarantee that a significant
misalignment of the exchange rate will not occur."

9. In January 1980, employment in maquiladora plants reported
in Ciudad Juarez, Nuevo Laredo, Reynosa, and Matamoros accounted for 85 percent of total employment in the states of
Chihuahua and Tamaulipas. Between January 1980 and April
1983, however, growth in maquiladora employment in the four
cities grew 25.2 percent, while maquiladora employment outside the cities grew 39.6 percent

10. To see if including interior data led to stronger results for
the maquiladora variable, state maquiladora data were
substituted for the city data used in the regressions in Table
2. The results were mixed, with Brownsville showing a
stronger and significant effect in the maquiladora variable
but with the other cities showing no effect

11. The Mexican government has been adjusting the exchange
rate by 13 centavos per day since September 1983 and has
announced plans to continue the adjustment through 1984.

Economic ReviewlMay 1984

The results of this study suggest that border cities
can reduce the impact of future peso shocks on
their economies by expanding the manufacturing
base on the U.S. side of the border and encouraging
the development of maquiladora industries on the
Mexican side. They can do so by aggressively
attracting industries well suited to take advantage
of region-specific characteristics and the low wages
along the border.
Preliminary empirical evidence reported in this
article also supports the hypothesis that further
development of maquiladora plants could aid in
reducing employment effects from devaluations.
Further research is required to untangle the relationships between existing maquiladora development
and employment diversification along the Texas
border. Such studies are important because the
maquiladora program is likely to continue its rapid
growth and the Mexican government has continued
to promote maquiladora investment. '2
An additional aspect of this study relates to the
heterogeneous nature of the impact of peso
devaluations on Texas border cities. Unless the
least-diversified border cities, like Laredo, keep pace
with the industrial expansion of EI Paso, the
response of border cities to exchange rate shocks
may widen in the future.

12. In the Official Gazette for August 15,1983, the Mexican
government announced a decree for the promotion of the
maquiladora industry This decree made several changes
easing restrictions on maquiladora operations. For example,
maquiladora plants are no longer required to export qualitycontrol rejects; they need not export goods through the same
port where they import raw materials; and they are authorized to sell 20 percent of production, as long as they are not
in direct competition with Mexican industries. For additional
changes and a more detailed version of the contents of this
decree, see American Chamber of Commerce of Mexico,
Maquiladora Newsletter, September 1983, 3-14.

Time Series Forecasting Models
of the Texas Economy: A Comparison
By James

Hoehn, William C. Gruben, and Thomas B. Fomby*

This article compares time series models for
forecasting the Texas economy, ranging from extremely simple specifications to some rather complex methods. Movements in seven major Texas
economic variables were forecast using these
various techniques. The models were used to examine the forecasting power embedded in a
variable's own past movements, in the past
movements of other Texas variables, in the past
movements of a set of national variables, and in
combinations of these classes of variables.

* James G. Hoehn, formerly an economist at the
Federal Reserve Bank of Dallas, is an economist
at the Federal Reserve Bank of Cleveland.
William C. Gruben is a senior economist at the
Federal Reserve Bank of Dallas. Thomas B. Fomby
is an associate professor of economics at Southern
Methodist University and a consultant at the
Federal Reserve Bank of Dallas. The views
expressed are those of the authors and do not
necessarily reflect the positions of the Federal
Reserve Bank of Dallas or the Federal Reserve
System.
Economic Review/May 1984

As a group, the time series models utilized have
three noteworthy characteristics. First. they are
relatively simple, compared with the large, multiequation structural forecasting models that often
receive considerable attention. Second, also unlike
structural models, these time series models are
designed only to forecast, not to explain economic
interrelationships. For example, it is unwise to use
time series models to estimate the economic impact
of a change in governmental programs or to
calculate the likely economic effect of some shock
in the private sector. Third, the time series models
all forecast movement of one variable on the basis
of past movements in that variable. Some models
also incorporate information based on past
movements of other variables, but only to the extent that these other variables are useful in predicting later behavior, without regard to causal linkages.
The out-of-sample forecast results of the models
showed that no single time series approach was consistently superior in predicting the values of all
seven Texas variables. In addition, the more
mathematically complicated approaches to
forecasting did not always prove superior to less
sophisticated methods. In fact, results suggest that
great care must be taken in constructing the
11

relatively complicated and much-praised vector
autoregression models if they are to prove even the
forecasting equals of simple univariate time series
models.
For example, a type of vector autoregression
model reported as valuable in a regional model of
the Ninth Federal Reserve District proved for the
seven Texas variables to be the poorest forecaster
of all models constructed.' However, it was also
found that the accuracy of univariate time series
models diminished more rapidly with the length of
the forecast horizon than did that of some of the
multivariate models.
Time series approaches used
The differences between various time series models
lie in the ways each incorporates information about
the own past movements of a dependent variable
and about the past movements of other variables in
the forecasting process. These differences involve
dissimilarities not only in the explanatory variables
used but in the functional forms applied to the
variables.
One of the simplest approaches to forecasting on
the basis of a variable's own past behavior is the
assumption of a "random walk" with drift. The random walk with drift implies that a variable's growth
can be characterized as unrelated deviations from
some average growth rate. This article illustrates
that the behavior of some Texas variables can as
well be characterized as a random walk as by the
alternatives exam ined.
The autoregressive integrated moving average
(ARIMA) approach to forecasting incorporates a
variable's past movements to forecast its future
changes. For this univariate single-equation method

1. See Paul A. Anderson, "Help for the Regional Economic
Forecaster: Vector Autoregression," Federal Reserve Bank of
Minneapolis Quarterly Review, Summer 1979,2-7. The author
compares his VAR model's ex ante, out-of-sample results with
ex post, within-sample errors of an annual structural model of
the Philadelphia region and with the same errors for an
average of structural model forecasts for seven regions. He
does not compare the forecast errors of his VAR model with
those of other types of time series models, such as univariate
models. Such a comparison would be useful because
univariate models often outperform large structural models.
See, for example, the remarks of C. W. J. Granger and Paul
Newbold in Forecasting Economic Time Series (New York:
Academic Press, 1977), 289-300.

of forecasting, George Box and Gwilym Jenkins have
developed an approach for choosing which patterns
of behavior to incorporate and which to ignore 2
Box-Jenkins ARIMA models were examined as
part of this research, but another ARIMA model
specification was also applied for the Texas
economy, the ARIMA (2, 1,0). I n the (2, 1,0) configuration, there are two lags in an equation (the 2
in the 2,1,0), the data are expressed in first differences (the 1 in the 2, 1,0), and there are no
moving-average parameters in the equation (the 0 in
the 2,1,0), unlike the configurations in some other
ARIMA equations.
Transfer functions represent a level of sophistication only slightly higher than the ARIMAs. Transfer
function models used in this study included regression of a variable's growth rate on two lags of its
growth rate plus two lags of the growth rate of one
or possibly more variables.
Two other types of transfer function models were
also examined. One, the "closed-region" model,
included seven equations. In each equation the
growth rate of one of the seven Texas variables was
regressed on two own lags plus two lags of the
growth rates of each of the other six Texas
variables.
To examine the usefulness of national information
in forecasting the Texas economy, a seven-equation
"trickle-down" model was also constructed. In each
of these equations, the growth rate of one of the
seven Texas variables was regressed on two own
lags plus two lags of five national variables.
The information thus acquired with regard to the
relative forecasting power of different individual
variables, different sets of variables, and different
functional forms in forecasting each of the seven
Texas variables was then applied in the construction
of three alternative vector autoregression (VAR)
models. I n a V AR model, all variables ina system of
equations are used to forecast movements in every
variable in that system.
The closed-region model described above can be

2. A common reference source for discussions of this procedure
is George E. P. Box and Gwilym M. Jenkins, Time Series
Analysis, Forecasting and Control (San Francisco: Holden-Day,
1970). A more rudimentary explanation is found in Charles R.
Nelson, Applied Time Series Analysis for Managerial
Forecasting (San Francisco: Holden-Day, 1973).
Federal Reserve Bank of Dallas

Table 1
GLOSSARY OF VARIABLES
Regional variables

TlPI

CPIDFW
PAYROLL
TEMP

Texas industrial production index.
consumer price index for Dallas-Fort Worth metropolitan area (quarterly averages from
interpolation of available monthly figures; deseasonalized using the X-11 procedure).
nonagricultural wage and salary employment in Texas.
total civilian employment in Texas.

RTPY = Texas personal income, deflated by the CPIDFW (seasonally adjusted using the X-11 procedure).
RTRET = Texas retail sales, deflated by the CPIDFW (seasonally adjusted using the X-11 procedure).
TLF = Texas civilian labor force.
National variables

LEAD
COINC
IPI

NEMP
FYAVG

index of 12 leading economic indicators.
index of four roughly coincident economic indicators.
industrial production index.
total nonagricultural civilian employment (persons 16 years of age and over).
Moody's all-industry average corporate bond yield.

NOTE: All series were seasonally adjusted by the publishing agency except the three regional series that were adjusted by the
authors, using the X-ll computer procedure of the Commerce Department. The national series were taken from the
CITIBASE data bank; most of the national variable names are the same as those in that file
Seasonally adjusted data were used in this initial exploration in order to render more transparent the resulting models and
their relative success in exploiting economic relationships as opposed to their ability to deal with seasonality. Time series
that include (seasonal) moving-average parameters are generally best when seasonal factors are not strictly deterministic.
SOURCES OF PRIMARY DATA: Board of Governors, Federal Reserve System.

Business Week.
Federal Reserve Bank of Dallas
MoodyRs Investors Service
U.S. Department of Commerce, Bureau of Economic Analysis
U.S. Department of Commerce, Bureau of the Census.
U.S. Department of Labor, Bureau of Labor Statistics.

considered a form of V AR model because every
variable that is a left-hand-side variable in any equation is also a right-hand-side variable in all equations. The closed-region model is a simple VAR
model, however, in the sense that prior restrictions
on the values of the coefficients and on the standard deviations of these variables are not imposed.
It should be distinguished from so-called Bayesian
VAR models, in which such prior restrictions are
imposed.
The nature of prior restrictions as they are often
appl ied to Bayesian V AR models, along with the
rationales for including them, will be discussed in
later sections. I ndeed, an important purpose of this
article is to present the first published comparison
of alternative approaches to prior specifications for
Economic Review/May 1984

regional VAR modeling. The article also contrasts
the forecasting ability of models having different
prior specifications with results derived from
univariate time series procedures.
Another function of this article is that, with
respect to vector autoregression modeling, it offers
some new methodology for the selection of prior
restrictions. These selection procedures, based on information gained from some of the other time series
forecasting models constructed in this study, improved the forecasting power for a V AR model of
the Texas economy. Even with these improved procedures for deciding on the prior restrictions to impose, however, Bayesian VAR modeling does not
seem to offer consistently better results than
ARIMA forecasts.
13

The forecasting problem

the form, denoted ARIMA (p, d, q), of

The purpose of all the forecasting procedures
outlined is to predict the following seasonally adjusted Texas quarterly variables: (1) the Texas industrial production index (TIP/); (2) the consumer
price index for the Dallas-Fort Worth metropolitan
area (CPIDFW); (3) nonagricultural wage and salary
employment (PA YROLL); (4) total employment
(TEMP); (5) Texas personal income, deflated by the
CPIDFW (RTPy); (6) Texas retail sales, deflated by
the CPIDFW (RTRET); and (7) the Texas labor force
(TLF). More information about the variables appears
in Table 1.
Estimations were generally performed on growth
rates, rather than on raw data. All variables were
first placed in natural logarithmic form. Except in
the VAR models, estimations were performed on
first differences of the logarithms, which are essentially the growth rates of the original data.
The objective of the alternative forecasting
procedures used in this study was to minimize the
root mean square error (RMSE) of out-of-sample
forecasts. To achieve this goal, various specifications were examined with regard to the withinsample and out-of-sample error reductions they offered compared with a set of benchmark equations.
For the within-sample examinations, amendments
to various equations were considered in light of
their power to reduce standard error of equation.
Such power was measured by the statistic

(1 -

where SEE A is the standard error of some equation,
A, used to forecast a given variable and SEE B is the
standard error of another equation, B, used to
forecast the same variable. If the value for I BA is
positive, B represents an improvement over A in
terms of standard error of equation because a
positive value for I signifies a lower SEE value for B
than for A. Conversely, a negative value for IBA
means that equation B has poorer within-sample
forecasti ng characteristics than A.

Univariate ARIMA models
ARIMA models treat each Texas variable in isolation
in estimation and in forecasting. Such a model takes

3. Box and Jenkins, Time Series Analysis, 74, 87-93.

~lL -

~2L 2

= Jl +

... -

(1 -

~pLP)(1 - L)d Yt

elL -

e2L2 - ... -

eqLq)a t ,

where Yt is the natural logarithm of the series and at
is a normally distributed unobservable random
variable with zero mean, finite and constant
variance, and zero autocorrelation at all lags 3 The
expression L is a lag, or backward shift, operator.
There are p autoregressive terms (lagged y's) and q
moving-average terms (lagged a's). Typically,
economic time series that exhibit growth must be
transformed to natural logarithms and differenced
once (making d equal 1 , to signify first differences)
in order to make assumptions about the disturbance
term plausible for any p and q. That practice was
followed in the study described in this article.
ARIMA models can be identified using methods
established by Box and Jenkins. These methods first
infer plausible candidate equation forms from
sample autocorrelations, subsequently subject them
to diagnostic tests, and repeat this process (if
necessary) until an adequate model is found. The
Box-Jenkins approach seeks a simple representation
adequate to characterize the behavior of the series.
It is useful to ask statistically if a given ARIMA
equation forecasts any better than a model that
assumes a variable behaves as a random walk with
drift-that is, any discrepancy from a long-term
average growth rate does not persist. The (p, d, q)
form of the ARIMA would be expressed as (0,1,0).
This random walk specification means that recent
past movement in a variable, as well as recent
lagged disturbances in that movement from some
long-term stable rate of change, gives no extra information about future movement.
Four of the seven Texas variables proved to be
nothing more than such random walks. For total
employment, the Texas labor force, Texas personal
income, and Texas retail sales, each quarter's data
are new draws from the same hat. If the growth rate
of one of the variables deviates significantly from
its long-term average, that information should not
motivate revision of the forecast of the next
quarter's growth rate.
Growth rates of the Texas industrial production
index the Dallas-Fort Worth consumer price index,
and ~onagricultural employment, on the other hand,
deviate from a long-term average growth rate in a
Federal Reserve Bank of Dallas

Table 2

Table 3

UNIVARIATE ARIMA MODELS

UNIVARIATE ARIMA (2, 1, 0) MODELS

(1) Texas industrial production index

(1 -

(1 - L)ln(T1Pl t ) = .01783

.63L)et .

Variable (y)

SEE = .01538; 1= 11.1.
To

Chisquare

6
12
18
24

6.2
15.1
19.4
24.3

Signifi-

cance

.19
.13

.25
.33

SEE

.89L)(1- L)ln(CPIDFW t ) = .02051

.00769; I

(1 -

.38L)er-

Chisquare

Significance

6
12
18
24

1.7
6.5
9.1
17.0

.67
.69
.87
.71

(3) Payroll employment

(1 - .73L)(1 - L)ln(PAYROLL t ) = .01145

= .00432;

SEE

.01579
.00768
.00443
.00825
.01364
.02175
.00641

.19
.51
.59
-.03
-.01
.02
.04

at
I(B,A)'

9.0
29.7
28.4
-2.9
-.1
1.3
.6

standard error of ARIMA (2, 1, 0)
1 I B A = [ 1 . .
X 100.
(, )
standard deviation of (1 - L)ln(y)
2
NOTE: R: is the coefficient of determination adjusted
for degrees of freedom.

29.7.
To

SEE

TIPI.
CPIDFW.
PAYROLL
TEMP .
RTPY
RTRET .
TLF

~2L2)(1- L) In (Yt)

(2) Consumer price index, Dallas-Fort Worth

(1 -

~1L -

et .

= 30.1.
To

Chisquare

Signiflcance

6
12
18
24

.8
7.2
9.1
19.0

.94
.70
.91
.65

The other four series (TEMP, RTPY, RTRET, and TLF) are
modeled in natural logs as random walks with drift:
(1 - L)ln(TEMP t ) = .00884 + e t , and so on.

systematic way. The patterns of deviation imply that
very recent past growth rates of these series can be
used meaningfully to project future growth rates.
Table 2 presents the ARIMA equations for these
three variables. Compared with estimates assuming
a simple random walk with drift, the Box-Jenkins
ARIMA models reduced standard error of equation
for nonagricultural employment by 30.1 percent, for
the Dallas-Fort Worth consumer price index by 29.7
Economic Review/May 1984

percent, and for the Texas industrial prod uction
index by 11.1 percent.
It was also useful to compare the forecasts of the
ARIMA (2, 1,0) equations with those of a random
walk with drift. Recall that simple ARIMA (2, 1, 0)
models were different from the Box-Jenkins ARIMA
models, since the latter were given whatever form
seemed to be adequate. Nevertheless, as Table 3
shows, the ARIMA (2, 1,0) functions improved standard error of equation, compared with forecasts
based on the assumption of a random walk with
drift, by almost as much as the Box-Jenkins equations did. Like the Box-Jenkins ARIMAs, the
ARIMA (2, 1, 0) functions offered considerable improvement for the Dallas-Fort Worth consumer
price index, nonagricultural employment, and the
Texas industrial production index. Also like the BoxJenkins ARIMAs, however, the ARIMA (2, 1, 0) equations were unable to improve standard error of
equation greatly for any of the other four variables,
relative to a random walk with drift.

Mu Itivariate closed-region
and trickle-down models
Multivariate time series models to forecast the
Texas variables included two general types: the
closed-region model, incorporating only Texas data,
and the trickle-down model, incorporating only
national variables plus own lags. These were used
15

Table 4
IMPROVEMENT IN STANDARD ERROR OF EQUATION
FROM ADDITION OF REGIONAL VARIABLES
I ndependent variables

Row
sum
Reduction in standard error, relative to standard error of ARIMA (2,1,0) model, that results
from including two lagged growth rates of the column variable (Percent)

TlPI
Dependent variable

TIPI
CPIDFW
PAYROLL
TEMP.
RTPY
RTRET .
TLF .

Column sum
Less CPIDFW and TLF rows.

CPIDFW

-1.6
-2.1
1.7
2.4
-1.1
-2.2
.3

-.9
.0
3.4
7.3*
3.6

PAYROLL

6.7*
6.3*

TEMP

RTPY

RTRET

TLF

10.1 *
8.3*
3.2

3.7
4.5
1.9
-1.8

4.7
4.7
-1.1
-.4
.5

5.9*
5.4*
.1
-1.1
1.1
-2.2

5.0*
-2.3
-1.4
-.8

.3
-1.1
-2.2

-2.0
-1.8

-1.0

11.8

13.5

18.6

12.1

8.9

9.2

8.2

8.0

12.5

9.4

3.7

3.8

29.5
27.1
4.9
7.7
1.9
2.4
-.4

* Significant at the .05 level (two-tailed test), using an F statistic with 2 numerator degrees of freedom and 40 denominator degrees of
freedom.

to supplement own lags of the variable to be explained. I n both cases, each Texas variable was
initially regressed on two own lags and two lags of
other variables.
Since all regression equations in these two classes
of multivariate models contained two lags of each
variable, a useful standard by which to compare
their performance is the set of ARIMA (2, 1,0) equations. In fact, the ARIMA (2,1,0) equations were
constructed for such comparisons.
To begin tests of the forecasting power tied to
within-region interactions, regression equations involving only regional variables were constructed.
Each of the seven Texas variables was regressed on
two own lags plus two lags of one of the other six
variables. For example, the Texas industrial production index was regressed on two own lags plus two
lags of nonagricultural employment. Likewise, the
Texas industrial production index was regressed on
two own lags plus two lags of the Dallas-Fort Worth
consumer price index. Forty-two regression equations were required to produce all possible combinations of two own lags plus two lags of another
Texas variable.
Table 4 shows the information gain from an equation with two own lags plus two lags of one other
Texas variable compared with the ARIMA (2, 1,0) for
16

the same regressor. For example, an equation
regressing the Texas industrial production index on
two own lags plus two lags of nonagricultural
employment reduces the standard error of equation
(SEE) by 6.7 percent compared with the SEE of the
Texas industrial production index ARIMA (2, 1, 0).
Inclusion of some variables actually increased the
SEE. These cases are recognized by the negative
signs on their I values. For example, the equation
regressing Texas personal income on two own lags
plus two lags of nonagricultural employment
resulted in a 2.3-percent increase in error.
These results suggest that regional interaction
variables alone cou Id significantly aid forecasts of
industrial production and consumer prices with information from the three labor series. Predictions of
household employment and deflated retail sales appear to gain some information from consumer
prices. The Texas industrial production index has little value in aiding predictions of other variables, but
predictions of it benefit from consideration of other
series. Overall, the employment series provide the
most information about future Texas economic
events, at least when considered within sample.
As a final attempt to examine the predictive
power that regional variables have on one another,
a comprehensive closed-region model was conFederal Reserve Bank of Dallas

Table 5
IMPROVEMENT IN STANDARD ERROR OF EQUATION
FOR COMPREHENSIVE CLOSED-REGION AND TRICKLE-DOWN MODELS
Dependent
variable

TIP/
CPJDFW.
PAYROLL
TEMP.
RTPY.
RTRET .
TLF

Trickle-down model

Closed-region model
SEE

R"2

SEE

R"2

.01466
.00672
.00440
.00749
.01378
.02293
.00626

.30
.63
.51
.16
-.01
-.09
.08

7.2
12.5
.7
9.2
-1.0
-5.4
2.3

1.56
2.07
1.04
1.75
.93
.76
1.16

.01441
.00584
.00443
.00792
.01265
.01842
.00644

.32
.72
.51
.06
.15
.30
.03

8.7
23.9
-.1
4.0
7.3
15.3
-.5

1.84
4.06
.99
1.36
1.69
2.85
.96

Information gain, measured by percentage reduction in standard error relative to standard error of ARIMA (2, 1,0)
model.
2. F(12, 30); the critical values are 1.77 at the .10 level, 2.09 at the .05 level, and 2.84 at the .01 level.
3. F(10, 32); the critical values are 1.82 at the .10 level, 2.16 at the .05 level, and 2.98 at the .01 level.
NOTE: R"2 is the coefficient of determination adjusted for degrees of freedom.

structed. This model was composed of seven regression equations, one with each of the seven Texas
variables on the left-hand side. The right-hand side
included two own lags plus two lags of each of the
other six Texas variables. The F and I statistics
presented in Table 5 suggest that regional interactions aid prediction of industrial production but fail
to confirm the large gain for consumer prices that
might be expected from the results of Table 4. The
closed-region model provides a 12.5-percent reduction in the SEE of the consumer price growth rate, a
9.2-percent standard error reduction for the total
employment within-sample forecasts, and a 7.2-percent reduction for the Texas industrial production
forecasts.
However, as it stands, the closed-region model appears very much "overparameterized." Each equation in the closed-region model has so many righthand-side variables that multicollinearity and loss of
degrees of freedom interfere with forecast accuracy.
Further analysis could possibly uncover a more efficient closed-region model using exclusion restrictions. Variables with parameters not statistically different from zero, for example, could be deleted.
Because economic conditions in Texas are affected by the same events as in the nation as a
whole, it is also appropriate to search among national economic indicators for information about
Economic Review/May 1984

future conditions in Texas. The following key
national variables were chosen as those most likely
to improve time series forecasts of the Texas
economy:4 (1) the composite index of leading indicators (LEAD); (2) the index of roughly coincident
indicators (CO INC); (3) the U.S. industrial production
index (/PI); (4) U.S. nonagricultural employment
(NEMP); and (5) Moody's all-industry average corporate bond yield (FYAVG). Fuller descriptions of
these variables appear in Table 1.
In order to examine the improvement over the
ARIMA (2, 1,0) that these national variables give to
forecasts of the seven Texas variables, the following
procedures were used. Growth rates of each of the
seven regional variables were regressed on (1) two
own lags plus two lagged growth rates of the index
of leading economic indicators and (2) these
variables plus two lagged growth rates of one of the
other four variables. This design reflects the prior
notion that the leading index is the single most
powerful source of information for forecasting.

4. The 5 national variables were chosen from a set of 14 by procedures described in James G. Hoehn and William C. Gruben
with Thomas B. Fomby, "Some Time Series Methods of
Forecasting the Texas Economy," Federal Reserve Bank of
Dallas Research Paper no. 8402 (Dallas, 1984).

Table 6
IMPROVEMENT IN STANDARD ERROR OF EQUATION
FROM ADDITION OF NATIONAL VARIABLES
Dependent
variable

TlPI

CPIDFW

PAYROLL

TEMP

RTPY

RTRET

TLF

Reduction in standard error, relative to standard error
of ARIMA (2, 1,0) model, that results
from including two lags of LEAD with two own lags
of the column variable (Percent)

LEAD

12.2*

5.9*

2.0

0.0

-1.0

1.5

-1.5

Reduction in standard error, relative to standard error
of an equation with two own lags of the column variable
plus two lags of LEAD, that results from adding to
the same equation two lags of the row variable (Percent)

COINC.
IPI.
NEMP.
FYAVC.

-1.2
-2.5
.9
-.1

9.9*
10.0*
9.7*
15.4*

1.9
3.5
-2.3
-.2

-1.0
.6
-1.0
2.7

-7.9*
12.2*
6.2*
7.3*

10.6**
17.4*
6.8*
7.0*

-.2
4.5
-2.0
1.7

* Significant at the .05 level when equation is compared with the benchmark equation.
** Significant at the .01 level when equation is compared with the benchmark equation.

Table 6, with the I values pertinent to each equation, reveals that the index of leading economic indicators by itself was able to effect a 12.2-percent
improvement in SE E over the ARiMA (2, 1,0) for the
Texas industrial production index equation and a
5.9-percent improvement for the Dallas-Fort Worth
(PI equation. The addition of the coincident index
to the leading index in the equations reduced the
within-sample forecasting power for the Texas industrial production index but improved this power
for deflated Texas personal income and retail sales,
as well as for the Dallas-Fort Worth consumer price
index. Regressions containing two own lags, two lags
of the leading index, and two lags of U.S. industrial
production had greater power in within-sample
predictions of the Dallas-Fort Worth consumer
price index, Texas personal income, and Texas retail
sales but had poor results in equations predicting
the other variables. Generally, national variables
showed little success in forecasting the Texas labor
series, just as the closed-region model had fared
poorly on this score.
Finally, a trickle-down model was constructed
relating growth rates in each of the seven Texas
variables to two own lags and two lags of each of
the five key national variables. Table 5 shows the
18

standard errors of the equations and the information
gains relative to the ARIMA (2, 1, 0) models. Not surprisingly, considering the results in Table 6, this
trickle-down model achieved considerable withinsample success for consumer prices and deflated
retail sales. The F statistics are highly significant for
consumer prices and significant for deflated retail
sales. The trickle-down model outperforms the
closed-region model for four of the seven variables.

Out-of-sample performance of ARIMA,
dosed-region, and trickle-down models
The usefulness of the closed-region and trickle-down
models can be assessed by constructing forecasts
outside the sample and comparing their accuracy
with that of the univariate forecasting equations.
The out-of-sample forecasting period chosen was the
first quarter of 1981 through the second quarter of
1983. Each model's parameters were reestimated
each quarter to reflect new data, but the general
form of the model was left unchanged.
For each of the seven variables, a sample of 10
one-period-ahead forecasts, 9 two-period-ahead
forecasts, and so on, to 5 six-period-ahead forecasts,
was obtained for each of the four models. The i-step
forecast error is the actual log of the variable less
Federal Reserve Bank of Dallas

Table 7

OUT-Of-SAMPLE fORECAST PERfORMANCE
Of SELECTED UNIVARIATE MODELS
AND MULTIVARIATE MODELS
Variable,
forecast horizon
(quarters ahead)

Univariate models
BoxARIMA
Jenkins
(2,1,0)

Multivariate models
ClosedTrickleregion
down

Root mean square errors

TlP/: 1
2
3
4
5
6

.0240
.0446
.0626
.0842
.1075
.1260

.0234
.0446
.0584
.0808
.1049
.1259

.0218
.0439
.0615
.0827
.1090
.1309

.0239
.0417
.0509
.0629
.0805
.1022

CPIDFW: 1
2
3
4
5
6

.0078
.0156
.0250
.0357
.0501
.0679

.0078
.0148
.0231
.0325
.0455
.0621

.0074
.0146
.0260
.0416
.0613
.0831

.0052
.0111
.0181
.0280
.0421
.0587

PAYROLL: 1
2
3
4
5
6

.0072
.0150
.0267
.0411
.0567
.0658

.0074
.0148
.0270
.0415
.0572
.0657

.0083
.0152
.0263
.0406
.0551
.ot>31

.0081
.0168
.Q280
.0410
.0539
.0629

TEMP: 1
2
3
4
5
6

.0068
.0101
.0129
.0169
.0202
.0220

.0072
.0105
.0133
.0172
.0201
.0215

.0096
.0104
.0118
.0159
.0218
.0241

.0096
.0139
.0131
.0146
.0144
.0159

RTPY: 1
2
3
4
5
6

.0127
.0164
.0229
.0296
.0343
.0414

.0140
.0172
.0238
.0310
.0345
.0425

.0124
.0181
.0219
.0296
.0280
.0295

.0185
.0241
.0240
.0255
.0262
.0357

RTRET: 1
2
3
4
5
6

.0235
.0379
.0477
.0581
.0686
.0790

.0233
.0394
.0509
.0628
.0749
.0866

.0255
.0449
.0562
.0596
.0596
.0516

.0270
.0372
.0418
.0456
.0618
.0798

TLF: 1
2
3
4
5
6

.0067
.0071
.0040
.0048
.0079
.0084

.0061
.0064
.0039
.0057
.0080
.0083

.0084
.0077
.0060
.0057
.0082
.0081

.0071
.0101
.0074
.0185
.0102
.0107

Economic Review/May 1984

the forecast log of the variable, conditional on information available j quarters ago and earlier. The
root mean square errors of univariate models serve
as appropriate benchmarks for evaluating multivariate alternatives because if more complex
models cannot forecast better, univariate forecasting models are probably the most useful bases for
judgmental forecasts.
Table 7 presents the RMSEs for each of the four
models. There was I ittle difference in forecast accuracy between the Box-Jenkins and ARIMA (2, 1, 0)
models. This suggests that autoregression models of
low order, such as the ARIMA (2,1,0), may forecast
nearly as well as ARIMAs built using Box-Jenkins
identification procedures, at least for the seasonally
adjusted series studied here.
While the overparameterized closed-region model
achieved few successes relative to the univariate
equations, it did perform as well or better for all
but one of the six out-of-sample personal income
forecast horizons and for the last four steps ahead
in the case of nonagricultural employment.
However, the promising aspect of within-sample
performance of this model in predicting the Texas
employment series bore relatively little fruit in outof-sample forecasts. Taken as a whole, the closedregion model is an unattractive alternative to
univariate equations. Even in the more distant
nonagricultural employment forecasts, where the
closed-region model proved better than the
univariate models, the superiority was very slight.
The trickle-down model suffers from somewhat
less overparameterization than the closed-region
model and outperformed any other model in this
study in out-of-sample forecasts of the Dallas-Fort
Worth consumer price index. The trickle-down
model had mixed success compared with the
univariate equations for all other Texas variables
except the labor force, where it failed. However,
the trickle-down model forecast a little better than
the closed-region model.
The univariate models tend to lose their superiority to the multivariate models at the longer forecast
horizons. For a one-quarter-ahead forecast for the
seven Texas variables, ARIMA (2, 1, 0) functions are
superior to the trickle-down model in six out of
seven cases, while the Box-Jenkins ARIMAs are
superior to the trickle-down model in five out of
seven cases. Conversely, for a six-quarter-ahead
forecast, the trickle-down model is superior to the
19

ARIMA (2, 1, 0) in six out of seven cases and
superior to the Box-Jenkins ARIMA in five out of
seven cases. This tendency is far less pronounced
for the closed-region model.
The forecasting superiority of the trickle-down
model compared with the closed-region model is
also a function of the length of the forecast period.
One quarter ahead, the forecasting quality of the
two models is about even. By the sixth quarter
ahead, the trickle-down model exhibits marked
superiority. Generally, this study suggests that the
relative attractiveness of a given time series modeling procedure over others is a function of the
forecast horizon.
Vector autoregression
Given the prior notion that information about the
future course of each Texas series ought to be present in both U.S. and Texas variables, it is tempting
to build a model that uses both. While Texas and
U.S. variables could be included together in a
forecasting equation, the problem of too many
right-hand-side variables discourages the procedure
of including all of them. To do so spends precious
degrees of freedom and can lead to serious multicollinearity. Consequently, parameter estimates
become inaccurate. As a result, parsimonious
models generally forecast better than those that
are not.
Nevertheless, the preceding results make it clear
that information useful in forecasting Texas
variables is widely diffused. A multivariate
forecasting approach would be highly desirable if
there were a method of capturing the information
embedded in both Texas and U.S. data while
avoiding the problems of overparameterization.
Under such circumstances, vector autoregression
may offer possibilities for capturing information in
an attractively eclectic format.
I n recent years, vector autoregression has been
used by some economists as a medium for summarizing the relationships at various lags among
groups of variables. Vector autoregression is simply
a set of regressions, with the current value of each
variable being regressed on the lagged values of all
the variables in the system. Since all variables in the
system are used to forecast movements in every
variable in the system, there are no exogenous
variables in a vector autoregression model. Thus,
the closed-region model described in this article can
20

be considered a very simple VAR model because
every variable that is a left-hand-side variable in any
equation is also a right-hand-side variable in all
equations. The trickle-down model is not a VAR
model because, with the exception of own lags,
every right-hand-side variable is exogenous to the
model.
While the closed-region model can be considered
a V AR model and the trickle-down model cannot
be, neither forecast consistently better than the
univariate models. Clearly, vector autoregression
does not automatically solve forecasting problems.
Both equations had too many parameters.
Much of the problem of overparameterization,
however, involves excessive coefficient variance and
consequent imprecision in coefficient estimation,
primarily as a result of multicollinearity. More
generally, the number of observations typically
available for vector autoregression is inadequate for
obtaining precise estimates of the large number of
free parameters in a VAR model. One way of addressing these problems in vector autoregression is
by imposing restrictions on the values and variances
of a model's coefficients. I n the case of the VAR
models of the Texas economy, these Bayesian procedures were carried out by means of the RATS
(Regression Analysis of Time Series) modeling
package, which greatly facilitated the creation of
VAR models and the imposition of restrictions on
them.'
The prior distribution generally used in the

5. Thomas A. Doan and Robert B. Litterman, in User's Manual,
RA TS Version 4.1 (Minneapolis: VAR Econometrics, 1981),
demonstrate clearly how to impose alternative prior specifications. Thomas Doan, Robert Litterman, and Christopher A.
Sims ("Forecasting and Conditional Projection Using Realistic
Prior Distributions," NBER Working Paper Series, no. 1202
[Cambridge, Mass.: National Bureau of Economic Research,
1983]) provide some evidence that vector autoregressions with
well-chosen prior distributions can improve national economic
forecasts relative to univariate autoregressions, even in a
system of 10 variables. However, this result is subject to
several caveats. The improvement over univariate equations is
slight, the univariate benchmarks are arbitrarily specified
rather than identified by Box-Jenkins methods, and the prior
distributions are selected ex post facto. Nevertheless, the result
is interesting, in that apparently no other forecasting method
has yet been shown to deliver a systematic improvement over
univariate methods in a national model with as many variables
and over as long a period. Possibly other time series methods
employing more parsimony could do so.

Federal Reserve Bank of Dallas

Table 8
OUT-OF-SAMPLE FORECAST
PERFORMANCE OF VECTOR
AUTOREGRESSION MODELS
Variable,
forecast horizon
(quarters ahead)

VAR I

VAR II

VAR III

Root mean square errors

T1PI: 1
2
3
4
5
6

.0256
.0478
.0699
.0935
.1156
.1364

.0229
.0414
.0620
.0831
.1054
.1316

.0199
.0346
.0504
.0668
.0854
.1061

CPIDFW: 1
2
3
4
5
6

.0112
.0248
.0411
.0601
.0830
.1093

.0073
.0139
.0244
.0387
.0570
.0802

.0067
.0126
.0223
.0357
.0535
.0753

PAYROLL: 1
2
3
4
5
6

.0110
.0224
.0361
.0485
.0578
.0642

.0088
.0174
.0298
.0427
.0529
.0611

.0081
.0156
.0271
.0400
.0506
.0593

TEMP: 1
2
3
4
5
6

.0078
.0120
.0163
.0211
.0251
.0281

.0069
.0096
.0131
.0189
.0237
.0292

.0067
.0090
.0115
.0169
.0200
.0230

RTPY: 1
2
3
4
5
6

.0139
.0187
.0262
.0331
.0376
.0440

.0173
.0252
.0324
.0371
.0396
.0406

.0168
.0249
.0320
.0357
.0354
.0330

RTRET: 1
2
3
4
5
6

.0231
.0384
.0480
.0574
.0658
.0742

.0278
.0426
.0532
.0600
.0640
.0686

.0267
.0429
.0533
.0568
.0549
.0485

TLF: 1
2
3
4
5
6

.0066
.0068
.0047
.0058
.0082
.0088

.0059
.0056
.0056
.0074
.0094
.0122

.0054
.0052
.0030
.0040
.0055
.0057

literature to restrict the characteristics is the random walk. I n this approach the analyst imposes
prior values of unity on the coefficient of the first
own lag and zero on all other coefficients. Parameters are allowed to deviate from the prior values
to a degree determined by both the data and the
tightness of the priors. The degree of tightness is
controlled by the standard deviations imposed on
the priors. For example, as the standard deviations
are increased, the parameters will tend to be closer
to prior values; hence, we say that the priors have
been tightened.
Some believe that efficient estimation of VAR
models requires little theoretical knowledge or feel
for regional data and that a simple random walk
prior distribution can be imposed, with I ittle effort
at diagnosing the relative usefulness of alternative
levels of restrictiveness. 6 Experience in construction
of the Texas VAR models suggests that these claims
are not universally appl icable. Considerable time
and care are required to produce a model that
forecasts even as accurately as ARIMA models. In
the Texas study, this nondiagnostic approach (noted
as VAR I) to imposing prior restrictions produced
the most inaccurate forecasts of all models considered, as a comparison of the RMSEs in the VAR I
column of Table 8 with any other RMSEs in Tables 7
and 8 will show.
In constructing a VAR model of the Texas
economy, three alternative specifications of prior
restrictions were imposed. The choice of prior
distributions of coefficient values had a substantial
effect on the forecast performance of the estimated
model. (Although different prior specifications
were imposed in each of the three models, an unconstrained constant and a I inear time trend were
included in all. 7 )
One approach to VAR model construction involved setting priors based on judgment derived
from previous analyses undertaken in this study.
Each of the seven Texas series was treated separately. The within-sample results of univariate,

6. See Anderson, "Help for the Regional Economic Forecaster."
The VAR I model's priors were patterned after those of
Anderson's model.
7. See Hoehn, Gruben, and Fomby, "Some Time Series Methods
of Forecasting the Texas Economy," for further information on
prior specifications imposed on the three VAR models.

Economic Review/May 1984

closed-region, and trickle-down models were used to
form rough notions about the extent to which the
behavior of a given Texas variable reflected its own
past, movements of other Texas variables as a
block, and the performance of national variables as
a block. The priors then were set along these dimensions. Even this approach is crude, but it does take
advantage of the feel for the data that can be derived from examination of the univariate, closedregion, and trickle-down models.
For example, the growth rate of the Dallas-Fort
Worth consumer price index displayed considerable
autocorrelation, so the own-lag coefficients in a
VAR model were given wide prior distributions. The
own-lag coefficients were not restricted to values
very close to 1 or 0; narrow restrictions were not imposed on their variances. Conversely, the closedregion model was of some help within sample but
performed poorly out of sample. Hence, priors were
tightened on lags of other regional variables. The
national variable coefficients were given more
freedom to seek their own levels in light of the
relatively good performance of the trickle-down
model.
Although the performance of this second model,
VAR II in Table 8, generally falls a bit short of the
univariate benchmarks, the model represents a
substantial improvement over VAR I. Compared
with the Box-Jenkins ARIMA for the 42 RMSEs
reported per model (including an RMSE for each of
the seven variables for each of six quarter-ahead
forecasts), VAR I has a lower RMSE in only 6 cases,
while VAR II has a lower RMSE in 15 cases.
Unlike the trickle-down model, however, there is
no consistency of forecast-horizon results for the
cases in which the VAR II proves more accurate
than the univariate models. VAR II sometimes beats
the univariate models in short-horizon forecasts, as
for the Texas industrial production index and
Dallas-Fort Worth consumer price index, and
sometimes is superior in longer-horizon forecasts, as
for Texas nonagricultural employment and retail
sales. However, V AR II is never consistently superior
to the univariate forecasts for any of the variables,
nor is it superior for most forecasts over a given
horizon.
Ex post analysis of the effect of alternative priors
suggests that those of the V AR II model were
generally too restrictive. In light of this analysis, the
overall tightness priors were raised twofold, imply22

ing a looser prior distribution, although the personal
income and labor force equations were subjected to
tighter priors.
The result of these changes was the VAR III
model. V AR III performs better than either of the
univariate models, but its relative success is not
spectacular. In the 42 comparisons of RMSEs (six
different steps ahead for each of seven Texas
variables), VAR III beats the Box-Jenkins ARIMAs 26
times, loses 14 times, and ties twice. V AR III beats
the ARIMA (2, 1, 0) 27 times and loses 15 of the
matches. The V AR III model outperforms all other
time series models, univariate or multivariate, in
forecasting the Texas labor force. It also provides
the best or second-best forecasts for the Texas industrial production index, depending on the forecast
horizon, but always beats the univariate models for
this variable. VAR III does not consistently beat the
univariate models on any other forecasts, and for
the other variables and forecast horizons where it is
superior, VAR III does not often beat the univariate
models by very much. The forecast horizons in
which VAR III beats the univariate models show a
pattern similar to that of the trickle-down model,
which had its greatest relative success in forecasts
for more distant time horizons. For VAR III the pattern is not highly pronounced, but the model does
have more success against the Box-Jenkins
ARIMA-74 percent-and the ARIMA (2,1,0)-71
percent- in the more distant half of the forecast
horizons (four, five, and six quarters ahead) than in
the earlier half, where it beat both univariate
models 57 percent of the time.
I n spite of the unspectacular performance of even
the most accu rate of the three V AR models vis-a-vis
the univariate models, the results may have implications for other regional VAR modeling. The relative
success (compared with VAR I) of the VAR II model,
which incorporates prior information derived from
the earl ier analysis, suggests that a strong feel for
the data and their interrelationships can aid in the
construction of a more accurate Bayesian V AR
model. A second method of potentially improving
forecast accuracy is to fine-tune the priors on the
basis of out-of-sample experience with the VAR
model. This Texas time series study included experiments with both of these methods of bettering
the model. The superiority of VAR III to VAR II and
V AR I demonstrates that these approaches amel iorated forecast accuracy. Given time and resources,
Federal Reserve Bank of Dallas

further improvements could probably be realized
along these lines, but effort was required to achieve
even relatively moderate improvement over the
univariate models.
It should also be noted that the fine-tuning of the
priors, which resulted in the improvement of VAR
III over VAR II, was performed ex post facto. Prior
restrictions were altered in VAR III in light of the
RMSEs estimated from VAR II. Because such RMSEs
cannot be known except in retrospect (the difference between a forecast value and an actual
value cannot be calculated unless the actual value
is known), the improvements VAR III showed over
VAR II would be difficult to make in a real, ex ante
forecast.

Summary and conclusion
The preceding discussions outline steps toward
developing efficient time series forecasting models
of the Texas economy. Intraregional interactions are
not easy to exploit for forecasting purposes. Among
the seven Texas series studied, the two employment
series seem the most important for the regional
forecaster to watch as indicators of future changes
in other series. National-regional interactions
showed themselves a little easier to exploit, and

Economic Review/May 1984

they appear to aid in forecasting Texas industrial
production, consumer prices, and deflated retail
sales.
For the period, region, and variables under study,
it was evident that vector autoregression was not as
clearly superior a forecast procedure as some
analysts of other regions have believed it to be for
their areas. Indeed, for the overall out-of-sample
forecast period of the models employed for Texas,
univariate models generally performed about as
well as any of the multivariate models studied. For
forecast periods of less than one year, there was no
evidence that any multivariate model was superior
to the univariate models. A highly polished VAR
model, VAR III, gave moderately better forecasts
for more distant time horizons.
Experience in building time series forecasting
models of Texas suggests that effective forecasting
through vector autoregression can be a considerably
complicated procedure. Care in imposing prior
restrictions on coefficients is important.
A more promising approach for further research
would exploit only the relationships found to be
significant here. Recent explorations suggest that
this parsimonious approach can yield systematic improvements over single-variable ARIMAs.

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