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FEDERAL RESERVE BANK OF DALLAS
FIRST QUARTER 1998
..

_-Crude Oil and Gasoline Prices:
An Asymmetric Relationship?
Nathan S. Balke, Stephen P A. Brown and
Mine K Yii.cel

Has NAFTA Changed
North American Trade?
David M. Gould

The Dynamic Impact of
Fundamental Tax Reform
Part 1: The Basic Model
Evan F Koenig and Gregory W Huffman

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

Economic Review
Federal RtlSe!Ve Bank 01 Dalla
Robert D. McTeer. Jr.
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Helen E. Holcomb
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Harvey Rosenblum
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W. Michael COl
VicIl Pmlll!l1l ·fld &:orrOllllc Advisor

Senior Economists and
Assistant Vice Presidents
Stephen p. A. Bro
John Duca
Robert WGilmer

Evan FKoenig

Director, Center lor Latin American
Economics, and Assistant Vice President
William C Gruben
Senior Economist and
Re!earch Officer

MineK VOcel
Economists
Robert Formami
David M Gould
Joseph H Haslag
Keith It Pblilips
Stephen D. Pr
Marcl Rossell
Jason L SavIng
Fiona D. Sgalla
Lori L Taylor
Lucmda Vargas
Mark . Wynne
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Research Associates
Professor Nathan S. Balke
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PrQfessor Thomas B Fomby
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Pro essor Finn E Kydlanrl
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Pro essor Roy J Ruffin
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Editors
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Evan F Koenig
Publications Director
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Contents

Crude Oil and Gasoline
Prices: An Asymmetric
Relationship?
Nathan S. Balke, Stephen P. A. Brown
and Mine K. YOcel

Page 2

Has NAFTA Changed
North American Trade?
David M. Gould

Page 12

The Dynamic Impact of
Fundamental Tax Reform
Part 1: The Basic Model
Evan F. Koenig and Gregory W. Huffman

Page 24

Gasoline is the petroleum product whose price is most visible
and, therefore, always under public scrutiny. Many claim there is an
asymmetric relationship between gasoline and oil prices-specifically, gasoline price changes follow oil price changes more quickly
when oil prices are rising than when they are falling. To explore
this issue, Nathan Balke, Stephen Brown, and Mine Yucel use
several different model specifications to analyze the relationship
between oil prices and the spot, wholesale, and retail prices of
gasoline. They find asymmetry is sensitive to model specification
but is pervasive with the most general model.

The controversy over the success or failure of NAFTA is now
bleeding over into discussions about the benefits of extending the
trade accord to other countries in the Western Hemisphere. The
NAFTA debate has typically focused on its impact on employment.
But to understand the overall economic effects of NAFTA, it is
important to first determine its impact on trade. In this article, David
Gould explores NAFTA's effects on North America's trading patterns
since its implementation in 1994. He finds that although it is difficult to distinguish any effect of AFTA on trade between Canada
and Mexico or Canada and the United States, trade between the
United States and Mexico has significantly increased since 1994.

The Internal Revenue Service remains unpopular, the U.S.
savings rate remains low, and pressure to efficiently raise significant
new tax revenues seems certain to grow once the baby boom
generation reaches retirement age. Consequently, it is likely that
alternatives to the current income tax system will receive substantial political and media attention in coming years.
In this first of two articles on the economic impact of fundamental tax reform, Evan Koenig and Gregory Huffman describe a
framework for analyzing how the adoption of a flat-rate consumption tax would affect the economy over time. Their analysis indicates that replacing the income tax with a consumption tax would
have an immediate positive impact on saving and lead, in the long
run, to higher levels of consumption, wages, and stock prices and
to lower interest rates. In the short run, however, interest rates
would probably rise, and consumption and stock prices would
probably decline.

Crude Oil and
Gasoline Prices:
An Asymmetric
Relationship?

Gasoline accounts for about half the U.S.
consumption of petroleum products, and its
price is the most visible among these products.
As such, changes in gasoline prices are always
under public scrutiny. Many claim to observe an
asymmetric relationship between gasoline and
oil prices — specifically that gasoline prices
respond more quickly when oil prices are rising
than when oil prices are falling (Figure 1 ).
President George Bush gave these concerns
official weight during the Gulf War when he
asked the oil companies to show restraint in
raising prices for their products.
Much of the previous research provides
econometric support for public claims of asymmetry in the movements of gasoline and crude
oil prices. Bacon (1991) found asymmetry in the
U.K. gasoline market, and Karrenbrock (1991),
French (1991), Borenstein, Cameron, and Gilbert
(1997), and a GAO report (1993) all found some
evidence of an asymmetric response in U.S.
gasoline markets. Norman and Shin (1991) found
a symmetric response in U.S. gasoline markets.
Of these studies, one of the most comprehensive and compelling is that of Borenstein,
Cameron, and Gilbert (1997), hereafter identified as BCG. They use a series of bivariate errorcorrection models to test for asymmetry in price
movements in each of the various stages in the
production and distribution of gasoline from the
crude oil price through the refinery to the retail
pump, using weekly and biweekly data from
1986 to 1992. They find strong and pervasive
evidence of asymmetry.
As Shin (1992) has argued, however, the
periodicity of the data, the sample period of
estimation, and the model specification may
have affected the results obtained in previous
studies. To explore these issues, we extend the
work of BCG by using several different model

Nathan S. Balke
Research Associate
Federal Reserve Bank of Dallas
and
Associate Professor of Economics
Southern Methodist University
Stephen P. A. Brown
Senior Economist and Assistant Vice President
Federal Reserve Bank of Dallas
Mine K. Yücel
Senior Economist and Research Officer
Federal Reserve Bank of Dallas

any claim to observe

an asymmetric relationship
between gasoline and oil
prices…that gasoline prices
respond more quickly when
oil prices are rising than when
oil prices are falling.

Figure 1

Spot Crude Oil Prices and Retail Gasoline Prices
Index, January 1987 = 100
250
Spot crude
Pump

200

150

100

0
’87

’88

’89

’90

’91

’92

’93

’94

’95

’96

The time-series analysis involves several
steps. We check whether the prices are stationary. We then test for Granger causality, which
allows an assessment of the lead– lag relationship between each pair of prices. Finally, we
calculate the variance decompositions to assess
the sources of shocks to the variables.

specifications with weekly data from 1987
through early 1996. We find that most of the
price volatility originates upstream. We also find
econometric evidence of asymmetry in the
extended sample. The findings are sensitive to
model specification but not to sample period.
Although popular opinion attributes asymmetry to market power, a number of competing
explanations have been offered. This article presents an econometric exercise that attempts to
identify whether asymmetry occurs; it does not
address how asymmetry might arise. For an
overview of the possible explanations, see the
box entitled, “Why Does Asymmetry Arise?”

Data
To analyze the relationships between crude
oil and gasoline prices, we use weekly data from
January 1987 through August 1996. The oil price
is the spot price for West Texas Intermediate
crude, the spot price for gasoline is the New
York Harbor Spot Price for unleaded regular,
and the retail price is the self-service pump
price for regular unleaded motor gasoline, with
and without taxes. These series are obtained
from the Weekly Energy Statistics of Haver Analytics. The wholesale price is from the Oil Price
Information Service and represents an average
wholesale price for unleaded gasoline across all
U.S. wholesale distributors reporting data continuously from 1986 through August 1996.

THE ORIGINATION AND TRANSMISSION
OF PRICE SHOCKS
In theory, price shocks can originate at any
point from crude oil prices to the final price at the
gasoline pump. Shocks originating at an intermediate step, such as the wholesale price of gasoline, may reflect a bottleneck in distribution,
while price shocks originating farther upstream
are more likely to represent the effects of variation in crude oil supply. Price shocks originating
at the retail level are more likely to represent
variation in U.S. demand for gasoline. Given the
history of oil-supply shocks and indications that
demand for gasoline is relatively stable, intuition
suggests that price shocks are more likely to originate upstream and be transmitted downstream.
To examine where price shocks originate
and how they are transmitted across the U.S.
market for gasoline, we use time-series methods.
Specifically, we test for Granger causality and
compute variance decompositions for each pair
of upstream and downstream prices, including
spot crude oil prices and spot, wholesale, and
retail gasoline prices. As reported below, both
the causality tests and variance decompositions
generally confirm the intuition that price shocks
more frequently begin upstream and are then
transmitted downstream.
To motivate the relationship between a
pair of upstream and downstream prices, consider a simple markup model,
(1)

Stationarity
As an initial step in our econometric work,
we perform several diagnostic checks to assess
the correct specification for the various series. We
test for nonstationarity using augmented Dickey–
Fuller and Phillips –Perron tests and conclude
that we can reject the hypothesis that the series
have a unit root. Because all our price series
appear to be stationary, we represent the relationship between any pair of prices in log levels.
Causality
A causal relationship between two variables implies that changes in one variable lead
changes in the other. To assess the lead–lag
relationships for each pair of variables, we perform bidirectional Granger causality tests on
each of the ten pairs of upstream and downstream prices as follows:
m

i =1

(3 )

PDt = a + bPUt ,

where PDt is a downstream price, PUt is an
upstream price, and a and b are parameters
indicating the relationship between the upstream and downstream prices.1 The markup, a,
represents the cost of refining, marketing, transportation, and/or distribution. The scalar, b,
allows for differences in units and heat content
but may also reflect other market phenomena.

FEDERAL RESERVE BANK OF DALLAS

(2) PDt = α1 + ∑ β1,i PU t −i + ∑ δ1,i PDt −i + µ1,t and
i =1

i =1

PU t = α 2 + ∑ β2,i PDt −i + ∑ δ 2,i PU t −i + µ 2,t ,

where PDt is the downstream price; PUt is the
upstream price; α 1, β1,i , δ1,i , α 2, β2,i , and δ2,i are
parameters to be estimated; and µ 1,t and µ 2,t are
white-noise residuals. The lag length used for
estimation of each equation is the shortest lag
length that yields white-noise residuals (as indicated by the Ljung–Box Q statistic with a probability of 10 percent).

ECONOMIC REVIEW FIRST QUARTER 1998

Why Does Asymmetry Arise?
With a number of studies showing that gasoline prices respond more quickly when crude oil prices rise
than when they fall, analysts have offered a number of explanations for the phenomenon.1 Explanations include
market power, search costs, consumer response to changing prices, inventory management, accounting practices, and refinery adjustment costs. For the banking industry, Neumark and Sharpe (1992) show that market
concentration is an explanatory variable for the asymmetry found in interest rate movements. For the gasoline
markets, however, no one has posited econometric tests that would allow the testing of the various explanations
(including market power) for price asymmetry against the available data. Without such tests, it remains a matter
of speculation whether the asymmetric response of gasoline prices to movements in crude oil prices is the result
of market power or more benign forces.

Market Power and Search Costs
Market power is probably the greatest concern to those who observe that gasoline prices respond more
quickly when crude oil prices rise than when they fall. Yet no formal model shows a relationship between market
structure and asymmetric response of downstream prices to changes in upstream prices.2 Were such a model to
exist, it might involve firms that are concerned with maintaining a tacit collusion and/or consumer search costs.
Consider an industry with a few dominant firms that are engaged in an unspoken collusion to maintain
higher profit margins. Reputation can be important to maintaining such a tacit agreement (Tirole 1990). If the
firms value the tacit agreement and have imperfect knowledge of the upstream prices its competitors are paying,
then each firm would face an asymmetric loss function in which it would be more reluctant to lower its selling
price than to raise it. When upstream prices rise, each firm is quick to raise its selling prices because it wants to
signal its competitors that it is adhering to the tacit agreement by not cutting its margin. When the upstream price
falls, each firm is slow to lower its selling price because, in doing so, it runs the risk of sending a signal to its
competitors that it is cutting its margin and no longer adhering to the tacit agreement. In the gasoline markets,
such an explanation could be applied to each upstream price and its adjacent downstream price.
In the retail gasoline market, consumer search costs could lead to temporary market power for gas stations
and an asymmetric response to changes in the wholesale price of gasoline. (See BCG, Norman and Shin 1991,
Borenstein 1991, and Deltas 1997.) Each gas station has a locational monopoly that is limited only by consumer
search. After consumers have searched, the profit margins at each gas station are pushed down to a roughly
competitive level. When wholesale prices rise, each station acts to maintain its profit margins and quickly passes
the increase on to customers. When wholesale prices fall, however, each station temporarily boosts its profit margins by slowly passing the decrease on to customers. Only after the customers engage in a costly and timeconsuming search to find the lowest prices are the stations forced to lower prices to a competitive level.

More Benign Explanations
Although the existence of asymmetry could be consistent with market power, it is not the only explanation
that economists have offered for the asymmetric response of gasoline prices to movements in crude oil prices.
Alternative explanations include consumer response to changing prices, inventory management, accounting
practices, and refinery adjustment costs.
An asymmetric consumer response to changing gasoline prices may contribute to the asymmetry between
movements in crude oil and gasoline prices. If consumers accelerate their gasoline purchases to beat further
increases when its price is rising, they will increase inventories held in automobiles and quicken the pace at
which the price rises. If consumers fear running out of gasoline and do not slow their purchases of it when its
price is falling by as much as they accelerated their purchases when prices rose, then the price of gasoline will
fall more slowly than it rose.
Similarly, firms in the oil industry may view the short-run costs of unexpected changes in their inventories
as asymmetric. (See BCG.) If the costs of operations rise sharply when inventories are reduced below normal
operating levels, a reduction of upstream supply could lead a firm to raise its output prices aggressively to prevent a loss of inventories. If an increase in inventories above normal operating levels has a relatively small effect
on costs, the firm could be less aggressive in reducing its selling prices when it experiences an increase in
upstream supply. Hence, inventories would buffer downstream price movements less when prices are rising
than when they are falling.
The asymmetry arising from changes in inventories could be enhanced by FIFO (first in, first out) accounting. If inventories fall when upstream supply is reduced, the firm will sell the products incorporating the higher
upstream price sooner. If inventories rise when upstream supply is increased, the firm will sell the products
incorporating the lower upstream price later.
Refiners also face high adjustment costs to changing their output, and, when possible, they slowly adjust output. When crude oil supplies are reduced and inventory reductions are costly, however, refiners as a group have
little choice but to reduce output quickly, which would lead to fairly quick increases in gasoline prices. When crude
oil supplies are increased, however, refiners slowly increase output, delaying the decreases in gasoline prices.

Notes
1

Pricing asymmetries have been observed in a number of industries, including banking (Neumark and Sharpe 1992) and agriculture (Mohanty, Peterson, Wesley, and Kruse 1995).
Variations of the kinked-demand model of oligopoly do not suggest an asymmetrical movement in the output price of an industry
in response to common shocks to the input prices of the firms in that industry. See Scherer (1980) and Neumark and Sharpe
(1992).

Table 1

Significance of Granger Causality Tests
(Variable at left is the dependent variable)

Causality runs from the upstream price
to the downstream price if the coefficients β1,i
are jointly significantly different from zero.
Similarly, causality runs from the downstream
price to the upstream price if the coefficients β2,i
are jointly significantly different from zero.
In most cases, upstream prices seem
to contain market information that is later
incorporated in the downstream prices. As
Table 1 shows, we find that causality runs
from the upstream price to the downstream
price for each pair, with two exceptions. The
spot price for crude oil does not appear to
lead the spot price for gasoline, nor does the
retail price of gasoline without taxes seem
to lead the retail price of gasoline including
taxes. We do find, however, that the spot
price for gasoline leads the spot price for
crude oil, and the retail price including taxes
leads the retail price excluding taxes. These
findings suggest the possibility that for these
two pairs of prices, information is incorporated in the downstream price a bit more
quickly than in the upstream price. We also
find that each of the gasoline prices Grangercause the spot price for crude oil, which suggests that each of these prices contains market
information that is later incorporated into the
spot price for crude oil.2

Oil
Spot gasoline
Wholesale
Retail without tax
Retail with tax

Spot
gasoline

Wholesale

Retail
without tax

—
.53
.002
.0
.0

.014
—
.0
.0
.0

.015
.176
—
.0
.0

.024
.097
.455
—
.0

Retail
with tax
.049
.229
.088
.0
—

Table 2

Decomposition of Variance
(Percentage of forecast error variance of dependent variable explained
by shocks to independent variable)

Oil
Spot gasoline
Wholesale
Retail without tax
Retail with tax

Oil

Spot
gasoline

Wholesale

Retail
without tax

Retail
with tax

—
48.9
63.5
63.3
45.8

18.1
—
85.8
84.7
42.8

2.7
1.8
—
87.2
83.7

4.4
.47
.15
—
91.5

.21
.65
.53
.47
—

NOTE: The variance decompositions are from bivariate VARs. The variable at left is the dependent variable. The pair orderings are from upstream to downstream.

distant pairing with the wholesale price of gasoline, the spot price of crude oil accounts for
about two-thirds of the variance in the gasoline
price over the long run.

Long-Run Sources of Variance
To find out which price shocks have been
sources of volatility during the sample period,
we construct a bivariate vector autoregressive
(VAR) model to represent each relationship and
calculate the variance decomposition for each
pair of prices.3 For given time horizons, the variance decomposition apportions the stochastic
variability in a given price to shocks originating
in itself and to shocks originating in the price
with which it is paired. We consider a 30-week
time horizon, which should represent the long
run because the variance decomposition shows
a minimal change after 30 weeks.
As Table 2 shows, the variance decompositions generally suggest that over the long run,
price shocks originate in upstream prices and
are transmitted downstream. In addition, the
variance decompositions suggest that proximity
enhances the importance of the upstream price
as a source of variation in a downstream price.
The one exception is in the relationship between the spot price for crude oil and the spot
price for gasoline. In its pairing with the spot
price of gasoline, the spot price for crude oil
accounts for about one-half of the variance in
the gasoline price over the long run. In its more

FEDERAL RESERVE BANK OF DALLAS

Oil

A BASIC MODEL OF ASYMMETRY
Given the findings that price volatility most
often originates in the upstream price of any
price pair and that causality is stronger going
from upstream prices to downstream prices, we
restrict our inquiry to those cases in which the
downstream price is the dependent variable and
the upstream price is the independent variable,
as is suggested by Equation 1. The relationships
between upstream and downstream prices, coupled with the finding that each of the variables
is stationary, suggest modeling asymmetry in
levels as follows:
n

i =0
n

i =1

(4 ) PDt = α + ∑ βi PU t −i + ∑ γi PDt −i
n

+ ∑ δiU t −i PU t −i + ∑ λi Dt −i PDt −i + µt ,
i =0

i =1

where Ut – i is a variable that takes a value of one
when PUt – i is greater than PUt – i – 1 and is zero
otherwise; Dt – i is a variable that takes a value of
one when PDt – i is greater than PDt – i – 1 and is
zero otherwise; α, βi, γi, δi, and λi, are parameters to be estimated; and µt is a white-noise

ECONOMIC REVIEW FIRST QUARTER 1998

Table 3

Significance of Asymmetry Tests for Levels Model
(Variable at left is the dependent variable)
Asymmetry
type

Oil

Spot
gasoline

Wholesale

Retail
without tax

Spot gasoline

Indep. Var.
Total

.075
.109

—
—

Wholesale

Indep. Var.
Total

.239
.097

.011
.0

—
—

Retail without tax

Indep. Var.
Total

.0
.0

.42
.24

.08
.013

—
—

Retail with tax

Indep. Var.
Total

.0
.0

.89
.048

.35
.067

.15
.28

between the results above and those of BCG,
we consider the differences between the specification of Equation 4 and that used by BCG. A
model similar in specification to that used by
BCG yields substantially different results from
the levels model.
Having found that the shorter data series
they utilized are difference stationary, BCG uses
an error-correction model similar to Equation 4
for estimation. Allowing for asymmetry, including in the error-correction process, one representation of the error-correction model is
n

i =0
n −1

i =1

(5) ∆PDt = a + ∑ bi ∆PU t −i + ∑ ci ∆PDt −i

residual.4 To facilitate comparison with BCG and
to control for seasonal and time-varying pricing
patterns, we include 51 weekly dummies and a
time-trend variable in each regression.5 The lag
length used for estimation is the shortest lag
length that yields white-noise residuals.
The regression’s specification allows for
asymmetry in the response of the downstream
price to arise either from its own history or from
the upstream price. Asymmetry is indicated if
the coefficients δi and λi are jointly significantly
different from zero.
Table 3 indicates that symmetry is rejected
in half the price pairs at the 5 percent significance level, but the results are not very systematic. For instance, the tests indicate that
retail prices for gasoline, both with and without
taxes, respond asymmetrically to crude oil
prices, while the retail price with taxes responds
asymmetrically to the spot price for gasoline,
but the retail price without taxes does not. In
contrast, the retail price of gasoline without
taxes responds asymmetrically to the wholesale
price, but the retail price with taxes does not.
In two of the pairings —spot gasoline with
retail including taxes and wholesale with retail
without taxes —the asymmetry seems to arise
from the dependent variable’s own dynamics.
The lack of consistent results makes it difficult
to determine in which stages of the market
asymmetry arises. In addition, dynamic simulations indicate that for those cases in which
asymmetry is statistically significant, it is relatively small.
These findings contrast with those of BCG,
who find pervasive evidence of asymmetry that
is large in magnitude, using data from 1986 to
1992. We use a shorter sample, 1987–92, and
find it has no effect on the results.

∑dU
i

i =0

n −1

t −i

∆PU t −i + ∑ fi Dt −i ∆PDt −i
i =1

+ y (PU t −1 − zPDt −1 ) + µt ,
where ∆PDt is the first difference of PDt , the
downstream price; ∆PUt is the first difference of
PUt , the upstream price; a, bi, ci, di, fi , and y are
parameters to be estimated; z is the estimated
parameter from the long-run relationship between PDt and PUt ; and µt is a white-noise residual.
In estimation, however, BCG do not make
use of the long-run restriction implied by the
error-correction process, as the coefficients on
the levels variables in their specification are left
unrestricted, despite finding that their data
series are difference stationary. Therefore, in the
absence of asymmetry, their model would be
equivalent to the levels model shown in
Equation 4. Like BCG, we do not impose a longrun restriction in the estimation (which would
not be supported by stationary data), but unlike
BCG, we allow for asymmetry in the levels variables of the error-correction process, which
allows us to rewrite Equation 5 as
n

i =0
n −1

i =1

(6 ) PDt = α + ∑ βi PU t −i + ∑ γi PDt −i
+

∑ζU
i

i =0

n −1

t −i

∆PU t −i + ∑ ηi Dt −i ∆PDt −i
i =1

+ δU t −1PU t −1 + λDt −1PDt −1 + µt ,
where α, βi, γi, ζi, ηi, δ, and λ are parameters to
be estimated, and µt is a white-noise residual.6
As with Equation 4, we include 51 weekly dummies and a time-trend variable in the regression.
The lag length used for estimation is the shortest
lag length that yields white-noise residuals. As is
the case for Equation 4, the specification of Equation 6 allows for asymmetry in the response of
the downstream price to arise either from its own
history or from the upstream price. Asymmetry
is indicated if the coefficients δi, λi, ζ, and η are
jointly significantly different from zero.

AN ALTERNATE SPECIFICATION
Because the sample period used for estimation does not seem to explain the difference

Table 4

Significance of Asymmetry Tests for Error Correction Model
(Variable at left is the dependent variable)

Although Equation 6 differs from Equation
4 only in its specification of asymmetry, estimation with Equation 6 indicates more pervasive
asymmetry.7 As Table 4 shows, symmetry is
rejected in nine of the ten price pairs. The errorcorrection specification barely rejects the hypothesis that the retail price of gasoline without
taxes responds asymmetrically to the spot price
of gasoline, but this is the only pairing in which
asymmetry is not indicated. In two pairings —
spot gasoline with wholesale and wholesale
with retail without taxes — asymmetry seems to
arise from the dependent variable’s own
dynamics. The pervasive asymmetry indicated
by the error-correction model is consistent with
the findings of BCG. Use of a shorter sample
period, 1987– 92, does not significantly affect
the results.

Asymmetry
type

Oil

Spot
gasoline

Wholesale

Retail
without tax

Spot gasoline

Indep. Var.
Total

.004
.004

—
—

Wholesale

Indep. Var.
Total

.004
.001

.08
.0

—
—

Retail without tax

Indep. Var.
Total

.0
.0

.21
.08

.06
.007

—
—

Retail with tax

Indep. Var.
Total

.001
.0

.035
.0

.0
.001

.0
.0

upstream price. Figures 2 through 6 plot the
differences between the downstream price’s
response to an increase and to a decrease in the
upstream price.8 The solid line in each figure
represents the point estimate of the response,
and the dashed lines represent a confidence
band of two standard deviations.9
Figures 2 through 6 show that the asymmetry implied by the error-correction model is
substantially different from that implied by the

The Magnitude of Asymmetry
To assess the extent of the asymmetry
implied by the two models, we examine the
response of the downstream price to both a permanent one-time increase in the upstream price
and to a permanent one-time decrease in the

Figure 3

Difference in Response of
Wholesale Gasoline Price to
Rising and Falling Price of Crude Oil

Figure 2

Difference in Response of Spot Gasoline
Price to Rising and Falling Price of Crude Oil
Error-correction specification

Error-correction specification

Percent

1.12

.64

.96
.48
.80
.32

.64
.48

.16

.32
0
.16
–.16

0
–.16

–.32

10 11 12 13 14 15 16

Period

10 11 12 13 14 15 16

Period

Levels specification

Percent

1.12

.64

.96

.48

.80
.32

.64
.48

.16

.32

.16
–.16

0
–.16

–.32

10 11 12 13 14 15 16

Period

FEDERAL RESERVE BANK OF DALLAS

10 11 12 13 14 15 16

Period

ECONOMIC REVIEW FIRST QUARTER 1998

Figure 4

Figure 5

Difference in Response of Retail Price
(With Tax) to Rising and Falling
Price of Crude Oil

Difference in Response of Wholesale
Gasoline Price to Rising and Falling
Spot Price of Gasoline

Error-correction specification

Percent

.25

.50

.20

.25

.15
0

.10
–.25

.05
–.50

0
–.05

–.75

10 11 12 13 14 15 16

Period

10 11 12 13 14 15 16

Period

Levels specification

Percent

.25

.50

.20

.25

.15
0
.10
–.25
.05
–.50

0
–.05

–.75

10 11 12 13 14 15 16

Period

10 11 12 13 14 15 16

Period

The one anomalous response is that of
wholesale prices to changes in the spot gasoline
price (Figure 5 ). In this case, both the errorcorrection model and the levels model imply
that wholesale prices respond more to a
decrease in the spot price than to an increase.
The difference is not statistically significant in
either model, however, in contrast to the F-tests
reported in Tables 3 and 4.

levels model. For the error-correction model,
the difference in the response of the downstream price to an increase versus a decrease in
the upstream price is generally statistically
significant. For the levels model, the difference
is statistically significant only in a few cases.
Furthermore, the magnitude of the asymmetry
implied by the error-correction model is several
times larger than that implied by the levels
model, particularly during the first eight weeks
following a change in the upstream price. Even
for the price pairs in which the levels model
does indicate significant asymmetry, the magnitude of the asymmetry is substantially smaller
than that implied by the error-correction model
(for example, see Figure 4).
For most of the error-correction models,
the asymmetry peaks one or two weeks after
the initial change in the upstream price and
then slowly dies out. When retail (both with
and without taxes) is the downstream price,
the asymmetry can be fairly long-lived — longer
than four months. In the few cases in which the
levels model shows asymmetry, the asymmetry
is quite persistent.

DIFFERENCES IN SPECIFICATION
The fact that the two models yield such
different results is puzzling. Under the null
hypothesis of no asymmetry, the two models
are identical (as the long-run restriction is not
placed on the error-correction model). The differences arise solely in the specification of
asymmetry.
To highlight the similarities and differences of the specifications represented by
Equations 4 and 6, we create a generalized
model in which the two specifications are
nested. With some algebraic manipulation, the
generalized model can be written as

Table 5

i =0
n

i =1

Significance of Nesting Tests for Levels and
Error-Correction Models

(7 ) PDt = a + ∑ bi PU t −i + ∑ ci PDt −i

(Variable at left is the dependent variable)
Asymmetry
type

+ ∑ diU t −i PU t −i + ∑ fi Dt −i PDt −i
i =0
n −1

i =1
n −1

i =0

i =1

+ ∑ giUt −i PUt −i −1 + ∑ hi Dt −i PDt −i −1 + µt ,
where a, bi, ci, di, fi, gi, and hi are parameters to
be estimated, and µt is a white-noise residual.
As with Equations 4 and 6, we also include 51
weekly dummies and a time-trend variable. The
levels specification (Equation 4 ) is obtained if
the coefficients gi and hi are zero. The errorcorrection specification is obtained if gi = –di
and hi = –fi for all i except i = 1, and dn = 0 and
fn = 0.
Unfortunately, the differences between the
models do not seem to lend themselves to
sharply diverging economic interpretations.
Consequently, we use Equation 7 to test for
asymmetry and the restrictions imposed by the
two models. Asymmetry is indicated if the coefficients di, fi, gi, and hi are jointly significantly

.35
.30
.25
.20
.15
.10
.05
0
4

10 11 12 13 14 15 16

Period

Levels specification
Percent
.35
.30
.25
.20
.15
.10
.05
0
–.05

10 11 12 13 14 15 16

Period

FEDERAL RESERVE BANK OF DALLAS

Spot gasoline

LM
ECM

.01
.06

—
—

Wholesale

LM
ECM

.006
.277

.002
.132

—
—

Retail without tax

LM
ECM

.002
.28

.242
.592

.052
.011

—
—

Retail with tax

LM
ECM

.0
.392

.020
.301

.014
.457

.0
.143

Asymmetry
type

Oil

Spot
gasoline

Wholesale

Retail
without tax

Spot gasoline

Indep. Var.
Total

.077
.009

—
—

Wholesale

Indep. Var.
Total

.014
.004

.013
.0

—
—

Retail without tax

Indep. Var.
Total

.001
.0

.193
.18

.034
.002

—
—

Retail with tax

Indep. Var.
Total

.002
.0

.061
.002

.022
.006

.0
.0

different from zero. The restriction representing
the levels specification is rejected if the coefficients gi and hi are jointly significantly different
from zero. The restriction representing the
error-correction specification is rejected if gi =
–di and hi = –fi for all i except i = 1, and dn = 0
and fn = 0 are jointly significantly rejected.
Table 5 shows that for eight of the ten
price pairs, the restrictions implied by the levels
model are rejected, but the restrictions implied
by the error-correction model cannot be
rejected. For one pairing — spot gasoline with
retail sans tax — the restriction implied by either
model cannot be rejected. In the pairing of
wholesale with retail sans tax, the restriction
implied by the levels model cannot be rejected,
but the restriction implied by the error-correction model is rejected.
For each of the nine pairings in which one
specification seems to be preferred over the
other, the preferred model indicates asymmetry.
For the one pairing in which neither set of
restrictions can be rejected, neither model indicates asymmetry. As shown by Table 6, asymmetry tests conducted with the general model
are substantially consistent with the results from
the preferred model for each pairing.

Percent

Retail
without tax

(Variable at left is the dependent variable)

Error-correction specification

Wholesale

Significance of Asymmetry Tests for General Model

Difference in Response of
Retail Price (with Tax) to
Rising and Falling Wholesale Price

Spot
gasoline

Table 6

Figure 6

–.05

Oil

ECONOMIC REVIEW FIRST QUARTER 1998

Asymmetry Reconsidered
We have considered two model specifications to test for asymmetry in the response of
gasoline prices to crude oil prices. Even though
the two models differ only in their specification
of asymmetry and are otherwise identical, they
yield dramatically different results. A levels
specification indicates that asymmetry is only
found in a few cases and is small. An errorcorrection specification (without a long-run
restriction) indicates that asymmetry is pervasive
and large.
Unfortunately, the differences in specification do not seem to lend themselves to economic interpretation, which leaves us with a
statistical criterion with which to evaluate the
divergent findings. In most cases, tests with a
more general model indicate that the errorcorrection model seems to fit the data better
than the levels model, which suggests that the
apparent asymmetry is one that operates on
the rate of change in prices. If we accept the
error-correction specification and conclude that
asymmetry is pervasive and large, however, we
must be concerned that the findings are sensitive to model specification.

NOTES

While retaining responsibility for any errors or omissions in the analysis, the authors thank Jim Dolmas,
Fred Joutz, Evan Koenig, Jayeong Koo, Don Norman,
and Marci Rossell for helpful comments on earlier
drafts of the paper, and Carrie Kelleher and Dong Fu
for able research assistance.
We conceptualize the relationship between upstream
and downstream prices as a markup model but conduct our estimation in levels and natural logs. Although
the results are substantially similar for both specifications, we report these results for natural logs because
that specification is scale invariant.
Causality tests conducted with forms of the model that
allowed for asymmetry yielded substantially similar results.
We use a Choleski decomposition that decomposes
the residuals µ1,t and µ2,t into two sets of impulses that
are orthogonal to each other. This permits the covariance between the residuals to be taken into account.
The Choleski decomposition imposes a recursive
structure on the system of residuals in which the ordering of the residuals associated with each dependent
variable is specified. If the covariance between the
residuals is sufficiently high, the ordering can affect
the results. We found that changing the ordering had
little effect on the results, except the pairing of spot
crude oil with spot gasoline.
The inclusion of a contemporaneous upstream price
term raises a concern about the possibility of simultaneous equation bias. The upstream origin of the

shocks mitigates much of this concern, and BCG
found that failure to instrument the variable has no
appreciable effect on the results.
Statistical tests indicate that the seasonal dummies are
significant in all regressions and the time-trend variable is significant in some regressions. Robustness
checks indicate that the seasonal dummies and the
time-trend variable have little effect on the results.
The presence of the dummies, Ut – i and Dt – i , prevents us from rewriting the asymmetric differenced
terms as levels terms without placing restrictions on
the resulting coefficients. See Equation 7 below.
The differences between Equations 4 and 6 are best
seen in Equation 7 below.
Not all figures are presented here. The remaining
figures are available from the authors.
Because the models are nonlinear, some care must
be taken in computing these responses. For all the
responses, we consider a one-unit change in the
upstream price, given that the upstream price is
initially equal to its sample mean. Because lagged
values of the downstream price enter the model,
downstream prices are set equal to the steady value
implied by the model when the upstream price is
equal to its sample mean. The confidence bands are
calculated by Monte Carlo Integration. For each repli~
cation, we randomly draw the model parameters, β ,
from its posterior distribution, which is assumed to
be N(β̂, V (β̂) ), where β̂ and V (β̂) are the estimated
parameters and their variance-covariance matrix,
~
respectively. For a given realization of β , we then
calculate the responses of the downstream price to
an increase and a decrease in the upstream price.
This is repeated 1,000 times to form the two-standarddeviation confidence band.

REFERENCES
Bacon, Robert W. (1991), “Rockets and Feathers:
The Asymmetric Speed of Adjustment of U.K. Retail
Gasoline Prices to Cost Changes,” Energy Economics
13 (July): 211–18.
Borenstein, Severin (1991), “Selling Costs and Switching
Costs: Explaining Retail Gasoline Margins,” Rand Journal
of Economics 22 (Autumn): 354 – 69.
Borenstein, Severin, A. Colin Cameron, and Richard
Gilbert (1997), “Do Gasoline Prices Respond Asymmetrically to Crude Oil Prices?” Quarterly Journal of
Economics 112 (February): 305 – 39.
Deltas, George (1997), “Retail Gasoline Price Response
Asymmetries to Wholesale Price Shocks” (Paper presented at the Western Economic Association Meeting,
Seattle, July 9 –13).
French, Mark (1991), “Asymmetry in Gasoline Price

Changes” (Washington, D.C.: Board of Governors of the
Federal Reserve System, August, Draft paper).

American Petroleum Institute Research Study no. 060
(Washington, D.C., August).

Karrenbrock, Jeffrey D. (1991), “The Behavior of Retail
Gasoline Prices: Symmetric or Not?” Federal Reserve
Bank of St. Louis Review, July/August, 19 – 29.

Scherer, F. M. (1980), Industrial Market Structure and
Economic Performance, 2nd ed. (Chicago: Rand
McNally).

Mohanty, Samarendu, E. Peterson, F. Wesley, and Nancy
Cottrell Kruse (1995), “Price Asymmetry in the International Wheat Market,” Canadian Journal of Agricultural
Economics 43 (November): 355 – 66.

Shin, David (1992), “Do Product Prices Respond Symmetrically to Changes in Crude Oil Prices,” American
Petroleum Institute Research Study no. 068 (Washington,
D.C., December).

Neumark, David, and Steven A. Sharpe (1992), “Market
Structure and the Nature of Price Rigidty: Evidence from
the Market for Consumer Deposits,” Quarterly Journal of
Economics 107 (May): 657– 80.

Tirole, Jean (1990), The Theory of Industrial Organization
(Cambridge, Mass.: MIT Press).
U.S. General Accounting Office (1993), “Energy Security
and Policy: Analysis of the Pricing of Crude Oil and
Petroleum Products,” GAO/RCED-91-17 (Washington,
D.C.: Government Printing Office, March).

Norman, Donald A., and David Shin (1991), “Price
Adjustment in Gasoline and Heating Oil Markets,”

FEDERAL RESERVE BANK OF DALLAS

ECONOMIC REVIEW FIRST QUARTER 1998

The North American Free Trade Agreement has been one of the most hotly debated
trade accords in recent history. NAFTA’s critics
regard the expansion of free trade to a developing country like Mexico as a dangerous
precedent. They envision U.S. jobs lost in a
flood of goods from a country with an average
wage one-fifth that of the United States. Others
see NAFTA as a boon to U.S. employment and
living standards through greater trade and
investment opportunities.1
These opposing expectations for NAFTA
have been largely matters of speculation and
based on assessments of other trade accords. But
now that NAFTA has been in operation for more
than three years, the question is not what the
trade accord is likely to do but what it has done.
Typically, the debate over NAFTA has
focused on jobs. However, to really understand
NAFTA’s effects on employment or living standards, it is important to first answer the
more fundamental question of what effect it
has had on trade. Changes in trade patterns
caused by a lowering of trade barriers are ultimately the mechanism by which jobs and living
standards are influenced. This article examines
how NAFTA, since its inception, has affected
trade between the United States, Canada, and
Mexico, holding constant other important factors that affect trade. Without controlling for
these other factors, the effects of NAFTA are
difficult to discern, which can lead to wrong or
conflicting conclusions about the accord’s
effects on trade.
In the three years since NAFTA’s implementation, both its supporters and opponents
have used changes in the pattern of trade flows
to justify their positions. Supporters have argued
that during 1994, the year NAFTA took effect,
U.S. trade with Mexico grew nearly 10 percent
faster than the average of the previous five years
(Figure 1 ). Opponents claim that any expansion
in trade in NAFTA’s first year was quickly
reversed when expectations about its benefits
fell to earth with the 1995 peso crisis. During
1995, U.S. imports from Mexico grew nearly 25
percent, but exports dropped 11 percent.
Since Mexico began to recover from its
deep recession in late 1995, U.S. exports to
Mexico have resumed rapid growth, but claiming the success or failure of NAFTA based on a
superficial examination of the ups and downs
of trade flows can be a mistake. The acccord’s
effects may be much more or less than a simple
glance at these flows would suggest because
NAFTA does not exist in an economic or policy
vacuum.

Has NAFTA Changed
North American
Trade?
David M. Gould
Senior Economist and Policy Advisor
Federal Reserve Bank of Dallas

ypically, the debate over

NAFTA has focused on jobs.
However, to really understand
NAFTA’s effects on employment
or living standards, it is
important to first answer the
more fundamental question of
what effect it has had on trade.

assessment of NAFTA’s effects, past or future,
must use an economic model to judge how
trade interacts with the larger economy.
The techniques used to determine
NAFTA’s future impact fall into two broad categories. First is the computable general equilibrium (CGE) modeling technique, in which
analysts model a simplified economy and simulate what would happen to it if tariffs and
nontariff barriers fall according to the NAFTA
schedule.3 Typically, CGE models are static—
that is, the structure of the economy cannot vary
over time in response to changing trade patterns.
More recently, however, a model by Kouparitsas
(1997) allows for changes in capital investment
and its reallocation across economic sectors and
countries over time. Allowing capital flows to
change over time in response to NAFTA generates a much larger benefit to freer trade.
Although these two types of studies make
different assumptions about the economy’s
structure and the degree of competition in various sectors, both find an increase in income
and trade under NAFTA. There is also substantial agreement about how NAFTA will affect
Canada, Mexico, and the United States. In general, because Mexico’s is the smallest economy,
it reaps the largest benefit relative to its GDP
(Kehoe and Kehoe 1994). The United States
benefits modestly, and Canada does not have
much benefit beyond that resulting from its
1989 free trade agreement with the United
States.
Other studies use a partial equilibrium
analysis to examine the effects of NAFTA. That
is, they focus on particular sectors and assume

Figure 1

U.S. Trade with Mexico
Billions of U.S. dollars
70

NAFTA
Imports

60
50
40

Exports
30
20
10
0
’88

’89

’90

’91

’92

’93

’94

’95

’96

SOURCE: International Monetary Fund, Direction of Trade
Statistics.

Worldwide economic changes that likely
influenced bilateral trade within North
America were already under way when NAFTA
took effect. For example, U.S. real gross
domestic product increased 3.5 percent in
1994, influencing the United States’ supply and
demand for imports and exports worldwide.
As Figure 2 shows, U.S. trade with the world,
excluding Mexico and Canada, grew faster in
1994 than in the previous six years. Likewise,
Mexican real GDP increased 5.2 percent, and
the real value of the peso was quite high in
1994, both factors that would have boosted
U.S. exports to Mexico. As a result, it is
unlikely that NAFTA and its lower trade barriers were the only influence on bilateral trade
flows. To isolate the effects of NAFTA, one
must account for the effects of changes in
income, exchange rates, and trade with other
countries; only then can NAFTA’s impact on
trade be ascertained.
In the first section of this article, I discuss
previous analyses of NAFTA and compare them
with my methodology. I next specify and estimate a model of the accord’s effects on North
American trade flows, and I assess how much
trade has been influenced by NAFTA. I conclude by evaluating NAFTA’s success.

Figure 2

U.S. Trade with the World,
Less Mexico and Canada
Billions of U.S. dollars
600

Imports

500

400
Exports

300

DETERMINING NAFTA’S EFFECTS
Because most studies of how NAFTA affects
jobs, trade, and incomes in North America were
completed just before, or shortly after, the
treaty’s implementation, the majority of them
are forward-looking. This contrasts with the
backward-looking approach of more recent
studies, including this one.2 However, any

FEDERAL RESERVE BANK OF DALLAS

NAFTA

200

100

0
’88

’89

’90

’91

’92

’93

’94

’95

SOURCE: International Monetary Fund, Direction of Trade
Statistics.

ECONOMIC REVIEW FIRST QUARTER 1998

’96

in administrative rules, regulations, and expectations about the sustainability of free trade that
cannot be easily quantified. Changing expectations for the sustainability of free trade under
NAFTA are potentially among the most important aspects of the agreement. If NAFTA did not
create a credible commitment to free trade, new
investment would not flow into export industries to take advantage of reduced trade barriers.
Without a credible free trade agreement, the
benefits of the trade accord would be much
lower. Expectations for a more stable and open
trading environment affect trade by providing
the incentive for firms to make long-term capital commitments. These expectations cannot be
easily accounted for using the methodology
cited previously because it is difficult to translate them into price changes.
Of course, there are potential pitfalls to
this methodology as well. In particular, the
model is unlikely to control for all the factors
important to bilateral trade flows. Factors may
be attributed to NAFTA that should not be. For
example, when NAFTA took effect on January 1,
1994, political unrest was developing in Mexico,
resulting in the armed Zapatista movement
and two political assassinations later that year.
Inasmuch as the uncertainty generated by this
unrest reduced trade, it would reduce the estimated trade effects of NAFTA. Even though the
events are independent of NAFTA, they would
be indistinguishable in the context of the empirical model. If political uncertainty could be
measured and included in the model, this
would not be a problem.
However, even if important economic or
political events are excluded from the model,
they may not bias the estimated NAFTA effects
if they and the accord’s implementation were
not simultaneous. Factors such as the peso
crisis are unlikely to bias the analysis because
exchange rates and incomes (the two factors
most affected by the crisis) are included in
the model. In other words, a majority of the
peso crisis’ effects on trade are likely to be
taken into account.6 Still, because NAFTA was
implemented in a rather tumultuous period
in Mexico that resulted in reduced trade, the
estimated effects of NAFTA may be biased
downward.

that the rest of the economy is unaffected.
Determining NAFTA’s trade effects in this context usually entails multiplying reduced-form
price elasticities (a measure of how price
changes translate into quantity changes) by the
expected changes in tariff and tariff-equivalent
trade barriers to determine how trade in various
sectors is likely to change. In 1993, the U.S.
International Trade Commission (USITC) completed a comprehensive study of NAFTA that
used reduced-form price elasticities to determine how much NAFTA would affect trade in
various U.S. economic sectors.4 Hufbauer and
Schott (1993) discuss NAFTA in a broad context
and, based on their expectations of how trade
would change under NAFTA, estimate how jobs
in various sectors may be affected. They estimate changes in the number of jobs using
Department of Commerce data on jobs supported directly and indirectly by exports to
Mexico in 1990. They find that NAFTA and
Mexico’s economic reforms would increase the
net number of U.S. jobs by about 170,000 in
1995 (Hufbauer and Schott 1993, 14).
In general, these partial equilibrium studies estimate that the United States will increase
its exports of high-tech goods, grains and
oilseed, and mechanical parts used in Mexican
assembly plants. Increases are projected for
U.S. imports of automobiles, apparel, glassware,
household appliances, and certain horticultural
products.
NAFTA SINCE ITS IMPLEMENTATION
Unlike the studies cited above, which
have sought to predict how NAFTA will affect
trade, this article’s intent is to measure how
NAFTA has already affected it. To assess the
effects of NAFTA in its first three years, a model
of bilateral trade flows in North America is
empirically estimated with pre- and postNAFTA data. The analysis is based on a widely
used model of bilateral trade flows that
includes incomes, prices, and exchange rates
(see the box entitled “The Gravity Model of
Bilateral Trade”). Once the fundamental determinants of trade flows are accounted for, any
extraordinary flows that have occurred since
NAFTA’s inception are attributed to the free
trade agreement.5
This type of analysis has at least two benefits. First, the analysis can estimate trade flows
utilizing data since NAFTA’s implementation.
Second, it can capture most of the potentially
important aspects of NAFTA, including tariff and
nontariff barrier reductions, as well as changes

ESTIMATING THE EFFECTS OF NAFTA
To assess the effects of NAFTA since its
implementation, the following benchmark
model of Canadian, Mexican, and U.S. bilateral
trade flows is estimated using quarterly data

The Gravity Model of Bilateral Trade
The empirical bilateral trade model in this article is based on the gravity equation, which derives its
name from its resemblance to Newton’s law of gravity. The model was originally formulated from ad hoc
assumptions but had its intuitive appeal in describing trade flows as increasing as the economic “distance”
between two countries shrinks. It describes bilateral trade flows between two countries as a function of their
incomes, populations, the physical distance between them, and trade barriers. If countries with similar
incomes have similar preferences for goods but produce different types of products, they are likely to trade
more with each other than with other countries. Trade is also likely to increase the closer the countries
are and the lower the trade barriers between them. The gravity model has been used to describe many
different types of flows, such as immigration, shopping patterns, and car traffic, as well as interregional
trade. It has been used extensively in international trade applications because it provides an empirically
tractable framework.
The ad hoc assumptions behind the gravity equation have been replaced by microeconomic foundations. Anderson (1979), Helpman and Krugman (1985), Bergstrand (1985), and Bikker (1987) have developed variants of the gravity model based on utility and profit maximization. The empirical model this article
uses is based on Bergstrand’s theoretical foundation for the gravity equation, which is based on the
assumption that producers maximize profits subject to a constant elasticity of transformation (CET) technology, and consumers maximize a constant elasticity of substitution (CES) utility function subject to a
budget constraint (Bergstrand 1985). Assuming that individual bilateral trade flows are small relative to total
trade, the equation for bilateral trade is
(B.1)

PX ij = Yi (σ −1) /(γ + σ)Y j( γ +1) /(γ + σ)Tij− σ( γ +1) /(γ + σ)Cij− σ( γ +1) /( γ + σ)Eijσ( γ +1) /( γ + σ)
 N

*  ∑ Pik1+ γ 
 k =1,k ≠i


−(σ −1) /( γ − η) /(1+ γ )( γ + σ )

 N

*  ∑ Pkj*1− σ
 k =1,k ≠ j


( γ +1)(σ − µ ) /(1− σ )( γ + σ )

(1+ η) /(1+ γ )
 N


+ Pii1+ η 
*  ∑ Pik1+ γ 
 k =1,k ≠i





−(σ −1) /( γ + σ )

−( γ +1) /( γ + σ )

(1− µ ) /(1− σ )
 N


+ Pjj1− µ 
*  ∑ Pkj*1− σ 
 k =1,k ≠ j
,




where PXij is the value of aggregate trade flows from country i to country j,
Yi is the aggregate income of country i,
Yj is the aggregate income of country j,
Pik is the price received for country i ’s product in the k th country,
P kj* = PkjTkj /Ekj is the price paid for buying k ’s product in the j th market,
Tij is 1 plus the ad valorem tariff rate on i ’s product in the j th market,
Cij is a nontariff barrier on i ’s product in the j th market,
Eij is the exchange rate between country j ’s currency in terms of i ’s currency,
γ is the constant elasticity of transformation in the supply between different export goods (0 ≤ γ ≤ ∞),
η is the CET between the supply of exports and domestically produced goods (0 ≤ η ≤ ∞),
σ is the constant elasticity of substitution between the demand for different imported goods
(0 ≤ σ ≤ ∞), and
µ is the CES between the demand for imported and domestic goods (0 ≤ µ ≤ ∞).
As shown in Equation B.1, the value of aggregate trade flows from country i to country j depends on
nine terms. In the order of their appearance in the equation, they are (1) the income of the exporting
country, (2) the income of the importing country, (3) tariffs, (4) nontariff barriers, (5) the exchange rate,
(6) an export price index for exports to all countries to which the exporting country exports, (7) an import
price index for imports from all countries from which the importing country imports, (8) an index of domestic
prices for the exporting country, and (9) an index of domestic prices for the importing country.
These nine terms can be sorted into three categories: (1) income in the exporting and importing countries, which reflects the potential demand and supply; (2) wedges between the export and import price of
the traded goods due to tariffs and nontariff barriers; and (3) price terms reflecting the substitutability
between this traded good and the others.
Equation B.1 serves as the basis for the empirical model describing trade flows between the NAFTA
countries. Changes in tariff and nontariff barriers are proxied by a binary variable for NAFTA. Because
country-specific data for the price terms are not available, the empirical analysis uses proxies. To account
for the exchange rate, domestic prices, and the terms of trade between the bilateral trade partners, GDP
price deflators and the bilateral real exchange rate between the partners are used. To account for the terms
of trade with other trading partners, a multilateral real exchange rate with the rest of the world is used.
Economic events, such as the beginning of Mexico’s trade liberalization in 1985 and Canada’s free trade
agreement with the United States in 1989, are proxied by binary variables.

FEDERAL RESERVE BANK OF DALLAS

ECONOMIC REVIEW FIRST QUARTER 1998

mented until 2009. Tariff rates in many sectors
are to be reduced over a fifteen-year period (see
the box entitled “What Has NAFTA Done?”).
Consequently, these results should be seen as a
preliminary look into NAFTA’s effects on aggregate trade.
The estimated equations are in the appendix.10 Overall, the equations explain the growth
of trade relatively well.11 However, the effects of
NAFTA on trade flows (in size and statistical significance) vary a great deal between countries.
Figures 3 through 8 show what the estimation
results imply for actual exports and imports
between the United States, Canada, and Mexico.
The shaded bands on both sides of trade estimated without NAFTA represent a 90 percent
confidence interval derived from the statistical
error of the estimate.12

from 1980 though 1996. The empirical equations are based on the gravity model, which
is derived from standard microeconomic foundations (Bergstrand 1985). All variables are
seasonally adjusted quarterly data and are expressed in log first-differences (growth rates):7
(1) M tij = α 0 + α1M tij−q + α 2Yt i−q + α 3Yt −j q + α 4 E tij−q
+ α 5E tiw−q + α 6Pt i−q + α 7Pt −j q + α 8 Dt
+ α 9NAFTAt + et ;
(2) X tij = β0 + β1X tij−p + β2Yt i−p + β3Yt −j p + β4 E tij−p
+ β5E tiw−p + β6Pt i−p + β7Pt −j p + β 8 Dt
+ β 9NAFTAt + µt .
The variables are defined as follows: M ij is
country i ’s imports from country j; i and j are
either the United States, Canada, or Mexico; t
refers to the date; p and q are the number of
periods a variable is lagged; X ij is country i ’s
exports to country j; Y i is real GDP of country
i; Y j is real GDP of country j ; P i is country i ’s
GDP price deflator; P j is country j ’s price deflator; E ij is the real exchange rate between
countries i and j; E iw is the real exchange rate
between country i and the world (excluding
country j ); and D is a binary variable that represents changes in trade regimes not associated
with NAFTA. For trade with Mexico, D equals 1
beginning in 1985, the period in which Mexico
begins liberalizing trade. For trade between
Canada and the United States, D equals 1 beginning in 1989, representing the period of the
U.S.– Canada free trade agreement. NAFTA is
a binary variable representing the period in
which the accord was implemented. The variable NAFTA equals 1 beginning the last quarter
of 1993.8 α and β are estimated coefficients, and
e and µ are error terms.
The variables in Equations 1 and 2 can
be sorted into four categories: (1) lagged trade
(M tij–p , X tij–q ), which reflects the adjustment process of trade to a new equilibrium; (2) income
in the exporting and importing countries (Y j,
Y i ), which reflects the potential demand and
supply for the traded goods; (3) price and real
exchange rate terms (P i, P j, E ij, E iw), reflecting
the substitutability of nontraded and traded
goods in the NAFTA countries and the rest of
the world; and (4) one-time trade liberalization
variables, reflecting changes in trade regimes
and NAFTA (D, NAFTA).
The size and statistical significance of the
coefficient on the NAFTA variable tell us the
degree to which NAFTA affects bilateral trade
flows in North America.9 It should be noted that
NAFTA is not scheduled to be fully imple-

The United States and Mexico
Figures 3 and 4 show NAFTA’s estimated
effects on bilateral trade flows between the
United States and Mexico. As the dotted line in
Figure 3 indicates, U.S. exports are estimated to
have grown faster than they would have had
there not been a trade agreement. On average,
U.S. export growth is about 16.3 percentage
points higher per year with NAFTA. While the
increase in growth is not extraordinary, the
cumulative effect is about $21.3 billion more in
exports than what would have occurred without
NAFTA. The statistical significance of this effect
is high, as shown by the 90 percent confidence
interval lines that exclude the observed data on
U.S. exports to Mexico.
For U.S. imports, as shown in Figure 4,
the boost from NAFTA is also relatively high.
On average, import growth is about 16.2 percentage points higher per year with NAFTA.
Since NAFTA became law, the cumulate impact
amounts to about $20.5 billion in additional
imports because of the agreement. However,
NAFTA’s statistical significance for U.S. imports
from Mexico is only marginal. The 90 percent
confidence interval lines show that we cannot exclude the possibility that trade without
NAFTA would have been different from trade
with NAFTA.
The United States and Canada
Figures 5 and 6 show the estimated effects
of NAFTA on bilateral trade flows between the
United States and Canada. As both figures show,
trade between the two countries has not been
affected much by NAFTA. This is not surprising,
given that a free trade agreement with Canada
was negotiated in 1989 and NAFTA did not alter

Figure 3

Figure 4

U.S. Exports to Mexico

U.S. Imports from Mexico
Billions of U.S. dollars

Billions of U.S. dollars
60

100

NAFTA

90
50

90% confidence

80
70

40
Actual

Without
NAFTA

50
40
Without
NAFTA

Actual

90% confidence

90%
confidence

10
0

0
’88

’89

’90

’91

’92

’93

’94

’95

’88

’96

’89

’90

’91

’92

’93

’94

’95

’96

SOURCES: International Monetary Fund, Direction of Trade
Statistics; author’s calculations.

that accord significantly. However, even the
1989 agreement, as measured by the binary
variable D ij in the U.S.–Canada trade equations,
does not seem to play a strong role in determining trade flows. Although trade may have
been liberalized in some sectors, aggregate
trade does not seem to be influenced much.13
This may be because trade between the countries has been generally open for some time.
Figures 5 and 6 show an 8.6 percent average
annual increase in U.S. exports to Canada and a
3.9 percent increase in U.S. imports from Canada
due to NAFTA. The NAFTA effect on both exports and imports is statistically insignificant.
Canada and Mexico
The effects of NAFTA on exports and
imports between Canada and Mexico appear in
Figures 7 and 8. As the figures show, the esti-

mated effects are very imprecise, with a wide,
90 percent confidence band. One possible reason for the difficulty in measuring the effects of
NAFTA in these equations is that trade between
Canada and Mexico is a very small share of each
country’s total and is subject to much more
unexplained volatility than is trade with the
United States.14 In these equations, the NAFTA
trade effects are estimated to be negative, which
raises the possibility that NAFTA may have
diverted Canadian–Mexican trade toward the
United States or other countries. But because
the effects are so imprecise, the possibility that
the effects are zero or even positive cannot be
excluded.
In summary, it is important to remember that
there is a wide statistical margin of error for
most of the estimated NAFTA trade effects, so
they should be viewed in relative rather than abso-

Figure 5

Figure 6

U.S. Exports to Canada

U.S. Imports from Canada

Billions of U.S. dollars

160

180

NAFTA

160

140

90% confidence

90% confidence
140

120

100
80

Without
NAFTA

100

Actual

Without
NAFTA

Actual

90% confidence

60
60

90% confidence
40

0
’88

’89

’90

’91

’92

’93

’94

’95

’96

’88

SOURCES: International Monetary Fund, Direction of Trade
Statistics; author’s calculations.

FEDERAL RESERVE BANK OF DALLAS

’89

’90

’91

’92

’93

’94

’95

SOURCES: International Monetary Fund, Direction of Trade
Statistics; author’s calculations.

ECONOMIC REVIEW FIRST QUARTER 1998

’96

Figure 7

Figure 8

Canadian Exports to Mexico

Canadian Imports from Mexico

Billions of U.S. dollars

NAFTA

12
90% confidence

90% confidence

10
8
8
6

Without
NAFTA

6
90%
confidence

Without
NAFTA
2

Actual

90% confidence

Actual
0

0
’88

’89

’90

’91

’92

’93

’94

’95

’96

’88

’89

’90

’91

’92

’93

’94

’95

’96

SOURCES: International Monetary Fund, Direction of Trade
Statistics; author’s calculations.

lute terms. While it is likely that NAFTA affected
U.S.–Mexican trade, it is unlikely that it affected
U.S.–Canadian or Canadian–Mexican trade.

The share of total trade between the
NAFTA countries slightly increased, suggesting
that if there was trade diversion, it was small.
But to determine the extent of trade diversion in
North America, it is also important to consider
whether increased trade between NAFTA countries came at the expense of trade with the rest
of the world. In other words, did NAFTA shift
trade away from countries outside of NAFTA, or
did NAFTA simply increase trade within North
America at a faster rate than trade increased
with the rest of the world? Figure 10 shows that
it was the latter; that is, trade with countries outside North America also grew after NAFTA’s
implementation. The share of total trade
between North American countries increased

TRADE DIVERSION VERSUS TRADE CREATION
To judge NAFTA’s effects on the
economies of Canada, Mexico, and the United
States, it is also important to consider North
American trade flows in the context of trade
with the rest of the world. In other words, did
NAFTA create new trade opportunities within
North America, or did it simply divert trade from
countries outside NAFTA? If the increased trade
caused by NAFTA was simply a shuffling of
trade from other, more efficient trading partners,
then NAFTA’s benefit would shrink. Although a
detailed examination of this issue is not within
the scope of this article, a glance at how the distribution of trade flows has changed since
NAFTA can tell us whether the accord may be
associated with trade diversion.
Figure 9 shows how the distribution of
trade flows between the NAFTA countries and
the rest of the world changed from 1993, the
year before NAFTA began, to 1996, three years
after NAFTA started. As the figure shows, trade
within North America has increased relative to
trade with the rest of the world, but the increase
is slight. The share of U.S. trade with Canada
and Mexico increased from 27.8 to 29.4 percent
between 1993 and 1996, with most of that
increase attributed to greater U.S. trade with
Mexico. Canadian trade with the rest of North
America also increased, from a share of 77.3
to 80.4 percent. Mexico’s trade share with
North America changed very little, from 71 to
71.6 percent.15

Figure 9

Trade Shares of NAFTA Countries,
Before and After the Treaty’s Inception
Percent
100

0
1993
1996
United States
Rest of World

1993
1996
Canada
Mexico

Canada

1993
1996
Mexico
United States

SOURCES: International Monetary Fund, Direction of Trade
Statistics; author’s calculations.

What Has NAFTA Done?
On January 1,1994, NAFTA substantially reduced trade barriers across a market with more than 380 million people and a combined gross domestic product of roughly $7.6 trillion. Although
trade barriers have already been lowered significantly, NAFTA will
not be completely phased in until 2009. Most of the declines in tariffs have been on the Mexican side because Mexico started with
higher tariffs than the United States or Canada. In 1992, Mexican
tariffs on imports from the United States averaged about 10 percent when weighted by the value imported; at the same time, U.S.
tariffs on imports from Mexico averaged about 4 percent. Because
Canada and the United States negotiated a separate free trade
agreement in 1989, NAFTA affected trade between the two countries very little.
NAFTA substantially reduces, but does not eliminate, nontariff
trade barriers, such as import quotas, sanitary regulations, and
licensing requirements. Canada and the United States traditionally
have had few restrictions on capital flows, whereas Mexican laws
prohibited private ownership in the petroleum industry and parts of
the petrochemical industry, restricted foreign investment in the
financial and insurance sectors, and institutionalized communal
ownership of agricultural lands. The petroleum industry is still offlimits to foreign investment, although parts of the petrochemical
industry are set to be privatized. Many laws against foreign investment in the financial and insurance sectors have been eliminated
or substantially reduced. Although NAFTA set a schedule for liberalizing the banking sector, the 1995 peso crisis helped generate
the political momentum to speed the opening of this sector by
decreasing the restrictions on foreign ownership of existing banks.
NAFTA has not been without glitches, but the problems are
probably fewer than what they would have been without the agreement. The opening of trucking between the United States and
Mexico has been delayed, and tariffs have increased for some
products. The United States levied additional tariffs on Mexican
straw brooms, and in response Mexico levied tariffs on U.S. alcoholic beverages, flat glass, notebooks, and some types of wood
furniture. There have also been disputes over agricultural products,
such as avocados and tomatoes. Although these disputes are troublesome, their effect on overall trade has been small. Moreover,
NAFTA may have limited a protectionist response to the 1995 peso
crisis. Unlike Mexico’s 1982 crisis, when the Mexican government
raised tariffs dramatically in the hope of generating a trade surplus
to boost foreign reserves, during the 1995 crisis no such political
response occurred.

because trade within North America grew faster
than did trade with countries outside of North
America. Consequently, although trade diversion is a possibility, it is unlikely to be a large
problem. Moreover, because trade under
NAFTA was liberalized between countries with
very different comparative advantages, it is
unlikely that it caused a shift from optimal
trading patterns.

Here are some specifics by sector on how NAFTA has
reduced trade barriers.1

Automobiles
NAFTA immediately decreased Mexican tariffs on automobiles
from 20 to 10 percent in 1994 and is set to drop them to zero by
2004. Tariffs on most auto parts will be eliminated by 1999. The
agreement includes rules of origin specifying that to qualify for
preferential tariff treatment, vehicles must have 62.5 percent North
American content, which is an increase over the 50 percent provision in the U.S.– Canadian free trade agreement.
By 2004 NAFTA eliminates requirements that automakers
supplying the Mexican market produce the cars in Mexico and buy
Mexican parts. It has already eliminated mandatory export quotas
on foreign-owned auto manufacturing facilities in Mexico, and by
1999 it eliminates the Mexican restriction on bus and truck imports.

Textiles and Apparel
NAFTA immediately eliminated trade barriers on more than 20
percent of Mexican – U.S. trade in textiles and apparel. Over six
years it eliminates barriers on another 60 percent. The accord’s
rules of origin require that, to receive NAFTA tariff preferences,
apparel be manufactured in North America from the yarn-spinning
state forward.

Agriculture
NAFTA immediately reduced tariffs to zero for half of U.S.
agricultural exports to Mexico. The other half of agricultural goods
tariffs are to be eliminated by 2009. NAFTA immediately eliminated
Mexico’s licensing requirements for grains, dairy, and poultry.

Financial Services
NAFTA immediately reduced, and will eliminate by 2000,
Mexico’s restrictions on Canadian and U.S. ownership and provision of commercial banking, insurance, securities trading, and
other financial services. Under NAFTA, Canadian and U.S. financial
firms are allowed to establish wholly owned subsidiaries in Mexico
and to engage in the same range of activities as similar Mexican
firms.
1

Much of the following is described in Kehoe and Kehoe (1994).

Figure 10

Trade with the World as a Share of GDP
(Excluding trade between NAFTA countries)
Percent
70
60
50
40

HAS NAFTA BEEN A SUCCESS?

Certainly, NAFTA is not the solution to all
the economic problems that ail North America,
but it is not the disaster that critics claimed it
would be. NAFTA is foremost a free trade agreement, and as such its benefits derive from a shift
in resources to industries that reflect a nation’s
comparative advantage and away from indus-

FEDERAL RESERVE BANK OF DALLAS

10
0
1993
1996
United States

1993
1996
Canada

1993

1996
Mexico

SOURCES: International Monetary Fund, Direction of Trade
Statistics and International Financial Statistics.

ECONOMIC REVIEW FIRST QUARTER 1998

tries that do not. It is important to understand
that this shift implies that the benefits come
from both increased imports and exports.
Accordingly, the best way to judge a free trade
agreement is by whether it increases imports
and exports, and not by whether it increases
exports and decreases imports. By this criterion,
NAFTA has been a success for the United States
and Mexico. As expected, NAFTA has meant
little for the Canadian economy.
After accounting for the effects of economic variables important to bilateral trade
flows—such as income, exchange rates, and
prices—NAFTA is found to have a significant
positive effect on trade flows between the
United States and Mexico. NAFTA is not found
to have a significant impact on trade between
the United States and Canada or Canada and
Mexico. These findings are not surprising, given
that the United States negotiated a free trade
agreement with Canada five years before the
implementation of NAFTA and that most of the
trade liberalized under NAFTA is between the
United States and Mexico.
Although this empirical analysis controls
for economic shocks that would affect trade
through changes in incomes and exchange
rates, such as the 1995 peso crisis, it cannot control for all external shocks, nor can it capture all
aspects of NAFTA’s influence on trade. Perhaps
the largest omission from the analysis is trade
barriers that were not erected because of the
free trade agreement but would have been
without it. This issue was particularly relevant
during the 1995 peso crisis. Unlike previous
periods of economic turmoil in Mexico, trade
was relatively unimpeded during the peso crisis.
NAFTA, by enhancing the economic ties
between the North American countries, may
have limited a protectionist response to the
peso crisis and helped facilitate a return of
foreign investment and economic growth to
Mexico.
Has NAFTA destroyed U.S. jobs? Clearly,
NAFTA has neither spelled the death of the
U.S. workforce, nor has it generated a dramatic
increase in the number of U.S. jobs. What
dominates the employment picture in any year
are movements in a country’s own business
cycle, not trade. U.S. income grew fairly
smoothly between 1994 and 1996; as a result,
U.S. employment grew by 3.6 million. In contrast, Mexico experienced a currency crisis and
deep recession in 1995; its employment fell
but is now recovering with the economy.
Ultimately, freer trade does not determine the
number of jobs available in a country, but it

does determine the types of jobs available.
In the three years since NAFTA’s implementation, there has been a clear trend toward
increased trade in North America and higher
productivity in the United States. How much of
that greater productivity is due to NAFTA is
unknown. As time passes, and more economic
data become available, cyclical factors and
economic shocks will fall to the background
and a clearer picture of NAFTA’s effects on the
economy will emerge.
NOTES

I thank Baoyuan Wang for excellent research assistance, and Evan Koenig, Bill Gruben, and Lori Taylor
for their comments and suggestions. Any remaining
errors are my own.
The early controversy can perhaps be best summarized by quotes from Ross Perot and President Bill
Clinton during the NAFTA debate in 1993: “NAFTA will
pit American and Mexican workers in a race to the
bottom. In this race, millions of Americans will lose
their jobs” (Perot 1993, i ); “I believe the Nafta will
create 200,000 American jobs in the first two years
of its effect” (Clinton 1993).
See, for example, Gould (1996), Weintraub (1997), and
USITC (1997).
For an excellent survey of general equilibrium models
applied to NAFTA, see Kehoe and Kehoe (1994).
In creating the reduced-form price elasticities, the
USITC study assumes that foreign and domestic
goods are imperfect substitutes for each other. In
other words, the goods have separate markets in
which equilibrium prices and quantities are established. See USITC (1993) for a description of this
methodology.
The methodology used here is an extension of the
work done by Gould (1996). Other recent studies have
used a similar methodology to assess the trade and
sectoral effects of NAFTA. See USITC (1997).
See Gould (1996) for an assessment of how the peso
crisis affected trade independent of NAFTA. See Neely
(1996) for a discussion of why NAFTA did not cause
Mexico’s peso crisis.
Log first-differences, as opposed to a simple log-linear
relationship, were used because tests on the dependent and many of the independent variables could not
reject the hypothesis of nonstationarity. Consequently,
the equations estimate the growth of exports and
imports.
Because trade growth equations are estimated, the
effects of NAFTA are assumed to influence the growth
of trade. However, according to traditional long-run
models of trade, lower tariffs only influence the level,
not the growth, of trade. Because trade is unlikely to
jump to a new, higher level instantaneously, the growth
of trade is likely to be affected in the transition to a

new, higher level. This is especially true for the short
period that NAFTA has been observed and because
NAFTA is being phased in over fifteen years.
NAFTA may also affect bilateral trade flows indirectly
through income and prices. Although these indirect
effects are likely to be important over the long run,
over the short run these effects are probably small.
Because of this, these secondary effects are ignored
in the estimation.
The equations were estimated with ordinary least
squares and the errors terms checked to see if they
follow a white-noise pattern. The lag structure of the
equations was determined according to the Akaike
information criterion. To determine how trade would
have grown without NAFTA, the estimated NAFTA
effect was excluded from the estimated exports and
imports equations, and trade flows were calculated
with the actual data for the independent variables. To
provide the best estimates, the error term (which
reflects the degree to which the equation does not
match the data) was included in the calculation. Data
sources are given in the appendix.
The adjusted R 2 on the equations varies from 0.67 in
the U.S. – Mexico export equation to 0.18 in the
Canada – Mexico import equation. Most of the equations have an R 2 between 0.30 to 0.40, which is not
uncommon for similar growth equations. The adjusted
R 2 measures the proportion of the variation in the leftside dependent variable that is explained by the rightside dependent variables, adjusting for the number of
variables in the equation.
The confidence interval shows the degree of certainty
we can have in the estimated effects. If the confidence
interval around the estimated effects of trade without
NAFTA excludes the actual observed trade under
NAFTA, we can say with 90 percent certainty that
trade with NAFTA is different from trade without it.
If the 90 percent confidence interval includes the
observed trade under NAFTA, we can say that there is
less than a 90 percent certainty that trade is different
with NAFTA than without it.
An inherent problem in studying aggregate exports
and imports is that the analysis cannot explain
changes in sector-specific trade flows caused by
NAFTA. For example, imports in one industry may
expand, while imports in another industry may contract. In aggregate, however, imports overall would
appear to remain stable. An attempt was made to
study sector-specific trade data, but because equivalent sector-specific price information across countries
does not exist, the empirical results were poor.
This is indicated by the relatively low adjusted R 2 of
the Canada – Mexico trade equations.
A bilateral trade intensity index, defined as the share
of country j’s trade in country i ’s world trade relative to
the share of country i ’s world trade in total world trade
[Iij = (Tij /Tiw)/(Tjw /Tw)], also shows a slight increase

FEDERAL RESERVE BANK OF DALLAS

among NAFTA partners since 1993. See Yeats (1997)
for a discussion of this index applied to Mercosur’s
trade.

REFERENCES
Anderson, James (1979), “A Theoretical Foundation for
the Gravity Equation,” American Economic Review 69
(March): 106.
Bergstrand, Jeffrey (1985), “The Gravity Equation in
International Trade: Some Microeconomic Foundations
and Empirical Evidence,” Review of Economics and
Statistics 67 (August): 474.
Bikker, Jacob A. (1987), “An International Trade Flow
Model with Substitution: An Extension of the Gravity
Model,” Kyklos 40 (3): 315 – 37.
Clinton, Bill (1993), quoted in Bob Davis, “Two Years
Later, the Promises Used to Sell Nafta Haven’t Come
True, But Its Foes Were Wrong, Too,” Wall Street Journal,
October 26, 1995, A24.
Gould, David M. (1996), “Distinguishing NAFTA from the
Peso Crisis,” Federal Reserve Bank of Dallas Southwest
Economy, September/October, 6 –10.
Helpman, Elhanan, and Paul Krugman (1985), Market
Structure and Foreign Trade: Increasing Returns,
Imperfect Competition, and the International Economy
(Cambridge, Mass.: MIT Press).
Hufbauer, Gary C., and Jeffrey J. Schott (1993), NAFTA:
An Assessment (Washington, D.C.: Institute for
International Economics).
Kehoe, Patrick J., and Timothy J. Kehoe (1994), “Capturing NAFTA’s Impact with Applied General Equilibrium
Models,” Federal Reserve Bank of Minneapolis Quarterly
Review, Spring, 17– 34.
Kouparitsas, Michael A. (1997), “A Dynamic Macroeconomic Analysis of NAFTA,” Economic Perspectives
21 (January/February): 14 – 35.
Neely, Christopher J. (1996),”The Giant Sucking Sound:
Did NAFTA Devour the Mexican Peso?” Federal Reserve
Bank of St. Louis Review, July/August, 33 – 47.
Perot, Ross (1993), Save Your Job, Save Our Country:
Why NAFTA Must Be Stopped — Now! (New York:
Hyperion).
U.S. International Trade Commission (USITC 1997), “The
Impact of the North American Free Trade Agreement on
the U.S. Economy and Industries: A Three-Year Review,”
USITC Investigation no. 332 – 81, June.

ECONOMIC REVIEW FIRST QUARTER 1998

U.S. International Trade Commission (USITC 1993),
Potential Impact on the U.S. Economy and Selected
Industries of the North American Free-Trade Agreement,
USITC Publication 2596 (Washington, D.C.: USITC,
January).

Yeats, Alexander (1997), “Does Mercosur’s Trade Performance Raise Concerns About the Effects of Regional
Trade Arrangements?” World Bank Policy Research
Working Paper no. 1729 (Washington, D.C., February).

Weintraub, Sidney (1997), NAFTA at Three: A Progress
Report (Washington, D.C.: Center for Strategic and
International Studies).

Appendix
Regression Results
U.S.(i ) – Mexico( j )

Dependent
variable

U.S.(i ) – Canada( j )
Exports

Imports

Canada(i ) – Mexico( j )

Exports

Imports

Exports

Imports

Constant term

.027
(.794)

–.061
(.713)

–.025
(.688)

–.029
(.078)

–.229
(.224)

.169
(.042)

Lagged dependent
variable

–.679
(.074)

–.901
(.050)

–.441
(.659)

–.209
(.098)

–.299
(.341)

–.323
(.012)

3.623
(.031)

.289
(.209)

3.953
(.334)

2.793
(.135)

9.474
(.366)

2.560
(.543)

.082
(.050)

–3.046
(.539)

–1.095
(.394)

.104
(.425)

3.677
(.255)

.335
(.841)

E ij

– 2.147
(.000)

–.610
(.317)

–.171
(.536)

.178
(.427)

–.863
(.053)

–.435
(.181)

E iw

– 2.971
(.047)

–.061
(.316)

–2.062
(.430)

–.418
(.665)

6.748
(.497)

5.742
(.007)

.963
(.616)

13.716
(.292)

3.438
(.106)

4.208
(.009)

–17.100
(.384)

–5.847
(.149)

–.533
(.704)

–.191
(.608)

.477
(.724)

–.877
(.578)

–1.185
(.368)

–.890
(.099)

D ij

–.029
(.522)

.026
(.722)

–.005
(.825)

.008
(.550)

–.008
(.951)

–.003
(.994)

NAFTA

.073
(.015)

.072
(.119)

.031
(.191)

.018
(.374)

–.111
(.240)

–.038
(.453)

Adjusted R 2

.67

.35

.36

.31

.27

.18

Equation F statistic
(significance level)

.000

.030

.080

.002

.120

.050

LM test for autocorrelation
(significance level)
Lag structure

.31

.53

.20

.25

.01

.24

Degrees of freedom

NOTE: Coefficients are the sum of the lagged terms. Significance level of F statistics (the null hypothesis that all lagged
coefficients are equal to zero) are in parentheses.

Data Sources
Variable

Definition

Source

Seasonally adjusted value of merchandise imports, in millions of U.S. dollars

International Monetary Fund, Direction
of Trade Statistics

Seasonally adjusted value of merchandise exports, in millions of U.S. dollars

International Monetary Fund, Direction
of Trade Statistics

Seasonally adjusted GDP price deflator

International Monetary Fund,
International Financial Statistics

Seasonally adjusted real GDP

International Monetary Fund,
International Financial Statistics

Seasonally adjusted real exchange rate

Trade-Weighted Value of the Dollar,
Federal Reserve Bank of Dallas, and
author’s calculations

Seasonally adjusted real exchange rate
with rest of the world

Trade-Weighted Value of the Dollar,
Federal Reserve Bank of Dallas, and
author’s calculations

FEDERAL RESERVE BANK OF DALLAS

ECONOMIC REVIEW FIRST QUARTER 1998

The Dynamic Impact
Of Fundamental
Tax Reform
Part 1:
The Basic Model

Interest in fundamental tax reform has
waned since the early months of the 1996 U.S.
presidential campaign when it was the subject
of intense political and media debate. In coming
years, a resurgence of interest seems almost certain. After all, the Internal Revenue Service
remains unpopular, the U.S. savings rate remains low, and pressure to efficiently raise substantial new tax revenues will grow once the
baby boom generation reaches retirement age
and federal entitlement spending begins to balloon. Now, while the rhetoric is still somewhat
subdued, may be a good time to review the
impact a major tax overhaul would have on
the economy.
In this first of two articles on the economic
impact of fundamental tax reform, we describe
a framework useful for analyzing how the adoption of a flat-rate consumption tax would affect
interest rates, the savings decision of a typical
household, and the investment and hiring decisions of a typical firm.1 We are less concerned
with obtaining precise quantitative estimates of
these effects than we are with establishing their
direction and explaining the forces behind
them. Moreover, our focus throughout is on the
macro economic impact of tax reform. We will
largely ignore the issues of who would be likely
to gain most from reform and who might suffer
losses. We take this approach partly because
our analytical framework isn’t well suited to
addressing distributional questions, partly because the distributional impact of tax reform has
already been adequately discussed elsewhere,
and partly because windfall losses can often be
reduced or eliminated through careful design of
transition rules and the appropriate conduct of
monetary policy.2 In any event, a tax reform that
succeeds in raising the economy’s growth
potential—even if only temporarily or only by
a small amount—is likely to yield long-run
net economic benefits to the vast majority of
people. Our hope is that an improved understanding of the macroeconomic effects of tax
reform will help readers keep potential shortterm windfall losses in perspective.
Consistent with results obtained by others
in complicated numerical simulation exercises,
our analysis indicates that adoption of a flat-rate
consumption tax can be expected to have an
immediate positive impact on saving and lead,
in the long run, to higher levels of consumption,
wages, and stock prices, and to lower interest
rates. In the short run, however, real interest
rates are likely to rise, and consumption and
real stock prices are likely to fall. These results
are subject to important qualifications. First, our

Evan F. Koenig
Senior Economist and Assistant Vice President
Federal Reserve Bank of Dallas
Gregory W. Huffman
Professor
Southern Methodist University
and
Research Associate
Federal Reserve Bank of Dallas

doption of a flat-rate

consumption tax can be
expected to have an immediate
positive impact on saving and
lead, in the long run, to higher
levels of consumption, wages,
and stock prices, and to lower
interest rates. In the short run,
however, real interest rates
are likely to rise, and
consumption and real stock
prices are likely to fall.

analysis ignores international capital flows. Such
flows potentially exert a moderating influence
on consumption and interest rate movements.
However, different countries treat foreignsource income very differently for tax purposes,
making it difficult to draw general conclusions.3
Second, we ignore enforcement, avoidance, and
administrative costs. Certainly, tax-reform advocates hope that these costs will fall. However,
the magnitude of the cost savings will depend
greatly on the specifics of how tax reform is
implemented. Opinion is divided over whether
the potential savings are significant. Third, there
is no individual earnings uncertainty in our
model. Consequently, there is no “precautionary” savings motive. Simulations undertaken by
Engen and Gale (1997) and Engen, Gravelle, and
Smetters (1997) suggest that this omission is
more important quan titatively than it is qual itatively.4 Finally, our analysis holds the supply of
labor fixed: we defer discussion of the variablework-effort case to a follow-up article, which
will appear in a subsequent issue of Economic
Review. As it turns out, the qualitative effects of
tax reform in an economy with variable work
effort differ little from those derived here—provided that tax reform leaves the tax rate on labor
income unchanged.
We begin with a review of the basic features of the current tax system and three seemingly distinct, but actually equivalent, alternative
types of flat-rate consumption tax. We then
derive equations that characterize the savings
and investment decisions of households and
firms, conditional on the tax system. Each of
these equations has a straightforward graphical
interpretation. Using a set of diagrams, we analyze first the long-run, then the short-run impact
of tax reform on output, consumption, investment, and interest rates. As already noted, the
second article in this series achieves additional
realism by extending the basic model to include
variable work effort. Moreover, our second article uses simulations to explore the dynamic
effects of tax reform in economies with capital
adjustment costs and long-run growth effects.

income level. It makes no distinction between
real capital gains and capital gains that simply
reflect inflation. Similarly, depreciation allowances are based on nominal book values rather
than replacement values.
We abstract from much of the complexity
of the actual tax code. Thus, we assume that
inflation is low enough that we can ignore its
impact and conduct our analysis entirely in real
terms. We allow wage income, corporate earnings, and interest and dividend income to be
taxed at different rates but assume that the different marginal tax rates applied to these types
of income are independent of the level of
income. Each household feels free to buy and
sell stock and other assets, but because households are assumed to be identical to one
another, they never have occasion to do so.
Consequently, there are never any realized
capital gains. Firms’ investment in plant and
equipment is financed entirely from retained
corporate earnings.5 All corporate earnings not
used to finance investment or pay taxes are distributed to households as dividends. Although
these assumptions may seem extreme, for our
purposes they simply strip the current tax system down to its essential features.
The alternative tax system that we analyze
differs from the present system in two respects.
First, it would replace the current hodgepodge
of tax rates—under which some types of income are taxed more than once—with an integrated, flat-rate system of taxation. Second, it
would base taxation on consumption rather
than income.
There are three different versions of the
flat-rate consumption tax: the national retail
sales tax, the value-added tax (VAT), and the
Hall–Rabushka tax (after which the Armey–
Shelby flat tax was modeled).6 Under a retail
sales tax, each consumer good is taxed on its
entire value at the time of final sale. No tax is
collected on goods at intermediate stages of
production or distribution. In contrast, a VAT
collects a little piece of tax revenue at each stop
along the production and distribution chain,
based on the amount of value added to the
good at that stop: under a VAT, firms pay tax on
their sales less the sum of their purchases from
other businesses. The Hall–Rabushka tax works
in exactly the same way as a VAT, except each
firm’s employees are paid with pretax dollars,
and it is the employees who write checks to the
government for the taxes due on the wage component of value added. (The nonwage component of value added—corporate cash flow or
sales less purchases from other businesses less

ALTERNATIVE TAX SYSTEMS
Overview
The U.S. system of individual income
taxes, payroll taxes, and corporate income taxes
is exceedingly complex, involving numerous
exemptions, deductions, credits, and carry-over
provisions. It taxes different types of income at
different rates, and the marginal tax rate applied
to any given type of income may vary with

FEDERAL RESERVE BANK OF DALLAS

ECONOMIC REVIEW FIRST QUARTER 1998

after-tax dividends are (1 – τd )[(1 – τp )(y – wn –
δk) – ∆k ]. In the United States, the average marginal federal tax rates on wages and corporate
profits are each about 35 percent, while the
tax rate on interest (and dividend) income is
roughly 25 percent.8
Under our alternative tax plan, a single tax
rate, τ, is applied to both wage income, wn, and
corporate cash flow, y – wn – δk – ∆k. Interest
on newly-issued government debt is tax free.
(To prevent a windfall gain to “coupon clippers,” the interest on bonds that were issued
prior to tax reform would have to remain taxable to recipients.) The U.S. Treasury estimates
that implementing the Armey–Shelby version of
the Hall–Rabushka tax system would require a
22.4 percent average marginal tax rate on labor
income (Auerbach 1996). Replacing the revenue
from the current federal payroll tax would bring
this tax rate up to a level roughly comparable
to the rates of wage and profit taxation under
the current system—that is, approximately 35
percent.9
We can use the government budget constraint to see the connection between the current tax system and our flat-rate alternative. In
our stylized model of the current system, the
government budget constraint is given by

wages— continues to be taxable to the firm. See
Gentry and Hubbard 1997 for a nice discussion
of what is included in nonwage value added.)
Effectively, the Hall–Rabushka tax is a valueadded tax where each worker is treated as an
independent contractor. There is substantial
controversy over which of these taxes would be
easiest to implement, in practice (Slemrod
1996). However, for our purposes, all three are
equivalent. For no better reason than that it is
closest in appearance to the current tax system,
we have chosen to model the Hall–Rabushka
flat tax.
Details
We assume that output is produced from
capital (plant and equipment) and labor, subject
to a constant-returns-to-scale production technology (so that a doubling of all inputs into the
production process doubles output).7 The constant-returns-to-scale assumption allows us to
measure all quantities on a per-worker basis.
For example, we will use y to denote output
per worker produced by the representative firm,
n to denote hours of employment per worker,
and k to denote capital per worker. Each period,
a certain fraction, δ, of existing capital wears
out and must be replaced if the capital stock is
not to shrink. Net investment (the net change
in the capital stock from one period to the
next) will be denoted by ∆k. We use w, R, and
r to denote the real before-tax wage, the real
before-tax interest rate, and the real after-tax
interest rate, respectively; while g, b, and ∆b
denote real government purchases, the real
stock of government bonds outstanding, and
net new government indebtedness, all measured on a per-worker basis.
We make several simplifying assumptions.
As noted above, in our model economy all
capital investment is financed from retained
earnings, and all other earnings are paid out
either as taxes or as dividends. There is no role
for government transfer payments in a world
where all households are identical, so we will
ignore them. Within each tax regime, tax rates
are assumed constant through time. There is
no uncertainty. Finally, tax reform is not
announced in advance.
In our model of the current tax system, the
government applies three different tax rates to
three different types of income. Wage income,
wn, is taxed at rate τw . Corporate profits, y – wn
– δk, are taxed at rate τp. Any after-tax profits
that are not used to finance net new investment
are distributed as dividends and are taxed at the
same rate, τd , as is interest income, Rb. Hence,

(1)

∆b = g + rb – {τw wn + τp(y – wn – δk)
Wage taxes

Profits taxes

+ τd [(1 – τp )(y – wn – δk) – ∆k ]}.
Dividend taxes

This equation simply says that the government
must issue more debt whenever its expenditures (on goods and services, and net interest)
exceed the revenue it receives from taxing
wage, profit, and dividend income. In an economy with a flat-rate consumption tax, in contrast, the government budget constraint takes
the form
(2) ∆b = g + rb – [τwn + τ(y – wn – δk – ∆k )]
Wage taxes

Cash flow taxes

= g + rb – τ(y – δk – ∆k )
= g + rb – τ(c + g ),
where c = y – δk – ∆k – g and denotes real consumption expenditures. Note that imposing a
uniform tax on wage income and corporate
cash flow is equivalent to taxing the sum of
household and government spending on goods
and services.
We stated above that one can think of our
alternative tax plan as being two steps removed
from the current tax system. The first step takes
us from the current system to an integrated, flatrate income tax. In our model, this step is

accomplished by setting τd = 0 (eliminating the
double taxation of corporate earnings) and τw =
τp ≡ τ′. Equation 1 reduces to
(1′ )

Figure 1

Choosing Between Current and
Future Consumption

∆b = g + rb – τ ′(y – δk).

ct + 1

Note the similarity between Equation 1′ and the
second line of Equation 2. To complete the
move from our current income tax system to
a flat-rate consumption tax requires only the
additional step of allowing firms to deduct all
purchases of plant and equipment, not just
depreciation on existing plant and equipment,
before calculating their tax liability.10

Optimum

UTILITY AND PROFIT MAXIMIZATION
Indifference curve
Budget line
(Slope –(1 + r ))

In this section, we discuss the implications
that utility and profit maximization have for the
relationship between the variables in our model
economy. This discussion lays the necessary
groundwork for all of our subsequent analysis.
To keep the model as simple as possible, we
assume that there are no capital adjustment
costs and that the supply of labor is exogenously fixed. These assumptions are relaxed in
the sequel to this article.

45°

consumption. (A parallel outward shift in the
household budget line shifts the point of
tangency between the budget line and the
household’s indifference curves to the northeast.) It is also standard to assume that MRS (ct ,
ct + 1) = 1 + ρ, for some fixed ρ > 0, whenever
ct = ct + 1. (The representative household’s indifference curves have slope – (1 + ρ) where they
cross a 45° line extending out from the origin.)
The parameter ρ is the household’s pure rate of
time preference.
From our assumptions about household
preferences, it follows immediately that MRS (ct ,
ct + 1) > 1 + ρ if, and only if, ct + 1 > ct . However,
we have already seen that an optimizing household will equate the marginal rate of substitution between current and future consumption
to one plus the after-tax interest rate. Hence,

The Household Savings Decision
The optimality conditions of the representative household equate the rate at which the
household is willing to trade one good for
another (the marginal rate of substitution between the goods) to the relative market prices
of the goods. For example, suppose that we
denote by MRS (ct , ct + 1) the number of units of
consumption at time t + 1 required to compensate the representative household for the loss of
one unit of consumption at time t. Moreover,
suppose that rt denotes the after-tax interest rate
at time t (so that rt = (1 – τd )R t under the current tax system and rt = Rt after tax reform).
Then only when 1 + rt = MRS (ct , ct + 1) will the
household’s allocation of consumption across
time be optimal.11 Graphically, the household
will allocate consumption so as to be at a point
of tangency between its intertemporal budget
constraint and one of its indifference curves
(Figure 1 ).
It is standard to assume that the marginal
rate of substitution is decreasing in its first argument and increasing in its second argument.
In the present case, this condition means that
households tend to prefer smooth consumption paths to uneven ones. (The indifference
curves in Figure 1 are convex to the origin.)
Also, households respond to an increase in
wealth by demanding more current and future

FEDERAL RESERVE BANK OF DALLAS

(3)

ct + 1 > ct
⇔ MRS (ct , ct + 1) > 1 + ρ
⇔ rt > ρ.

In words, consumption will be rising through
time if, and only if, the real after-tax interest rate
exceeds the pure rate of time preference.
Intuitively, a high after-tax rate of return on saving is needed to induce households to defer
consumption.
The Business Investment Decision
The optimality conditions that characterize
the representative firm’s investment decision are
different under a consumption tax than they are
under the current income tax system. We look
first at the income tax case, then turn our attention to the consumption tax case.

ECONOMIC REVIEW FIRST QUARTER 1998

investment is (1 – τ)(MPk + 1 – δ) units of output in period t + 1. (The firm has MPk additional
units of newly produced output to sell in period
t + 1, plus used equipment worth 1 – δ units of
output.) Therefore, the marginal return to
investment just equals the marginal cost of
investment when

Investment Under an Income Tax. Under an
income tax system, after-tax dividends are
(4)

(1 – τd )[(1 – τp )(y – wn – δk) – ∆k ].

Hence, increasing period-t investment by one
unit requires that period-t dividends be cut by
(1 – τd ) units. If used to purchase government
bonds, these (1 – τd ) units of period-t output
would yield (1 + rt )(1 – τd ) units of output in
period t + 1. The firm should continue to increase its capital investment as long as it can
give shareholders a better marginal return than
they would receive under this fallback strategy.
With one additional unit of capital available in period t + 1, the firm’s production will
be higher than would otherwise have been the
case, but so will its depreciation costs. On net,
taxable profits rise by MPk – δ, where MPk
denotes the marginal product of capital—the
increment to production from an additional unit
of capital. After-tax profits rise by (1 – τp )(MPk –
δ). Moreover, because it increased capital
investment in period t, the firm will be able
to avoid one unit of capital investment in period
t + 1. Thus, altogether, the firm will be able
to increase period t + 1 dividends by 1 + (1 –
τp )(MPk – δ) units of output if it increases current investment by one unit. Of course, only the
fraction (1 – τd ) of these dividends will be available to shareholders after taxes.
Summarizing, when it increases period-t
investment by one unit, the firm deprives its
shareholders of (1 + rt )(1 – τd ) units of output
in period t + 1 and, in exchange, gives them
(1 – τd )[1 + (1 – τp )(MPk – δ)] units of output. A
profit-maximizing firm will expand investment
until the marginal return to investment just
equals the marginal cost of investment:

(1 – τ)(MPk + 1 – δ) = (1 – τ)(1 + rt )
or, equivalently, when
(5′)

Under the consumption tax, firms invest up to
the point where the net-of-depreciation marginal product of capital equals the real interest
rate.
The Output Market
Of course, business investment and household savings decisions are not independent of
one another. They are linked by the requirement that the sum of consumption, investment,
and government purchases equals the total
amount of output produced. Formally, we must
have f (k, n 0 ) = c + δk + ∆k + g, where f (•, •)
gives the amount of output produced per
worker as a function of the amount of capital
per worker and the number of hours of employment per worker (held fixed at n 0 ). Turning this
equation around,
(6)

(7)

∆k > 0 ⇔ c < f (k, n 0 ) – g – δk.

Equation 7 simply states that the capital stock
will increase when consumption is low relative
to production (net of government purchases
and depreciation) and will decrease when consumption is high relative to production. In the
former case, there is more than enough output
available, after deducting household and government consumption, to replace plant and
equipment as it wears out. In the latter case, so
much output is being consumed that firms are
unable to replace worn-out plant and equipment. One can think of f (k, n 0 ) – g – δk as
being the level of consumption that is sustainable, given the capital stock and the level of
government purchases.

or, equivalently,
(1 – τp )(MPk – δ) = rt .

Thus, under the current income tax system,
firms invest up to the point where the marginal
product of capital net of depreciation and incremental profits taxes equals the after-tax interest
rate.
Investment Under a Consumption Tax. Under
the Hall –Rabushka version of the flat-rate consumption tax, after-tax dividends are
(4′)

∆k = f (k, n 0 ) – c – g – δk.

Hence,

(1 – τd )[1 + (1 – τp )(MPk – δ)] = (1 + rt )(1 – τd ),

(5)

MPk – δ = rt .

The Labor Market
Finally, consider the labor market. As
noted above, we assume that the supply of
labor is fixed at n = n 0. The demand for labor
is determined by profit maximization. The representative firm will demand additional labor as

(1 – τ)(y – wn – δk – ∆k).

Hence, the opportunity cost of capital investment is (1 – τ) units of period-t output or, equivalently, (1 – τ)(1 + rt ) units of output in period
t + 1. The marginal, after-tax return to capital

Under a flat-rate consumption tax, the
investment-optimality condition is Equation 5′.
It says that the representative firm will add
to its capital stock up to the point where netof-depreciation marginal product of capital
just equals the after-tax interest rate. So now
the critical interest rate is MPk – δ rather than
(1 – τp )(MPk – δ). The capital demand curve is
still downward sloping, but it is proportionately
higher than the capital demand curve under the
income tax. See the blue line plotted in the bottom panel of Figure 2.

long as the incremental labor adds more to
revenues (through increased production) than it
adds to costs (through increased wages). Under
either tax system, the increment to revenues is
simply the marginal product of labor —denoted
by MPn —and the increment to costs is simply
the real wage, w. Hence, profit maximization
implies that
(8)

MPn = w.

The marginal product of labor must equal the
real wage.

The Long-Run Impact of Tax Reform
Long-run equilibrium in the capital market
occurs where the capital-demand and capitalsupply schedules intersect. In the bottom panel
of Figure 2, this intersection occurs at point E
in the economy with a corporate income tax,
and at point E ′ in the economy with a flat-rate
consumption tax. The after-tax interest rate is
the same in the two economies, but the economy with the consumption tax has a larger
steady-state capital stock—for realistic parameter values, 29 percent higher. (See the box titled
“A Numerical Example” on page 37.) A higher
capital stock means more output—roughly 9
percent more than under an income tax.12
What of the pre tax interest rate? In steady
state under either tax system, we know that r = ρ.
Under a consumption tax, households do not
pay tax on their interest income. So R = r = ρ
under a consumption tax. Under an income
tax, in contrast, interest is taxed at rate τd , so
R = r/(1 – τd ) = ρ/(1 – τd ). Thus, the steady-state
pretax interest rate is lower (by about 25 percent) under a consumption tax than under an
income tax.
What of the stock market value of the typical firm? Under a consumption tax, each additional unit of capital investment costs
shareholders 1 – τ units of current after-tax dividends (Equation 4′). Hence, each unit of capital is worth 1 – τ units of consumption at the
margin, and the real value of the firm is (1 – τ)k.
Over time, this value approaches (1 – τ)kE ′,
where kE ′ is the steady-state capital stock. Under
an income tax, each unit of capital investment
costs shareholders 1 – τd units of current aftertax dividends (Equation 4). So the real value of
the firm is (1 – τd )kE in steady state. Whether tax
reform ultimately raises or ultimately lowers
stock prices is, in general, ambiguous. The capital stock is clearly higher after reform, but the
tax rate applied to corporate cash flow after reform might also very well be higher than the current tax rate on dividends. (Recall that τd ≈ 0.25,

THE EFFECTS OF TAX REFORM: THE LONG RUN
In this section, we develop a set of diagrams that summarizes the optimality and market-clearing conditions we derived above. We
use this set of diagrams to analyze the long-run
impact of a flat-rate consumption tax on consumption, the capital stock, and interest rates.
We also consider the long-run impact of tax
reform on wages and the stock market. All discussion of the transition from one long-run
equilibrium to another is deferred until later in
the article.
The Demand for Capital and the
Long-Run Supply of Capital
Our model economy abstracts from any
source of sustained growth, such as technological change. Consequently, the long-run equilibrium in our model will be characterized by a
constant level of consumption and a constant
capital stock. We already know (from Equation
3) that households will be content with a constant level of consumption if, and only if, the
after-tax interest rate equals the pure rate of
time preference: rt = ρ. Thus, there is only one
after-tax interest rate consistent, in the long run,
with the optimality condition that governs
household saving decisions: as shown in the
bottom panel of Figure 2, the long-run capitalsupply curve is horizontal at the pure rate of
time preference.
The capital-demand curve differs depending on the tax regime. According to the investment-optimality condition for a firm subject to a
corporate income tax (Equation 5), the real
after-tax interest rate that will just induce the
representative firm to hold a given quantity of
capital is (1 – τp )(MPk – δ). Assuming that the
marginal product of capital is decreasing in the
capital stock, this optimality condition defines a
downward-sloping relationship between r and
k. See the gray line plotted in the bottom panel
of Figure 2.

FEDERAL RESERVE BANK OF DALLAS

ECONOMIC REVIEW FIRST QUARTER 1998

Figure 2

Pre-Reform and Post-Reform Long-Run Equilibria
c

cE ′
cE

E′
y – g – δk

kE ′

E′

MPk – δ

(1 – τp)(MPk – δ)

Long-run capital supply

kE ′

whereas replacing the revenues from the current income and payroll tax systems, while
allowing for some initial amount of wage
income to be tax exempt, requires τ ≈ 0.35.) As
noted above, realistic parameter values suggest
that the steady-state capital stock is almost 29
percent higher under a consumption tax than
under an income tax. Consequently, it is reasonable to expect that real stock prices would
ultimately increase by a little less than 12 percent as a result of tax reform.
What of the pretax wage? From profit
maximization, we know that the wage rate
equals the marginal product of labor (Equation

8). With a constant-returns-to-scale production
technology, the marginal product of labor
depends only on the capital/labor ratio. Since
the steady-state capital stock is higher under a
consumption tax than under an income tax, the
same must be true of steady-state labor productivity and the steady-state real wage. For realistic parameter values, the real wage rises by
about 9 percent in the long run.
We know that consumption is constant in
the long-run equilibrium of our model economy
—but constant at what level? We can use the
top panel of Figure 2 to find out. This panel
shows a plot of the function f (k, n 0 ) – g – δk ,

away from the bottom panel of the diagram and
to the top panel.13 We demonstrate that consumption at first must decline following tax
reform to make room for increased investment.
The stock market is also likely to decline, while
interest rates are likely to rise.

which we know from our discussion of the
output-market clearing condition (Equation 7)
is the formula for the maximum sustainable
level of consumption. In plotting sustainable
consumption, we have assumed that capital is
necessary for producing output (f (0, n 0 ) = 0)
and that the net marginal product of capital
(MPk – δ = f1(k, n 0 ) – δ) is positive at low levels
of capital and decreasing in the quantity of
capital. Consequently, the y – g – δk curve has
vertical intercept –g and an inverted-U shape. It
attains its maximum when the marginal product
of capital equals the depreciation rate ( f1(k, n 0 )
– δ = 0).
To find the steady-state level of consumption graphically, we need only move upward
from points E and E ′ in the lower panel of
Figure 2 to the corresponding points along
the curve plotted in the upper panel. Since the
y – g – δk curve is necessarily upward sloping
over the relevant range, a higher steady-state
capital stock implies a higher steady-state level
of consumption. In the diagram, the steady-state
level of consumption under the consumption
tax (cE ′ ) is greater than the steady-state level of
consumption under the income tax (cE ).
To review, the key difference between an
income tax and a consumption tax is that the
former does not allow firms to expense their
capital investment. (Compare Equations 4 and
4′, or Equations 1′ and 2.) Consequently, the
trade-off between current dividends and future
dividends is distorted under an income tax:
shareholders have a bias in favor of current
dividends that is lacking under a consumption
tax. (Compare Equations 5 and 5′.) This bias
drives firms to demand less capital, at any given
after-tax interest rate, than they would under a
consumption tax. Because the after-tax interest
rate must, in steady state, equal the pure rate of
time preference, the capital stock ends up at a
lower level under an income tax. Since the
steady-state capital stock is lower under an income tax, so are steady-state output and steadystate consumption.

The Phase Diagram
Since our interest is in how the U.S. economy would evolve following tax reform, we
analyze the short-run dynamics of an economy
in which the government relies on a flat-rate
consumption tax to meet its revenue needs.
Consider first the dynamics of consumption.
From Equation 3 (the optimality condition for
household saving) we know that households
are willing to defer consumption if, and only if,
the after-tax interest rate exceeds the pure rate
of time preference. However, from Equation 5′
(the optimality condition for investment) we
know that for the representative firm to be willing to hold its capital stock, the after-tax interest
rate must equal the net marginal product of capital. Putting these two conditions together, we
find that consumption will be rising over time if,
and only if, the net marginal product of capital
exceeds the pure rate of time preference:

The bottom panel of Figure 3, much like the
bottom panel of Figure 2, shows a plot of the
net marginal product of capital. Clearly, the net
marginal product of capital exceeds the time-

Figure 3

Short-Run Dynamics of Consumption
c

∆c = 0

∆c < 0
∆c > 0

kE ′

THE EFFECTS OF TAX REFORM: DYNAMICS

So far we have considered only the longrun effects of tax reform. If we are interested in
the path of the economy between steady states,
we must modify our graphical apparatus.
Fortunately, the required changes are not
large — our new diagram is quite similar to
Figure 2. However, because interactions between consumption and capital are important in
the short run, the focus of our analysis shifts

FEDERAL RESERVE BANK OF DALLAS

∆c > 0 ⇔ MPk – δ > ρ.

(9)

MPk – δ

E′

kE ′

ECONOMIC REVIEW FIRST QUARTER 1998

preference rate ρ if, and only if, the capital
stock is less than the steady-state capital stock,
kE ′. Hence,
(10)

Figure 5 combines Figures 3 and 4. In the
figure’s top panel, arrows show the directions
of consumption and capital movement for different levels of consumption and capital. Its
bottom panel shows how the after-tax interest
rate varies with the capital stock. As in Figure
2, the economy’s unique steady state is point
E ′. In this steady state, r = ρ, k = kE ′, and c = cE ′
= f (kE ′, n0 ) – g – δkE ′. Point E ′ is called a saddle-path equilibrium. For each initial capital
stock, there is a unique level of consumption
such that the economy will approach E ′. Any
other initial consumption level would put the
economy on either an explosive or an implosive path—a path that cannot be optimal.14 In
the diagram, if the economy starts at some arbitrary capital stock kA < kE ′, then households will
choose consumption level cA < cE ′ and the
economy will follow the dashed path from
point A toward point E ′. As the capital stock
increases, the after-tax interest rate falls from rA
toward ρ. Similarly, if the economy starts at
some capital stock kB < kE ′, then households will
choose consumption level cB > cE ′ and the
economy will follow the dashed path from
point B toward point E ′. The interest rate rises
from rB toward ρ.

∆c > 0 ⇔ k < kE ′.

In words, consumption will be increasing over
time if, and only if, the capital stock falls short
of its steady-state level. Intuitively, if capital is
scarce relative to labor, then the return on new
capital investment will be high, inducing households to sacrifice some current consumption in
exchange for higher future consumption.
In the top panel of Figure 3 we put an
upward-pointing arrow to the left of kE ′, reflecting the fact that consumption will be increasing over time whenever k < kE ′. Similarly, we
place a downward-pointing arrow to the right
of kE ′. At kE ′ itself, we put a vertical line, labeled
∆c = 0, to indicate that here consumption tends
to neither rise nor fall.
We turn now to the dynamics of the capital stock. Equation 7 says that the capital stock
will tend to fall, over time, at points above the
curve y – g – δk in the top panel of Figure 2. At
points below the curve, the capital stock will
tend to increase. The intuition is that a level of
consumption that is high relative to the capital
stock can be achieved only by not replacing
capital equipment as it wears out. If, on the
other hand, consumption is low relative to the
capital stock, then there is more than enough
output left over (after meeting the demands of
households and the government) to replace
worn-out capital, and the capital stock rises
over time. In Figure 4, the y – g – δk curve is
relabeled as ∆k = 0, and arrows are placed
above and below it, pointing to the left and
right, respectively.

The Effects of Tax Reform: The Short Run
Consider an economy in steady state
under an income tax. Suddenly, the income tax
is replaced with a consumption tax.15 We know
that the economy starts at point E in the upper
panel of Figure 6, and eventually ends up at
point E ′. What happens along the way? Our
phase diagram gives us the answer. We know
that point E ′ is a saddle-point equilibrium under
the new tax system: there is a unique path
for consumption and the capital stock that
simultaneously satisfies all of the utility and
profit maximization conditions and that is
neither explosive nor implosive. This path runs
through E ′, and movements along the path are
governed by the set of directional arrows
depicted in the figure. For any given initial capital stock, households will choose the level of
consumption that puts the economy on this
convergent path.
In the upper panel of Figure 6, the economy jumps downward from point E to point A
the instant that tax reform is put into effect.
Intuitively, the after-tax return on capital jumps
upward from ρ to rA = ρ/(1 – τp ) with the switch
to a consumption tax. (In the lower panel of
Figure 6, the economy jumps upward from
point E to point A.) The higher marginal return
to capital means that households are willing to

Figure 4

Short-Run Dynamics of Capital
c

∆k < 0

∆k = 0
∆k > 0

Figure 5

Combined Short-Run Dynamics
c
∆c = 0

cE ′

E′

kA
r

∆k = 0

kE ′

MPk – δ

E′

k
kA

kE ′

take a cut in dividends (reduce their consumption) in order that firms may finance the acquisition of additional capital through higher
retained earnings. As the capital stock gradually
expands, the economy moves up the dashed
saddle path from point A toward point E ′ in the
upper panel of Figure 6, and down the capital
demand curve from point A to point E ′ in the
lower panel.
The pre tax interest rate, R, is subject to
conflicting influences in the short run. In the
initial steady state, R = ρ/(1 – τd ). Immediately
after reform is implemented, R = rA = ρ/(1 – τp ).

FEDERAL RESERVE BANK OF DALLAS

Thus, the before-tax interest rate will fall if, and
only if, τp < τd . In fact, though, τp ≈ 0.35 > 0.25
≈ τd . Hence, the pretax interest will likely rise
by about 15 percent with the imposition of a
consumption tax before gradually declining to
its new steady-state level (ρ).
The immediate impact of tax reform on
stock prices also depends upon relative tax
rates. The steady-state level of stock prices
under an income tax is (1 – τd )kE . Immediately
following the move to a consumption tax, the
level of stock prices is (1 – τ)kE . If, as argued
above, τd ≈ 0.25 and τ ≈ 0.35, then stock prices

ECONOMIC REVIEW FIRST QUARTER 1998

Figure 6

Dynamic Response to Tax Reform
c
∆c = 0

cE ′
cE

∆k = 0

kE
r

E′

kE ′

MPk – δ

(1 – τp)(MPk – δ)

E′

will fall by about 13 percent upon the implementation of tax reform. However, this result is
sensitive to changes in our assumptions about
the features of tax reform. For example, if existing payroll taxes are kept in place (so that the
consumption tax need only replace the revenue
from the current income tax), then the U.S.
Treasury estimates that τ ≈ 0.224. In this case,
stock prices would actually jump upward
slightly following tax reform. In any event,
following their initial jump, stock prices vary
with the capital stock, gradually rising toward
(1 – τ)kE .

Finally, the pretax wage rate is linked to
the capital stock via the marginal product of
labor (Equation 8). Since the capital stock
doesn’t jump, neither does the wage rate. As the
capital stock gradually increases, so does the
wage rate. Whether the after -tax wage rate
jumps upward or downward depends entirely
on the size of τw relative to τ. Under our basecase scenario, these tax rates are equal.
Consequently, the after-tax wage, like the pretax wage, does not initially move.
An illustrative simulation of the effects of
fundamental tax reform is presented in the box.

Table 1

Impact of Fundamental Tax Reform in the Basic Model
Variable
Output, capital
Consumption
After-tax interest rate
Pretax interest rate
Stock market
Real wage

SUMMARY AND CONCLUDING REMARKS
Table 1 summarizes our principal findings.
The first column of the table shows the immediate impact that the adoption of a consumption
tax can be expected to have on each of several
variables. The second column shows the longrun impact of tax reform. Ordinarily, when we
tax a good or activity, we expect to see less of
it in the marketplace. However, a tax on consumption causes the economy to achieve a
higher level of consumption, in the long run,
than would be observed under an income tax.
The resolution of this paradox is that society
accumulates greater real wealth under a consumption tax than it does under an income
tax—an accumulation that is made possible
because the initial effect of the consumption
tax is to reduce consumption.
Is the eventual increase in consumption
worth the initial decline? In the simple model
economy examined here, the answer is unambiguously yes. Because the supply of labor is
fixed in our model economy, the only component of the income tax that is distortionary is the
profits tax: it reduces the demand for capital at
any given after-tax interest rate. Because the
consumption tax eliminates this distortion, it
necessarily raises social welfare.
The real world is obviously more complicated than our model economy. Most pertinently, household labor supply is not
exogenously fixed: any tax on labor income
distorts households’ labor–leisure choices. If
moving from an income tax to a consumption
tax significantly worsens this labor-market distortion, it may reduce social welfare despite the
fact that, at the same time, it eliminates an
investment-saving distortion.
Fortunately, it is relatively easy to explain
how the results obtained here would change,
qualitatively, if the supply of labor was endogenous. We address this issue in Part 2 of our
article. Part 2 also considers the sensitivity of
our results to capital adjustment costs and to a
specification of the production function that has
each firm’s output depend on the aggregate
capital stock as well as its own.

NOTES:

NOTES
1

Howitt and Sinn (1989) undertake a more sophisticated analysis within a similar framework.
For simulation exercises that examine the impact of tax
reform on different age groups, see Auerbach and
Kotlikoff (1987) and Auerbach (1996). Feenberg, Mitrusi,
and Poterba (1997) present a careful analysis of the
impact of tax reform on the distribution of consumption.

FEDERAL RESERVE BANK OF DALLAS

Immediate impact
0
–
+
+a
–b
0

Long-run impact
+
+
0
–
+c
+

Assumes that profits are currently taxed more heavily than is interest.
Assumes that the new tax rate on corporate cash flow will exceed the current tax rate
on dividends.
Assumes that (1 – τ)kE ′ exceeds (1 – τd )kE .

Sarkar and Zodrow (1993) discuss windfall gains and
losses resulting from tax reform and how they might be
mitigated. Monetary policy affects the distribution of
wealth primarily through unanticipated inflations, which
benefit debtors at the expense of lenders, and unanticipated deflations, which have the opposite effect.
Hines (1996) contains a general discussion of complications that arise in an open-economy setting.
Mendoza and Tesar (1995) construct a formal model.
In otherwise identical models, the inclusion of a precautionary savings motive cuts the impact of tax
reform on output, consumption, and the capital stock
roughly in half.
According to the Federal Reserve Board’s flow of
funds accounts for the nonfarm, nonfinancial corporate
business sector, internal funds averaged 94.8 percent
of capital expenditures over the ten-year period from
1985 through 1994. In contrast, credit market borrowing averaged only 32.5 percent of capital expenditures.
For more detailed descriptions of these alternative
approaches, see Koenig and Taylor (1996), Hall and
Rabushka (1996), Metcalf (1996), and Moore (1996).
We ignore human capital and the associated investment in education and training.
The statutory tax rate on corporate profits is 35 percent. The tax rate on wage income can be obtained by
adding 14 percent (representing federal payroll taxes)
to the 22 percent marginal income tax rate reported in
Auerbach (1996). The actual tax rates on household
interest and dividend income are 22 percent and 27
percent, respectively (Auerbach 1996). For comparison, Mendoza, Razin, and Tesar (1994) obtain an estimate of 32 percent for the U.S. corporate capital
income tax rate and an estimate of 34 percent for the
tax rate on U.S. labor income. Triest (1996) estimates a
38 percent average marginal tax rate on labor income.
Personal income tax deductions and exemptions that
are excluded from our model (and that would be eliminated under most tax-reform proposals) account for
the relatively low revenue yield of the current system,
despite high marginal tax rates.
Triest’s (1996) estimate of the required flat-tax rate (39
percent) is somewhat higher than ours, but not much
different from his own estimate of the current average
marginal tax rate on labor income (38 percent).
The alert reader will have noted that the transition can

ECONOMIC REVIEW FIRST QUARTER 1998

be completed in a single step by setting τp = 0 and τw
= τd ≡ τ ′. However, this approach breaks down in the
real world, where not every firm is able to finance its
capital investment out of its own retained earnings.
If 1 + rt > MRS (ct , ct + 1), then it will be advantageous
to the household to reduce its period-t consumption by
one unit and buy a bond. Principal and interest on the
bond (received in period t + 1) will be more than
enough to compensate the household for the reduction
in ct. Similarly, if 1 + rt < MRS (ct , ct + 1), then it will be
advantageous to the household to sell a bond from its
portfolio and use the proceeds to increase its period-t
consumption by one unit.
These estimates are meant to convey no more than the
likely order of magnitude of the economy’s response to
tax reform. They are sensitive to the assumed profits
tax rate and to the assumed capital-elasticity of output.
Other studies have generally reported a slightly
weaker baseline output response.
Moreover, we implicitly switch to a continuous-time
version of the model described above.
Think of a marble on a saddle. The surface of the saddle looks like a U when viewed from the side and like
an inverted U when viewed from either end. The point
in the middle of the saddle is the steady state. A marble placed precisely at this point will remain stationary.
In principle, a marble placed at the exact middle of
one of the saddle’s ends will move toward the steady
state rather than fall off the saddle on either side.
For a gradual reform analysis, see Howitt and Sinn (1989).

“Distributional Implications of Introducing a Broad-Based
Consumption Tax,” in Tax Policy and the Economy, ed.
James M. Poterba (Cambridge, Mass.: MIT Press), 1– 47.
Hall, Robert E., and Alvin Rabushka (1996), “The Flat
Tax: A Simple, Progressive Consumption Tax,” in
Frontiers of Tax Reform, ed. Michael J. Boskin (Stanford,
CA: Hoover Institution Press), 27– 53.
Hines, James R. (1996), “Fundamental Tax Reform in an
International Setting,” in Economic Effects of Fundamental
Tax Reform, eds. Henry J. Aaron and William G. Gale
(Washington, D.C.: Brookings Institution Press), 465 – 502.
Howitt, Peter, and Hans-Werner Sinn (1989), “Gradual
Reforms of Capital Income Taxation,” American
Economic Review 79 (March): 106 – 24.
Koenig, Evan F., and Lori L. Taylor (1996), “Tax Reform:
Is the Time Right for a New Approach?” Federal Reserve
Bank of Dallas Southwest Economy, Issue 1, January/
February, 5 – 8.
Mendoza, Enrique G., and Linda L. Tesar (1995),“SupplySide Economics in a Global Economy,” International
Finance Discussion Paper no. 507 (Washington, D.C.:
Board of Governors of the Federal Reserve System, March).
Mendoza, Enrique G., Assaf Razin, and Linda L. Tesar
(1994), “Effective Tax Rates in Macroeconomics: CrossCountry Estimates of Tax Rates on Factor Incomes and
Consumption,” Journal of Monetary Economics 34
(December): 297– 323.

REFERENCES
Auerbach, Alan J. (1996), “Tax Reform, Capital Allocation, Efficiency, and Growth,” in Economic Effects of
Fundamental Tax Reform, eds. Henry J. Aaron and
William G. Gale (Washington, D.C.: Brookings Institution
Press), 29 – 82.

Metcalf, Gilbert E. (1996),“The Role of a Value-Added Tax
in Fundamental Tax Reform,” in Frontiers of Tax Reform,
ed. Michael J. Boskin (Stanford, CA: Hoover Institution
Press), 91–109.

Auerbach, Alan J., and Laurence J. Kotlikoff (1987),
Dynamic Fiscal Policy (Cambridge, England: Cambridge
University Press).

Moore, Stephen (1996),“The Economic and Civil Liberties Case for a National Sales Tax,” in Frontiers of Tax
Reform, ed. Michael J. Boskin (Stanford, CA: Hoover
Institution Press), 110 – 20.

Engen, Eric M., and William G. Gale (1997), “Consumption Taxes and Saving: The Role of Uncertainty in Tax
Reform,” American Economic Review Papers and
Proceedings 87 (May): 114 –19.

Sarkar, Shounak, and George R. Zodrow (1993), “Transitional Issues in Moving to a Direct Consumption Tax,”
National Tax Journal 46 (September): 359 – 76.

Engen, Eric M., Jane Gravelle, and Kent Smetters (1997),
“Dynamic Tax Models: Why They Do the Things They
Do,” National Tax Journal 50 (September): 657– 82.

Slemrod, Joel (1996), “Which Is the Simplest Tax System
of Them All?” in Economic Effects of Fundamental Tax
Reform, eds. Henry J. Aaron and William G. Gale
(Washington, D.C.: Brookings Institution Press), 355 – 91.

Feenberg, Daniel R., Andrew W. Mitrusi, and James M. Poterba (1997), “Distributional Effects of Adopting a National
Retail Sales Tax,” in Tax Policy and the Economy, ed.
James M. Poterba (Cambridge, Mass.: MIT Press), 49 – 89.

Triest, Robert K. (1996), “Fundamental Tax Reform and
Labor Supply,” in Economic Effects of Fundamental Tax
Reform, eds. Henry J. Aaron and William G. Gale
(Washington, D.C.: Brookings Institution Press), 247–78.

Gentry, William M., and R. Glenn Hubbard (1997),

A NUMERICAL EXAMPLE
It will be useful to consider an example of an
economy as described in the main text, which will
enable us to quantify the responses to fundamental
tax reform. Consider an environment in which
households are identical and have preferences
described by a utility function of the form

profits. Assuming that interest income is initially
taxed at a 25 percent annual rate, tax reform would
see the pretax interest rate jump upward from 5.4
percent to 6.3 percent, then gradually fall to 4.1
percent.

∞

∑ t = 1 log(ct )/(1 + ρ)t ,

Figure A

where ct is household consumption at time t, and ρ
is the pure rate of time preference. With this utility
function, the marginal rate of substitution between
current and future consumption [MRS (ct , ct + 1)] is
simply (1 + ρ)(ct + 1/ct ). Consistent with Equation 3,
the optimality condition 1 + rt = MRS (ct, ct + 1)
takes the form
ct + 1 1 + rt
=
,
ct
1+ ρ

Capital
Index, initial steady state = 1
1.30
1.25
1.20
1.15
1.10

where rt is the real after-tax interest rate.
We assume that production per household is
a simple function of capital per household: y = k θ.
It follows that the marginal product of capital (MPk )
is θk θ – 1. Investment optimality conditions (Equations 5 and 5′ for an economy with an income tax
and an economy with a consumption tax, respectively) become

rt = (1 – τp )(θktθ

–1

1.05
1
.95
.90
0

100

Time (quarters)

– δ)

Figure B

and

Consumption
rt = θktθ

–1

– δ,

Index, initial steady state = 1
1.05

where δ is the depreciation rate for capital and τp is
the corporate income tax rate. Finally, Equation 7,
which governs the evolution of the capital stock,
takes the form

kt + 1 – kt = ktθ – ct – gt – δkt ,

.95

where gt denotes government purchases at time t.
We assume that a period is a quarter of a
year and let ρ = 0.01 and δ = 0.02. These parameter values imply that the average annual rate of
return on capital is just over 4 percent in steady
state, and the annualized depreciation rate is just
over 8 percent. The technology parameter, θ, is set
equal to 0.35. Government purchases are constant
through time.
Figures A, B, and C show the response of
the capital stock, consumption, and after-tax rate
of return to fundamental tax reform. Initially, the
economy is assumed to be in steady state with a
corporate income tax rate of 35 percent. (Interest,
dividend, and wage taxes may also be in effect, but
these are irrelevant to our simulations.) Suddenly,
in period 0, the income tax is replaced by a consumption tax. In the figures, the initial steady-state
levels of consumption and capital are normalized
to unity. As can be seen, convergence is fairly complete after 100 periods, or 25 years. However, consumption does not rise above its initial steady-state
level for 40 periods, or 10 years. The after-tax
annual interest rate jumps from 4.1 percent to
around 6.3 percent before gradually falling back to
its old level. As noted in the main text, the pretax
interest rate (not shown in the figures) may jump
upward or downward when tax reform is implemented, depending upon the relative magnitudes
of the tax rates on interest income and corporate

FEDERAL RESERVE BANK OF DALLAS

.90

.85

.80
0

100

Time (quarters)

Figure C

After-Tax Interest Rate
Percent per year
6.5

5.5

4.5

4
0

50
Time (quarters)

ECONOMIC REVIEW FIRST QUARTER 1998

100

Full text of Review (Federal Reserve Bank of Dallas) : First Quarter 1998

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