Discussion Paper No.

519

TARIFFS, TIME PREFERENCE,
AND THE CURRENT ACCOUNT UNDERWEAKLY NONSEPARABLE PREFERENCES

Shinsuke Ikeda

October 2000

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Tariﬀs, Time Preference, and the Current
Account under Weakly Nonseparable
Preferences∗
Shinsuke IKEDA†
The Institute of Social and Economic Research, Osaka University
October 2000

Abstract
Incorporating weakly nonseparable preferences into the familiar time-preference
model, we emphasize a role of steady-state welfare changes in determining theeﬀect of permanent tariﬀs on the current account. The eﬀect consists of: awelfare eﬀect, due to steady-state welfare changes, which is negative (positive)
when preferences toward imports are more (less) wealth-enhanced than toward
exports; and a substitution eﬀect, which occurs only with initial distortion. Even
without initial distortion, a marginal tariﬀ has a first-order welfare eﬀect on thecurrent-account. Its sign does not depend on whether impatience is increasing or
decreasing in wealth.

Keywords: Tariﬀ; time preference; weakly nonseparable preferences; current
account
JEL classification: F41; F32; F13∗Forthcoming in Review of International Economics.
Correspondence. Shinsuke Ikeda, The Institute of Social and Economic Research,
Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 560-0047, Japan. Telephone: +81-66879-8568. Fax: +81-6-6878-2788. E-mail: ikeda@iser.osaka-u.ac.jp†

Tariffs under Weakly Nonseparable Preferences

11

Introduction

Together with the increased importance of tariﬀs as a commercial policy
in international trade arrangements (e.g., the Uruguay GATT round), thelast fifteen years have witnessed the reexamination of the macroeconomic
eﬀects of tariﬀs using modern dynamic optimizing models. The first and still
most important contribution is Razin and Svensson (1983). Using a twoperiod model, they show how a permanent rise in tariﬀs aﬀects savings andthe current account by changing the interest rate in the utility terms if thepresent subutility function diﬀers from the future one. With the resultant
preference-shift, a permanent tariﬀ aﬀects the price indices diﬀerently forpresent and future expenditures, changes the real interest rate, and thereby
influences savings through a substitution eﬀect.1
Their seminal work stimulated many subsequent studies,2 though it relies on some restrictive assumptions. First of all, by using exogenous timevarying subutility functions, the preference-shifting is incorporated in theform of an externality to consumers.3 A more natural and reasonable modeling would entail endogenous preference-shifting. Secondly, as Svensson and
Razin (1983) show using a two-period framework, a change in the terms oftrade aﬀects savings through (i) a substitution eﬀect, due to compensateddemand shifts, and (ii) a welfare eﬀect, owing to changes in welfare. However, Razin and Svensson (1983) assume that preferences are homotheticallyseparable over time, thereby implicitly neglecting a welfare eﬀect.
To ease the restrictions, we incorporate a type of preference nonseparability to examine the eﬀects of a permanent change in tariﬀs for a small
country model. By extending the familiar time-preference model, à la Uzawa(1968) and Epstein and Hynes (1983), consumer preferences are specified as
weakly nonseparable, in the sense that the intratemporal marginal rate of
substitution between two goods, imported and exported goods, depends on
1

In the case of a temporary rise in tariﬀs, it always raises the real interest rate, increases
saving, and hence improves the current account even if the subutility function is timeinvariant. See Razin and Svensson (1983).
2
For example, Van Wijnbergen (1987) focuses on a real wage rigidity to derive theeﬀects of permanent and temporary tariﬀs which are distinct from what Svensson and
Razin obtain. O’Rourke (1989) argues that a permanent tariﬀ reduction worsens thecurrent account under a short-run sectoral immobility of capital. Ostry (1990) shows thatin the presence of initial tariﬀs, temporary tariﬀs can worsen the current account througha temporary income reduction which is magnified by the initial distortion.
3
For detailed discussions, see also Svensson and Razin (1983), particularly p.108.

Tariffs under Weakly Nonseparable Preferences2

future consumption through current welfare. Relative preferences toward thetwo goods then depend on current welfare and hence on current wealth. Putotherwise, when wealth increases, preferences toward one good can be moreor less enhanced than those toward the other good. With the preference
structure, a permanent rise in import tariﬀs induces a change in steady-state
welfare and wealth so as to make preferences shift away from imports in favor of exports. The current account must adjust in the interim run to bringabout the steady-state welfare change. Our main interest is to focus on thischannel which is neglected in the literature. The resultant current-accountadjustment is generated by endogenous preference shifts.
Weakly nonseparable preferences are considered in endogenous time preference models by Lucas and Stokey (1984), Judd (1985), Epstein, Ham, andZin (1988), Shi (1994), and Ikeda (2000a, b). Shi (1994) conducts the most
systematic analysis on this topic. He characterizes the consumption-leisurechoice under weakly nonseparable preferences to discuss implications of distortionary taxation on capital and/or labor. His key finding is that even a
marginal tax can aﬀect steady-state welfare. Our idea is to apply this property to the analysis of tariﬀs in a two-commodity framework. My companion
paper (Ikeda (2000a)) examines the eﬀect of a terms-of-trade deterioration
using a model similar to the one in this paper. In contrast to the literature(e.g., Obstfeld (1982)), it shows that the Harberger-Laursen-Metzler eﬀect
can occur even with increasing impatience. It will turn out that weakly
nonseparable preferences make more diﬀerence when they are applied to theanalysis of tariﬀs, especially the eﬀect of a marginal increase in tariﬀs without
initial distortion.
Based on the usual assumption that the degree of impatience measured
by time preference is increasing in current wealth, we first show that a permanent rise in tariﬀs raises or lowers steady-state welfare, depending onwhether preferences toward exports are more or less wealth-enhanced thanthose toward imports. As in Svensson and Razin (1983), the eﬀect on thecurrent account is decomposed into two, possibly oﬀsetting eﬀects: (i) a substitution eﬀect and (ii) a welfare eﬀect. (i) has a first-order magnitude onlywith initial distortion and is positive, whereas (ii) has a first-order negative(positive) eﬀect even without initial tariﬀs when preferences toward imported
goods are more (less) wealth-enhanced than toward exports. This property isin sharp contrast to what Razin and Svensson (1983) obtain: in their modela marginal tariﬀ without initial distortion can have a first-order substitution
eﬀect but no welfare eﬀect. We will clarify how their result depends on theTariffs under Weakly Nonseparable Preferences3

two restrictive assumptions we pointed out at the outset. Nevertheless, theworking of our model will turn out to be economically very similar to thatof Razin and Svensson’s model: in both of the models, a permanent tariﬀ
without initial distortion improves (deteriorates) the current account only
when relative preferences toward imports are, endogenously or exogenously,
weakened (enhanced) in the future (i.e., in the new steady state), in whichcase the import tariﬀ makes present goods more (less) expensive than future
ones. Our contribution lies in that the result here is obtained by focusing
on a welfare eﬀect in an infinite-horizon model with endogenous preference
shifting.
The Uzawa-type time-preference is sometimes criticized for its unappealing feature that the property of dynamics depends crucially on the assumption of increasing impatience (e.g., Svensson and Razin (1983) and Mansoorian (1993)). To address this issue, we also examine the case of decreasing
impatience, showing that the assumption in this regard does not play sucha crucial role under weakly nonseparable preferences. In particular, without
initial distortion, the sign of the eﬀect on the current account depends solely
on whether preferences toward exports are more or less wealth-enhanced than
toward imports, but not on whether impatience is increasing or decreasing
in wealth, i.e., not on whether preferences toward present goods are more orless wealth-enhanced than toward future goods.
There are a couple of studies which have incorporated intertemporally
dependent preferences to analyze the eﬀect of permanent tariﬀs. By thestraightforward application of Uzawa’s time-preference model, Engel and
Kletzer (1986) show that a first-order distortion caused by a tariﬀ leads
to an improvement in the current account. Mansoorian (1993) emphasizes
habit persistence as an important determinant of the eﬀect of permanent
tariﬀs. Our study can be diﬀerentiated from these studies in several points.
First of all, they invariably assume identically weakly separable preferences,
excluding implicitly a welfare eﬀect which we emphasize. Secondly, their arguments are limited to the case of non-marginal tariﬀs. In our model, evenmarginal tariﬀs without initial tariﬀs always have a first-order (welfare) eﬀect
on saving. Thirdly, a permanent tariﬀ here can increase steady-state welfare,Tariffs under Weakly Nonseparable Preferences4

whereas in their model tariﬀs harm it.4,5
The rest of the paper is organized as follows. Section 2 presents ouranalytical framework and derives the equilibrium dynamics. In section 3,
the eﬀects of a permanent increase in tariﬀs are examined. In section 4, thecase of decreasing impatience is examined. Section 5 concludes the paper.

2
2.1

The analytical framework
The model

Consider a small open economy populated with infinitely-lived identical agents.
They consume domestic goods d and foreign goods f. The economy is endowed with constant units y of the domestic good and nothing of the foreign
good at each instant. All the foreign-good consumption f is thus imported
from abroad. By the small-country assumption, the relative price p of the foreign good in terms of the domestic one is exogenously given. An import tariﬀ
τ is levied on consumption f .6 The government just refunds the tariﬀ revenue to consumers in the lump-sum manner. The representative agent holds
non-human wealth in the form of bonds b. Bonds can be either purchased or
issued freely at a constant interest rate r in the international market.
Consumers’ preferences are characterized by endogenous utility-discounting
and weak nonseparability. Their lifetime utility U is specified as:
µ Z t
¶
Z ∞
u(d (t) , f (t)) exp −θ (d (s) , f (s)) ds dt,(1)
U (0) =
0

0

4
As in these existing models focusing on consumer preferences, we assume away any
supply-side adjustments. For this point, see Sen and Turnovsky (1989), Gavin (1991) andTurnovsky (1991). See also Engel and Kletzer (1990), in which an overlapping-generations
model is developed to examine the eﬀect of a tariﬀ through intergenerational redistributionof income that is caused by factor-price changes and by the distribution of tariﬀ revenue.
5
Surprisingly, empirical research on the current-account eﬀects of tariﬀs is very few
and the result is controversial. For example, Dornbusch (1987) reports that it is positive,
whereas Ostry and Rose (1992) show that tariﬀ changes have no significant eﬀects on
macroeconomic variables such as the real trade balance. See also Backus et al. (1994),
which report that signs of correlation between the terms of trade and the trade accountdiﬀer internationally.
6
A part of domestic-good consumption d may also be imported if the representative
agent holds positive net foreign assets. Throughout the paper, however, we restrict ourattention to import tariﬀs which are imposed only on f .

Tariffs under Weakly Nonseparable Preferences5

where u (·, ·) represents a felicity function and where θ (·, ·) > 0 is a discounting function. We assume:θd , θf = 0 and θd + θf > 0,
where θd = ∂θ/∂d, etc. This assumption implies increasing marginal impatience in the sense that time preferences are increasing in current welfare.7
When we define the generating function g as
g (d, f, φ) = u (d, f ) − φθ (d, f ) ,(2)

where φ (t) represents the lifetime utility U (t) from the consumption stream
after time t, g generates φ by the law of motion,µ Z t¶φ̇ = −g (d, f, φ) s.t. lim φ (t) exp −θ (d (s) , f (s)) ds = 0,t→∞0where a dot represents the time derivative. Note that gd and gf equal thecurrent-value marginal utilities of d (t) and f (t) respectively, defined in termsof the Voltera derivative. We assume gd > 0 and gf > 0. The marginal rateof substitution between d (t) and f (t) is then given by the ratio of gf and
gd , i.e., dd (t) /df (t)|U (0)=const. = (gf /gd ) (d (t) , f (t) , φ (t)). The preferences
are weakly nonseparable if gf (t) /gd (t) really depends on φ (t) and hence on
the consumption stream after t.
To characterize weak nonseparability, we follow Shi (1993) in introducing
a nonseparability index ξ as
ξ (d, f, φ) ≡θd θf1 ∂ (gf /gd )=− .
gf /gd∂φ
gd gf

By definition, the weak nonseparability of preferences is captured by a nonzero
ξ and weak separability by ξ = 0.8 A positive (negative) ξ implies that a risein lifetime utility shifts preferences away from consumption d to f (f tod). When ξ >(<)0, preferences toward foreign goods f are referred to as
more (less) wealth-enhanced than those toward d. For an ³alternative´ interθd θfuf
ud
pretation, the index can be rewritten as ξ (d, f, φ) = gd gf θf − θd . With
7

See Lucas and Stokey (1984). This implication will be seen explicitly in (10) below.
For example, consider three cases: (i) θ is constant (time-additive preferences); (ii) u
is constant (e.g., Epstein and Hynes (1983)); and (iii) θ is a transform of u (e.g., Uzawa(1968)). In these cases, in which preferences are weakly separable, ξ indeed equals zero.
8

Tariffs under Weakly Nonseparable Preferences

6

a positive (negative) ξ, therefore, the relative elasticities of u to θ with respect to f are larger (smaller) than those with respect to d. As shown later,
under weakly nonseparable preferences, such a discrepancy in the relative
elasticities allows a change in tariﬀs to aﬀect steady-state welfare u/θ.
As for the second-order derivatives of g, we assume: gdf = 0 and
gdd < 0, gf f < 0,

θgdd
θgf f
<
ξ
<
−
.
gd2
gf2

(3)

Inequality (3) ensures the local concavity of consumers’ preferences.9
Consumers maximize lifetime utility (1) subject to: (i) the flow budget
constraint,ḃ (t) = rb (t) + y − d (t) − (p + τ (t)) f (t) + x (t) ,(4)where x represents a lump-sum transfer from the government; (ii) the initialcondition, b0 =given; and (iii) the no-Ponzi game condition, lim exp (−rt) b (t) ≥t→∞
0. Letting λ denote the current-value shadow price of savings, the first-orderconditions are given by:
gd (d, φ) (≡ ud (d, f ) − φθd (d, f )) = λ,(5)

gf (f, φ)= p + τ,gd (d, φ)(6)λ̇ = (θ (d, f ) − r) λ,(7)φ̇ = −g (d, f, φ) .

(8)

To eliminate λ from the Euler condition (7), define ¯the rate of time prefd
erence ρd with respect to d as ρd = −d ln Ωd (t) /dt¯d=0
˙ , where Ω (t) ≡³ R´
tgd (d (t) , φ (t)) exp − 0 θ (d (s) , f (s)) ds represents the present-value marginal utility of d. Then, from (5), (7) can be rewritten as¢
gd ¡d˙ = −r − ρd (d, f, φ) ,
(9)
gdd
where

ρd (d, f, φ) = θ (d, f ) −9θd (d, f)g (d, f, φ) .
gd (d, φ)(10)

See Shi (1994) for the proof. The assumption that gdf = 0 is made just for brevity.

Tariffs under Weakly Nonseparable Preferences

7

The rate of time preference ρf with respect to f can also be defined in thesame manner. From (8) and (10), in the steady state, the rates of time
preference equal the discount rate θ.
The government follows the balanced-budget principle:
τ (t) f (t) = x (t) .
Throughout the paper the government is assumed to keep the time path of
τ (t) flat after the initial point in time. Given an endogenously-determinedf (t), x (t) is determined to satisfy this equation. Combining the budget equation for the government with consumers’ one yields the balance of payment
equation,ḃ (t) = rb (t) + y − d (t) − pf (t) .

2.2

(11)

Equilibrium dynamics

Given the initial bond stock, the equilibrium dynamics for (b, d, f, φ) arecompletely described by (8), (6), (9), (11), and the no-Ponzi game condition.
The steady-state equilibrium, (b∗ , d∗ , f ∗ , φ∗ ), is determined by the following
equations:¡ d ∗ ∗ ∗ ¢ρ (d , f , φ ) = θ (d∗ , f ∗ ) = r,
(12)φ∗ = u (d∗ , f ∗ ) /r,(13)

gf (f ∗ , u (d∗ , f ∗ ) /θ (d∗ , f ∗ ))= p + τ,gd (d∗ , u (d∗ , f ∗ ) /θ (d∗ , f ∗ ))(14)

rb∗ = d∗ + pf ∗ − y.

(15)

In the above, (12) represents d˙ = 0 where (10) and g ∗ = 0 are substituted
successively into (9). (13) comes from (2) and (12) with g ∗ = 0. (14) is
obtained by substituting (12) and (13) into (6). (15) represents ḃ = 0 (see(11)).
(12) and (14) jointly determine d∗ and f ∗ . φ∗ and b∗ are then givenby (13) and (15), respectively. Figure 1 illustrates the determination of
the steady-state equilibrium. Schedules RR0 and F F 0 represent (12) and(14), respectively: RR0 represents the locus of (d∗ , f ∗ ) which equalizes thesteady-state rate of time preference to the world interest rate; and F F 0 is theTariffs under Weakly Nonseparable Preferences8

locus along which the intratemporal marginal rate of substitution equals thetariﬀ-adjusted relative price. The RR0 -schedule, say the steady-state time
preference curve, necessarily has a negative slope, whereas the slope of F F 0
can be of either sign. The figure depicts a normal case in which F F 0 is
positively sloping. The steady-state consumption (d∗ , f ∗ ) is determined at
the intersection point E of schedules RR0 and F F 0 . Given this, the externalbalance condition (15) is depicted as schedule BB 0 , which goes through point
E with slope −1/p. Its horizontal intercept, point B, represents rb∗ + y andhence gives the steady-state bond stock b∗ .
We can depict the eﬀect of an initial tariﬀ τ by using a line segment
0
T T going through point E with slope −1/ (p + τ ). From (14), schedule T T 0
can be regarded as the linear approximation of the steady-state indiﬀerence
curve around point E: {(d∗ , f ∗ ) | u (d∗ , f ∗ ) /θ (d∗ , f ∗ ) = utility at E}. The
slope of the schedule, −1/ (p + τ ) (= −gd /gf from (14)), is smaller or larger
in magnitude than the gradient at point E of schedule RR0 , i.e., −θd /θf , as ξis positive or negative. In figure 1, ξ is assumed to be positive. Note also thatthe gradient of curve RR0 at point E is assumed to be larger in magnitude
than 1/p, the slope of the external balance line BB 0 . It will be shown laterthat the relative magnitudes of the gradients of three schedules RR0 , T T 0 ,and BB 0 , determine the signs of the eﬀects of a tariﬀ change on φ∗ and b∗ .
To obtain the local dynamic system for X ≡ (d, φ, b), solve (6) for f ,which can be substituted into (8), (9), and (11). By linearizing the resulting
system around the steady state, we have Ẋ (t) = AX̂ (t) ;
³ g2 ξ 2
´
ξgf2
gd
rθd
f
− gf f+0no gdd gf f ξg2 gd


2
g
f
dd
A ≡  −gd 1 + (p + τ )
(16)
,
r
+
0
g
g
ff
ff


ξg
−1 − p (p + τ ) ggfddf
p gf ffr

where the hats placed above the variables denote deviations from their steadystate values, e.g., dˆ(t) = d (t) − d∗ .
We can show that the linear system has two positive and one negativeroots, with the negative one being given by
r
ω≡

r−

4g 2 g 2

r2 + gdddgfff Ψ2,

Tariffs under Weakly Nonseparable Preferences

where

½

rθd θfΨ=− ξ +
gd gf
2

µ

gdd
gf f
+
θd gd θf gf

¶¾

,

9

(17)

which can be shown to be positive under increasing impatience and (3) (seeappendix A for the proof). It follows that the relevant dynamic system
exhibits saddle point stability.
The resultant saddle trajectories can be derived from the eigen vectors
associated with (16) asḃ (t) = ω b̂ (t) , b̂ (0) = b0 − b∗ ,
Ã!
(r − ω) gf2
g
(r
−
ω)
f
f
dˆ(t) =
ξ+b̂ (t) ,gf f ∆
gf2
¶
µ
(r
−
ω)
g
g
g
(r
−
ω)
f
d
dd
− ξ b̂ (t) ,fˆ (t) =gf f ∆
gd2½¾(r − ω) gd
2 gdd
φ̂ (t) =1 + (p + τ )b̂ (t) ,
∆
gf f

(18)
(19)

(20)

(21)

where

"
¾#
½
gf2
p
gf f (r − ω)
gdd (r − ω)
∆=
ξ+
+
−ξ
,
2
gf f
gf
p+τ
gd2

which is positive under the concavity assumption (3).
(18) gives monotonic dynamics for state variable b. Given the dynamics,
transitional paths for d, f , and φ are determined on stable arms (19), (20),and (21), respectively. With (3), the saddle trajectories are all positivelysloping, implying³ that´ both consumption goods are normal. In figure 1, theˆˆstable arm for d, f obtained from (19) and (20) is depicted by a positivelysloping schedule SS 0 . This could be regarded as the Engel-curve.

Tariffs under Weakly Nonseparable Preferences

310

The eﬀect of a permanent increase in tariﬀs

Let us examine the eﬀects of an unanticipated, permanent increase in the
tariﬀ τ at the initial point in time, t = 0.10 Since the equilibrium dynamics
along the saddle trajectory are monotonic, the sign of the current-accounteﬀect in the short run is the same as that of the steady-state eﬀect on net
foreign assets.
Formally the steady-state eﬀect of a permanent rise in τ can be derived
from (12) through (15) asrθfdd∗= 2 > 0,
dτ
gf Ψ

(22)

df ∗
rθd
= − 2 < 0,
dτ
gf Ψ

(23)

dφ∗
ξ
=−
T 0 as ξ S 0,dτΨ (p + τ )
µ
¶
p
τ θf
τ θf
db∗
=
− ξ T 0 as
T ξ.
dτ
gf Ψ (p + τ ) pgf
pgf

(24)

(25)

(22) and (23) reveal that an increase in τ shifts consumption from f ∗ tod∗ . From (24), the eﬀect on φ∗ can be either positive or negative according
to whether d is more or less wealth-enhanced than f. This is because when
ξ <(>)0, i.e., when preferences toward d are more (less) wealth-enhanced
than those toward f , the relative elasticities of u to θ with respect to d arelarger (smaller) than those with respect to f . Given that any changes in(d∗ , f ∗ ) should take place to keep θ equal to r, the positive eﬀect of the increase in d∗ given by (22) on u∗ /θ∗ dominates (is dominated by) the negativeeﬀect of the decrease in f ∗ shown by (23). Intuitively, in the long run, welfare adjusts so as to promote consumption substitution from f ∗ to d∗ : whenpreferences toward d∗ are more (less) wealth- and hence welfare-enhanced
than toward f ∗ , steady-state welfare increases (decreases) to enhance thepreferences toward d∗ .
10

Recent empirical studies report that average tariﬀ-rates contain unit roots in many
countries (e.g., Gardner and Kimbrough (1989), Gardner, Slottje, and Kimbrough (1992),
and Bohara and Kaempfer (1994)). That is, tariﬀ shocks can be actually viewed aspermanent.

Tariffs under Weakly Nonseparable Preferences

11(25) reveals that the eﬀect on b∗ depends crucially on the relative magnitudes of τ θf /pgf and ξ, which capture the following eﬀects on spending,respectively: (i) a substitution eﬀect, caused by compensated consumption
shifts; and (ii) a welfare eﬀect, due to changes in steady-state welfare givenby (24). A substitution eﬀect is proportionate to initial tariﬀ τ and weakly
positive, whereas the welfare eﬀect can take either sign. When ξ is negative,
a permanent rise in τ improves b∗ and hence the current account. In the caseof a positive ξ, in contrast, the same policy may deteriorate them due to anegative welfare eﬀect.11
These steady-state eﬀects can be illustrated completely by using theschedules in figure 1. From the definition of ξ and (6), we have τ θf /pgf T ξ as
1/p T θd /θf : whether a substitution eﬀect is stronger or weaker than a welfare eﬀect is shown in the figure by whether the slope of the external balanceline BB 0 is larger or smaller than the gradient at the steady-state point of thesteady-state time preference curve RR0 . Recall also that the signs of ξ andhence of a welfare eﬀect are determined by the relative gradients of schedules
RR0 and T T 0 (see section 2.2). We can thus taxonomize the eﬀect of tariﬀs on(b∗ , φ∗ ) according to possible orders for the gradients of schedules BB 0 , RR0 ,and T T 0 . For example, figure 2 depicts the case in which ξ > τ θf /pgf > 0(i.e., θd /θf (= |gradRR0 |) > 1/p(= |gradBB 0 |) > gd /gf (= |gradT T 0 |)). An
increase in τ shifts the F F 0 schedule to the right, thereby bringing the steadystate point from point E0 to E1 . Since point E1 is located below T T 0 , φ∗ isreduced by the tariﬀ change. With schedule BB 0 shifting from E0 B0 to B1 B10 ,b∗ changes from B0 to B1 . Point E2 , the intersection of the new F F 0 -scheduleand the T T 0 -curve, represents compensated consumption which generates theinitial utility at point E0 . Point B2 , therefore, gives net foreign assets which
are required to maintain the initial living standard. The eﬀect on net foreign
assets is composed of a substitution eﬀect, B0 → B2 , and a welfare eﬀect,
B2 → B1 . In the present case, b∗ and hence the current account deteriorate
due to a dominant negative welfare eﬀect.
11

Formally welfare and substitution eﬀects can be defined by using:φ∗ = u (d∗ , f ∗ ) /θ (d∗ , f ∗ ) andgf (f ∗ , φ∗ )= p + τ,gd (d∗ , φ∗ )which can be obtained from (12) to (14). From the equations above, consumption andhence total spending d∗ + pf ∗ (of the country) can be solved as functions of p + τ andφ∗ . The eﬀect of p + τ on the spending function is a substitution eﬀect and that of φ∗ awelfare eﬀect. For more detailed discussions, see Ikeda (2000a).

Tariffs under Weakly Nonseparable Preferences

12

Note that even a marginal tariﬀ from no initial distortion has a firstorder welfare eﬀect whereas there is no first-order substitution eﬀect in theabsence of initial tariﬀs. This property is in marked contrast to what is
obtained by Razin and Svensson (1983): they show that without initial tariﬀs there is a first-order substitution eﬀect but no welfare eﬀect. Their result
comes from two critical assumptions. First of all, they assume that subutility
functions are time-varying, for which case a permanent tariﬀ aﬀects the relative prices of present and future expenditures, changes the real interest rate,
and thereby has a first-order intertemporal substitution eﬀect.12 Secondly,in their model, intertemporal preferences are assumed to be homothetically,and hence weakly separable, so that there is no welfare eﬀect. In contrast,
instead of assuming exogenous time-varying subutility functions,13 we haveendogenized a preference-shift by incorporating weakly nonseparable preferences into a model with a time-invariant instantaneous utility function. This
produces a first-order welfare eﬀect on one hand, and makes a substitution
eﬀect disappear on the other hand.
Notwithstanding the contrast, however, the resultant relationship between preference-shifting and the current-account eﬀect is fairly consistent
with what Razin and Svensson premise: in both of the models, a permanent,
marginal tariﬀ improves (deteriorates) the current account only when relative preferences toward imports are, endogenously or exogenously, weakened(enhanced) in the future (i.e., in the new steady state), in which case a permanent rise in consumers’ import prices makes present spending more (less)expensive in real terms than future one. In this sense, our analysis can be
regarded as a natural dynamic extension of Razin and Svensson (1983).
A remarkable diﬀerence of our result from what is obtained in the literature of dynamic analysis, e.g., Engel and Kletzer (1986) and Mansoorian(1993), also lies in the presence of steady-state eﬀects on welfare without
initial distortion. Since they assume weakly separable preferences and timeinvariant felicity functions, a marginal change in tariﬀs from zero cannot havea first-order eﬀect on any economic variables. In the case of weak nonseparability, a demand shift caused by the tariﬀ change can aﬀect steady-state
welfare and the other variables in the first order. This produces two interesting possibilities which cannot be obtained by the previous literature.
12

Substitution eﬀects are defined with respect to both intratemporal and intertemporal
relative prices. See Svensson and Razin (1983), p.103.
13
To be more precise, Razin and Svensson assume that consumers choose consumption,
taking the time-dependent shift of subutility functions as given, i.e., as an externality.

Tariffs under Weakly Nonseparable Preferences

13

First, a rise in tariﬀs can increase steady-state welfare if preferences toward
exportable-good consumption is more wealth-enhanced than toward imports.
Second, in contrast to the conventional wisdom, the current account can beworsened if preferences toward imports are suﬃciently wealth-enhanced, as
shown in figure 2.
As the final remark, distinguish the eﬀect on welfare φ (0) from that on
steady-state welfare. Tariﬀs in this model cannot enhance welfare φ (0), eventhough they improve steady state welfare if ξ < 0. In fact, (21), (24), and(25) yield
½
µ
¶¾
τ gf2
dφ (0)ωθd θf gdd
gf f
=
Ψ+
+
5 0.
dτ
gd gf
θd gd θf gf
Ψ∆ (p + τ )2 gf f
With initial distortion, therefore, an increase in tariﬀs is definitely harmful,as in other small country models (e.g., Sen and Turnovsky (1989) and Mansoorian (1993)). Without initial tariﬀs, a marginal change in tariﬀs has nofirst-order eﬀect on welfare. This is natural since there is no other distortion.14

4

The eﬀect of decreasing impatience

By assuming weak separability, Svensson and Razin (1983) show that (i) increasing (decreasing) impatience is a necessary and suﬃcient condition forstability (instability) of the steady state, and that (ii) a permanent termsof-trade deterioration worsens (improves) the current account if and only if
impatience is decreasing (increasing) in current welfare. From these discussions, they criticize analyses using the Uzawa-type time-preference model for
their crucial dependence on the assumption of increasing impatience. How
crucially does our result in the previous section depend on the assumption?
To examine this issue, let us next consider the case of decreasing impatience:θd , θf 5 0 and θd + θf < 0.
14

As for initial responses in consumption, from (19) and (21), when db∗ /dτ > 0,
domestic-good consumption instantly jumps upward less than in the steady state whereas
foreign-good consumption jumps downward more than in the steady state. In contrast,
when a negative welfare eﬀect is so large that db∗ /dτ < 0, the initial upward jump ind overshoots its long-run increase while the initial discrete fall in f comes short of its
long-run reduction (compare point E01 with E1 in figure 2).

Tariffs under Weakly Nonseparable Preferences

14

Let us begin with the case of no initial distortion: τ = 0. From (17), Ψ isnegative under decreasing impatience. From the definition of ω, the smaller
root ω thus takes a positive value.15 It follows that the equilibrium saddle
dynamics are unstable or stable as impatience is decreasing or increasing,16
as in Svensson and Razin’s finding (i).17
The impact eﬀect on current-account ḃ at time zero can be obtained from(18) asdb∗
dḃ (+0)
= −ω
,
dτ
dτ

(26)

which implies:signdḃ (+0)db∗= −sign= −signξ,
dτ
dτ

(27)

under decreasing impatience, where the last equality comes from (25).
This reveals that, as in the case of increasing impatience (without initial
tariﬀs), the current-account eﬀect is positive or negative as ξ is negative or
positive. In sum, given the sign of nonseparability index ξ, the sign of thecurrent-account eﬀect of a permanent increase in tariﬀs does not depend onwhether impatience is increasing or decreasing, in contrast to the Svensson
and Razin critique: whether consumer preferences toward “present goods”
are more or less wealth-enhanced than toward “future goods,” the current
account will improve (deteriorate) if the preferences toward exports are more(less) wealth-enhanced than toward imports.
In the presence of initial distortion τ > 0, we obtain from (25)µ¶
τ θfdḃ (+0)= sign
sign
−ξ ,
dτ
pgf
implying that, opposite to the case of increasing impatience, a substitution
eﬀect, the first term on the right hand side, aﬀects negatively the current
account under decreasing impatience. When preferences are weakly separable, therefore, the sign of the current-account eﬀect depends crucially on
whether impatience is increasing or decreasing, as is criticized by Svensson
15

We are maintaining the assumption that gd , gf > 0 and gdd , gf f < 0.
Even when ω is positive, the saddle path satisfies the no-Ponzi-game condition.
17
Following Svensson and Razin (1983, pp. 117-118), we neglect the possibility in theunstable case that the country may get so large to violate the small-country assumption.
16

Tariffs under Weakly Nonseparable Preferences

15

and Razin (1983). This crucial dependence is mitigated under weakly nonseparable preferences since the sign of a welfare eﬀect does not depend onthat property.

5Concluding remarks

Svensson and Razin emphasize that the current account eﬀects of exportoriented or import-substitution policies, which alter the internal terms oftrade, depend crucially on policy-induced changes in wealth and interest
rates, rather than on the direct eﬀect of the terms-of-trade change (Svensson
and Razin (1983), pp.100-101). However, they, as well as other authors, basically assume weakly separable preferences, thereby implicitly assuming away
preference-shifts between exports and imports, caused by “policy-inducedchanges in wealth.” It is this channel that we have focused on in this paper. With weakly nonseparable preferences, a permanent rise in tariﬀs has
a first-order eﬀect on steady-state welfare and thereby on the current account. To obtain credible prediction about the eﬀects of tariﬀs, empiricalresearch about consumers’ preferences is indispensable, especially regarding
how the marginal rate of substitution between exports and imports depends
on current wealth.18
This paper and the companion one (Ikeda, 2000a) imply that weakly
nonseparable preferences have an important implication for optimal wealthaccumulation. For example, suppose that consumers’ preferences toward acertain good are more wealth-enhanced than the other goods. Then, thestronger the preferences toward this luxury-type good are, the more wealthconsumers will accumulate. As an interesting application, Ikeda (2000b)
examines how intratemporal preferences toward this kind of luxury goods
indeed aﬀect economic growth and long-run wealth distribution.

AppendixA

Positivity of Ψ

To prove the positivity of Ψ, we first show the following property:
18

For empirical implications of weakly nonseparable preferences, see Ikeda (2000a).

Tariffs under Weakly Nonseparable Preferences

16

Property A: Under the regularity assumptions given in the text, ξ mustsatisfy the following property:(i) if ξ > 0, then ξ 2 < −rθd gf f;
gd gf2(ii) if ξ < 0, then ξ 2 < −rθf gdd.
gf gd2

Proof. Since ξ < gθdd by the definition of ξ and the positivity of gf , we have
ξ < gθdd . It follows that when ξ > 0, we haveξ2 <θdθd θgf f
ξ<−,gd
gd gf2where the second inequality comes from the third inequality in (3). In theθsame way the second relation can be proven by using the property that ξ > gffeven if ξ < 0 and (3).
From (i) in property A, when ξ > 0, the definition of Ψ impliesµ¶rθd gf frθd θf gdd
gf frθf gdd
Ψ>
−
+
> 0.
=− 2
2
gd gf
gd gf θd gd θf gf
gd gf
Similarly when ξ < 0, it should hold valid thatµ¶gf f
rθd gf frθf gdd rθd θf gdd
Ψ> 2
−
+
=−
> 0.
gd gf
gd gf θd gd θf gf
gd gf2

Acknowledgments
The author is grateful to N. Fujimoto, A. Tkachuk, M. Yamaguchi, andtwo anonymous referees of the Review of International Economics for helpful comments on earlier versions of the paper. A part of this research was
conducted while the author visited the Institute of Asian Research and theDepartment of Economics, the University of British Columbia in 1999.

Tariffs under Weakly Nonseparable Preferences

17

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f

B ′

R

F
T ′
S
E
steady-state indifference curve

S ′

F ′

R ′

-1/p

-1/(p +τ )dO

BFigure 1. Equilibrium under Tariffs: ξ > 0,θ d / θ f > 1 / p.

T

f

B1′

R

F
T′
E0

E01

E2
E1

substitution effectF′T
welfare effect

R′
R′

d
O

B1

B0

B2

Figure 2. An Increase in Tariffs: θ d / θ f > 1 / p > 1 /( p + τ ).