POLICY RESEARCH WORKING PAPER   14 24 .
C.ovnirlaaY      .  th..... .:  -<;9
Terms-of-Trade Shocks                                         C;ntnIaa'erh
eect of terms-of-Ttrade'shock S c-
and Optimal Investment                                    ' .'providea misleading vis
-.:- their impact: on, invese
and Optimal Investment                            *~~~~~~~S.~;an  ~jthneccW.'
Another Look at the Laursen-Metzler
Effect
Luis Serven                                                   erbf d
unrealistic. ;t.X-
.7~~~~-
Pohcy Rmm-c Departmen
:Y.9,..;'.
The World Bank
Policy Researc Department                                                     ..    ¾
Macroeconomics and Growti Division
February 1995                                                           ..



POLICY RESEAs CH WORKING PAPeR 1424
Summary findings
Conventional analyses of the effect of terms-of-tradc         In this framework, the response to a permanent terms
shocks provide a misleading view of their impact on         of trade improvement is unambiguous: The long-run
investment and the current account, says Serven, because    capital stock, and rhus investment, must rise, and the
capital goods imports are excluded from the analytical      current account must deteriorate - exactly the opposite
framework. He argues that such an exclusion is both         of the Laursen-Metzler effect.
arbitrary and unrealistic.                                    A transitory improvement in the terms of trade raises
Servrn reexamines the consequences of permanent and    saving but has an uncertain effect on investment. So, the
transitory changes in the terms of trade in a rational-     impact on the current account is generally ambiguous
expectations model of a small open economy with             and is shown to depend on three factors: the import
intertemporally optimizing agents, and with trade in both    contents of consumption and investment, the duration of
consumption and capial goods.                               the windfall, and the degree of intertemporal
substitutability in both consumption and investment.
This paper - a product of the Macrocconomics and Growth Division, Policy Research Department - is part of a larger
effort in the department to understand the macroeconomic impact of policy shifts and ext:rnal shocks. Copies of the paper
are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Emily Khine, room
Nl 1-061, extension 37471 (29 pages). February 199S.
The Policy Research Working Paper Series disseminates the findings of work m progress to encouwage the exchange of ideas about
development waues. An objectie of the sries is to get the findings out quickly. even if the presetions are less than fully polisheb The
papers carry tbe names of the asthors and sbouid be wsed and cited accordingly. The findings, interpeations, and conclisions are the
authors' own and should not he attributed to the World Bank, its Executive Board of Directorsm or any of its member countrim
Produced by the Policy Research Dissemination Center



Terms-of-Trade Shocks and Optimal Investment:
Another Look at the Laursen-Metzler Effect
Luis Serven
The World Bank
1818 H St., N.W.
Washington, DC 20433
Fax (202) 522-3518
Internet: lserven@worldbank.org
Conventional analyses of the effect of terms-of-trade shocks provide a misleading view of their
impact on investment and the current account due to the exclusion of capital goods imports from the
analytical framework - a feature that is both arbitrary and unrealistic. This paper reexamines the
consequences of permanent and transitory changes in the terms of trade in a rational-expectations model
of a small open economy with intertmnporally optimizing agents, and with trade in both consumption and
capital goods. In the paper's framework, the response to a permanent terms of trade improvement is
unambiguous: the long-run capital stock, and thus investment, must rise, and the current account must
deteriorate - exactly the opposite of the Laursen-Metzler effect. In turn, a transitory improvement in
the terms of trade raises saving but has an uncertain effect on investment. Thus, the impact on the
current account is generally amnbiguous, and is shown to depend critically on three factors: the import
contents of consumption and investment, the duration of the windfall, and the degree of intertemporal
substitutability in both consumption and investment.
JEL Classification Codes: F41, E22, F32.
* I thank Peter Montiel for detailed comments, and Lawrence Bouton for efficient research assistance.



I.    Introduction
Capital goods represent the leading import item for many countries. In 1990, they accounted for
nearly 30 percent of total imports (and close to 33 percent of non-fuel imports) in OECD countries, and
more than 33 percent in developing countries (over 37 percent of their non-fuel imports)'. These facts
indicate that investment typically has a high import content (certainly higher than consumption),
particularly in less-developed economies. As a result, import prices should be expected to exert a major
influence on the cost of capital and thereby on investment decisions.
However, this point has received very limited attention in open-economy macroeconomic analysis,
largely due to the fact that conventional models often rule out investment imports altogether. One
important azea where this omission may be particularly misleading concerns the current account impact
of terms of tr_de shocks, an issue that over the last decade has attracted renewed attention.
The analytical debate on terms-of-trade shocks has evolved around the notion, first proposed by
Laursen and  letzler (1950) and Harberger (1950), that a terms-of-trade loss causes a current account
deterioration. through its adverse impact on real income and thereby on saving. Since the early 1980s,
this proposition has been re-examined in the context of macroeconomic models embodying spending
decisions explicitly derived from intertemporal optimization. For the most part, the new literature has
focused on the response of saving to changes in the terms of trade. Along these lines, Sachs (1981),
Obstfeld (1982, 1983), Svensson and Razin (1983) and Svensson (1984) explored the impact of terms-of-
trade shocks on the intertemporal consumption decisions of forward-looking agents in a variety of
frameworks. A key result emerging from this work was the crucial distinction between permanent and
transitory, anticipated and unanticipated terms-of-trade shocks, whose respective effects on saving
generally differ.
More recently, the analytical perspective has been broadened by a number of papers considering
'Tlese figures are derived from the UNCTAD daabase; imports of capital goods exrludepassengercars andotherconsumer
durables. I am grateful to Lant Pritchett for kindly providing this data.



2
the current account impact of terms of trade changes in models incorporating also investment decisions
likewise derived from intertemporal optimization. In this vein, Matsuyama (1988) introduces a q-based
investment rule in an overlapping generations model with a Heckscher-Ohlin production structure; his
analysis emphasizes the role of factor intensities in the current account response to changes in the terms
of trade. Sen and Turnovsky (1989) develop an infinite-horizon model likewise inr:orporating capital
accumulation subject to installation costs; their framework underscores the labor-leisure decision as the
r.entral mechanism  of adjustment to terms-of-trade shocks.  Murphy (1992) introduces a similar
specification of investment in a two-sector framework with traded and nontraded goods to explore the
contribution of real exchance rate adjustment to shaping the current account response to terms-of-trade
disturbances. Van Wincoop (1993) investigates the consequences of a resource boom in an three-sector
economy including a construction industry producing nontraded capital.
In spite of the wide variety of analytical frameworks employed by this literature, one feature
common to virtually all of them is the assumption (implicit or explicit) that investment has zero import
content.' This precludes any direct impact of changes in the terms of trade on the real cost of capital
goods, and therefore tends to downplay the role of investnent in the current account response. Yet the
empirical evidence summarized above shows that such an assumption is completely unwarranted.
This paper re-examines the effects of terms-of-trade shocks in a simple model that allows for
imports of both consumption and capital goods, and with saving and investrnent plans determined
optimally. The analysis focuses on the impact of unanticipated permanent and transitory disturbances.
The results show that allowing for capital goods imports has major consequences for the validity
of the Laursen-Metzler effect A permanent terms-of-trade windfall raises investment and must cause a
' For example, Murphy (1992), Sen and Turnovsky (1989), van Wmcoop (1993) and also Cha (1993), all asume that capital
goods are produced only domesdcally. In an earlier contribution, Bnrno (1982) explores the consequences of a resource boom
in a two-sector economy employing traded capital goods, but under the simplifying assumption that the boonung sector uses no
capital. See Brock and Tumovsky (1993) for a recent overview of alternative specifications of the investment process in two-
sector models.



3
current account deficit - contrary to the traditional wisdom. By contrast, a temporary windfall has an
ambiguous impact on the current account, except in the extreme - albeit popular in the literature -- case
of zero import content of investment, in which the current account turns initially into surplus, along
Laursen-Metzler lines. In the general case, however, the current account outcome depends on the import
contents, and the degree of intertemporal substitutability, of both consumption and investment.
The paper is organized as follows. Section 2 lays out the analytical model, and Section 3
describes its equilibrium dynamics. The effects of permanent Lad transitory terms-of-trade disturbances
are explored in Section 4. Finally, Section 5 concludes.
2.    A stylized model of a small open economy
To highlight the role of investment decisions for the dynamics of the current account, the
analytical framework will be k-ept as simple as possible'. We consider an economy completely
specialized in the production of a good that can be used for domestic consumption and investment, or
exported. The domestic good is an imperfect substitute for an importable good which is also available
for consumption and investment. Production of the domestic good makes use of capital and labor
according to a constant-returns technology. The economy faces given world interest rates and goods
prices. We let Tr denote the terms of trade - i.e., the exogenously given relative price of the exportable
in terms of the importable.
The economy's salient feature is an investment technology with two basic characteristics: first,
investment goods are (costlessly) produced by combining domestic goods and imports according to a
constant-returns-to-scale specification:4
'The model in this section is a somewhat simplified version of that in Serven (1994).
'This specification of investment is similar to that used by Gavin (1992b) and Serven (1992, 1994).



4
J = J (4Jr)                                           (I)
where J,) and JF respectively denote domestic and foreign goods used as inputs to the investment process,
and the function J(.) is homogeneous of degree one. Second, the installation of new investment goods
involves convex costs, assumed quadratic for simplicity. Thus, total investment J differs from effectively
installed new capital I:
= 1+(2)
2 K
where the positive parameter 0 measures the slope of marginal installation costs. For simplicity, we
abstract from depreciation, so that net capital accumulation equals the installation of new capital.
The homogeneity of J (.) allows a two-stage investment decision: at the first stage, total investment
is determined; its cost-minimizing allocation between domestic goods and imports can be decided at the
second stage. Specifically, the investment technology (1) implies the existence of an exact investment
price index pr = prj{r), with PK' > 0 and PK" <0, that measures the (minimized) cost in terms of imports
of one unit of real investmente.
The economy is populated by a representative, infinitely-lived agent who can borrow and lend
at the given world interest rate r in terms of imports.6 Work entails no disutility, and hence the agent
supplies inelastically her entire labor endowment, which for notational simplicity will be ignored. Thus,
the production technology can just be expressed as Y. = Y(K), where Y denotes real output of the
domestic good, with Y' >O, Y" <O. The agent's objective is to maximize the utility functional
exp (- Pt) -:)   I_  dt
5 Actually, homotheticity of J(.) would be sufficient to pernit twostage investment budgeting, although the price index in
thc text would then depend on both mad J. See also Hayashi and Inoue (1991) for a similar two-step specication of investment
decisions.
6 Alteratively, r could be given in terms of exports. The assumption in the text is probably more realistic for the case of
a small, price-taking economy.



5
where B is the discount rate, 1/0 is the elasticity of intertemporal substitution in consumption, Cm and CF
respectively denote the instantaneous consumption of domestic and imported goods, and again for
analytical convenience the function C(.) will be assumed homogenous of degree one. Thus, just like in
the case of investment, consumption decisions can be characterizWd as the result of a two-stage budgeting
process C can be interpreted as the real consumption index, and the expenditure function associated with
it can be expressed pc(wr)C, where the exact consumption price index Pc (with Pc'>O and pc"<O)
represents the (minimized) cost in terms of the importable of one unit of real consumption.
Putting all these pieces together, the representative agent's problem can be written
Maximize         exp(- fi  Q61 -9  dt                                           (3a)
subject to          I                                                           (3b)
A    [wrY()-pc(Cr)C-p@xr) [I             + rKA                   (3c)
lim   exp(-r-t)A  = 0                                           (3d)
K(, Ao given.
The right-hand side of (3c) is just the agent's current account surplus, with A denoting her net foreign
assets; in turn, (3d) rules out the trivial solution of unbounded external borrowing. The current-value
Hamriltonian for this problem is
H   C  A [lrY(k) Pc(r)C-PT(7r) |I+ . .| +rAJ  + Q(4)
where X and Q are the shadow values of the stocks of foreign assets and capital, respectively. It will be
useful to define q r Q/X as the shadow value of capital in terms offoreign assets; then the first-order
conditions for this problem include, in addition to (3b)-(3d), the following:



6
c-I    1                                ~~~~~~~~~~~~(5a)
[?p.(7r)J
C         [Xpl( ]q                                    (5b)
4' [Pz(7r)    J
= ' (3-rr) X                                       (5c)
' q7 - [r tY (  + pc(T2[] ]J                                (5d)
Equation (5a) is just the standard characterization of the optimal consumption path. In turn, (5b) is
Tobin's investment rule, linking capital accumulation to the shadow value of capital relative to its
replacement cost, with both measured in terms of foreign assets. As (5c) makes clear, a stationary
solution for the model cannot exist unless the rate of time preference equals the world interest rate, as
will be assumed henceforth7; in such case, the shadow value of foreign assets X must remain constant
along the adjustment path. Finally, (5d) is the arbitrage condition describing the trajectory of q.
Combining (5a) with the budget constraint (3c-d), it is straightforward to solve for the equilibrium
value of X:
A(r) + W(t)                         AO=  +   o+WO                   (6)
l | CtI) [p(7r(s))]1  dsJ      IJ l   e"'P.(r(s))]T   dsJ
where the second equality follows from the constancy of X over time, and W  denotes nofinnmcial
wealth, defined as
W(t) -  J e-'.    [(s)Y(K(s)) p         r( A   ±s))T(O+±cs) 11  ds            (6')
L              1~ ~~~~2 K(s)JJ
z See Cha (1993) for an analysis of permanet rms-of-bade shocks in an intertemporally-optimizing famork wich
allows the ate of time preference to differ from the world interest rate. Unrlic this paper, however, Chs assumesdt invesbt
goods are produced domestically, and therefore output and thc capital stocik are wholly unaffected by terms of tmde change.



7
Thus, W is the present discounted value of the entire future stream of output net of investment expenses;
A+W therefore represents total wealth (financial plus non-financial) in terms of foreign goods.'
Replacing (6) into (5a) above, optimal consumption can be expressed:
C(t) - [A (t) + Wt)] [       pcww](t))]         1                      (7)
[ Je re-'   [pc(r()] 7 ds ]
Consumption behavior depends on two factors: first, total wealth; and second, intertemporal price
speculation (to use Obstfeld's (1983) terminology), captured by the term in large square brackets in the
above expression, that reflects the sensitivity of consumption to the present and future anticipated path
of consumption prices. This will be an important issue in what follows, and can be highlighted by time-
differentiation of (5a) above, which yields:
C        r @ [t  -p (7r) ---   = -   SC(r)X                       (8)
where sc(r) 2 7rpc'(r)/pc(7r) is the share of domestic goods in consumption expenditure. This is just
a restatement of Dornbusch's (1983) well-known characterization of the optimal consumption path: as
long as consumption has some domestic content (i.e., Pc ; 1), it must follow a rising (declining) path
if the terms of trade are worsening (improving). The reason is that anticipated terms of trade
deterioration raises the real interest rate in terms of consunption above the rate of time preerence,
encouraging substitution towards the future; anticipated terms-of-trade improvement has the opposite
effect. The slope of the consumption path is determined by the elasticity of intertemporal substitution
1/O and the share of domestic goods in consumption expenditure; the larger they are, the higher the
' It is important to note that X bdeaves like an asset price, and in the absence of any unanticipatd shocks must remain
constant at the value given in die text; in a closely related famework, this is underscored by Obstfeld (1983), whoe also derives
an exprcssion analogous to (6).



8
sensitivity of consumption growth to anticipated terms-of-trade changes.9
To explore the effect of changing terms of trade on the trajectory of investment, use (Sd) to write:
(    Iq ))- (r  -sr()7r]  *Qi) - [ -7( Y](  +                            (5d')
dt pX(-T)                     -        I..L.. C'(K) 2K
where, like with consumption, SK(r) °  7rpg'( )/pK(7r) is the share of domestic goods in investment
expenditure. Thus, terms of trade changes impact on the time path of q/pK -- and thereby of investment -
- through two channels. First, as long as capital has some import content, terms of trade changes affect
the value of the marginal product of capital relative to its price, TY'/PK(Vr). Second, analogously with
consumption, to the extent that investment has some domestic content anticipated terms of trade changes
are also reflected in the real interest rate in terms of capital goods (the first term in brackets in the right-
hand side): pending an expected terms of trade rise (fall), the real interest rate in terms of capital is below
(above) r-; ceteris paribus, this reduces (raises) the user cost of capital and provides an incentive for the
intertemporal reallocation of investment towards (against) the present.'" The extent to which these two
forces impact on the time path of capital accumulation depends on 1/i, which in this sense provides a
measure of intertemporal substitutability analogous to that given by 1/9 in the case of consumption.
The discussion has been limited so far to the intertemporal allocation of aggregate consumption
and investment. However, their cost-minimizing intra-temporal allocation between domestic goods and
imports follows immediately from Shephard's lemma:
CN   P PC(i * C                                     (9a)
C, =   cPC(T) - rpI(T)* C                                (9b)
9In tum, whether consumpion expenditure pcC moves over time ui the same or in opposite direcdon to the terms of tmde
depends on whether 9 is larger or smaler ihan unity, respectively.
" This issue is explored at length in Serven (1992).



9
Cap(1r)  (I + 2K                                        (9c)
Ji,  Erx() - 7Fpk(T)J * (I  -  -!)                          (9d)
2 K
This completes the description of the model." Its dynarnics are discussed next.
3.     Eaiiilibrium dynamics
The model's dynamics can be summarized in the time paths of the shadow price of capital q, the
stock of capital, and foreign assets. In fact, the dynamics are recursive, with the time paths of q and K
determined by (5b) and (5d), independently of the foreign asset stock. Further, while the capital stock
is a predetermined variable, its shadow value q is free to jump at any point in time in response to
unanticipated shocks or to the arrival of new information about the future paths of the exogenous
variables.
For given terms of trade xr, the top panel of Figure 1 depicts the dynamics of the capital stock
and its shadow value near the long-run equilibrium. Along the horizontal KK line, q = p,.(,r) or, in
words, the shadow value of capital equals its replacement cost; therefore, investment is zero and the
capital stock is constant. In turn, along the downward-sloping QQ line, q = 7rY'(K)/r, and hence q is
constant (from (5d)). The long-run equilibrium is at E where the KK and QQ lines intersect; at such
point,
Y'(X) = r,p,(T)                                     (11)
where a bar over a variable denotes its steady-state level. In words, the value of the marginal prod-act
"In fact, there is implicidy one more relation - namely, the clearing condition for the domestic goods market- -which can
be used to determine the economy's real exports. Using X to denote the latter, this would read:
Y=- Cm + JN + X



10
of capital equals its user cost, given by the real interest rate times the price of capital goods. The long-
run equilibrium is a saddlepoint, and the negatively-sloped line SS depicts the unique convergent
trajectory. Along the SS line, q and K move in opposite directions towards the long-run equilibrium:
intuitively, as the capital stock rises (falls) towards its steady-state level, investment must simultaneously
decline (rise) towards zero.
[Figure 1]
Consider now the trajectory of consumption and the current account. Under constant terms of
trade, it follows from (5) and (6) that real consumption and total wealth [A+WI must be constant as well.
From (7), consumption equals C=r [A+W]/pc(i), which is just permnment income - i.e., the annuity
value of total wealth -- in terms of consumption goods. Therefore saving equals the difference between
current income (inclusive of interest on net foreign assets) and permanent income:
S(r) = IY(K(r)) + r-A(r) - rt[A(t)+W(t)] = IrY(K(t)) - r W(t)
and the current account balance is
A(Qt) = S( )- p ()J(t) =  4Y(K(t)) - r W(t)) - pvCr)    (q*t)+-......  =    Q)   (12)
L  2 K(t)J
where the last equality follows from (6'); thus, the current account deficit equals the rate of change of
non-financial wealth".
However, it is important to note that near the steady-state equilibrium the current account balance
is determined by the trajectory of investment alone, because along the adjustment path any deviation of
12 This can be seen to follow direcdy from the constancy of totl wealh A+W under consint tems of tnde; we (6) inlthe
text.



11
saving from its long-run level (equal to zero") is just of second-order magnitude. This can be seen by
recalling that, from the above expressions, saving equals the difference between current output (in terms
of imports) and the annuity value of non-financial wealth r W. But near the steady state non-financial
wealth can be approximated as":
r   i[Y'(K)-r p,(i)I  e-'-(`)f(s)ds                       (13)
From (1 1) above, the term in square brackets is zero, and therefore nnn-financial wealth just equals the
capitalized value of current output ;rY(KC(t))/r'.  The intuitive reason is that, near the long-run
equilibrium, ongoing net investment and the ensuing change in output over time have no first-order
impact on non-financial wealth, because each additional unit of capital earns a marginal return equal to
its user cost -- a simple consequence of the envelope theorem.
Thus, under constant terms of trade, saving equals zero near the steady state. Equivalently,
current and permanent income are equal up to a first-order approximation and, from (7) above,
consumption equals current income:
CC:)  [r *A t + iY(K(t)]                                      7'
[  PC(T)        ]
' Long-un saving must equal zero as a consequence of the assunption of no capital deprciation. With nonzao
depreciation, long-run saving would be positive instead; nevertheless, with constant tenrs of trade, near the steady state saving
would remnin conswnt at its long-run level along the adjustnent trajectory, up to a first-order approxtion.
"4 Here we use the fact that near the long-run equilibrium the quadratic adjustment-cost component of investnent is only
of second-order magnitude and can be ignored; however, see Gavin (1992a) for a discussion of the practical relevance of such
second-order effects. In the text we employ the first-order approximation
Y(I(s)= Y(K()) (      f [d Y(K(s)]  - Y(K(t)) + f Y'(TQ.&(s) ds
I ds               ~~~~~~~~~~t



12
This in tum implies that the current account deficit is equal to investment expenditure. Hence,
under constant terms of trade the accumulation of capital and foreign assets near the steady state must
proceed in opposite directions: capital accumulation (decumulation) must be matched by a current account
deficit (surplus)."5 This inverse relationship between the stocks of capital and foreign assets along the
adjustment path is captured by the downward-sloping AA line in the bottom panel of Figure 1.
4.    Terms-of-trade shocks
A permaneni terms-of-trade improvement
The consequences of a permanent terms-of-trade shock in this model can be easily illustrated.
Assume that the economy is at the long-run equilibrium E. in Figure 2, with a capital stock IC, and
foreign assets A., when the terms of trade rise unexpectedly and permanently from r0 to sr; since the
terms of trade remain flat after the initial rise, the consumption- and investment-based real interest rates
remain unchanged at r'.
Consider first the impact on the capital stock and its shadow value, already analyzed by Gavin
(1992b) and Serven (1992) in closely related (but simpler) models. In Figure 2, the permanent increase
in the terms of trade shifts both the QQ and KK schedules upward, to Q'Q' and K'K', respectively. The
QQ schedule shifts vertically by the full amount of the terms of trade change; in turn, the precise extent
of the shift of KK depends on the domestic content of investment goods. If capital goods are fully
domestic, as conventionally assumed, then PK(7r) = S, and the KK schedule would also shift by the full
amount of the terms of trade improvement. In such case, the new long-run equilibrium would be at E,
with an unchanged capital stock (and real output); likewise, the current account and the fbreign asset
stock would remain wholly unaffected.
15 The same result is obtained by Sen and Turnovsky (1989) and Murphy (1992).



13
(Figure 2]
If capital goods have an import content, however, the KK schedule shifts by less than the QQ
line, and therefore the new long-run equilibrium at El in Figure 2 is to the right of the initial one, and
involves a higher capital stock. The reason is that the terms of trade improvement raises the marginal
product of capital in terms of foreign goods above its real user cost (see (I1) above), and more so the
higher the import content of investment goods"6; thus the optimal capital stock rises to K,. In the short
run, the shadow value of capital jumps to q' on the new convergent path S'S' and investment rises;
thereafter, the adjustment involves a rising capital stock and falling q, with investment gradually declining
towards zero.
What about consumption and saving ? From (7'), real consumption jumps on impact to the new
constant level
C  er   A. + rY(K.)J
Differentiating this expression with respect to Tr, and evaluating the result at 7r, =  r0. the change in
consumption can be expressed
dC        =    1  [Y(Q-sc()[r A° + Y(Q           =   !   [C  -r-A
1*7r     Pc(7)                   r                CI)
where C.O denotes consumption imports at the initial equilibrium. Since at the initial equilibrium the
current account was balanced at zero investment, CFO - r'AO = solY(Q  - CNJ which in turn equals the
value of exports in terms of foreign goods at the initial steady state; thus, the new consumption level must
t6 Clearly, this effect is maximum in the extmeme case of zero domestic content of investment (pc - 1), in which doe ucer
cost of capital remains unchanged and thcrefore the KK schedule does Sot shift at alL



14
be higher -- as long as the original equilibrium involves positive exports of the domestic good.17
After the initial change the terms of trade remain at 7r,, and therefore the adjustment proceeds
along the lines discussed in the previous section: saving remains unchan-ed at zero" and, since
investment has risen, the current account must be in deficit throughout the adjustment to the new long-run
equilibrium - exactly the reverse of the Laursen-Metzler effect."  Thus, as capital is accumulated the
foreign asset stock declines from AO to A, along the AA line in the bottom panel of Figure 2.
A transitory terms of trade improvement
Consider now the case of a purely temporary terms of trade windfall, which from the practical
viewpoint is probably a more interesting scenario.?0 Assume that at time 0 the terms of trade rise
unexpectedly from 7r0 to 7r,, and it is immediately recognized that at time T they will decline back to vr.
permanently.
What are now the consequences for consumption, investment and the current account ? The
answer is a bit more complex than in the previous experiment because, as discussed earlier, with time-
varying terms of trade the equilibrium paths of both consumption and investment reflect in part the effects
of changing real interest rates in terms of consumption and investment goods, respectively.
Oterwise, as noted by Obstfeld (1983), the domestc good would be imported rather tn exported, and the rise in the
erms of tade would rcally amount to a loss rather than a windfall.
More precisely, the change in saving is only of second-ordermagnitude, as described earier. 71e fact dIatwih homothetie
preferences saving is wholly unaffected by unanticipated permanent terms-of-tmde changes was rigorously shown by Svensson
and Razin (1983) and Svensson (1984). However, this ceases to be true if non-traded goods are introduced in the aalyical
framework; see Gavin (1990).
" Scn and Turnovsky (1989), using a model broadly similar to the present one - but assurrng that capital goods have no
import content and highlighting the laborlleisure decision - likewise find that a permanent terns-of-tbade improvement may
cause a curent account deterioration, through an investment boom triggerd off by substitution between consumption and leis
More generally, in a two-sector framework with both traded and non-kaded goods, a permanent terms-of-trade improvement
unambiguously causes an investment boom if nontraded goods arn capital-intensive. If non-traded goods are instead labor-
intensive, an investment boom can still rcsult if the import content of capital used in the cxport sector is high enough.
2 See Cuddington and Urzua (1989) and Mendoza (1992) for evidence dat the majority of observed  rmna-of-tmde
fluctuations are purely transitory.



15
Consider first the response of investment. In the long run, with the terms of trade unchanged
at 7r0, the capital stock must remain at its original level Ko. Pending the anticipated terms of trade
decline, however, investment is subject to the influence of two factors. On the one hand, the price of
new capital is transitorily high and expected to fall back to pK(r); as discussed earlier, this raises the real
interest rate in terms of capital goods and, ceteris paribus, discourages investment prior to T - more so
the larger the domestic content of investment goods. On the other hand, the transitory terms of trade gain
also raises the profitability of capital, boosting the value of its marginal product above its user cost (i.e.,
Tr,Y'(K.) > rp[(7r,)); this amounts to a transitory investrnent incentive, which is larger the higher the
import content of capital.
Two extreme scenarios deserve mention. If capital has no domestic content (p, = 1), its relative
price is unaffected by the terms of trade improvement, the real interest rate in terms of capital is constant
at r-, and the first of the two effect above is nil; therefore investment must rise in the short run.
Conversely, if capital is fully domestic (i.e., pg(Or) - r, as conventionally assumed), then the
profitability effect disappears, and investment must fall in the short run.
In the general case, however, the short-run response of investment reflects the two opposing
forces above, and is therefore ambiguous.2' Its sign depends on three key factors: (i) the import contnt
of capital: the higher it is, the larger the transitory incentive and the smaller the disincentive just
described. (ii) The persistence of the terms of trade gain, as measured by T: the larger T, the longer-
lasting the profitability increase and the more distant in the future the rise in the real interest rate in terms
of capital, thus making it more attractive to install extra capital in the short run. (Wii) Marginal
installation costs (as measured by O): the costlier it is to install capital, the lesser the net payoff from
adding capital now and removing it later in response to a purely transitory profitability rise.
Figure 3 depicts two possible scenarios. In both cases the economy starts from the initial
2' The intuitive argument that follows is formalized in the appendix.



16
equilibrium at EiO, with S0SO representing the convergent path. If the terms of trade rise were permanent
rather than transitory, the new long-run equilibrium would be at E,, with the convergent path S'S', as
discussed earlier. Figure 3 (a) corresponds to the case in which the transitory profitability incentive is
large -- either because the import content of capital is high, or the terms-of-trade improvement is long-
lasting -- relative to marginal installation costs. Thus, on impact q jumps to a point such as q' above
pK(7r,), so that q/PK rises and net investment turns positive. During the period of high terms of trade,
the system displays a clockwise motion: q falls rnonotonically, and capital accumulation eventually must
give way to decumulation as the anticipated terms of trade fall draws near. At time T, when the terms
of trade return to their initial level w0, the system must be at a point such as FT on the original convergent
path S0SO. The price of capital goods declines back to PK(lro), q/PK rises, and investnent jumps
upward"; the aujustment then involves continued capital decumulation (albeit at a reduced rate) and
rising q.
Figure 3(b) portrays an alternative scenario of low import content of capital, short-lived terms
of trade improvement, and/or high marginal installation costs. In such case, the terms of trade windfall
causes q to rise initially by less than p,,, and therefore net investnent turns negative. Over time, both
q and K keep falling; at instant T, when the terms of trade deteriorate back to wr0, the system must be at
a point like FT on S0SO. The fall in p,c then causes investment to rise, and the system travels along the
SOSO locus towards the initial steady state.
[Figure 3]
22 Since the tenns of trade deterioration at time T is perfectly anticipated, q cannot jump at that instant; hence qIp(1) ist
rise abruptly, and so must invesment. Notice also that at time T the capital stock may be above or below Ko. In die bn  caw,
net investment tu rns from negative to positive; in ie former (depcted in Figure 3a), it remains negative, but decelerateoward
zero.



17
Let us now turn to the consumption response to the temporary terms-of-trade windfall; in a
context of fixed output and no investment, this has been studied by Obstfeld (1983). The transitory
windfall must raise welfare, and therefore real consumption must rise above its initial level CO at least
at some point in the adjustment path. However, the new consumption trajectory need not be wnformly
above C0. The reason is that the path of consumption reflects two forces: on the one band, real wealth
rises with the temporary terms of trade windfall; on the other hand, as long as consumption has some
domestic content, the anticipation that the terms of trade will deteriorate at time T raises the consumption-
based real interest rate prior to that date, encouraging intertemporal substitution towards the future.
Thus, at instant T, when the terms of trade return to their initial level, the consumption-based real interest
rate falls back to r' and real consumption must show an upward jump, rising above C.; thereafter, with
no furEher changes in the terms of trade, consumption remains flat. Prior to T, however, consumption
may be above or below C0 depending on the strength of the intertemporal substitution effect.
Analytically, letting C, denote the consumption level prevailing during the period of high terms
of trade, the appendix shows that it can be approximated as
C,   r'A     r + 7r,Y(KO) - e' T(r-1ir) Y(K(7))
61=p(7r,)(I -e-` 2 + e-., k(w 67 1- 7pl C1)-71
and therefore, for small terms of trade changes,
dCI    [= YK) -CJ(I-e   Z_)-c'            IC,                 (14)
dirl '""PCO
Thus, whether consumption rises or falls in the short run depends on three factors. First, the domestic
content of consumption, captured by the initial consumption of the exportable C,.: the larger it is, the
bigger the incentive to postpone consumption and the more likely an initial consumption fall. Second,
the anticipated persistence of the temms of trade windfall, as captured by T: the larger T, the more distant



18
in the future the anticipated decline in the price of consumption, and the lesser the incentive to postpone
consumption. Third, the elasticity of intertemporal substitution 1/0: the lower substitutability, the weaker
the intertemporal substitution towards the future in response to the transitory incentive, and the less likely
an initial consumption fall; in particular, 1/ :5 1 suffices to guarantee that consumption will increase
in the short run.
After the initial impact, the consumption trajectory remains flat at Cl until instant T; at such date,
it must rise discontinuously to its new long-run level. Using C' to denote the latter, (5a) implies that C'
= C1(pc(Tri)Jpc(wO)Y'I. Using (14) above, we have
dC'      - (I - e'`) YK   C          
which is positive as long as the initial equilibrium involves positive exports of the domestic good;
therefore; C' must be unambiguously above the initial consumption level CO.
Given this trajectory of consumption, what happens to saving ? It is easy to see that, following
the initial terms of trade improvement, saving must rise as a result of both intertemporal smoothing of
the real income vain and intertemporal consumption substitution towards the future.' Pending the terms
of trade deterioration, with consumption expenditure constant at pc(w1t)Cq, saving will be rising further
if the investment response is positive and real output is terefore growing; it will be declining in the
opposite case. At time T, when the terms of trade return permanently to their initial level, saving returns
to zero, as described in the previous section.
Finally, what happens with tfie current account ? The above discussion clearly shows that, in
contrast with the unambiguous current account deterioration resulting from a permanent terms of trade
gain, the impact of a purely transitory windfall is much less clear-cut: while saving must rise
3 However, if die world interest rate were fixed in rms of the ecpotable radter dhn the importbe (as assumed), dt
consumption-based real interest rate wouldfaU inste  of nsing, and the jutemporal ubsfttion effect would tun agam the
consumption smoodiing effect; hus, the overall effe on saving would be ambiguous.



19
unambiguously in the short run, investment may rise as well in response to the temporarily higher
profitability of imported capital. Thus, the sign of the change in the economy's saving-investment balance
is in principle indeterminate. The only exception is the special case of zero import content of capital
goods, in which investment is assured to fall; this reinforces the saving rise, and the current accoun' must
unambiguously improve.
Nevertheless, the earlier discussion has identified the three key factors that shape the current
account response in the general case: (i) the import content of consumption and investment, (ii) the
persistence of the terms of trade improvement, and (iii) the degree of intertemporal substitutability in
consumption and investment.
Higher import contents moderate the transitory rise in consumption- and investment-based real
interest rates, and therefore dampen the incentive to postpone expenditures; moreover, a larger import
content of investment also leads to a more significant short-run improvement in the profitability of capital,
thereby encouraging investment. Through both channels, higher import contents make a short-ran current
account deterioration more likely.
Likewise, the longer-lasting the improvement in the terms of trade, the more likely a short-run
current account deficit: as the anticipated rise in consumption- and investment-based real interet rates
becomes more distant in the future, the incentive to the intertemporal reallocation of expenditure against
the present is reduced, while investment is additionally encouraged as the transitory profitability
improvement becomes more persistent?'
Finally, it is worth underscoring the mutually opposing influences on the current account of
intertemporal substitutability in consumption and invesmentu - with the latter measured by the inverse
'In the limit, as T approachesinfinity, ie cuent account wouid detdoe lilce underdthe pemnetsock: d ientive
to postpone expenditures would vaish, the 2mm paih of consunmpion would be 1lat, and investnent would nce narly rine in
the face of a more and mor pergite profitabilt imrovement
2 A similar result is obtined in Serven (1994) in a related model conerig the cunrnt account respouse to permanent
fiscal shocks.



20
of the installation cost parameter, 1/X. With higher consumption substitutability, the short-run saving
rise is larger and a current account improvement hence more likely. Conversely, higher investment
substitutability(lower installationcosts) favors a positive investmentresponse to the transitoryprofitability
improvement, which tends to result in current account deterioration.
Graphically, the bottom panels of Figure 3 (a) and (b) portray two possible scenarios of current
account response. Scenario (a) assumes that the short-run investment rise (displayed in the top panel)
outweighs the saving increase, and hence the current account initially turns into deficit. At first, the
capital stock is rising and foreign assets are falling; however, as the anticipated terms of trade
deterioration draws near, net investment decelerates and eventually turns negative, while the current
account is improving and eventually turns into surplus. At instant T, when the terms of trade return to
their original level, the figure assumes that the system is at (KMT), AM), with the capital stock above,
and foreign assets below, the initial level.'6  The terms of trade deterioration then causes a rise in
investment (which nevertheless remains negative) and a drop in saving, so that the current account
deteriorates (but nevertheless remains in surplus). Thereafter, the adjustment involves an upward motion
along the A'A' line, parallel to AA through (KMI), AM), until the initial capital stock Ka is restored,
which involves a foreign asset stock equal to A.
Scenario (b) in turn depicts the alternative case of an initial investment drop. The current account
turns immediately into surplus, and the system displays a clockwise motion with falling capital and rising
foreign assets; pending the terms of trade loss, the investment decline keeps accelerating and the current
account improves further. At time T foreign assets must be above, and the capital stock below, their
initial levels; investment rises abruptly and the current account turns into deficit. Thereafter, the system
moves downward along the A'A' line to reach- the long-run equilibrium at the initial capital stock,
26 As noted carlier, this need not be the case, and the opposite tuation (capital stock undershooting and foreign asset
overshooting) is also possible. In the later case, the adjustment after time T would involve positive net investnent and a current
account deficit.



21
involving now an increased foreign asset stock.
5.     Concluding! Remarks
This paper has examined the impact of terms of trade shocks in an aggregate franework whose
distinguishing characteristic is to allow for imports not only of consumption goods, but also of productive
capital -- an essential feature of real-world economies that is nevertheless ignored in many open-economy
aggregate models. The analysis has focused on the effects of unanticipated permanent and transitory
terms-of-trade shocks on intertemporally-optimizing consumption and investment decisions.
The results can be summarized in three main points. First, as long as capital has an import
content, permanent changes in the terms of trade alter the long-run capital stock and output in the same
direction: an improvement in the terms of trade raises the profitability of capital and thereby increases
the steady-state capital stock and output; a deterioration has the opposite effect.  With capital
accumulation subject to convex installation costs, the somewhat surprising consequence is that a
permanent terms of trade gain must tead to an investment boom and a current account deficit, while a
permanent loss must cause a surplus.
Second, the current account impact of a temporary terms of trade change is ambiguous. As the
literature has amply documented, saving must rise transitorily with a temporary windfall and decline with
a temporary loss. As this paper has shown, however, if capital goods have an import content investment
may move in the same direction as saving, making the current account outcome indeterminate. The
reason is that during a temporary windfall investment imports are transitorily cheap in terms of domestic
output, and thus the profitability of capital is transitorily high; therefore, a short-term investment boom
(followed later by a slump) may result. The opposite happens with a temporary terms of trade loss. The
exception to this general ambiguity is the special case of zero import content of capital, in which
investment is assured to fall with a transitory terms of trade gain and rise with a loss; under such extreme



22
scenario - which is nevertheless the one assumed almost invariably in conventional aggregate models --
the Laursen-Metzler effect obtains: a temporary terms of trade deterioration causes a short-term current
account deficit, and an improvement causes a surplus.
Third, the analysis has shown that in the general case the short-run current account response to
a transitory shock depends on three key factors. One, the import contents of consumption and investment
-- the higher they are, the lesser the saving response and the stronger the impact on the profitability of
capital, making it more likely that a temporary windfall will lead to a short-run current account deficit
(and a loss will lead to a surplus). Two, the persistence of the shock, which acts in the same direction -
- the longer-lasting it is, the lesser the incentive to postpone (anticipate) consumption and raise Oower)
saving in response to a temporary windfall Ooss), and the stronger the incentive to raise (cut) investment
in reaction to the short-term profitability rise (decline). Three, intertemporal substitutability in
consumption and investment - with the latter measured by (the inverse of) the slope of marginal
installation costs -, which have mutually opposing influences on the saving-investment balance: higher
consumption substitutability amplifies the saving response to temporary terms of trade shocks, making
it more likely that a windfall will cause a short-term surplus and a gain will cause a deficit. Conversely,
higher investment substitutability (i.e., lower installation costs) magnifies the investment response to
temporary profitability changes, which tends to result in a short-term investment boom (and a likely
current account deterioration) in response to a transitory windfall, and a slump (and current account
surplus) in response to a temporary loss.



23
Rererencesl
Brock, P. and S. Turnovsky (1993): "The Dependent Economy Model with both Traded and Non-Traded
Capital Goods," MM  Working Paper Number 4500.
Bruno. M. (1982): "Adjustment and Structural Change Under Supply Shocks", Scandinavian Journal of
Economics 84, p. 199-221.
Buiter, W. (1984):  "Saddlepoint Problems in Continuous-Time Rational Expectations Models,"
Econometrica 52, p. 665-80.
Cha, B. (1993): "Dynamic Effects of a Terms-of-Trade Shock on a Small Open Economy," Economics
Letters 43, p. 205-210.
Cuddington, J. and C. Urzua (1989): "Trends and Cycles in the Net Barter Terms of Trade: a New
Approach," Economic Journal 99, p. 426-42.
Dornbusch, R. (1983): "Real Interest Rates, Home Goods, and Optimal External Borrowing," Journal
-of Political Economy 91, p. 141-153.
Gavin, M. (1990): "Structural Adjustment to a Terms of Trade Disturbance: the Role of Relative Prices,"
Journal-of International-Economics 28, p.217-43.
(1992a): "Income Effects of Adjustment to a Terms-of Trade Disturbance and the Demand for
Adjustment Finance," Journal of Development Economics 37, p. 127-153.
_ (1992b): "Monetary Policy, Exchange Rates and Investment in a Keynesian Economy," Journal
of International Money and Finance 11, p. 145-161.
Harberger, A. (1950): "Currency Depreciation, Income and the Balance of Trade," Journal of Political
Economy 58, p.47-60.
Hayashi, F. and T. Inoue (1991): "The Relation Between Firm Growth and Q with Multiple Capital
Goods: Theory and Evidence from Panel Data onJapanese Firms," Econometrica 59, p. 731-753.
Laursen, S. and L. Metzler (1950): "Flexible Exchange Rates and the Theory of Employment," Review
of Economics and Statistics 32, p. 281-299.
Matsuyama, K. (1988): "Terms of Trade, Factor Intensities and the Current Account in a Life-Cycle
Model," Review of Economic Studies 55, p. 247-262.
Mendoza, E. (1992): "The Terms of Trade and Economic Fluctuations," mimeo, International Monetary
Fund.
Murphy, R. (1992): "TheTerms of Trade, Investment and the CurrentAccount," Joumal of Intenational
Economic Integration, p. 58-79.



14
I II,qI 1,1't,  M       l''lVp 11 "9    Ap 'iep        '  SGwi;rIulln,J    owl     I    II   N 'III   ',l liliq   III  IsIilt'   Iq   l1ii'  i  I   Imtell  N'liIll'rl'ti
'1"  (jIlatlllll    v  inut  Intltt   ull   I!c     ul     rnle:11h,  )'1 Ill
Il P  Izt        lit 'I IIP II II#I I[I   I II '1 Slfl - III IIIIII II 1|11 1111  it 1111|11811fiI   '    I ml   Alt   m  MI %|11,`J!iItIl
hilellIiI      ilt l ut   1 Mualtey  luti'd  I lItIiiUet    l ., p    I      14 t'
';ut Ii:, 1            tI Plll I    'l"   I 'Irl I glit Ar'-autlul f hll          AliIir eii               lItili   A lqlIlltn i  iIIIf lii  lI 11' 1'l  / liq, '' ttitkIin  I'Ill'ilieln
ti   l      iIltllmnic  A tiivity   it  'Atl  )filB
';pg11   1'  1111(1s      II InivqkI1 ll'dy                ''III    ` P1,r liii ulIhII II r 1    lrginn ci lv    i   rule itfind I        'fil' lil lil Ar ir nilm llims    it lIt'
r - nutilititiilgru, e'  lit,   Illl    l .  111nell MrivItl  Ik'l';,"  jUtillill til  InlelinIItI  llill I                     a     k      Ri  ,I 'p))1 'W Itl
'fri9 v'i'11,  I    it'Ill,')   "A  niilr'lilit III t-ill  Il'slnipi' ?1 sle' I fi l,nilp,pt   mIII I                 lii' I I )i'IIl nli ni-  el IInIvrqine'git, "  p111pet'i
11e"4g     iir,41 l  el  lii' X   I Will Aii    llsgriIis;;  N'lrlIip.i t III' Ilr e,iiitIi                    It  irleI
1(114 It ,  '  '1 |ltnl I hesiselq 11111e111e' 1l. Iliii  Itel I 'xcliiiiij 1tliai, fiiiii  te   I 'ilI t             ipill Ai'i iiiiil'"  Wtilill llnills
t'el lsti   I'  Win ) k    1 hlig¶ I'llrnI     \I  il iti' 1111,1 ilir   lilil i             l           VtIl 11l           il    lilitl          lillull'k.4
mil   lUltil  (I  IJ il I,   "I 'l,                   p W'IPi itii    Iltl  thi'  Id   nlU   l ll"   I     'lttl-i        A-iiiii'i,   Utl  e   I? Al nil  .I In vif i uti ii  Imm lu
111111  A     It lis,Iii      Jii     li U ll U  lilt' 11e I       .Inn iii iauli ' i niitl  alit'  i ni                        al1
usW  ineisiq l        o   1w 1')1)   "5t               II         llti       Iit i im    the' I   ' l' liii   u        n  Se'isn  ",  13w  upelI   ha
Rrtewlv I? r1 111 )tIh



*~~~~~~                                                                     ~~                 ~    ~~~~~~          ~ ~~~~~~~~~ I_ .I  .  *  ,        .      . --   d. =  F. T..;|-,_-. MIs  6.%;  WM ,i 7r a   UYUU_pr.
I;~~      ~~~ '    1 1' 
|~~~~~~         *.                          I =                    ii             I' l     , 
*~! in«                                  1 .  -                                                it       !q
' !  ; v            |~      ~~~      ~~~~~~~~ ' i !   I                  I          l,  
II. I
I                            -  
: | X ! : 4 II   1 '              :        I:



26
The sign of this expression is given by the term in square brackets; the latter is clearly increasing in T -
- the duration of the shock - and in (1-sr) - the import content of investment. Note also that the larger
the adjustment cost parameter I, the smaller j and hence the more likely is the term in brackets to be
negative, leading to a short-run decline in invesunent.
2. 7he response of consumpyion to a temporary shock
To find the trajectory of consumption, it is necessary first to compute non-financial wealth. From
(13) in the text, WM  = TrOY(K()/r; thus, from (6') we have:
W(t) = fe  o  [7c IY(K(s))-prVi)(s)] ds + e-' 71 ()
Integrating using the same approximation as in fn. 14 in the text, we find
WV)   ICIY(K(t)) + c')YK() -)
Replacing this expression into (7) and evaluating the result at t=O, we obtain the expression for C, given
in the text.



Figure 1
Equilibrium dynamics
Q    Q
K~~~=                   K
K               K.
A A
I            A
I             K



Figure 2
A permanent tenns of trade improvement
Q         S
Q           ,
q!
K'~~~~~~~~~tK
EC                K
A
h8 ---___
I    I
I    I    \
K     K.          K
.~~



Figure 3
A trausitoy teTms of trade improvement
(a)                          (b)
Q 
So 1X  }X-                           El
Es
o.)  _____t___%  ~~Pt)  -__-_---    s,
so   R                     so
Ks K      K              KT e 
A   A                      A   A'
A~
AT
As 
AT …-i- -i
I                             A~~~~~~~~ 
Ks KT      KKT Ka                    K
0      T       Tim         0      T       r



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