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Reviving the Salter-Swan Small Open Economy Model∗
Stephanie Schmitt-Groh´e†^ Mart´ın Uribe‡
July 3, 2020
Abstract This paper provides microfoundations to the Salter-Swan policy framework, a graphical apparatus designed to ascertain the exchange-rate and fiscal stance of a policymaker with internal and external economic targets. The environment is an infinite-horizon small open economy producing tradable and nontradable goods that takes world prices and world interest rates as given and is populated by optimizing households and firms. The economy is subject to terms of trade, interest rate, and discount factor shocks. The internal target of the government is the unemployment rate and the external target is the current account. Downward nominal wage rigidity and financial frictions serve as the rationale for meaningful policy intervention.
JEL classification: F41. Keywords: Internal Balance, External Balance, Small Open Economy, Salter Swan dia- gram, exchange rate policy, fiscal policy, nontradable goods
∗We thank Jeffrey Frankel for commissioning this work for the 2020 ISOM conference. We thank for comments Jeffrey Frankel, Tommaso Monacelli and participants at the 2020 ISOM conference. Ken Teoh provided excellent research assistance. †
‡Columbia University, CEPR, and NBER. E-mail: stephanie.schmittgrohe@columbia.edu. Columbia University and NBER. E-mail: martin.uribe@columbia.edu.
1 Introduction
This paper provides microfoundations to the Salter-Swan policy framework. The Salter- Swan policy framework is a graphical apparatus for policy analysis in small open economies. In this apparatus, the targets of the policy maker are the internal and the external balance of the country. Internal balance means that the economy achieves full employment and price stability. External balance means that the country runs neither excessive current account deficits nor large current account surpluses. The instruments available to the policymaker are the exchange rate and fiscal policy. The theoretical framework underlying the Salter-Swan policy theory is the tradable and nontradable goods model (also known as the Australian or dependent economy model) in the tradition of Swan (1955), Meade (1956), Salter (1959), Corden (1960), and Dornbusch (1974).^1 The key insight of the tradable and nontradable goods model is the distinction between adjustment in aggregate demand and adjustment in its composition, the so called expenditure switch, when the economy is buffeted by exogenous aggregate disturbances, and the pivotal role played by the relative price of nontradables in facilitating the expenditure switch. The following example illustrates the adjustment mechanism in the tradable and non- tradable goods model: Suppose the country interest rate premium increases. This generates a contraction in domestic absorption as households and firms substitute future for current spending. Given the relative price of nontradables in terms of tradables (the real exchange rate), the demand for tradables and nontradables falls. The increased gap between tradable output and tradable absorption can be exported. However, the increased gap between supply and demand of nontradables cannot be exported by definition. Thus, market clearing in the nontradable sector requires a decline in the relative price of nontradables. The fall in the relative price of nontradables causes a re-composition of aggregate expenditure away from tradables and toward nontradables and a re-composition of aggregate output in the opposite direction. In the adjustment mechanism invoked by the tradable and nontradable goods model, the terms of trade (the relative price of exportables in terms of importables) plays no role. In fact, the model assumes that this variable is exogenous. Indeed, in the traditional international trade literature, this is the definition of a small open economy, one that can view the terms of trade as exogenous because it is too small to have any monopoly power. The insight that in a small open economy macroeconomic adjustment does not materialize through changes (^1) For a historical analysis of the development of the dependent economy model, see Metaxas and Weber (2016).
At the same time, the increase in tradable output has a positive income effect on tradable consumption, which tends to deteriorate the current account. However, the net effect is positive, because, as dictated by the intertemporal approach to the current account, the marginal propensity to consume out of current income is less than one. An increase in gov- ernment spending, by elevating domestic absorption, has a direct negative effect on the trade balance. But, indirectly, it also lowers domestic absorption via a negative wealth effect on consumption. The direct effect dominates, however, because, as mentioned, the marginal propensity to consume out of disposable income is small. The fact that devaluations and government spending have opposite effects on the current account implies that if the objec- tive of the government is to keep the current account at a given target level, then these two policy variables must move in the same directions. This prediction of the model gives rise to an external balance schedule like the one in the Salter-Swan policy framework. The intersection of the internal balance and the external balance schedules determines the desired policy mix for the nominal exchange rate and the level of government spending. At these values of the policy instruments, the current account and the level of employment achieve their respective target levels. The resulting apparatus allows for the analysis of the government policy reaction to internal and external aggregate disturbances. The contribution of the present paper is to derive the internal and external balance schedules of the Salter- Swan model as the outcome of a micro-founded dynamic general equilibrium model of a small open economy. One undesirable prediction of the Salter-Swan framework is that the government must respond to an exogenous increase in the costs of external funds with a fiscal expansion so as to avoid too large a current account surplus. In policy debates fiscal expansions are typically summoned to stimulate domestic demand and not for the sole purpose of lowering current account surpluses. This counterfactual implication of the Salter-Swan model is a consequence of the assumption that the government has an ad hoc fixed target for the current account balance. To overcome this limitation, in an extension, the paper adds an extra layer of microfoundations to the Salter-Swan model by introducing financial frictions in the form of a collateral constraint on external borrowing of the type often used in the sudden stop literature (Mendoza, 2002; Uribe, 2006; Korinek, 2011; Bianchi, 2011; Benigno et al., 2013 and 2016; Schmitt-Groh´e and Uribe, 2017 and 2020). In the presence of collateral constraints the external objective becomes one whereby the government dislikes current account deficits but does not mind current account surpluses. In this version of the model, an in the costs of external funds does not put the country off its external balance since sudden stops generate current account reversals even in the absence of government intervention. However, it does put it off its internal balance, since absent policy intervention, it causes
involuntary unemployment. A currency depreciation, by eroding real wages, turns out to be a sufficient instrument to restore internal balance. This paper is related to a literature in which the external and internal balance framework is derived in the context of models in which all goods are internationally tradable. In this class of models it is assumed that the economy is large enough to be able to alter its terms of trade through exchange rate and fiscal policy. An early contribution along these lines is Meade (1951) and a textbook treatment can be found in Caves, Frankel, and Jones (2007, Chapter 18). The emphasis of this line of research on the effects of policy on the terms of trade is relevant for large advanced economies in light of the empirical fact that for such economies movements in the real exchange rate materialize largely through movements in the relative price of internationally traded goods (Engel, 1999). The remainder of the paper is organized in nine sections. Section 2 presents the model. Section 3 characterizes the equilibrium. Sections 4 and 5 derive the internal balance and the external balance schedules, respectively. Section 6 analyzes the policy response to terms-of- trade shocks using the derived microfounded Salter-Swan diagram. Section 7 analyzes the policy response to interest rate shocks. Section 8 uses the new Salter-Swan framework to study how the policy response changes when external borrowing is subject to a collateral constraint. Section 9 characterizes the effects of a domestic demand shock taking the form of an increase in the subjective discount factor. Section 10 closes the paper with a discussion of the results.
2 The Model
Consider an open economy that produces and consumes tradable and nontradable goods. Suppose that the economy is small in the sense that it takes as given the foreign price of the tradable good and the world interest rate. In both sectors, output is assumed to be produced with labor. Also, labor is assumed to be perfectly mobile across sectors. Short-run adjustment is hindered by the presence of downward nominal wage rigidity, as in Schmitt- Groh´e and Uribe (2016). The government can affect the allocation of resources via fiscal and exchange-rate policy. These are the basic ingredients of the Salter-Swan model. For expositional convenience, we consider a perfect foresight economy that suffers a vari- ety of temporary domestic and external shocks, including terms-of-trade shocks, productivity shocks, and country-spread shocks. We assume that one period after a purely temporary shock wages adjust flexibly to ensure full employment.
and Φt denotes profits received from the ownership of firms. The law of one price holds for tradable goods, which is a key assumption of the Salter- Swan framework. This assumption is also empirically plausible for most countries, espe- cially since the emergence of the U.S. dollar as a dominant currency for invoicing of trade (Gopinath, et al., 2019). Letting P (^) tT ∗denote the world price of the tradable good expressed in foreign currency, we then have that
P (^) tT = EtP (^) tT ∗.
A second important characteristic of the Salter-Swan model is that the economy is small. This implies that P (^) tT ∗is exogenous to the domestic economy. For simplicity, we normalize it to unity, P (^) tT ∗= 1, which implies that the domestic price of the imported tradable good equals the nominal exchange rate, P (^) tT = Et.
Dividing the right- and left-hand sides of the sequential budget constraint by the nominal exchange rate, we can write
cTt + ptcNt + dt + τt = wtht + φt + (^) 1 +dt+1 r , (1)
where pt ≡ P (^) tN /Et denotes the relative price of nontradables in terms of tradables, wt ≡ Wt/Et denotes the real wage rate expressed in units of tradables, and τt and φt denote tax payments and profits also in units of tradables. The variable 1/pt is often referred to as the real exchange rate because it determines the relative price of a unit of consumption in the foreign country in units of consumption in the domestic country. The household chooses sequences {ct, cTt , cNt , dt+1}∞ t=0 to maximize its lifetime utility func- tion subject to its sequential budget constraint and to a no-Ponzi-game constraint of the form limt→∞(1 + r)−tdt ≤ 0. Because preferences are strictly increasing in consumption, at the optimum the no-Ponzi-game constraint holds with equality,
tlim→∞(1 +^ r)−tdt^ = 0.^ (2)
The first-order conditions associated with the household’s optimization problem are the budget constraint (2) and
pt = A^2 (c
Tt , cNt ) A 1 (cTt , cNt ) (3)
and (^) ( cTt+ cTt
)σ = β(1 + r). (4)
To avoid an inessential trend in consumption of tradables, we assume that the subjective and market discount rates are equal to each other,
β(1 + r) = 1.
This assumption and the Euler equation (4) imply that consumption of tradables is constant over time. So we can write cTt = cT^ ,
where cT^ is a constant to be determined in equilibrium.
2.2 Firms
Firms in the traded and nontraded sectors use labor as the sole input. The production technologies take the form ytT = ATt FT (hTt )
and yNt = ANt FN (hNt ), (5)
where yti, hit, Ait, and Fi, for i = T, N, denote output, labor input, a productivity shock, and the production function in the traded and nontraded sectors, respectively. The production functions are assumed to be increasing and strictly concave. The internationally traded output, ytT , is assumed to be exported at the price P (^) tX. We assume that the law of one price holds for the exported tradable good, that is,
P (^) tX = EtP (^) tX ∗,
where P (^) tX ∗denotes the international price of the exported tradable good expressed in foreign currency. The country is assumed to be a price taker in the market for the exported good. The country’s terms of trade, which we denote by pxt , is given by the ratio of export to import prices, that is,
pxt ≡ P^ tX P (^) tT^ =^
P t X∗ P (^) tT^ ∗^.
The country takes pxt as exogenous.
denote employment in period t, we have that ht must satisfy
ht ≤ ¯h.
Combining the sequential budget constraints of the government and the household, we have that external debt evolves according to
cTt + γgt + dt = pxt yTt + (^) 1 +dt+1 r.
The household is assumed to start period 0 without any debt, d 0 = 0. Then, substituting this expression repeatedly into itself and using the transversality condition (2) yields
cT^ = (^) 1 +r r
∑^ ∞
t=
1 + r
)t (pxt ytT − γgt). (10)
This expression says that each period domestic consumption of traded goods equals the annuity value of the stream of current and future expected disposable tradable income. It represents the backbone of the intertemporal approach to the current account.
3 Equilibrium
To fix ideas, consider the effects of a purely transitory deterioration in the terms-of-trade, pxt. (Since pxt and ATt are both exogenous and always appear multiplying each other, we could equivalently interpret the shock as a drop in labor productivity in the export sector, ATt .) Specifically, suppose that before period 0 the terms of trade were at a steady-state level pxss, and that in period 0 they unexpectedly drop to px^ < pxss. Suppose further that in period 1 pxt returns to its long-run value pxss and stays at that level thereafter. In period 0, agents understand that the fall in the terms of trade is purely transitory. Suppose that prior to period 0, the economy was in a steady state with full employment. Since there are no shocks after period 0 and the nominal wage is assumed to adjust flexibly when period 0 is over, we have that in period 1 the economy reaches a steady state with full employment. The focus of the analysis is the effect of the terms-of-trade deterioration on employment and the current account in period 0. To facilitate notation we drop the time subscript to denote values prevailing in period 0 and denote steady-state values after period 0 with the subscript ss. Recall that the nominal wage rate in period 0, W , is predetermined. This will be the source of imbalances when shocks hit the economy. We assume that government spending is nil before and after the shock, gt = 0, for t 6 = 0, and we normalize the productivity factors
in the traded and nontraded sectors to unity, ATt = ANt = 1, for all t. Combining the household’s optimality condition, (3), the firm’s optimality conditions (5)-(7), and the market clearing conditions, (8) and (9), in period 0, we obtain
p = A^2 (c
T (^) , FN (h − hT (^) ) − g) A 1 (cT^ , FN (h − hT^ ) − g)
p =
W/E
F (^) N′ (h − hT^ ),^ (12)
and pxF (^) T′ (hT^ ) = W/E. (13)
The intertemporal resource constraint (10) and the fact that the economy is in a full- employment steady state starting in period 1 imply that
cT^ + (^) 1 +γr r g = (^) 1 +r r pxFT (hT^ ) + (^) 1 +^1 r pxssFT (hTss). (14)
Finally, because the economy is in a full-employment steady state starting in period 1, we have that hTss is determined by the expression
A 2 (cT^ , FN (¯h − hTss)) A 1 (cT^ , FN (¯h − hTss)) =^
pxssF (^) T′ (hTss) F (^) N′ (¯h − hTss).^ (15)
Equilibrium conditions (11)-(15) form a system of five equations in five unknowns, cT^ , p, h, hT^ , and hTss, given the prices W and px, and the policy variables E and g. To ensure that labor demand in period 0 does not exceed labor supply in equilibrium, it must be the case that 0 < hT^ < h ≤ ¯h. Since we are considering an adverse shock, namely, a fall in px, which, absent a policy change would require a fall in nominal wages to achieve full employment, and since the nominal wage is assumed to be downwardly rigid, we take W to be predetermined.
4 Internal Balance
Because the aggregator function is concave and the production functions are increasing and concave, equation (15) implies that hTss is a strictly decreasing function of cT^ , which we write as hTss = HssT(c −T ).
Intuitively, because tradable and nontradable goods are normal goods, a higher steady-state level of tradable consumption must go hand-in-hand with higher consumption of nontrad-
Figure 1: The Demand for Labor Derived from the Demand for Goods
h
p
D(h; W/E −
, g
, px
Using equations (13) and (16) to eliminate hT^ and cT^ from equation (11) yields
p =
A 2
CT^ (W/E, γg, px^ ), FN
h − F (^) T′^ −^1
( W/E
px
− g
A 1
CT^ (W/E, γg, px^ ), FN
h − F (^) T′^ −^1
( W/E
px
− g
which we can write more compactly as
p = D(h −
; W/E
−
, g
, px
Figure 1 depicts this relationship in the space (h, p). The function D is a complex equilibrium condition, but it primarily captures the demand for labor derived from the demand for nontradable goods (with the second occurrence of the word ‘demand’ determining the use of the letter D in denominating the function): an increase in the relative price of nontradables, p, causes a reduction in the demand for nontradables, which, given the real wage, induces firms to cut the demand for labor. Consider now the intuition behind the negative sign underneath the real wage rate, W/E. As discuss earlier, an increase in real labor costs depresses both the demand for tradable goods, cT^ , and employment in the tradable sector, hT^. The former effect lowers the demand for nontradables, and the latter increases the supply of nontradables (because, holding constant h, a fall in hT^ implies an increase in hN^ ). Both effects put downward pressure on the price of nontradables.
The relationship between government spending, g, and the relative price of nontradables, p, holding constant h, is in principle ambiguous, but most likely positive. On the one hand, an increase in the public demand for nontradable goods reduces one for one the supply of nontradable goods disposable for private consumption, yN^ − g,—the second argument of the numerator and denominator of the right hand side of equation (18)—elevating the price of nontradables that clears the market. This is a direct effect. On the other hand, an increase in (nonproductive) government consumption makes households poorer, which reduces the demand for consumption goods,—the first argument of the numerator and denominator of the right hand side of equation (18)—thereby depressing the price of nontradables. This effect is indirect and, as we argue next, small. Recall that the crowding out effect of a tran- sitory increase in government spending on tradable consumption is given by the marginal propensity to consume (equation 17), which is less than r. Also, typically government spend- ing is concentrated on goods with a significant nontraded component, such as administrative services, education, and health, and not on tradable goods (small γ). Thus, the most likely scenario is one in which the partial derivative of the function D with respect to g is positive. For the remainder of the paper, we will assume that this is indeed the case. Finally, the function D(h; W/E, g, px^ ) is increasing in px. A terms of trade appreciation makes households richer, which boosts the demand for consumption and puts upward pres- sure on the relative price of nontradable consumption goods. Furthermore, a rise in the terms of trade drives up employment in the traded sector, reducing, holding constant total employment, the number of hours available for the production of nontradables. This in turn results in a reduction in the supply of nontradable goods, which requires an increase in the equilibrium relative price of nontradables. Now use equation (13) to eliminate hT^ from equilibrium condition (12). This yields
p = W/E F (^) N′
h − F (^) T′^ −^1
( W/E
px
which, in compact form, can be written as
p = S(h
; W/E
, px −
We denote this function S because it primarily reflects the demand for labor derived from the supply of nontradable goods. Figure 2 depicts the relationship between total employment, h, and the relative price of nontradables, p, implied by this function. Given the real wage, W/E, and the terms of trade, px, employment in the traded sector is fixed (equation (13)). Thus, an increase in total employment h must be fully allocated to the nontradable sector.
Figure 3: Equilibrium Determination of Employment and the Real Exchange Rate
h
p
D(h; W/E −
, g
, px
S(h; W/E
, px −
¯h
p^0 A
to this shock, the D and S schedules both shift to the left, as shown in Figure 4. The new equilibrium occurs at point B. The negative disturbance causes involuntary unemployment in the amount ¯h − h′. The reason is that because the nominal wage is downwardly rigid and the monetary authority keeps the nominal exchange rate fixed, the real wage stays at its pre-shock level, which causes firms in the traded sector to cut employment in response to the exogenous decline in the world price of the good they produce. In addition, at the pre-shock real wage and relative price of nontradables, firms in the nontraded sector are unwilling to hire the displaced workers. Inspection of equations (18) and (20) (the primitives of the schedules D and S, respectively) reveals that the shift in the D schedule is larger than the shift in the S schedule, so that, as shown in Figure 4, p falls (or the real exchange rate depreciates). Thus the dominant effect is that the negative terms-of-trade shock makes households poorer, inducing them to cut consumption, which in turn depresses the relative price of the nontraded good. Because of downward nominal wage rigidity and the central bank’s keeping the exchange rate unchanged, the real wage is unchanged. Facing lower prices and unchanged marginal costs, firms in the nontraded sector, like firms in the traded sector, cut employment. As a result of the negative terms-of-trade shock, the economy suffers involuntary unemployment. In a more realistic setting in which the terms of trade shock is persistent as opposed to purely temporary and nominal wages are downwardly rigid for more than one period, the absence of policy intervention would give rise to a protracted spell of elevated unemployment.
Figure 4: Equilibrium Response of Employment and the Real Exchange Rate to a Deterio- ration in the Terms of Trade
h
p
D(h; W/E −
, g
, px
D(h; W/E, g, px′ )
S(h; W/E
, px −
S(h; W/E, px′ )
¯h
p^0 p′
h′
A
B
Note. px′^ < px.
As time goes by, nominal wages would gradually decline reducing real labor costs and slowly restoring full employment. Graphically, this adjustment process would consist in a gradual shift of both the demand and the supply schedules to the right until their intersection takes place at ht = ¯h. Consider now the role of exchange-rate policy in restoring full employment. Figure 5 picks up from the equilibrium with unemployment following a deterioration in the terms of trade depicted in Figure 4. Prior to the devaluation, the economy is at point B, where unemployment equals h¯ − h′. Suppose that the government devalues the domestic currency from E to E′^ > E. This policy intervention causes the D schedule to shift up and the S schedule to shift down. The new equilibrium is at point C, where unemployment is lower (¯h − h′′^ < ¯h − h′). The intuition why a devaluation is expansionary is as follows: In the initial situation (point B), the real wage is too high to clear the labor market. Unemployment puts downward pressure on the real wage, but this variable is downwardly rigid due to the combination of nominal wage rigidity and a given exchange rate. The devaluation lowers the real wage fostering employment by firms in both the traded and the nontraded sectors. As Figure 5 is constructed, the economy continues to have involuntary unemployment after the devaluation. However, a sufficiently large devaluation would have restored full employment. Beyond this level, devaluations have no additional real effects and cause wage and price inflation.
Figure 6: Effect of an Increase in Government Spending on Employment and the Real Exchange Rate
h
p
D(h; W/E −
, g
, px′
D(h; W/E, g′^ , px′ )
S(h; W/E
, px′ −
¯h
p′
p′′
h′^ h′′
B
C
Note. g′^ > g.
the nontraded sector. Recall that employment in the traded sector depends only on the real wage and the terms of trade (equation 13), both of which are unchanged. Firms in the nontraded sector expand employment incentivized by an increase in the relative price of the good they produce, p. In turn, p increases because government spending puts pressure on the aggregate absorption of nontradables. The increase in the demand for labor brought about by the fiscal expansion does not result in nominal wage inflation, because, as the figure is drawn, the economy continues to suffer unemployment, h′′^ < ¯h. A sufficiently large fiscal stimulus, all other things equal, could create a demand for labor larger than ¯h, which would cause nominal wages to rise. Unlike in the classic IS-LM model, in the present model government spending crowds out private consumption. In fact, it crowds out both tradable and nontradable consumption. Tradable consumption falls because the higher taxes required to finance the elevation in public spending have a negative wealth effect. Nontradable consumption falls for the same reason and because of the increase in the relative price of nontradables. Comparing the exchange-rate policy and the fiscal policy responses to the unemployment
in developing countries (Miyamoto, Nguyen, and Sheremirov; 2019) and depreciation in advanced countries (Monacelli and Perotti, 2010; Ravn, Schmitt-Groh´e and Uribe, 2012).
caused by the deterioration in the terms of trade, we note that, while both policies are effective at reducing unemployment, the former induces a depreciation of the real exchange rate (a fall in p) and the latter an appreciation (an increase in p). Summing up, we have established that the equilibrium level of employment, given by the solution for h of the equilibrium condition
D(h; W/E, g, px^ ) = S(h; W/E, px)
depends positively on the nominal exchange rate, E, the level of government spending, g, and the terms of trade, px. We can write this equilibrium relationship as
h = H(E
, g
, px
To avoid clutter, we do not include W in this expression because throughout the analysis that follows the downward nominal wage rigidity is assumed to be binding. Consider now the government-spending and exchange-rate combinations, (g, E), that guarantee full employment, h = ¯h. This relationship is implicitly given by the equation
¯h = H(E, g; px).
Solving for E, we obtain E = I(g − ; px −
This is the microfounded version of the Internal Balance schedule in the Salter-Swan model. It is depicted in Figure 7 as a downward sloping relationship in the space (g, E). Because devaluations and increases in government spending both foster employment, the Internal Balance schedule is downward sloping. For pairs (g, E) below the Internal Balance schedule, the economy suffers from involuntary unemployment. For policy mixes above the schedule, there is full employment and further economic stimulus leads to excessive price and wage inflation. Consider now a terms-of-trade deterioration (a fall in px). This shock shifts the Internal Balance schedule up, as shown in Figure 8. This is because, holding policy constant, a terms-of-trade decline causes unemployment. As a result, for a given nominal exchange rate, the government needs to increase government spending to achieve full employment. Alternatively, for a given level of government spending, the government must devalue the currency to return to full employment.
