The safe stationary state

We compute the stationary state of equations (4.13) under the assumption that the borrowing constraint does not bind in the tradable sector. We will show later that this is indeed the case. We introduce a reduced parameter ψ = _R∗^1+g(1+τ). The parameter ψ increases with financial openness (i.e. it decreases withτ), technological progress (g), and the amount of international liquidity (i.e. it decreases with R^∗).¹¹ To derive the equations determining the safe stationary state, we use the fact that δψp^Hy^N = i^N and δψy^T =i^T. The financial structure of the intermediate sectors is given by

w^N = (1−γ)(¹_δ −1) approximately equal to the difference between the growth rate and the domestic interest rate.

Long-run dynamics Then, the investment expenditures of sector N, the real exchange rate, and the savings of households are given by

i^N = a^N To complete the description, the relative investment level in both sectors follows from The important equation is (4.14f), which is the long-run version of the market clearing condition for N goods. It determines the relative size of the non-tradable sector ^I_I^NT = ⁱ_i^NT, that is, the allocation of capital between the non-tradable and the tradable sectors. Once known, this ratio completely determines the stationary state and the value of all variables can be easily deduced from it.¹² Note that, from equations (4.14a), W^N/W^T is equal to I^N/I^T in the safe stationary state, and thatY^N/Y^T is increasing with I^N/I^T (with the elasticityδ) so that we can refer without ambiguity toI^N/I^T as the sectoral structure of the economy.

Sectoral structure in the long run

How does the economy adjust to an exogenous permanent shock? In the short run productive capacities are predetermined in the intermediate sectors and the market equilibrium has to be achieved by a change in the real exchange

12The stationary real exchange rate and the investment expenditures i^N are deduced from ⁱ_i^NT by (4.14d) and (4.14c). Then, internal funds and debt levels are given by equa-tions (4.14a) and (4.14b) and savings from households by (4.14e).

rate alone (see the within-period equilibrium in section 4.3). In the long run, on the contrary, the sectoral structure itself can change and thus accommodate a permanent shock. Part of the adjustment still comes from the real exchange rate whose value in the stationary state depends on the sectoral structure I^N/I^T.¹³ Here, we are mainly interested in the way the economy adjusts to a change in the external financing conditions, i.e. to a shock in the domestic interest rate R^D. Such a shock can reflect both a change in the amount of available international liquidity (i.e. a change inR^∗) or a change in the degree of financial openness (i.e. a change in τ).

Let us studyI^N/I^T as a function ofψ. The functionh(ψ), defined by equa-tion (4.14g), is continuous, positive, and U-shaped on the interval (a,+∞), whereais the maximum value of (1−γ) and 1 +_s(1−α)^α −1

. Therefore, as the left-hand side of equation (4.14f) is strictly increasing withI^N/I^T, the sectoral structure I^N/I^T is also a U-shaped function ofψ on the relevant interval. We plot it in figure 4.3, calibrating the parameters with data from Argentina in the nineteen-nineties (see appendix D.6 for details on the calibration). The ψ-axis starts with ψ =ψ^A= ^1+g_RA, where R^A is the autarchic interest rate (see appendix D.4 for its derivation).

Suppose that the economy is initially in the autarchic stationary state ψ = ψ^A and the capital account is liberalized so that τ diminishes and ψ increases. If the financial opening is mild and ψ does not increase too much, the relative size of the non-tradable sector is smaller in the new stationary state and there is a real depreciation in the long run. If on the contrary it is large enough, capital is reallocated toward the non-tradable sector in the long run and the stationary real exchange rate appreciates.

To get the intuition behind this it is useful to discuss the case of zero household savings (β = 0). Then, in the closed economy (ψ =ψ^A= ^1−γ_δ ) firms have zero debt and finance all their investment expenditures by using their internal funds. When the economy opens to capital inflows, entrepreneurs issue debt abroad provided that R^D < R^A. This has two opposite effects on the demand for non-tradable goods. On the one hand, it allows domestic entrepreneurs to invest more, increasing the demand for N goods. On the other hand, entrepreneurs have to pay their debt back, which diminishes both internal funds and dividends (in relative terms) and leads to a decrease in investment and consumption. The net effect on the demand for N goods in

13Note that the long-run real exchange rate also depends on the ratio of sectoral produc-tivities, a usual Balassa-Samuelson effect. Cf. equation (4.14d).

Long-run dynamics

0.95 0.96 0.97 0.98 0.99 1.00 1.01

IN IT

ψ

Figure 4.3: Sectoral structure in the safe stationary state: ^I_I^NT is plotted againstψ on the interval

ψ^A,(1−γ)[1 +λ(¹_δ −1)]

, for α = 48%, µ = 46.22%, η = 49%, γ = 11%, δ= 0.947,β = 0.053, andλ= 2.5.

the stationary state is given by ηψ(b^N +b^T)

When ψ < ^{µγ+η(1−γ)}_η capital outflows that pay back the external debt reduce more the demand for N goods than new capital inflows increase it. This induces a shift of resources from the non-tradable sector to the tradable sector.

On the contrary whenψ > ^{µγ+η(1−γ}_η ⁾ the net effect on the demand for N goods is positive and capital is reallocated to sector N in the long run.¹⁴ When ψ = ^µγ+η(1_η ^−γ) the ratio I^N/I^T is exactly equal to its stationary value in the closed economy.

14The mechanism described here is similar to the so-called “Dutch disease” phenomenon.

See Kalantzis (2005) and chapter 5 for a model specifically relying on this effect.

Financial structure in the long run

The financial structure of firms, described by the ratio Wⁱ/Πⁱ, depends onψ in an unambiguous way. From equations (4.14a) and (4.14b) we have

Bⁱ

Πⁱ = δ 1−δ

1− 1−γ δψ

, i=N, T.

The lower the domestic interest rate R^D, the higher ψ, and the higher the ratio ^B_Πⁱi. A decrease in the domestic interest rate always leads to a more leveraged financial structure in the long run.

Restrictions on ψ

We have to impose some constraints on ψ to insure the existence of a safe stationary state with good properties.

To begin with, equations (4.14a) and (4.14b) imply that internal funds and debt levels only reach a stationary state when ψ >(1−γ).

Then, we want entrepreneurs to be net debtors in the stationary state.

Therefore, we need ψ ≥ ^1−γ_δ .

Another constraint is that the definition of a safe equilibrium path requires the economy to be in the high equilibriumHin each period. The high equilib-rium is characterized by the fact that the borrowing constraint does not bind for N firms. Therefore, the safe stationary state only exists ifi^N ≤λw^N. This is the case as long as ψ ≤ψ⁺= (1−γ)[1 +λ(¹_δ−1)]. Under this assumption sector T is not constrained in the steady state either.

Lastly, the ratio I^N/I^T does not converge to a positive value when h(ψ)≥1. We know thath(ψ)−→+∞whenψ tends toa⁺ or to +∞and we can easily check that h(1) < 1. Therefore, there exists ψ^min and ψ^max, with a < ψ^min < 1 < ψ^max, such that h(ψ) < 1 for all ψ ∈ (ψ^min, ψ^max). More precisely,ψ^min andψ^maxare zeros of the denominator ofI^N/I^T andW^N/W^T. Let us make a mild assumption on the saving rate s.

Assumption 4.3.

s(1−α) α

δ 1−γ −1

< 1−µγ−η(1−γ) 1−η(1−γ)

Long-run dynamics This assumption is always satisfied whenδ <1−γ. When not, it sets an upper limit on the saving rate s= _1+β^β . Under this assumption, we can show that ^1−γ_δ > aand h(^1−γ_δ )<1. Therefore, we haveψ^min < ^1−γ_δ .

To sum it up we impose the following restriction on ψ.

1−γ

δ ≤ψ ≤min(ψ⁺, ψ^max)