Exercise 6.2

Interest-Rate Shocks, Investment, And the Trade Balance

⬅ Return

Problem

Consider a two-period, small open economy populated by a large number of households with preferences given by

\[ \ln c_1 +\ln c_2, \]

where \(c_1\) and \(c_2\) denote consumption in periods \(1\) and \(2\), respectively, and \(\ln\) denotes the natural logarithm. Households start period 1 with a zero net asset position. They have no endowments in either period, but can produce goods in period 2 by operating the technology

\[ y_2 = A\sqrt{i_1}, \]

where \(y_2\) denotes output in period 2, \(A >0\) is a productivity factor, and \(i_1\) denotes investment in period 1. In period 1, households can participate in the international financial market, where the interest rate is \(r\). They are subject to a no-Ponzi-game constraint of the form \(d_2\le0\), where \(d_t\), for \(t=1,2\), denotes one-period debt assumed in period \(t\) and maturing in period \(t+1\).

  1. Write down the household’s budget constraints in periods 1 and 2.

  2. Derive the household’s intertemporal budget constraint.

  3. State the household’s maximization problem.

  4. Compute the equilibrium values of consumption, investment, the trade balance, the current account, and external debt in periods 1 and 2.

  5. Suppose now that the interest rate increases to \(r'>r\). Characterize the effect of this shock on investment and the trade balance in period 1. Is it qualitatively in line with the related SVAR evidence examined in this chapter? Explain.

  6. Suppose that in period 1 agents learn that a positive productivity shock elevates \(A\) to \(A'>A\). Analyze the effect of this innovation on the equilibrium levels of investment and the trade balance in period 1. How does this effect relate to the SVAR evidence studied in this chapter?

Answer

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