Exercise 6.1

Countercyclical Interest Rate Shocks

⬅ Return

Problem

Consider a two-period small open endowment economy. Household preferences are given by:

\[ \log c_1 + \log c_2, \]

where \(c_1\) and \(c_2\) denote consumption in periods 1 and 2, respectively. Let \(y_1\) and \(y_2\) denote the endowments in periods 1 and 2, respectively. Households enter period 1 with zero net foreign assets, \(d_0=0\). Assume free international capital mobility. The world interest rate is \(r^*\) and households 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 due in \(t+1\).

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

2. Derive the household’s intertemporal budget constraint.

3. Write down the household’s utility maximization problem.

4. Characterize the equilibrium allocation of consumption and the trade balance in periods 1 and 2.

5. Now assume that in period 1 the economy is hit by a negative (and purely temporary) endowment shock. Find the change consumption and the trade balance in period 1. Is the response of the trade balance in period 1 pro- or countercyclical. Explain your findings.

6. As documented earlier in this chapter, in emerging economies the country interest rate tends to be countercyclical. To reflect this regularity assume now that when \(y_1\) falls, \(r^*\) increases. Let \(\eta\equiv -\frac{d\ln(1+r^*)}{d\ln y_1}\) denote the elasticity of the gross interest rate with respect to the period-1 endowment. Find conditions, in terms of \(\eta\), \(y_1\), \(y_2\), and \(r^*\), that guarantee that consumption moves procyclically and the trade balance moves countercyclically in period 1 in response to a period-1 endowment shock. Provide an intuitive explanations for your findings.

Answer

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