Macro1_PS3

# Has a variance σ 2 θ explain intuitively what value

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Unformatted text preview: has a variance σ 2 θ . Explain intuitively what value would one expect for b (i.e whether b is biased downward or upward depending on the variance of θ ). Then use the de nition of the OLS estimator to prove your claim. iii) How do changes in k a ect your answer to the previous question ? What happens to b as k approaches 1 ? Explain intuitively. How would you use these results to investigate the pre- dictability of the spread depending on di erent monetary regimes ? iv) Give some historical examples of changes in monetary regimes. How would you use the pre- vious results to study theses events. 3 A two-country endowment model with two periods : in- troduction to the intertemporal interpretation of the cur- rent account Consider the pure endowment model, in which equilibrium holds when S 1 + S * 1 = 0 (respectively domestic and foreign saving at t=1). Home's utility function is U 1 = logC 1 + βlogC 2 Foreign has an analogous log utility function, with its consumption levels and time preference factor distinguished by asterisks. Governments consume no resources. 1- Explain why the condition S 1 + S * 1 = 0 is su cient for the general equilibrium. Write the budget constraints given that Home receives perishable endowments Y 1 and Y 2 in the two periods. Maximize the utility function under the budget constraint, nd the Euler equation and then show because we have data about the period t + 1 . The variable on the right hand side of the equation (the spread between both one and two period and time t) is relatively exogenous because the dependent variable is the spread between the two rates at two di erent period....
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