Maurice Tutor

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Category > Management Posted 15 Jan 2018 My Price 8.00

Convergence regressions

Convergence regressions.

(a) Convergence. Let yi denote log output per worker in country i. Suppose all countries have the same balanced-growth-path level of log income per worker, y∗. Suppose also that yi evolves according to  .

(i) What is yi(t) as a function of yi(0), y∗, λ, and t ?

ii) Suppose that yi(t) in fact equals the expression you derived in part (i) plus a mean-zero random disturbance that is uncorrelated with yi(0). Consider a cross-country growth regression of the form yi(t) − yi(0) = α + βyi(0) + εi . What is the relation between β, the coefficient on yi(0) in the regression, and λ, the speed of convergence? (Hint: For a university OLS regression, the coefficient on the right-hand-side variable equals the covariance between the right-hand-side and left-hand-side variables divided by the variance of the right-hand side variable.) Given this, how could you estimate λ from an estimate of β?

(iii) If β in part (ii) is negative (so that rich countries on average grow less than poor countries), is Var(yi(t)) necessarily less than Var (yi(0)), so that the cross-country variance of income is falling? Explain. If β is positive, is Var(yi(t)) necessarily more than Var(yi(0))? Explain.

Xi , ui , and ei are uncorrelated with one another. Consider a cross-country growth regression of the form yi(t) − yi(0) = α+ βyi(0) + εi . Suppose one attempts to infer λ from the estimate of β using the formula in part (a)(ii). Will this lead to a correct estimate of λ, an overestimate, or an underestimate?

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Maurice Tutor
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Status NEW Posted 15 Jan 2018 09:01 PM My Price 8.00

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