Using Lewis’ Two-Sector Model, explain why Kuznets’ hypothesis on income-per- capita and Gini can have inverted U-shape.

In economics we are often faced with causal problems where the endogeneity arises because of simultaneity. A classic example is that if you are interested in estimating a demand curve, the issue is what you observe in the data are equli- birum and prices and quantity which is not only a function of demand but also a function of supply. In this excercise we will generalize the problem of simultaneity bias. Consider a situation where we are interested in the effect of Ti on Yi, i.e. obtaining a consistent estimate of α. But Yi also effects Ti. Let Xi be some exogenous covariates affecting both Yi and Ti. Let us imagine you have an exogenous variable Z which only effects Ti but does not directly effect Yi. In particular, consider the following structural equations: Yi = αTi+Xi′β+ui (1) Ti = ρYi+Xi′γ+Ziδ+νi (2) where E(ui | Xi,Zi) = 0 and E(vi | Xi,Zi) = 0 (a)  Show why you cannot you use OLS to estimate α consistently in model 1? (b)  Solve for the reduced form equation for Ti…

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The Excel file (Forecasting Assignment Data) contains quarterly motorcycle shipments for Harley-Davidson from 2000 through 2006. Forecast Harley-Davidson quarterly motorcycle shipments for 2007 using 1) Holt’s Method  2) Winter’s Method 3) Linear Trend Model  4) Quadratic Trend Model  5) Quadratic Trend with Seasonal Indices Model  In addition, make a recommendation of which forecasting method you think Harley-Davidson should use and why. Year Quarter Period DemandAt 2000 1 1 49,057   2 2 53,329   3 3 48,077   4 4 54,129 2001 1 5 54,154   2 6 60,161   3 7 56,611   4 8 63,535 2002 1 9 64,669   2 10 65,540   3 11 67,474   4 12 65,970 2003 1 13 70,608   2 14 76,025   3 15 67,458   4 16 77,056 2004 1 17 74,090   2 18 82,034   3 19 80,578   4 20 80,587 2005 1 21 76,716   2 22 77,128   3 23 87,585   4 24 87,588 2006 1 25 79,506   2 26 79,796   3 27 97,046   4 28 92,848