6. (Lecture 10) (13 points) Use the data in PHILLIPS for this exercise. As we mentioned in Lecture 7, instead of the static Phillips curve model, we can estimate an expectations-augmented Phillips curve of the form Ainft = Bo + Bjunem+ + et, where Ainft = inft - inft-1. i. (3 points) Estimate this equation by OLS and report the results in the usual form. In estimating this equation by OLS, we assumed that the supply shock, et, was uncorrelated with unem. If this is false, what can be said about the OLS estimator of B1? ii. (2 points) Suppose that et is unpredictable given all past information: E(etlinft-1, unemt-1, ... ) = 0. Explain why this makes unemt-1 a good IV candidate for unemt. iii. (3 points) Does unemt-1 satisfy the instrument relevance assumption? [Hint: You need to run a regression to answer this question.] iv . (5 points) Estimate the expectations augmented Phillips curve by 2SLS using unemt-1 as an IV for unem. Report the results in the usual form and compare them with the OLS estimates from (i).a. To calculate the average price per unit, we divide the total GDP by the number of units sold: Average price per unit = Total GDP f Number of units sold Average price per unit = $100,000,000 / 275,000 units Average price per unit = $363.64 b. To calculate the velocity of money, we use the equation: Velocity of money = GDP / Money Supply Velocity of money = $100,000,000 / $25,000,000 Velocity of money =4 MNow, projecting to the next year: i. The number of units that will be sold next year: Number of units = Current units * (1 + Growth rate) Number of units = 275,000 * (1 + 0.10) Number of units = 275,000 * 110 Number of units = 302,500 units ii. The expected GDP given the expected money supply increase: Expected GDP = Current GDP * (1+ Money supply growth rate) Expected GDP = $100,000,000 * (1+ 0.20) Expected GDP = $100,000,000 *1.20 Expected GDP = $120,000,000 iii. The implied price per unit next year: Implied price per unit = Expected GDP / Number of units Implied price per unit = $120,000,000 /302,500 units Implied price per unit = $396.69 iv. The implied rate of inflation as a result: Implied rate of inflation = (Implied price per unit - Current price per unit) / Current price per unit * 100% Implied rate of inflation = ($396.69 - $363.64) / $363.64 * 100% Implied rate of inflation = 9.07% v. The maximum amount the money supply could increase to maintain the government's 2% targeted inflation rate: Let's denote the maximum amount the money supply could increase as M. Using the quantity theory of money: Expected Inflation Rate = Money Supply Growth Rate - Real GDP Growth Rate 2% = M/ $25,000,000 - 10% 2% = M / $25,000,000 - 10% 2% = M/ $25,000,000 - 010 2% = M / $25,000,000 - $2,500,000 Now, solving for M: M = $25,000,000 - $2,500,000 M = $22,500,000 S0, the maximum amount the money supply could increase to maintain the government's 2% targeted inflation rate is $22,500,000