ps1_sol-1 - Introduction to Econometrics Professor Alexei...

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Introduction to Econometrics Professor Alexei Onastki Problem Set 1 – September 23 Problem 1) [ Stock and Watson 2.1 ] (a) Probability distribution function for Y Outcome (number of heads) Y = 0 Y = 1 Y = 2 probability 0.25 0.50 0.25 (b) Cumulative probability distribution function for Y Outcome (number of heads) Y < 0 0 Y < 1 1 Y < 2 Y 2 Probability 0 0.25 0.75 1.0 (c) = ( ) (0 0.25) (1 0.50) (2 0.25) 1.00 Y EY μ = Using Key Concept 2.3: and 22 var( ) ( ) [ ( )] , YE Y E Y =− 2 2 (1 0.50) (2 0.25) = ( ) (0 0.25) 1.50 so that 2 var( ) ( ) [ ( )] 1.50 (1.00) 0.50. Y E Y = = Problem 2) [ Stock and Watson 2.6 ] The table shows that Pr ( 0, 0) 0 045, XY == = . Pr ( 0, 1) 0 709, = . = . = . Pr ( 1, 0) 0 005, Pr ( 0 241, Pr ( 0) 0 754, X . = =. 0 246, Pr( X 0) 0 Y 050, . 0 950. Y (a) × = + × = =×. +×. =. . () 0 P r ( 0 ) 1P r ( 1 ) 0 0 050 1 0 950 0 950 Y Y Y
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(b) (unemployed) Unemployment Rate (labor force) Pr( 0) 0 050 1 0 950 1 ( ) # # YE = Y = == . =− . (c) Calculate the conditional probabilities first: Pr ( 0, 0) 0 045 Pr ( 0| 0) 0 0597, Pr ( 0) 0 754 XY YX X = =. = = = . Pr ( 1) 0 709 Pr ( 1| 0) 0 9403, Pr ( 0) 0 754 X = = = = . Pr ( 1, 0) 0 005 Pr ( 0| 0 0203, Pr ( 0 246 X = = = = . Pr ( 0 241 Pr ( 0 9797 Pr ( 0 246 X = = = = . . The conditional expectations are ( | 0 Pr ( 1 Pr ( 0 0 0203 1 0 9797 0 9797, ( | 0) 0 Pr( 0| 0) 1 Pr( 0) 0 0 0597 1 0 9403 0 9403 EYX Y X Y X Y X Y X = = ×= = + = = ×. +×. ==× = =+ × = = =×. . (d) Use the solution to part (b), Unemployment rate for college grads 1 ( | 1 0.9797 0.0203.
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This note was uploaded on 12/20/2009 for the course ECON 1300 taught by Professor Natski during the Fall '09 term at Columbia.

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ps1_sol-1 - Introduction to Econometrics Professor Alexei...

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