Question

Introductory Econometrics, please help!

Question 3 (22.5) The expectations augmented Phillips curve postulates where ΔΡ is the actual inflation rate, π is the expected inflation rate, and u is the unemployment rate, with "ư, indicating equilibrium (the NAIRU-Non-Accelerating Inflation Rate of Unemployment). Under the assumption of static expectations (7-4, ), i.e. that you expect this period's inflation rate to hold for the next period (the sun shines today, it will shine tomorrow"), then the prediction is that inflation will accelerate if the unemployment rate is below its equilibrium level. The accompanying table below displays information on accelerating annual inflation and unemployment rate differences from the equilibrium rate (cyclical unemployment), where the latter is approximated by a five-year moving average. You think of this data as a population which you want to describe, rather than a sample from which you want to infer behavior of a larger population. The data is collected from United States quarterly data for the period 1964:1 to 1995:4 Joint Distribution of Accelerating Inflation and Cyclical Unemployment, 1964:1-1995:4 (u -u)>0 Total (Y=1) 0.383 0.156 0.297 0.164 Total 1.00 (a) (b) (c) Compute the marginal Probability of X and Y and sketch a graph for each. Compute E(Y) and E(X), and interpret both numbers in this particular example.(5) Calculate E(Y Y = 1) and E(Y | X = 0). Interpret your results in this particular example (7.5) Bonus (5 points):If there was independence between cyclical unemployment and acceleration in the inflation rate, what would you expect the relationship between the two expected values to be? (d)What is the probability of inflation to increase if there is positive cyclical unemployment? Negative cyclical unemployment?

Answer 1

Answeŕ:

It will makes you happy..i hope it will helps you.

solutions of the followings parts are given below:

Ex = sigma_x x P (x = x) = 0 times P (x = 0) + 1 times P (x = 1) = 0 times 0.539 + 1 times 0.461 = 0.461 Ey = sigma_y y P (y = y) = 0.547 expected inflation rate over period 1966: 1 to 1995: 2 is 0.461 & expected unemployment over that period E (y Vertical-bar x = 1) = sigma_y P (y = y Vertical-bar x = 1) = 0 times P (y = 0, x = 1)/P (x = 1) + 1 times P (y = 1, x = 1)/P (x = 1) = 1 times 0.164/0.461 = 0.3557 E (y Vertical-bar x = 0) = 1 times 0.383/0.539 = 0.7106 if there was independence between cyclical unemployment & acceleration in inflation rate then E (y Vertical-bar x = 1) = E (y Vertical-bar x = 0) in this case y take values 0, 1 so if we have E (y Vertical-bar x = 1) notequalto E (y Vertical-bar x = 0)