The Expectations Augmented Phillips Curve Postulates
?P = ? - $\bar { u }$

question 46

Essay

The expectations augmented Phillips curve postulates
?p = ? - f (u - $\bar { u }$ ),
where ?p is the actual inflation rate, ? is the expected inflation rate, and u is the unemployment rate, with "-" indicating equilibrium (the NAIRU - Non-Accelerating Inflation Rate of Unemployment). Under the assumption of static expectations (? = ?p_-1), 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
$\begin{array}{|c|c|c|c|}\hline & \begin{array}{c}(u-\bar{u})>0 \\(Y=0)\end{array} & \begin{array}{c}(u-\bar{u}) \geq 0 \\(Y=1)\end{array} & \text { Total } \\\hline \begin{array}{c}\Delta p-\Delta p-1>0 \\(X=0)\end{array} & 0.156 & 0.383 & 0.539 \\\hline \begin{array}{c}\Delta p-\Delta p-1 \leq 0 \\(X=1)\end{array} & 0.297 & 0.164 & 0.461 \\\hline \text { Total } & 0.453 & 0.547 & 1.00 \\\hline\end{array}$
(a)Compute E(Y)and E(X), and interpret both numbers.
(b)Calculate E(Y $\mid X$ = 1)and E(Y $\mid X$ = 0). 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? Given that the two means are different, is this sufficient to assume that the two variables are independent?
(c)What is the probability of inflation to increase if there is positive cyclical unemployment? Negative cyclical unemployment?
(d)You randomly select one of the 59 quarters when there was positive cyclical unemployment ((u - $\bar { u }$ )> 0). What is the probability there was decelerating inflation during that quarter?

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Definitions:

Z Lines

Positions within muscle fibers that mark the boundaries of sarcomeres, playing a critical role in muscle contraction by anchoring actin filaments.

I Bands

The light-appearing regions of a sarcomere in striated muscle fibers, primarily composed of thin actin filaments.

Zones of Overlap

In muscle physiology, refers to the regions within a sarcomere where actin and myosin filaments overlap, crucial for muscle contraction.

Brevis

Refers to a muscle that is short in length, commonly used in anatomical names of muscles that are shorter than a nearby muscle (e.g., Flexor Pollicis Brevis).