Suggested Solutions to Problem Set 8

Transcription

1 Suggested Solutions to Problem Set 8 Problem 1: a: The average unemployment rate from 1959 to 2002 is % 5.9%. b/c: 27 out of 43 years have a strictly negative sign for the product (π t π t 1 )(u t u n ), i.e. roughly 63%. This means weak evidence in favor of this version of the expectationaugmented Phillips curve. Year Change in Inflation Rate u-u_n Product Sign ,3-0,4-1, ,3 0,8-0, ,3-0,4-0, ,3-0,2 0, ,4-0,7-0, ,4-1,4-0, ,1-2, ,2-2,1-0, ,2-2,3-2, ,5-2,3-1, ,5-1,0-0, ,0 0, ,9-0,3 0, ,3-1,0-1, ,9-0,3-0, ,6 2,6 1, ,2 1,8-5, ,5 1,2 0, ,4 0,2 0, ,2-0,1-0, ,8 1,2 0, ,4 1,7 0, ,2 3,8-12, ,7-7, ,4 1,6-0, ,6 1,3-0, ,9 1,1-1, ,7 0,3 0, ,5-0,4-0, ,5-0,6-0, ,3 0, ,5 0,9-0, ,2 1,6-1, ,5 1,0 0, ,6 0,2-0, ,3 0, ,3-0,5 0, ,1-1,0 0, ,5-1,4 0, ,3-1,7-0, ,6-1,9-1, ,3-1,2-0, ,3-0,1 0,1 1 d: See the scatter plot on the next page. The slope of the trend line is approximately, 0.43, i.e. a = 0.43, i.e., yes, the line has a negative slope, as predicted by the Phillips curve. This trend line was computed as the best linear fit to the data. Hint (for future occasions): Excel allows you to automatically add a trend line to a diagram. Click on Diagram and then Add Trend Line. For this diagram a linear trend was chosen. 1

2 Another way to answer this question is to choose two points of the data, whose connecting line represents the data well. Two such points (the data points are marked in the scatter plot) may be from the years 1968: (u t u n, π t π t 1 ), = ( 2.3, 1.2) and 1983: (u t u n, π t π t 1 ), = (3.7, 2). The slope of the line connecting these points is given by: (π t π t 1 ) 1983 (π t π t 1 ) 1968 (u t u n ) 1983 (u t u n ) 1968 = = As can be seen, this eyeball value is close to the best fit value, US Phillips Curve 5,0 4,0 3,0 2,0-2,3, 1,2 1,0 π_tπ_t-1 0,0-3,0-2,0-1,0 0,0 1,0 2,0 3,0 4,0 5,0-1,0 y = -0,4292x + 0,0972-2,0 3,7; -2,0-3,0-4,0 u-u_n 2

3 Problem 2: a: The text discusses two main reasons for the flattening of the Phillips curve: Globalisation and increased credibility/competence of central banks. Globalisation leads to a diminishing price setting power on the part of U.S. firms, as well as reduced wage setting power on the part of U.S. workers: If it is easy to buy a German or a Japanese car, U.S. car makers cannot just raise their prices in response to wage increases, because U.S. customers would switch to foreign cars. This keeps inflation in check, even at low levels of unemployment. If central banks have become more successful at keeping inflation at bay, and workers believe that, then they will abstain from aggressive wage bargaining, so that the wageinflation spiral cannot even start. b: Why does the SRAS become flatter? To answer this question, we need the equation for the SRAS curve from lecture notes 6: P = (1 + β)p e (1 a + a Y N + z) = (1 + β)pe (1 a + z) + (1 + β)pe a Y. N From this equation you can see that the slope of the SRAS in (P, Y ) space is given (1+β)p by: e a. Hence, if a decreases, the SRAS becomes flatter. What are the effects of this N flattening on the changes of output and the price level caused by a decline in aggregate demand? Figure 1: Short Run Effects - Overview Flattening of the SRAS Curve and a Negative Shock to Aggregate Demand LRAS SRAS AD P AD* B2 A flatter SRAS B1 C The effects of SRAS becoming flatter are summarized in this figure. The short-run decline in output, caused by a downward shift in aggregate demand, is sharper. The price decline becomes smaller. The economy moves from A to B2, instead of from A to B1. In the extreme case of a horizontal SRAS, there would be no price response and a very sharp output decline. Y 3

4 c: Since the unemployment rate and output are inversely related, the increase in the unemployment rate becomes sharper. Recall from lecture notes 5 the equation that relates output and unemployment: Y = (1 u)n. Since β has not changed, the nominal wage must go in lock step with p, which means that the effect on w is also mitigated. Recall the price setting equation from lecture notes 5: p = (1 + β)w. The effect on the real wage is zero (β remains unaltered). The following table summarizes the short-run effects: Y P u w w P sharper decline smaller decline sharper increase smaller decline no effect d: What are the long-run effects? By assumption the LRAS has not changed. Since in the long-run (i) output is exclusively determined by the LRAS curve and (ii) the price level by the LRAS and AD* curve (point C) and (iii) none of these curves are affected by a change in a (for LRAS by assumption on z), the long-run effects of a change in aggregate demand are the same for different values of a. 4

5 Problem 3: a: A few of Milton Friedman s influential ideas in economics are: Challenged Keynesian view of government intervention. Claimed: that government governs best which governs least. Government intervention should only be allowed to control the supply of money. - Proposed the natural rate of unemployment and the idea that unemployment cannot be driven below a certain leven without producing inflationary pressures. Challenged the idea of a rigid tradeoff between unemployment and prices (Phillips curve). Predicted the joint increase of unemployment and prices in the 70s, a phenomenon later labeled stagflation. Proposed flexible exchange rates and open financial markets, once thought to be measures that would destabilize economies and international capital flows. Advocated the promotion of publicly-funded vouchers for students to attend private schools, a policy that has not been fully implemented to date. Introduced the idea of a negative income tax to eliminate poverty, what we call today the Earned Income Tax Credit. Proposed the permanent income hypothesis, the idea that people smooth their consumption based on their expected long-run earnings. b: Note that the quantity theory of money equation holds for every period t. In particular, Similarly, M t V t = P t Y t. (1) M t 1 V t 1 = P t 1 Y t 1. (2) Taking logs on both sides of equations (1) and (2), and subtracting the logged equation (2) from the logged equation (1), we obtain: (ln M t ln M t 1 ) + (ln V t ln V t 1 ) = (ln P t ln P t 1 ) + (ln Y t ln Y t 1 ). Each of the four subtractions in parentheses corresponds to the growth rates of money, velocity, prices, and output, respectively. Let us call the first one, the growth rate of money, m; let π denote inflation (the growth rate in the aggregate price level); and let g be the growth rate of real output. Since we are assuming that velocity is constant over time, ln V t = ln V t 1, so: π = m g. 5

6 c: To obtain money velocity, we multiply real GDP by the price level. This multiplication yields nominal GDP. We then divide nominal GDP by the narrow measure of money, M1, in each year. The results are shown in the table below under the column title Velocity using M1. We also calculate velocity using the alternate, broad measure of money, M2, and show the results in the next column titled Velocity using M2. If the quantity theory of money equation actually held, we would observe a constant velocity measure over time. At first glance, we see that velocity is not constant period after period, and we actually see a pronounced increase in velocity when using M1 as our relevant measure of money. When we look at velocity using M2, we see that velocity is relatively stable, although we do observe a slight increase in the last few years. What this suggests is that, no matter what definition of money we use, the quantity theory of money does not hold on a period-by-period basis (i.e., in the short-run). However, when we use the broad measure of money, in the long-run velocity seems to be relatively constant. To better assess whether the quantitative theory of money holds, we graph the velocity results using the two alternative definitions of money. The graph confirms what we concluded in the previous paragraph. Clearly, velocity is not constant over time when we use the narrow measure of money, M 1 (represented by the red line in the graph, the corresponding values on the left axis). However, velocity is more or less constant over time when we use M2 (shown by the blue line in the graph, the corresponding values on the right axis). Another way of seeing this is by using the expression we derived in part (b) of this problem. If the growth rate of velocity is zero over time, that implies that the quantity theory of money does not hold. In the last two columns, we show the growth rate of velocity using the two alternative measures of money. Taking the average of these two columns, we observe that only when we use M2 as our money measure the growth rate of velocity is (approximately) zero. This implies that using the narrower definition of money, the quantity theory of money does not hold. 6

7 Real GDP (Y) Money supply Money supply Price level (P) Velocity Velocity Velocity Velocity (in billions of (M1 in billions (M2 in billions (GDP deflator, using M1 using M2 growth rate growth rate Year 1996 dollars) of dollars) of dollars) 1996 = 100) (=PY/M1) (=PY/M2) using M1 (%) using M2 (%) Averages:

8 Velocity of money using M1 and M V under M V under M2 (=PY/M1) (=PY/M2) 8