Econ 100B: Economic Analysis MacroeconomicsProblem Set #2 Solutions

Due Date: July 9, 2015

1. Comparing the growth rates of Y and C shown on slide 19 of lecture 5:

(a) Would you characterize the direction of these fluctuations as generally procyclical,countercyclical, or acyclical? Why?

The direction of these fluctuations is generally procyclical because almost all of themovements in Y have a similar directing in the movement of C.

(b) Would you characterize the timing of these fluctuations as generally leading, lag-ging, or coincident? Why?

The direction of these fluctuations is generally coincident because almost all of themovements in Y have a similar timing in the movement of C.

(c) What is it about the relationship between Y and C that might explain youranswers to questions (1a) and (1b)

C is roughly 70% of Y so one would expect the fluctuations of C and Y to becorrelated.

2. Compare and contrast the timing and direction of the fluctuations of Y and CPIinflation (shown on slide 29 of lecture 5) during (i) the recession associated with thefinancial crisis just before 2010 and (ii) the recession in the mid 1970s. Read thefinal paragraph on page 296 (312) of the first (second) edition of Mishkin to find thename of the phenomenon depicted in mid-1970 recession: what is the name of thisphenomenon?

In the recent financial crisis the fluctuations of Y and CPI inflation show the fluctuationin CPI inflation to be procylical with a lag. By contrast, the mid-70s recession shows thefluctuation in CPI inflation to be countercyclical and coincident. This phenomenon of acontempraneous increase in inflation and decrease in aggregate output is referred to asstagflation.

3. How do the models that the Classicals emphasize and those that the Keynesians em-phasize differ?

The primary difference between the Classicals and the Keynesians is on the time that ittakes the economy to respond to shocks. The Classicals see return to equilibrium as a rapidphenomenon that needs no intervention; they focus on long-term models. The Keynesianssee return to equilibrium as a potentially long phenomenon and that intervention can helpshorten the time it takes to return to equilibrium; they focus on short-term models.

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4. Beginning with the second equation for Y in the middle of slide 24 of lecture 6, carryout the algebra needed to obtain the equation for the IS curve.

Beginning with

Y = C + mpc Y d + I +G+ NX (C + I + NX) r , (1)

we see that the substitution Y d = Y T = Y T yields

Y = C + mpc (Y T

)+ I +G+ NX (C + I + NX) r . (2)

Collecting terms in Y we find that

Y (1 + mpc) = C mpc T + I +G+ NX (C + I + NX) r , (3)

which, after dividing both sides by (1 + mpc) and moving mpc T to the end of thesum of autonomous components, yields the IS curve:

Y =

(C + I +G+ NX mpc T

)(1 mpc)

(C + I + NX)(1 mpc)

r (4)

5. If the IS curve does not shift when autonomous consumption increases by $225 MMand autonomous taxes increase by $300 MM, what can we infer about the marginalpropensity to consume?

Given that the IS curve did not shift following the changes in these autonomous componentsit follows that these changes have offset (or cancelled) one another. Referring to Equation(4) we see that this implies that

C mpc T = 0 , (5)or

$225 MM mpc $300 MM = 0 , (6)or

mpc =$225 MM

$300 MM= 0.75 . (7)

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6. In our derivation of the IS curve we made the simple assumption that taxes are com-pletely autonomous: T = T . A more realistic tax function would be one where taxesincrease with income as described by T = T + tY . Follow the steps you undertook inquestion (4) with this more realistic tax function to derive a new IS-curve equation.

Returning to

Y = C + mpc Y d + I +G+ NX (C + I + NX) r , (8)

but now substituting with Y d = Y T = Y T tY yields

Y = C + mpc (Y T tY

)+ I +G+ NX (C + I + NX) r .

(9)

Collecting terms in Y we find that

Y [1 mpc (1 t)] = C mpc T + I +G+ NX (C + I + NX) r , (10)

which, after dividing both sides by [1 mpc (1 t)] and moving mpc T to the end ofthe sum of autonomous components, yields the IS curve:

Y =

(C + I +G+ NX mpc T

)[1 mpc (1 t)]

(C + I + NX)[1 mpc (1 t)]

r (11)

7. Referring to this article on Bloomberg:

(a) What short-term tool did Chinas central bank use to inject money into theChinese economy?

Reverse-repurchase agreement.

(b) Briefly explain how this short-term tool works (i.e. how does using this tool resultin more money in the Chinese economy? (Some online research may need to bedone to answer this question.).

In a repurchase agreement one party sells a security to another party and agrees torepurchase that security at an agreed time in the future and at a agreed price. Typicaltimes involves are short, such as overnight or a week. A summary of this approach tomanaging liquidity can be found on Investopia

For the party selling the security (and agreeing to repurchase it in thefuture) it is a repo; for the party on the other end of the transaction (buyingthe security and agreeing to sell in the future) it is a reverse repurchaseagreement.

This is a collateralized loan with the difference in price being the interest on the loan.By buying securities from commercial banks and agreeing to sell them back at a slightlyhigher price the Peoples Bank of China is making short-term collateralized loans tothe commercial banks at low interest rates. The short-term cash that the commercialbanks receive from the Peoples Bank of China through repurchase agreements isthen lent out by the commercial banks, and in so doing the repurchase agreementsultimately result in more money in the Chinese economy.

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http://www.bloomberg.com/news/articles/2015-01-22/pboc-conducts-first-reverse-repos-in-a-year-to-ease-cash-squeezehttp://www.investopedia.com/terms/r/reverserepurchaseagreement.asp

(c) How much money did the Peoples Bank of China inject into their economy?

If we restrict ourselves to reverse repurchase agreements, then according to this ar-ticle the Peoples Bank of China injected 50 billion yuan ($8.05 billion) into theireconomy. There were, however, a number of short-term instruments being used andan alternative reading is that the Peoples Bank of China injected 419.5 billion yuan(= 50 billion in reverse repurchase agreements + 269.5 billion of 3-month loans beingextended + 50 billion in the medium-term lending facility + 50 billion of six-monthtreasury deposits. Either answer is acceptable

(d) Assuming this was not in response to a change in inflation, (i) what term in theirMP curve did the Peoples Bank of China change and (ii) was this monetary-policymove by the Peoples Bank of China expansionary or contractionary?

If this was not in response to a change in inflation then the Peoples Bank of Chinachanged the autonomous component of the MP curve. Since their action was toincrease the amount of money in the economy this monetary-policy move was expan-sionary.

8. The goal of this exercise is to estimate Okuns law using data from the Federal Reserve.Download the following time-series from FRED:1

The civilian unemployment rate (UNRATENSA): U . The natural rate of unemployment (NROU): UN . Real gross domestic product (GDPC1): Y . Real potential gross domestic product (GDPPOT): Y P .

(a) From these time series calculate and plot the unemployment gap, U UN , andthe output gap 100 (Y Y P )/Y P as a function of time (and on a quarterlybasis) from the first quarter of 1949 to the end of 2014.

(b) Create a scatter plot of the unemployment gap as a function of the output gap.Your graph should look similar to the graph on slide 27 of lecture 8.

-10

-5

0

5

10

40 50 60 70 80 90 00 10 20

GA

P (

%)

TIME (year)Source: FRED / BLS

Output GapUnemployment Gap

-6

-4

-2

0

2

4

6

-10 -5 0 5 10

Unem

plo

ym

ent G

ap (

%)

Output Gap (%)Source: FRED / BEA, BLS

The graph for part (a) is on the left and that for part (b) is on the right.

1For purposes of this exercise we will ignore the seasonality inconsistency in the GDP measures.

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(c) Perform a linear regression on the data in the graph you generated for Question(8b) and show the regression result as a line on your graph. (Note: The regressionmethod you used in the analysis of the Cobb-Douglas data can be used here.)

The regression result shown as a black line in the scatter plot above (obtained usingthe trendline option in Excel) is gU = 0.5028gY + 0.019 (R2 = 0.84) where gUdenotes the unemployment gap and gY denotes the output gap.

(d) Does your regression analysis support the equation for Okuns Law discussed inclass? Why?

Yes. The equation for Okuns law discussed in class is gU 0.5gY (cf. slide 27 oflecture 8). The regression analysis agrees with this to one place after the decimal andis thus consistent with the approximation discussed in class.

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9. In class it was observed that Okuns law is seen internationally, albeit with differentvalues of the coefficient relating the output gap to the unemployment gap. Referringto the table below:

Country CoefficientUnited Kingdom -0.38

Spain -0.88Finland -0.50Japan -0.16

(a) In which of these countries is Okuns law most similar to that of the United States,and why?

Okuns coefficient in the U.S. is -0.5 which is most similar to that of Finland.

(b) Identify the country from which the IMF data on the following page was obtained.Show your work. (Note: The regression method you used in the analysis of theCobb-Douglas data can be used here. Also, it is often a good idea to copy & pastedata from PDF files to Excel or other analysis tools.)

Given the table of Okuns coefficients and the data, identification of the country fromwhich the data originated is an exercise in (i) determining the Okun coefficient andthen (ii) identifying the country from the table. To obtain the Okun coefficient werun a regression on the data which results in the line shown in the figure below

-1.0

-0.5

0.0

0.5

1.0

-5 -4 -3 -2 -1 0 1 2 3 4 5

Source: IMF

UN

EM

PL

OY

ME

NT

GA

P (

%)

GDP GAP (%/year)

The equation of the line in this figure is

gU = 0.163gY + 0.0017 (12)

where gU is the unemployment gap and gY is the output gap; the R2 is 0.71. From

this regression we see that Okuns coefficient is -0.163 which most closely matchesthat of Japan; the data is from Japan.

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10. Using the adaptive-expectations form of the short-run Phillips curve:

(a) Identify the term in the equation that corresponds to expected inflation and brieflyexplain what the form of this term says about how people form their expectationof inflation.

The adaptive-expectations form of the short-run Phillips curve is

t = t1 (Ut UN) + t (13)

and the term that corresponds to expected inflation is t1.

(b) Briefly describe how inflation will change if unemployment is held at a constantlevel below the natural rate of unemployment.

If unemployment is held at a constant level below the natural rate of unemploymentthen we will have Ut < UN ; a negative unemployment gap. A negative unemploymentgap will, given the negative sign in front of and the fact that > 0, give rise to anincrease in inflation. Inflation will rise until the negative unemployment gap is dealtwith.

(c) Derive the expression for the long-run Phillips curve.

In equilibrium there is no change in any of the variables in the Phillips curve as timepasses. This means that t = t1. Substituting this back into our Phillips curve andremoving common variables the long-run Philips curve is

(Ut UN) = t (14)Ut UN = t/ (15)

Ut = UN + t/ (16)

or

Ut = UN (17)

if one treats t as an infrequent event.

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GapYear Output Unemployment1980 0.01 0.211981 0.21 0.081982 0.95 0.021983 2.52 0.271984 2.25 0.301985 0.38 0.181986 2.00 0.321987 2.18 0.401988 0.82 0.071989 2.14 0.211990 4.01 0.411991 4.44 0.481992 2.48 0.531993 0.48 0.341994 0.50 0.151995 0.31 0.101996 0.98 0.131997 1.57 0.331998 1.50 0.141999 2.57 0.492000 1.04 0.362001 1.42 0.512002 2.02 0.742003 1.17 0.582004 0.26 0.042005 0.89 0.242006 1.76 0.512007 3.45 0.762008 1.75 0.612009 4.31 0.492010 0.42 0.512011 1.53 0.10

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