Download Document

Economics 514
Macroeconomic Analysis
Due: November 15, 2007
1. Consumption Function
The permanent income hypothesis suggests that temporary changes in output have
relatively small effects on consumption but permanent changes have 1- for-1 impacts
on the level of consumption. A simple model that incorporates both of these effects is
of the form
C
ct  ln(Ct )
yt  ln Yt
cyt  ln t
Yt
(1)
ct  b1  yt  b2   cyt 1  b3 
where b1 is the short-term marginal propensity to consume out of wealth and b3 is the
long-term average of the log of the ratio of consumption to output. Whenever the
consumption-to-output ratio is above the long-term level, consumption will grow
more slowly than output.
a. Simulation
Study the properties of this consumption function.
Assume that output follows an AR(1) process.
yt  a1  yt 1   t
i.
ii.
iii.
Begin by assuming that output starts at a level of Y-1 = 1 so that y-1 = 0 .
Assume that there is a one-time 10% shock to output at time 0 so that  0 = .1
and  j =0 for all j > 0 and the shock is temporary so a1 = .75. Calculate the
level of output for periods j = 0-20.
Use this data on output to calculate the path of consumption. We can rewrite
equation (1) as:
ct  (b2  b3 )  (1  b2 )  ct 1  b1  yt  (b1  b2 )  yt 1
Set b1 = .3 and b2 = .1. Set b3 = ln( ½ ) so the long-run consumption-to-output
ratio is C =.5. Assume that consumption is at that ratio initially so that Ct-1
Y
= .5. Calculate consumption for periods j = 0-20.
Calculate the response of consumption to a permanent shock. Assume that
there is a one-time 10% shock to output at time 0 so that  0 = .1 and  j =0 for
all j > 0 and the shock is permanent so a1 = 1. Calculate the level of output and
consumption for periods j = 0-20.
b. Estimation
Estimate the parameters of the model using simple multivariate regression.
ct  0  1  yt  2  cyt 1  t
Get data on annual consumption and output from the United Nations Statistical
Database for Japan from period 1970-2009.
UN Main Aggregates Database
i.
ii.
iii.
Download series GDP by Expenditure, Constant Prices –National
Currency. The table should include data on both “Household Consumption
Expenditure” or C and “Gross Domestic Product” or Y. Use both those
variables to calculate real consumption, C.
Use these variables to calculate series for yt , ct and cyt 1 from 1971-2009.
Use these series and the linear regression tool in Microsoft Excel to estimate
β0, β1, and β2. Select Tools, Data Analysis, Regression with variable ct as
the left hand side Y range and variables yt and cyt 1 as the right hand side X
range.
2.
Intertemporal Elasticity of Substitution
Use data from to calculate the relationship between consumption and the real interest
rate. Consumption theory suggests that we can write an equation in the form
C
ln( t )   .ln(   (1  rt ))
Ct 1
Ct 1
)   .ln   .ln(1  rt )
Ct
C
Estimate a regression of the form ln( t 1 )  b0  b1 ln(1  rt )   t over the period t =
Ct
1970 to 2009.using data from World Bank’s World Development Indicators Link
 ln(
From the link follow
and
From
Japan and hit
.
Real Interest Rate
and
(%). From
Household final consumption
expenditure (constant LCU)
and hit
. From Year
and
hit
. Choose
and
. What is the estimated
intertemporal elasticity of substitution? Is it more or less elastic than 1?
3.
Real Cost of Capital and Investment
You want to check the sensitivity of investment in Japan to the real capital rental rate.
Use annual Japanese data from UN Main Aggregates Database to construct a capital
rental rate series.
a. Calculate inflation and investment goods inflation. Calculate a price series for
output, Pt, and investment goods, PtI. First, get data from GDP by Expenditure,
Current Prices –National Currency on GDP and Gross fixed capital formation and
then from GDP by Expenditure, Constant Prices –National Currency on GDP
and Gross fixed capital formation. Calculate the price series for each measure as the
ratio of the current price level to the constant price level. Calculate inflation for
P
each series as the continuous growth rate of each series.  t  ln( t
),
Pt 1
 tI  ln( Pt
I
Pt I 1
) . Calculate the relative price of investment goods as the ratio of
the investment index to the output price index: ptI  (
Pt I
Pt
)
b. Use the real interest rate from Question 2 to calculate the capital rental rate.
Assume that the quarterly depreciation rate is δ = .08. Use the above data to
R
calculate the quarterly capital rental rate t P   rt    ( tI1   t 1 )  ptI .
t
Compare this series with the series you would get if you assumed that the real
price of investment goods was always equal to pI = 1, (rt + δ). Calculate the
average for both series over the period 1971 to 2008.
c. Calculate the investment to capital ratio.
i.
Estimate the capital stock in 1970, t = 0. Assume in that period, the
R
marginal product of capital equals the average of t
calculated in
Pt
Y1970 R
 . Use the constant price measure of GDP to
K1970 P
measure output in period 1970 along with the assumption that α = ⅓ to
calculate K0.
ii.
Calculate a capital series recursively. Starting from period 0, use the
investment series in column D) and the initial capital level calculated
in section ii) to estimate the capital stock in every period.
Kt+1 = (1- δ)Kt + It.
I
iii.
Calculate the investment to capital ratio in each period t
Kt
Y
d. Calculate the output to capital ratio. ykt  ( t )
Kt
e. Use the Excel regression package to estimate the effect of GDP growth and the
capital rental rate on the investment to capital ratio. Estimate the model,
It
R
 b0  b1 t  b2 ykt   t over the period 1980 to 2008.
Kt
Pt
section b. 
f. Are both coefficients of the correct sign? Which has the stronger effect on
investment?
4.
Precautionary Savings
Estimate the effect of volatility on savings rates using Chinese provincial data. The
following dataset has data on the average consumption and average disposable
income (both in current dollars).
Chinese Provincial Data
http:\\home.ust.hk\~davcook\ChinaPrecautionaryData.xls
a. Calculate the personal savings rate as
Disposable Incomet ,i  Consumption Expendituret ,i
. Calculate the average
st ,i 
Disposable Incomet ,i
1 2003
from 2000 to 2003. s i   st ,i
4 t  2000
b. Calculate constant dollar disposable income. Download data on China’s price
level from the UN website. UN Main Aggregates Database. Download the series
“GDP, Implicit Price Deflators – National Currency”. Use the implicit price index
divided by 100 as the price level, P. To get constant dollar disposable income for
each year, YDt, divide the disposable income for a given year t, by Pt.
YDt ,i
c. Calculate the growth rate of real disposable income as gtYD
,i  ln(
YDt 1,i
).
Calculate this for each province for each year.
YD
d. Calculate the mean g i
 iYD 
g


2003
t 1993
YD
t ,i
1 2003 YD

 gt ,i and standard deviation
11 t 1993

YD 2
 gi
10
of real disposable income growth.
e. Estimate the model si  b0  b1 iYD   t . Does income volatility have a positive,
zero, or negative impact on savings.