Download Homework Assignment 1

Homework Assignment 1
Economics 514
Macroeconomic Analysis
Due: October 9th, 2007
Data Problems
1. Researchers at the University of Pennsylvania have assembled a database on
comparable levels of output and investment for a large number of countries. Use the
data from Penn-World Tables. Data can be obtained here:
Penn World Tables
http://pwt.econ.upenn.edu/php_site/pwt62/pwt62_form.php
(Note: To retrieve data from this site, you need to download a .csv file. This file can
be copied to Notepad. The notepad file can be opened by Excel as a spread sheet).
Calculate the average growth rate of TFP in China over the period 1965-2003. Do
this in a number of steps.
Assume a Cobb-Douglas production function with α = ⅓.
A. Calculate the average growth rate of output. Download information on Real GDP
per Capita (Constant Price: Chain Series) denoted RGDPCH and the Population
denoted variable denoted POP. Use this data to calculate total real GDP, Y.
Remember to calculate the average continuous growth rate of a series, you only need
to know (the logarithms of) the start and end values of the series.
B. Calculate the average growth rate of labor. Download data on Real GDP Chain
per Worker denoted RGDPWOK. The share of the population who are workers is the
ratio of RGDPCH/RGDPWOK. To calculate the number of workers, multiply this
share by POP. Labor hours are not available so assume a constant number of hours
worked per worker.
C. Calculate the average growth rate of capital. You have no direct measure of
capital. Construct a measure of capital using the perpetual inventory method. First,
calculate the level of investment in every period. Download Investment Share of
RGDPL which is denoted KI. Multiply (KI/100) by your measure of total GDP, Y to
get a series for Investment. Estimate the capital stock in 1953 by assuming that in
Y
1953, the capital productivity level was 1953
 1 . Beginning from 1953,
K1953
recursively calculate the capital stock in all subsequent periods using the equation
Kt 1  (1   ) Kt  It with an assumed depreciation rate of 8%.
D. Assume a Cobb-Douglas production function with α = ⅓. Calculate the average
growth rate of TFP over the period 1965-2003. Now, go back and calculate the
average growth rate of TFP over the periods 1965-1984 and 1983-2003. Has TFP
growth been accelerating in China or declining?
Accelerating
Average
1965-2003 0.079135 0.019331 0.080645 0.039366
1965-1984 0.066193 0.024137 0.065044 0.028421
1985-2003 0.092758 0.014273 0.097068 0.050886
2. Differences in Human Capital and Differences in Productivity
Compare the level of technology in East Asia with those in Latin America. Assume a
production function in each country of the form:
Yt  Kt ( At Ht Lt )1

H t  e1
yearst
yt  kt ( At )1 e  yearst
where Ht is human capital which is a function of the number of years of schooling.
Your assignment is to calculate comparable levels of technology in year 2000 for a
number of Latin American countries (Argentina, Brazil, Chile and Mexico) and a
number of East Asian economies (Hong Kong, Singap ore, South Korea, and
Taiwan). Do this in a number of steps.
A. Gather data on Labor Productivity. Researchers at the University of Groningen
have accumulated data on GDP per hours worked (in 1990 US dollars). Download
data from year 2000 for y for each economy from this site.
Groningnen Total Economy Database
http://www.ggdc.net/dseries/totecon.html
B. Gather data on Human Capital: Researchers at Harvard University have a human
capital dataset. In particular, get data on each country on the average number of
years of education of the population 25 years old or older in each country from
the data set by Robert Barro and Jong-Wha Lee of Korea University. That data
can be downloaded in an Excel file on this page. Calculate the human capital
under the assumption that  = .08.
Barro-Lee International Data on Educational Attainment, Appendix Data Tables
http://www.cid.harvard.edu/ciddata/ciddata.html
C. Calculate steady state Capital Productivity. You have no information on the
capital stock for each country. Instead assume that capital productivity in the
country is at its steady state level associated with the balanced growth path. To
calculate this, you need data on: the growth rate of technology, assume gA= .02;
the depreciation rate, assume δ= .08, the investment rate, s; and the population
growth rate, n. To calculate s and n, use data from the Penn World Tables derived
from the site linked in the previous question. Calculate the average of investment
as a share of GDP over the years 1987-1997(i.e. the average of KI/100) as a proxy
for s. If the data is not complete for all countries, use whatever years are available
to calculate the average. Calculate the average continuous growth rate of
population over the same period (i.e. the growth rate of POP) as a proxy for n.
Hong
Kong
Taiwan
Argentina
Chili
Singapore
Brazil
Mexico
South
Korea
6.51
6.15
5.46
5.41
5.34
4.57
4.12
2.77
Calculate the technology level of each country. Rank them in order of labor
productivity, human capital, and technology.
We can
GDP per Hour, in 1990 GK $ y
Hong
21.16
Kong
Singapore
18.83
South
12.80
Korea
Taiwan
17.13
Argentina
12.58
Brazil
8.01
Chili
13.74
Mexico
8.62
years of
education
n
s
{y/k]^SS
H
Technology
9.47
1.68%
24.79%
0.43
2.13
6.51
8.12
2.99%
40.73%
0.29
1.91
5.34
10.46
8.53
8.49
4.56
7.89
6.73
0.94%
0.90%
1.35%
1.65%
1.58%
1.87%
39.69%
19.61%
14.11%
15.76%
19.34%
16.21%
0.25
0.51
0.73
0.68
0.55
0.67
2.31
1.98
1.97
1.44
1.88
1.71
2.77
6.15
5.46
4.57
5.41
4.12
Computational Problems
Macroeconomics often uses computer simulations to study theoretical models. Do a
couple of simulation exercises for an economy with a Cobb-Douglas production
function
1
2
1
2
Yt  Kt 3 ( At Lt ) 3
yt  kt 3 ( At ) 3
a depreciation rate of 8% (δ=.08), a population growth rate of 1% (n = .01),and an
annual technology growth rate of 2% (gA = .02).
3. Golden Rule
Assume that the economy was on its balanced growth path. Normalize technology at
L
time t to At = 1. Assume a constant labor hours per population of t
= 500.
POPt
Output is used for consumption and investment, Ct + It = Yt and investment is a
constant share of output. Calculate consumption per capita at different levels of invest
rates s = 1100 , 1 4 , 13 , and
state labor productivity.
1
2
. Which investment rate generates the highest steady
We can write steady state capital productivity as a function of s
Y 
K 
 
SS

n  gA 
and output on the balanced growth path as a function
s

  Y  SS   1
BGP
of capital productivity yt       At . Per capital output is
K  
Yt
L
C
Y
and per capita consumption is t
 ytBGP  t
 (1  s)  t
POPt
POPt
POPt
POPt
Maximum Consumption per Capita
s
Steady State
Capital Productivity
0.01
11
0.25
0.44
0.333333
0.33
0
.
5
0
.
2
2
Steady State
Labor Productivity
0.301511
1.507557
1.740777
2
.
1
3
2
0
0
7
Output
Capita
150.7557
753.7784
870.3883
1
0
6
6
.
0
0
Consumptio
per Capita
149.2481
565.3338
580.2589 Golden Rule: s = α
4
5
3
3
.
0
0
1
8
4. Convergence
Assume that the investment rate for the economy is at the level which generates
the highest level of consumption per capita. Examine the dynamics of the neoclassical model. Start in period 0. In that period, technology is A0 = 1 and k0 = 1.5.
Calculate labor productivity in period 0 and the labor productivity if the economy
were on its balanced growth path. What is the percentage gap between the actual
level of the economy and the balanced growth path (y0 and yBGP). Calculate the capital
productivity in period 0. Use this to calculate the growth rate of the capital labor ratio,
k  g k  kt 1  kt between period 0 and period 1. Use the growth rate of the capital
t 1
k
kt
A  At
labor ratio and the growth rate of technology A  gtA1  t 1
to calculate k1 and
A
At
A1. Use these numbers to calculate actual and balanced growth path labor productivity
and capital productivity in period 1. Use capital productivity to calculate the growth
rate of the capital-labor ratio in period 1. Calculate technology and the capital labor
ratio in period. 2. Repeat. Calculate the path of actual labor productivity as well as the
balanced growth path for periods 0 through 30. How large is the percentage gap at
period 30.
We can calculate the path of technology by assuming constant growth At = (1+gA)t A0.

  Y  SS   1
1
BGP
The balanced growth path is written as yt       At  .33 2 . We can write the
K  


growth of the capital labor ratio and the growth rate. Initial output is
y0  k0 3  A0 3  3 1.5  1.14
1
2
.and initial capital productivity is .763. The growth rate of the
kt 1  kt
Y
 s t  (n   ) while the growth rate of labor
kt
Kt
y y
productivity is gty1  t 1 t  13 gtk1  23 gtA1 . Using thes growth rates and projecting
yt
forward, we would have the following results.
capital-labor ratio is gtk1 
t
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Capital
Productivity
0.763143
0.701033
0.651347
0.610838
0.577289
0.549135
0.525244
0.504773
0.487089
0.471701
0.458227
0.446363
0.435865
0.426535
0.418212
0.41076
0.404068
0.398041
0.3926
0.387676
0.38321
0.379153
Capital-Labor
Growth Rate
0.161837
0.141341
0.124944
0.111576
0.100505
0.091215
0.08333
0.076575
0.070739
0.065661
0.061215
0.0573
0.053835
0.050757
0.04801
0.045551
0.043343
0.041354
0.039558
0.037933
0.036459
0.035121
Labor Productivity
Growth Rate
0.067279
0.060447
0.054981
0.050525
0.046835
0.043738
0.04111
0.038858
0.036913
0.03522
0.033738
0.032433
0.031278
0.030252
0.029337
0.028517
0.027781
0.027118
0.026519
0.025978
0.025486
0.02504
t
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Technology
1
1.02
1.0404
1.061208
1.082432
1.104081
1.126162
1.148686
1.171659
1.195093
1.218994
1.243374
1.268242
1.293607
1.319479
1.345868
1.372786
1.400241
1.428246
1.456811
1.485947
1.515666
Balanced
Growth Path
1.740777
1.775592
1.811104
1.847326
1.884273
1.921958
1.960397
1.999605
2.039597
2.080389
2.121997
2.164437
2.207726
2.25188
2.296918
2.342856
2.389713
2.437507
2.486258
2.535983
2.586702
2.638436
Labor
Productivity
1.144714
1.22173
1.295579
1.366812
1.435871
1.50312
1.568864
1.63336
1.69683
1.759465
1.821435
1.882887
1.943955
2.004759
2.065407
2.125999
2.186626
2.247372
2.308316
2.369531
2.431086
2.493046
Capital
Labor Ratio
1.5
1.742756
1.989078
2.237603
2.487266
2.73725
2.986927
3.235829
3.483613
3.730042
3.974962
4.218288
4.459995
4.700101
4.938662
5.175767
5.411527
5.646076
5.879562
6.112146
6.343998
6.575297
%
Gap
41.92%
37.39%
33.50%
30.13%
27.18%
24.58%
22.28%
20.23%
18.40%
16.75%
15.27%
13.94%
12.72%
11.62%
10.62%
9.71%
8.88%
8.12%
7.43%
6.79%
6.20%
5.67%