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Econ 314: Project 1Answers and Questions
Examining the Growth DataTrends, Cycles, and Turning Points
The Growth Experience0
24
68
lgdp
1950 1960 1970 1980 1990 2000yr
Trend Growth RatesTrend growth vs. 1960 income
02000400060008000
10000120001400016000
Chin
a
Nepa
l
Bots
wana
Bangla
desh
Zim
babw
e
Dom
. R
ep.
Bra
zil
Ja
maic
a
Hong
Kong
Costa
Ric
a
Ja
pan
Spain
South
Afr
ica
Irela
nd
Italy
Arg
entin
a
Belg
ium
Norw
ay
UK
Sw
eden
Austr
alia
New
Zeala
nd
Lu
xem
bourg
Sw
itzerland
Country
19
60
pe
r-c
ap
ta G
DP
0
2
4
6
8
10
Inc in 1960 Trend Rate
Cycle Turning Points12
.513
13.5
14
1950 1960 1970 1980 1990 2000year
United Kingdom Fitted values
Peaks
Troughs
Measuring Growth RatesCompounding and Growth Rate Formulas
Product growth formulaContinuously compounded:
( ) ( 1) , ( ) ( 1) ,
( ) ( ) ( )
a bA t A t e B t B t e
C t A t B t
( ) ( 1) ( 1) ( 1) ( 1)
( 1) .
a b a b
a b
C t A t e B t e A t B t e
C t e
Formula holds exactly.
Product growth formulaAnnually compounded:
1 1(1 ), (1 )
,t t t t
t t t
A A a B B b
C A B
1 1
1
(1 )(1 )
(1 ).t t t
t
C A B a b
C a b ab
Formula holds approximately.Close when ab is small.
Trend growth vs. average growth Trend rate is slope of best-fit line What is average growth rate?
From period 0 to 2:
.2
lnln
2lnlnlnln
02
0112
GDPGDP
GDPGDPGDPGDPg
Trend growth vs. average growth Trend rate is slope of best-fit line What is average growth rate?
From period 0 to T:
.lnln
lnlnlnln
0
011
TGDPGDP
TGDPGDPGDPGDP
g
T
TT
Trend growth vs. average growth
Year
Actual Log GDP - Egypt Fitted values
1950 1960 1970 1980 1990
16.5
17
17.5
18
18.5
lnGDPT – lnGDP0
T
Is Trend Growth Stable?Examining the Record
Is the trend stable?5
67
89
1950 1960 1970 1980 1990 2000year
Single trend for Japan
Is the trend stable?Stability Test for Japan
Source | SS df MS Number of obs = 51-------------+------------------------------ F( 3, 47) = 5988.24 Model | 39.488173 3 13.1627243 Prob > F = 0.0000 Residual | .103310446 47 .002198095 R-squared = 0.9974-------------+------------------------------ Adj R-squared = 0.9972 Total | 39.5914834 50 .791829668 Root MSE = .04688------------------------------------------------------------------------------ lgdp_jpn | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- year | .0908236 .0013825 65.69 0.000 .0880424 .0936049 d | 115.4399 3.557021 32.45 0.000 108.2841 122.5957 dyear | -.0585122 .0018037 -32.44 0.000 -.0621408 -.0548836 _cons | -171.915 2.711848 -63.39 0.000 -177.3706 -166.4595------------------------------------------------------------------------------
Is the trend stable?5
67
8
1950 1960 1970 1980 1990 2000year
Cyclical GDP: Single trend-.4
-.20
.2.4
clgpd
_jpn
1950 1960 1970 1980 1990 2000year
Cyclical GDP: Split trend-.1
-.05
0.0
5.1
c2lg
dp_j
pn
1950 1960 1970 1980 1990 2000year
Are there two breaks?5
67
8
1950 1960 1970 1980 1990 2000yr
lgdp Fitted values
Cyclical series with two breaks-.
1-.
050
.05
.1cl
gdp
1950 1960 1970 1980 1990 2000yr
Stationarity and TrendsIs Log-Linear Trend Appropriate?
“Definition” of stationarity Stationary variable:
Same mean, variance, etc. at all times
Nonstationary variable: Different level, variability, etc. over time Includes trended or drifting variables ln GDP is nonstationary for all countries
Kinds of nonstationary series Trend stationary
Deviations from a fixed trend line are stationary
Shocks from trend line are temporary Difference stationary
Difference (yt - yt -1) is stationary, but may have nonzero mean (drift)
Shocks are permanent
Difference stationary series Random walk:
Random walk with drift:
tttt
ttt
eyyy
eyy
1
1
tttt
ttt
eayyy
eayy
1
1
Fitting a trend to random walk with drift
ln GDP
time t
Positive shock at t
Trend-stationary process reverts to fixed trend line
Difference-stationary process follows new, higher trend line
Fitting a trend to random walk with drift
ln GDP
time t
Positive shock at t
Trend-stationary process reverts to fixed trend line
Difference-stationary process follows new, higher trend line
Trend line
Fitting a trend to random walk with drift?10
10.5
1111
.512
1950 1960 1970 1980 1990 2000year
Chile Trend line - Chile
Barely stationary time series
Stationary as long as < 1. Random walk (nonstationary) if = 1. How much difference is there between = 1 and
= 0.998? Not much! Very hard to tell the difference with small samples
.10,1 ttt eyy
Consider first-order autoregressive process:
Detecting non-stationarity
Examine behavior of three series: E = “White noise” process AUTO = Stationary autoregressive process
with = 0.998 based on E WALK = Random-walk process ( = 1)
based on E
3 series: 100 observations
-16
-12
-8
-4
0
4
25 50 75 100
E WALK AUTO
3 series: 1000 observations
-20
-10
0
10
20
30
250 500 750 1000
E WALK AUTO
3 series: 10,000 observations
-50
0
50
100
150
200
250
2500 5000 7500 10000
E WALK AUTO
Testing for stationarity Complex econometric task Low power with small samples
Difficult to tell = 1 from = 0.998 Macroeconomists rarely have more than a
few dozen observations that can be assumed to follow the same model
Is the Business Cycle Global?Cross-Country Correlation in
GDP and Growth
GDP Correlation across Countries (partial sample)
Red indicates statistical significance at 0.05 level.
| lgdpARG lgdpAUS lgdpBEL lgdpBGD lgdpBRA lgdpBWA lgdpCHE-------------+--------------------------------------------------------------- lgdpAUS | 0.9731 1.0000 lgdpBEL | 0.9721 0.9952 1.0000 lgdpBGD | 0.8779 0.9606 0.9258 1.0000 lgdpBRA | 0.9670 0.9860 0.9945 0.8967 1.0000 lgdpBWA | 0.8986 0.9796 0.9774 0.9555 0.9765 1.0000 lgdpCHE | 0.9517 0.9695 0.9766 0.8902 0.9709 0.9368 1.0000 lgdpCHN | 0.9166 0.9614 0.9403 0.9926 0.9221 0.9694 0.8765 lgdpCRI | 0.9780 0.9930 0.9957 0.9277 0.9935 0.9770 0.9753 lgdpDOM | 0.9682 0.9928 0.9901 0.9566 0.9867 0.9901 0.9536 lgdpESP | 0.9707 0.9854 0.9936 0.8939 0.9899 0.9541 0.9899 lgdpGBR | 0.9667 0.9978 0.9913 0.9683 0.9807 0.9795 0.9637 lgdpHKG | 0.9148 0.9892 0.9889 0.9521 0.9807 0.9891 0.9641 lgdpIRL | 0.9415 0.9731 0.9609 0.9786 0.9448 0.9810 0.8957 lgdpITA | 0.9662 0.9896 0.9950 0.9243 0.9943 0.9817 0.9876 lgdpJAM | 0.9266 0.9373 0.9508 0.8260 0.9439 0.8819 0.9859 lgdpJPN | 0.9649 0.9861 0.9943 0.8979 0.9931 0.9642 0.9888 lgdpLUX | 0.9348 0.9674 0.9490 0.9799 0.9254 0.9481 0.8966 lgdpNOR | 0.9654 0.9939 0.9906 0.9606 0.9865 0.9928 0.9477 lgdpNPL | 0.9041 0.9784 0.9542 0.9917 0.9289 0.9777 0.9188 lgdpNZL | 0.9721 0.9832 0.9842 0.9246 0.9790 0.9544 0.9873 lgdpSWE | 0.9651 0.9924 0.9955 0.9287 0.9903 0.9702 0.9879 lgdpZAF | 0.9670 0.9905 0.9965 0.9129 0.9965 0.9750 0.9813 lgdpZWE | 0.9502 0.9834 0.9929 0.9025 0.9932 0.9710 0.9693
Growth Correlation across Countries (partial sample)
Red indicates statistical significance at 0.05 level.
| dlgdpARG dlgdpAUS dlgdpBEL dlgdpBGD dlgdpBRA dlgdpBWA dlgdpCHE-------------+--------------------------------------------------------------- dlgdpAUS | 0.1564 1.0000 dlgdpBEL | -0.0214 0.2282 1.0000 dlgdpBGD | -0.0453 0.0373 -0.1525 1.0000 dlgdpBRA | 0.1719 -0.0229 0.4139 -0.4083 1.0000 dlgdpBWA | -0.1491 0.1170 0.2482 -0.2898 0.2515 1.0000 dlgdpCHE | 0.0725 0.2017 0.6910 -0.0291 0.2503 0.0247 1.0000 dlgdpCHN | 0.3598 -0.1534 -0.3292 0.1350 -0.3923 -0.3808 -0.3173 dlgdpCRI | 0.2731 0.2673 0.0947 -0.0729 0.2426 0.0975 -0.0294 dlgdpDOM | -0.0103 0.0936 0.2444 0.1274 0.1431 0.0857 0.1904 dlgdpESP | 0.0690 0.0177 0.5137 -0.1825 0.3269 0.0438 0.4256 dlgdpGBR | 0.0946 0.5347 0.3743 -0.1678 0.1470 0.0753 0.3704 dlgdpHKG | 0.1212 0.2218 0.3662 -0.0932 0.3083 -0.0885 0.2327 dlgdpIRL | -0.1584 0.0863 0.1344 -0.0318 -0.1917 0.1266 0.0116 dlgdpITA | 0.0040 0.2391 0.6121 -0.0027 0.4549 0.2880 0.6058 dlgdpJAM | 0.0233 0.0889 0.2823 -0.1468 0.1601 -0.1291 0.4663 dlgdpJPN | -0.0125 0.1004 0.5290 -0.2788 0.4306 0.0166 0.5597 dlgdpLUX | 0.0406 0.0288 0.2727 -0.0178 0.0014 0.2350 0.1008 dlgdpNOR | 0.3090 -0.0042 0.1593 -0.3860 0.4475 0.1658 -0.0861 dlgdpNPL | -0.1916 -0.1163 -0.2844 0.2797 -0.2934 -0.2608 -0.4133 dlgdpNZL | 0.1967 0.2395 0.3512 0.0937 0.2439 -0.1179 0.3190 dlgdpSWE | -0.0920 0.2621 0.5957 0.0078 0.3820 -0.0466 0.5004 dlgdpZAF | 0.0609 0.3794 0.4953 -0.0800 0.3445 0.0107 0.4709 dlgdpZWE | -0.0366 -0.1575 0.2970 -0.2195 0.1408 -0.0826 0.2658
Final ConclusionEcon 314 Students Do
Good Work!!