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Econ 314: Project 1 Answers and Questions Examining the Growth Data Trends, Cycles, and Turning...
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Transcript of Econ 314: Project 1 Answers and Questions Examining the Growth Data Trends, Cycles, and Turning...
![Page 1: Econ 314: Project 1 Answers and Questions Examining the Growth Data Trends, Cycles, and Turning Points.](https://reader033.fdocuments.in/reader033/viewer/2022052701/56649f2a5503460f94c4441c/html5/thumbnails/1.jpg)
Econ 314: Project 1Answers and Questions
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Examining the Growth DataTrends, Cycles, and Turning Points
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The Growth Experience0
24
68
lgdp
1950 1960 1970 1980 1990 2000yr
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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
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Cycle Turning Points12
.513
13.5
14
1950 1960 1970 1980 1990 2000year
United Kingdom Fitted values
Peaks
Troughs
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Measuring Growth RatesCompounding and Growth Rate Formulas
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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.
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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.
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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
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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
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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
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Is Trend Growth Stable?Examining the Record
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Is the trend stable?5
67
89
1950 1960 1970 1980 1990 2000year
Single trend for Japan
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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------------------------------------------------------------------------------
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Is the trend stable?5
67
8
1950 1960 1970 1980 1990 2000year
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Cyclical GDP: Single trend-.4
-.20
.2.4
clgpd
_jpn
1950 1960 1970 1980 1990 2000year
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Cyclical GDP: Split trend-.1
-.05
0.0
5.1
c2lg
dp_j
pn
1950 1960 1970 1980 1990 2000year
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Are there two breaks?5
67
8
1950 1960 1970 1980 1990 2000yr
lgdp Fitted values
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Cyclical series with two breaks-.
1-.
050
.05
.1cl
gdp
1950 1960 1970 1980 1990 2000yr
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Stationarity and TrendsIs Log-Linear Trend Appropriate?
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“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
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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
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Difference stationary series Random walk:
Random walk with drift:
tttt
ttt
eyyy
eyy
1
1
tttt
ttt
eayyy
eayy
1
1
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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
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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
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Fitting a trend to random walk with drift?10
10.5
1111
.512
1950 1960 1970 1980 1990 2000year
Chile Trend line - Chile
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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:
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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
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3 series: 100 observations
-16
-12
-8
-4
0
4
25 50 75 100
E WALK AUTO
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3 series: 1000 observations
-20
-10
0
10
20
30
250 500 750 1000
E WALK AUTO
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3 series: 10,000 observations
-50
0
50
100
150
200
250
2500 5000 7500 10000
E WALK AUTO
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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
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Is the Business Cycle Global?Cross-Country Correlation in
GDP and Growth
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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
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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
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Final ConclusionEcon 314 Students Do
Good Work!!