Download Econ 314: Project 1

Econ 314: Project 1
Answers and Questions
Examining the Growth Data
Trends, Cycles, and Turning Points
4
2
0
lgdp
6
8
The Growth Experience
1950
1960
1970
1980
yr
1990
2000
1960 per-capta GDP
16000
14000
12000
10000
8000
6000
4000
2000
0
China
Nepal
Botswana
Bangladesh
Zimbabwe
Dom. Rep.
Brazil
Jamaica
Hong Kong
Costa Rica
Japan
Spain
South Africa
Ireland
Italy
Argentina
Belgium
Norway
UK
Sweden
Australia
New Zealand
Luxembourg
Switzerland
Trend Growth Rates
Trend growth vs. 1960 income
10
8
6
4
2
Country
Inc in 1960
Trend Rate
0
14
Cycle Turning Points
13
13.5
Peaks
12.5
Troughs
1950
1960
1970
1980
1990
year
United Kingdom
Fitted values
2000
Measuring Growth Rates
Compounding and Growth Rate Formulas
Product growth formula
Continuously compounded:
A( t )  A( t  1) ea , B( t )  B( t  1) eb ,
C ( t )  A( t ) B( t )
C ( t )  A( t  1) ea  B( t  1) eb  A( t  1) B( t  1) ea b
 C ( t  1) ea b .
Formula holds exactly.
Product growth formula
Annually compounded:
At  At 1 (1  a), Bt  Bt 1 (1  b)
C t  At Bt ,
C t  At 1 Bt 1 (1  a)(1  b)
 C t 1 (1  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:
g

ln GDP2  ln GDP1   ln GDP1  ln GDP0 
2
ln GDP2  ln GDP0
.
2
Trend growth vs. average growth


Trend rate is slope of best-fit line
What is average growth rate?
From period 0 to T:
g

ln GDPT  ln GDPT 1     ln GDP1  ln GDP0 
T
ln GDPT  ln GDP0
.
T
Trend growth vs. average growth
Actual Log GDP - Egypt
Fitted values
18.5
18
lnGDPT – lnGDP0
17.5
17
T
16.5
1950
1960
1970 Year
1980
1990
Is Trend Growth Stable?
Examining the Record
9
Is the trend stable?
5
6
7
8
Single trend
for Japan
1950
1960
1970
year
1980
1990
2000
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
------------------------------------------------------------------------------
5
6
7
8
Is the trend stable?
1950
1960
1970
year
1980
1990
2000
0
-.2
-.4
clgpd_jpn
.2
.4
Cyclical GDP: Single trend
1950
1960
1970
year
1980
1990
2000
-.1
-.05
0
c2lgdp_jpn
.05
.1
Cyclical GDP: Split trend
1950
1960
1970
year
1980
1990
2000
5
6
7
8
Are there two breaks?
1950
1960
1970
1980
yr
lgdp
Fitted values
1990
2000
-.1
-.05
0
clgdp
.05
.1
Cyclical series with two breaks
1950
1960
1970
1980
yr
1990
2000
Stationarity and Trends
Is 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:
yt  yt 1  et
yt  yt  yt 1  et

Random walk with drift:
yt  yt 1  a  et
yt  yt  yt 1  a  et
Fitting a trend to random walk with drift
ln GDP
Difference-stationary process
follows new, higher trend line
Positive
shock at t
Trend-stationary process
reverts to fixed trend line
t
time
Fitting a trend to random walk with drift
ln GDP
Difference-stationary process
follows new, higher trend line
Trend line
Positive
shock at t
Trend-stationary process
reverts to fixed trend line
t
time
10
10.5
11
11.5
12
Fitting a trend to random walk with drift?
1950
1960
1970
1980
1990
year
Chile
Trend line - Chile
2000
Barely stationary time series
 Consider first-order autoregressive process:
yt  yt 1  et , 0    1.



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
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
4
0
-4
-8
-12
-16
25
50
E
WALK
75
AUTO
100
3 series: 1000 observations
30
20
10
0
-10
-20
250
E
500
750
WALK
AUTO
1000
3 series: 10,000 observations
250
200
150
100
50
0
-50
2500
E
5000
WALK
7500
AUTO
10000
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)
|
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
Red indicates statistical significance at 0.05 level.
Growth Correlation across
Countries (partial sample)
| 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
Red indicates statistical significance at 0.05 level.
Final Conclusion
Econ 314 Students Do
Good Work!!