Econ 314: Project 1

1
Econ 314 Project 1

• Answers and Questions

2
Examining the Growth Data

• Trends, Cycles, and Turning Points

3
The Growth Experience
4
Trend Growth Rates
5
Cycle Turning Points
Peaks
Troughs
6
Measuring Growth Rates

• Compounding and Growth Rate Formulas

7
Product growth formula

• Continuously compounded

Formula holds exactly.
8
Product growth formula

• Annually compounded

• Formula holds approximately.
• Close when ab is small.

9
Trend growth vs. average growth

• Trend rate is slope of best-fit line
• What is average growth rate?
• From period 0 to 2

10
Trend growth vs. average growth

• Trend rate is slope of best-fit line
• What is average growth rate?
• From period 0 to T

11
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
1980
1990
Year
12
Is Trend Growth Stable?

• Examining the Record

13
Is the trend stable?
Single trend for Japan
14
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 gt 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
Pgtt 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 ----------
--------------------------------------------------
------------------
15
Is the trend stable?
16
Cyclical GDP Single trend
17
Cyclical GDP Split trend
18
Are there two breaks?
19
Cyclical series with two breaks
20
Stationarity and Trends

• Is Log-Linear Trend Appropriate?

21
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

22
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

23
Difference stationary series

• Random walk
• Random walk with drift

24
Fitting a trend to random walk with drift
25
Fitting a trend to random walk with drift
26
Fitting a trend to random walk with drift?
27
Barely stationary time series

• Consider first-order autoregressive process

• Stationary as long as ? lt 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

28
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

29
3 series 100 observations
30
3 series 1000 observations
31
3 series 10,000 observations
32
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

33
Is the Business Cycle Global?

• Cross-Country Correlation in GDP and Growth

34
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.
35
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.
36
Final Conclusion

• Econ 314 Students Do Good Work!!