2. Econ 314: Project 1 Answers and Questions

3. Examining the Growth Data Trends, Cycles, and Turning Points

4. The Growth Experience

5. Trend Growth Rates

6. Cycle Turning Points Peaks Troughs

7. Measuring Growth Rates Compounding and Growth Rate Formulas

8. Product growth formula Continuously compounded: Formula holds exactly.

9. Product growth formula Annually compounded: Formula holds approximately. Close when ab is small.

10. Trend growth vs. average growth Trend rate is slope of best-fit line What is average growth rate? From period 0 to 2:

11. Trend growth vs. average growth Trend rate is slope of best-fit line What is average growth rate? From period 0 to T:

12. Trend growth vs. average growth Year Actual Log GDP - Egypt Fitted values 19501960197019801990 16.5 17 17.5 18 18.5 lnGDP T – lnGDP 0 T

13. Is Trend Growth Stable? Examining the Record

14. Is the trend stable? Single trend for Japan

15. 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 ------------------------------------------------------------------------------

16. Is the trend stable?

17. Cyclical GDP: Single trend

18. Cyclical GDP: Split trend

19. Are there two breaks?

20. Cyclical series with two breaks

21. Stationarity and Trends Is Log-Linear Trend Appropriate?

22. “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

23. Kinds of nonstationary series Trend stationary Deviations from a fixed trend line are stationary Shocks from trend line are temporary Difference stationary Difference (y t - y t -1 ) is stationary, but may have nonzero mean (drift) Shocks are permanent

24. Difference stationary series Random walk: Random walk with drift:

25. Fitting a trend to random walk with drift

27. Fitting a trend to random walk with drift?

28. 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  Consider first-order autoregressive process:

29. 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

30. 3 series: 100 observations

31. 3 series: 1000 observations

32. 3 series: 10,000 observations

33. 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

34. Is the Business Cycle Global? Cross-Country Correlation in GDP and Growth

35. 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

36. 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

37. Final Conclusion Econ 314 Students Do Good Work!!