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Econ 314: Project 1. Answers and Questions. Examining the Growth Data. Trends, Cycles, and Turning Points. The Growth Experience. Trend Growth Rates. Cycle Turning Points. Peaks. Troughs. Measuring Growth Rates. Compounding and Growth Rate Formulas. Product growth formula.

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econ 314 project 1

Econ 314: Project 1

Answers and Questions

examining the growth data

Examining the Growth Data

Trends, Cycles, and Turning Points

measuring growth rates

Measuring Growth Rates

Compounding and Growth Rate Formulas

product growth formula
Product growth formula

Continuously compounded:

Formula holds exactly.

product growth formula1
Product growth formula

Annually compounded:

Formula holds approximately.

Close when ab is small.

trend growth vs average growth
Trend growth vs. average growth
  • Trend rate is slope of best-fit line
  • What is average growth rate?

From period 0 to 2:

trend growth vs average growth1
Trend growth vs. average growth
  • Trend rate is slope of best-fit line
  • What is average growth rate?

From period 0 to T:

trend growth vs average growth2
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

is trend growth stable

Is Trend Growth Stable?

Examining the Record

is the trend stable
Is the trend stable?

Single trend for Japan

is the trend stable1
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

------------------------------------------------------------------------------

stationarity and trends

Stationarity and Trends

Is Log-Linear Trend Appropriate?

definition of stationarity
“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
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
Difference stationary series
  • Random walk:
  • Random walk with drift:
barely stationary time series
Barely stationary time series
  • Consider first-order autoregressive process:
  • 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
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
testing for stationarity
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

Is the Business Cycle Global?

Cross-Country Correlation in GDP and Growth

gdp correlation across countries partial sample
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
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 0.53470.3743 -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 -0.38600.4475 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

Final Conclusion

Econ 314 Students Do Good Work!!