Econ 314: Project 1Answers and Questions

Examining the Growth DataTrends, Cycles, and Turning Points

The Growth Experience0

24

68

lgdp

1950 1960 1970 1980 1990 2000yr

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

Cycle Turning Points12

.513

13.5

14

1950 1960 1970 1980 1990 2000year

United Kingdom Fitted values

Peaks

Troughs

Measuring Growth RatesCompounding and Growth Rate Formulas

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.

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.

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

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

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

Is Trend Growth Stable?Examining the Record

Is the trend stable?5

67

89

1950 1960 1970 1980 1990 2000year

Single trend for Japan

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

Is the trend stable?5

67

8

1950 1960 1970 1980 1990 2000year

Cyclical GDP: Single trend-.4

-.20

.2.4

clgpd

_jpn

1950 1960 1970 1980 1990 2000year

Cyclical GDP: Split trend-.1

-.05

0.0

5.1

c2lg

dp_j

pn

1950 1960 1970 1980 1990 2000year

Are there two breaks?5

67

8

1950 1960 1970 1980 1990 2000yr

lgdp Fitted values

Cyclical series with two breaks-.

1-.

050

.05

.1cl

gdp

1950 1960 1970 1980 1990 2000yr

Stationarity and TrendsIs 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:

Random walk with drift:

tttt

ttt

eyyy

eyy

1

1

tttt

ttt

eayyy

eayy

1

1

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

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

Fitting a trend to random walk with drift?10

10.5

1111

.512

1950 1960 1970 1980 1990 2000year

Chile Trend line - Chile

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:

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

-16

-12

-8

-4

0

4

25 50 75 100

E WALK AUTO

3 series: 1000 observations

-20

-10

0

10

20

30

250 500 750 1000

E WALK AUTO

3 series: 10,000 observations

-50

0

50

100

150

200

250

2500 5000 7500 10000

E WALK AUTO

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)

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

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

Final ConclusionEcon 314 Students Do

Good Work!!