lecture 14 econometrics
Post on 14-Apr-2018
224 Views
Preview:
TRANSCRIPT
-
7/29/2019 Lecture 14 econometrics
1/35
Lecture 15. Dummy variables, continued
Seasonal effects in time series
Consider relation between electricity consumption Y and electricityprice X .
The data are quarterly time series.
First model
tttuXY ++= lnln 21
What is the interpretation of 2 ?
-
7/29/2019 Lecture 14 econometrics
2/35
Because electricity consumption depends on the weather and specialcircumstances (Christmas, summer holidays) we expect is to be
different in the quarters, even if the price is constant.
Solution: Define
11 =tD ift is the first quarter of a year
01=
tD if not
Define 432 ,, ttt DDD analogously for the other quarters.
-
7/29/2019 Lecture 14 econometrics
3/35
To allow for differences in the average consumption betweenquarters we write
44332211 DDD +++=
Substitution in the regression model gives
ttttttuXDDDY +++++= lnln 24433221
Why not 1tD in model?
-
7/29/2019 Lecture 14 econometrics
4/35
Average electricity consumption in the four quarters (given price tX )
Quarter 1ttt
XXYE ln)|(ln 21 +=
Quarter 2ttt
XXYE ln)|(ln 221 ++=
Quarter 3ttt
XXYE ln)|(ln 231 ++=
Quarter 4ttt
XXYE ln)|(ln 241 ++=
Interpretation 432 ,, : Relative change (relative to quarter 1) of
electricity consumption in quarters 2,3,4.
-
7/29/2019 Lecture 14 econometrics
5/35
Change of reference quarter to quarter 2:
44331211 DDD +++=
Intercept in the four quarters
Reference quarter is quarter 1
4131211 ,,, +++
Reference quarter is quarter 2
4131121 ,,, +++
-
7/29/2019 Lecture 14 econometrics
6/35
Hence
24423322211 ,,, ===+=
The same relations hold for the OLS estimates. Change of referencequarter does not require re-estimation.
Same result holds for change in reference category for any
qualitative variable with more than two values (e.g. earlier example
with type of work)
-
7/29/2019 Lecture 14 econometrics
7/35
If we want to investigate whether price elasticity depends on seasonwe write
48372652 DDD +++=
Substitution gives
ttttttt
ttttt
uXDXDXD
XDDDY
+++
+++++=
lnlnln
lnln
483726
54433221
-
7/29/2019 Lecture 14 econometrics
8/35
Price elasticities in the four quarters
Quarter 1 5
Quarter 2 65 +
Quarter 3 75 + Quarter 4 85 +
-
7/29/2019 Lecture 14 econometrics
9/35
Tests:
Average demand does not change with the season
Price elasticity constant over seasons
Derive price elasticities if we choose period 2 as reference period.
-
7/29/2019 Lecture 14 econometrics
10/35
Structural change
Events may change the relation between economic variables.
Consider time series data on dependent variableY
andindependent variable X for e.g. years nt ,,1K= .
In year 0nt= some event happens.
This event induces a structural change if the regression
coefficients change due to the event.
-
7/29/2019 Lecture 14 econometrics
11/35
Original model (no structural change)
ntuXYttt
,,1, K=++=
Model with structural change in0
n :
011 ,,1, ntuXY ttt K=++=
nntuXYttt
,,1,)( 02121 K+=++++=
-
7/29/2019 Lecture 14 econometrics
12/35
This is equivalent to introducing the dummy variable
0=t
D for 0,,1 nt K=
1=
t
D
fornnt
,,10K+=
with the model
ntuXDXDYtttttt
,,1,2121
K=++++=
Test for structural change can be done in two ways
Estimate separate models and compare ESS
Estimate model with dummy and test 0,0 22 ==
This gives the same value for the test statistic.
-
7/29/2019 Lecture 14 econometrics
13/35
Outliers
There may be individual observations that do not fit the relation
See output/graphs
Reason:
Omitted variables
Error in the data
Some unknown event/circumstance
How to check this?
-
7/29/2019 Lecture 14 econometrics
14/35
Introduce dummy variable
123, =iD for observation 23 (and 0 otherwise)
Include this in the regression model and test whether coefficient is 0.
See output.
-
7/29/2019 Lecture 14 econometrics
15/35
Dependent Variable: LNWAGEMethod: Least SquaresDate: 11/01/01 Time: 08:42
Sample: 1 49Included observations: 49
Variable Coefficient Std. Error t-Statistic Prob.
C 6.864366 0.186127 36.88002 0.0000EDUC 0.052987 0.017107 3.097432 0.0034
EXPER 0.020776 0.006321 3.286999 0.0020AGE -0.002250 0.003804 -0.591382 0.5574
RACE 0.071479 0.081543 0.876575 0.3856GENDER 0.242610 0.071645 3.386300 0.0015
R-squared 0.470916 Mean dependent var 7.454952Adjusted R-squared 0.409395 S.D. dependent var 0.312741S.E. of regression 0.240344 Akaike info criterion 0.100786Sum squared resid 2.483904 Schwarz criterion 0.332438Log likelihood 3.530733 F-statistic 7.654508Durbin-Watson stat 1.708658 Prob(F-statistic) 0.000032
-
7/29/2019 Lecture 14 econometrics
16/35
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
5 10 15 20 25 30 35 40 45
LNWAGE Residuals
-
7/29/2019 Lecture 14 econometrics
17/35
obs Actual Fitted Residual Residual Plot
1 7.20415 7.20983 -0.00568
2 7.79770 7.64738 0.150323 7.44717 7.47824 -0.03107
4 7.28688 7.44899 -0.16212
5 7.40184 7.57869 -0.17685
6 7.20415 7.27025 -0.06610
7 7.37901 7.36391 0.01509
8 7.04229 7.06440 -0.02211
9 7.35628 7.78801 -0.43173
10 7.31055 7.61880 -0.30825
11 7.11802 7.16206 -0.0440412 7.20415 7.19236 0.01179
13 7.20415 7.36341 -0.15926
14 8.12829 7.90676 0.22153
15 7.51698 7.67094 -0.15396
16 6.88857 7.34406 -0.45549
17 7.20415 7.54399 -0.33984
18 7.35628 7.14941 0.20687
19 7.07918 7.21830 -0.13911
20 7.20415 7.41777 -0.21362
21 7.20415 7.35979 -0.15564
22 7.68110 7.56638 0.11472
23 7.24566 7.69937 -0.45372
24 7.65681 7.51358 0.14323
25 7.70436 7.68690 0.01746
26 8.18172 7.69434 0.48738
27 7.58680 7.32344 0.26337
28 7.11802 7.09935 0.01866
29 7.56320 7.43966 0.12354
30 7.68018 7.43267 0.2475131 7.76853 7.35286 0.41568
32 7.20415 7.41537 -0.21122
33 7.51698 7.28394 0.23304
34 7.86825 7.65101 0.21724
35 7.83716 7.72690 0.11026
36 7.37901 7.39163 -0.01262
37 7.51698 7.69670 -0.17973
38 7.70436 7.45990 0.24446
39 7.33237 7.18733 0.1450440 7.28688 7.29798 -0.01110
41 8.10380 8.01117 0.09263
42 8.25140 7.75389 0.49751
43 7.51698 7.48605 0.03093
44 7.28688 7.29015 -0.00328
45 7.26753 7.58319 -0.31567
-
7/29/2019 Lecture 14 econometrics
18/35
Dependent Variable: LNWAGEMethod: Least SquaresDate: 10/29/01 Time: 22:21
Sample: 1 49Included observations: 49
Variable Coefficient Std. Error t-Statistic Prob.
C 6.789626 0.182398 37.22432 0.0000GENDER 0.261107 0.069438 3.760286 0.0005
AGE -0.001271 0.003687 -0.344724 0.7320EXPER 0.018787 0.006149 3.055107 0.0039
EDUC 0.061945 0.016981 3.647842 0.0007RACE 0.065118 0.078464 0.829904 0.4113D23 -0.530696 0.249938 -2.123314 0.0397
R-squared 0.522205 Mean dependent var 7.454952Adjusted R-squared 0.453948 S.D. dependent var 0.312741S.E. of regression 0.231101 Akaike info criterion 0.039638Sum squared resid 2.243118 Schwarz criterion 0.309898Log likelihood 6.028867 F-statistic 7.650623Durbin-Watson stat 1.653329 Prob(F-statistic) 0.000014
-
7/29/2019 Lecture 14 econometrics
19/35
Dependent Variable: LNWAGEMethod: Least SquaresDate: 11/01/01 Time: 08:47
Sample: 1 49Included observations: 49
Variable Coefficient Std. Error t-Statistic Prob.
C 7.401588 0.160656 46.07096 0.0000GENDER 0.276639 0.074299 3.723311 0.0006EXPER 0.017241 0.004698 3.669938 0.0007EDUC 0.022429 0.013386 1.675632 0.1018
AGE -0.002105 0.002676 -0.786674 0.4362RACE 0.095861 0.060972 1.572208 0.1240D23 -0.293381 0.187884 -1.561503 0.1265
CLERICAL -0.419411 0.083845 -5.002245 0.0000CRAFTS -0.342397 0.081728 -4.189469 0.0002MAINT -0.525459 0.092669 -5.670253 0.0000
R-squared 0.778514 Mean dependent var 7.454952Adjusted R-squared 0.727402 S.D. dependent var 0.312741S.E. of regression 0.163285 Akaike info criterion -0.606736Sum squared resid 1.039816 Schwarz criterion -0.220650Log likelihood 24.86503 F-statistic 15.23148Durbin-Watson stat 1.985725 Prob(F-statistic) 0.000000
-
7/29/2019 Lecture 14 econometrics
20/35
Application: Election 2000 in Florida
Effect of butterfly ballot in Palm Beach County on Buchanan vote
Data for all Florida counties
Votes candidates
Size and demographic composition of counties (census). What isrelevant?
-
7/29/2019 Lecture 14 econometrics
21/35
Model
Dependent variable?
Independent variables?
How do we check whether Palm Beach is different?
-
7/29/2019 Lecture 14 econometrics
22/35
Election 2000 in Florida: Butterfly ballot in Palm Beach county
Outcome of 2000 presidential election disputed.
Claims of voting irregularities in Florida.
One issue was a confusing ballot design in Palm Beach county, thebutterfly ballot.
Order of punch holes different from order of the two main candidates,Bush and Gore.
Claim: Many voters mistakenly voted for Buchanan, the candidate of
the Reform Party.
-
7/29/2019 Lecture 14 econometrics
23/35
Research question: Did Buchanan get an unusually large fraction of thevotes in Palm Beach county?
-
7/29/2019 Lecture 14 econometrics
24/35
Regression model
Dependent variable: log of fraction votes for Buchanan.
Independent variables
Percentage of population Hispanic
Percentage of population Black
Percentage of population over 65
Percentage of population with college degree
Income (1000$ per year)
Population (10000)
-
7/29/2019 Lecture 14 econometrics
25/35
Descriptive statistics
Date:04/06/05Sample: 1 67
Time: 22:14
FRACBUCHA FRACGORE FRACBUSH PERCBLACK PERCHISPAN PERCOVER6 PERCCOLLE INCOME1000 POPULATION
Mean 0.004697 0.428125 0.551544 15.89701 6.288060 16.80293 13.89701 26.18864 21.87156Median 0.003976 0.430705 0.549881 14.40000 3.500000 14.60939 11.90000 25.71800 8.191900Maximum 0.017452 0.676075 0.741084 61.80000 54.40000 33.43856 37.10000 38.13000 204.4600Minimum 0.000897 0.241105 0.310129 2.300000 0.900000 6.974674 5.200000 17.09800 0.628900Std. Dev. 0.003218 0.091383 0.092058 11.07191 8.186436 7.011421 6.588534 4.794646 36.05383Skewness 1.912928 0.348309 -0.282254 1.926733 3.699223 0.846034 1.203425 0.446578 3.023152
Kurtosis 7.448237 3.331569 3.187830 7.627821 19.94750 2.718083 4.690722 2.364601 13.30769
J arque-Bera 96.10031 1.661643 0.988110 101.2424 954.6232 8.214687 24.15201 3.354070 398.6674Probability 0.000000 0.435691 0.610147 0.000000 0.000000 0.016451 0.000006 0.186927 0.000000
Observations 67 67 67 67 67 67 67 67 67
-
7/29/2019 Lecture 14 econometrics
26/35
OLS results: Basis equation
-
7/29/2019 Lecture 14 econometrics
27/35
Signs of coefficients plausible?
Interpretation of coefficients: dependent variable is log!
-
7/29/2019 Lecture 14 econometrics
28/35
OLS residuals: Graph
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
5 10 15 20 25 30 35 40 45 50 55 60 65
LNFRACBUCHANAN Residuals
-
7/29/2019 Lecture 14 econometrics
29/35
OLS residuals: Table
-
7/29/2019 Lecture 14 econometrics
30/35
-
7/29/2019 Lecture 14 econometrics
31/35
OLS results: Palm Beach dummy
To check whether Palm Beach is special include dummy that is 1 for PalmBeach (observation 50) and 0 otherwise
-
7/29/2019 Lecture 14 econometrics
32/35
Interpretation of Palm Beach dummy
dy 794.1521.2ln ++= "
Hence
794.1lnln = normalobserved yy
so that
103.51
794.1
==
ey
yy
normal
normalobserved
i.e. fraction 5 times higher than expected. Fraction is .00789.
-
7/29/2019 Lecture 14 econometrics
33/35
Sensitivity check: Include log fraction Bush vote
-
7/29/2019 Lecture 14 econometrics
34/35
Effect on Bush and Gore vote
-
7/29/2019 Lecture 14 econometrics
35/35
top related