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ECONOMETRICS

创建日期：2024-06-05 17:19:54

所属分类：经济Economics

标签： ECONOMETRICS

ECONOMETRICS

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ECONOMETRICS

LECTURE SLIDES #7A TOPICS
 Adjusted R-Squared
 Qualitative Information
 Dummy Variable and Multiple Groups
 Key references 6.3 , 7.1, 7.2 and 7.3
2
MORE ON GOODNESS OF FIT
 General remarks on R-squared
 High R-squared does not imply there is a causal interpretation
 Low R-squared does not preclude precise estimation of
marginal effects
 R-squared will always increase (at least never decrease) when we
add an extra variable
 How to construct a version of R-squared that takes into account
this fact
3
MORE ON GOODNESS OF FIT...
 Adjusted R-squared accounts for degrees of freedom
�2 = 1 − ( ⁄ ( − − 1))( ⁄ ( − 1))
 Adjusted R-squared imposes a penalty for adding new
regressors
 Adjusted R-squared may increase or decrease when add a
variable
 Potentially useful in comparing models with alternative
numbers of regressors
 Adjusted R-squared may be negative
�2 = 1 − (1 − 2)( − 1)/( − − 1)
4
ADJUSTED R-SQUARED IN STATA
5

_cons 4.821997 .2883396 16.72 0.000 4.253538 5.390455
lsales .2566717 .0345167 7.44 0.000 .1886224 .3247209

lsalary Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 66.7221632 208 .320779631 Root MSE = .50436
Adj R-squared = 0.2070
Residual 52.6559944 207 .254376785 R-squared = 0.2108
Model 14.0661688 1 14.0661688 Prob > F = 0.0000
F(1, 207) = 55.30
Source SS df MS Number of obs = 209
. reg lsalary lsales
USING FIT TO CHOOSE BETWEEN MODELS
 If models are nested – one is a special case of other
= 0 + 1 +
= 0 + 1 + 22 +
 First model is nested within second depending on 2
 Could choose between models on basis of test of 0:2 = 0
 Could also decide on basis of fit using �2
 Implicitly selecting a specific critical value
 �2 for first model increases relative to second iff t-statistic for
estimate of 2 is greater than one in absolute value
6
USING FIT TO CHOOSE BETWEEN MODELS...
 Models are nonnested if neither model is special case of other
= 0 + 1 log +
= 0 + 1 + 22 +
 Can’t impose restrictions on 1 & 2 to move to log model
 Testing option not available but can compare fit
 Using RDCHEM data log model 2 = .061 while quadratic model
yields 2 = .148 but comparison unfair to first model
 �2 = 0.030 for log & �2 = 0.090 for quadratic model
 Even after adjusting for difference in degrees of freedom quadratic
model is preferred
7
USING FIT TO CHOOSE BETWEEN MODELS...
 Models with different dependent variables will typically
be non-nested
 Here neither R-squared nor adjusted R-squared should be
used for comparison
 Continuing previous ex. what if comparison between log() = 0 + 1 + 22 +
= 0 + 1 + 22 +
 Now not possible to compare fit
 Comparing how well variation in log is explained
versus with how well variation in is explained
 Extent of variation in these two could be very different
8
QUALITATIVE INFORMATION
 Thus far variables have been quantitative – number of
bedrooms, years of education, hourly wage, …
 Many features likely to appear in analyses are
qualitative
 Gender of individual, their occupation, whether they are
employed or not, …
 Industry classification of firm, its credit rating, whether or not it
paid a dividend last quarter, …
 One way to incorporate qualitative information is to use
dummy (binary, indicator) variables
 Equals 1 or 0 representing presence or absence of feature
 May appear as dependent or as independent variables 9
DUMMY EXPLANATORY VARIABLE
 Single dummy independent variable
= 0 + 0 +
= 1 if person is a woman & = 0 otherwise
 Choice of who is the dummy is arbitrary
 Using zero/one also arbitrary but useful for
interpretation
 In our example being a woman is choosen for the dummy
variable being equal to 1. By using the binary female,
we have chosen male to be the base/benchmark group.
10
DUMMY VARIABLE
= 0 + 0 +
 Specified model is regression representation of
conditional means:
= 0 = 0
= 1 = 0 + 0
= 1 − = 0 = 0
11
DUMMY EXPLANATORY VARIABLE
 Have relied on ZCM assumption
 To better estimate gender effect need to control for other
factors
= 0 + 0 + 1 +
= 1, − = 0, = 0
 0represents difference in mean wage between men & women
with the same education
12
DUMMY EXPLANATORY VARIABLE
13
 Implication of this
particular model
 Difference does not
depend on level of
education
 Data determine this
difference
 Graphically, model
specifies an intercept shift
according to gender
DUMMY VARIABLE TRAP
 What happened to the male dummy?
 Why can’t we estimate
= 0 + 0 + 0 + 1 + ?
 Answer: There is a perfect multicollinearity problem (MLR.3 not
satisfied)
+ = 1
 Male & female dummy variables are perfectly collinear with
the intercept
 An example of the dummy variable trap
 More latter when talk about multiple groups

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1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 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