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ECON6300/7320 Econometrics

创建日期：2024-06-12 17:16:25

所属分类：经济Economics

标签： ECON6300

Econometrics

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ECON6300/7320

Course Information
▶ The course will focus on estimation and inference methods
that are widely used in applied microeconomics.
▶ The course has a topics-based structure, and theory and
applications are closely integrated.
▶ Whenever you learn a method theoretically (lecture), there
will be an R exercise with data for the method (practical)
▶ The course will provide econometric skills that could be
used in quantitative research at the Graduate level.
3 / 54
Course Meetings: Lectures and Tutorials
▶ Lectures
▶ Go through theory, illustrating examples, perhaps some
proofs, and Q& A
▶ Tutorials
▶ See the Course Timetable posted on Blackboard for the
time and location.
▶ Focus is on practical implementation in R
▶ Start from week 2 (Introduction to R programming)
4 / 54
Assessment
▶ Two assignments + Final problem set.
▶ Analytical and empirical problems.
▶ Assignments 1-2 each cover 1/3 topics of the course (30%
each).
▶ Final problem set is comprehensive and covers the entire
course (40%).
5 / 54
Learning Resources
▶ Recommended Textbooks:
▶ Hansen, E.B. (2022). Econometrics. Princeton University
Press. (H)
▶ Cameron, A.C., and P.K. Trivedi (2005).
Microeconometrics: Methods and Applications. Cambridge
University Press. (CT)
▶ There are many other useful texts, e.g., Greene,
Wooldridge, etc. See ECP.
▶ As the semester progresses, lecture notes, slides,
datasets, problem sets, etc. will be provided. It is however
strongly encouraged that you read the relevant part of the
textbook and other references.
6 / 54
This week: math review
▶ You are EXPECTED to have a basic grasp of
mathematics/statistics. If most of the concepts we cover today are
unfamiliar to you, this course may be unsuitable (unless it is
compulsory (!!!)).
▶ Random Variables, Expectation, Variance, Covariance
▶ Point Estimation, Hypothesis Testing, Interval Estimation
▶ Linear Algebra: vector and matrix and their operations
7 / 54
Math Review random variable
▶ Informally, a Random Variable (RV) takes on numerical values
determined by an experiment.
▶ Example: Consider an experiment in which a fair coin is tossed. Then,
the possible outcomes are Head and Tail, i.e., {H,T}. Then, we define
a random variable X as follows;
X =
{
0 if the outcome is T
1 if the outcome is H
The X could be either 0 or 1 whenever the coin is tossed.
Each time, the realisation of X would be different.
The uncertainty can be summarised as Pr(X = 0) = 0.5.
8 / 54
Math Review probability functions
▶ The uncertainty of a random variable, say X , is represented by its
cumulative distribution function (CDF), defined as
FX (x) := Pr(X ≤ x)
▶ When FX (x) is a continuous function, X is said to be a continuous
random variable. For a continuous random variable, the probability
density function (PDF), denoted by fX (x), is a function that satisfies
Pr(a < X < b)︸︷︷︸
=FX (b)−FX (a)
=
∫ b
a
fX (t)dt
▶ If FX (x) is differentiable, we have
fX (x) =
d
dx
FX (x)
▶ If FX (x) is a step function, X is discrete, which we do not cover today.
9 / 54
Math Review expectation
▶ A function of a random variable is also a random variable. For example,
exp(X ), log(X ), etc. More generally, g(X ) with some function g(·).
▶ Suppose X have the PDF fX (x). The expectation of g(X ) is
E [g(X )] :=
∫ ∞
−∞
g(t) · fX (t)dt
which represents the central tendency of the random variable, g(X ).
▶ As a special case with g(X ) = X ,
E [X ] :=
∫ ∞
−∞
t · fX (t)dt
which is the expectation of X , or the expected value or the mean
▶ Consider another case with g(X ) = (X − E [X ])2.
V (X ) := E [(X − E [X ])2]
which is called the variance that represents the variability of X . Note
that
√
V (X ) is the standard deviation of X .
10 / 54
Math Review expectation
▶ E [X ] and V (X ) are the population parameters, or theoretical moments.
You need to know the distribution to compute E [X ] and V (X ).
▶ E [X ] must be distinguished from the sample mean (average). For
example, when you observe some numbers x1, . . . , xn, its average is
xn :=
1
n
n∑
i=1
xi
which is NOT the expectation of the distribution
▶ Similarly, you must distinguish V (X ) and the sample variance
1
n
n∑
i=1
(xi − xn)2
11 / 54
Math Review expectation
1. E [c] = c, for any constant c
2. E [aX + b] = aE [X ] + b for any constants a and b
3. a1, . . . , an are constants, and X1, . . . ,Xn are RV’s. Then,
E
[
n∑
i=1
aiXi
]
=
∑
i=1
aiE [Xi ].
As a special case, we have
E
[
n∑
i=1
Xi
]
=
∑
i=1
E [Xi ].
4. V (c) = 0, for any constant c.
5. V (aX + b) = a2Var(X ) for any constants a and c.
12 / 54
Math Review joint distribution
▶ Suppose X and Y are jointly distributed with the joint PDF fXY (x , y).
▶ The marginal PDF of X can be obtained by integrating Y out,
fX (x) =
∫ ∞
−∞
fXY (x , y)dy
▶ X and Y are independent if and only if for all x and y
fXY (x , y) = fX (x)fY (y)
▶ The expectation of g(X ,Y ) for some function g(X ,Y ) is
E [g(X ,Y )] =
∫ ∞
−∞
∫ ∞
−∞
g(x , y)fXY (x , y)dxdy
13 / 54
Math Review covariance
▶ If g(X ,Y ) = (X − E [X ])(Y − E [Y ]), then we have the covariance,
C(X ,Y ) = E [(X − E [X ])(Y − E [Y ])]
▶ If C(X ,Y ) > 0, the X and Y move in the same direction.
If C(X ,Y ) < 0, they move in the opposite direction.
▶ |C(X ,Y )| ≤√V (X )√V (Y ). So, the correlation coefficient
ρXY :=
C(X ,Y )√
V (X )
√
V (Y )
is always between -1 and 1.
▶ If X and Y are independent, C(X ,Y ) = 0. But, the converse is not
generally true
14 / 54
Math Review conditional distribution
▶ Suppose X and Y are jointly distributed with the joint PDF fXY (x , y).
Then, the conditional PDF of Y given X = x is
fY |X (y |x) := fXY (x , y)fX (x)
which summarises the distribution of Y when X takes a value x .
▶ If X and Y are independent, fY |X (y |x) = fY (y) and fX |Y (x |y) = fX (x)
15 / 54
Math Review conditional expectation
▶ The conditional expectation of Y given X = x is
E [Y |X = x ] =
∫ ∞
−∞
yfY |X (y |x)dy
▶ The conditional variance of Y given X = x is
V (Y |X = x) = E
[
(Y − E [Y |X = x ])2
∣∣∣X = x]
▶ E [Y |X = x ] and V (Y |X = x) are functions of x .
▶ When x is not specified, E [Y |X ] and V (Y |X ) are random.

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25579 1ECE 273 M122 COMP4434 1ELEC ELEC5620M STAT0010 BFF2401 MXB361 MATH3811 CS330 CMT307 FIT1033 CptS 583 UP 431 MATH6005 AF5343 CS2435 ECOM30002 ES50061 CS 2506 ECMT6002 CODE 00099F MT4539 ESSAY ICM317 MATH1231 MFIT5010 BMA547 MATH334 CIVL2201 MATH39032 T-04 CIVE97119 EMESTER CAB302 CAB301 59PM STAT802 ISYS3412 RM3 COSC 2123 AcF 311 MATH2022 1FINAL 4CCS1PHC ICM 142 ENVS3023 Math 4023 I1 ACSE8 FIN B385F CS-275 STA 4109-01 A31021 EE140 MT1 EE124 ECO-6004B Inf2-IADS CS126 IS2184 UL18 MATH5092 ECOM009 COMP 6211 ELEC202 MKT3019 IAB230 FIT5046 584-S21 COMP3210 CO250 A29401 MATH 136 MGT6174 ECMT6007 DATA2001 MAT 443 MATH10222 PHDE0071 ELE00123M COSC1295 MAT00045H MATH32032 1004GRC MAS223 COMP10001 DATA3404 CIVL2110 STAT2008 FNCE10002 EEE6431 COM6515 COMP9120 NBS8185 ECTE942 ECON 405 MATH314301 STAT 2011 COMPSCI 350 COMP20007 CMPSC-132 ECON5002 STA 35 MTH6108 FIT5147 MTH6150 100C FINA 5260 DESC9115 ECON4998 NBS8257 GMM ECON 6070 BSA2 ECE599 STATS 102B STA120 INFS601 BFC3241 MATH20602 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CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 MOEC0021 STA 106 ENGG 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 BCPM0008 ECN 620 QBUS6830 ECSE-415 ECON5102 MGMT20005 MAT 653 ECO 480 COMP 5/600 CSSE 5600 ME 571 7CCMMS61 CS 550 COMP2865 MATH3075 STATS 506 QTM 220 ISYS2120 FIT5106 STAT 153 MKTG3112 ECON2102 ELE2018 COMP3031 MSIN0010 SCC461 MATH237 CS246 CSC3065 CSE 101 ICTWEB411 COMP9313 ECOS 2025 FN620 MATH11111 MATH 3018 KE1068 FINA 6112 C++ MISM 6202 MSIN0105 CSC8631 MECO6935 COMP4121 ACCT2011 DPBS1150 EEL 3701C F19PL OPM 661 CSE 310 CS918 BIOL30001 ACCT3563 BANK3600 MET CS622 MATH367 ACCT5907 Continuing COMP5048 COMP61021 CS3334 GSOE9210 CSCI-570 COMP 5322 HW 2 ALY-6020 IEOR 4706 DATA 200 EBUS504 CGE12412 COMP4108 7SSMM800 ECMM171P MATE50002 CS225 RS 6003 BH2274 ELEC3111 MAT6669 ECON-UA 227 PHIL 1012 7SSMM603 TB028A P6 ECS708 CSC 427 CS6476 CSE 250A A1A2 ITS61504 EECS 376 model HW6 UV0010 ECON 6074 MG4F7 CMP-7030Y INFO3008 BFIP013 ECON 5068 MATH6002 CS3483 PSTAT 131 C31FM CSOR W4246 AAEC 5307 DATA ELEC362 COMSM0047 ECN6006 MA20224 BST351 MATH 323 MATH323 AA2021 COMP3811 COMP2013 IB9X60 INVP001 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ECOS3003 ELEC6252 C2511C PHY328 EC1060 ECON32202 COMP4002-E1 MATH3063 EFIMM0124 QBUS2310 ECON4411 FUNDAMENTALS ACCT20001 18YX RPM COMP 2711 QBUS6600 BUSS5221 ST3189 FIT1047 MAT344 EGB375 MATH60013 MATH96011 COMP3557 MAST20029 ECM159 EAE1011 ENSCEN 105 SECTION A STA 141C SOSE 2022 PAM006 COMP0048 M40007 ISOM2500 CMPE 142 A06472 MCC150 ACST 8083 GEOG6087 ECON920 FINM7008 ENVENG 4110 COMPSCI 361 ENGRCEE 21 PHYS 1112 ACF2100 ECMM108 COMPS267F MAT00050M MAST30025 CSIT970 MSCI 224 INT202 PUBL0054 MSDM5004 BMAN 21020 BMAN21020 MGMT1002 MATH11150 LAWS7023 ACTL30002 CIVL3340 MATH1002 ECON 8069 COMPSCI 351 IBUS7302 STAT4528 CHEM1101 STAT3925 BUSN 7008 Comp 3120 ECOS2040 SWEN90010 ENGN6528 ECM158 ECON20022 COMP6452 Calculation CITS1401 S1889112 BUS 351 ACTL30008 FIT2091 ECON6002 IBUS6020 PHI 001 ECON30290 MATH7501 ECON10004 MFIN7017 ISYS90043 LAWS7012 ECON30025 COMP30023 COMM1190 ECOM20001 GSBS6009 STAT 337 EMET8002 ECOM90001 ECOM30001 FINC 2012 BUSINESS ENGCV512 ECO 101H1 IB9520 FINM 3008 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