ec 3303 spring 10 intro 1

EC3303 Econometrics I

Department of Economics, NUS

Spring, 2010

JongHoon Kim

Spring 2010 1EC3303

Spring 2010 EC3303 2

EC3303 Econometrics ILecturer: JongHoon KIM, AS2, 04‐40Class: Thu, 14.00 – 16.00, LT11

Tutorials: Mon – Fri, 10.00 – 12.00, AS4, 01‐17

Contact via emails please…

Starts on Week3 (Jan 25‐29)

Office Hours: Mon, 13.00 – 15.00

Assessment: Final Exam 60% + Continuous Assessment 40%Problem sets 20% + Midterm test 20%

2 ‐ 3 After the Midterm breakTextbook:Stock, J.H. and M.W. Watson (2006): Introduction to Econometrics, Second edition.

Boston: Pearson Addison Wesley. (HB 139 Sto 2006, CL, HSSML)

Supplementary reading:Wooldridge, J.M. (2005): Introductory Econometrics: A Modern Approach, Third edition. Gujarati, Damodar N. (2003): Basic Econometrics, Fourth edition. NY: McGraw-Hill.

Any statistics textbook…


Chapter I. Introduction

1. Overview - What is Econometrics? (S-W Ch1)

Reasoning and

conjecture

Global warming/Chinese economy in 10 yrs time?

Effectiveness of “caning” in SG penal system?

High time to buy a car or a HDB flat?

Global warming/Chinese economy in 10 yrs time?

Effectiveness of “caning” in SG penal system?

High time to buy a car or a HDB flat?

Observed and stylized facts

A medical case in SG 2008: An upsurge(150 or so over 5 months) of low bloodpressure shock cases 7 in coma, 4 death…?

A medical case in SG 2008: An upsurge(150 or so over 5 months) of low bloodpressure shock cases 7 in coma, 4 death…?

Theory (Model)

data + statistical tools/methods

Economics + Metric(Measure) = Econometrics

Definitive/quantitative questions with definitive/quantitative answers


Examples:

(a) Effect of reducing class size on elementary school education

test scorei class sizeistudent i

meaningful effect? How large?

pure(distinguishable) effect?

(b) Effect of cigarette taxes on reducing smoking

cigarette consumptioni cigarette sales priceiprice elasticity?

other factors?reverse “causality”?

How much can Apple price‐gouge SG customers on its 4G i‐phones?

i-phone salesi i-phone retail pricei

(c) Forecasting future inflation rates – SG’s inflation rate2010?

Benefits of the Casinos/Universal Theme Park at Sentosa/Marina Bay?

How many will survive EC3303 through to Final Exam?


(d) Explaining abrupt crime drop in 1990s in US (Levitt, Freakonomics…)

1. Innovative policing strategy2. Increased reliance on prisons3. Changes in crack and other drug markets4. Aging of the population5. Tough gun-control laws6. Strong economy7. Increased number of police8. All other explanations

(increased used of capital punishment, gun buybacks, and etc.)


(d) Explaining abrupt crime drop in 1990s in US (Levitt, Freakonomics…)

1. Innovative policing strategy

4. Aging of the population5. Tough gun-control laws6. Strong economy

8. All other explanations (increased used of capital punishment, gun buybacks, and etc.)

2. Increased reliance on prisons3. Changes in crack and other drug markets

7. Increased number of police

Legalization of abortion -1973, US Supreme Court Ruling on Roe v. Wade

(d’) Seeking determinants of crime rates (Levitt(1996))

crime ratet incarceration ratet

year t

other factors?

reverse “causality”?


(e) Understanding global warming (the effect of CO2 emission)

Vol NorPoleIcet CO2 emissiontreversed “causality”?

?

true scale of the effect?…“global warming hoax”??

(f) And many, many more interesting issues awaiting…

“H1N1 Flu pandemic hoax(scam)”,“Renewal of the contract hosting the F1 race in SG”,


Econometrics = Economics + Metrictheory data

Sources of Data:

(controlled) experiment

observation

Typical Economic Dataset:

cross‐sectional data

time series data

multiple entities at a given point in time

Individuals (person, firm,…), localities (city, states,…),…

a single entity over multiple peroids in time

panel data multiple entities over multiple peroids in time (longitudinal data)

“Devils are in the detail(s).”“Data is the least deceiving window toward truth.”(provided you know how to tease them without bungling)

“Why? …Why?... Why?”


2. Review of Probabilities (S-W Ch2) why do we care?

2.1 Probability Space

the (imaginary) collection of the whole “outcomes” in life

Probability Space (Sample Space), ΩΩ

a specific happening(realization) Outcome, ω

a collection of certain outcomes Event, E

a subset of Ω (basic unit to assign probability!)

Examples: i) the event E of tossing a coin to “head”

ii) the event E of finishing today’s lecture at 3.35pm sharp

iii) the event E of STI index “gaining” tomorrow

Events are the subsets resulting from introducing division(“partition”) of Ω.Here, for example, E and Ec.

ω.

E

Spring 2010 EC3303 10

More than two events occurring when…(i) a partition w/ multiple cuts (into mutually exclusive events)

“disjoint”

Ω

An example: Rolling a dice into{1,2}, {3,4}, {5,6}

Ω

An example: … ?

Probalibity: A relative measure of the likelihoods of events, satisfying

(a) 0 ≤ P(E) ≤ 1,(b) P(Ω) = 1 for any E Ω, and(c) P(E1 E2 ) = P(E1) + P (E2) + , for disjoint E1, E2,

P( i=1Ei) ∑i=1P(Ei)∞ ∞

E1 E2 E3 F1 F2 F3 Fn…

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More than two events occurring when…(i) a partition w/ multiple cuts (into mutually exclusive events)

“disjoint”

Ω

An example: Rolling a dice into{1,2}, {3,4}, {5,6}

Ω

An example: … ?

Probalibity: A relative measure of the likelihoods of events, satisfying

(a) 0 ≤ P(E) ≤ 1,(b) P(Ω) = 1 for any E Ω, and(c) P(E1 E2 ) = P(E1) + P (E2) + , for disjoint E1, E2,

P( i=1Ei) ∑i=1P(Ei)∞ ∞

E F P(E) ≤ P(F),P(Ec) = 1 – P(E),P(E F) = P(E) +P(F) – P(E∩F),…

E1 E2 E3 F1 F2 F3 Fn…

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(ii) multiple (overlapping) partitions (each w/ multiple cuts)

Ω

E1 E2

F1

F2

P(E1∩F1), P(E1∩F2), P(E2∩F1), P(E2∩F2) Joint probability

Spring 2010 EC3303 13


Ω

E1 E2

F1

F2


P(E1) and P(E2) (or likewise, P(F1), P(F2) )Marginal probability

Spring 2010 EC3303 14


Ω

E1 E2

F1

F2


P(E1) and P(E2) (or likewise, P(F1), P(F2) )Marginal probability

P(E1|F1) =

Conditional probabilityP(E1∩F1)P(F1)

(likewise, P(E2|F1), P(E1|F2), P(E2|F2))From these…

Statistical Independence P(E1) = P(E1|F1)betn E1 and F1

“how likely E1 to happen is oblivious of F1”

( P(E1∩F1) = P(E1)P(F1))

P(E2) = P(E2|F1), P(E1) = P(E1|F2), P(E2) = P(E2|F2)Statistical Independencebetn the two paritions

In general, with much finer partitions…?

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How useful is it?

An example (from a German biostatistics text):A recently found contagious (and deadly) disease!You were tested positive (and diagnosed as so). Am I really infected? The prob.? The test’s known to detect 99 out of 100 true infected cases

98 out of 100 true uninfected cases

There is 1/1000 chance of getting infected.

Ω

E1 E2

F1

F2

tested positive tested negative

infected

not‐infeced

P(F1|E1) ?

= P(E1|F1)

= P(E2|F2)

= P(F1)

If in a population of 100,000…

99+1= 10099 1

99,900 = 1,998 + 97,902

1,998 97,902P(F1|E1) = =

P(E1∩F1)P(E1)

992,097

0.047

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2.2 Random Variables and Probability Distributions

A “random variable”, Y “a numerical summary of a random outcome” (S-W)??a collection of (possibly infinitely many) numbers, which

takes on(“realizes to”) one of them when a certain event happens

A “partition” a random variable

ΩE Ec

Y

1if E happens

0if Ec happens

Y Bernoulli(p)where p = P(E)


Y

y1with F1

… ynwith Fn

…

Rolling a dice n = 6Daily SGD vs. USD n = ∞

ΩF1 F2F3 Fn…

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The “probability distribution of Y,” PY

the list(ing) of all probabilities attached to all possible outcomes of Y( the wholesome of all probabilities of the events induced by Y)( the full knowledge of Pr{a ≤ Y ≤ b} for any a,b)

An example: Y Bernoulli(p) with p = P(E) Y 0 1p1 – p

P(Ec) P(E)finite(or countably many) values(“events”)Discrete random variable

(Discrete distn of a r.v.)

uncountably infinitely many values(“events”)Continuous random variable(Continuous distn of a r.v.)

Expressing/Describing a prob. distribution (of a r.v. Y) :

(i) tabulation feasible only in finite cases!(ii) p.m.f.(probability mass function) “pointwise probability (expression)”

p.d.f.(probability density function)(iii) c.d.f.(cumulative distribution function)“range‐wise probability (expression)”

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p.m.f.(probability mass function)“pointwise probability (expression)”

fY(x) = Pr{Y = x}For each possible value x of Y

0 1

1 – pp

only for discrete Y!

p.d.f.(probability density function)

“continuous version of pointwise probability”

μ

fY(x) (≠ Pr{Y = x})For each possible value x of Y

The height of pdf ≠ prob. why?

pmf of Bernoulli(p)

pdf of N(μ,1)

Spring 2010 EC3303 19


p.m.f.(probability mass function)“pointwise probability (expression)”

fY(x) = Pr{Y = x}For each possible value x of Y

0 1

1 – pp

only for discrete Y!

p.d.f.(probability density function)

“continuous version of pointwise probability”

μ

fY(x) (≠ Pr{Y = x})For each possible value x of Y

The height of pdf ≠ prob. why?

a b

Rather, Pr{a ≤ Y ≤ b} = ∫a fY(x)dxb

pmf of Bernoulli(p)

pdf of N(μ,1)

Spring 2010 EC3303 20

c.d.f.(cumulative distribution function)

“range‐wise probability (expression)”

FY(x) = Pr{Y ≤ x}

For each possible value x of Y

= ∑y ≤ x fY(x) (= fY(x)+ fY(x – 1)+ )discrete Y case

| |0 1

1 – p

p

1

= ∫–∞ fY(x)dyx

continuous Y case1

less intuitive than pmf /pdf, butmore convenience b/c always well‐defined

Spring 2010 EC3303 21

Expectations/Moments (of a r.v. Y)

Often, we focus only on certain characteristics of the distn PY, e.g.,“the middle value of all Y outcomes”,“the most likely value of Y”,“how scattered the range of all Y propable values are”,…

the mean of Y (= the expected value of Y)A measure of the center(ing) (counting in “prob”) of the distn PY

EY = y1fY(y1) + y2fY(y2) + + ykfY(yk) discrete Y with k outcomesprob.’s as proper weights

= ∑y yfY(y) ( ∫–∞ yfY(y)dy continuous version)∞

0 1

1 – pp

μ

μY =

μY

Spring 2010 EC3303 22


Often, we focus only on certain characteristics of the distn PY, e.g.,“the middle value of all Y outcomes”,“the most likely value of Y”,“how scattered the range of all Y propable values are”,…




μY =

μY

the variance of Y (= the expected value of the“squared-deviations of Y from μY”)A measure of the dispersion (counting in “prob”) of the distn PY

Var(Y) = (y1 – μY)2fY(y1) + + (yk – μY)2fY(yk) discrete Y with k outcomes

= ∑y (y – μY)2fY(y) ( ∫–∞ (y – μY)2fY(y)dy continuous version)∞

σ²Y =

σ²Y

= E(Y– μY)2

Spring 2010 EC3303 23





μY =

μY

the variance of Y (= the expected value of the“squared-deviations of Y from μY”)A measure of the dispersion (counting in “prob”) of the distn PY

Var(Y) = (y1 – μY)2fY(y1) + + (yk – μY)2fY(yk) discrete Y with k outcomes

= ∑y (y – μY)2fY(y) ( ∫–∞ (y – μY)2fY(y)dy continuous version)∞

σ²Y =

σ²Y

μ

√Var(Y)σY =

the standard deviation of Y

= E(Y– μY)2

Spring 2010 EC3303 24

Recall! (Important properties of μY and σ²Y ): Given a r.v. Y with μY and σ²YIf X = aY + b for any non-random numbers a, b,(a) EX = E(aY + b) = aEY + b = aμY + b(b) Var(X) = Var(aY + b) = a² Var(Y) = a²σ²YOther useful (higher) moments (of a r.v. Y)

the skewness of Y A measure of the asymmetry(inclination) of the distn PY

E(Y– μY)3

σ3Y

the kurtosis of Y A measure of the tail thinckness of the distn PY

E(Y– μY)4

σ4Y

Spring 2010 EC3303 25

Recall! (Important properties of μY and σ²Y ): Given a r.v. Y with μY and σ²YIf X = aY + b for any non-random numbers a, b,(a) EX = E(aY + b) = aEY + b = aμY + b(b) Var(X) = Var(aY + b) = a² Var(Y) = a²σ²YOther useful (higher) moments (of a r.v. Y)

the skewness of Y A measure of the asymmetry(inclination) of the distn PY

E(Y– μY)3

σ3Y

the kurtosis of Y A measure of the tail thinckness of the distn PY

E(Y– μY)4

σ4Y

Spring 2010 EC3303 26

2.3 Multiple RandomVariables (“More than one r.v.?”)

Remember! A “random variable”, Y


ΩE Ec

Y

1if E happens

0if Ec happens

Y Bernoulli(p)where p = P(E)


Y

y1with F1

… ynwith Fn

…

Rolling a dice n = 6Daily SGD vs. USD n = ∞

ΩF1 F2F3 Fn…

ec 3303 spring 10 intro 1

Documents

espring2010 ec3303

dataistheleastdeceiv

satisfyinga0 pe

increased reliance

introductory econometrics

basic econometrics

pe u f

gun buybacks