M01 StockWatson123635 03 Econ Part01

7/17/2019 M01 StockWatson123635 03 Econ Part01

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Introductionto Econometrics

Chapters 1, 2 and 3

The statistical analysis of

economic (and relateddata


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Brief Overview of the Course

! "conomics s#ggests important relationships$ often%ith policy implications$ t virt#ally nevers#ggests '#antitative magnit#des of ca#saleffects.

What is the quantitativeeffect of red#cing class si)e onst#dent achievement*

+o% does another year of ed#cation change earnings*

What is the price elasticity of cigarettes*

What is the effect on o#tp#t gro%th of a 1 percentage

point increase in interest rates &y the ,ed* What is the effect on ho#sing prices of environmental

improvements*


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This course is about using data tomeasure causa effects!

! deally$ %e %o#ld lie an e/periment

What %o#ld &e an e/periment to estimate the effect of classsi)e on standardi)ed test scores*

! #t almost al%ays %e only have o&servational(none/perimental data.

ret#rns to ed#cation

cigarette prices

monetary policy

! ost of the co#rse deals %ith diffic#lties arising from #singo&servational to estimate ca#sal effects

confo#nding effects (omitted factors sim#ltaneo#s ca#sality

correlation does not imply ca#sation3


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! 4earn methods for estimating ca#sal effects #singo&servational data

! 4earn some tools that can &e #sed for other p#rposes5 fore/ample$ forecasting #sing time series data5

! ,oc#s on applications theory is #sed only as needed to#nderstand the %hys of the methods5

! 4earn to eval#ate the regression analysis of others thismeans yo# %ill &e a&le to read6#nderstand empiricaleconomics papers in other econ co#rses5

! 7et some hands-on e/perience %ith regression analysis inyo#r pro&lem sets.

In this course #ou wi$


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! Empirica probem$ Class si)e and ed#cationalo#tp#t

Policy '#estion8 What is the effect on test scores (orsome other o#tcome meas#re of red#cing class si)e &y

one st#dent per class* &y 9 st#dents6class* We m#st #se data to find o#t (is there any %ay to ans%er

this withoutdata*

&eview of 'robabiit# and (tatistics)(* Chapters 2, 3+


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The Caifornia Test (core ata (et

All :-; and :-9 California school districts (n< =20

>aria&les8

! ?PthP

grade test scores (@tanford- achievement test$com&ined math and reading$ district average

! @t#dent-teacher ratio (@TB < no. of st#dents in thedistrict divided &y no. f#ll-time e'#ivalent teachers


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Initia oo/ at the data$(You should already know how to interpret this table)

This ta&le doesnt tell #s anything a&o#t the relationship&et%een test scores and the STR.


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o districts with smaer casses havehigher test scores

(catterpot of test score v. st#dent-teacher ratio

What does this figure show?


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*e need to get some numerica evidence on whetherdistricts with ow (T&s have higher test scores but how

1. Compare average test scores in districts %ith lo% @TBs to

those %ith high @TBs (estimation3

2. Test the n#ll3 hypothesis that the mean test scores in the

t%o types of districts are the same$ against the

alternative3 hypothesis that they differ (hypothesistesting3

D. "stimate an interval for the difference in the mean test

scores$ high v. lo% @TB districts (confidence interval3


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Initia data ana#sis$ Compare districts %ith small3 (@TB E20 and large3 (@TB F 20 class si)es8

1. Estimationof < difference &et%een gro#p means

2. Test the hypothesisthat < 0

3. Constr#ct a confidence intervalfor

Class @i)e Average score

(

@tandard deviation

(sY

n

@mall ;?G.= 1.= 2D9

4arge ;?0.0 1G. 192

Y


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1! Estimation

<

< ;?G.= ;?0.0

< G.=s this a large difference in a real-%orld sense*

@tandard deviation across districts < 1.1

Hifference &et%een ;0PthPand G?PthPpercentiles of test

score distrition is ;;G.; ;?.= < 9.2 This is a &ig eno#gh difference to &e important for school

reform disc#ssions$ for parents$ or for a school

committee*

1n

small

Yi

i=1

nsmall

Ysmall Ylarge

1n

large

Yi

i=1

nlarge


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2! 5#pothesis testing

t=Ys Y

l

ss2

ns

+ sl2

nl

=Ys Y

l

SE(Ys Y

l)

Hifference-in-meanstest8 comp#te the t-statistic$ (remem&er this*

! %here SE( is the standard error3 of $

the s#&scripts sand lrefer to small3 and large3

@TB districts$ and (etc.

Ys Yl Ys Yl

ss

2

=

1

ns 1(Y

iYs

)2

i=1

ns


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Comp#te the difference-of-means t-statistic8

< =.0?

ItI J 1.;$ so reKect (at the ?L significance levelthe n#ll hypothesis that the t%o means are thesame.

@i)e sY n

small ;?G.= 1.= 2D9

large ;?0.0 1G. 192

Y

t=Ys Ylss2

ns

+ sl2

nl

=657.4 650.0

19.42

238+ 17.9

2

182

=7.4

1.83


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3! Confidence interva

A ?L confidence interval for the difference &et%eenthe means is$

( M 1.;NSE(

< G.= M 1.;N1.9D < (D.9$ 11.0

Two equivalent stateents!1. The ?L confidence interval for doesnt incl#de 05

2. The hypothesis that < 0 is reKected at the ?L level.

Yl

Ys

Yl

Ys


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*hat comes ne6t7

! The mechanics of estimation$ hypothesis testing$and confidence intervals sho#ld &e familiar

! These concepts e/tend directly to regression andits variants

! efore t#rning to regression$ ho%ever$ %e %illrevie% some of the #nderlying theory ofestimation$ hypothesis testing$ and confidenceintervals8 Why do these proced#res %or$ and %hy #se these rather

than others*

We %ill revie% the intellect#al fo#ndations of statisticsand econometrics


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&eview of (tatistica Theor#

1. The probabiit# framewor/ for statistica inference

2. "stimation

D. Testing

=. Confidence ntervals

The probabiit# framewor/ for statistica inference

a Pop#lation$ random varia&le$ and distrition

& oments of a distrition (mean$ variance$ standarddeviation$ covariance$ correlation

c Conditional distritions and conditional meansd Histrition of a sample of data dra%n randomly from a

pop#lation8 Y1$ O$ Yn


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)a+ 'opuation, random variabe, anddistribution

Population

! The gro#p or collection of all possi&le entities of interest(school districts

! We %ill thin of pop#lations as infinitely large ( is an

appro/imation to very &ig3

Random variable Y

! Q#merical s#mmary of a random o#tcome (district averagetest score$ district @TB


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Population distribution of Y

! The pro&a&ilities of different val#es of Ythat occ#rin the pop#lation$ for e/. PrRY< ;?0S (%hen Yisdiscrete

! or8 The pro&a&ilities of sets of these val#es$ for e/.PrR;=0 Y ;;0S (%hen Yis contin#o#s.


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)b+ 8oments of a popuation distribution$ mean,variance, standard deviation, covariance,correation

mean< e/pected val#e (e/pectation of Y

< E(Y

< Y

< long-r#n average val#e of Yover repeatedreali)ations of Y

variance < E(Y YP2P

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