Econometric Analysis

Econ 141 Spring 2014

Lecture: January 22, 2014

Bart Hobijn

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The views expressed in these lecture notes are solely those of the instructor and do not necessarily

reflect those of the UC Berkeley, or other institutions with which he is affiliated.

Who am I

Name: Bart Hobijn

Email: bhobijn@berkeley.edu

Office hours: M-W after lecture and by

appointment

I will only respond to emails about this class through the above UC Berkeley

email address. Class-related emails to other addresses will be ignored.

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Overview of class

1. What this course is about

2. What you need to do for a grade

3. Structure of lectures and sections

4. Outline of the material covered

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1. What this course is about

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Main objective of course

• Description: “Introduction to problems of observation, estimation,

and hypothesis testing in economics. This course

covers the statistical theory for the linear regression

model and its variants, with examples from

empirical economics.”

• Econometrics and linear regressions are

everywhere!

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Increased labor market frictions?

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Jun-12

1%

2%

3%

4%

5%

2% 4% 6% 8% 10% 12%

Source: Daly, Hobijn, Sahin, and Valletta (2012)

Monthly observations; pre-2007-recession fit

Actual and fitted Beveridge Curve

Unemployment rate

Job openings rate

before 2007 recession

since 2007 recession

Fitted

Gap: 2.7%

Japan’s Phillips Curve looks like Japan

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-4

-2

0

2

4

6

8

10

-7 -6 -5 -4 -3 -2 -1 0

Source: Based on Gregor Smith (2006)

Minus unemployment rate versus 12-month CPI inflation (Jan 1980 - August 2005)

Japanese Phillips Curve

Minus the unemployment rate

Inflation (Percent)

Output growth forecasts

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Source: http://www.cbo.gov/publication/43846

Effect of minimum wage on employment

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Source: Card and Krueger, American Economic Review (1994)

Amazon recommendations

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Four levels of understanding…

• Theory

Theory and assumptions behind linear

regression model and its derivatives

• Case studies

Real-life applications of econometrics

• Practice

Do your own analyses in Excel and STATA

• Presentation

Learn how to best present your results using

tables, figures, and equations. 1/22/2014 Econ 141, Spring 2014 11

2. What you need to do for a grade

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Course requirements

1. Fulfill course prerequisites prerequizit

2. Stay enrolled see department enrollment policy

3. Complete three things for a grade

What when weight

a) Empirical assignment 04/30/2014 20%

b) Midterm 03/05/2014 30%

c) Final 05/16/2014 50% See course syllabus for details

4. Behave Zero-tolerance policy on academic dishonesty. Any episode will be handled in

accordance with university regulations, with no exceptions.

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3. Structure of lectures and course

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Learning Econometrics is

like learning to drive…

• You have to know theory and rules

– Lectures and textbook

• You have take a seat behind steering

wheel

– Practical examples

– Empirical assignment

• You have to practice

– Sections

– Student resources

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What you are expected to read

1. Main textbook James H. Stock and Mark W. Watson (2010) “Introduction

to Econometrics”, 3rd edition, Chapters 1 through 13.

2. Student resources that accompany book

3. Lecture slides

4. Additional materials Provided through the class’ bSpace site.

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What you are suggested to use

• Statistical software

– STATA

• Program Available in computer lab or obtain a student

copy of STATA/IC for $69 (six-month license).

• Tutorial Available at student resources for textbook

– Microsoft Excel

• Program Part of Microsoft office.

• Examples during lecture and section STATA examples in version 11 and Excel example workbooks for class are tested in Excel 2010 under Windows.

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What lectures add to class

• Additional theory

– Linear algebra

– Regression analysis in matrix notation

– Asymptotic theory

• Practical examples

– Use of STATA and Excel

– Real-life cases and applications

• Pointers to what is important

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Practice makes perfect

Sections cover

• Selected even-numbered problems from

book.

• Empirical problems from book.

• Software how-to’s for STATA and Excel.

• Additional problems about asymptotics and

matrix notation.

What is covered during sections is very representative

for what will be on the midterm and final.

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4. Outline of material covered

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Five main topics covered

I. Review of probability and statistics (Ch.2-3)

II. Simple linear regression model (Ch. 4-5)

III. Multiple regression model (Ch. 6-7)

IV.Assessing, validating, and presenting

regression results (Ch. 8-11)

V. Establishing causation rather than

correlation (Ch. 12-13)

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I. Review of probability and statistics

• Expectations, variance, and covariance

• Sample approximations of expectations

– Law of Large Numbers(LLN) and Central Limit

Theorem (CLT)

• Commonly used statistical distributions

– Normal, Student-t, Chi-squared, F

• Hypothesis testing

– Null versus alternative hypothesis

– Type-I and type-II errors and p-values.

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II. Simple linear regression model

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AUT

BEL

DNK

FIN

FRA

DEU

ITA

NLD

NOR

SWE

CHE

GBR1.5

1.7

1.9

2.1

2.3

2.5

2.7

1.5

1.7

1.9

2.1

2.3

2.5

2.7

30 40 50 60 70 80 90 100 110

Source: Maddison (2010)

Average annualized growth from 1900-2008

Convergence in Western Europe

1900 level of real GDP per capita (as percent of that in GBR)

Percent (annualized) Percent (annualized)

Assumptions and properties

𝑌𝑖 = 𝛽0 + 𝛽1𝑋𝑖 + 𝑢𝑖, sample 𝑖 = 1, … , 𝑛

• Assumptions under which we can estimate

𝛽0 and 𝛽1 based on sample information

• Properties of estimators: 𝛽 0 and 𝛽 1

– Their expectation

– Do they get close to 𝛽0 and 𝛽1 when 𝑛 big?

– How close do they get? What is their distribution?

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III. Multiple regression model

Mincer regression:

ln 𝑊𝑖 = 𝛽0 + 𝛽1𝑒𝑑𝑢𝑐𝑎𝑡𝑖𝑜𝑛𝑖 + 𝛽2𝑒𝑥𝑝𝑒𝑟𝑖𝑒𝑛𝑐𝑒𝑖 + 𝑢𝑖

. regress lnhrwage educ exp

Source | SS df MS Number of obs = 179560

-------------+------------------------------ F( 2,179557) =28337.60

Model | 14238.8902 2 7119.44509 Prob > F = 0.0000

Residual | 45111.3137179557 .251236731 R-squared = 0.2399

-------------+------------------------------ Adj R-squared = 0.2399

Total | 59350.2038179559 .330533161 Root MSE = .50124

------------------------------------------------------------------------------

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

-------------+----------------------------------------------------------------

Education | .1015499 .0004471 227.14 0.000 .1006737 .1024262

Experience | .0106627 .0000932 114.44 0.000 .01048 .0108453

Constant | .7211546 .0065248 110.53 0.000 .7083662 .7339431

------------------------------------------------------------------------------

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III. Multiple regression model

Mincer regression:

ln 𝑊𝑖 = 𝛽0 + 𝛽1𝑒𝑑𝑢𝑐𝑎𝑡𝑖𝑜𝑛𝑖 + 𝛽2𝑒𝑥𝑝𝑒𝑟𝑖𝑒𝑛𝑐𝑒𝑖 + 𝑢𝑖

. regress lnhrwage educ exp

Source | SS df MS Number of obs = 179560

-------------+------------------------------ F( 2,179557) =28337.60

Model | 14238.8902 2 7119.44509 Prob > F = 0.0000

Residual | 45111.3137179557 .251236731 R-squared = 0.2399

-------------+------------------------------ Adj R-squared = 0.2399

Total | 59350.2038179559 .330533161 Root MSE = .50124

------------------------------------------------------------------------------

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

-------------+----------------------------------------------------------------

Education | .1015499 .0004471 227.14 0.000 .1006737 .1024262

Experience | .0106627 .0000932 114.44 0.000 .01048 .0108453

Constant | .7211546 .0065248 110.53 0.000 .7083662 .7339431

------------------------------------------------------------------------------

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Return to education

𝜷 𝟏 = 𝟎. 𝟏𝟎

One more year of

education raises

wages by about 10%

Assumptions and properties

𝑌𝑖 = 𝛽0 + 𝛽1𝑋1𝑖 + ⋯ + 𝛽1𝑋1𝑖 + 𝑢𝑖, 𝑖 = 1, … , 𝑛

• Linear algebra Generalize estimators simple

regression model using matrix algebra.

• Assumptions Under which conditions can

we use estimators?

• Properties How do the properties of the

estimator in simple linear regression model

translate to multiple regression model?

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IV. Assessing and presenting results

• Test for hypotheses

• Various ways of specifying the model

• Violations of assumptions behind the model

and ways to deal with that in estimation

• Presenting data and results:

– Summary statistics and descriptive figures

– Regression-result tables

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V. Causation vs. correlation

• This commercial summarizes this issue in a

nutshell. Disclaimer: This is not an endorsement of Bud Light.

I actually do not drink it.

• How do we distinguish between

– Changes in the 𝑋 variable comove with changes

in the 𝑌 variable.

– Changes in the 𝑋 variable cause the changes in

the 𝑌 variable.

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Experiments used in UK

for policy analysis

• “Britain’s Ministry of Nudges” (NY Times, 12/08/2013)

– Performs experiments to measure success rate

of different government policies to nudge

subjects towards behavior that leads to improved

outcomes

– Improved program outcomes related to

• Job search intensity of the unemployed.

• Solar panel subsidy pick-up rates.

• Organ donor program participation.

• Pick-up of 401K programs.

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Quasi-experiment on loan quality

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Source:

“Did Securitization Lead

to Lax Screening?

Evidence from Subprime

Loans”

Benjamin J. Keys, Tanmoy

Mukherjee, Amit Seru and

Vikrant Vig

Quarterly Journal of Economics

(2010) 125 (1): 307-362.

doi: 10.1162/qjec.2010.125.1.307

Summary

Key topics/concepts

• Course requirements

• Course material

• Structure of lectures

and sections

• Outline of topics

Reading

• S&W Chapter 1

Exercises

• None.

• Review your mistakes

on Prerequizit.

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