Econ 399 Introductory Econometrics

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Econ 399Introductory Econometrics

• Multivariable Regressions
• Multivariable Inference
• Multivariable Statistical Adjustments

Lorne Priemaza, M.A. Lorne.priemaza_at_ualberta.ca

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1. Nature of Econometrics

• 1.1 What is Econometrics?
• 1.2 Steps in Empirical Economic Analysis
• 1.3 The Structure of Economic Data
• 1.4 Causality and the Notion of Ceteris Paribus
  in Econometric Analysis
• Note All uncredited quotes are from
  Wooldridges Introductory Econometrics (2006)

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1.1 What is Econometrics?

• Definition
• Econometrics is based upon the development of
  statistical methods for estimating economic
  relationships, testing economic theories, and
  evaluating and implementingpolicy

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1.1 What is Econometrics?

• Uses
• -What impact does the price of writable DVDs
  have on the price of movie popcorn? (estimating
  relationship)
• -Success of a marriage is inversely related to
  time spent dating. (testing theory)
• -Implementing a health care fee acts to eliminate
  waste. (evaluating policy)

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Econometrics vs. Math. Statistics (generally)

• Mathematical Statistics
• Deals with controlled Experimental Data
• Experimental Data Data collected in a controlled
  environment
• Researcher is an active collector in a
  controlled, artificial environment

• Econometrics
• Deals with problematic nonexperimental data
• Nonexperimental Data Observational Data,
  observations of agents in the real world
• Researcher is a passive collector of data from
  the real world

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1.1 What is Econometrics?

• Econometrics
• -Using a hidden camera in a supermarket, 27 of
  shoppers bought Captain Chocolates Chocolate
  Heart Attack in a Box (CCCHAB) with extra
  Chocolate marshmallows
• Mathematical Statistics
• -In a focus group of 57 people, 63 chose CCCHAB
  over the top 3 chocolate brands

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1.1 What is Econometrics?

• Note
• -Econometrics can use controlled experiments and
  statistics originally devised ways to deal with
  observable data
• -Due to monetary, scope and morality constraints,
  econometricians wrestle with nonexperimental data
  more often
• -ie a lab study on the mortality rate of middle
  class citizens using cell phones is monetarily,
  morally, and administratively unfeasible

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1.2 Steps in Empirical Economic Analysis

• -Empirical analysis generally arises from two
  areas
• Estimating a Relationship
• Ie What factors determine a hockey players
  salary?
• 2) Testing a Theory
• Ie Studying after 11pm is less effective than
  studying before 11pm.

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1.2 Steps in Empirical Economic Analysis

• An Empirical Analysis uses data to test a theory
  or estimate a relationship.

How?
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1.2 Steps in Empirical Economic Analysis

• 1) Formulate a question/hypothesis
• -Does income influence driving habits?
• 2) Construct an economic model
• Economic Models consist of mathematical
  equations that describe various relationships.
• -Drivingf(age, income, training, family,
  vehicle, location)

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1.2 Steps in Empirical Economic Analysis

• Economic Models Can Come From Formal Derivations
• Formal Derivations Arise From Economic
  Assumptions and Models
• -Economic agents are acting to maximize utility
• -Resources are scarce
• -Information is imperfect
• -An increase in price causes a decrease in
  quantity demanded
• -Nash Equilibrium

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1.2 Steps in Empirical Economic Analysis

• VERY SIMPLE Formal Derivations
• -Brushing ones teeth is a function of
  inputssimple production theory
• brushingf(time, toothpaste)
• -The amount of toothpaste purchased is a function
  of price, availability, income and price of
  substitutes (ie whitening strips)simple demand
  theory
• toothpastef(Ptp, avail, I, Py)

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1.2 Steps in Empirical Economic Analysis

• -Time is a function of income, work, sleep,
  family status, motivation (laziness)
• timef(I, work, sleep, family, motivation)
• -Therefore, brushing ones teeth is a function of
  the determinants of the inputs
• brushingf(Ptp, Availtp, I, Py, work, sleep,
• family, motivation)

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1.2 Steps in Empirical Economic Analysis

• Economic Models Can Also Arise From Intuition or
  Observation (ie statistics)
• -Tall people dont like Wii video games
• -Small businesses are less likely to change
  prices
• -Marks are higher in morning classes than
  afternoon classes
• -Impaired Driving Charges Jump 25 (Keith Gerein
  and Elise Stolete, Impaired Driving Charges Jump
  25, Edmonton Journal (4 January 2008), A1)
• -Couples living together have an 80 greater
  chance of divorce than those who dont (Barbara
  Vobejda, Number of Couples Cohabitating Soring
  as Mores Relax, Houston Chronicle (5 December
  1996), 13A)

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1.2 Steps in Empirical Economic Analysis

• Economic Models Can Also Arise From A Mixture of
  Formal Derivations, Intuition or Observation (ie
  statistics)
• -Tall people dont like Wii video games
• And
• -Quantity demanded is a function of price
• Therefore
• Wii game demandf(height, price)

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1.2 Steps in Empirical Economic Analysis

• 3) Specify an Econometric Model
• -Econometric Models have specific functional
  forms and OBSERVABLE parameters
• Ie brushingf(Ptp, Availtp, I, Py, work, sleep,
• family, motivation)
• Becomes

Where famSize estimates family status and u
takes into account unobservable factors
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Econ 299 Review
If we are interested in the impact of sleep on
teeth brushing, we are interested in the B5
parameter. Notice also that dBi/ dSleepi B5
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1.2 Steps in Empirical Economic Analysis

• Note
• For the most part, econometric analysis begins
  by specifying an econometric model, without
  consideration of the details of the models
  creation.
• -Loosely guided by economic theory and intuition,
  chose a functional form and include variables for
  the initial model
• -functional forms can be modified and variables
  added or deleted as statistical tests are done

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1.2 Steps in Empirical Economic Analysis

• 4) Formulate Hypothesis on the various parameters
  
• -Ask the questions or challenge the issues from
  part 1
• Ie if you believe that sleep has no impact on
  teeth brushing
• Ho B50
• HaB5?0

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1.3 The Structure of Economic Data

• Before a hypothesis can be tested and any
  conclusion made, data must be gathered.
• There exist a variety of types of economic data
• Cross-Sectional Data
• Time Series Data
• Pooled Cross Section Data
• Panel (Pooled) Data
• -Each data type has advantages and disadvantages.

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1.3 The Structure of Economic Data

• 1) Cross-Sectional Data
• -A sample of economic agents (households, firms,
  governments, groups, etc) at one point in time.
• Examples
• -Household spending this Christmas
• -current Wii prices across the city
• -class height
• -National Unemployment

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1.3 The Structure of Economic Data

• Generally the entire population cannot be polled,
  so a Cross-Sectional data set is assumed to be a
  RANDOM SAMPLE However, a sample of the
  population is not random if
• Bias occurs
• A sample selection problem occurs (some
  categories of respondents are more likely to
  respond than others)
• Sample size is too small
• Sample size is too large

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1.3 The Structure of Economic Data

• Bias Example
• -Interview university students to find out common
  society attitudes towards sex
• -Doing a landline phone survey to determine long
  distance plans
• Sample Selection Example
• -Rich households are less likely to report their
  incomes
• -Men are more likely to overestimate the number
  of their relationships

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1.3 The Structure of Economic Data

• Small Sample Size Example
• -Using this class as representative of the
  university population
• -Any study with less than 30-40 observations
• Large Sample Size Example
• -Asking 80 of this class their opinions on the
  text and expected grade
• -One students answer is affected by anothers

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1.3 The Structure of Economic Data

• 1) Cross-Sectional Data
• -Cross-sectional data is often used in
  microeconomics
• -labour economics
• -public finance
• -industrial organization (IO)
• -urban economics
• -health economics

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Cross-Sectional Wii Data
Obs. Person Hours Wii Played Hours Studied Utility Male
1 Alberta 5 8 24 0
2 Jayne 12 1 35 1
3 Dominique 3 12 22 0
4 Craig 4 4 23 1
5 Kristy 6 2 28 0
6 Josh 3 1 27 1
7 David 1 15 21 1
8 Francis 1 18 20 0
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1.3 The Structure of Economic Data

• 1) Cross-Sectional Data
• -Generally cross-sectional data will include an
  observation number
• -the order of these observations doesnt matter
• -Data may also include a DUMMY VARIABLE to
  indicate if a given observation has a given trait
  (male, educated, employed, etc.)
• -Dummy variables will be covered in chapter 7

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1.3 The Structure of Economic Data

• 2) Time Series Data
• -Time series tracks the movement of (one
  agent/groups) variables over time
• Examples
• -Stock, Wii or Xbox 360 prices
• -GDP
• -Player Stats
• -Edmontons vacancy rate

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1.3 The Structure of Economic Data

• 2) Time Series Data
• -Time series data also often uses a chronological
  observation variable
• -in this case, ORDER IS IMPORTANT!
• -few economic observations are independent across
  time
• -trending this terms observation depends
  somewhat on last terms observation
• -ie Income, weight, spending, happiness

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1.3 The Structure of Economic Data

• 2) Time Series Data
• -Time series data can vary in data frequency
  (daily, weekly, quarterly, etc.)
• -frequent time series data can exhibit seasonal
  patterns (ie ice cream sales fall in winter)
• -frequent time series data can be aggregated to
  evaluate all data on the same frequency

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Time Series Wii Data For Jayne
Week Hours Wii Played Hours Studied Utility
1 4 2 31
2 12 1 35
3 8 1 27
4 10 2 23
5 5 4 21
6 9 1 29
7 11 3 36
8 14 4 39
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1.3 The Structure of Economic Data

• 3) Pooled Cross Sections
• -Pooled Cross sections are a combination of
  RANDOM samples from different years
• -the same observation should not be followed over
  different years
• -Analysis is similar to cross sectional data,
  with the additional consideration of structural
  changes due to time
• -relatively new concept useful for analyzing
  policy effects

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Pooled Cross-Sectional Nintendo Data
Obs. Year Hours System Played Hours Studied Utility Male
1 1995 (pre Wii) 6 9 27 1
2 1995 9 5 35 1
3 1995 4 7 12 0
4 1995 7 2 25 0
5 2007 (post Wii) 6 5 17 0
6 2007 3 7 22 1
7 2007 1 11 25 0
8 2007 6 4 22 1
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1.3 The Structure of Economic Data

• 4) Panel (Pooled) Data
• -time series data for EACH cross-sectional agent
  in set
• -also called longitudinal data
• -preferred ordering is by grouping agents
• -ie first agent over time followed by second
  agent over time

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1.3 The Structure of Economic Data

• Panel (Pooled) Data Advantages
• -able to control for unobserved characteristics
• -able to study the effect of lags
• -able to work with a larger data set
• Panel (Pooled) Data Disadvantages
• -statistical problems of cross-sectional data
• -statistical problems of time series data
• -more difficult to work with

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Pooled Tuition
University Tuit 99/00 Tuit 00/01 Tuit 01/02 Tuit02/03
Alberta 3551.00 3770.00 3890.00 4032.00
British Columbia 2295.00 2295.00 2181.00 2661.00
Calgary 3650.00 3834.00 3975.00 4120.00
Concordia 1668.00 1668.00 1668.00 1668.00
Lethbridge 3360.00 3470.00 3470.00 3470.00
Manitoba 3005.00 2796.00 2807.00 2818.00
McGill 1668.00 1668.00 1668.00 1668.00
Ottawa 3760.00 3892.00 4009.00 4085.00
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1.3 The Structure of Economic Data

• Notes
• -panel data and pooled cross sectional data is
  not covered in this course, but can be used in
  the project report if extra research is done
• -as time series data is difficult to analyze due
  to trending, methods on dealing with time series
  data become obsolete and disproved over time

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1.4 Causality and the Notion of Ceteris Paribus
in Econometric Analysis

• One goal of econometric analysis is to examine
  the causality of two variables
• -a simple plotting of two variables or
  calculation of correlation will only see if the
  two variables move together
• -cant show causation
• -although many people use simple movement
  statistics to conclude about causation

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1.4 Causality and the Notion of Ceteris Paribus
in Econometric Analysis

• Ceteris paribus
• -causality can only be correctly examined Ceteris
  Paribus with all else held equal
• -one variables impact on another variable can
  only be isolated if all other variables remain
  constant

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1.4 Causality and the Notion of Ceteris Paribus
in Econometric Analysis

• Causation in a perfect, experimental world
• -causation is easier to isolate in an
  experimental world
• Take two identical agents and change one of their
  variables (X) and observe the change in Z (cross
  sectional study)
• Take an agent and exogenously change one variable
  (X) and observe the change in Z (time series
  study)
• -less accurate due to trending

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1.4 Causality and the Notion of Ceteris Paribus
in Econometric Analysis

• Causation in the real world
• -in the real world, variables change for a reason
• Ie the change in X is caused by a change in A
  and B, which itself causes a change in Y
• Is the change in Z due to the change in A, B, X,
  Y or Z?
• Zf(A)? Zf(B)? Zf(X)? Zf(Y)?
• Or Zf(A, B, X, Y)?

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1.4 Causality and the Notion of Ceteris Paribus
in Econometric Analysis

• Causation example
• Take the statistic Living together before
  marriage increases the chance of divorce

Living Together
Higher Divorce Chance
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1.4 Causality and the Notion of Ceteris Paribus
in Econometric Analysis

• Causation example
• BUT why do two people decide to live together?

Uncertainty about partner
?
?
Living Together
Higher Divorce Chance
?
Fear of Commitment
What actually affects divorce rates?
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1.4 Causality and the Notion of Ceteris Paribus
in Econometric Analysis

• Causation in the real world
• -in the real world, rarely can ALL variables be
  fixed
• -for example, some immeasurable factors (part
  of the error term) cant be fixed
• -ie Aptitude
• -the question is are enough variables fixed that
  a good case can be made for causality?

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1.4 Causality and the Notion of Ceteris Paribus
in Econometric Analysis

• Final Note
• -Even a perfectly controlled model can
  economically show causation between unrelated
  variables
• Ie Oilers standings and the amount of rainfall
  in New York
• -Any econometric model must have behind it some
  THEORY of causation