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					      Econ 399
   Introductory Econometrics


•Multivariable Regressions
 •Multivariable Inference
 •Multivariable Statistical
       Adjustments
     Lorne Priemaza, M.A.

  Lorne.priemaza@ualberta.ca
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 Wooldridge’s
     Introductory Econometrics (2006)
   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 implementing…policy”
   1.1 What is Econometrics?

•Uses
-What impact does the price of writable
DVD‟s 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)
       Econometrics vs. Math. Statistics
                        (generally)
• Econometrics                 • Mathematical Statistics
   – Deals with problematic         – Deals with
     nonexperimental                  controlled
     data                             Experimental Data
   – Nonexperimental                – Experimental Data:
     Data: Observational              Data collected in a
     Data, observations of            controlled
     agents in the real               environment
     world                          – Researcher is an
   – Researcher is a                  active collector in a
     passive collector of             controlled, artificial
     data from the real               environment
     world
   1.1 What is Econometrics?

• Econometrics
 -Using a hidden camera in a supermarket,
 27% of shoppers bought Captain Chocolate‟s
 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
   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
 1.2 Steps in Empirical Economic Analysis
-Empirical analysis generally arises from two
areas:

1) Estimating a Relationship
Ie: What factors determine a hockey
player‟s salary?

2) Testing a Theory
Ie: Studying after 11pm is less effective
than studying before 11pm.
1.2 Steps in Empirical Economic Analysis


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

                 How?
 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.”
   -Driving=f(age, income, training, family,
               vehicle, location)
 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
 1.2 Steps in Empirical Economic Analysis
VERY SIMPLE Formal Derivations…
-Brushing one‟s teeth is a function of
inputs…simple production theory:

 brushing=f(time, toothpaste)
-The amount of toothpaste purchased is a
function of price, availability, income and price of
substitutes (ie: whitening strips)…simple demand
theory

 toothpaste=f(Ptp, avail, I, Py)
 1.2 Steps in Empirical Economic Analysis
-Time is a function of income, work, sleep, family
status, motivation (laziness)

 time=f(I, work, sleep, family, motivation)

-Therefore, brushing one‟s teeth is a function of
the determinants of the inputs:

 brushing=f(Ptp, Availtp, I, Py, work, sleep,
            family, motivation)
 1.2 Steps in Empirical Economic Analysis
Economic Models Can Also Arise From Intuition or
 Observation (ie: statistics)
-Tall people don‟t 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 don‟t (Barbara Vobejda,
 “Number of Couples „Cohabitating Soring as Mores Relax,” Houston Chronicle (5 December 1996), 13A)
 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 don‟t like Wii video games
And
-Quantity demanded is a function of price
Therefore
Wii game demand=f(height, price)
    1.2 Steps in Empirical Economic Analysis
3) Specify an Econometric Model
  -Econometric Models have specific functional forms
  and OBSERVABLE parameters

  Ie: brushing=f(Ptp, Availtp, I, Py, work, sleep,
            family, motivation)
Becomes


Where famSize estimates family status and u takes into
 account unobservable factors
   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

δBi/ δSleepi = B5
    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 model‟s 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
 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: B5=0
   Ha:B5≠0
 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.
 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
 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:
1) Bias occurs
2) A sample selection problem occurs (some
   categories of respondents are more likely to
   respond than others)
3) Sample size is too small
4) Sample size is too large
 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
 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 student‟s answer is affected by another‟s
 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
          Cross-Sectional Wii Data
                   Hours Wii       Hours
Obs.   Person        Played          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
 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 doesn‟t 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
 1.3 The Structure of Economic Data
2) Time Series Data

-Time series tracks the movement of (one
 agent/group‟s) variables over time
Examples

-Stock, Wii or Xbox 360 prices
-GDP
-Player Stats
-Edmonton‟s vacancy rate
 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 term‟s observation depends
  somewhat on last term‟s observation
     -ie: Income, weight, spending, happiness
 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
       Time Series Wii Data For Jayne
          Hours Wii
Week        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
 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
Pooled Cross-Sectional Nintendo Data
                      Hours
Obs                   System Hours
  . Year               Played  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
 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
 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
                   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
 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
 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
    -can‟t show causation
    -although many people use simple movement
 statistics to conclude about causation
 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 variable‟s impact on another variable can
 only be isolated if all other variables remain
 constant
 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
a) Take two identical agents and change one of
   their variables (X) and observe the change in
   Z (cross sectional study)
b) Take an agent and exogenously change one
   variable (X) and observe the change in Z
   (time series study)
          -less accurate due to trending
 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?
Z=f(A)? Z=f(B)? Z=f(X)? Z=f(Y)?
Or         Z=f(A, B, X, Y)?
 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
 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?
 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) can‟t be fixed
           -ie: Aptitude

-the question is: are enough variables fixed that
   a good case can be made for causality?
 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: Oiler‟s standings and the amount of rainfall in
    New York

-Any econometric model must have behind it
   some THEORY of causation

				
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