Econ 399 Introductory Econometrics Multivariable Regressions Multivariable Inference

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) • Mathematical Statistics • Econometrics – Deals with controlled – Deals with problematic Experimental Data nonexperimental – Experimental Data: data Data collected in a – Nonexperimental controlled Data: Observational environment Data, observations of – Researcher is an agents in the real active collector in a world controlled, artificial – Researcher is a environment passive collector of data from the real 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 11 pm is less effective than studying before 11 pm.

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,

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), A 1) -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), 13 A)

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 fam. Size 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 B 5 parameter. Notice also that δBi/ δSleepi = B 5

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: B 5=0 Ha: B 5≠ 0

1. 3 The Structure of Economic Data Before a hypothesis can be tested any conclusion made, data must be gathered. There exist a variety of types of economic data: Ø Ø 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 Obs. Person 1 Alberta 2 Jayne 3 Hours Wii Played Hours Studied Utility Male 5 8 24 0 12 1 35 1 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 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

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 Obs. Year Hours System Hours 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 Tuit 02/03 Alberta 3551. 00 3770. 00 3890. 00 4032. 00 British Columbia 2295. 00 2181. 00 2661. 00 Calgary 3650. 00 3834. 00 3975. 00 4120. 00 Concordia 1668. 00 Lethbridge 3360. 00 3470. 00 Manitoba 3005. 00 2796. 00 2807. 00 2818. 00 Mc. Gill 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

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