Pre-regression Basics

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# Pre-regression Basics - PowerPoint PPT Presentation

Pre-regression Basics. Random Vs. Non-random variables Stochastic Vs. Deterministic Relations Correlation Vs. Causation Regression Vs. Causation Types of Data Types of Variables The Scientific Method Necessary &amp; Sufficient Conditions. Random Vs. Non-random Variables.

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Pre-regression Basics
• Random Vs. Non-random variables
• Stochastic Vs. Deterministic Relations
• Correlation Vs. Causation
• Regression Vs. Causation
• Types of Data
• Types of Variables
• The Scientific Method
• Necessary & Sufficient Conditions
Random Vs. Non-random Variables
• A random (stochastic, non-deterministic) variable is one whose value is not known ahead of time.
• What’s random to Jill may not be random to Joe.
Non-random Variables
• A non-random (deterministic, non-stochastic variable) is one whose value is known ahead of time or one whose past value is known.
• EX: Tomorrow’s date, yesterday’s temperature.
• Randomness & Time are linked
Probability
• Probability is the likelihood that a random variable will take on a certain value.
• EX: There is an 85% chance of snow tomorrow. Variable: Weather, Possible values: Snow, No snow.
• Probability Distribution: The set of all possible values of a random variable with the associated probabilities of each.
Continuous VS. Discrete Distributions
• A continuous distribution shows the probability of the different outcomes for a variable that can take one of several different values along a continuous scale.
• EX: Future inflation may be 3.001%, 3.002 % …50% etc. (The different possible values are close to each other along a smooth continuous scale)
Discrete Distribution
• A discrete distribution shows the probability of the different outcomes for a variable that can take one of several different values along a discrete scale.
• EX: The number of students in class next time may be 1, 2, 3 etc.
• In reality most distributions (in Econ) are discrete but we sometimes assume continuity for theoretical & analytical ease.
Subjective & Objective Distributions
• A subjective distribution is when a person has some idea of what the probabilities of the different outcomes (for a RV) are but does not have the exact numbers.
• EX: I have a pretty good guess that I will do well in this class.
Objective Distributions
• An objective distribution is when the probabilities of each outcome are based on the number of times the outcome occurs divided by the total number of outcomes.
• EX: The probability of drawing a red ball from a jar with 5 red balls and a total of 50 balls is 5/50 or 1 chance in 10.
• Should all probabilities of an event sum to one?
Intellectual Doubletalk
• A non-random variable is a random variable with a degenerate distribution.
• Translation: Any certain event can be expressed as random event that happens with probability one.
Stochastic Vs. Deterministic Relations
• Deterministic relationships are exact formulas where the dependent and independent variables are non-random.
• EX: Ohm’s Law Current = k*Voltage
• Stochastic relationships are not exact formulas that relate dependent and independent variables.
• EX: Quantity demanded = f(Price, Random Term)
• Sources of Randomness: Measurement error, unobservable variables etc.
Correlation Vs. Causation
• Loosely speaking correlation is the phenomenon of two (or more) given variables exhibiting a roughly systematic pattern of movement.
• Ex: Most of the time when stock prices fall the bond market rallies.
• Causation is when one of the variables actually causes the other variable to change.
• Correlation does not imply correlation.
• Causation implies correlation.
• Causation that is not supported by correlation needs to be examined carefully.
Regression Vs. Causation
• A significant sign on a regression coefficient does not imply causation.
• However if you suspect causation between X & Y and the regression does not support this you must proceed with caution. What is causing the lack of significance? Experimental design flaw, unobservable variables or poor theory?
Types of Data
• Time Series Data: The data are gathered over the same set of variables in different time periods.
• EX: Price and Quantity of Summit Pale Ale Beer for a ten year period.
• Cross Sectional Data: The data are gathered over the same set of variables at a point in time over different cross-sections.
• Ex: Quantity & Price of beer in ’02 across the fifty states.
• EX2: Advertising and sales data across different firms in MN in ‘02
Types of Data
• Pooled Data: The dataset is essentially a cross-sectional dataset collected over the same variables in each of several different time periods.
• EX: Cigarette Price & Quantity data in each of 50 states from 1955 – 1994.
Types of Variables
• Dependent (Endogenous)
• Independent(Exogenous)
• Discrete
• Continuous
• Categorical
Dependent Vs. Independent
• The determination of a dependent variable is explained by the theory.
• Independent variables come from outside the theory. We do not know what causes these variables but use the independent variables to study the dependent variable.
Simultaneity
• Simultaneity: A theory may have more than one dependent variable such that two or more dependent variables influence each other. Such a situation is referred to as a simultaneous relationship.
• EX: Equilibrium price and equilibrium quantity influence each other. Both are endogenous variables explained by price theory.
Discrete Vs. Continuous
• A discrete variable is one that takes on finitely many values. They do not have to be integers such as 1, 2, 3 etc.
• A continuous variable can take on infinitely many values.
• Dependent & Independent variables can be either discrete or continuous.
Categorical
• Some variables may be either discrete or continuous but may be grouped into categories for ease of analysis.
• EX: Age 0 – 10 yrs, 11 – 20 yrs etc.
Historical Origin of Regression
• Regression is the process of finding the line or curve that ‘best’ fit a given set of data points.
• Francis Galton “Family Likeness in Stature”, Proceedings of Royal Society London, vol. 40, 1886.
Necessary & Sufficient Conditions
• A is said to be a sufficient condition for B. If A happens B will be guaranteed to occur.
• EX: Ceteris Paribus, if it rains then the football field will be wet. Necessary & Sufficient Conditions.
Testing Causality
• If A is observed and ceteris paribus B does not occur then the idea that A causes B is called into question.
• EX: Theory: C.P. Price is negatively related to quantity demanded.
• We observe price falling and ceteris paribus quantity demanded also falls. Does the data support the theory?
Testing Causality
• Econometrically we can estimate an equation for demand.
• Q = f(Price, Income, Other Variables)
• What is the predicted sign on the coefficient of price? (Is it significant?)
Fallacies
• Denying the antecedent:

It did not rain therefore the football field cannot be wet (How about a sprinkler system?)

• Affirming the consequent:

The field is wet therefore it must have rained.

(Sprinklers may have been on)

Contrapositive
• The only logical equivalent to A=> B is the contrapositive statement ~B => ~A.
• EX1: If it rains then the field will be wet.

(Contrapositive) The field is dry therefore it did not rain.

• EX2: If cigarettes are addictive then past consumption influences present consumption.

(Contrapositive) If past consumption does not influence present consumption then cigarettes are not addictive.