Introduction Econometrics

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Introduction Econometrics

• José A. Pagán
• Professor of Economics and Director
• Institute for Population Health Policy
• The University of Texas-Pan American

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Introduction

• Econometrics means economic measurement
• It combines economic theory, mathematical
  economics, economic statistics and mathematical
  statistics
• economic theory (e.g., when price goes up,
  quantity demanded goes down)
• mathematical economics (e.g., express economic
  theory using math)
• economic statistics (data)
• mathematical statistics

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Classical methodology

• Statement of theory or hypothesis
• Specification of mathematical model
• Specification of econometric (statistical) model
• Obtain data
• Estimate parameters of the model
• Hypothesis testing
• Forecasting
• Use the model for policy

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Example Keynesian theory of consumption

• 1. Statement of theory or hypothesis
• 0ltMPClt1
• 2. Specification of mathematical model
• Y ß1 ß2X 0 lt ß2 lt 1
• 3. Specification of econometric (statistical)
  model
• Y ß1 ß2X u
• 4. Obtain data
• See Table I.1, page 6.

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Example Keynesian theory of consumption (2)

• 5. Estimate parameters of the model
• Y -184.08 0.7064Xi
• 6. Hypothesis testing
• Is 0.70 statistically less than 1?
• 7. Forecasting
• If X19977269.8 then Y 4951.3167
• 8. Use the model for policy
• Pick value of X to get desired value of Y (Y and
  X are called target and control variables,
  respectively)

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Chapter 1 The nature of regression analysis

• Galtons regression to mediocrity
• Regression analysis study of the dependence of
  one variable (the dependent variable) on one or
  more other variables (the explanatory variables)
• The goal is to predict the mean value of the
  dependent variable based on known values of the
  explanatory variables
• Example 1 Fathers and sons heights (Fig. 1.1,
  P. 18)
• Example 2 Education and earnings (human capital
  function)

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Chapter 1 The nature of regression analysis (2)

• In regression analysis we are interested in
  statistical dependence among variables, not in
  deterministic relationships.
• Regression analysis deals with dependence but not
  necessarily with causation.
• Regression is different from correlation in the
  sense that we define a dependent variable
  (random) and an explanatory variable (fixed)
  whereas in correlation both variables are random.
• A random (or stochastic) variable is a variable
  that can take any set of values, with a given
  probability.

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Types of data

• Time series data (data collected daily, monthly,
  yearly)
• daily stock market data, monthly unemployment
  rates
• Cross-sectional data (data collected at one point
  in time)
• a one-time household survey, a poll
• Pooled (cross-sectional observations collected
  over time, but they dont have to be the same
  person, firm, etc.)
• combining data from say a yearly household survey
  over multiple years
• Longitudinal/panel data (data from the same
  cross-sectional units collected over time)
• collecting data on the same persons over time
  (e.g., the National Longitudinal Survey of Youth
  Health and Retirement Study)

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Chapter 2 Two-variable regression analysis

• Unconditional expected value E(Y)
• Conditional expected value E(Y X)
• A population regression curve is simply the locus
  of the conditional means of the dependent
  variable for the fixed values of the explanatory
  variables
• Conditional expectation function (population
  regression) E(Y Xi) f(Xi)
• Population regression function could be something
  like E(Y Xi) Y ß1 ß2Xi
• ß1 and ß2 are called regression coefficients

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Chapter 2 Two-variable regression analysis (2)

• Linear regression means a regression that is
  linear in the parameters
• A linear regression can be non-linear in the
  variables
• Example Y ß1 ß2X2
• A linear regression must be linear in the
  parameters
• Some non-linear regression models can be
  transformed into a linear regression model (e.g.,
  YaXbZc can be transformed into lnY ln a bln
  X cln Z)

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Chapter 2 Two-variable regression analysis (3)

• Deviation of an individual Yi around its expected
  value is given by
• ui Yi - E(Y Xi), or Yi E(Y Xi) ui
• If we take the expected value on both sides of
  the equation above, we get that E(ui Xi) 0
• Thus, the assumption that the regression line
  passes through the conditional means of Y implies
  that the conditional mean values of ui are zero
• Disturbance term ui captures all the variables
  omitted from the model. Possible reasons include
• Vagueness of theory
• Unavailability of data
• Core variables versus peripheral variables
• Intrinsic randomness in human behavior
• Poor proxy variables
• Principle of parsimony
• Wrong functional form

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Chapter 2 Two-variable regression analysis (4)

• Lets now move from the population to the sample
• Sample regression function Yi ß1 ß2Xi
• Yi estimator of E(Y Xi) ß1 estimator of
  ß1 ß2 estimator of ß2
• Estimator rule, formula or method that tells us
  how to estimate the population parameter
• Estimate particular numerical value obtained
  using the estimator
• Note that Yi ß1 ß2Xi ui
• ui residual term (it is an estimate of ui).
• Our main objective in regression analysis is to
  estimate the population regression function using
  the sample regression function.
• Can we devise a rule that will make our sample
  regression function as close as possible to the
  population regression function?