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Download Model Identification Summarizing Empirical Estimation EconS 451: Lecture #9
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EconS 451: Lecture #9 Summarizing Empirical Estimation • Transforming Variables to Improve Model Model Identification Why do we believe that by taking prices and quantities and estimating a statistical relationship that we’ve estimated a Demand or Supply Relationship? • Using Dummy / Indicator Variables 35.00 30.00 • Issues related to Model Identification. Price 25.00 • Why Deflate Data? 20.00 15.00 10.00 • What time series do we use? 5.00 0.00 0.00 • How to identify: • Heteroskedasticity • Multicollinearity • Autoregression 20.00 40.00 60.00 80.00 100.00 Quantity Model Identification If the economy were perfectly static……it would be impossible to estimate either demand or supply. Model Identification Price S1 but supply and demand functions shift with the passage of time, thus allowing one or both to be estimated. S2 S3 Supply Price Demand D3 Quantity D2 D1 Quantity / Unit Time Deflating Price and Income Two Reasons • Economic • Estimate real price and income relationships instead of nominal. • Statistical • Reduce correlation between independent variables. • Reduce heteroskedasticity. Time Series • What time series to include? • Generally speaking, the greater number of observations the more confidence in estimated coefficients. • Time period should reflect the conditions under which you are attempting to capture. • What level (yearly, quarterly, monthly, weekly, daily, hourly, etc.) • Depends on the type of analysis and availability of data. 1 How to Identify…. How to Identify…. • Heteroskedasticity = non-constant error variance • Eg cross section of firms, the error term for large firms is consistently greater than the error of small firms. • Multicollinearity ? • Visual inspection of Residual Plot. • Goldfeld-Quandt Test. H 0 : σ 12 = σ 22 • Set Up and Test Hypothesis GQ = • Economic logic. • Odd signs for estimated coefficients may be first clue. • Correlation Matrix H1 : σ 12 ≠ σ 22 ∧ 2 1 ∧ 2 2 σ ≈ Fdf1 ,df 2 σ Multicollinearity How to Identify…. • Autoregression = error terms are correlated over Correlation matrix time Quantity of Red Roses (doz.) Quantity of Red Roses (doz.) Price of Red Roses (per/doz.) Quantity of Orchids (doz.) Per Capita Income Quantity of Tulips (doz.) 1.00 yt = β 0 + β1 xt + ε t Price of Red Roses (per/doz.) -0.80 1.00 Quantity of Orchids (doz.) -0.76 0.97 1.00 Per Capita Income -0.71 0.48 0.57 1.00 Quantity of Tulips (doz.) -0.44 0.81 0.98 0.42 Durbin-Watson Test Statistic T d = ∧ ∑ (e t =2 t T ∧ − et −1 )2 ∧2 ∑e t =1 • Residuals Plot • Test Using Durbin-Watson Statistic 1.00 H0 : ρ = 0 H1 : ρ > 0 ε t = ρε t −1 + vt What to do if you find……. • Hetereoskedasticity Add variable to account for difference between groups • Multicollinearity t • Drop correlated variable (s) from estimation. ∧ d ≈ 2 (1 − ρ ) • Autoregression • Add variable to account for the missing factor over time 2 Summary Questions • What are the five assumptions of the classical linear regression Summary Questions • Explain the process involved with identifying the appropriate functional form to use when estimating a statistical model. model? • What rules do we use to identify a model from price and quantity • Describe in words, how Ordinary Least Squares works. • What is measured by the R-Square term? • How can you determine if a variable is statistically significant? • What steps do you take to determine the appropriate functional form for estimating an equation? • When would you ever utilize an indicator (dummy) variable in your relationships ? • Why do we deflate data? • What issues should we consider when conducting time-series estimations ? • What techniques can be used to identify Heteroskedasticity and Multicollinearity? • If these are present……how do we correct these problems? estimation…..and how would you do it? 3
