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Binary Regression Models

Binary Regression Models. Binary Models. In a number of contexts the dependent variable, Y, is nominal and binary Examples: Does a consumer Buy or Not Buy? Did the Dow go Up or down? Was a loan application accepted?. Binary Models.

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Binary Regression Models

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  1. Binary Regression Models

  2. Binary Models • In a number of contexts the dependent variable, Y, is nominal and binary • Examples: • Does a consumer Buy or Not Buy? • Did the Dow go Up or down? • Was a loan application accepted?

  3. Binary Models • The problem with the linear regression is that it does not account for the fact that Y can only be 0 or 1 • Two popular models to deal with this are: • The Logit Model • The Probit Model

  4. The Binary Regression Logic • Think of the decision maker choosing Y based on the relative difference in utility she gets from Y=1 and Y=0 • If this difference is greater than some threshold (error) then Y=1 otherwise Y=0, so…

  5. The Probit and Logit Models • The Probit model assumes that the errors are standard normal • The Logit Model assumes that errors are Logistic NORMDIST in EXCEL

  6. Estimating the s • Two approaches: • A) Non-Linear Least Squares (NLLS) • Where we minimize • B) Maximum Likelihood • Where we maximize

  7. Fitted Probabilities/Values • Note that by plugging in the  you only get the fitted probabilities • To get predicted values you have to check if the fitted probabilities are above ½ • Lets try all of this in EXCEL… (maybe in GRETL?)

  8. Time Series Topics

  9. Time Series Topics • Topics to discuss: • Concepts and Terms • Autocorelation • Autoregression: [AR(p)] • Distributed Lag Models (ADL) • Conditional Heteroskedasticity • We will only have a basic introduction, if you are interested think about Bill Schwert’s APS 425 course.

  10. Concepts & Terms • Time Series: • A variable for which we have data over time • Lags: • First Lag: Yt-1 • s-th Lag: Yt-s • First Differences: Y = Yt – Yt-1 • Stationarity: • The time series Yt is stationary if the distribution of Yt does not change over time • Trend: • A persistent long term movement of a variable over time • Deterministic vs. Stochastic

  11. Autocorrelation • The correlation of Yt with its own past values (lags) • Also known as serial correlation • First Autocorrleation: Is the corrleation of Yt with Yt-1 • More generally: • The numerator in the above is a related construct called Autocovariance

  12. Autoregression • As the name suggests it is a regression of Yt on past values • Example: AR(1) • Special cases • Random Walk: • Random Walk with Drift

  13. Autoregression AR(p) • The AR(1) model can be generalized to include multiple lagged terms • This gives us the AR(p) model • How large should p be? • Use the Bayesian Information criterion number of coefficients including intercept

  14. Forecasts • Forecasts vs. Prediction • Generating a forecast: • Forecast Error • Root Mean Squared Forecast Error • Pseudo Out of Sample Forecasting • Simple Out-of Sample Forecasting • Iterated Multiperiod Forecasts

  15. Conditional Heteroskedasticity Models • We know that heteroskedasticity refers to the fact that the error variance is not constant • Conditional heteroskedasticity is when we can make this heteroskedasticity a function of something • ARCH: Autoregressive Conditional heteroskedasticity • GARCH: Generalized ARCH

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