Making Sense Making Numbers Making Significance Ulf H. Olsson Professor of Statistics.

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Presentation transcript:

Making Sense Making Numbers Making Significance Ulf H. Olsson Professor of Statistics

Ulf H. Olsson True Process Theoretical Domain Empirical Domain Making Sense

Ulf H. Olsson Making Numbers Estimation Theoretical Domain Empirical Domain (Error of) Estimation If the model is correctly specified, different estimators should have similar values asymptotically (White, 1994)

Ulf H. Olsson Making Numbers 1) Structural Errors 2) Incorrect functional form 3) Distributional assumptions => Different estimators will produce different results => The empirical domain is among other things a function of the chosen estimator

Ulf H. Olsson Making Numbers (Estimator) s i : sample element : parameter vector : model implied element (parameter function)

Ulf H. Olsson Making Numbers (Cov. Estimator) S: sample covariance : parameter vector : model implied covariance

Ulf H. Olsson Econometric Model Klein’s Model (1950 )

Ulf H. Olsson Making Numbers (OLS and TSLS) CT = *PT *PT_ *WT, R² = (1.303) (0.0912) (0.0906) (0.0399) CT = *PT+0.186*PT_ *WT, R² = (1.453) (0.138) (0.146) (0.0439)

Ulf H. Olsson Making Significance “ Weak Test”

Ulf H. Olsson Making Significance ”Strong Test”

Ulf H. Olsson Making Significance

Ulf H. Olsson Making Significance Reject-Support (RS) The researcher wants to reject H 0 Society wants to control Type I error The researcher must be very concerned about Type II error High sample size works for the researcher If there is too much power, trivial effects become highly significant.

Ulf H. Olsson Making Significance Accept-Support (AS) The researcher wants to accept H 0 Society should be worrying about controlling Type II error The researcher must be very careful to control Type I error High sample size works against the researcher If there is too much power, the researcher’s theory can be rejected by a significance test even though it fits the data almost perfectly

Ulf H. Olsson Making Sense A strong theory will give precise predictions!

Ulf H. Olsson Making sense is more important than making numbers, it is even more important than making significance ?