Assessing studies based on multiple regression

Question 1

Threats to external validity

(2)

Answer 1

1. Differences in populations - when the population being studied is not relevant for understanding populations in other areas
2. Differences in settings/contexts - assuming the population being studied is generalisable accross different contexts e.g. impacts of changing class sizes in unimelb is not generalizable to ANU as there are different contexts

Question 2

Threats to internal validity

Answer 2

1. Unbiasedness and consistency of estimators - threat of violation of any of the least squares assumptions
2. Hypothesis tests and confidence intervals should be correct - threat of inaccuracy of tests and intervals in small samples and heteroskedasticity

Question 3

Omitted variable bias

Threat to internal validity with multiple regression analysis

Answer 3

Emerges when there is a variable not included in the regression that is correlated with the dependent variable and with one of the independent variables causing the independence assumption to fail

Question 4

Misspecification of the regression function

Threat to internal validity with multiple regression analysis

Answer 4

Functional form misspecification of the regression function (wrong order) yield biased OLS estimates. How to avoid:
* Plot/visualise the data using scatter plots to see if nonlinear relationships potentially exist
* Tru linear and non-linear specifications and test whether quadratic, cubic etc.

Question 5

Measurement error and errors-in-variables bias

Threat to internal validity with multiple regression analysis

Answer 5

Errors in the measurement of data e.g. errors-in-variables bias in using economics test scores when wanting to test maths scores which although likely correlated are not the same

Question 6

Classical measurement error

Threat to internal validity with multiple regression analysis

Answer 6

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Question 7

Missing data and sample selection bias

Threat to internal validity with multiple regression analysis

Answer 7

If data is missing as a function of the dependent variable then there is a risk that X is correlated with u, and omitted variable bias is present - this is known as sample selection bias

Question 8

Simultaneous casuality

Threat to internal validity with multiple regression analysis

Answer 8

Occurs if the Y is causing X ie. reverse causality from which arises the issue of simultaneous causality which is another way in which omitted variable bias can arise.

Question 9

Sources of inconsistency in OLS standard errors

Threat to internal validity with multiple regression analysis

Answer 9

• Heteroskedasticity - when the variance of u depends on X which is not accounted for whill result in the computation of incorrect standard errors and hence incorrect t-stats and confidence intervals
• Correlation of the error term across observations - if the eroor term is correlated across time or space you can also end u with incorrect standard errors, t-statistics and confidence intervals.

Question 10

Forecasting

Answer 10

We can generate a forecast of Y using predicted values from the regression with forecast error = Y - Y(hat)
- This arises issues of external validity as we need to ensure that the underlying population drawn can generalise in such a way that we can forecast outcomes in other situations/contexts