Question

c) Which theorem gives th (a) State the OLS assumptions in a simple linear regression model. (3) b] How do you modify the OLS assumptions if you have a control variable? (2) (c) Discuss the problem of omitted variable bias. (5)

Answer 1

OLS Assumption: The regression model is linear in the coefficients and the error term This assumption adresses the functional form of the model. In statistics, a regression model is linear when all terms in the model are either the constant or a parameter multiplied by arn independent variable Assumption The regression model is linear in the coefficients and the error term The error term has a population mean of zero All independent variables are uncorrelated with the error term Observations of the error term are uncorrelated with each other The error term has a constant variance (no beteroscedasticity) No independent variable is a perfect linear function of other explanatory variables Modify OLS Assumption If linearity assumptions don't hold, then you need to change the functional form of the regression, which can be done by taking non-linear transformations of independent variables (i.e. you can take log o logX instead of X as your independent variable) and then check for linearity Consider control variables just like the other explanatory variables and put them in stata (for example if x1 and x2 are the explanatory variables I need and x3 and x4 are control variables, I simply type regress y x1 x2 x3 x4) and then, when I get the results Problem of omitted variable The problem of omitted variables occurs due to misspecification of a linear regression model, which may be because either the effect of the omitted variable on the dependent variable is unknown or because the data is not available. This forces you to omit that variable from your regression, which results in over-estimating (upward bias) or under-estimating (downward) the effect of one of more other explanatory variables Two conditions must hold for omitted variable bias to exist. a) b) The omitted variable must be correlated with the dependent variable The omitted variable must be correlated with one or more other explanatory/ independent variables Example the size of the house in square feet is correlated with the price of the house as well as the number of rooms. Hence, omitting the size of house variable results in omitted variable bias The omitted variables problem is one of regression analysis' most serious problems. The standard approach to the omitted variables problem is to find instruments, or proxies, for the omitted variables but this approach makes strong assumptions that are rarely met in practice. This paper introduces best

projection reiterative truncated projected least squares (BP-RTPLS), the third generation of a technique that solves the omitted variables problem without using proxies or instruments. This paper presents a theoretical argument that BP-RTPLS produces unbiased reduced form estimates when there are omitted variables. This paper also provides simulation evidence that shows OLS produces between 250% and 2450% more errors than BP-RTPLS when there are omitted variables and when measurement and round-off error is 1 percent or less.