Leadership
1. Introduction * Explain how it is possible to estimate the partial effect of the exogenous variables, even if ceteris paribus assumption is false.
We can estimate the partial effect of the exogenous variables, even if ceteris paribus assumption is false. It is possible by estimating parameters of the linear model. It let us get results, which we could obtain by comparing observations which do differ in values of one explanatory variable. That way we can estimate the effect on variable yicausedby changes of xkiceteris paribus even though the ceteris paribus assumption is false for all observation in the sample.
* Write down the linear model in conditional expectation form and in the error form and explain why the conditional expectation form of the model is more realistic than the assumption that the regressors are deterministic.
Model in conditional expectation form:
E(a1x1+……….+aKxK|z)=a1E(x1)+……….+aKE(xK)
Model in error form: y=E(y|x)+u
E(u|x)=0
The conditional expectation form of the model is more realistic than the assumption that the regressors are deterministic, because can be used for nonexperimental data. If we use Clasical Regression model assuming that regressors are deterministic (fixed) it will not be realistic for the nonexperimental data.
* What assumptions about the error term are related to random sample assumption? Give some examples when the random sample assumption can fail in a cross-section. How can we deal with such cases?
Random sample assumption can fail in a cross-section when samples are not representative of underlying population, in fact some data sets are constructed by intentionally oversampling different parts of the population.
2. Ordinary least squares and instrumental variable estimation * In what case the omitted variable can result in the asymptotic bias of an estimator? When the effect of an omitted variable is negligible?
Consider following model, which assumes additive effect of
We can estimate the partial effect of the exogenous variables, even if ceteris paribus assumption is false. It is possible by estimating parameters of the linear model. It let us get results, which we could obtain by comparing observations which do differ in values of one explanatory variable. That way we can estimate the effect on variable yicausedby changes of xkiceteris paribus even though the ceteris paribus assumption is false for all observation in the sample.
* Write down the linear model in conditional expectation form and in the error form and explain why the conditional expectation form of the model is more realistic than the assumption that the regressors are deterministic.
Model in conditional expectation form:
E(a1x1+……….+aKxK|z)=a1E(x1)+……….+aKE(xK)
Model in error form: y=E(y|x)+u
E(u|x)=0
The conditional expectation form of the model is more realistic than the assumption that the regressors are deterministic, because can be used for nonexperimental data. If we use Clasical Regression model assuming that regressors are deterministic (fixed) it will not be realistic for the nonexperimental data.
* What assumptions about the error term are related to random sample assumption? Give some examples when the random sample assumption can fail in a cross-section. How can we deal with such cases?
Random sample assumption can fail in a cross-section when samples are not representative of underlying population, in fact some data sets are constructed by intentionally oversampling different parts of the population.
2. Ordinary least squares and instrumental variable estimation * In what case the omitted variable can result in the asymptotic bias of an estimator? When the effect of an omitted variable is negligible?
Consider following model, which assumes additive effect of