Assignment Task :


Question 1: A distributed-lag model. To study the relationship between real housing investment per capita (pcinvt) and housing prices (pricet), I collect 42 years of annual data on each time series. I begin by considering the following model, with the variables in logarithms:

Standard

 

  1.   Compute the long-run propensity (LRP) of prices on investment, and also explain how this number should be interpreted.

  2.  The results shown above are not sufficient to test whether the LRP is zero. Describe which additional regression you would need to run, and which statistical test you would perform based on the results of this additional regression.

  3.  If housing prices would have a unit root, how would you need to modify your regression model in order to obtain consistent estimators?

  4.  We are concerned that housing prices might have a unit root, so we estimate the model

 

Question 2: Endogeneity. In this question, we are interested in studying the effect of a job seekers’ training programme that was offered, five years ago, to people who had been unemployed for at least a year at that time. This year, we interviewed the people to whom this training had been offered, and collected the following data on each of them: whether they are currently employed (yi = 1) or not (yi = 0); whether they participated in the training programme (parti = 1) or not (parti = 0); their gender (femalei = 1 or 0), how many years of education they completed before being offered this training (educi), and which state or territory they lived in five years ago (eight dummies, making the ACT the omitted category as usual − sorry, nothing personal). We then estimate the following model:

Dummies

  1.  For each regressor in this model, briefly argue whether you think it is endogenous or exogenous, and why.

For the remainder of this question, assume that parti is suspected to be endogenous, and all other regressors can safely be assumed to be exogenous. This is not necessarily the correct answer to part (a), but it does make things easier.

  1.  If you estimated the regression model by OLS, do you think βˆ1 would be biased towards zero or away from zero? Why?

  2.  One way to mitigate endogeneity problems is to use a proxy variable. Pretending that you were in charge of data collection, think of something that could be a good proxy variable, and describe why it is a good choice.

  3.  Another way to mitigate endogeneity problems is to use an instrumental variable. Pretending that you were in charge of data collection, think of something that could be a good instrumental variable, and describe why it is a good choice.

 

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  • Uploaded By : Grace
  • Posted on : January 07th, 2018

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