Social and Natural Experiments - Training Programme - Housing Investment - Economics Assignment Help

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:

1.  Explain carefully how the estimate βˆ1 = 3.259 should be interpreted, in economic terms.

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

3.  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.

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

5. 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:

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.

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

3.  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.

4.  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.

5. Assume that OLS estimation resulted in βˆ1 = 0.10 with standard error 0.04, and IV estimation resulted in βˆ1 being either 0.17 or 0.03 (whichever is consistent with your answer in part (b)) with standard error 0.05. Test whether endogeneity was actually a problem in this model.

Question 3: A system of equations. Consider the following simplified description of fresh tuna sales on Sydney’s fish market. Consumers decide how much tuna they want to buy on a day (y1, in kilograms) given the price that they observe (y2, in dollars per kilogram) and some other exogenous information x1. Conversely, sellers set the price y2 based on the demand that they observe y1, and some other exogenous information x2. (Assume that this market is so efficient that, on any given day, all sellers charge the same price.) Thus, we are dealing with a system of simultaneous equations:

1. Think of some observable variables that x1 and x2 could be (one suggestion for x1 and one suggestion for x2 is enough), and justify your answer.

2.  One way to estimate these six parameters is by using two-stage least squares. Describe in detail which regressions you would need to run.

From here on, we will no longer be using 2SLS. We will rewrite the structural form that is given above into its reduced form instead, estimate that reduced form, and hope that we can recover the structuralform parameters from our reduced-form estimators.

3.  Find the reduced form of this system of equations.

4. Which algebraic condition do we need to impose on the structural-form parameters in order to be able to identify them from our reduced-form estimation?

5.  Briefly comment on whether the condition that you found in part (d) is likely to be satisfied in reality.

Question 4: Generalised least squares. We have discussed two alternative ways of dealing with heteroskedasticity. We could either continue to use the OLS estimator but robustify its standard error using White’s correction, or discard the OLS estimator and use the FGLS estimator instead.

(a) (4 marks) Each of these two choices has its advantages and disadvantages. List one advantage of each choice relative to the other.

We similarly have two alternative ways for dealing with autocorrelation at our disposal, but we did not talk much about them during the lectures. I do not want to get into robust standard errors for this problem (the relevant correction is named after Newey and West, in case you would like to know), but the purpose of this question is to explore how to use FGLS in this context.

If we estimate these parameters by δˆj, we are now doing FGLS rather than GLS.

In parts (b) and (c) of this question, assume that the only problem with our regression model yt = β0 +β1xt +ut is autocorrelation. So everything like model specification, exogeneity, homoskedasticity, and normality is fine; the only issue is that ut is correlated with its past values. Specifically, it follows an AR(2) process: ut = ρ1ut−1 + ρ2ut−2 + et, where et is nicely i.i.d.

2. How would you apply GLS in this situation? That is, what are, and u∗t? As a hint, if your original sample had T observations, your transformed regression will only be estimated on T − 2 observations.

3.  How would you apply FGLS in this situation? That is, which additional parameters need to be estimated, and how would you do that?

4.  Finally, assume that both problems (heteroskedasticity and autocorrelation) exist. We have the same model that we just discussed, but now et is heteroskedastic; nothing else changes. Describe how FGLS would work in that situation. No need for formulas because they are rather messy; just describe the general idea.

Question 5: Social and natural experiments. There is a lot of speculation regarding the causal effect of having a woman as the CEO on a firm’s long-term profitability. Some say that women and men are not different in any ways that are important for this purpose, so the effect should be zero; some say that women tend to make more prudent decisions, which is good for profitability; some say that women tend to be more risk-averse, which hurts profitability in the long run. Being an econometrician, I do not want to take a stance on which of these commentators are right. Rather, I would like you to design an experiment that could estimate this causal effect.

1.  Identify at least three things that are wrong with simply regressing many firms’ profit margins over the last five years on a dummy that equals one for firms that currently have female CEOs and zero for all other firms.

2.  Leaving all practical considerations aside for the moment, assume that you could run a social experiment. Describe how you would set up this experiment, which data you would collect, and which regressions you would run.

3. More realistically, you will need to use observational data, and hence run a natural experiment. Describe how you would decide which firms get to be part of this experiment, which data you would collect, and which regressions you would run.

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