Modeling the Acreage of Canola in Canada

Estimating the Model

1. Canola is a very important field crop in Canada. Estimate the following model: AC t = ?1 + ?2PC t-1 + ?3PWt-1 + ?4AC t-1 + ?5 AC t-2 + et Where: AC t is the acreage (area planted) of canola in Canada in year t; PC t-1 is the price of canola in the previous year; PWt-1 is the price of wheat in the previous year; AC t-1 is the acreage of canola in the previous year; and et is the error term. Use data for 1980 – 2020. Everything should be converted to acres and dollars per bushel as needed; do not report things in hectares or tonnes. (a) Estimate the model above and fully report/interpret your results. (30 marks) (b) Test for autocorrelation using the Lagrange Multiplier test (you cannot use the bounds test because this model has a lagged dependent variable). (10 marks) (c) If there is autocorrelation, correct for it using Generalized Least Squares. If there is no A/C, you do not have to correct for it. (10 marks) (d) It is customary to truncate (i.e “cut off”) the lag lengths (i.e. whether you use (t-1), (t-2), or go even further back) for acreage at the point where they are no longer statistically significant. Re-estimate the above, but find the appropriate lag length for acreage. It might turn out to be two years, but it might not (that was just my guess). Find the correct lag length. (10 marks) (e) Some might hypothesize that structural change occurred in the canola market around 2006. Check whether this occurred. (10 marks) 2. Continuing with our question from the midterm exam, test whether lockdowns have been effective in combatting COVID-19 cases in Manitoba. Start your dataset on October 1st . Think very carefully about the variables you want to put in your model (our model from the midterm is a good starting place) and carefully explain why you chose the variables and functional form you did. One of your challenges is how to handle lockdowns with a dummy variable since (1) lockdowns, if they are effective, take some time to show their effect, and (2) the lockdowns became more severe at some point. Carry out any necessary misspecification tests. (60 marks) 3. We talked quite a bit this semester about the household income/food expenditure example; the data for which can be found on the course homepage in Table3-1.dat. When we talked about heteroskedasticity in Lecture 11, we assumed that the variance structure for this dataset took the following form: var(et) = ?t 2 = ?2 ´ xt and then, of course, we divided everything by the square root of xt to get rid of our heteroskedasticity using Generalized Least Squares (hint: look at slide 17 of Lecture 11 to see why our correction (dividing by the square root of x) worked for the type of heteroskedasticity previously assumed is present in the HI/FE model). Now for our household income/food expenditure data, let’s suppose that instead of var(et) = ?t 2 = ?2 ´ xt, we assume our variance structure takes on the following forms (a) and (b) below. For each of those forms, first (on the written portion of your exam submission), explain the correction you are employing for each variance structure (and why it will work), then secondly (in your Excel work) transform the data in such a way that if our assumption about the variance structure is correct, the heteroskedasticity will be gone. Then use a GQ test to check whether the heteroskedasticity has, in fact, been eliminated by the correction you employed. Fully report the results of your models. Which of the three corrections (i.e. the one we did previously, plus the two new ones) is the “best”, in your opinion, and why?