**Math/Physic/Economic/Statistic Problems**

UCD’s late submission policy will be applied

(https://www.ucd.ie/governance/resources/policypage-latesubmissionofcoursework/).

Only PDF uploads will be accepted. You can hand write if you like, but must come as PDF and not JPEG, DOCX etc

All questions (and parts of questions) carry equal marks

**Question 1**

The file sales.data contains 157 weekly observations on sales revenues (sales) and advertising expenditure (adv) in millions of dollars for a large Midwest department store for 2005-2007.

(a) Estimate a VAR model of sales and advertising. Choose the lag length but be sure to justify it.

(b) Do sales Granger cause advertising or vice-versa of both? Carefully state the null hypothesis of any tests you employ and carefully state the conclusion.

(c) Generate a set impulse response functions and discuss their economic interpretations. Be careful to state any identification assumptions that are implicit in your interpretation.

**Question 2**

The quantity theory of money says that there is a direct relationship between the quantity of money in the economy and the aggregate price level i.e. if the quantity of money doubles, then the price level

should also double). Use the file qtm.dta to answer the following.

(a) Assess the stationarity of the time series and their order of integration.

(b) Test whether they are co integrated.

(c) Estimate the single equation error-correction model. Interpret the coefficients and test the quantity theory of money.

(d) Reverse the role of the two variables in part (c) and repeat the analysis. Interpret and compare with part (c).

(e) Use now the Johansen methodology and estimate a VECM (pay attention on whether you need to include a trend). Are your conclusions different?