Stuck on homework and I have no idea how to do it please help

Question 1 The fiscal multiplier (FM) is defined as the dollar change in output caused by a dollar increase in public spending by the government: FM = aGt where Y, is GDP in dollars in year t and G, is public spending in dollars in year t. In empirical work, however, economists usually estimate the percentage change in output associated to a percentage change in government spending. Suppose you have a dataset for the US containing the time-series of Yr and G, for the last 50 years. Also assume that the ratio ~ is constant over the period considered. (a) Write down the model that economists usually estimate and show how to back out the fiscal multiplier. Does the estimated coefficient capture a causal effect? Explain why/why not. (b) Several economists argue that changes in government spending are usually followed by deci- sions to change the interest rate by the central bank. They also believe, however, that the tax code usually does not change after a spending reform. Suppose you also have data on tax rates (7;), on the interest rate (re) and on the unemployment rate (ut). Which regression would these economists like you to estimate? (c) Some of these economists also believe that the has been a change in the way the economy works after the year 1980, and this might change the fiscal multiplier for the US economy. How would you verify their hypothesis, at the same time taking into account the concern in point (b)? Please describe all the steps of the procedure in details (what you estimate, what your hypothesis is, how you verify it and so on...) (d) In points (b) and (c), are you estimating a causal effect? Why/why not? (e) Irrespective of whether you have an endogencity problem, propose an instrument and argue why it is valid