# Econometrics

This is the question and partsThe tax multiplier (TM) is defined as the dollar change in output caused by a dollar increase in
tax revenues by the government:
TM =
∂(Yt) / ∂(Tt) where Yt
is GDP in dollars in year t and Tt
is tax revenues in dollars in year t. In empirical work,
however, most economists estimate the percentage change in output associated to a percentage
change in tax revenues first, and then back out the tax multiplier. Suppose you have a dataset for
the US containing the time-series of Yt and Tt for the last 50 years. Also assume that the ratio Yt/Tt
is constant over the period considered. (a) Write down the model that most economists estimate. Show how they recover the tax multiplier from the estimated coefficient. (b) Does the tax multiplier estimated in point (a) capture a causal effect? Explain why/why not. (c) Several economists worry that changes in tax revenues are accompanied by changes in government spending, which also affect GDP. They believe, however, that the interest rate set
by the central bank does not respond to changes in tax revenues. Suppose you also have data
on government spending (Gt), on the interest rate (rt) and on the unemployment rate (ut).
Which regression would these economists like you to estimate? (d) Some of these economists also believe that the has been a change in the way the tax policy
affects the economy after 2000, and this might change the tax multiplier for the US economy.
How would you verify their hypothesis, at the same time taking into account the concern in
point (c)? Please describe all the steps of the procedure in details (what you estimate, what
your hypothesis is, how you verify it and so on…) (e) In points (c) and (d), are you estimating a causal effect? Why/why not?

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