In this question you will consider the relationship between the real interest rate (r), the long-run growth rate (g), and debt sustainability. a. Starting from the equation for the government’s budget constraint,
Bt = (1 + r)Bt−1 + (Gt − Tt), derive an expression for the path of the debt-to-GDP ratio over time.
b. What is the steady-state value of the debt-to-GDP ratio? What is the relationship between this value and the deficit-to-GDP ratio, the interest rate, and the growth rate?
c. Suppose that r = 0.01, g = 0.04, and the government targets a maximum long-run debt-to-GDP ratio of 0.6 (60%). What is the maximum allowable deficit-to-GDP ratio?
d. Suppose instead that the government is currently running a budget deficit equal to 4% of GDP (0.04). Given the above values for r and g, What is the implied long-run debt-to-GDP ratio?
e. What does the relationship between growth, interest rates, and the debt-to-GDP ratio imply about the ability of monetary policy to influence debt sustainability? Assuming the monetary authority can effectively hit its interest rate target at all times, is there a sense in which the sustainability (or lack thereof) of government debt is a policy choice?