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ECON 23950: Economic Policy Analysis
Problem Set 5
1 Short Questions (Pseudo TFU)
1. How is money multiplier diferent from velocity of money conceptually? Is there any correlation between them theoretically and/or empirically? Download the relevant data and show the two series on the same diagram.
2. Can the central bank always increase seigniorage by printing more money?
3. True/False/Uncertain: The Fed can control money supply.
4. TFU? With the money demand equation below
the infiation rate will be equal to the rate of money growth minus the rate of economic growth at steady state where all growth rates are constant over time.
5. TFU? The level of debt today can be expressed as both (1) the accumulation of deficits from the beginning of the world and (2) the present discounted value of all future surpluses. Hint: Solve the government budget constraint both forward and backward in time.
2 Fiscal Theory of the Price Level
Let’s consider the model we discussed in class regarding the FTPL. We have two periods (t = 0, 1). The initial period budget constraint for the government is written as
B0 + P0G0 = B1 + P0T0 + M1 - M0
and that for the second period is
(1 + R)B1 + P1G1 = B2 + P1T1 + M2 - M1
1. Combine the equations above to derive the equation below. Describe and explain your steps carefully.
2. Explain the last term 
in the equation above. Why does it make sense to have nominal interest rate in the numerator and the real interest rate in the denominator? Explain intuitively.
From this point onward, let’s assume that G0, G1 are fixed. B0, M0 are also given and fixed. Suppose that the government cut taxes (in real terms) in period zero (T0 ↓). We will think about the consequences of this policy on the price levels below.
3. Suppose that, along with the current tax cut, the government raised the future tax (T1) by (1 + r) times the amount of tax cut. Analyze the efect on P0 and P1 . Explain your results intuitively.
Hint: In the previous models where we expressed debt in units of goods, this was simply not allowed as the government has to meet the following budget constraint:
In other words, as long as G0, G1 and b0 (initial period debt in units of goods) are fixed, a reduction in T0 necessitates an increase in T1 by the amount (1 + r). Think about how the situation has changed when the government issued nominal debt B0 as opposed to real debt b0 .
4. Suppose instead that the government kept the future tax (and money supply M1) as constant. Analyze the efect of T0 ↓ on P0 and P1 . Explain your results intuitively. See the hint above.
5. Can the government do the above operation? In other words, can the government still meet the intertemporal budget constraint? If yes, who is paying extra in what form? Explain.
3 Fiscal Shock in Baxter and King (1993) –Bonus Question
Let’s go back to the fiscal multiplier issue–this time, we use a more complete and realistic model with both capital and labor as factor inputs. A drawback of the approach is that we may not obtain a closed-form solution and thus have to use a numerical technique to solve the model. This is where your human capital investment in Matlab/Dynare pays off!
In this model economy, there are three sectors: household, firm, and government. The representative household, taking as given the prices (w, r, rk ), maximizes the lifetime utility
subject to the period-by-period budget constraint
Ct + Kt+1 - (1 - δ)Kt + Tt + Bt+1 = wtLt + rt(k)Kt + (1 + rt)Bt + Πt
with given K0 and B0 . The government levies lump-sum taxes every period to satisfy the following constraint:
Gt + (1 + rt)Bt = Tt + Bt+1
The representative firm, taking prices as given, maximizes the current profit every period:
Πt = A0Kt(α)Lt(1)-α - wtLt - rt(k)Kt
1. Set up the Lagrangian for the household and derive the first order conditions of the house- hold. Derive the optimal equations (MRS and Euler).
2. Set up the maximization problem for the firm and derive the optimal conditions. Interpret them.
3. Define the competitive equilibrium of the economy. Describe all the market clearing con- ditions.
4. Does the Ricardian Equivalence hold in this economy? Why or why not?
5. Show the equations that can be used to solve for the steady state of the economy. You now realize that the solution is more complicated when we deal with two inputs instead of one!
Now, let’s put this in Matlab/Dynare and analyze how the economy reacts to a shock in G. First, we will simplify the fiscal sector to make our experiment easy. We let government collect lump-sum taxes to balance its budget every period such that
Gt = Tt = G
Second, we need to determine numerical values for the structural parameters of the model. Following King and Rebelo (1999), we calibrate the model to mimic the US economy. Calibration amount to choosing the parameters of the model in such a way that the model replicates certain aspects of the data we take as stylized.
Under the hypothesis that the economy is at (or near) a steady state, it follows from the Euler equation that the rate of time preference should equal the real rate of interest. According to King and Rebelo (1999), the average real rate of return to capital in the US has been 6.5% per annum over the period 1948-1986. This gives us the estimate of P = (1.065)0.25 - 1 = 0.0159. The annual rate of depreciation of the capital stock is set at 10%, which implies δ = 0.0241. With Cobb-Douglas technology, Q equals the share of capital income in output which King and Rebelo set equal to two-thirds: Q = 1/3. Baxter and King (1993) suggest that the average post- war share of government consumption in output was 20% in the US. The preference parameter E is chosen such that the steady state labor supply in the model is 20% of the total available time. This gives us E = 0.183. Finally, A0 is a scale parameter, which can be chosen freely. We set A0 = 1.442 to normalize steady state output to unity.
6. The Dynare code is provided on canvas (baxterking.mod). First, open the file and un- derstand that the model block lists out equations describing the optimality conditions, the production function, and the resource constraint. Run it first and report the steady state values numerically. Hint: You will need to move the file to the working folder in your hard drive and change the directory of Matlab accordingly to successfully run the program. You can either (1) enter “oo .steady state” in the Matlab command window to show the endogenous variables in order of declaration used in the var block or (2) read of of automatic output that is created after running the dynare code.
7. Rewrite the code slightly so that you can study a quantitative impact of a permanent 1% increase in government spending. You need to set the end value of G = 0.202 and run it again. Report the new steady state values.
8. Run the plot code (baxterkingplot.m). Print out the impulse response functions.
9. Comment on your findings. How is the immediate impact diferent from the long run adjustment? Explain.
10. You now realize that you can analyze many types of shocks. As an optional and bonus exercise, you can replace the lump sum tax with labor income tax τt(w) and capital income tax τtk to analyze responses of the economy to an unanticipated, permanent shock in the tax rates, separately. Summarize and report your findings.
4 Reading FOMC statements
Go to the Fed’s website and look up the statements from the latest FOMC meeting.
1. What is the Federal Funds rate? How is it diferent from the discount rate?
2. How has the statement changed from the last time? How does the committee view the economy and inflation outlook diferently?
3. What is forward guidance? How is it expressed in the most recent statement?
4. How does the market view the likelihood of the rate hike in the next meeting? Explain what data you ought to look at and why.
5 The Ends of Four Big In ations
Sargent (1982) analyzes the experience of four European countries during their hyperinflation periods in the 1920s. Although he analyzes hyperinflations, very similar policy implications can be drawn for the fight with much milder inflation rates. The cases of hyperinflations, however, allow for a much clearer identification of the impact of diferent policies.
1. Some argue that fighting inflation is costly in terms of forgone output because of the persistent inflation expectations. Sargent claims that this view is not correct, and inflation is only perceived to be persistent due to specific characteristics of the government’s policy. Explain Sargent’s view.
2. Look at Figures 2.1-2.4. Are these figures consistent with the view that a decisive and committed change in the policy regime can lead to an abrupt end of the hyperinflation? Explain.
3. What is the diference between a gold-standard currency and a fiat currency?
4. Sargent diferentiates between government regimes, and government actions. What is the diference between these two?
5. Characterize the main common traits in the fiscal policy of the four hyperinflation countries (Austria, Hungary, Poland, and Germany) during the hyperinflationary period and after its end.
6. Characterize the main common traits in the monetary policy during and after the hyper- inflationary period.
7. How did Czechoslovakia avoid the hyperinflation?