Abstract
This paper uses wavelet-based optimal control to simulate fiscal and monetary strategies under different levels of policy restrictions. The model applies the maximal overlap discrete wavelet transform to US quarterly GDP data and then uses the decomposed variables to build a large 80-dimensional state-space linear-quadratic tracking model. Using a political targeting design for the frequency range weights, we simulate jointly optimal fiscal and monetary policy where: (1) both fiscal and monetary policy are dually emphasized, (2) fiscal policy is unrestricted while monetary policy is restricted to achieving a steady increase in the market interest rate, (3) only monetary policy is relatively active, while fiscal spending is restricted to achieving a target growth rate, and (4) monetary policy emphasizes short-run stabilization, while fiscal policy utilizes political cycle targeting. The results show that fiscal policy must be more aggressive when the monetary authorities are not accommodating the fiscal expansion and that the dual-emphasis policy leads to a series of interest rate increases that are balanced between a steadily increasing target and a low, fixed rate. This research is the first to construct integrated fiscal and monetary policies in an applied wavelet-based optimal control setting using US data.
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Notes
We use a Daubechies 4-tap wavelet for MODWT, with periodic boundary conditions.
The two-stage procedure ensures that business and growth cycles are properly identified, as these cycles are most apparent in the first-differenced series. This mirrors conventional macroeconomic practice, where real GDP growth is identified either by log differencing or by first differencing the original level time series. If discrete wavelet analysis is applied to the level series, volatility in the cycles is not fully identified, as the trend tends to dominate the cyclical composition of the series.
The modified smooth is calculated as a residual. First, the first difference wavelet crystals are summed sequentially, observation by observation, to convert to level equivalent cycles. Then, these level equivalent cycles are then summed and the residual (or modified smooth) is calculated as the difference between the actual series and the sum of these level equivalent cycles. This ensures that the level equivalent cycles and the modified smooth sums to the original series (by construction).
Once again, the MODWT uses a 4-tap Daubechies wavelet. The boundary condition in this instance is reflecting.
The results also suggest that a more complete econometric model, which includes modeling the labor market and the international sector, may provide improved measurements.
Fort details on Fed policies, see https://www.federalreserve.gov/newsevents/testimony.htm.
Treasury bill rates can be accessed at https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=billrates.
For the CBO budget projections beginning in 2015, see https://www.cbo.gov/publication/49973.
The initial value of the national debt is assigned to be 100% of GDP, but the actual value does not affect the simulations, since only the discrepancy between the current value and initial value has an impact on the state equations and the tracking errors. Thus, the initial debt value can be chosen arbitrarily.
The parameter on the government spending tracking error has been increased by 50% at frequency range 1. This is necessary, since the increased parameter penalty weights on the consumption and investment tracking errors at frequencies 1 and 2 caused their relative weights to increase relative to all of the government spending tracking errors. Since fiscal policymakers will more aggressively use government spending at the political cycle frequency ranges 3 and 4 (and 2, to a slightly lesser extent), the relatively larger weight on the government spending tracking error at frequency range 1 dampens the use of fiscal policy at the shortest cycles, thus counterbalancing the frequency 1 consumption and investment tracking error parameter increases that were introduced solely due to the short-term stabilization emphasis by monetary policymakers.
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Crowley, P.M., Hudgins, D. What is the right balance between US monetary and fiscal policy? Explorations using simulated wavelet-based optimal tracking control. Empir Econ 55, 1537–1568 (2018). https://doi.org/10.1007/s00181-017-1326-2
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DOI: https://doi.org/10.1007/s00181-017-1326-2