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Appendix A Data Sources
Output: Real GDP (NIPA Table 1.1.3 line 1).
Government spending: Real federal government consumption expenditures and gross investment (NIPA Table 1.1.3 line 22).
Personal income tax base: Personal income (NIPA Table 2.1 line 1) less government transfers (NIPA >Table 2.1 line 17) plus contributions for government social insurance (NIPA Table 3.2 line 11), deflated by the GDP deflator (NIPA Table 1.1.9 line 1).
Corporate income tax base: Corporate profits (NIPA Table 1.12 line 13) less Federal Reserve Bank profits (NIPA Tables 6.16 B-C-D), deflated by the GDP deflator (NIPA Table 1.1.9 line 1).
Average personal income tax rate: Sum of federal personal current taxes (NIPA Table 3.2 line 3) and contributions for government social insurance (NIPA Table 3.2 line ) divided by the nominal personal income tax base.
Average corporate income tax rate: Federal taxes on corporate income excluding Federal Reserve banks (NIPA Table 3.2 line 9) divided by the nominal corporate income tax base.
Debt: Federal debt is total public debt as percent of GDP (FRED, Federal Reserve Bank of Saint Louis).
Defense spending news: Valerie Ramey’s news series (e.g., Ramey, 2019).
Narrative corporate income taxes: Mertens and Ravn narrative series (Mertens and Ravn, 2013).
Appendix B Empirical Results: Robustness Checks
To assess the robustness of our baseline specification and whether a corporate income tax cut results to a more expansionary effect in periods of low-debt, we proceed with further checks. Within our STVAR framework we report results for specifications in which we replace
Ramey’s military news with alternative measures of fiscal news, or we change the ordering of the variables, or we treat a narratively identified measure of corporate taxes as our shock. The results of our checks include:
a) The aggregate narratively identified tax news measure of Mertens and Ravn (2012). This is the only case that we do not find a strong evidence of debt-dependent effects (Figure B.1). We observe that the output responses are debt-dependent around the 5th quarter, with output being more expansionary in periods of low debt, compared to periods of high debt.
b) The aggregate narratively identified unanticipated tax measure. The results for this specification are very close to our baseline specification (Figure B.2).
c) The corporate narratively identified unanticipated income tax cut series, order first in our VAR specification and treated as the shock. In both states the output is contractionary, but not statistically significantly different in the short run (Figure 5). After 4 quarters, the effect on output at the high-debt state remains negative, but turns positive for the low-debt state.
d) Finally, we conducted some checks in which we changed the ordering of the variables. Interestingly, when we order government spending as the 5th variable, in this case the effect on output is contractionary in a high-debt state (Figure B.4).
Appendix C Model Solution
This appendix lists the equilibrium conditions of the baseline model and describes the procedure to solve the model fully nonlinearly.
Fotiou: Fiscal Affairs Department, International Monetary Fund; Shen: Department of Economics, Oklahoma State University; Yang: Fiscal Affairs Department, International Monetary Fund. We thank Antoine Arnoud, Huixin Bi, Vitor Gaspar, Shafik Hebous, Marialuz Moreno Badia, Ryota Nakatani, Adrian Paralta Alva, Catherine Pattillo, Juan F. Rubio-Ramirez, David Savitski, the Office of Tax Analysis at the U.S. Treasury, an anonymous referee, and participants in the seminar of the Fiscal Affairs Department, IMF and the 2019 Midwest Macro Meetings for helpful comments and discussion.
International Monetary Fund (2019) projects the U.S. net public debt to increase from 80 percent of GDP in 2012 to 94 percent in 2024 and the Japanese net debt from 147 percent in 2012 to 154 percent in 2024.
For example, we could define a dummy variable of high-debt being equal to one in periods that the economy has a debt ratio above, say 60 percent of GDP. However, this would limit our data points under study for the high-debt regime. Instead, in our framework all the data points are included in the analysis but have different weights in different periods.
For example, in the U.S., the reduction in income tax rates in 1964 was partially reversed in 1968 because of the spending needs arising from the Vietnam War and the inflationary pressure (see Yang (2009)). In Japan, out of concern of fiscal sustainability, a series of reductions in corporate income tax rates were followed by consumption tax hikes from five to eight percent in 2014 and to ten percent in 2019.
Ramey (2019) provides a thorough survey on empirical fiscal policy studies and discusses how the different identification approaches—i.e., the structural identification based on structural vector autoregressive models (e.g., Blanchard and Perotti, 2002; Mountford and Uhlig, 2009) and the narrative approach (e.g., Romer and Romer, 2010)—may result in different multiplier estimation results.
Sims and Wolff (2018) study the theoretical effects of business-cycle state dependent tax multipliers.
The order follows Auerbach and Gorodnichenko (2012), which assumes that shocks in tax revenues and output have no contemporaneous effect on government spending, and taxes respond to their own shock but also to government spending. In robustness checks, we also use narratively constructed, exogenous corporate tax changes to address the endogeneity concerns and try different ordering in the baseline specification. See Section 2.3.
The NIPA corporate data do not include proprietors’ income and taxes.
We also estimate with the series of the unanticipated corporate income tax changes ordered last. The debt-dependent corporate income tax effects are even more pronounced than those presented in Figure 5.
As transfers are a non-distorting instrument in our model, they do not play a role on the effect of capital income tax cut.
See Appendix 2 in Jones (2002) for the method and data used for constructing average capital and labor income tax rates with the NIPA data.
The calculation is based on the data in Table A1 in Devries et al. (2011). Sensitivity analysis analyzes an average fiscal adjustment duration often years.
The capital income tax rates reported in Table 5 of Congressional Budget Office (2017) are 0.155, 0.181, and 0.191 for 2017, 2027, and 2047 and in Table 5 of Congressional Budget Office (2018a) are 0.147, 0.165, and 0.170 for 2018, 2028, and 2048. The effective marginal tax rate is the share of the return on an additional dollar of investment made in a particular year that will be paid in taxes over the life of that investment.
Following (10), when fiscal policy actually switches from the tax cut regime to the fiscal adjustment regime, the capital income tax rate increase from the level after the tax cut would be quite large, because of the large difference between the targeted debt level (70 percent of output) and the current debt level (120 percent of output). Sensitivity analysis explores an alternative value of the debt target.
Since the nonlinear model has both transfers and capital income tax reversals as adjustment instruments, an alternative specification in the linear model is to replace
When plotting the policy functions against debt, other state variables are set at their steady-state values.
As we focus on the capital income tax cut effect in the simulation exercise, βt is dropped from the state space to facilitate numerical convergence.