Write 2 paragraphs about Fiscal Policy and the Nominal Term Premium article. No max word count, ONLY 2 PARAGRAPHS, or formatting requirements but must be submit to my tutor's work as my own.

Horvath, R., KASZAB, L., & Marsal, A. (2022). Fiscal Policy And the Nominal Term Premium. Journal of Money, Credit, and Banking, 54(2-3), 663-683. https://4x10htxce-mp01-y-https-doi-org.proxy.lirn.net/10.1111/jmcb.12858

Abstract Distortionary income taxation in a standard New Keynesian model substantially increases the nominal term-premium on long-term bonds relative to a model with lumpsum taxes. Also the empirical level of the nominal term premium can be matched with lower risk-aversion coe cient in case of a model with income taxes relative to a model with long-run ination risks. Keywords: zero-coupon bond, nominal term premium, third-order approximation, distortionary income taxation JEL: E13, E31, E43, E44, E62 1 Introduction Long-term nominal bonds deliver term-premium in order to compensate for future inflation and consumption risks the bond-holder has to bear. Rudebusch and Swanson (2012) make use of a basic New Keynesian model and finds that the term premium can be large and volatile. They assume the simplest fiscal scenario where government spending is financed with lump-sum taxes and deficits are not allowed. Further they show that long-run inflation risks like uncertainty about the inflation target substantially increase the term-premium. Van Binsbergen et al. (2012) estimate a simplified version of the model in Rudebusch and Swanson (2012) with Bayesian methods and points toward further investigation of the model with a fiscal structure added. There are several empirical papers like Engen and Hubbard (2004), Laubach (2003) and Canzoneri et al. (2002) who find a positive connection between deficit and long-term bond yields using various econometric methods. This paper proposes a simple alternative way to generate long-run inflation risks. In particular, we introduce distortionary income taxation into the model of Rudebusch and Swanson (2012) and find that the term premium on nominal bonds is higher than with lump[1]sum taxes. Thus, fiscal policy provides another good reason why long-term nominal bonds are risky. Further we show that the model with income taxation is able to generate the mean level of the empirical nominal term premium with a risk-aversion coincident that is much lower than the one needed in case of the model with long-run inflation risks. Rudebusch and Swanson (2012) show that a basic New Keynesian model approximated to the third order in the sense of Taylor series is able to generate large and volatile term premium that is in line with US data. The term-premium is constant to the second order while it becomes time-varying to the third-order. The only asset in their model is a default[1]free government bond. These assets are risky as their real payor covaries positively with consumption. In particular, shocks that result in low consumption, high inflation and, thus, low real yields are important sources of the term premia. There are no liquidity risks in their model. The most important feature of Rudebusch and Swanson (2012) model are Epstein-Zin preferences. Earlier papers in the literature considered preferences with consumption habits (see, for instance, de Paoli et al. (2006) and the literature review in Rudebusch and Swanson (2008)). With habits households are mainly concerned about sudden changes in consumption. However, with Epstein-Zin preferences they are unhappy with changes in consumption over medium and long horizons as well as short horizons. The household can onset short-run changes in consumption by modifying its labor supply and savings (also known as precautionary savings) but its ability to smooth consumption at medium- and long-run is much more limited. This paper departs from Rudebusch and Swanson (2012) who assume that government spending is financed by lump-sum taxes in each period. In their model there is no deficit allowed and, hence, no role for government debt. Below we show that allowing for government debt change properties of the term-premium to a small extent if deficit is financed by lump[1]sum taxes. As an alternative of lump-sum taxes we introduce distortionary taxation into the Rudebusch and Swanson (2012) model following Linnemann (2006) who postulates that government collect revenue by levying the same tax rate on labor and profit income. When government debt is paid back through income taxes the mean term-premium is substantially higher than with lump-sum taxes and similar in magnitude to what can be obtained using 2 the long-run inflation risk version of Rudebusch and Swanson (2012). Also the fit of the model with our fiscal extension and the one with long-run inflation risks relative to US data are quite similar using the baseline calibration of Rudebusch and Swanson (2012). The paper is organized as follows. Section 2 describes the model. Section 3 is on calibration and solution method. Section 3 provides details about the main results. The last section concludes.

3 Calibration and solution method Calibration can be found in Table (1) that follow the baseline parameter values of Rudebusch and Swanson (2012). The coincident in the lump-sum tax rule ( ) is the one of Corsetti et al. (2012). Unlike Linnemann (2006) who linearizes his model to the first-order we make use of the tax-rule in its non-linear form so that is needed to pin down the steady-state tax rate which is given by = ((1= )(b=y)(1= ) + g=y)=(1 + = ). The quarterly steady[1]state debt-to-GDP ratio (b=y) of sixty per cent is based on Rossi (2012). As a baseline we set = 0:12 so that the steady-state tax rate is 0:2767 which is slightly higher than that of Linnemann (2006)2 . The whole model is approximated to the third order using Dynare (Adjemian et al. 2011) in Matlab when calculating all the moments in table (2) and (3). To speed up calculations for gure (1) we used second-order approximation as unconditional means unlike standard deviations are quite similar in magnitude for second- and third[1]order approximations. Results Figure (1) shows that there is positive linear relationship between the risk-aversion coincident and mean of the nominal term premium. The straight line reproduces the baseline model of Rudebusch and Swanson (2012) without debt and long-run risks. The introduction of debt into the baseline model with lump-sum taxes raises the term-premium (see dashed line). The baseline model with long-run risks is depicted with dots. The model with debt and income taxes are demonstrated for two different values of the coefficient in the policy rule, (see the circles and diamonds). One can see that the extension of the Rudebusch and Swanson (2012) model with debt and distortionary taxes generates a term-premium close to the one obtained with long-run risks for both values of . When taxation is distortionary the curve is steeper than with lump-sum taxes implying higher inflation/real risks in case of income taxation. Binsbergen et al. (2012) and Piazzesi and Schneider (2006) show that a DSGE model successfully replicates several properties of the term-structure when consumption growth and inflation are negatively correlated contemporaneously and forecast each other with a negative sign. The Rudebusch and Swanson (2012) model features temporary productivity shocks in order to generate the previous patterns. In particular, a temporary negative shock to productivity leads to a fall in consumption and an increase in inflation due to the rise in marginal cost. As a result, nominal bonds carry positive term premia as depressed consumption is associated with a time of low real bond yields due to higher inflation. Our fiscal extension with income taxation has the implication similar to that of productivity shocks. To shed light on the mechanism let us study what happens after a positive innovation to government spending that needs to be financed sooner ( is close to two) or later ( is close to zero) with income taxes. Higher taxes on income imply less hours worked and lower output because households substitute away from labor to leisure. Also higher income taxes means higher real marginal cost and higher inflation through the New Keynesian Phillips curve (see equation (2)). The effect of the previous channel is magnified by positive steady-state debt (see b > 0 in equation (7)) establishing direct connection between taxes and real interest rate which surely rises after a stimulative shock according to the logic of the Taylor rule to curb inflation expectations (Linnemann, 2006). It would be of interest to test the significance of the size of the steady-state debt-to-GDP ratio. However, it is impractical to carry out an experiment with zero steady-state debt-to-GDP ratio because this would 7 result in a steady-state tax rate that is extremely low (around 1.8 percent). Table (2) summarizes means and standard deviations of selected macro and finance variables using the baseline calibration of Rudebusch and Swanson (2012). Note that the mean value of the nominal term premium is very similar across the four versions of the baseline model. Regarding the standard deviations of finance variables, it is the model with inflation risks that fits the data best. With the introduction of lump-sum taxes and endogenous debt (column three) we improve upon the performance of the baseline model. The macro and finance moments derived using the model with long-run inflation risks (column four) and the one with fiscal extension (column five) are roughly similar. The moments reported in column one (called RS) are directly comparable with those in Rudebusch and Swanson (2012). We note that the standard deviations of macro and finance moments in column one (called RS) are slightly lower than those of Rudebusch and Swanson (2012, pp. 124, column 3 of table 2) for at least two reasons. First, they calculate theoretical moments while we obtain simulated moments. Second, they use a numerical precision of 90 digits available in software Mathematica while we have only sixteen digits available in Matlab. Rudebusch and Swanson (2012) decrease their baseline values of IES and Frisch elasticity and increase the CRRA parameter in order to match US data. A lower IES means that households dislike changes in consumption over time more than with a higher IES. A lower Frisch elasticity implies that households are less able to use their labor supply too set negative shocks to consumption. As a consequence, consumption stream is more volatile for relatively low values of IES and Frisch elasticity. Also a higher risk-aversion coefficient represents that households are more concerned about changes in future consumption low and, therefore, require higher compensation in order to hold risky bonds whose real return co-moves positively with the consumption stream. In Table (3) we lower the IES from 0.5 to 0.09 and the Frisch elasticity from 2/3 to 0.28 leaving other parameters at the level of the baseline calibration. The risk-aversion coefficient of 106 is chosen so that the model with fiscal policy can match a nominal term premium of 1.06 inferred from US data. Indeed after a reduction in the values of IES and Frisch elasticity the macro and finance variables exhibit higher standard deviations. Still some of the simulated moments like the standard deviation of the excess holding period return and the slope for a 10-year bond (denoted by SD(x (40)) and SD(R(40) Also importantly, the model with fiscal policy produces a mean of the nominal term premium (1.06) that is higher than the one with inflation-risks (0.72). The version of the model with inflation risks is able to generate the empirical mean of the term premium (1.06) only if the risk-aversion coefficient is 155. Thus, it follows that a particular level of the average nominal term premium can be achieved with lower CRRA using the fiscal extension compared to the inflation risk alternative. However, it is also true that the inflation-risk model performs better in terms of matching standard deviations of US data.

5 Conclusion Fiscal policy can be an important source of long-run nominal risks in the sense that nominal term premium on government bonds rises substantially when spending is financed through income taxes relative to lump-sum taxes. Also employing the model with income taxes we can match the empirical level of the nominal term premium with lower risk-aversion coefficient than the one needed in case of the model with long-run inflation risks. In a companion paper we augment the above model with physical capital as in de Paoli et al. (2006) and find our main message to be robust.