Is a Period of Low Interest Rates a Good Time to Increase Government Debt? *

Transcription

1 Is a Period of Low Interest Rates a Good Time to Increase Government Debt? * Julio Garín Claremont McKenna College Robert Lester Colby College Jonathan Wolff Miami University Eric Sims University of Notre Dame & NBER August 1, 217 PRELIMINARY AND INCOMPLETE: PLEASE, DO NOT DISTRIBUTE Abstract Many have recently argued that periods of low interest rates are advantageous times for governments to increase expenditure by issuing debt. The logic behind such an argument is simple: with low interest rates issuing debt is comparatively inexpensive. The objective of this paper is to argue that this logic may in fact be too simplistic. Whether or not it is a good time to issue debt depends not on whether interest rates are low, but rather on why interest rates are low. We focus on fiscal sustainability, which requires that newly issued debt equal the present discounted value of primary fiscal surpluses. We show that if interest rates are low because of an increased preference for saving (i.e. a change in the discount factor), then fiscal sustainability requires increasing debt in a period of low interest rates. In contrast, if interest rates are low because of a decline in trend output growth, then it is not sustainable to increase debt. * We are particularly grateful to Nam Vu, William Even, seminar participants at Miami University, the University of Notre Dame, and Colby College. The usual disclaimer applies. Author contact information: Garín: jgarin@cmc.edu; Lester: rblester@colby.edu; Sims: esims1@nd.edu; Wolff: wolffjs@miamioh.edu

2 1 Introduction Government borrowing costs are at record lows; markets are in effect pleading with the government to borrow and spend. So why not do it? It s completely crazy that public construction as a percentage of GDP has declined to record lows even as interest rates have done the same. - Paul Krugman, The Cases for Public Investment February 27, 21 With global real interest rates at historic lows (Figure 1), several prominent economists and other political commentators have argued that now is a good time for governments to engage in fiscal expansion and increase debt. The logic behind such arguments is quite simple with interest rates low, it is a comparatively good time to borrow. In spite of this simple and seemingly unassailable logic, our objective in this paper is to argue that the case for increasing debt in a time of low interest rates is in fact not so clean-cut. In particular, when thinking about whether it is a good or bad time to increase debt, we argue that it matters not so much whether interest rates are low, but rather it is important to understand why interest rates are low. Figure 1: Real Interest Rate Note: The ex-post real interest rate is defined as the annual yield on a three month treasury bill minus one period ahead inflation as measured by the GDP deflator. The line defined as trend is extracted from the HP filter with a smoothing parameter of 1. We must first clarify what is meant by the adjectives good or bad. For the purposes of this paper, we focus not on a measure of aggregate welfare or output, but rather on fiscal sustainability. Fiscal sustainability requires that the present discounted value of government debt in the far off future approach zero. A sustainable fiscal plan requires that newly issued government debt equal the present discounted value of future primary surpluses, defined as the difference between tax revenues 1

3 and non-interest expenses. We consider different structural sources of lower equilibrium real interest rates. We consider it a good time to increase government debt if the present discounted value of primary surpluses increases when interest rates fall (holding all future fiscal behavior constant), and a bad time to increase debt if the present discounted value of primary surpluses falls when interest rates fall. We begin in Section 2 with a simple two period model of the economy in which output is exogenous and there is no capital accumulation. Output grows between periods at rate z and a representative household discounts future utility flows at a discount factor β (, 1). A standard Euler equation pins down an equilibrium real interest rate. The interest rate is decreasing in β and increasing in z. Put differently, the interest rate could be low either because the household is relatively more patient (i.e. β is higher) or because the economy is expected to grow more slowly (i.e. z is lower). A government consumes a fraction of output, g, each period, and raises revenue through a proportional tax on output, τ. Fiscal sustainability requires that the current debt-gdp ratio equal the present discounted value of the future primary surplus. Using the equilibrium expression for the real interest rate, we show that the sustainable debt-gdp ratio depends only on β, g, and τ. If interest rates are low because β is high, it is sustainable to increase the current debt-gdp ratio. If interest rates are low because z is low, in contrast, it is not sustainable to adjust the current debt-gdp ratio without altering the future spending or tax shares. The intuition for these results is fairly straightforward in the simple model. When β is high, there is no impact on the value of the future primary surplus. The fact that the interest rate is low means that you discount the future surplus less, so it is sustainable to increase the debt-gdp ratio in the present. When z is low, in contrast, the future primary surplus will be lower than otherwise because output will grow more slowly. This effect exactly offsets the impact of the lower real interest rate, leaving the sustainable current debt-gdp ratio unaffected. In Section 3 we extend the analysis to a real business cycle model with endogenous labor supply and capital accumulation. The government raises revenue by taxing labor and capital income, and consumes a fraction of output and spends another fraction of output on transfer payments. Productivity growth drives trend growth in output. The steady state analysis of the model works out identically to the two period model with exogenous output. The sustainable debt-gdp ratio is increasing in β but is unaffected by the trend growth rate of productivity. We also consider transition dynamics. In particular, we examine what happens to output, the real interest rate, and the present discounted value of future primary surpluses after a permanent increase in the discount factor or decrease in the trend growth rate, both of which lower the equilibrium real interest rate. The sustainable debt-gdp ratio increases initially and continually increases after an increase in patience, but it initially decreases before returning to its original steady state after a reduction in the trend growth rate. In other words, it is a good time to increase debt when interest rates are low because of an increased preference for saving, but it is not a good time to do so when interest rates are low because trend output growth is low. Broadly speaking, the literature can be divided into work explaining why real interest rates 2

4 are low and other work explaining the policy consequences of these low real interest rates. Since these papers are complimentary and often overlap, we relate to both of them. Carvalho, Ferrero, and Nechio (21) argue that an aging of the population and a slowdown in population growth account for a one and a half percentage point decline in the real interest rate over the last 2 years in developed economies. Cette, Fernald and Mojon (21) also favor a prolonged decline. Along similar lines, Gagnon et al (21) show that the decline in fertility rates and increase in employment rates during the 19s and 7s account for a one percentage point decline in the real rate since the 198s. Rachel and Smith (21) argue that the lower relative price of capital goods and decline in trend growth account for another one and a half percentage point decline in the real rate. Krueger and Ludwig (27) show that the effects of the demographic transition are exacerbated in the US once one allows international trade. The reason is that other developed countries are aging even faster than the US which leads capital to flow to the US which pushes down the return on capital in equilibrium. Other reasons for low real interest rates include rising premia on the safety and liquidity of US Treasury securities (e.g. Hall (21), Vissing-Jorgensen (212), and Del Negro et al (217)), lingering effects of the Financial Crisis and Great Recession (e.g. Juselius, Borio, Disyatat, and Drehmann (21)), and the global savings glut as described by Bernanke (2). Of particular importance to our paper is the role of lower productivity growth in lowering real interest rates. The decline in trend output growth starting in the 197s has been well documented by Gordon (21) and others. Fernald and Jones (214) make the case that, if anything, TFP growth will most likely be lower in the future. The idea here is that the growth rate of research scientists in the developed world has been growing faster than the population growth rate. Since the growth rate of scientists will eventually have to equal the growth rate of the population, the US and other developed economies are benefiting from favorable transition dynamics. Of course, this effect will be dampened to the extent new research scientists come from developing countries. The quantitative effects of lower trend growth on real interest rates is still being debated. Williams (21) and Laubach and Williams (21) argue that lower trend growth can account for a significant decline in the natural real interest rate (the real interest rate that would prevail when the economy is operating at its potential level) since 199. On the other hand, Hamilton et al. (21) argue that the relationship between trend output growth and the natural rate is more tenuous. Turning from the causes of low real interest rates to their effects, a number of authors have considered the implications of low real interest rates on policy. In particular, Alvin Hansens (1939) theory of secular stagnation has made a recent comeback within academic and policy circles. The basic idea is that recessions can be very persistent and perhaps permanent if there is an oversupply of savings. Eggertsson and Mehrotra (214) formalize this in an overlapping generations New Keynesian model where a temporary deleveraging shock which reduces the debt level for some agents affects the distribution of savings across generations which has long lasting effects. An increase in government debt (not necessarily spending) increases the real interest rate and causes the economy to escape the slump. Eggertsson, Mehrotra, Singh, and Summers (21) examine this problem in an open economy model and show that fiscal policy has positive externalities across countries. 3

5 We view our paper as complimentary to both segments of the literature. While low real interest rates are some combination of aging, low productivity growth, internationalization, and lingering effects of the Great Recession, we do not take a stand on their quantitative significance. Moreover, we consider neither the multiplier effects of government spending in low interest rate environments nor the effects of government spending on welfare. These simplifications allow us to make an intuitive but frequently overlooked point: a decrease in the real interest rate can loosen or tighten the government budget constraint. While we believe the simplicity is a net benefit, it is important to recognize the limitations of our model. Many of these limitations can be tackled in future work. 2 A Two Period Model To illustrate our main point cleanly, we begin with a simple two period model. There is no uncertainty over the future. A representative household has logarithmic preferences over current and future consumption and does not supply labor. Income is exogenous. The household can save through one period bonds at a given real interest rate. The household s problem is: max ln C t + β ln C t+1 (1) C t,b t,c t+1 s.t. C t + B t B t 1 Y t + r t 1 B t 1 (2) B t 1 is the stock of bonds with which a household enters a period. C t is consumption and Y t is exogenous income. β (, 1) is a discount factor. The interest rate on bonds carried from t to t + 1 is r t. The first order condition is the familiar Euler equation: 1 + r t = 1 β C t+1 C t (3) Output is equal to an exogenous productivity variable, Z t. The growth rate of productivity between t and t + 1 is given by z t, which is known in period t: Z t+1 = (1 + z t )Z t (4) The government enters period t with a given stock of debt, D t 1. Each period, it consumes some output and raises tax revenue. Its flow budget constraint in period t is: G t + r t 1 D t 1 T t + D t D t 1 () Government consumption is G t and tax revenue is T t. The period t + 1 government budget constraint is: G t+1 + r t D t T t+1 + D t+1 D t () 4

6 Fiscal sustainability requires that D t+1 = i.e. that the government not die in debt. Imposing this allows us to solve for new debt issued in t as: D t = r t [T t+1 G t+1 ] (7) This expression requires that new debt issued in period t equal the present discounted value of the future primary surplus. We assume that the government consumes a known fraction of output in period t + 1, g t+1 (, 1), and also that tax revenue is a known fraction of output, τ t+1 (, 1). These fractions need not be constant across periods. These definitions allow us to rewrite (7) as: D t 1 = [τ t+1 g t+1 ] (8) Y t r t Since output equals productivity, and productivity growth across periods is exogenous and known, we can equivalently write (8) as: D t Y t = 1 + z t 1 + r t [τ t+1 g t+1 ] (9) Market-clearing in the economy requires that the household hold all debt issued by the government, which gives the usual resource constraint that Y t = C t + G t. This equivalently implies that C t = (1 g t )Z t. We can then use this in conjunction with the Euler equation, (3), to solve for an expression for the equilibrium real interest rate: 1 + r t = 1 β 1 g t+1 1 g t (1 + z t ) (1) From (1), we can deduce that the interest rate can fall for one of two reasons: either there is an increased propensity to save (i.e. the household is relatively more patient, so β is higher), or the growth rate of productivity between the present and the future, z t, declines. (1) can be combined with (9) to derive an expression for the current debt-gdp ratio consistent with fiscal sustainability: D t Y t = β 1 g t 1 g t+1 [τ t+1 g t+1 ] (11) The debt-gdp ratio consistent with fiscal sustainability depends only on the household s discount factor, β, and the tax and spending shares, τ and g, respectively. It does not depend on z t. Assume that the government initially is running a deficit, so that the debt-gdp ratio and the future primary surplus are both positive. If the real interest rate falls because of an increase in β, then, given future tax and spending plans, the government should increase its debt-gdp ratio by either increasing period t spending or cutting period t taxes. In contrast, if the real interest rate falls because of a decline in z t, then fiscal sustainability requires that the government not adjust its current debt-gdp ratio. In spite of a low interest rate, increasing debt in this case would necessitate either a future increase in taxes or a decrease in spending, or some combination thereof.

7 3 An Infinite Horizon RBC Model The simple two period model from Section 2 cleanly makes the point that whether it is sustainable to issue more debt depends not on whether interest rates are low, but rather on why interest rates are low. In this section, we consider an infinite horizon real business cycle model with endogenous capital accumulation, variable labor supply, and different distortionary tax instruments. We show that the same basic intuition from the two period model with exogenous output carries over to this more general framework. The model consists of three principal actors: a representative household, a representative firm, and a government. We briefly describe the decision problems of each actor in the subsections below. 3.1 Household A representative household lives forever. It receives flow utility from consumption and disutility from labor. It can save by accumulating bonds or accumulating capital. Its problem can be written: max C t,b t,n t,k t E t j= β j ln C t+j θ N 1+χ t+j 1 + χ s.t. (12) C t + I t + B t B t 1 (1 τ N )w t N t + (1 τ K )R t K t + Π t + T R t + r t 1 B t 1 (13) K t = I t + (1 δ)k t 1 (14) (13) is the flow budget constraint and (14) is the law of motion for capital. K t 1 and B t 1 are the stocks of capital and bonds with which the household enters a period and are given. C t is consumption and N t is labor supply. The parameter χ is the inverse Frisch labor supply elasticity and θ is a scaling parameter. I t is investment. Capital depreciates at δ (, 1). The real wage is w t and the real rental rate on capital is R t. τ N and τ K are fixed tax rates on labor and capital income, respectively. Π t is profit distributed from ownership of the firm and T R t is a lump sum transfer payment from the government. The optimality conditions for the household are standard: 1 1 = β(1 + r t ) E t (1) C t C t+1 1 C t = β E t 1 C t+1 [(1 τ K )R t+1 + (1 δ)] (1) θn χ t = 1 C t (1 τ N )w t (17) 3.2 Firm A representative firm produces output using capital and labor, both of which are leased on a period-by-period basis from the household. The production technology is:

8 Y t = Zt 1 α Kt 1N α t 1 α (18) Z t is an exogenous productivity variable, and the parameter α (, 1) defines capital s share of output. The firm s problem is static, and its objective is to pick K t 1 and N t to maximize period profit: max K t 1,N t The optimality conditions are standard: Π t = Zt 1 α Kt 1N α t 1 α w t N t R t K t (19) 3.3 Government R t = αzt 1 α Kt 1 α 1 Nt 1 α (2) w t = (1 α)zt 1 α Kt 1N α t α (21) Government spending, G t, and transfers, T R t, are assumed to be fixed fractions of output each period, g (, 1) and t (, 1), respectively. As mentioned above, we also assume that capital and labor taxes are time-invariant. Rather than formally writing down the government s budget constraint and imposing fiscal sustainability in the solution to the model, we instead simply define terms equal to the present discounted value of future expenditure and revenue, respectively. These can be written recursively as fractions of current output as: EX t 1 Y t+1 = E t G t+1 Y t 1 + r t Y + T R t+1 + EX t+1 t Y t+1 Y t+1 Y t+1 REV t 1 Y t+1 = E t τ N w t+1 N t+1 Y t 1 + r t Y + τ K R t+1 K t+1 + REV t+1 t Y t+1 Y t+1 Y t+1 We then define a variable we call fiscal sustainability, SUS t, as the difference between these two: SUS t = REV t Y t (22) (23) EX t Y t (24) Were we to formally impose fiscal sustainability in the solution to the model, the variable SUS t would equal the debt-gdp ratio. Since the solution to the model using standard techniques requires some notion of sustainability, we would formally write down a flow budget constraint for the government and include lump sum taxes. This would make the debt sustainable but indeterminate. We can think of the variable SUS t as measuring the present discounted value of future primary surpluses from non-lump sum taxes. In the analysis which follows, we wish to examine how this fiscal sustainability measure reacts to permanent shocks which alter the equilibrium real interest. 7

9 3.4 Market-Clearing Conditions and Stationarizing the Model The aggregate resource constraint is standard: Y t = C t + I t + G t (2) We assume that aggregate productivity obeys a non-stationary but deterministic process where z is the growth rate: Z t+1 = (1 + z)z t (2) Many variables inherit trend growth from Z t. Exceptions include the real interest rate, the rental rate on capital, labor hours, and fiscal variables expressed as ratios relative to output. For all other variables, let lower case letters denote stationarized transformations, e.g. x t X t /Z t. 3. Steady State The variables pertaining to fiscal sustainability introduced in Section 3.3 are stationary because they are expressed as fractions of output. Along the balanced growth path, output grows at a constant rate given by Y t+1 C t+1 C t Y t = 1 + z. Similarly, consumption grows at the same rate as output, so = 1 + z. This means that the steady state real interest rate can be written: 1 + r = 1 + z β Note that this is the same expression for the equilibrium real interest rate in the two period model, (1). Given firm optimality conditions and the expression for the steady state real interest rate, the steady state values of the fiscal variables are: (27) EX Y = β (g + t) (28) 1 β REV β Y = 1 β ((1 α)τ N + ατ K ) (29) SUS β = 1 β (1 α)τ N + ατ K (g + t) As in the two period model of Section 2, the growth rate of productivity drops out of the steady state fiscal sustainability condition, (3). An increase in β, which would lower r, would result in a higher value of SUS. This means that the government can afford to permanently increase the debt-gdp ratio. As in the two period model, the growth rate variable, z, drops out of the steady state expression for the fiscal sustainability variable. This again means that a reduction in the trend growth rate, which lowers the steady state interest rate in (27), does not allow a government to sustainably increase its debt-gdp ratio without committing to some future increase in tax rates are reduction in expenditure shares. (3) 8

10 4 Quantitative Analysis with Transition Dynamics Above we showed how the sustainable level of steady state debt-gdp is unaffected by changes in the trend growth rate of output, but is impacted by changes in the discount factor. We now undertake a quantitative analysis to demonstrate that this also holds when taking transition dynamics into account. We set values for the parameters of the model as follows. The unit of time is a quarter. We assume that β =.99 and δ =.2. The inverse Frisch labor supply elasticity is set to χ = 1. The parameter governing capital s share of income is set to α = 1/3. The parameter governing the disutility of labor, θ, is set to be consistent with steady state labor hours of 1/3. We assume that the steady state growth rate of productivity is.. This translates into a two percent annualized rate of trend growth in output, and a steady state annualized real interest rate of about percent. We assume that g =, t =.1, and τ N =.3. We then solve for a value of τ K to be consistent with SUS = (equivalently, a steady state debt-gdp ratio of percent if lump sum taxes were to be ignored and fiscal sustainability were imposed). This implies τ K = 2. The model is solved by log-linearizing about the steady state implied by these parameters. We consider the following quantitative experiment. Up until period t, we assume that the economy sits in the steady state / balanced growth path implied by this parameterization. Then, in period t, there is an unexpected and permanent change in either z or β which lowers the steady state real interest rate by 1 basis points (in particular, from percent annualized to percent). This involves, respectively, reducing z from. to.24 or increasing β from.99 to.992. Figure 2 plots time paths of log output and the real interest rate. The black lines show the time paths if the economy were to stay in the original steady state. The dashed lines show the transition dynamics when either z or β change. The left column considers reductions in z, while the right column considers an increase in β. The upper row plots the time paths of log output, while the bottom row plots the time paths of the real interest rate. 9

11 Interest Rate Interest Rate Log Output Log Output Figure 2: Time Paths of Output and Interest Rate. Reduction in z. Increase in Horizon Horizon Horizon Horizon Notes: this figure plots the paths of output (top row) and interest rates (bottom row) in response to exogenous shocks to productivity declines (left column) and household patience (right column). Solid black lines display variable paths in the absence of the corresponding shock and dashed lines display paths with the shock. The reduction in z and increase in β lead to the same change in the steady state real interest rate and produce similar transition dynamics. In both cases, the real interest rate initially increases slightly before steadily declining towards the new steady state while the stock of capital adjusts. The reduction in z initially leads to a small output increase (owing to a negative wealth effect on labor supply), but thereafter output grows at a slower rate forever. In the case of an increase in β, output initially increases and remains on a higher level trajectory than it otherwise would have, but the the change in β does not affect the long run growth rate of output. Figure 3 shows the time paths of the fiscal sustainability variable, SUS t, conditional on permanent changes in either z or β. It is structured similarly to Figure 2. Consistent with the analytical analysis above in Section 3., the steady state value of SUS t is unaffected by the decline in z while it increases after an increase in β. In terms of transition dynamics, initially the value of SUS t temporarily falls after the reduction in z. Intuitively, this initial decline occurs because expected output growth falls immediately, whereas it takes some time for the real interest rate to decline. In contrast, the value of SUS t initially jumps up after a permanent increase in β. It initially 1

12 Fiscal Sustainability Fiscal Sustainability undershoots relative to its new steady state. This undershooting occurs because it takes time for the real interest rate to decline. Figure 3: Time Paths of Fiscal Sustainability 2 Decrease in z.7 Increase in Horizon Horizon Notes: this figure plots the path of future primary surpluses in response to exogenous shocks to productivity declines (left column) and household patience (right column). Solid black lines display variable paths in the absence of the corresponding shock and dashed lines display paths with the shock. Figure 3 makes clear in a more realistic quantitative framework the main point from Section 2. Whether or not it is sustainable to issue more debt in a period low interest rates depends on why interest rates are low. In the case of low interest rates driven by a decline in trend productivity growth, in the long run it is not sustainable to increase the debt-gdp ratio, and in the short run sustainability requires reducing it. The opposite is the case when low interest rates are caused by an increase in subjective patience. Because the results shown in Figure 3 are based on particular parameter values, a natural question to ponder is whether or not they depend on the assumed values of those parameters. The answer is that the basic pattern of response of SUS t are qualitatively the same regardless of parameter values. A Model with Government Investment Having shown that the sustainable level of debt is unaffected by changes in trend growth, we now consider the impact of public investment at low interest rates on the sustainability of debt. Following the arguments of several prominent economists, public investment can enhance the growth of the economy making future debt repayment easier and, when coupled with low interest rates, is a particularly cost effective way of stimulating the economy. To consider the merit of this argument, we derive an extension of our baseline model in which the fiscal authority accumulates productive capital via a process similar that of the household and provides this capital at no cost to the firm. Denoting government capital as K G,t and government investment as I G,t, the capital accumulation 11

13 equation of the fiscal authority appears as: K G,t = I G,t + (1 δ G )K G,t 1 (31) Here, δ G (, 1) is the depreciation rate of public capital. We model government investment as a fixed fraction of output, i G (, 1). Assuming an output elasticity to public capital of η (, 1), the production function of private firms appears as: Y t = Zt 1 α K η G,t 1 Kα t 1Nt 1 α (32) Traditional calibrations of η generally place its value between and.1. 1 expenditure in the presence of government investment appears as: Finally, aggregate Y t = C t + I t + G t + I G,t (33) Adjusting for the presence of public capital, our public expenditure variable now appears as: EX t Y t = 1 Y t+1 E t G t r t Y + I G,t+1 + T R t+1 + EX t+1 t Y t+1 Y t+1 Y t+1 Y t+1 In steady state, the ratio of expenditure to output is (34) EX Y = β 1 β [g + τ + i G] (3) The definitions of revenue to output ratio and the fiscal sustainability variable are identical to the previous section. Moreover, because factor shares for labor and capital continue to be constant at 1 α and α respectively so the revenue to GDP ratio is the same as before. However, in steady state, the sustainability condition is SUS β = 1 β (1 α)τ N + ατ K (g + t + i G ) Again, notice that z does not enter into the steady states for the fiscal variables. Therefore, a reduction in z will not affect sustainability in the long run, but may in the short run. When stationarizing the model, we must explicitly account for the presence of government investment. In Appendix A, we provide a detailed exposition of the model as well as the full process for stationarizing and derivation of the new steady state. Using our extended model, we reconsider the quantitative experiments from Section 4. In particular, we consider a permanent reduction in z (or permanent increase in β) big enough to decrease the real interest rate by one percentage point in steady state when η =. Because the 1 α growth rate of output in steady state is 1 α η, the steady-state real interest rate increases as η goes 1 See, for example, Baxter and King (1993), Leeper, Walker, and Yang (21), and Leduc and Wilson (213). (3) 12

14 up. The interest rate and output results for a decrease in z for various values of η are shown in Figures 4 and?? respectively. Figure 4: Time Paths of the Interest Rate Interest Rates. 2 =. 2 =.2. 2 = =.7. 2 = = = = = Notes: this figure plots the paths of the interest rate for various values of η after a reduction in z. 13

15 Figure : Time Paths of Output Log Output 2 =. 2 =.2. 2 = =.7. 2 = = = = =... Notes: this figure plots the paths of output for various values of η after a reduction in z. Just as in the previous section, the real interest rate declines in steady state although the transition is not immediate as the capital stock takes time to transition to the lower steady state. This transition process takes longer the bigger is η. Since public capital takes time to transition too, the more important public capital is to production (i.e. the bigger is η) the slower are the transition dynamics. Qualitatively, this would be the same as raising α. The responses of output look the same qualitatively as in the previous section. On impact, labor supply increases due to a negative wealth effect and output increases. As capital accumulation slows down labor demand shifts to the left and output falls to a permanently lower balanced growth path. The results for fiscal sustainability are shown in Figure. In steady-state the debt to GDP ratio is and is not affected by the size of η. A decrease in z causes the sustainability variable to drop on impact for all values of η but the drop is the biggest for large values of η. These results are again related to the dynamics of the real interest rate. Because the interest rate takes longer to decline with a large η, the government can afford less debt along the transition path. Consequently, the inclusion of public capital actually makes the case for greater deficit spending weaker. 14

16 Figure : Time Paths of Output Fiscal Sustainability 2 = 1 2 = = = =.1 2 = =.1 2 =.17 2 = Notes: this figure plots the paths of output for various values of η after a reduction in z. Conclusion We have argued that the seemingly unassailable argument to incur debt when interest rates are low is in fact a bit too simple. Rather, why interest rates are low matters for the affordability of public debt. We have not attempted to right down a model in which government debt is beneficial or detrimental. Rather, we have taken a relatively standard RBC model, which is the backbone of medium-scale models popular in policy literature today, and augmented the model with exogenous growth. The model makes a simple, but critical, point that not all low interest rate scenarios are created equal and, accordingly, policy makers should take seriously the implications of low interest rates. 1

17 7 References 1

18 8 Appendix Model 17