Aging and deflation from a fiscal perspective

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Aging and deflation from a fiscal perspectiveR Mitsuru Katagiri a, Hideki Konishi b, Kozo Ueda b,∗ a b

International Monetary Fund, Washington D.C., United States Waseda University, Tokyo 169-8050, Japan

a r t i c l e

i n f o

Article history: Received 4 June 2015 Revised 28 January 2019 Accepted 28 January 2019 Available online xxx JEL classification: D72 E30 E62 E63 H60

a b s t r a c t Negative correlations between inflation and aging are observed across developed nations. To understand such correlations from a politico-economic perspective, we embed the fiscal theory of the price level into an overlapping-generations model, with short-lived governments choosing tax rates and bond issues. Aging is deflationary when caused by an increase in longevity but inflationary when caused by a decline in birth rate. Over the past 40 years, aging has generated non-negligible deflationary pressure in Japan. Our analysis sheds new light on the controversy over the burden of national debt and the commitment effect of strategic debt creation. © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license. (http://creativecommons.org/licenses/by/4.0/)

Keywords: Deflation Fiscal theory of the price level Politico-economic equilibrium

1. Introduction In recent years, developed nations have observed negative correlations between inflation and demographic aging. Fig. 1 shows a negative relationship between the GDP deflator and growth of the working-age population in the OECD countries, implying that countries facing population aging were more likely to have experienced disinflation in the previous decade (see Shirakawa, 2012). Particularly, as shown in Fig. 2, Japan suffered from concurrent aging and deflation in the past two decades.1 However, this interconnectedness between population aging and deflation is puzzling because population aging is a factor that is expected to reduce future fiscal surpluses due to increasing social security expenditure and declining income

R An earlier version of this paper was prepared in part while Konishi was a visiting scholar at the Institute for Monetary and Economic Studies, Bank of Japan. We thank the editor (Yuriy Gorodnichenko), anonymous referee, Toni Braun, Giuseppe Fiori, Philipp Harms, Burkhard Heer, Selo Imrohoroglu, Eric Leeper, and other conference and seminar participants at the Bank of Finland/CEPR, the Bank of Japan, Bundesbank, Canon Institute, CEF, EEA-ESEM, European Public Choice Society Meeting, and Paris School of Economics. The views expressed in this paper are those of the authors and do not necessarily reflect the official views of the Bank of Japan. Konishi and Ueda are grateful for the financial support from the Japan Society for the Promotion of Science (#25380373 for Konishi and #30708558 for Ueda) and the Ministry of Education, Culture, Sports, Science and Technology (Strategic Research Foundation at Private Universities, S1411025). ∗ Corresponding author. E-mail addresses: [email protected] (M. Katagiri), [email protected] (H. Konishi), [email protected] (K. Ueda). 1 After the release of our first draft, a few empirical studies documented the deflationary effects of demographic aging (e.g., Anderson et al., 2014; Gajewski, 2015; Juselius and Takats, 2015). An article issued in the Economist (2015) concisely introduces some recent studies that examine the relationship between aging and inflation.

https://doi.org/10.1016/j.jmoneco.2019.01.018 0304-3932/© 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license. (http://creativecommons.org/licenses/by/4.0/)

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Fig. 1. Aging and deflation in OECD countries. Source: OECD Databases.

Fig. 2. Recent aging and deflation in Japan. Note: The blue solid line records the change in the share of the population aged 65 years or above (measured in % on the left vertical axis), and the red dashed line represents the annual rate of change in the consumer price index (measured in % on the right vertical axis). Source: IMF World Economic Outlook Databases, 2012. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

tax revenue, thereby generating an inflationary pressure rather than the very low rate of inflation observed recently in Japan and other developed countries. In this study, we investigate the concurrent population aging and deflation in the framework of the fiscal theory of the price level (FTPL) by analyzing the impact of price changes on income distribution across generations. We undertake the following two extensions in the standard FTPL framework. First, we embed the FTPL into an overlapping-generations (OLG) model, instead of a model with an infinitely-lived representative consumer, to highlight how aging affects the intergenerational income distribution by inducing price changes through its impacts on government budget. Second, and importantly, we consider the political economy of fiscal policy and incorporate the effect of aging in the choice of tax rates and bond issues. This contrasts with the standard FTPL framework, which considers the policy variables as given. Specifically, we set up a model in which policies are chosen by a succession of short-lived governments that stays in power for just one period. Those governments make policy decisions under the political influence of existing generations, by considering the general Please cite this article as: M. Katagiri, H. Konishi and K. Ueda, Aging and deflation from a fiscal perspective, Journal of Monetary Economics, https://doi.org/10.1016/j.jmoneco.2019.01.018

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Fig. 3. Revisions to Japan’s total fertility rate forecasts. Source: http://www.boj.or.jp/en/announcements/press/koen_2012/ko121114a.htm/.

Fig. 4. Revisions to Japan’s life expectancy forecasts. Source: http://www.boj.or.jp/en/announcements/press/koen_2012/ko121114a.htm.

equilibrium effects on the price level and the real interest rate as well as the expected strategic responses of future governments.2 Let us now introduce three outstanding features of Japan’s political economy, which motivate this study. First, for, approximately, two decades, the zero-interest rate policy of the Bank of Japan produced a policy interaction called fiscal dominance or, as per Woodford (1995) and Cochrane (2005), a combination of passive monetary policy with a non-Ricardian active fiscal policy. Second, to a certain extent, demographic aging in Japan was unexpected. While Fig. 3 shows that the official forecasts of Japan’s birth rate (formally, the total fertility rate) were repeatedly revised downward, Fig. 4 shows that the official forecasts of life expectancy in Japan were continually revised upward.3 Third, recently, the political influence of the older generation overtook that of the younger generation due to changes in political participation. Fig. 5 not only shows that 2 This extension contributes to the following three (of four) important research topics proposed by Leeper and Walker (2011) regarding the FTPL: integrating heterogeneity and policy uncertainty, identifying policy behavior, and quantifying fiscal limits. 3 These figures are taken from a speech by Nishimura (2012), the former Deputy Governor of the Bank of Japan.

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Fig. 5. Japan’s voter turnout rates by age. Note: The voter turnout rate is the fraction of eligible voters who cast a ballot in an election. The figure illustrates the voter turnout by age in the Japanese lower house election nos. 31–45 (from 1967 to 2009). Specifically, the lines with circles, Xs, asterisks, triangles, diamonds, and squares, respectively, represent the turnout rates of people in their 20s, 30s, 40s, 50s, 60s, and 70s. Source: The Association for Promoting Fair Elections.

the voter turnout rate (the fraction of eligible voters who cast a ballot) in elections to the Japanese lower house increased with age, but that the differences in turnout rates between the age groups also widened. Analyzing the Markov-perfect equilibrium in the dynamic policy-setting game after incorporating the three aforementioned features, we find that population aging affects the price level differently depending on its causes. Specifically, the price level rises when the birth rate unexpectedly declines, while it decreases with an unexpected increase in the life expectancy. Our main result is driven by the following two counteracting impacts of demographic aging on the current price level: one is economic, and the other is political. The economic impact of population aging is inflationary because the resultant contraction in a tax base or the increase in social expenditures reduces the fiscal surplus. However, the government may choose an offsetting policy to ease price changes when demographic aging will force the government to favor the older generation; this scenario will give rise to the political effect. Provided that policy tools for direct transfer to the older generation are limited, deflation can be an effective way to cater to the old as they are the main holders of nominal assets. Our analysis shows that if the birth rate declines, then the government is inclined to maintain its solvency, partly by generating inflation at the cost of the older generation’s well-being and partly by making the younger generation pay more taxes. Conversely, if the life expectancy increases, then the elderly who survive longer than expected might face a shortage of savings during their retirement. Thus, the government attempts to suppress inflation to increase the real value of the government bonds held by the older generation, thereby contributing to the concurrent progress of aging and deflation. Our numerical simulation shows that aging over the past 40 years in Japan has brought about an annual deflation of about 0.6 percentage points. Our dynamic policy-setting game to obtain the above result also has two novel implications on controversial issues in the economics of government debt. Unlike previous literature, such as Bowen et al. (1960) and Barro (1974), we find that the current larger fiscal deficit produces a temporary price rise that only affects the well-being of the existing generations who hold nominal assets, but does not impact the well-being of the future generations, even without altruistic bequest motives. This result further casts doubt on the strategic debt creation argument, which argues that each government strategically accumulates debt to “tie the hands” of a successor that it disapproves.4 In the FTPL framework, irrespective of the amount of the accumulated nominal debt, each government can pursue a fiscal policy in its own interest, owing to the adjustments in the price level.5 Thus, short-lived governments have no incentive to accumulate debt strategically. Following Sargent and Wallace (1981), the foundations of the FTPL literature were developed by Leeper (1991), Sims (1994), Woodford (1995), and Cochrane (2005), among others.6 While several studies incorporate the FTPL frame4

For more details on the strategic debt creation, see Persson and Svensson (1989), Aghion and Bolton (1990), and Tabellini and Alesina (1990). Concerning the relationship between inflation and government debt, see also Reinhart and Rogoff (2011), Hall and Sargent (2011), and Hilscher et al. (2014). 6 See Bassetto (2002) and Buiter (2002) for a critical view. Empirical studies were conducted by Canzoneri et al. (2001), Bianchi and Ilut (2017), and Bianchi and Melosi (2017). 5

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work into an OLG model (e.g., Bassetto and Cui, 2018; Braun and Nakajima, 2018; Cushing, 1999), Sims (2013) is most closely related to our study in terms of model structure. The study also uses a two-period OLG model with nominal government debt and discusses how the price level is determined within the FTPL mechanism. Although not dealing with the FTPL, Bullard et al. (2012) is also similar to our analysis in that it focuses on income redistribution to the older generation through deflation. Finally, Cochrane (2011) argues that an increase in the real discount factor can explain deflation even with the conventional fiscal theory because of an increase in the present value of fiscal surpluses. While these studies develop models and provide policy implications similar to ours, they do not endogenize political decisions on fiscal policy variables. To the best of our knowledge, our study is the first to analyze the public choice of fiscal policy variables such as income tax rates and bond issues in the FTPL framework.7 The remainder of this paper is organized as follows. Section 2 constructs a simple endowment economy model with two overlapping generations and analyzes the Markov perfect equilibrium, wherein a succession of short-lived governments chooses tax rates and bond issues. Section 3 generalizes the model in the previous section and performs a numerical simulation. Section 4 provides our concluding remarks. 2. An endowment economy with overlapping generations We consider an endowment economy with overlapping generations in which the government imposes taxes on the younger generation and issues new public bonds to repay those held by the older generation. We embed an FTPL mechanism into the framework. To use the terminology of Woodford (1995) and Cochrane (2005), the government behaves in a non-Ricardian manner, and the price level is based on a valuation equation for government debt. In this section, we first describe the economic equilibrium, assuming that taxes are exogenous. Subsequently, we endogenize them by embedding political decision making into the model and characterize a politico-economic equilibrium. 2.1. Economic equilibrium with an exogenous fiscal policy Assume two overlapping generations, the young and the old, in each period. In period t, the population consists of Nt young households and θt Nt−1 old ones, where θ t is a survival probability of the young born in period t − 1 independent across households. In other words, a young household born in period t will survive and become old in period t + 1 with probability θt+1 ∈ (0, 1] or will die at the end of period t with probability 1 − θt+1 . We interpret the survival probability θ t as a measure of longevity for the older generation in period t. We also define nt := Nt /Nt−1 and call it the birth rate. Demographic aging occurs in period t either by an increase in θ t or by a decline in nt , where both parameters are stochastic; therefore, the economy faces aggregate uncertainty. Governments tax only young households. This is an endowment economy with no storable technology. Each young household born at the beginning of period t y o receives one unit of endowment income and consumes ct units in period t and ct+1 units in period t + 1 if it survives. The household can save and insure against the risk of longevity by buying nominal annuities in competitive insurance markets. A , which would stochastiEach annuity unit contracted in period t will pay out benefits in nominal terms in period t + 1, Rt+1 cally depend on the realization of the survival probability. Owing to market incompleteness, annuity contracts that promise benefits in real terms are unavailable. Let At be the amount of nominal annuity each young household buys in period t. Its budget constraint is then expressed as

cty +

At = 1 − τt , Pt



o ct+1

=

A Pt Rt+1

Pt+1



(1) At , Pt

(2)

where Pt is the price level in period t and τ t is the income tax rate in period t (τ t ≥ 0). Annuities are backed by government bonds and insurance companies invest their sales of annuities in these bonds. Let Rt be the one-period gross nominal interest that a one-dollar nominal government bond sold in period t promises to pay in period t + 1. Competitive markets ensure that insurance companies break even in equilibrium, that is, A Rt+1 =

Rt

θt+1

,

(3)

which means that the nominal annuity benefits per old household will decrease as more households survive, while the nominal interest rate is determined independently of demographic changes. y o A young household in period t chooses ct and ct+1 to maximize its expected life-time utility, subject to budget constraints (1) and (2), respectively. For simplicity, we suppose that households’ utility functions are logarithmic; thus, their expected lifetime utility can be expressed as

log cty + β Et 7



 o , θt+1 log ct+1

(4)

Christiano and Fitzgerald (20 0 0) consider optimal distorting taxation to a certain extent, but not in a politico-economic aspect.

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where β is a discount factor and Et represents the expectation operator. Utility is normalized to zero when the household is dead in period t + 1. By combining (1)–(3), we reduce the budget constraints into

cty +

θt+1 rt+1

o ct+1 = 1 − τt ,

(5)

where

rt+1 ≡

Rt Pt Pt+1

(6)

is the real interest rate that a young household faces in period t. It depends on the realization of the price level in the next period.8 A young household’s utility maximization yields its demand for goods and nominal annuities as follows:

cty =

1 − τt , 1 + β Et θt+1

o ct+1 =

(7)

(1 − τt )Et θt+1 β rt+1 , 1 + β Et θt+1 θt+1

At = Pt at =

Pt β (1 − τt )Et θt+1 , 1 + β Et θt+1

(8)

(9)

where at ≡ At /Pt denotes a young household’s savings in real terms. Under our specification of logarithmic utility functions, a higher real interest rate increases the consumption of the older generation without affecting the savings of the younger generation. The government in period t imposes a tax, τ t , on each young household in real terms and issues nominal bonds, Bt , to repay its outstanding debt, Rt−1 Bt−1 , inherited from its predecessor and held by the older generation in period t.9 The budget balance calls for

Rt−1 Bt−1 = Bt + Pt Nt τt ,

(10)

in period t. Now, by taking the government’s initial outstanding debt, R−1 B−1 , and a stream of taxes and nominal interest rates, ∞ , as given, we consider a dynamic general equilibrium of the economy from period 0 onward. It is de{τt , Rt }t=0 ∞ fined by a sequence {at , rt+1 , Pt , Bt }t=0 that satisfies (6), (9), (10), and the market-clearing condition for government bonds,

Nt Pt at = Bt .

(11)

Two remarks are in order about the definition. First, extending (10) forward from period 0 and making use of (11), we can demonstrate that P0 is determined to hold

⎧  −1 ⎫⎤ ⎨  ⎬ t rs ⎦, = n0 ⎣τ0 + E0 τt P0 ⎩ s=1 ns ⎭ t=1

R B  1 −1 −1 N−1

⎡

∞

(12)

a fundamental valuation equation for government bonds in the FTPL framework, as long as the economy tends to its steady state.10 Second, combining (10) and (11) yields

rt at−1 = nt (at + τt ),

(13)

which equates the dissavings by the old with the sum of the savings by the young and the fiscal surplus of the government in period t ≥ 1. With the budget constraint for the young and old, Eq. (13) is equivalent to the goods-market clearing condiy tion in period t, cto = nt (1 − ct ), owing to Walras’ law. As rt determines the purchasing power of the old, Eq. (13) pins down rt to clear the goods market in period t. In period 0, with the old households holding a given nominal outstanding debt of the government, the same goods-market clearing condition determines the equilibrium price level. The next proposition reveals the equilibrium outcome precisely.

8 No physical capital exists in the economy. If it does, then the real return on government bonds may be constrained by the real return from physical capital due to the arbitrage condition. However, Sims (2013) argues that investments in physical capital cannot be an equilibrium when its rate of return is less than unity. 9 Our results hold even if debt maturity is extended beyond one period because only the aggregate size of debt matters for older generations. See Online Appendix A for details. 10 If the tax rate and survival probability are constant, then we will have rt+1 /nt+1 > 1 in the steady state to ensure that the right-hand side of (12) does not explode.

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Proposition 1. Given the government’s initial outstanding debt, R−1 B−1 , and a stream of taxes and nominal interest rates, ∞ , the equilibrium real interest rates and price levels {r ∞ {τt , Rt }t=0 t+1 , Pt }t=0 follow

1 + β Et θt+1 β Et+1 θt+2 + τt+1 , β (1 − τt )Et θt+1 1 + β Et+1 θt+2  1 n (τ + β E θ )

rt+1 = nt+1

R

t−1 Bt−1

Nt−1

Pt

=

t

t

t t+1

1 + β Et θt+1

.

(14) (15)

Proof. Apply (13) to period t + 1 and rewrite at and at+1 by using (9). Then, since the real savings by the young do not depend on real interest rates, we obtain (14) straightforwardly. To obtain Pt , rewrite at in (13) by using (9) and replace rt at−1 with (Rt−1 Bt−1 )/(Nt−1 Pt ) by using (6) and (11). This will give (15).  According to (14), the equilibrium real interest rate depends not only on the current and future tax rates but also on the future birth rate and survival probabilities. Specifically, a higher tax rate in periods t and t + 1 increases the real interest rate realized in period t + 1. Since these increases in tax lead every household to consume less in period t + 1, subsequent declines in the price level raise the real interest rate, expanding consumption by the old to clear the goods market. Conversely, a decline in the birth rate in period t + 1 lowers the real interest rate in the same period, because the consumption of the old must decrease in line with the decrease in the savings of the young. Further, if we assume that Et θt+1 = Et+1 θt+2 , from (14), then an expected future increase in survival probability will lower the real interest rate in period t + 1 for the following reason. A continuing higher survival probability results in every generation saving more when young and consuming more when old, while leaving the government’s savings unchanged. This creates excessive supply (demand) in the bonds (goods) market, eventually increasing the price level in period t + 1 relative to that in period t and decreasing the real interest rate. Concerning the equilibrium price level in each period, we can say from (12) and (14) that, in general, it is influenced by the streams of tax rates, survival probabilities, and birth rates, given the government’s nominal debt outstanding at the beginning of that period.11 Therefore, the impact of a rise in future tax rates on the current price level is, generally, ambiguous, owing to the fact that a change in future tax rates affects the allocation of consumption between the younger and older generations and thus changes the equilibrium real interest rates, as we see in (14). Such an ambiguous fiscal implication sharply contrasts with the one commonly reiterated in FTPL literature. The reason is that the latter assumed away the repercussion between fiscal surpluses and the equilibrium real interest rates under the assumption of an infinitely-lived representative household. In fact, if we employ it instead of overlapping generations in our model, then the consumption will be constant over time; therefore, the equilibrium real interest rates should also be constant at 1/β , irrespective of the stream of tax rates. Then, Eq. (12) provides a standard prediction that a rise in future tax rates unambiguously deflates the current price level. It also follows that a future reduction in birth rate inflates the price level from a reduction in future tax revenues. Certainly, we cannot discuss the fiscal implication of longevity in the standard FTPL models because of the assumption of infinitely-lived households. Our model specification renders the equilibrium price level in each period depending only on the current tax rate, current birth rate, and future expected survival probability. Specifically, a higher current tax rate and a higher expected future survival probability deflate the price level; however, a lower current birth rate inflates it.12 It may look surprising that tax and demographic parameters from period t + 1 onward have no impact on the current price level in (15). The reason is that, as we see in (9), the savings function of the young does not respond to any changes in the real interest rate, a property guaranteed under logarithmic utility functions and the absence of old-age income except pension benefits. With this property, the effects of those future parameters on government surpluses are canceled by the changes in the real interest rates they induce in equilibrium. It is worth remarking that the derivation of (15) does not need to specify how the central bank sets a nominal interest rate Rt . In Online Appendix B, we discuss a case in which the central bank follows the Taylor-type rule and show that the equilibrium for the inflation rate is determinate if the coefficient on the inflation rate in the rule is below one. Thus, one may assume a passive monetary policy such as the one keeping the nominal interest rate constant. 2.2. The burden of public debt We consider the indirect utilities of the young and old households in period t achieved in equilibrium. An old household is concerned only about consumption in period t, and a young household cares for consumption in periods t and t + 1. Ignoring terms unrelated to taxes, the following proposition shows how the utilities of the old and the young depend on tax rates in equilibrium. 11 In many existing models, such as Sargent and Wallace (1981), Rohrs (2016), Song et al. (2012), Ono (2014), Eq. (12) does not serve as a valuation equation for government debt, but as a budget constraint on the stream of tax rates. This can be attributed to the fact that these studies assumed that the government issues real bonds, each promising to pay a fixed amount of numeraire goods for every contingency in the next period. In such a situation, the left-hand side of (12) is predetermined in real terms at the beginning of period t and is equal to rt−1 Bt−1 /(Nt−1 Pt−1 ); thus, there is no room for the fiscal policy to affect the price level. 12 The deflationary effect of a higher survival probability partly depends on our assumption that fiscal surpluses in each period do not change in response to the population of the older generation. We will generalize this restrictive assumption in the more general model developed in the next section.

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Proposition 2. The equilibrium utilities enjoyed by the old and the young in period t are determined independent of the policy choice in period t − 1, expressed, respectively, as

vto = log(τt + β Et θt+1 ),

(16)

vty = log(1 − τt ) + β Et [θt+1 log(β Et+1 θt+2 + τt+1 )].

(17)

Proof. Concerning the old, plugging (3) and (11) into (2) leads to the equilibrium consumption of an old household in period t as

cto =

Rt−1 Bt−1 nt (τt + β Et θt+1 ) = , θt Nt−1 Pt θt (1 + β Et θt+1 )

(18)

where Eq. (15) is used to derive the expression on the right-hand side. Then, taking its logarithm and ignoring terms unrelated to tax rates yields (16). Concerning the young, the equilibrium consumption in period t is given by Eq. (7), and the one in period t + 1 is obtained from (18). Plugging them into (4) and ignoring terms unrelated to tax rates yield (17).  It is worth noting that in deriving the expressions in (16) and (17), we have considered the impacts of taxes, τ t and τt+1 , on utilities through changes in the equilibrium price level, Pt , and real interest rate, rt+1 , which have been shown in Proposition 1. As we have seen in (12), the current price level adjusts to equate the real value of the assets with the discounted sum of the current and future fiscal surpluses. Such forward-looking price adjustments lead the equilibrium indirect utilities of the young and the old to be realized independently of the government debt outstanding and past tax policies, whereas making them dependent only on the current and future tax policies. y Particularly, the observation of vt and vto being independent of Bt−1 and τt−1 provides an interesting implication for the long-running controversy on the burden of the national debt. Even in the absence of altruistic bequests, the burden of government debt cannot be shifted to future generations in the world of fiscal dominance, but must be paid by the current generation holding nominal assets. If the government lowers the tax rate and increases bond issues in period t, the current price level would rise, and the real interest rate would decrease as long as future taxes are kept constant, as we can see from (14) and (15). There is no impact on the utilities of households born in period t + 1 or later. It must be noted that this implication does not depend on our specification of logarithmic utilities at all and contrasts sharply with the findings obtained from the same OLG framework used by Bowen et al. (1960) and Barro (1974), among others.13 Our argument is based on the issuance of nominal government bonds and fiscal dominance. Concerning real government bonds, the accumulation of deficit forces future governments to increase taxes, and thus reduce the welfare of future generations. However, for nominal government bonds, adjustments in the current price level make such future fiscal adjustments unnecessary. To the best of our knowledge, this argument is yet to be discussed in the literature. 2.3. Politico-economic equilibrium Until now, we treated fiscal variables as exogenously fixed. However, it is unrealistic to assume that they are independent of changes in the demographic structure. With this perspective, we consider the politico-economic interactions in which the choices of policy variables respond to a change in current and future demographic parameters. To endogenize government policies and characterize the politico-economic equilibrium, we assume that tax rates and bond issues are chosen by a succession of short-lived governments, following Song et al. (2012), among others. Each government remains in power for only one period and chooses policies to maximize the weighted average of the young and old households living in that period, by considering their general equilibrium repercussions with the real interest rates and the price level. The government in period t, which we call government t hereafter, takes over the nominal government debt Bt−1 from government t − 1 and chooses a tax rate τ t and the outstanding government debt Bt . Following the spirit of the probabilistic voting model, its objective function is formulated as a weighted average of constituents in period t,

Wt = γt vto + vty ,

(19)

where γ t represents the political bias toward the well-being of the old We will confine our analysis to the Markov-perfect equilibrium of this dynamic tax-setting game. Our model is unique in that each government pays attention to income redistribution by bringing about changes in the price level with their fiscal y policies. Recall that the expressions for vto and vt given in Proposition 2 have already incorporated the general-equilibrium repercussions caused by taxes, which affect rt+1 and Pt through (14) and (15). It is also worthwhile to notice that government t must anticipate the policy response by government t + 1 when it tries to maximize Wt . Such a dynamic policy interaction arises because τt+1 affects rt+1 , as we saw in (14). generation.14

13 As is well known, Bowen et al. (1960) argue that the young can avoid these burdens by selling their bonds to the next generation. Barro (1974) argues that the young generation would neutralize the burden of increased debt by increasing bequests by the same amount to keep the next generation’s welfare unchanged. 14 For the probabilistic voting model, see Persson and Tabellini (20 0 0, Ch. 3) among others.

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The policy decisions of successive governments are usually considered intertemporally linked due to the inheritance of an outstanding debt. This is typically highlighted in the literature on strategic debt creation pioneered by Persson and Svensson (1989) and Tabellini and Alesina (1990), in which each short-lived government attempts to manipulate its successor’s unfavorable policy-making by strategically accumulating public debt. Behind the intertemporal linkage of government behavior is the assumption that government bonds are real and each government must honor its repayment.15 In our model, however, since the governments issue nominal bonds and are in a position of fiscal dominance, the price level adjusts to eliminate the linkage from the past governments; each government can pursue its own optimal policy regardless of how much nominal debt it inherits from its predecessor. This is because the price level is determined in a forward-looking manner to satisfy (10), which does not constrain government t’s policy decision anymore but serves as a valuation equation for its bonds. Proposition 3. If γt > β Et θt+1 , then, in the Markov-perfect equilibrium, government t chooses

τt =

γt − β Et θt+1 , 1 + γt

(20)

which leads to the equilibrium real interest rate and price level, respectively, as

rt+1 = Pt =

nt+1 (1 + γt ) γt+1 , β Et θt+1 1 + γt+1

R

t−1 Bt−1

1 + γ nt γt

Nt−1

t

.

(21) (22)

Otherwise, τt = 0. Proof. Government t’s objective function is obtained by substituting (16) and (17) into (19). The maximization problem is unconstrained because we have already considered (14) and (15) when deriving (16) and (17). Thus, only the intertempoy ral linkage appearing here is between the choices of τ t and τt+1 . They determine rt+1 through (14), affecting vt in (17). However, no policy variables relating to the past governments’ choices, such as Bt−1 and τt−1 , appear in government t’s optimization problem. This implies that government t − 1’s choice on τt−1 cannot constrain government t’s optimal choice on τ t . Accordingly, if we confine our attention to a Markov perfect equilibrium of this dynamic tax game, we can solve it with ∂ τt+1 /∂ τt = 0. Subsequently, it will be straightforward to obtain government t’s optimal choice for τ t , as shown in (20). Further, plugging (20) into (14) and (15) yields (21) and (22), respectively.  In what follows, we will assume γt > β Et θt+1 . To intuitively understand why intertemporal strategic policy linkage disappears, let us examine if government t’s optimal choice on τ t must change in response to an increase in nominal bond issues in period t − 1, Bt−1 , resulting from government t − 1’s tax reductions. Larger nominal bond issues in period t − 1 will affect government t’s policy decision if and only if it becomes more indebted in real terms to the old in period t, with the holders of all nominal bonds outstanding. However, those bonds are valued through (15) such that, in the absence of any tax changes in current and future periods, the price level Pt increases at the same rate as the nominal value of bond issues, leaving their real value Bt−1 /Pt unchanged. With such a price-level adjustment, in turn, government t will not be required to change its optimal choice on τ t in response to a change in government t − 1’s policy choice. 2.4. Comparative statics Let us first examine the comparative statics with respect to γ t , using (20)–(22). Subsequently, it is demonstrated that given the population structure, a greater political bias toward the older generation increases the tax rate and real interest rate but decreases the price level realized in the Markov perfect equilibrium. From these results, the greater political influence of the older generation through a relatively high voter turnout rate, as shown in Fig. 5, is one explanation for the recent concurrent deflation and aging in Japan. The government, led by the older generation’s strengthened political influence, attempts to suppress inflation and increase the real value of the government bonds held by the older generation. However, the political bias may interact with the population structure. Aging may increase bias toward the older generation. To address this issue, let us suppose that the political bias is proportional to the population ratio between the older and younger generations;

γt =

ωt θt nt

,

(23)

where ωt > 0. Then, we have the following proposition. Proposition 4. If γ t satisfies (23), then

Pt =

15

R

t−1 Bt−1

Nt−1

 1  1 + , ωt θt nt

(24)

Aghion and Bolton (1990) note that the strategic bias of debt accumulation is eliminated if governments default on their debt.

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M. Katagiri, H. Konishi and K. Ueda / Journal of Monetary Economics xxx (xxxx) xxx Table 1 Effects of aging.

Increase in the older generation’s political power (ωt ↑) Decrease in birth rate (nt ↓) Increase in life expectancy (θ t ↑)

Tax (τ t )

Bond (bt )

Price (Pt )

Real interest rate (rt+1 )

+ + +

– – +

– + –

+ 0 0

and hence a rise in θ t lowers the price level, whereas a decline in nt increases it. Proof. Plugging (23) into (22) and arranging the terms yield (24), and the statement follows straightforwardly.  Eq. (24) demonstrates that the price level responds only to current, unexpected demographic changes; the impacts of future expected changes are nullified by the associated repercussions in tax rates and real interest rates. Interestingly, the response depends on the causes of demographic aging. If the birth rate declines, a contraction in the tax base will reduce the fiscal surplus, and without any tax changes, inflation occurs to maintain solvency solely at the cost of the well-being of the old. However, since the political influence of the old is strengthened simultaneously, the government is forced to impose higher taxes on the younger generation to mitigate inflation. Conversely, if an unexpected increase in life expectancy occurs, then the older people will face a savings deficit during their unexpectedly longer retirement period. In such a situation, the strong political power of the older generation when compared to the younger generation will compel the government to suppress inflation and support the former’s well-being by bringing about deflation. Two remarks are in order. First, while the nominal interest rate is not explicitly specified in the above formulation, in Online Appendix B, we show that the equilibrium inflation rate is determinate if the coefficient on inflation is non-negative and below one in the monetary policy rule. This implies that once fiscal policy is endogenized, we do not need to assume an active fiscal policy to ensure a dynamically stable outcome. As long as monetary policy is passive, the endogenous choice of the fiscal policy by governments leads to determinacy. Second, the expected future demographic changes do not affect the current price level in our model because the savings of the young do not respond to the real interest rate. This is due to the assumption of logarithmic utility functions and the absence of old-age income except pension benefits; however, in general, the expected future demographic changes do not influence the current price level, unless they affect the sum of the savings of the young and the government’s current fiscal surpluses. Thus, such effects should be much smaller than imagined within a standard FTPL framework, unless the elasticity of savings to real interest rates is high. Finally, focusing on the impacts of simultaneous change in the current and future demographic structure, which seems to be the case according to Figs. 3 and 4, let us assume that θt = Et θt+1 and nt = Et nt+1 . Additionally, assume ωt = Et ωt+1 for convenience. Then, the equilibrium tax and real interest rates, respectively, reduce to

τt = 1 − ((1 + βθt ))/(1 + ((ωt θt )/nt )) rt+1 =

ωt . β

(25) (26)

The comparative statics results are summarized in Table 1, which we will refer to later in a simulation analysis. 2.5. Government policy Governments do not impose tax on old households in the model; however, inflation acts as a substitute to tax. This structure is the key to triggering tension between the tax imposed on the young households and inflation for governments. Thus, if we instead assume that governments can impose a tax on old households, the results will change quantitatively to weaken the tension. In Online Appendix C, we discuss a case in which governments impose consumption tax both on young and old households. We find that (i) governments have no incentive for strategic debt accumulation, (ii) the equilibrium allocation of consumption between young and old households is exactly the same as it is when the governments tax income, and (iii) the equilibrium price level is the only difference between the two tax scenarios. Since the effective price paid by the older households is higher by a factor of the consumption tax rate, the equilibrium price level must be lower by as much in the case of consumption tax. Another possible tax scenario to be considered is that governments impose different taxes on the young and old households, and optimize the tax rates in each period. In this case, the FTPL cannot uniquely identify the price level because a higher tax rate to the old is a perfect substitute for inflation as a way of income distribution. For example, if government t increases its tax rate on the old’s consumption by 1%, keeping the tax rate on the young’s unchanged, the equilibrium price level will decrease by 1% to achieve the goods-market clearing in period t, and hence the old’s utility will remain unchanged. These offsetting price adjustments result in numerous equilibrium tax rates on the old’s consumption and the associated equilibrium price levels. Please cite this article as: M. Katagiri, H. Konishi and K. Ueda, Aging and deflation from a fiscal perspective, Journal of Monetary Economics, https://doi.org/10.1016/j.jmoneco.2019.01.018

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Finally, an unexpectedly higher survival rate induces deflation in our model, partly because we assume that the old households are entirely responsible for its negative financial effects on pension benefits, which results in a shortage of savings in their retirement. Instead, if we assume that the government compensates at least a part of the shortage, an unexpectedly higher survival rate reduces government surplus in a manner similar to that of an unexpectedly lower birth rate, producing an inflationary impact on the price level to maintain solvency. If this is the case, such an economic effect on the price level counteracts the political effect that forces governments to deflate the price level. 3. Quantitative investigations using a generalized model In this section, we construct a more general model to quantitatively examine whether population aging in Japan accounts for the country’s recent deflation and its extent through the mechanism we described in the previous section. We extend the model in three major directions. First, we consider a production economy with variable labor supply. Second, we generalize the utility functions and employ the constant relative risk aversion (CRRA) class. Third, we introduce two types of government expenditure—government consumption and transfer to the older generation. Within this framework, we derive a politico-economic equilibrium and perform a numerical simulation. 3.1. The model A young household in period t supplies labor t and receives before-tax labor income t . We assume linear production technology, and thus the real wage is normalized to unity. An old household does not supply labor and its consumption relies entirely on annuity income and the per-capita government transfer gT > 0.   y o , and  to maximize its utility, uy (cy ,  ) + β E θ o o The household chooses ct , ct+1 t t t t+1 u (ct+1 ) , subject to budget cont straints:

cty + at = (1 − τt )wt t o ct+1 =

rt+1 at

θt+1

(27)

+ gT ,

(28)

where at ≡ At /Pt . The consumption, labor supply, and demand functions for annuities are determined to satisfy the first-order conditions. A short-lived government remains in power for just one period. The law of motion for government debt is

Rt−1 Bt−1 + Pt Nt gt = Bt + Pt Nt τt t .

(29)

Government spending per young household, gt , consists of its own consumption, gC , and transfer to the older generation, gT ; thus, it is defined by Nt gt ≡ (Nt + θt Nt−1 )gC + θt Nt−1 gT . The tax rate, τ t , is now proportional to the labor income. If we rewrite government debt Eq. (29) in real terms, we have

rt bt−1 = nt bt + nt τt t − (nt + θt )gC − θt gT ,

(30)

where bt ≡ Bt /(Nt Pt ). By expanding (30) forward to infinity, we obtain a valuation equation similar to (12),

⎧ 

⎡

⎨ 1 ∞

t−1 Bt−1 = nt ⎣st + Et sk Nt−1 Pt ⎩

R

k=t+1

k  rh nh

h=t+1

−1 ⎫⎤ ⎬ ⎦, ⎭

(31)

where sh ≡ τh h − (1 + θh /nh )gC − θh gT /nh is a fiscal surplus per young household in period h. It must be noted that Pt is the only variable determined by the right-hand side of this expression at the beginning of period t. The general equilibrium system is as follows. The market-clearing conditions for goods and bonds are, respectively,

nt cty + θt cto + (nt + θt )gC = nt t ,

(32)

at = bt ,

(33)

which are not independent, owing to Walras’ law, whenever (30) holds. Now, consider the politico-economic equilibrium of the model. The objective function of each short-lived government is given by

Wt = γt vto + vty ,

(34)

vty

where vto and represent the indirect utilities of the old and young households in period t, respectively. Subsequently, we have the following proposition about the government’s objective function. Please cite this article as: M. Katagiri, H. Konishi and K. Ueda, Aging and deflation from a fiscal perspective, Journal of Monetary Economics, https://doi.org/10.1016/j.jmoneco.2019.01.018

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Proposition 5. The objective function of each short-lived government does not depend on the policy choice made by its predecessor, and government t’s is given by



Wt =

γt u

o

nt bt + nt τt t − (nt + θt )gC

 +β Et

 θt+1 u

o

θt



+ uy ( (1 − τt )t − bt , t )

nt+1 bt+1 + nt+1 τt+1 t+1 − (nt+1 + θt+1 )gC

θt+1

 .

(35)

Proof. To derive the government objective function, we use (27), (28), (30), and (33). See Online Appendix D for the detailed proof of this equation and the mathematical explanation to solve for the equilibrium.  As in the previous analysis, bt−1 does not appear in government t’s objective function. Thus, as far as a Markov perfect equilibrium is concerned, government t + 1’s choice of bt+1 and τt+1 is independent of government t’s choice of bt ; the government’s strategic interactions disappear owing to the adjustments in the price level. Then, formally, it is only the bond market-clearing condition (33) that constrains government t’s policy choice. Thus, behind the market-clearing condition, there are first-order household conditions for utility maximization, and the demand for government bonds at depends on the tax rate τ t and real interest rate rt+1 . 3.2. Simulation In this subsection, we conduct numerical simulations. We first calibrate the model to fit Japanese data and then quantitatively investigate the effects of demographic and political changes on the Japanese economy. We also conduct comparative statics and compute the transition paths. 3.2.1. Calibration We specify the utility functions as

uy (ct , t ) =

(ct )1−σ (t )1+1/υ −χ , 1−σ 1 + 1/υ

(36)

(ct )1−σ , 1−σ where σ , χ , and υ represent the inverse of the elasticity of consumption, a utility weight, and the Frisch elasticity of labor supply, respectively. We set σ = 1 and υ = 0.516 and calibrate χ to have labor supply close to unity in the equilibrium. We assume that a period consists of 40 years and that β is equal to 0.9940 (1% annually). Government spending is set to satisfy uo (ct ) =

gC = gT = 0.01. The variables associated with the demographic structure and political influence are calibrated as follows. We simulate an initial steady state as a benchmark, by using data for 1976, and next consider an unexpected change in the demography occurring in this state. We derive the demographic parameters θ and n from the forecasts of the National Institute of Population and Social Security Research (IPSS) released in 1976. We assume that the economy converges consistently with long-term forecasts, and hence use the forecasts for 2050. We set the survival probability θ equal to 0.482, following the survival rate of people until the age of 77.5 in 2050. The birth rate n is set to 1.058, which is the growth rate of the population aged 20 years to 24 years old in 2050. To measure the political influence of the older generation ω, we use the data on voter turnout rates shown in Fig. 5. Specifically, we choose the 34th election held in 1976 and set ω equal to 0.969, which is the ratio of the voter turnout rate of the 20–59 years age group to that of the 60–79 years age group. As parameters for a new steady state, we use the long-term forecasts for 2060 published in 2012. The survival rate is now 0.781, which is significantly higher than the forecast published in 1976. The birth rate, on the other hand, declines to 0.629. Concerning the measure of the older generation’s political influence, we use the result of the 46th election held in 2012. This allows us to set ω equal to 1.230, which is also higher than that in 1976. 3.2.2. Comparative statics We first calculate and compare the tax and real interest rates (in annual terms) realized in the steady-state politicoeconomic equilibria by changing one of the parameter values of θ , n, ω, υ , gC , and gT , keeping the other parameters fixed at their 1976 levels. Fig. 6 gives the results. The blue lines with circles represent the tax rates (the vertical axis on the left-hand side) and the green lines represent the real interest rates (the vertical axis on the right-hand side). The figure shows that the results in this generalized model are not qualitatively different from those of the previous section, summarized in Table 1. The tax rate increases in response to an increase in life expectancy θ , a decline in birth rate n, and an increase in the older generation’s political influence ω. It also increases with government expenditure, irrespective of gC and gT . However, the real interest rate is almost unaffected by changes in demographic parameters θ and n. Only an increase in the older generation’s political power ω can increase the real interest rate. 16 See Imrohoroglu and Kitao (2009) and Trabandt and Uhlig (2011) for studies highlighting the importance of incorporating variable labor supply into the model.

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Fig. 6. Comparative statics for the tax rate and real interest rate. Note: The blue lines with circles represent the tax rate τ (left axis), and the red lines represent the annualized real interest rate r (right axis). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

3.2.3. Transition path We next calculate the changes in the tax rate and real interest rate when the economy experiences unexpected simultaneous changes in the demographic parameters θ and n with a change in ω. For this experiment, we assume the following scenario. First, the economy is initially in the steady state with the parameter values for θ , n, and ω observed in 1976 in Japan. Second, the unexpected demographic changes occur at the beginning of the next period when these parameter values jump to the levels in 2012 and stay constant afterwards. The annualized inflation rate is calculated from the path of real interest rates by assuming that the nominal interest rates remain constant at the level of the real interest rate at t = 0. Fig. 7 illustrates the transition paths of the tax rate τ , the annualized real interest rate r, the real value of the outstanding government debt per young household bt , and the annualized inflation rate π t . The figure shows that the inflation rate falls by about 0.6 percentage points annually. Considering the finding in the previous section that an increase in θ and ω leads to deflation, while a decrease in n leads to inflation, this result suggests that the effects of the increases in θ and ω dominate those of the decrease in n. Given that the Japanese economy did not experience a deflationary spiral, the deflation in this exercise is moderate but sensible. Contrarily, the size may be significantly large because aging is a long-term development and our result suggests that aging leads to a deflation of this size persistently over a period of 40 years. The figure also shows that the tax rate rises from 10% to 40%, as is predicted by the analysis in the previous section. The real value of outstanding government debt per young household decreases, which is consistent with the actual decline in the saving rate reported by Chen et al. (2007). Finally, the real interest rate rises by about 0.6 percentage points annually. It must be noted that, in the long run, that is, from t = 2 onward, the real interest rate increases even more. Our findings in the previous section and in Fig. 6 suggest that such a rise is brought about by an increase in ω. 4. Concluding remarks In this study, we considered the effects of population aging on fiscal balances and general prices by embedding the FTPL within a simple OLG model in which fiscal policy decisions are endogenized in the spirit of a probabilistic voting model. A key feature of our model is that the government uses the fiscal impact on general prices as a means to redistribute income between the current younger and older generations, and, owing to this, short-lived governments cannot transfer the fiscal burdens to the future generations by issuing government bonds. Our main findings are as follows. First, population aging stemming from an increase in longevity leads to deflation by increasing the political influence of the older generation, as does an increase in the election turnout rate among older voters. This happens because, to appease older voters, the government increases its income tax rates (which harms the young) to avoid an increase in prices (which would harm the old). Second, population aging stemming from a decline in Please cite this article as: M. Katagiri, H. Konishi and K. Ueda, Aging and deflation from a fiscal perspective, Journal of Monetary Economics, https://doi.org/10.1016/j.jmoneco.2019.01.018

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Fig. 7. Transition path under Japan’s aging population. Note: t = 0 corresponds to 1974. At t = 1, unexpected demographic and political changes occur, which corresponds to the year 2012. From t = 2 onward, demographic and political parameters do not change. The inflation rate at t = 0 is set at zero.

birth rate leads to inflation by shrinking the tax base and raising fiscal expenditure. These findings revealed that the effects of population aging on general prices depend on the cause of aging. The numerical simulation showed that aging in Japan over the past 40 years brought about an annual deflation of about 0.6 percentage points. Our study represents the first step in embedding the FTPL in a politico-economic framework. This approach presents two main challenges. The first is to address Japan’s accumulation of government bonds over the past 40 years. Our finding that aging improves fiscal balances by increasing the tax rate imposed on the young seems questionable in reality. Second, it would be interesting to introduce foreign investors buying government bonds into the model. It is well known that around 90% of Japanese government bonds are held by domestic investors. This fact justifies the use of a closed economy model in which only domestic investors are present. However, if the government cares less about foreign investors than domestic ones, it might devalue its bonds if the proportion of bonds held by foreign investors was to increase. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jmoneco.2019.01. 018. References Aghion, P., Bolton, P., 1990. Government domestic debt and the risk of default: a political-economic model of the strategic role of debt. In: Dornbush, R., Draghi, M. (Eds.), Public Debt Management: Theory and History. Cambridge University Press, Cambridge, pp. 315–345. Anderson, D., Botman, D., Hunt, B., 2014. Is Japan’s population aging deflationary? In: IMF Working Paper, pp. 14–439. Barro, R., 1974. Are government bonds net wealth? J. Polit. Econ. 82, 1095–1117. Bassetto, M., 2002. A game-theoretic view of the fiscal theory of the price level. Econometrica 70, 2167–2195. Bassetto, M., Cui, W., 2018. The fiscal theory of the price level in a world of low interest rates. J. Econ. Dyn. Control 89, 5–22. Bianchi, F., Ilut, C., 2017. Monetary/fiscal policy mix and agents’ beliefs. Rev. Econ. Dyn. 26, 113–139. Bianchi, F., Melosi, L., 2017. Escaping the Great Recession. Am. Econ. Rev. 107 (4), 1030–1058. Bowen, W.G., Davis, R.G., Kopf, D.H., 1960. The public debt: a burden on future generations? Am. Econ. Rev. 50, 701–706. Braun, A.R., Nakajima, T., 2018. Why prices don’t respond sooner to a prospective sovereign debt crisis? Rev. Econ. Dyn. 29, 235–255. Buiter, W.H., 2002. The fiscal theory of the price level: a critique. Econ. J. 112, 459–480. Bullard, J., Garriga, C., Waller, C., 2012. Demographies, redistribution, and optimal inflation. Federal Reserve Bank St. Louis Rev. 94 (6), 419–440. Canzoneri, M.B., Cumby, R.E., Diba, B.T., 2001. Is the price level determined by the needs of fiscal solvency? Am. Econ. Rev. 91, 1221–1238. Chen, K., Imrohoroglu, A., Imrohoroglu, S., 2007. The Japanese saving rate between 1960 and 2000: productivity, policy changes, and demographics. Econ. Theory 32, 87–104.

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