Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

-ed in Chapter 14 in the he OLG setting, the pran- '' is in the Ramsey model relevant (compare (17.173)

IP

rule for public capital that alization of the public rate

• vo equalities in (17.173) tic and private capital. For

g:' (with 17 < EL) so that these results that output

I

1/(q.,-0

(17.174)

ms for the steady-state ,,.ization of this optimum. 4- a way that the private accumulation coincide The answer is affirmative )0! .- v instruments. In the can be mimicked in the s the public capital stock) age-specific lump-sum ). The latter instrument is nal mix of consumption

I

omic policy circles has rnment budget deficit. pies pointing at a fundaple, in Chapter 6 we saw e of return represents no in which these expendi- - er do or do not feature nting approach they are

, 41 re in the deficit).

r items for which pro-

; items are treated in the :feral credit and loan

Chapter 17: Intergenerational Economics, II

programmes, future commitments of programmes like medicare and social security, changes in the value of government assets, government retirement liabilities, etc. It is fair to say that there is no consensus as to how to measure the deficit.

Auerbach, Gokhale, and Kotlikoff (1991, p. 57) give the most radical statement of the problem to date by arguing that "... every dollar the government takes in or pays out is labeled in a manner that is economically arbitrary". They suggest doing away with the concept of the government deficit altogether and to focus instead on what they label the generational accounts. The background to their proposal is the notion that "[title conceptual issue associated with the word 'deficit' is the intergenerational distribution of welfare". Auerbach et al. (1991, p. 57) and that the intertemporal budget constraint of the government should be the focus of attention. In words, this constraint says that "the government's current net wealth plus the present value of the government's net receipts from all current and future generations (the generational accounts) must be sufficient to pay for the present value of the government's current and future consumption" (1991, p. 58).

Auerbach et al. (1991, 1994) claim a number of advantages that a system of generational accounts has over the traditional government budget deficit: (i) generational accounts are invariant to changes in accounting labels, (ii) they bring out the zero-sum feature of the intertemporal government budget constraint (what some generation gets will have to be paid for by some other generation), and (iii) they can be used to study the fiscal and intergenerational consequences of alternative policies.

In this subsection we follow Buiter (1997) by illustrating the system of generational accounts in a simple version of the Diamond—Samuelson model. Assuming that the population is constant (so that 14_1 = Lt = 1), the government (flow) budget identity is given by:

where T° and Ti are the taxes paid by the old and young respectively, and G9t and GI are pure public consumption goods that the government provides free of charge to, respectively, the old and the young. Following Buiter (1997, p. 607) we assume that these public goods are non-rival and non-excludable. Iterating (17.175) forwards in time yields the following expression:

The Foundation of Modern Macroeconomics

By letting T cc in (17.176) we find that the government NPG condition is:

If there is government debt outstanding at time t (Bt > 0 on the left-hand side of (17.179)), then the solvent government must ultimately run primary surpluses. Note that (17.178) does not require the government to pay off its debt eventually. All that solvency requires is that government debt must not grow faster in the long run than the rate of interest.

The household sector is standard. Households consume during youth and old age (Cl and Ct°+1 , respectively), practise consumption smoothing by saving which can be in the form of physical capital or government bonds. The relevant expressions characterizing the household sector are:

Equations (17.180)-(17.182) are the same as (17.150)-(17.151) and (17.182) is the same as (17.58) but with the size of the (young) population set equal to unity (Lt = 1). The consolidated budget constraint facing households is obtained in the usual manner by combining (17.180) and (17.181):

where Tt,t is the present value of (lump-sum) taxes that a generation born in period t (second subscript) must pay over the course of its life seen from the perspective of period t (first subscript):

T°

Ttt t+1 (17.184)

+

1 + rt+i

We can now develop the generational accounts for existing and future generations by decomposing the government budget constraint (17.179). Because it is very easy indeed to get tangled up in the different subscripts identifying time and generations we show some of the details of the derivation. 18 First we note that by using (17.177)

18 A more direct derivation makes use of the fact that the discount factor in (17.169) satisfies the following property:

'r •

Using this property in (17.179) yields (17.186) in a single step.

I equation (17.179) can be

Bt =( i 1+ rt )[74?

1

1 + rt ) (1 -I

( 1

1 + rt ) (1 -1

-ERt_i,, [G,_ T=0

Next we look for terms p

Bt = ( 1 rt ) Tt°

1

• (1 rt 1

1

+1 + rt

- ERt_i,, [6 : _

T =0

In the first line of (17.1 and the lifetime taxes, expressed in present-vale t - 1. The same holds f( the second and third

is debt at the beginni: t - 1), over which ink.,

Equation (17.186) givi The first line contains whilst lines two and thr( Kotlikoff and co-auth , format as:

00

Bt + ERt_i,, [Gt°_

T=0

(1(17.180)

(17.181)

(17.182)

-.151) and (17.182) is the

idon set equal to unity --holds is obtained in the

(17.183)

;eneration born in period t from the perspective of

(17.184)

and future generations ►. Because it is very easy ring time and generations `e that by using (17.177)

:dor in (17.169) satisfies the

In the first line of (17.186) we find the remaining taxes to be paid by the old at time t and the lifetime taxes, Tt,t, of the young at time t. Both these terms are, however, expressed in present-value terms, i.e. they are discounted back to the end of period t-1. The same holds for all the other terms pertaining to future generations (namely the second and third lines in (17.186)). The reason for this discounting is that Bt is debt at the beginning of period t (which was accumulated at the end of period t — 1), over which interest must be paid at the beginning of period t.

Equation (17.186) gives the generational accounts for the different generations. The first line contains the accounts for the two existing generations at time t, whilst lines two and three contain the generational accounts for future generations.

Kotlikoff and co-authors often write the generational accounts in a more compact format as:

and also present genera ,8 allow for transfers, distoi model.

In Table 17.2 the first males in 1991, e.g. the r row marked '40' gives ti were thus born in 1951►. for the different gener.: respectively, the underl 1J the second column mean value to the government I 1991, the present value of $250,000 whilst the pa. in 1991 has a negative ger transfers (on disability, hi of taxes.

The final row labelled 'F typical future generatk.. sures the present value ( holds for newborns in be meaningfully compa, striking generational imix have a generational acc, newborns in 1991 have u

Discussion

Buiter (1997) agrees with traditional me.. for the effects of fiscal p

but also on the interger. critical of the method (,- following three issues. hi with the validity of thy. model is a simple represL, ically on the followi r _ a finite lives, (ii) generatiL are complete (no borrowi equivalence is valid (see uninformative about the rational distribution of 1992). A similar conclusic

(existing old)

(existing young)

(future generations)

sum of outstanding gov- umption (left-hand side) and future generations

Accounting system in the 71 to an actual empirical 1. 65-75) explain in detail lied to actual economies. rS males. (This table is an p. 80.) Of course, for the

• )n must contain much ble 17.2 therefore distin-

-! gives the accounts for articipation, family struc-

-neteen five-year cohorts

Chapter 17: Intergenerational Economics, II

and also present generational accounts for females.) Furthermore, Auerbach et al. allow for transfers, distorting taxes etc. that were abstracted from in the stylized model.

In Table 17.2 the first column gives the age of the particular generation of US males in 1991, e.g. the row marked '0' pertains to agents born in 1991 whereas the row marked '40' gives the data for agents who were 40 years of age in 1991 (who were thus born in 1951). The second column gives the net generational accounts for the different generations whilst the third and fourth columns distinguishes, respectively, the underlying tax payments and transfer receipts. A positive entry in the second column means that the particular generation will pay more in present value to the government than it will receive. For example, for a 40-year old male in 1991, the present value of taxes to be paid during his remaining lifetime amount to $250,000 whilst the present value of transfers is $69,900. In contrast, a 70-year old in 1991 has a negative generational account of $80,700 because the present value of transfers (on disability, health, and welfare transfers) far exceeds the present value of taxes.

The final row labelled 'Future' in Table 17.2 gives the generational account for the typical future generation. For future generations, the generational account measures the present value of net payments over their entire lives. Since the same holds for newborns in 1991, the figures for newborns and future generations can be meaningfully compared. As Auerbach et al. (1994, p. 82) point out, there is a striking generational imbalance in US fiscal policy in the sense that future newborns have a generational account of $166,500, which is a whopping $87,600 more than newborns in 1991 have to pay.

Discussion

Buiter (1997) agrees with the proponents of the generational accounting method that the traditional measure of the government deficit is a meaningless indicator for the effects of fiscal policy not only on aggregate demand and private saving but also on the intergenerational distribution of resources. He is nevertheless quite critical of the method of generational accounting. Buiter's objections centre on the following three issues. First, the usefulness of generational accounts "lives or dies with the validity of the life-cycle model" (1997, p. 606), of which the Diamond model is a simple representation. The validity of the life-cycle model depends critically on the following assumptions (which must all hold): (i) households have finite lives, (ii) generations are not linked via operative bequests, and (iii) markets are complete (no borrowing constraints). If condition (ii) is violated and Ricardian equivalence is valid (see Chapter 6), then the generational accounts are completely uninformative about the effect of the government budget on both the intergenerational distribution of resources and on saving (see Buiter, 1997, p. 612 and Bohn, 1992). A similar conclusion follows if condition (iii) is violated and households face

647

The Foundation of Modern Macroeconomics

binding liquidity constraints because in that case the timing of tax payments over the life cycle matters (in addition to the present value of these taxes).

Second, even if the strict life-cycle model is valid, generational accounts should be interpreted quite carefully. Indeed, existing applications of the generational accounting method say nothing about the intergenerational distribution of benefits from government spending on public goods. Take, for example, the case of a government abatement programme aimed at cleaning up the natural environment. If the environment improves only slowly over time, future generations may be the principal beneficiaries of the policy measure even though the current generations have paid for it. In generational accounts, the tax payments associated with the programme feature prominently but the benefits to future generations are not included.

Third, the method of generational accounting does not take into account the general equilibrium repercussions of alternative budgetary policies. In particular, the method ignores (i) the endogeneity of the various tax (and subsidy) bases and (ii) the endogeneity of pre-tax factor prices and incomes. Buiter gives several examples for which the general equilibrium effects turn out to be quite important (1997, pp. 616-622). 19

In principle all the issues raised above can be studied with the aid of a computable dynamic general equilibrium model although the construction of such a model is clearly not a trivial task. On the one hand, such models can readily deal with the general equilibrium repercussions of alternative budgetary policies (see Auerbach and Kotlikoff, 1987) and can be extended to include all kinds of market imperfections and alternative intergenerational linkages. On the other hand, there are huge practical difficulties in quantifying the (intergenerational) welfare effects of public spending. In this context, the method of generational accounting is valuable because its data can provide some of the inputs needed for a realistic simulation model.

17.4 Punchlines

In this chapter we study the discrete-time overlapping-generations model that was developed by Diamond and Samuelson. Just as in the Blanchard-Yaari model (studied in the previous chapter), the demographic structure of the population plays a central role in the Diamond-Samuelson model. One of the attractive features of the model is its ability to capture the life-cycle aspects of economic behaviour in an analytically tractable fashion. Because of its flexibility and simplicity, the model has played a central role during the last four decades in such diverse fields as

19 Fehr and Kotlikoff (1995), on the other hand, present a number of general equilibrium examples where the generational accounting method appears to work quite well.

macroeconomics, mon, environmental econon We start this chapt, Samuelson model featur live for two periods, calle both periods of life but t ply one unit of labour. to finance their consumj there is no public debt a This means that savi ng for production in the nc to produce the homog. vided the relevant staL oversaving occurring. In a low rate of time preie accumulate too much ca We next apply the h,, old-age pensions. Two p fully funded system and the government taxes - returns principal plus The fully funded system prices, or welfare. Intu, during youth attract the hold therefore does n behalf by the governrne Matters are different

on the young are usee4 same period. The yield not the market rate of i of population growth. T such a system (or the wage rate, and increase if the economy is dynar (falls short of) the rate (inefficient) economy, c generations born in

Two further aspects be reinterpreted as a pa cient economy it is in . t a fully funded system) i in the standard model I initiative without mai,.

a of tax payments over se taxes).

ational accounts should Dns of the generational al distribution of ben- 'nr example, the case of 1, the natural environ- , future generations may iota rzh the current gener-

. • ments associated with ire generations are not

I

)t take into account the )olicies. In particular, the ibsidy) bases and (ii) the r gives several examples quite important (1997,

I the aid of a computable lAction of such a model is readily deal with the y policies (see Auerbach

Inds of market imperfec- t- er hand, there are huge 1) welfare effects of pub- ii is valuable a realistic simulation

I

:rations model that was chard—Yaari model (stud- f population plays )f the attractive features 5 of economic behaviour lity and simplicity, the 5 in such diverse fields as

' general equilibrium examples

Chapter 17: Intergenerational Economics, II

macroeconomics, monetary theory, public finance, international economics, and environmental economics.

We start this chapter by formulating a simplified version of the Diamond— Samuelson model featuring time-separable preferences. In this model households live for two periods, called "youth" and "old age" respectively. They consume during both periods of life but they work only during youth, when they inelastically supply one unit of labour. Young households save part of their labour income in order to finance their consumption during old age (life-cycle saving). In the basic model there is no public debt and household saving takes the form of capital formation. This means that saving by the young in one period equals the capital stock available for production in the next period. Perfectly competitive firms use capital and labour to produce the homogeneous good. The model has a well-defined steady state provided the relevant stability condition is satisfied. There is a distinct possibility of oversaving occurring. Indeed, if the households are relatively patient, and thus have a low rate of time preference, they may well save too much for retirement and thus accumulate too much capital and render the steady state dynamically inefficient.

We next apply the basic model to study the macroeconomic and welfare effects of old-age pensions. Two prototypical pension systems are distinguished, namely the fully funded system and the pay-as-you-go (PAYG) system. In a fully funded system the government taxes the young, invests the tax receipts in the capital market, and returns principal plus interest to the old in the form of a pension in the next period. The fully funded system is neutral and does not affect consumption, capital, factor prices, or welfare. Intuitively, the household knows that its pension contributions during youth attract the same rate of return as its own private savings. The household therefore does not care that some of its saving is actually carried out on its behalf by the government.

Matters are different under a PAYG system. In such a system the taxes levied on the young are used to finance the pension payments to the old living in the same period. The yield that the household earns on its pension contributions is not the market rate of interest (as in the fully funded system) but rather the rate of population growth. The PAYG system is not neutral. Indeed, the introduction of such a system (or the expansion of an existing one) crowds out capital, lowers the wage rate, and increases the interest rate. Steady-state welfare decreases (increases) if the economy is dynamically efficient (inefficient), i.e. if the interest rate exceeds (falls short of) the rate of population growth. Intuitively, in a dynamically efficient (inefficient) economy, crowding out of capital reduces (increases) the welfare of the generations born in the new steady-state generations.

Two further aspects of the PAYG system are discussed. First, a PAYG system can be reinterpreted as a particular kind of debt policy. Second, in a dynamically efficient economy it is impossible to abolish a pre-existing PAYG system (in favour of a fully funded system) in a Pareto-improving fashion. Intuitively, it is not possible in the standard model to compensate the old generation at the time of the policy initiative without making at least one other (present or future) generation worse

649

The Foundation of Modern Macroeconomics

off. (Pareto-improving reform may be possible, however, if the reform reduces a pre-existing distortion in the economy. We consider the particular example where labour supply is endogenous and the pension contribution is distorting.)

The basic model can also be used to study the macroeconomic effects of population ageing. A useful measure to characterize the economic impact of demography is the dependency ratio, which is defined as the number of retired people divided by the working-age population. A reduction in the growth rate of the population leads to an increase in the dependency ratio. Under a PAYG system an anticipated reduction in fertility reduces expected pensions and lifetime income, and causes households to increase saving. As a result, the long-run capital-labour ratio rises.

In the second half of the chapter we consider a number of extensions and further applications of the Diamond-Samuelson model. In the first extension we introduce human capital into the model and study the implications for economic growth. Young agents are born with the average stock of currently available knowledge and can spend time during youth engaged in training. Provided the training technology is sufficiently productive, the young choose to accumulate human capital. In the aggregate this mechanism provides the engine of growth for the economy.

In the second extension we augment the human capital model by assuming that the parent must choose the level of training of its offspring. If the parent derives utility from the human capital of its offspring then it is quite possible that the parent will not devote the socially optimal amount of time on training its children. Intuitively, the underinvestment result follows from the fact that the parent fails to take into account all welfare effects (on its children and grandchildren) of its training efforts. In such a situation it may well be socially optimal to have a system of mandatory public education.

In the third extension we show how public infrastructure can be introduced into the overlapping generations model. We show how public investment affects the macroeconomy and derive simple modified-golden-rule expressions calling for an equalization of the rate of return on public and private capital and the social planner's rate of time preference. In the final extension we illustrate and evaluate the pros and cons of the method of generational accounting in the context of a simple Diamond-Samuelson model.

Further reading

Classic papers on pensions are Samuelson (1975a, b) and Feldstein (1974, 1976, 1985, 1987). In recent years a large literature has been developed on the issue of pension system reform. See Diamond (1997, 1999), Feldstein (1997, 1998), and Sinn (2000). For a recent survey on the economic effects of ageing, see Bosworth and Burtless (1998).

The Diamond—Samuelson model has been generalized in a number of directions. Barro (1974) studies intergenerational linkages. Jones and Manuelli (1992) consider the growth

effects of finite lives. Tirol of asset bubbles. Gra' • cycles. Michel and de la I foresight and perfect fore of age-specific taxes rent: introduce uncertainty in Varian (1988). Barro and 13& cations of endogenous ft Srinivasan (1997), and two-sector version of the 0

The Diamond—Sam uelso lic finance applications, (1996). On the economics Zhang (1996), Buiter and K1 policy applications include John and Pecchenino (1

There is a large literature Gokhale, and Kotlikoff (19 For critical papers on th International applications (1999).

if the reform reduces a particular example where

is distorting.)

onomic effects of popula- - impact of demography of retired people divided th rate of the population i system an anticipated time income, and causes f ri 1-labour ratio rises.

r extensions and further st extension we introduce

• for economic growth. available knowledge and d the training technology _ human capital. In the

crIr the economy.

model by assuming that ing. If the parent derives is quite possible that the e on training its children. fact that the parent fails

wind grandchildren) of its optimal to have a system

re can be introduced into c investment affects the pressions calling for an

►rvital and the social planstrate and evaluate the in the context of a simple

irlstein (1974, 1976, 1985, issue of pension system Sinn (2000). For a recent

'Mess (1998).

:rnber of directions. Barro

2)consider the growth

Chapter 17: Intergenerational Economics, II

effects of finite lives. Tirole (1985) and O'Connell and Zeldes (1988) consider the possibility of asset bubbles. Grandmont (1985) presents a model exhibiting endogenous business cycles. Michel and de la Croix (2000) study the model properties under both myopic foresight and perfect foresight. Bierwag, Grove, and Khang (1969) show that a full set of age-specific taxes renders debt policy redundant. Abel (1986) and Zilcha (1990, 1991) introduce uncertainty into the model. On intergenerational risk sharing, see Gordon and Varian (1988). Barro and Becker (1989) present a model of endogenous fertility. For applications of endogenous fertility models, see Wildasin (1990), Zhang (1995), Robinson and Srinivasan (1997), and Nerlove and Raut (1997). Galor (1992) and Nourry (2001) study a two-sector version of the Diamond-Samuelson model.

The Diamond-Samuelson model has been applied in a large number of fields. For public finance applications, see Auerbach (1979a), Kotlikoff and Summers (1979), and Ihori (1996). On the economics of education, see Loury (1981), Glomm and Ravikumar (1992), Zhang (1996), Buiter and Kletzer (1993), and Kaganovich and Zilcha (1999). Environmental policy applications include Howarth (1991, 1998), Howarth and Norgaard (1990, 1992), John and Pecchenino (1994), John et al. (1995), and Mourmouras (1993).

There is a large literature on generational accounting. Some key references are Auerbach, Gokhale, and Kotlikoff (1991, 1994), Kotlikoff (1993a, b), and Fehr and Kotlikoff (1995). For critical papers on the topic, see Bohn (1992), Haveman (1994), and Buiter (1997). International applications of the method are collected in Auerbach, Kotlikoff, and Leibfritz (1999).

651

Epilogue

Changes

The field of macroeconomics has certainly changed a lot over the past twenty five years. When we took our first courses in macroeconomics in the mid-1970s, the leading textbooks were Branson (1972) at the intermediate level and Turnovsky (1977) at the graduate end of the spectrum. Both of these books contain extensive treatments of the IS-LM model and all its variations and extensions. In contrast, at the beginning of the new millennium, though the IS-LM model is still treated in most intermediate texts, it has vanished almost completely from the advanced texts. 1

A comparison between the past and the present thus reveals that the once dominant IS—LM model, with its emphasis on the demand side of the economy, has fallen on hard times in recent years. There is no doubt that the rational expectations revolution of the 1970s has a lot to do with the reduced role of the IS-LM model. In part as a result of this revolution, macroeconomists started to develop dynamic models which are based on explicit microeconomic foundations and give more attention to the supply side of the economy. Modern graduate textbooks therefore contain extensive discussions of dynamically optimizing representative agents (households, firms, the government) endowed with perfect foresight (or rational expectations). 2

To outsiders it may appear that macroeconomics is a field in disarray, with proponents of two competing approaches battling it out to achieve the position once held by the IS-LM model. According to this view, current macroeconomics is somewhat like a boxing match. In the blue corner of the boxing ring, we find the "new classicals" who stress flexible prices and wages and emphasize market clearing. In the red corner we find the "new Keynesians" who like to work with models incorporating sticky prices and wages and are willing to assume various degrees of market imperfection.

I Most intermediate texts still make use of the IS-LM model. See e.g. Mankiw (2000a) and Blanchard (2000a). Most graduate texts barely mention the IS-LM model. See Romer (2001), Turnovsky (1997, 2000), and Ljungqvist and Sargent (2000).

2 Intermediate texts incorporating the optimization approach are Barro (1997) and Auerbach and Kotlikoff (1998).

Even though this pictt similarity with the reairl, Goodfriend and King (15 a new synthesis over t identify the key aspects (

•The NNS takes from should be explicitly ( intertemporal opt'

•The NNS takes from tition and costly pr..

•The NNS takes fro: of economic fluctu-

Just like the old neocAa ments from new classical it appears as if the cur.. characterized as a tango. debate about the usefulno larly, economists of all optimizing behaviour of macroeconomics as a t..

In his comment on GI macroeconomists need 1 namely intertemporal op He argues that putting to tion constitutes the core that what distinguishes I the different ingredients

Blanchard suggests tha interaction) is by means place the approach of I': behaviour. In the bottoi (1977) and Taylor (198( in the bottom right corn Akerlof and Yellen (198! markets.

Blanchard argues that r he finds it an overstatt.

3 Blanchard (1997, p. 290► about: "In rather schizophrei,., of consumption and investmei and nominal rigidities used as improve on the shortcomings.