Households

According to the scheduling of decisions, explained in the last section, it becomes apparent that household agents make their decisions after firms. Nevertheless, the decisions of household agents are central to the model and rather complex. Therefore, we start with analyzing the household sector. During the simulation, private household agents face two decisions: (i) The decision of di- viding present disposable income (or better receipts) into consumption expenditures and financial savings. (ii) Furthermore, they choose to allocate the consumption expenditures to several goods. Consequently, an agent can choose how much income he would like to save in one risk–less financial asset and how much income (or wealth) he should spend to buy consumption goods. We should bear in mind that individual savings behavior should be linked to interest rate movements. This is one implication of the macro bindings of Agent Island (see section 1.3), as it is our aim to imple- ment monetary transmission channels into the model. This implies a reaction of individual savings behavior to the interest rate policy of the central bank.

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In fact, the monetary transmission process in the model works faster: Changes of the credit interest rate influence decisions of consumer goods firms in the same period. Hence, monetary transmission is already effective within one year. See section 3.4.3 for a discussion of this topic.

The examination of the first decision, the decision of saving, is one of the most complex tasks one can undertake in economic theory. This is also true in the context of designing an agent–based model. In constructing such a model one should follow the aim of designing valid agents, by taking into consideration the complexity of the whole simulation. The latter is one restriction. In order to reveal the complex process of designing the savings decision, we first give a brief review of the various perspectives that have been developed during the ‘history of economic thought’. In a next step, we connect these findings to our model, in which we have the results of ‘face validation’ in mind. In doing so, we find out that some special restrictions have to be incorporated into the model. Throughout this subsection we illustrate the theories we adopt, and we explain why we rule others out. This can be also helpful in further research on this topic.

Brief Review of the Theory of Savings in the History of Economic Thought

The first theoretical analysis of the savings decision takes place at the end of the nineteenth and the beginning of the twentieth century, by the advocates of ‘neoclassical’ theory. They built their perception of savings on the notion of ‘intertemporal substitution’ and the process of balancing

marginal utility over time.16 _{According to this view, the straightforward interpretation of savings is}

the postponing of today’s consumption into the future. This is called ‘intertemporal substitution’. Moreover, it is assumed that present consumption is evaluated in a superior manner when compared to future consumption. This point is captured by the time preference rate ρ > 0. Discounting

further consumption by (1 + ρ)T _{yields the results that a certain amount of one consumption good}

tomorrow delivers less utility than the same amount today. In order to fulfill ‘intertemporal substi- tution’, a household seeks for a fee, i.e. he asks for an ‘intertemporal price’ as a compensation for the postponing of consumption somewhat into the future: A higher interest rate induces cheaper future consumption relative to present consumption. In this respect a change in the interest rate activates the ‘intertemporal substitution effect’. Then again, a higher interest rates induces higher future income, if the agent is a net creditor. This indicates that the agent needs less savings in order to fulfill a given future consumption, which is called the ‘intertemporal income effect’. In case of a creditor, both effects (the substitution and the income effect) aim in opposite directions,

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insofar it is theoretical a priori ambiguous whether a higher real interest rate causes increasing or decreasing savings. Additionally, if the agent is a net debtor, substitution and income effect aim in the same direction. In addition to the substitution and income effects, rates of return also effect savings through a ‘wealth effect’: A higher real interest rate reduces the present value of future income streams. Hence, consumption is depressed even if the substitution and income effects cancel each other out (Schmidt-Hebbel et al., 1992). This short review describes the underlying interest– rate–mechanism identified by neoclassic economics. We will refer to this point below.

In the 1930s the emerging ‘Keynesian’ theory replaced the ‘neoclassical’ view of savings and their utility oriented perspective. In his macroeconomic theory Keynes, 1936, replaced the microe- conomic view by a more heuristic approach, which is described as the ‘absolute income hypothesis’. His theory centered on the marginal propensity to consume: Households employ a marginal rate of consumption to their disposable income. With the help of his theory building, it is possible to derive a residual savings function. Several followers of Keynes developed this behavioral theory of consumption further in various directions: According to Duesenberry, 1967, the savings and con- sumption behavior is interdependent within households. This idea of a ‘relative income hypothesis’ is related to the ‘habit persistence hypothesis’. Under ‘habit persistence’, the level of consumption (and savings) is determined by lagged consumption (Brown, 1952). Intuitively the habit persistence theory says, the more the consumer eats today, the more hungry he wakes up tomorrow. We will apply the basic ‘Keynesian’ consumption function, the ‘habit persistence’ approach as well the ‘rela- tive income hypothesis’. Especially the last two theories mark an important detail in our framework as worked out in the process of ‘face validation’: They guarantee smooth consumption profiles over time, which are necessary to match the empirical data. At the end of the day, these ‘Keynesian’ approaches differ from older and from newer theories of consumption, as they build on ‘psychological factors’ rather than on an optimal ‘intertemporal choice’.

The ‘Keynesian’ approach is exposed to criticism of the so–called ‘Lucas Critique’, which is the initial point of ‘modern’ macroeconomics that builds on explicit ‘microfoundation’. The ‘Lucas Cri- tique’ says that it seems to be naive to predict the effect of a policy experiment based purely on

correlations in historical data. Especially, predictions through high–level aggregated historical data seem doubtful (Lucas, 1976). The Lucas Critique implies that if we want to predict the effect of a policy experiment, we must model the ‘deep parameters’, i.e. preferences, technology and resource constraints, which govern individual behavior. Then it is, in turn, possible to predict what individ- uals will do, conditionally on the change in policy, and add up individual behaviors to calculate the macroeconomic outcome. Surely, an agent–based model builds on individual behavior and macroe- conomic emergence from the micro structure. Consequently, the core of the ‘Lucas Critique’ does not apply to our model of Agent Island, because we do not specify the parameters of any aggregate rela- tionship, such as an aggregate consumption function. However, individual behavior on Agent Island is designed through routines, which usually represent rules–of–thumb; these rules reflect individual preferences differently compared to ‘orthodox’ economics. So far it is for example not absolutely clear, as to how human savings behavior and maybe the underlying preferences change in reaction to the environment. What we know from empirical investigations is that savings behavior depends on several determinants—but we cannot identify the preferences of agents. As we will see, our model characterizes an interactive savings behavior based upon the behavioral approach of ‘Keynesian’ economics. Hence, we do not model the ‘deep parameters’ of private household agents, as orthodox economics does. We simply do not know them.

In response to these ‘Keynesian’ approaches, a renaissance of the ‘neoclassical’ perspective emerged in the fifties. These authors, rooted in neoclassical tradition, pick up the seminal idea of Fisher, 1930, and build their theory on the basis of the maximization of ‘intertemporal utility’: The ‘permanent income hypothesis’ of Friedman and the ‘life–cycle hypothesis’ of Modigliani and Brumberg (Friedman, 1957; Modigliani and Brumberg, 1955) comprise the view that rational agents smooth consumption over time. The basic version of Friedman’s ‘permanent income hypothesis’ sets consumption equal to the annuity value of the sum of assets and the discounted present value of expected future work income (Flavin, 1981). Such a result can be derived from the maximization un- der uncertainty of a quadratic intertemporally additive utility function under the assumptions that the real interest rate and the time preference rate are constant and equal to one another (Deaton, 1992). If the horizon is assumed to be infinite, Flavin’s version of the ‘permanent income hypothesis’

takes the form cT = r 1 + r(AT + ∞ X k=0 E_{TyT +k} (1 + r)k),

where r is the real interest rate, cT is the real consumption in period T , yT +k is the real work

income in year T + k, whose expectation conditional on information available at time T is ETyT +k,

and AT is the real value of the single asset whose return is defined as r (Flavin, 1981). For current

purposes the equation can be rewritten in order to obtain a savings function: Savings are defined as the difference between disposable income and consumption. We assume that disposable income is the sum of earnings and asset income. By putting the pieces together one obtains the following function of savings in period T (for its derivation see Campbell and Deaton, 1989):

sT = − ∞ X 1 E_T ∆yT +k (1 + r)k. (2.2.1)

It should be noted that both equations, defining cT as well as sT, are precisely equivalent.

Usually this savings function is labeled as ‘saving for a rainy day’ or the ‘rainy day’ equation. This characterization marks the notion that savings equal the discounted present value of expected future falls in income. According to this, individuals are saving today for bad (or ‘rainy’) times in the future. Thereby, equation (2.2.1) is derived from the assumption underlying the ‘permanent income hypothesis’, i.e. that optimal consumption is flat over time. The important insights of this analysis are (i) that likewise flat earnings imply no need to save, and (ii), if earnings are growing, households should dissave in order to enhance their current consumptions to the optimal flat levels. Thus, equation (2.2.1) indicates that the ‘permanent income hypothesis’ is strongly questionable in growing economies, where one can identify a positive relationship between income growth and

savings (Deaton, 1997).17 _{In fact, this ‘positive’ relationship grounds on an insight of the empirical}

findings in the literature on savings behavior.18 _{Campbell and Deaton summarize these points as}

17

The hypothesis that consumption responds to predictable income movements is referred to as ‘excess sensitivity’ of consumption. According to the view of the ‘permanent income hypothesis’, consumption should respond to the changes in permanent income signaled by innovations in the current income. If, in addition, consumption responds to current income beyond that attributable to the role of current income signaling changes in permanent income, this is termed ‘excess sensitivity’ of consumption to current income. Thus, the ‘permanent income hypothesis’ suggests an ‘excess sensitivity’ of zero. According to Flavin, there is substantial evidence against the ‘permanent income hypothesis’ in terms of this ‘excess sensitivity’ analysis (Flavin, 1981).

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follows:

“We believe that the answer to the question with which we began, ‘Why is consumption so smooth?’ lies not in the truth of permanent income hypothesis, but rather in its inadequacy. Whatever it is that causes changes in consumption to be correlated with lagged changes in income, whether it is that measured consumption and income are time averages of continuous processes, or that real interest rates vary, or that the marginal utility of consumption depends on other variables besides consumption, or that some consumers are liquidity constrained or that consumers adjust slowly through inertia or habit formation, the same failure of the model is responsible for the smoothness of consumption relative to permanent income.” (Campbell and Deaton, 1989, p. 372)

To sum up these findings concerning the ‘permanent income hypothesis’, we find that it does not feature in a prominent role in our framework, because we want smooth consumption behav- ior within a framework of growing income patterns. Moreover, the savings behavior rooted in the ‘permanent income hypothesis’ implies complex calculations as well as far–forward looking and ‘ra-

tional expectations’19_{, which in turn mark its foundation as unsuitable for our agent–based model.}

Note that agents face ‘true uncertainty’, so that it is clearly impossible to calculate at any date

T the ‘rational expectations’ outcomes for dates T + 1 to ¯T in an agent–based environment. In

general, it would be pretty difficult to form reasonable expectations for income growth, inflation and nominal interest until the termination of the simulation. Hence, we evaluate the ‘permanent income hypothesis’ as an suboptimal candidate for the design of individual savings behavior on Agent Island.

At the end of the day, our model touches the ‘permanent income hypothesis’ at one point, where the role of ‘windfall profits’ are easy to determine. According to the permanent income hypothe- sis ‘windfall profits’ do not enhance present consumption. Within all income sources the interest income class exhibits clear properties of ‘windfall profits’: If the present nominal interest rate is

19

Not all applications of the ‘permanent income hypothesis’ build on ‘rational expectations’ and on far–forward locking behavior. In fact, Milton Friedman himself initially states: “The permanent income component is not to be regarded as expected lifetime earnings. [...] It is to be interpreted as the mean income at any age regarded as permanent by the consumer unit in question, which in turn depends on its horizon and foresightedness” (Friedman, 1957, p. 93). But all modern interpretations of the theory build on ‘rational expectations’ and on far–forward locking behavior. It could be the task for further work in agent–based research to design and incorporate a reasonable ‘myopic permanent income hypothesis’.

relatively large to its mean, agents receive relatively large incomes from financial assets. But this can be expected to be short–lived. Then again, in this class it is an easy task to define a proxy for ‘permanent interest income’, namely the historical average real interest rate applied to the present stock of financial wealth; the difference between this ‘proxy permanent interest income’ and the ‘present interest income’ is treated as ‘windfall interest income’, which does not influence present consumption. This perspective mirrors the idea of the ‘permanent income hypothesis’. In contrast, it would be much more complex to find that part of labor income, which is due to ‘windfall profits’. If the human capital of an agent had to be determined, it would be an easy task to calculate an ap- proximation of ‘permanent labor income’, and via that the ‘windfall labor income’. But the difficult task would be to find a plausible proxy for the human capital, i.e. the present value of all future

labor income streams.20 _{This is again due to the fact that agents are exposed to ‘true uncertainty’}

when evaluating the future path of their income growth.

Finally, in the process of ‘face validation’ it became obvious that there was some contradiction in the model: In an early version of Agent Island, private household agents calculate their savings and consumption based upon present interest income rather than permanent interest income. In this case, inflation is rising up to hyperinflation, in situations of high nominal and real interest rates. By contrast, evidence from central banking practices as well as from monetary theory suggests that rising interest rates, nominal and especially real interest rates imply downside pressure on inflation.

Knut Wicksell’s monetary theory gives a clear notion of the reasoning behind this mechanism.21

Apparently, the contradictory phenomenon of our early design is a result of the fact that rising nominal interest rates induce rising present interest incomes, which in turn induce strong nominal consumption growth (based upon present interest incomes) and thus inflation. This induces again rising interest rates, and so on. From this perspective it is imperative to cancel out that effect by employing ‘proxy permanent interest income’ instead of actual interest income. In this case impli- cations of short–term movements of the nominal interest rate are cancel out.

Similar to the ‘permanent income hypothesis’ the ‘life–cycle hypothesis’ is not a good candidate

20

Note that interest rates do not feature a long term trend, while labor income patters can do.

21

for the design of a savings behavior within the simulation. Both hypotheses imply complex calcula- tions and far–forward looking and ‘rational expectations’. Again, it would be too complex for our framework to form expectations for income growth as well as life–cycle income patterns, inflation and nominal interest rates. Besides this, on condition that ever–working and infinitive living agents are assumed, the retirement of households is ruled out. In this case, the underlying perspective of the ‘life–cycle hypothesis’, i.e. the existence of hump–shaped income profiles, is not given. In sum, we did not treat the integration of a ‘life–cycle perspective’, because we identify already many difficulties in the chosen—much simpler—approach. The ‘life–cycle hypothesis’ would therefore overload the complexity of the model additionally. Moreover, the empirical evidence of the ‘life–cycle hypothesis’ (such as that of the ‘permanent income hypothesis’) is questionable: For example, the interest- ing study of Carroll and Summers investigates both hypotheses intensively with cross–country and cross–sectional data. According to this study, both hypotheses have to be rejected. They come to the results that “there is clear evidence that consumption and income growth are much more closely linked than those theories predict” (Carroll and Summers, 1991, p. 305). However, both theories would be good candidates for the savings design in our model with respect to incorporation of the real interest rate. But we do not integrate them according to the reasoning stated above.

By far, the most active area of research (within the field of ‘orthodox’ economics) in recent years has been the move away from ‘life–cycle models’ towards a ‘richer’ class of models, still within the general framework of ‘intertemporal choice’ under uncertainty. In ‘discrete time’, op- timization follows the maximization of an expected utility function in the form of e.g. EU =

E₀P∞

T =01/(1 + ρ)Tu(C(T )) with u(C(T )) = C(T )1−θ/(1 − θ) (Romer, 1996). Thereby θ is the

coefficient of ‘constant relative–risk–aversion’ (the inverse of the ‘elasticity of substitution’ between consumption at different dates); it determines the households willingness to shift consumption be- tween periods. That is, the smaller θ is, the more willing the private household is to allow its consumption to vary over time. In addition, savings are decreasing in the real interest rate if θ is larger than 1, and increasing in if θ is below 1. In the first case, if θ is large, the individual has a strong preference for similar levels of consumption in the different periods and the ‘income effect’ dominates. In the second case, with θ less than 1, the ‘substitution effect’ of a rise in the real interest

rate dominates the ‘income effect’ (Romer, 1996).

Turning back to the ‘expected utility function’: The maximization is subject to an intertemporal budget constraint, which leads to the well–known ‘Euler equation’ as the optimality condition. This