RDP 2006-07: Household Saving and Asset Valuations in Selected Industrialised Countries 2. Household Saving in Standard Theoretical Models

The determinants of household saving are complex and are likely to vary both through time and across countries. The theoretical literature identifies several motives for saving, and four, in particular, dominate (see Browning and Lusardi 1996 and Callen and Thimann 1997):

1. life-cycle saving to provide resources for retirement;
2. consumption smoothing in the face of (relatively temporary and unexpected) fluctuations in income;
3. precautionary (buffer-stock) saving to finance unexpected losses in income; and
4. liquidity constraints, which are relevant in the case of large lifetime expenditures (including house purchases, education, etc).

In developing a theoretical framework to help tie these concepts together and underpin the econometric analysis of the determinants of saving, a useful starting point is to consider models of the Life Cycle/Permanent Income Hypothesis (LC/PIH) of consumption. These link consumption and saving to income and wealth according to motives 1 and 2 above.^[5] In the standard LC/PIH model, outlined in Blanchard and Fisher (1989) and consistent with the presentation of Dvornak and Kohler (2003), a representative consumer chooses consumption in each period so as to maximise expected lifetime utility:

subject to a series of period-flow budget constraints:

where C_t represents consumption at time t, Y_t income, A_t non-human wealth holdings, r_t the interest rate and β the discount rate.

On the basis of this simple framework, it follows that the optimal consumption path implied by the first-order condition of the above problem will look something like:^[6]

That is, consumption is a function of current assets (non-human wealth) and permanent (or lifetime) income, which is the sum of current and discounted expected future labour income (human wealth). In what follows, savings are defined according to the concept relevant to the national accounts, namely, the difference between income and consumption. The more persistent is an unexpected change in income, the larger will be the effect on consumption (and the smaller will be the effect on saving). The opposite is true for more temporary changes in income.

In order to make the problem tractable for the purposes of empirical analysis, current income can be assumed to follow a stochastic AR(1) process, thereby allowing consumption to be expressed as a function of current assets and current income. Furthermore, wealth can be split into two broad sub-components: financial (W^fin) and non-financial (W^{non fin}), which can be thought of as largely consisting of housing wealth. This yields the following expression for consumption on the basis of Equation (1) above:

Given that real saving is equal to real (disposable) income less real consumption, a corresponding expression for saving (S_t) is therefore:

In the above expression, (1 − ϕ₁) represents the marginal propensity to save out of current disposable income while the ϕ₂ and ϕ₃ coefficients reflect the marginal propensity to offset saving due to valuation gains in wealth (that serve to reduce the need to save out of current income). This is consistent with the notion in the literature that capital gains would be expected to have a negative effect on saving (see Ludwig and Sløk 2004).^[7]

A split between financial and non-financial wealth may be warranted for a number of reasons. First, under the behavioural life-cycle hypothesis, households may earmark certain assets for current expenditure while others are reserved for long-term savings.^[8] Second, and related to the first point, the effect on consumption and saving depends on whether the shocks to wealth are perceived to be transitory or permanent, and this may differ across asset classes. Third, as housing is both a household asset and a consumption item, the wealth effect from this channel is debatable. On the one hand, while an increase in the price of housing benefits existing homeowners, it is accompanied by an offsetting increase in the implicit rental cost of housing and therefore simply represents a transfer of wealth within the household sector between current homeowners and renters or future homeowners. On the other hand, housing can also be used as collateral for borrowing for liquidity-constrained households and thus may help to explain the common finding of a positive effect of rising housing wealth on consumption – see Debelle (2004).

While the above specification gives a basic set of determinants of household saving, other factors may also exert an influence. In particular, liquidity constraints may influence saving decisions, leading some households to build up precautionary savings and others to limit consumption according to current, rather than permanent, income. In practice, households may face limits on their ability to borrow against future income. For instance, marketable assets are normally required as collateral to borrow large amounts of money, credit limits commonly apply, and interest rates tend to be higher on unsecured loans. Hence, developments that lead to a relaxation of credit constraints can have a persistent (though transitory) impact on aggregate savings. In particular, a relaxation of borrowing constraints will tend to reduce aggregate savings, with the reduction building through time as an increasing proportion of the population takes on higher debt levels. This occurs as new generations come of age and take on debt (to a greater extent than previous generations at the same stage of life) while older generations, with some degree of savings and limited future labour income available to service debt, have little or no incentive to respond to an easing in credit constraints. On this basis, a term capturing the effects of financial innovation is warranted in empirical analysis of the determinants of household saving.

The direction of the impact on savings of reduction of liquidity constraints, and financial innovation more generally, is somewhat ambiguous. While financial deregulation over the past decades has made it generally easier for households to borrow through time,^[9] financial system developments may have also provided opportunities for, and returns to, financial saving (Callen and Thimann 1997, Boone, Girouard and Wanner 2001 and de Mello et al 2004).

There are several other broad factors which may affect aggregate household saving but are excluded from the empirical analysis. First are measures of demographic change. Rising old-age dependency ratios might be expected to have reduced saving through life-cycle effects. The Congressional Budget Office (2003) also notes the trend in recent times to postpone parenthood to later years, which increases child-rearing expenses in peak earning years when saving would otherwise be high. These dampening influences on saving are likely to be important, but in practice, including them is not straightforward. For example, it is not clear whether contemporaneous values of dependency are more relevant than forecasts of the dependency ratio. Also, when aggregating household-level saving, the influence of demographics on saving may cease to hold given interactions between the generations. In particular, bequests to younger cohorts may reduce aggregate saving even though older cohorts may not dissave, as indicated in de Mello et al (2004).

A second variable excluded from the empirical specification is the interest rate. Interest rates are usually of weak explanatory power and have an ambiguous impact on saving depending largely on the extent of credit constraints and on the relative magnitude of income and substitution effects – see Callen and Thimann (1997) and de Mello et al (2004). Interest rates have an indirect effect on saving through income and wealth effects. Interest rates could also be considered as capturing changes in the discount rate or general beliefs about future economic developments, as found by Parker (1999).^[10] Changes to nominal interest rates also capture shifts in inflation over time. A reduction in steady-state inflation would be expected to reduce saving to the extent that it represents a reduction in ‘macroeconomic volatility’ and therefore a motive for high precautionary saving (Loayza et al 2000).^[11]

A third variable excluded from the empirical specification involves institutional and tax factors. Such factors are likely to have an important impact on saving decisions, though these are difficult to capture quantitatively. Differences in tax and transfer system design across countries and through time within countries are likely to be important in explaining different saving behaviour of private households (see, for instance, Callen and Thimann 1997). In this sense, the use of unobserved fixed effects in panel regressions may be warranted to capture such effects insofar as they are invariant with respect to time and/or cross-sections.

Footnotes

Motives 3 and 4 above are not dealt with in the standard LC/PIH model, but are relevant to the discussion of credit constraints below. [5]

This requires a number of assumptions such as a constant interest rate equal to the rate of time preference (1−β) and a well-behaved utility function (see Dvornak and Kohler 2003). [6]

Wealth effects could be expected through realised capital gains (such as equity withdrawal for housing or dividend payments) that enhance households' ability to spend. These effects, however, may be complemented or even eclipsed by the influence of unrealised capital gains. Such effects – working, for example, through retirement savings accounts – may capture the potentially strong influence of expectations regarding the future evolution of wealth, and hence influence the consumption and saving behaviour of households. [7]

On top of ‘mental accounting’, differences in liquidity between asset types and varying bequest motives would also point in favour of separating the consumption/saving effects of financial and non-financial wealth – see Altissimo et al (2005). [8]

A list of significant financial innovations over the past decades can be found in Kohn (2005), where he notes the ability of new technologies in financial markets to reduce transactions costs, to allow the creation of new instruments that enable risk and return to be divided and priced to better meet the needs of borrowers and lenders, to permit previously illiquid obligations to be securitized and traded, and to make obsolete previous divisions among types of financial intermediaries and across the geographical regions in which they operate. [9]

The presence of hyperbolic discounting could lead to variation in consumers' rates of time preference over time and to dynamically inconsistent spending behaviour. This possibility could help to explain how low-income households can, on the basis of optimal decision-making, end up in a saving trap with little or no wealth accumulation – see Dynan, Skinner and Zeldes (2004) for a discussion. [10]

One further possible reason for a positive relationship is based on a statistical distortion that high consumer price inflation induces in the measure of the personal saving rate – see Connolly and Kohler (2004) and Shiller (2004). There is an upward bias in measured household saving during times of high inflation, such as the 1970s and 1980s, when creditors' real return on interest-bearing assets, which have a fixed nominal principal, is significantly lower than nominal interest rates would suggest (and households tend to be net holders of these assets). [11]