1. Dependence of savings rates on growth and demography: an illustration

Even if successive cohorts of the population have identical tastes and preferences, and the young save only to dissave when they are old, growth and demographic composition can affect the aggregate savings rate by making the young savers more affluent and more numerous than the older dissavers. It is fairly straightforward to construct models in the life-cycle-overlapping-generations framework to illustrate this dependence of the savings rate on growth and demography. We shall adapt Diamond (1965) to do so.

Consider a perfectly certain world with only one commodity and overlapping generations of agents who live for two periods--working during the first and in retirement during the second--with Cobb-Douglas production and utility functions, and no bequest motive. Population grows at the rate of n per period and labor-augmenting technology progresses at θ per period.

Let c denote consumption, a asset holding, w labor income, and r the rate of interest, and let superscripts y and o specialize variables to the young and the elderly. We assume that a young agent at time t maximizes the following utility function:

subject to the two period constraints

Production is characterized by constant returns to scale:

where Y is output, K is capital, ${\text{N}}_{\text{t}}^{\text{Y}}$ the number of working people, A a given scale parameter, θ the rate of technical progress, and α is the marginal product of capital.

Notice that the elderly dissave and consume the entire stock of current capital at the end of the period. Next period’s production is carried out by capital financed entirely by the savings of this period’s young workers. Maximizing (1) subject to (2), it is easy to derive an individual young worker’s asset holdings $\left({\text{a}}_{\text{t}}^{\text{y}}\right)$ as (1-β) w_t and

implying

Assuming a competitive framework, labor’s share in total income is (1–α) in every period and from (5), in terms of the savings rate, we get the following savings function:

which shows that the savings rate in this economy depends solely on productivity (1–α), time preference (β), and growth $\left(\frac{\mathrm{\Delta }{\text{Y}}_{\text{t}}}{{\text{Y}}_{\text{t}}}\right)$.

In the steady state, growth in income $\left(\frac{\mathrm{\Delta }{\text{Y}}_{\text{t}}}{{\text{Y}}_{\text{t}}}\right)$ will equal $\mathrm{1}\mathrm{-}\frac{\mathrm{1}}{\mathrm{(}\mathrm{1}\mathrm{+}\mathrm{\theta }\mathrm{)}\mathrm{(}\mathrm{1}\mathrm{+}\mathrm{\text{n}}\mathrm{)}}$ and the savings rate (1-α)(1-β) times the steady-state growth rate. The equilibrium savings rate, thus, depends on productivity, time preference, technical progress (θ), and population growth (n). Despite the constancy of the average propensity to save (APS) of the individual, productivity growth and technical progress increase the aggregate savings rate by making the young savers more affluent than the young savers of last period who constitute the older dissavers of today. The age-dependency ratio, defined as the ratio of old to young, is $\frac{1}{(1+\text{n})}$. An increase in population growth decreases the ratio, increases the number of savers relative to dissavers, and increases the APS in the economy.

2. Empirical specification

The relationship between growth and the savings rate, as given in (6), does not explicitly bring out the dependence of the savings rate on the age structure of the population. For this, we need to derive the dynamic behavior of the simple Diamond-economy starting from an arbitrary initial configuration.

Note that in the simple illustrative economy described above, any arbitrary initial level of capital automatically determines the level of output by the condition of full employment. Given the level of output, the preference relation determines the level of savings and, hence, the capital stock for the next period. Thus, the entire future path of output in this economy can be traced out for any given initial configuration. Let

denote the output per worker in efficiency units at time t and in the steady state, respectively. A bit of algebra applied to this simple model leads to:

as a complete description of the growth path of the economy from any arbitrary initial value of z₀ for output per worker in efficiency units.

Using (9) in (6), after some manipulation we get

Approximating log(1–x) by –x, we have

which upon substitution of $\left(\frac{\text{S}}{\text{Y}}\right)\mathrm{by}-\log (1-\frac{\text{S}}{\text{Y}})=-\log \left(\frac{\text{C}}{\text{Y}}\right)$ leads to

Since C and Y always come together in the form of a ratio, it is possible to transform them to per capita terms and rewrite (12) as

where c and y are the natural logarithms of per capita real consumption and income ^1/ and

Though there is a direct one-to-one relationship between the rate of growth of population and the age-dependency ratio in our simple illustrative economy, in reality the latter also depends on a host of other demographic factors such as age-specific mortality rates and life expectancies. ^2/ Allowing for an adjustment period of two years, we replace the last term in equation (13), that is, β₄n, by β₄PR + β₅ΔPR -- a linear combination of the percentage of population between the ages of 15 and 64 (PR) and the change in the percentage (ΔPR). Furthermore, to test for the effect of changes in the terms of trade, of inflation and of the degree of export orientation, we add to equation (13) variables for the change in the terms of trade (ΔT), the rate of inflation (π), and the ratio of exports to GNP (x). For estimation purposes a random disturbance term, ε, is also included to obtain:

as an empirical specification of private consumption behavior. Note that it is very similar to the form proposed by Blinder and Deaton (1985).

There has been extensive discussion in the literature on the precise functional form and dynamic structure of consumption functions such as that specified in equation (14). Two general types of models stand out: the rational expectations-permanent income hypothesis by Hall (1978) and Flavin (1981), among others, and the error-correction model by Davidson et al. (1978). According to the rational expectations-permanent income framework of Hall (1978), foreseen changes in income should not affect private savings or consumption since these changes are already embodied in past savings decisions made in an intertemporal framework. In this formulation, growth should not affect savings so long as it is anticipated. Alternatively, however, it is often argued that, particularly in developing countries, because of liquidity constraints even anticipated growth may induce changes in savings behavior. For example, even if a consumer knows with certainty that his income is going to double next year, he may not be able to increase his current consumption adequately if he cannot obtain the credit to do so.

Let superscripts a and u distinguish between anticipated and unanticipated categories and let us rewrite (14) as

In the context of (15), it is easy to see that according to Hall’s (1978) hypothesis β₁=β₂=β₃=0. Furthermore, in the rational expectations-permanent income framework, there is the assumption of an “immortal” household through the operation of a bequest motive. As Rossi (1988) has shown, in this framework variations in per capita real consumption may be related to variations in demographic composition through “cost of children” or overhead costs, but it is independent of the level of the age-composition variable, that is, β₄=0, ${\mathrm{\beta }}_{\mathrm{5}}\mathrm{\gtrless }\mathrm{0}$. Thus, a test of rational expectations-permanent income hypothesis in the context of our model is obtained by testing the hypothesis:

Following Blinder and Deaton (1985), we shall call this the “surprise only” hypothesis.

Thus, there is a clear need to verify whether anticipated changes in income did matter in the determination of Asian savings rates in the light of Hall’s hypothesis and liquidity constraints. Moreover, if they did then we need to find out whether they affected the savings rate in the same way as unanticipated income, that is, to test the hypothesis:

An explanation of savings rates in terms of measured income is valid if and only if anticipated and unanticipated income affect savings in the same way.

Let us suppose that H₂ is not rejected and that the analysis of savings can be legitimately carried out in terms of measured income. Presumably the adjustment of savings to changes in income is far from instantaneous and there is a need to specify the dynamic adjustment pattern, that is, the lag structure. In many developed countries, the savings rate has been observed to vary procyclically in the short run but to remain constant over the long run. Is a similar pattern of adjustment of savings rates evident in Asian countries? Davidson et al. (1978) have proposed an “error-correction” model that has an attractive dynamic property: the consumption or savings ratio is constant in the long run and any short-term “error” or divergence of this ratio from its long-run value is corrected over time to ensure the constancy of the ratio in the steady state. A test of the error-correction model in the context of (15) takes the following form

Note that if the error-correction model is valid and we restrict the parameters such that β₁ + β₂ + β₃ = 0 then we can rewrite (15) as

Furthermore, ignoring the random error term in (16), in a noninflationary steady state with Δc_t = Δy_t = g, PR_t = PR_t = PR, and x_t = x, we have

The long-run average propensity to save increases with growth and a rise in the proportion of people in the working ages (i.e., PR) as long as β₁<0, 0<β₂<1, β₄<0.

Note that (15) involves anticipated and unanticipated variables that are unobservables. We follow Blinder and Deaton (1985) to generate these unobserved variables. Accordingly, let m and y^us denote money supply and U.S. gross national product (at constant 1980 prices) in logarithmic form, and t stand for a time trend factor. The unobserved anticipations z^a, for z = y, π and ΔT, are generated as one-period ahead forecasts from:

and the unanticipated values, z^u, as its residuals (v). Note that our formulation, (15) and (18), is identical to that proposed by Blinder and Deaton (1985). Equation (18) may be interpreted as an unrestricted reduced form equation with y^us serving as a proxy for world demand.

As Blinder and Deaton (1985) have pointed out, the functional form (15) “nests” both the Hall-hypothesis as well as the error-correction model. Moreover, we can adopt a sequential testing procedure--proceeding from H₁ to H₂ to H₃ --for discriminating among the alternative models. In the following section we carry out these sequential tests for choosing the appropriate model for each country in our sample and then check for overparameterization and conduct a simplification search. We also check for the absence of serial correlation, parametric stability, and “reliability” of steady-state predictions. Through this process one equation that best explains private savings is chosen for each country.

1. Concepts, data, and missing observations

We have deflated private consumption expenditure and disposable income at current prices by the implicit GDP deflator to arrive at private consumption and disposable income in real terms. These figures have been divided by population to obtain private consumption and disposable income in per capita real terms. Inflation is measured by the percentage rise in the consumer price index. ^1/ The other variables are self-explanatory, and the appendix contains details about the sources of data, problems of measurement, and limitations.

For India, data on personal disposable income were readily available and have been used to explain private consumption. The concept of income used for other countries is private disposable per capita real income. Aggregate private disposable income at current prices has been deflated by the implicit GDP deflator and divided by population to obtain the figures in per capita real terms. Aggregate private disposable income at current prices has been derived from GNP at current prices by adding (a) private unrequited transfers from abroad and (b) public sector subsidies, and by subtracting (c) all government taxes. ^1/ Because data on taxes and subsidies are not available for much of the 1960s, there are serious nonuniformities and discontinuities in our income series. Two easy options were not to use the concept of private disposable income or to use it with a much shorter sample period. However, the former would be incorrect while the latter would be a waste of useful information on all the other variables. We have assumed that, for the earlier period with missing observations, taxes, net of subsidies and as a proportion of total income, say, k, did not vary from year to year. Let z^* be the logarithm of “true” private real disposable income while z is its incorrectly measured counterpart, ignoring the net taxes levied by the government. Note that:

which under the assumption of constancy of k_t can be approximated by

We have utilized the data for the entire sample period by using $z_{\text{t}}^{*}$ as the income variable for the later years and z_t as the income variable for the earlier years with missing observations. We have used a dummy variable, taking the value unity for the years with missing observations and zero otherwise, to remedy the problem of data discontinuity for all the countries except India. ^1/

2. Tests of Alternative Models

Three versions of equation (15) were estimated by ordinary least squares (OLS): (a) an unrestricted version; (b) constraining ${\mathrm{\beta }}_{\mathrm{2}}\mathrm{=}{\mathrm{\beta }}_{\mathrm{2}}^{\mathrm{*}}$ consistent with H₂; and (c) constraining β₁ + β₂ + β₃ = 0 (and${\mathrm{\beta }}_{\mathrm{2}}^{\mathrm{*}}\mathrm{=}{\mathrm{\beta }}_{\mathrm{2}}$) consistent with H₃. Tables A1–A3 in the Appendix present the estimates.

Hypothesis H₁, that “only surprises matter”, is convincingly rejected by a traditional F-test at the 5 percent level of significance. The test seems to be valid since we could not detect any signs of serial correlation in the error structure for any country except Korea. The correlogram of residuals for Korea revealed a high negative value (–0.58) at the second lag. However, the serial correlation problem appears to be related to the absence of income terms with lags greater than two. This seems to weaken the case for the validity of the rational expectations-permanent income hypothesis in Korea. The general result that even anticipated movements in income or other variables have an impact in Asian countries is intuitively appealing in view of the likely liquidity constraints in these developing countries.

Hypothesis H₂, that decomposition of current income between the anticipated and unanticipated parts is not important, that is, ${\mathrm{\beta }}_{\mathrm{2}}\mathrm{=}{\mathrm{\beta }}_{\mathrm{2}}^{\mathrm{*}}$, is rejected at the 5 percent level of significance only in the case of Sri Lanka. ^2/ However, the estimated unrestricted version of the equation for Sri Lanka suffers from some serious deficiencies, for example, the long-run income elasticity is abnormally large (about 3). ^3/ In general, we find evidence to suggest that the decomposition of current income into anticipated and unanticipated categories is not of great importance in the countries under investigation, when lagged income and consumption are also included in the model as explanatory variables. At first sight this may appear to be a refutation of not only the rational expectation version of the permanent income hypothesis (PIH) but also the PIH per se. However, this is not true and due cognizance must be taken of the presence of lagged income and consumption terms in the relationship when interpreting the result regarding ${\mathrm{\text{H}}}_{\mathrm{2}}\mathrm{:}{\mathrm{\beta }}_{\mathrm{2}}\mathrm{=}{\mathrm{\beta }}_{\mathrm{2}}^{\mathrm{*}}$. As Davidson et al. (1978) have shown, a distributed lag formulation of the consumption function of the form (15) even under H₃ (which assumes the validity of ${\mathrm{\text{H}}}_{\mathrm{2}}\mathrm{:}{\mathrm{\beta }}_{\mathrm{2}}\mathrm{=}{\mathrm{\beta }}_{\mathrm{2}}^{\mathrm{*}}$) is consistent with distributed lag variants of the PIH. ^1/ A once and for all increase in income elicits very different responses in consumption behavior in our model even when ${\mathrm{\text{H}}}_{\mathrm{2}}\mathrm{:}{\mathrm{\beta }}_{\mathrm{2}}\mathrm{=}{\mathrm{\beta }}_{\mathrm{2}}^{\mathrm{*}}$, depending on whether the increase is permanent or temporary.

The overall goodness of fit of equation (15) under ${\mathrm{\text{H}}}_{\mathrm{2}}\mathrm{:}{\mathrm{\beta }}_{\mathrm{2}}\mathrm{=}{\mathrm{\beta }}_{\mathrm{2}}^{\mathrm{*}}$ is fairly impressive, especially because the dependent variable is the rate of growth of per capita private consumption in real terms and does not have a time trend. A straightforward way of testing the error-correction model (ECM) is to look at the value of long-run income elasticity of consumption obtained by estimating equation (15) under ${\mathrm{\text{H}}}_{\mathrm{2}}\mathrm{:}{\mathrm{\beta }}_{\mathrm{2}}\mathrm{=}{\mathrm{\beta }}_{\mathrm{2}}^{\mathrm{*}}$ and to judge whether it is significantly different from unity. The results of this exercise show that, in only three of the countries--Indonesia, the Philippines and Thailand--is the long-run elasticity significantly different from unity. Thus, at least for five countries there are reasons to believe that the ECM model is valid. Notice that the ECM model does not require “… that the data satisfy a unit elasticity restriction … [and]… only requires that the model satisfy this restriction and the data are consonant with the model.” ^2/ When income increases, the average propensity to consume can decrease in the short run because of an initial disequilibrium effect, but a long-run income elasticity that is less than unity implies that the APS increases ad infinitum in a steady state with growth in income--a result that is contrary to our priors.

The anomalous result in the case of Indonesia, the Philippines, and Thailand could well be because of overfitting--there are variables in our equations that do not really matter in the context of each of these countries. We, therefore, investigate whether the unsatisfactory results for these three countries are due to the presence of such redundant variables.

3. Factors that determine the private savings rate in each country

Though all the factors included in our model can, in theory, affect a country’s savings rate, they need not have played equally important roles in every country for historical, political, or structural reasons. For example, the rate of inflation in Malaysia and Singapore has not been high or volatile enough for the sample data to reveal the impact of inflation on the private savings rate in these two countries. Similarly, exports as a share of GNP in India have hardly grown over the sample period, and it is therefore difficult to detect the impact of this ratio on savings in India.

We conducted a simplification search to narrow down the list of important factors that influenced private savings in each of our sample countries. ^1/ The results are reported in Table 2. Note that the standard errors have not been corrected for “generated regressors.” ^2/

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It is interesting to note that the hypothesis ${\text{H}}_2:{\beta }_2={\beta }_2^{*}$ for Sri Lanka is not rejected at the 5 percent level of significance once the redundant variables are omitted from the equation. Similarly, it may be recalled that the hypothesis that the long-run income elasticity of savings is unity, that is, H₃ holds, was rejected for Indonesia, the Philippines, and Thailand when all the factors were included in the model. Once the superfluous variables are dropped from the equation, H₃ is not rejected for Indonesia, but it remains rejected for the Philippines and Thailand. Nevertheless, in the specification of the final chosen equation the assumption of unitary long-run income elasticity is retained for the Philippines and Thailand.

Growth unambiguously leads to increased private savings in all the eight countries and the coefficient of the income-growth variable is less than unity. According to our calculations, a one percentage point increase in the rate of growth of per capita real income leads on average to a one percentage point rise in the private savings rate in the steady state. The change in the average propensity to save, however, differs substantially between the short and the long runs. The short-run behavior of the APS depends on the extent of the initial disequilibrium. The coefficient of the feedback variable (the lagged ratio of consumption to income) is highly significant indicating that an acceleration in the rate of growth results in a substantially greater increase in the APS in the short-run than in the long-run. ^1/ In only one country, Korea, do changes in the rate of growth play an important role in determining private savings. However, Houthakker and Taylor (1970) and Davidson et al. (1978) found similar results for other countries.

On average, a one-point increase in the percentage of population between the ages of 15 and 64 leads to a 1.6 percentage point rise in the APS in the long run in India, Korea, Malaysia, Singapore, and Sri Lanka. We could not detect any lasting effect of age composition on savings behavior in Indonesia and the Philippines. ^2/ However, in Indonesia, where the age structure of the population has shown very little long-term movement, we find evidence that changes in the age-composition of the population (APR) affects private savings in the short run. These short-run movements are also found to be of importance in India, Korea, Malaysia, Singapore, and Thailand, indicating the existence of lags in the adjustment of savings to age composition. Thailand is the only country in which the private savings rate appears to decline in the long run with lower age-dependency; however, we are unable to find any satisfactory reasons for the large perverse coefficient of the age-composition variable in that country. ^3/

While the age composition of the population exerts a significant influence on the private savings rate in all the countries except the Philippines, ^4/ an important question arises regarding the significance of the demographic variables. Primary information on age composition is available only at intervals of ten years or so, when a census is conducted. For the intermediate years, the data are prepared by demographers through interpolation. The correlation between age composition and time trend can, therefore, be expected to be high in any of the countries in our sample. There is then the question of whether the coefficient of the age composition variable is identified or whether it simply captures the effect of a time trend or some other time-trending variable? We investigated the time-series property of the age-composition variable and found that it has a fairly complicated variation structure in every country--a simple time trend yields a high correlation coefficient but fails to explain the movements in the demographic pattern. Thus, there is no prima facie reason for undue skepticism. ^1/

On average, inflation has an adverse impact on private savings in the countries under study. However, the effect seems to vary considerably from country to county. Inflation, both anticipated and unanticipated, results in lower private savings in Indonesia. Unanticipated inflation reduces private savings in India while anticipated inflation does not have an impact. In Korea and the Philippines, on the other hand, only anticipated inflation matters. In Korea, it has an adverse impact on private savings while, in the Philippines, the effect seems to be the reverse. Inflation, whether anticipated or not, does not affect private consumption-savings behavior in the two low-inflation economies of Malaysia and Singapore as well as in Sri Lanka and Thailand.

In general, adverse movements in the terms of trade tend to depress private savings in the sample countries. Any anticipated deterioration in the terms of trade affects private savings adversely in India, Malaysia, Sri Lanka, and Thailand. Similar movements, when they are unanticipated, also affect private behavior in Malaysia, the Philippines, and Sri Lanka. As noted earlier, the effect of movements in the terms of trade on private consumption could not be estimated for Indonesia and Singapore, although as a major oil-exporter, Indonesia may have witnessed some sharp changes in its terms of trade during the reference period. For Korea, where there has been a very modest and gradual deterioration in the terms of trade, we could not find any evidence of the Laursen-Metzler-Harberger effect.

The Maizels-Lee hypothesis, that increased export-orientation augments savings, is for the most part rejected by the evidence. Even for Korea, exports as a proportion of GDP does not seem to have played a direct role in the determination of private consumption or savings. As can be verified from the sign of the relevant coefficient in Table 2, while private savings seems to have risen in line with increasing share of exports in GDP in Indonesia and Thailand, for Malaysia it seems to have declined. This may point to the possibility that exporters do not have a higher propensity to save relative to others in every country, or that the Maizels-Lee hypothesis is sensitive to the pattern of ownership of export industries.

To verify the reliability of the results, the final equations for each country are tested for (i) their error structure, (ii) parametric stability, and (iii) implied steady-state values. None of the equations reported in Table 2 seem to suffer from any first-order serial correlation. The Lagrange-multiplier (LM) test-statistic for first-order serial correlation, which is distributed as ${\text{X}}_1^2$, is not significant at the 5 percent level of significance. We could not detect any prima facie evidence of higher-order serial correlation in any country except Korea. In Korea, the statistic obtained by multiplying the sum of squares of the first four autocorrelations by the number of observations is a significantly high 14.47. The statistic is high for all the specifications tried out in this study. ^1/ We could not discover the source of the misspecification.

The final equations are parametrically stable. The Chow-test carried out with out-of-sample forecasts for the subperiod of the early 1980s does not reveal any nonconstancies.

The steady-state average propensity to consume (APC) is computed under the assumption that there is no growth in per capita income, no inflation or movements in the terms of trade. Exports are assumed to constitute 40 percent of GNP, as is the present case for Korea. Furthermore, 65 percent of the population is assumed to be between the ages of 15 and 64 in the steady state. The countries fall into three groups: Indonesia, Korea, the Philippines, Sri Lanka, and Thailand with a steady-state APS of roughly 0.2; Malaysia and Singapore with a steady-state APS of 0.4 approximately; and India with a steady-state APS of 0.3. ^2/