Personal Savings as a Function of Permanent Income. Robert Bruce Lung. Virginia Polytechnic Institute and State University

Transcription

1 Personal Savings as a Function of Permanent Income By Robert Bruce Lung Virginia Polytechnic Institute and State University Master of Arts in Economics Approved: Roger N. Waud, Chairman Thomas J. Lutton Richard P. Theroux July 17, 2002 Falls Church, Virginia Keywords: Permanent Income, Personal Savings, Marginal Propensity to Save

2 Personal Savings as a Function of Permanent Income By Robert Bruce Lung Abstract In this paper, a model to estimate personal savings is constructed using an estimate of permanent income. Traditional approaches to studying aggregate personal savings depend on many independent variables that serve as the determinants of personal saving. Because some of the determinants used in such approaches can be difficult to obtain, estimating aggregate saving in this manner can be time-consuming and arduous. Using an estimate of permanent income based on Friedman s Permanent Income Hypothesis (PIH), this paper creates a model to estimate personal savings and tests the model by examining the Marginal Propensity to Save (MPS) that is derived from it. Permanent income was estimated using a two-stage least squares (2SLS) method and aggregate personal savings is estimated using ordinary least squares (OLS). The empirical evidence reveals that savings estimates and marginal propensities to save are consistent with results obtained studies using conventional approaches except during periods in which a wealth effect occurs. During such periods, additional variables need to be added to the model to account for a wealth effect. This analysis therefore serves to further validate the PIH and shows that it can be applied to studying household savings as well as consumption.

3 Acknowledgments I wish to thank Dr. Roger Waud for his insight and encouragement with this topic. Dr. Waud s expertise was invaluable in understanding the Permanent Income Hypothesis. I thank Dr. Thomas Lutton for his patience and encouragement prior to and during the course of this thesis; his guidance and insight was critical in helping me understand the statistical methodology of econometric time-series analysis. I thank Dr. Swamy Paravastu for suggesting the study of savings using the Permanent Income approach and for his guidance and insight regarding quantitative and statistical methodology towards studying it. I also wish to thank Ms. Aniene Porter for all of her administrative assistance during my time in this program. iii

4 Table of Contents Personal Savings as a Function of Permanent Income i Abstract ii Acknowledgments iii Table of Contents iv Introduction 1 Part I 4 Consumption and Savings Theory 4 Literature Review 4 Consumption and Savings Theory Prior to Permanent Income 6 The Permanent Income Hypothesis 8 Part II 12 The Savings Function Based on Permanent Income 12 Empirical specification and Data 13 Estimating Permanent Income 13 Testing for Autocorrelation 15 Estimating Savings 16 Part III 25 Testing the Marginal Propensity to Save 25 Conclusion 29 References 33 iv

5 List of Tables and Figures Table 1. Distributed Lag Regression Results...14 Table 2. Permanent Income Regression Results...17 Table 3. Divided Sample Permanent Income Regression Results...19 Table 4. Permanent Income Regression Results Including Wealth and Interest Rate Effects...22 Table 5. The Marginal Propensity to Save with a one-percent rise in disposable income...26 Table 6. The Marginal Propensity to Save with a two-percent rise in disposable income...26 Table 7. The Marginal Propensity to Save with a three-percent rise in disposable income...27 Figure 1. The Marginal Propensity to Save out of Permanent Income...24 Figure 2. The Effects of Positive Income Shocks on the Marginal Propensity to Save...28 v

6 Introduction Economic research on aggregate savings is highly abundant in economic literature. Most of the research and empirical analysis on aggregate savings is based on econometric models that employ multivariate estimations in which savings is held to be a function of many different factors (Formaini & McKenzie 1999, Callen & Thimann 1997, Ul Haque, Pesaran & Sharma 1999). These studies tend to provide results that are consistent with economic theory although the results differ depending on the type and quantity of explanatory variables they include. One study claims that savings is more highly affected by public sector saving and consumption than by other factors that are commonly thought to influence saving behavior (Ul Haque, Pesaran & Sharma, P. 31). Other studies commonly use GDP or income growth, inflation and interest rates, ratios of wealth to GDP and demographic variables as important determinants of aggregate savings (Higgins, P. 4, Callen & Thimann, P. 13). In addition, Callen & Thimann point to corporate savings levels, tax and social security structures as well as the degree of financial deregulation as having important effects on savings behavior (Callen & Thimann, P. 10). One main drawback associated with these approaches is the fact that some of this data can be incomplete or difficult to obtain, particularly for Less Developed Countries (LDCs) or countries from the former Soviet Union. In addition, the results from such studies may be skewed by heteroskedasticity and autocorrelation, and the quantity of data that multivariate models treat render these models complex and difficult to work with. 1

7 While much research has been performed using the PIH to study consumption, its applicability to estimating savings is not as widespread. According to the PIH, consumers decide how to spend their income based on their expected lifetime income. This idea has led to consumption being treated as a function of permanent income (Friedman, P. 10). Empirical results of consumption models based on the PIH generally support its assertions (Serlenga, P ). As a result, there is a good possibility that the PIH could be used to create a model that generates aggregate personal savings estimates that are robust and consistent with economic theory. Another advantage of the PIH approach is that it can simplify research on savings by greatly reducing the type and amount of data required for generating savings estimates. While a savings function calculated within the framework of the PIH may not be immune from some of the issues related to a multivariate estimate, such as autocorrelation, it does not require the type and volume of data required for multivariate models. This reduced data burden simplifies the process of creating savings functions, which makes it easier to study the economic impact of savings. This paper is organized in the following manner. The first part contains a review of the theory behind consumption and savings and discusses some existing literature on aggregate consumption and savings. In the second part, the permanent income approach used to estimate personal savings is discussed. This includes the construction of a measure of permanent income as well as the results of the permanent 2

8 income-based savings approach. In the third part, I test the consistency of the marginal propensity to save (MPS) calculated from the model. In the last section I present some conclusions and discuss opportunities for future research. 3

9 Part I Consumption and Savings Theory The income that is available to households for consumption and saving is known as personal disposable income (Y d ) and can be represented as Y d = Y T (1) where Y is personal income and T is personal income taxes. Households have the choice of spending all or a portion of their disposable income. Therefore, a basic definition of aggregate personal saving, S, is that it is the portion of disposable income not used for consumption and is given by the equation, S = Y C (2). d The savings statistic that the permanent income approach this paper uses is the personal savings figure given by the Bureau of Economic Analysis (BEA) in its national income tables. The personal savings figure is used for two reasons. First, it is the statistic that economic theory tells us the most about. Second, it is appropriate because the permanent income hypothesis is best interpreted as a hypothesis about disposable income as measured by the personal disposable income data of the BEA. Literature Review Much of the research and analysis attempting to explain the behavior of personal savings uses variables thought to represent the motivations for saving. Callen and 4

10 Thimann state that the motivations for saving fall into four main categories: providing for retirement, the financing of anticipated large expenditures, precautionary saving, and to ensure adequate financial resources to maintain a stable consumption level (Callen & Thimann, P. 5). From these motivations, a common group of variables is used in many empirical studies of personal saving. Some of these variables include fiscal indicators (such as government saving & tax revenue), economic growth, household wealth, demographic variables, unemployment, the real interest rate and inflation, (Callen & Thimann, P. 5; Ul Haque, Pesaran & Sharma, P. 6). As far as fiscal indicators, some research has shown that high tax rates or a high degree of government saving has a negative effect on personal saving (Callen & Thimann, P. 6-7). Healthy economic growth evidenced by high rates of growth of gross domestic product (GDP) and per capita income is thought to have a positive effect on personal saving (Callen & Thimann, P. 6). The most common demographic variable thought to influence personal saving is the old-age dependency ratio, which is the ratio of a country s retired population (in the U.S. people who are 65 years and older) to its working age population. The implication drawn from Modigliani s life cycle hypothesis (LCH) is that the greater an old-age dependency ratio (meaning a higher number of retirees to people in the workforce), the lower is personal savings because retired people dissave during their retirement (Bentzel & Berg, P. 159; Callen & Thimann, P. 6; Ul Haque, Pesaran & Sharma, P. 4, Modigliani, P. 395). Unemployment is thought to have a negative effect on personal saving because as unemployment rises, incomes 5

11 decrease resulting in reduced savings (Callen & Thimann, P. 13). Inflation might be thought to have a negative effect on savings because as inflation rises the value of fixed income securities declines resulting in capital losses to households that hold such assets (Callen & Thimann, P. 11). However, it could have a positive effect because investors might try to offset the negative effect on fixed-income securities by investing more in real estate and other assets (precious metals) whose prices rise with inflation. Other studies have shown that unanticipated inflation can have a positive effect on savings by inducing households to save more (Deaton, P. 138). The real interest rate has been found to have a slight positive impact on household savings (Callen & Thimann, P. 6). Consumption and Savings Theory Prior to Permanent Income Because consumption accounts for about two thirds of GDP in the United States, early studies focused on consumption behavior. Starting with a series of observations, Keynes hypothesized that the more income households receive, the more they spend (Froyen, P. 278). This observation led to the development of the absolute income hypothesis (AIH) (Froyen, P. 279). According the AIH, as household income increases, consumption increases, though not by the same proportion as the rise in income. This led to the Keynesian consumption model that relates current consumption expenditures to current levels of disposable income. This model takes the form C = a + by d a > 0,0 < b < 1 (3) 6

12 where C is consumption, a is autonomous consumption, b is the marginal propensity to consume (MPC) and Y d is disposable income. The MPC represents the marginal change in consumption that is induced by a marginal change in disposable income. According to this model, consumption is not a constant fraction of disposable income (Froyen, P. 279). The Keynesian consumption to income relationship also implies the savings to income relationship, the Keynesian savings function S = a + ( 1 b) (4) Y d where a is autonomous saving and 1 b is the Marginal Propensity to Save (MPS). The MPS is the relative change in saving that is induced by a change in disposable income. The logic behind the MPS is very straightforward. If a one unit increase in Y d leads to an increase in consumption by b units, then the remainder of that one unit increase (represented by 1 b) is the increase in saving (Froyen, P. 75). The MPC and MPS are respectively the slopes of the Keynesian consumption and savings functions (Byrns and Stone, P. 167). Studies of historical consumption and savings rates for the United States have estimated MPCs to approximate 0.9 and MPSs to approximate 0.1 respectively (Greene, P. 299). The Keynesian consumption model also includes the Average Propensity to Consume (APC), which is the ratio of consumption to the level of disposable income C / Y ) APC (5) ( d 7

13 and can also be written as ( a / Yd ) + b APC (6) (Froyen P. 279). The APC is always larger than the MPC, which implies that as incomes rise, households spend less of their income on consumption and therefore, save more of their income. The Average Propensity to Save (APS) is therefore 1 APC [ a / Yd + (1 b)] APS. (7) The APC is useful because it allows researchers to look at consumption levels across income groups. The implications derived from the Keynesian consumption functions are that lower-income groups will consume a greater proportion of their income relative to high-income groups and that over time the APC will decrease as disposable income increases (APC low income > APC high income). While studies have shown that the APC has consistently been smaller for higher income groups relative to low-income groups, they ve also shown that the APC has been constant over long-run income growth, which suggests that the consumption to income relationship is proportional (Froyen, P. 281). This anomaly led to the additional research into consumption and savings behavior and the development of alternative theories of consumption, one of which is the PIH. The Permanent Income Hypothesis In response to the apparent deficiencies of models of consumption behavior, Friedman (1956) developed the PIH as an alternative explanation of household consumption behavior. The PIH begins to explain consumption behavior by first redefining measures 8

14 of disposable income. The values of disposable income Y d can be divided into two separate components: Y p, permanent income and Y T, transitory income so that Y = Y + Y (8) d p T (Friedman, P. 21). The permanent component of income is regarded by Friedman as the mean income at any age regarded as permanent by the consumer unit in question (P. 93). The transitory component is the unexpected gain or loss to a consumer unit s measured income caused by accidental occurrences (Friedman, P. 22). Therefore, the transitory component of income has an expected value of zero (E[Y T ] = 0) reflecting the notion that over time transitory income gains are offset by future transitory income losses. In addition, the notion that transitory income has an expected value of zero implies that it should be uncorrelated with permanent income (Romer, P. 334; Friedman, P. 27). Transitory income can therefore be thought of as unexpected income that occurs randomly such as money won through gambling or one-time tax rebates. On the other hand, permanent income can be treated as the portion of measured income that a consumer expects to have on a regular basis and is therefore the component of income that influences consumption (Froyen, P. 291). Therefore, in the long run, measured levels of disposable income are roughly equivalent to Friedman s definition of permanent income. In addition to a permanent measure of income, Friedman proposes that consumption can also be treated as having permanent and transitory components (Friedman, P. 11 & 26). Consumption can therefore be expressed as: 9

15 C = C p + C T (9) with the same type of assumptions behind the transitory and permanent components of consumption namely that (E[C T ] = 0) and C p is a function of permanent income Y p. The implication of this is that there can be permanent and transitory savings S = S p + S T (10) in which S p is the permanent component of savings and S T is the transitory component (Mayer, P.134). Because there are two components of consumption and savings (permanent and transitory) there are respective marginal propensities to consume and marginal propensities to save for each of the permanent and transitory components. The relationship between permanent income and permanent consumption is defined by the equation C = k( i, w, u) (11) p Y p where k is a function that is the ratio of permanent consumption to permanent income and is a function of variables other than the current level of income (Friedman, P. 26 & 119). The function k also represents both the average and the marginal propensities to consume (Friedman, P. 26). The variables (i, w, u) represent respectively the interest rate that a consumer can borrow or lend at, the ratio of non-human wealth to income, and the individual consumer s tastes and preferences (Friedman, P. 26). The function k is hypothesized to change from household to household because of the differences among them for the values they attach to i, w, and u (Friedman, P. 18). In addition, the value of k is hypothesized to change due to changes in the variables that determine it, 10

16 namely i, w, and u (Friedman, P. 119). Therefore, in the consumption function shown in (11), increases in consumption are proportional to increases in permanent income (Froyen, P. 292). This also implies that increases or decreases in savings will also be proportional to changes in permanent income since savings should be [ 1 k ( i, w, u)] (12) Y p As a result, 1-k is both the average and marginal propensity to save (Friedman, P. 196). 11

17 Part II The Savings Function Based on Permanent Income The estimate of savings as a function of permanent income requires a two-step process. The first step is to obtain a measure of permanent income. The second step is to generate the savings function using the measure of permanent income. Because permanent income is not an observable statistic, an estimate of permanent income has to be constructed. The approach that is taken is to select a proxy for permanent income from which an estimate of permanent income is produced. Once a robust estimate of permanent income is obtained, the savings function can be estimated. Based on the type and availability of macroeconomic data, the best proxy for permanent income was deemed to be an estimate of personal disposable income (Y d ). Disposable income represents the amount of income that any given household has after taxes and is therefore the portion of measured disposable income that a consumer expects to receive on a regular basis. As shown in Mayer (P. 362), Friedman s estimate of permanent income is obtained by calculating a weighted average of past and current income using t ' y p ( t') β exp[( β α)( t t')] y( t) dt (13) = where y t is observed income in period t, β is a coefficient of adjustment and α is a trend variable. Although Friedman suggests that (13) would produce the most accurate estimate of permanent income, he notes that the manner in which personal disposable 12

18 income is measured is fairly close to the concept of permanent income (Friedman, P. 116; Serlenga, P. 3). Empirical specification and Data The data used in the permanent income approach is from the Bureau of Economic Analysis s national income tables. Quarterly measurements of personal savings and personal disposable income from 1983 to 2001 were obtained from the BEA tables. Because disposable income is the sum of permanent and transitory income, a logical equation for estimating savings is: ( t ) 0 + β1y pt + β 2 S = β ( Y Y ) + u (14) at pt t where Y pt represents estimated permanent income, Y at is actual disposable income, Y pt subtracted from Y at is transitory income (Y T ), and u t is the error term or the difference between actual and estimated savings. In order to estimate (14) a measure of permanent income has to be constructed from the personal disposable income data. Estimating Permanent Income To create the permanent income variable, a distributed lag regression was estimated on for disposable income as a function of its own past values (Greene, P. 750). The disposable income data was lagged for two periods as follows: Y α + u (15) t = 0 + α1yt 1 + α 2Yt 2 t 13

19 where Y t is disposable personal income in period t and u t is the error term in period t. Once estimates of α are obtained the estimate of permanent income is Y pt = ^ ^ ^ 0 + α 1 Y + t 1 α 2 Yt 2 α (16) where Y pt is estimated permanent income in period t. The estimates, α 0 α, and α 2, are shown in Table 1. ^ ^, 1 ^ Table 1. Distributed Lag Regression Results ^ ^ ^ α 0 α 1 α 2 Coefficients Standard Errors T statistics To obtain transitory income, the permanent income estimate needs to be subtracted from actual disposable income Y t ^ ^ Y pt = u t (17) where u t represents transitory income. Before proceeding with estimating the savings equation (14), a test for first-order autocorrelation was performed on the estimated distributed lag regression of (15) to determine whether autocorrelation was present in the error terms. Autocorrelation will cause the parameter estimates to be biased. In this model of permanent income, the 14

20 error term represents the transitory income component so, if autocorrelation is significant this would mean that transitory income estimates are not randomly distributed, and would skew the permanent income estimates. Testing for Autocorrelation To determine whether autocorrelation is present a Durbin-Watson test is typically performed. The Durbin-Watson test uses the residuals of an OLS regression to check whether the error term in one period is related to the error term in the previous period plus a spherical disturbance (Kennedy, P ). However, the Durbin-Watson test is biased towards not finding any autocorrelation in the presence of lagged dependent variables (Greene, P. 542; Kennedy, P. 130). Therefore, the test that was conducted was a variation of the Durbin-Watson test known as the h-test, (Greene, P. 542). The h- statistic is given by d T h = (1 ) (18) Ts c d where T is the number of observations, (1 ) is the rho value and 2 2 sc is the estimated variance of the least squares regression coefficient on Y at-1. Large values of the H- statistic are indicative of significant autocorrelation because the hypothesis being tested, H 0, is that the H-statistic is zero or very close to it (Greene, P. 542). The h- statistic was computed by regressing the estimated error term on itself lagged one period u t α ρ (19). = + ut 1 15

21 d This regression produced two coefficients, the second of which is the ρ value or (1 ). 2 The h-statistic in this instance had a value of 0.405, which indicated a low degree of autocorrelation in the error terms. Estimating Savings Using our estimates of permanent and transitory income from (16) and (17) respectively, we estimate the savings equation (14) over the entire sample period (the 3 rd quarter of 1983 through the 2 nd quarter of 2001). Before the estimation was carried out, a few conjectures were made about the data. First, it was expected that the estimated values of personal savings would approximate the actual data to a large extent. Secondly, it was expected the marginal propensity to save out of permanent income would be greater than zero, but not more than 0.1. Because the permanent income hypothesis implies that there are two components of savings (permanent and transitory) as shown by (10), there have be two marginal propensities to save, one out of permanent income and one out of transitory income (Mayer, P. 134). According to the PIH, the majority of households consumption will come out of the permanent component of their measured income since that is the amount of income they expect to receive on a regular basis (Friedman, P. 21). In addition, because the transitory component is viewed by households as being incidental, the implication is that households consumption should respond less strongly to changes in transitory income than to changes in their permanent income (Friedman, P. 22, 28-9). Therefore, the third expectation was that the marginal propensity to save out of permanent income would be 16

22 smaller than the marginal propensity to save out of transitory income. The parameter estimates are shown in table 2 along with the standard errors and T-statistics. Table 2. Permanent Income Regression Results Intercept Y pt Y T = (Y at -Y pt ) Coefficients Standard Errors T statistics The regression results in table 2 were problematic for two main reasons. In the first case, the savings estimates that were calculated when the coefficients were inserted into (14) did not approximate the actual data well. The estimates were much higher than the actual data in the early part of the sample period and much lower than the actual data in the later part of the sample period. The initial conclusion was that the model did not estimate savings well. The second and more important problem was that the sign on the coefficient for permanent income (Y p ) was negative and that the T statistic was significant. The negative sign on the coefficient on Y p is problematic because that coefficient is the marginal propensity to save out of permanent income [equivalent to 1-k in (12)] and is the marginal propensity to save that can be compared against historical estimates of the marginal propensity to save of approximately 0.1 (Greene, P. 299). The negative value 17

23 for the marginal propensity to save means that it is less than zero over the entire sample period. A negative marginal propensity to save is contrary to the theory that the long-term marginal propensity to save is positive and inconsistent with historical calculations of the marginal propensity to save. As was expected, the value of the coefficient on transitory income (Y T ) was higher than the value of the coefficient on permanent income (Y p ). The data was then broken up into two equal periods and re-estimated to determine the consistency of the parameter estimates. The model in (14) was re-estimated using the data from the 3 rd quarter of 1983 through the 2 nd quarter of 1992 and from the 3 rd quarter of 1992 through the 2 nd quarter of The resulting parameters with standard errors and T-statistics are shown in table 3. 18

24 Table 3. Divided Sample Permanent Income Regression Results 1983-III to 1992-II Coefficients Standard Errors T statistics Intercept Y pt Y T = (Y at -Y pt ) III to 2001-II Intercept Y pt Y T = (Y at -Y pt ) The regression results in table 3 are noteworthy due to their dichotomous nature. The savings estimates calculated using the coefficients from the first sub-period produced savings estimates that approximated the actual data fairly closely. The marginal propensity to save out of permanent income was greater than zero, but smaller than historical estimates of the marginal propensity to save of approximately 0.1 (Greene, P. 299). The marginal propensity to save out of transitory income was much higher than the one out of permanent income, buttressing the idea that a consumer unit will spend less of a temporary increase in measured income than a permanent one. In addition, the T-statistics for both marginal propensities to save were significant. 19

25 On the other hand, the savings estimates calculated using the coefficients from the second sub-period produced savings estimates that approximated the actual data well for the early part of the sub-period, but then approximated the data very poorly between 1997 and Although the marginal propensity to save out of transitory income was consistent with the one in the first sub-period, the marginal propensity to save out of permanent income was negative, implying that the MPS is less than zero. In view of these results, it seemed either that there was a sharp and inexplicable period of dissaving in the 1990s or that something was missing from the model in (14). According to Friedman s permanent income hypothesis, k in (12) can change because of changes in w and i. Friedman further states that w and i can affect savings in opposite ways (P. 120) as follows: if i were to rise (fall), k would decline (rise) so that 1-k would become larger (smaller), leading to a greater (smaller) marginal propensity to save. On the other hand, if w were to increase (decrease), it would raise (lower) k, causing 1-k to become smaller (larger), leading to a smaller (larger) marginal propensity to save (Friedman, P. 120). In order to account for the possibility that changes in w and i may have affected the data, a proxy for wealth and an interest rate were added to the savings model as independent variables. The proxy for wealth and interest are the actual closing values of the S&P 500 index and the prime interest rate respectively at the end of each quarter in 20

26 the sample period. The marginal propensity to save out of permanent income, β 1 in (14), now becomes β 1t = δ 0 + δ 1( S & P500t ) + δ 2 * i (20) Both the S&P 500 and the prime interest rate are multiplied by the permanent income estimate, which results in the following savings function: S = β * Y + u (21). t 0 + δ 0 * Yp + δ1( S & P500* Yp) + δ 2( i * Yp) + β2 T t Again, taking the estimates of permanent and transitory income from (16) and (17) respectively, we estimate the savings equation (21) over the entire sample period (the 3 rd quarter of 1983 through the 2 nd quarter of 2001) with the results displayed in table 4. 21

27 Table 4. Permanent Income Regression Results Including Wealth and Interest Rate Effects 1983-III to 2001-II Coefficients Standard Errors T statistics Intercept Y pt S&P500*Y pt i*y pt Y T = (Y at -Y pt ) The regression results in table 4 reveal how personal saving in the U.S. has been affected by a wealth effect in the 1990s. Over the first half of the sample period (3 rd quarter of 1983 through the 2 nd quarter of 1992), the S&P500 index grew steadily and by the 2 nd quarter of 1992, had appreciated by 145%. Over the sample period s second half (3 rd quarter of 1992 through the 2 nd quarter of 2001), the S&P500 index rose more quickly than in the first half with much of the increase occurring between 1996 and As a result, the index s closing value at the end of the 2 nd quarter of 2001 represented a 200% appreciation over the value of the S&P500 at the end of the 2 nd quarter of In fact, by of the 1 st quarter of 2000 the index had appreciated over the 2 nd quarter of 1992 by 267%! The effect on the marginal propensity to save out of permanent income is borne out by the coefficient on the S&P500*Y p which is negative and whose T-statistic is significant. It also explains why the marginal propensity to save was negative in table 2. Abstracting from the wealth effect, the marginal propensity to 22

28 save out of permanent income is in Table 4, which is closer to historical estimates of the marginal propensity to save, and its T-statistic is significant. As in table 3, the marginal propensity to save out of transitory income was greater than the one out of permanent income and its T-statistic was also significant. The evolution of the prime interest rate did not exert much effect on saving. This is because over the sample period, the prime interest rate exhibited a more even fluctuation pattern than did the S&P500. Although it reached a high of 12.99% in the 3 rd quarter of 1984, it came down rapidly and alternated within a range of 6% to 11.36% thereafter. Had the interest rate risen (declined) over the sample period, it is likely that k would have been made smaller (larger) so that 1-k would have been larger (smaller), and the marginal propensity to save would have been greater (smaller). Since the T- statistic was insignificant, saving behavior did not seem to be significantly affected by the interest rate over the period As with the marginal propensities to save out of transitory income in table 3, the marginal propensity to save out of transitory income in table 4 was much higher than the one out of permanent income, consistent with the prediction of the permanent income hypothesis. Also, the T-statistic for the marginal propensity to save out of transitory income was significant. 23

29 Using the parameter estimates for permanent income and the S&P500 multiplied by permanent income from Table 4 (δ 0 and δ 1 ), estimates of the marginal propensity to save out of permanent income were calculated for the sample period as follows and displayed in Figure 1. β = ( S & P500 ) (20 ) 1t t Figure 1. The Marginal Propensity to Save out of Permanent Income MPS Parameter estimate on Permanent Income Marginal Propensity to Save III 1984-III 1985-III 1986-III 1987-III 1988-III 1989-III 1990-III 1991-III 1992-III Time 1993-III 1994-III 1995-III 1996-III 1997-III 1998-III 1999-III 2000-III These estimates show how the wealth effect affected personal saving over the sample period. As the S&P500 increased, the marginal propensity to save out of permanent income decreased over most of the sample period except in moments when the S&P500 declined. This drop in the marginal propensity to save is consistent with the decrease in personal savings over the sample period. 24

30 Part III Testing the Marginal Propensity to Save To determine whether the marginal propensity to save is consistent, a test was devised to discover how it behaved in the presence of an income shock. The test that was applied was to simulate hypothetical increases of 1%, 2% and 3% in disposable income in one quarter and hold subsequent levels of disposable income fixed to the level of the quarter prior to the one with the income increase. Then, future estimates of permanent and transitory income, and savings were performed. Finally, the marginal propensity to save was calculated by dividing the changes in estimated savings by the changes in disposable income. This test allowed us to examine the effects of the income shift on the marginal propensity to save. The expectation was that the marginal propensity to save would rise temporarily with the temporary growth in disposable income and would gradually recover to or near its original value in subsequent periods. Using the last period of the data set (the 2 nd quarter of 2001) as the base period, the hypothetical increases in disposable income were performed in the 3 rd quarter of 2001 and the subsequent periods of disposable income were frozen at the value of the 2 nd quarter of Estimates of permanent and transitory income, and savings were computed through the second quarter of 2002 using the parameter estimates from Table 1 and equation (16). The marginal propensity to save was calculated by dividing the changes in estimated savings by the changes in disposable income from the 3 rd 25

31 quarter of 2001 through the 2 nd quarter of The results are shown in tables 5 through 7 and displayed in figure 2. Quarter Table 5. The Marginal Propensity to Save with a one-percent rise in disposable income Estimated Savings Estimated Permanent Income S&P500*Estimated Permanent Income Prime Interest rate*estimated Permanent Income Transitory Income 2001-II S/ Y d (MPS) 2001-III IV I II Table 6. The Marginal Propensity to Save with a two-percent rise in disposable income Quarter Estimated Savings Estimated Permanent Income S&P500*Estimated Permanent Income Prime Interest rate*estimated Permanent Income Transitory Income 2001-II S/ Y d (MPS) 2001-III IV I II

32 Quarter Table 7. The Marginal Propensity to Save with a three-percent rise in disposable income Estimated Savings Estimated Permanent Income S&P500*Estimated Permanent Income Prime Interest rate*estimated Permanent Income Transitory Income 2001-II S/ Y d (MPS) 2001-III IV I II As can be seen in each table, the rise in disposable income in the 3 rd quarter of 2001 provokes a sharp increase in the marginal propensity to save for that period. In the two subsequent periods, the marginal propensity to save declines to around 0.1 or below 0.1. This sharp increase followed by a gradual return to a level near the estimated marginal propensity to save is shown graphically in figure 1. In the last observed period, the 2 nd quarter of 2002, the marginal propensity to save rises sharply. This sudden jump is explained by the fact that wealth began to decrease in The closing value of the S&P500 index at the end of the 2 nd quarter of 2002 was down almost 15% from the index s value at the end of the 1st quarter of At this point, the wealth effect had effectively become a poverty effect, leading to a change in saving behavior. This result is again consistent with the permanent income hypothesis as a decline in w increases the value of k, leading 1-k (the marginal propensity to save) to be greater. 27

33 Figure 2. The Effects of Positive Income Shocks on the Marginal Propensity to Save MPS 3% MPS 2% MPS 1% MPS II 2001-III 2001-IV 2002-I 2002-II Time One peculiar result of this test is the magnitude of the differences between the respective marginal propensities to save. The one-percent increase in disposable income produced a marginal propensity to save of in the period of the onepercent income shock while the two and three-percent increases in disposable income produced marginal propensities to save of and respectively. Since the income shocks are temporary, they represent transitory income and the marginal propensities to save are consistent with the permanent income hypothesis in that they are all larger than the estimated marginal propensities to save out of permanent income. However, the permanent income hypothesis assumes that the income elasticity of consumption for transitory income is zero, implying that all transitory income will be saved (Mayer, P. 60). What these results imply is that there may be a greater propensity to consume out of larger quantities of transitory income and a greater marginal 28

34 propensity to save out of smaller ones. For this situation, a few possible explanations materialize. One explanation is that it is possible that households treat a greater proportion of a large amount of transitory income as permanent income. Viewing transitory income this way would lead them to consume more of it, resulting in a smaller marginal propensity to save. A second explanation is that the increase in income may be viewed by households as part of their expected long-term income growth. In one survey of household income expectations, 74% of respondents who expected their incomes to rise indicated that they would significantly raise their consumption in response to an income increase (Mayer, P. 129). This suggests that some households may not distinguish pure transitory income from permanent income as assiduously as the permanent income hypothesis assumes. A third possibility is that a large amount of transitory income would facilitate the purchase of durable goods, thereby provoking a greater marginal propensity to consume and a lower marginal propensity to save. Conclusion This paper s intent has been to estimate aggregate personal saving as a function of function of permanent income in accordance with Friedman s Permanent Income Hypothesis. The permanent income approach required creating an estimate of permanent income and a savings model based on that estimate. After performing a test for first order autocorrelation in the error terms and finding that autocorrelation was not highly significant, savings was estimated as a function of permanent income. The initial savings estimates and the marginal propensity to save out of permanent income 29

35 exhibited characteristics that did not concur with economic theory, nor did they concur with historical estimates of the marginal propensity to save. A re-estimation of the data set broken up into two equal periods produced conflicting results. The savings and parameter estimates for the first half of the data set were consistent with economic theory and with historical estimates of those estimates. However, the savings and parameter estimates for the second half of the data set were inconsistent with economic theory and historical estimates. This set of results led to the conclusion that the model was misspecified. The permanent income hypothesis postulates that the marginal propensity to save is determined by the interest rate and non-human wealth. Using the prime interest rate and the S&P500 as a proxy for wealth, the data was re-estimated abstracting for any possible wealth or interest rate effects. The estimation of personal saving abstracting for wealth and interest rate effects produced savings estimates that approximated the actual data more closely. In addition, the marginal propensity to save was more consistent with both economic theory and historical estimates for that statistic. The estimation also revealed that there was a wealth effect in the 1990s as the value of stocks, represented by the S&P500 index, increased dramatically compared to their increase in value during the 1980s. This sharp increase in wealth led to a period of dissaving, which explains why the marginal propensity to save was initially negative. Once the wealth effect was introduced, the 30

36 marginal propensity to save was shown to be consistent with economic theory and in line with previous historical estimates. The consistency of the marginal propensity to save was then tested by hypothetically increasing disposable income, estimating future values of permanent and transitory income, savings and the marginal propensities to save. The results of the test showed that a one-time increase in disposable income, similarly to the tax rebate of 2001, dramatically increased the marginal propensity to save, but that the marginal propensity to save returned towards its original level as the income effect disappeared. In the final period of the test, the marginal propensity to save rose because of a sudden and sharp decline in wealth as represented by the S&P500 index. Some commentators have noted, based on observed levels of personal saving and the ratio of personal saving to disposable income, that personal saving in the U.S. has declined sharply over the past couple decades (Feldstein, P. 116; Roach, P. 35). They claim that this observed decline in personal saving is problematic for the U.S. economy because it reduces the amount of funds available for investment and capital formation (Froyen, P. 289). However, a deeper analysis of household saving that takes into account the increase in value of financial assets reveals that the marginal propensity to save is not very different from its historical estimates. This suggests that while the increase in household wealth in the U.S. may have led to some dissaving relative to 31

37 previous historical periods, the willingness to save as displayed by the marginal propensity to save has not been altered significantly. These results of this study lend support to the idea that meaningful savings estimates and marginal propensities to save can be generated using estimates of permanent and transitory income. However, changes in wealth and interest rates need to be taken account of in periods where these variables undergo substantial transformations. 32

38 References Bentzel, Ragnar and Lennart Berg The Role of Demographic Factors as a Determinant of Savings in Sweden. Ed. Franco Modigliani. New York: St. Martin s Press, Byrns, Ralph and Gerald Stone Economics Glenview: Scott, Foresman and Company (1989) Callen, Tim and Christian Thimann Empirical Determinants of Household Saving: Evidence from OECD Countries IMF Working Paper 181 (1997). Chiang, Alpha C. Fundamental Methods of Mathematical Economics New York: McGraw-Hill, Inc. (1984) 221. Deaton, Angus Savings and Inflation: Theory and British Evidence. Ed. Franco Modigliani. New York: St. Martin s Press, Feldstein, Martin Does the United States Save Too Little? American Economic Review, 67, February 1977; Formaini, Robert L. and Richard McKenzie Where Have all the Savings Gone? Southwest Economy Federal Reserve Bank of Dallas Sept/Oct 1999: 5-9. Friedman, Milton A Theory of the Consumption Function Princeton: Princeton University Press (1957) 10-11, 25-26, 31, 91-93, , 196. Froyen, Richard T. Macroeconomics, Theories and Policies Upper Saddle River: Prentice Hall (1999) 73 75, Greene, William H. Econometric Analysis Upper Saddle River: Prentice Hall (2000) , 299. Higgins, Matthew Demography, National Savings and International Capital Flows FRBNY Staff Report 34 (1997). Kennedy, Peter A Guide to Econometrics Cambridge: The MIT Press (1998) Mayer, Thomas Permanent Income, Wealth, and Consumption: A Critique of the Permanent Income Theory, the Life-Cycle Hypothesis, and Related Theories. Berkeley and Los Angeles: University of California Press, Ltd. (1972)

39 Modigliani, Franco The Life Cycle Hypothesis of Saving and Intercountry Differences in the Savings Ratio. The Collected Papers of Franco Modigliani Ed. Andrew Abel 5 vols. 1 st ed. Cambridge: The MIT Press, Vol. II Roach, Stephen Spending Ourselves into Oblivion. The New York Times, December 11, 1998; 35. Romer, David Advanced Macroeconomics New York: McGraw-Hill Higher Education (2001) Serlenga, Laura Three Alternative Approaches to Test the Permanent Income Hypothesis in Dynamic Panels diss., U of Edinburgh, Ul Haque, Nadeem M., Hashem Pesaran and Sunil Sharma Neglected Heterogeneity and Dynamics in Cross-Country Savings Regressions IMF Working Paper 128 (1999). 34

40 Robert Bruce Lung grew up in Reston, Virginia. After graduating from high school in Vita 1986, he served as an infantryman for three years in the U.S. Army. He then went to college and received a B.S. in International Politics in 1994 at the Walsh School of Foreign Service at Georgetown University, Washington DC. From 1994 to 1998, Mr. Lung worked as a foreign exchange consultant at Ruesch International and later as an financial analyst in the Office of Foreign Investment Studies at the U.S. Treasury. In late 1998, Mr. Lung decided to pursue his interest in finance and economics by pursuing a graduate degree in economics at Virginia Polytechnic Institute s Northern Virginia Center. In 1999, he joined Resource Dynamics Corporation in McLean, Virginia as an Associate and in 2001 was promoted to Senior Associate. Mr. Lung s academic interests are energy economics and monetary policy. In addition, Mr. Lung is an avid runner who competes in road races ranging from 5K to the marathon and who serves on the committees of the LAWS ½ Marathon and the Cherry Blossom 10-Miler. Mr. Lung is currently located at: Resource Dynamics Corporation 8605 Westwood Center Drive Suite 410 Vienna, VA