Stochastic Implications of the Hypothesis of Permanent Income-Life Cycle: Theory and Evidence
Stochastic Implications of the hypothesis of permanent income-life cycle: Theory and Evidence
Robert E. Hall
Center for Advanced Study in the Behavioral Sciences and the National Bureau of Economic Research
The optimization of the consumer is shown to imply that the marginal utility of consumption is developed according to a random motion with trend. To a reasonable approximation, consumption itself should be developed in the same way. In particular, no variable apart from current consumption should be of any value in predicting future consumption. This implication is tested with time-series data for the United States after the war. It is confirmed for real disposable income, which has no predictive power for consumption, but is rejected for a common price index. The role concludes that the evidence supports a modified version of the hypothesis-cycle permanent income life
As a matter of theory, hypothesis-cycle permanent income of life is widely accepted as the proper use of consumer theory to the problem of dividing consumption between present and future. Under scenario, consumers are estimates of their ability to consume in the long run and after setting the current consumption to the appropriate fraction of this estimate. The estimate may be indicated in the form of plenty, after Modigliani, in which case the fraction is the annuity value of wealth, or as permanent income, after Friedman, in which case the fraction must be the same one fOut.close . The main problem in empirical research based on the assumption has been made in fitting the model that relates the current and past observed income to expected future income. The relationship usually takes the form of a fixed distributed lag, although this practice has been criticized very effectively by Robert Lucas (1976). Moreover, the delay estimate is usually distributed puzzlingly short. Equations that aim to incorporate the principle of cycle-permanent income life
This research was supported by the National Science Foundation. I am grateful to Marjorie Flavin for assistance and numerous colleagues for helpful suggestions.
[Economr political journal, 1978, vol. 86, No. 6]
© 1978 by the University of Chicago. 0022-3808/78/8606-0005S01.44
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is really little different from the simple function of the Keynesian consumption where consumption is determined by contemporary income only.
Much empirical research is seriously weakened and may not take into proper account the endogeneity of income when it is the main independent variable in the function of consumption. Classic papers Haavelmo (1943) and Friedman and Becker (1957) clearly demonstrated how the practice of rent treated as a function of exogenous consumption seriously distorts the estimated function. Even so, regressions with consumption as the dependent variable continu3e shall be assessed and interpreted within the framework of cycle-permanent income life. 1
However, in simultaneous-equations econometric techniques principles that can be used to estimate the structural function when its right important variable is endogenous, these techniques consumption recline on the hypothesis that certain observed variables, used as instruments are truly exogenous all have an important influence on income. The two requirements are often contradictory, and the valuation is based on an uneasy compromise where it is uncertain Exogeneity of instruments. Furthermore, Exogeneity hypothesis is untested.
This paper takes an alternative econometric approach to study the hypothesis cycle-permanent income life wondering exactly what can be learned from a regression of consumption where it attaches to the principle that none of the right variables are exogenous. This comes from a theoretical examination of the implications of stochastic theory. When consumers maximize utility had the fu ture, It is shown that the conditional expectation of future marginal utility is a function of the level of consumption today only that”the rest of the information is irrelevant. That is apart of a trend, marginal utility obeys a random walk. If marginal utility is a linear function of consumption, then the characteristics of the consumption stochastic involved are also those of a random walk, again apart from a trend. Regression techniques can reveal if the conditional expectation of consumption or marginal utility given past consumption and other last variable. The strong implication of the hypothesis stochastic cycle permanent income-life is only delayed a period consumption must have a nonzero coefficient in this regression. This implication can be tested rigorously without any assumptions about Exogeneity.
The theoretical implication test proceeds as follows: The simplest implication of the hypothesis is that consumption was delayed more than one period has no predictive power for current consumption. A more rigorous testable implication of the random-walk hypothesis holds that consumption is unrelatedto any economic variable that is observed in earlier periods. In particular income, retarded should not have any explanatory power with respect to consumption. Previous research on consumption has been suggested that
Examples 1 are 1972 and the Darby blinder 1977.
LIFE CYCLE – PERMANENT INCOME HYPOTHESIS
delayed income might be a good predictor of current consumption, but this hypothesis is inconsistent with the smart, forward – looking consumer behavior that forms the basis of the theory of the permanent-income. If the previous valu3e consumption incorporates all the information about the well – being of consumers at the time, then delayed values of real income should have no additional explanatory valu3e once lagged consumption are included. The data support this view – have an income lagged slightly negative coefficient in an equation with consumption as the dependent variable and delayed consumption as the independent variable. Of course, contemporary – the rent is high explanatory value, but this does not contradict the principal stochastic implication of the hypothesis-cycle permanent income life.
As a final test of the random-walk hypothesis is tested, the predictive power of the common price val3ues corporate retarded. Changes in stock prices lagged by one quarter are found to have a measurable valu3e predicting changes in consumption, which in a formal sense refutes the simple random – walk hypothesis. However, the finding is consistent with a modification of the hypothesis that recognizes a short delay between changes in permanent income and corresponding changes in consumption. The finding that consumption moves in a manner similar to stock prices actually supports this amendment to the random – walk hypothesis since stock prices are well known to obey a random walk themselves.
The paper concludes with a discussion of the implications of the hypothesis-cycle permanent income pur3e life for macroeconomic analysis and policy forecasting. If each deviation from consumición their trend is unexpected and permanent, then the best forecast of future consumption level today is only adjusted for trend. Forecasts of future changes in income are irrelevant, since the information used in preparing them and joins in consumption today. In a forecast model, consumption should be treated as exogenous variable. For policy analysis, the hypothesis-cycle permanent income life pur3e supports the modern view that only unexpected changes in consumption afiect of politics – everything known about future changes in policy and are incorporated in the current consumption. Furthermore, unexpected changes in consumption afiect policy only to the extent of permanent income afiect them, and then their efficiency is expected to be permanent. Policies that have an efficient transitional income are unable to have a transitional efficient consumption. However, None of the results of the paper imply that af3iecting income policies have no effect on consumption. For example, a permanent tax reduction generates an immediate increase in permanent income and thus an immediate increase in consumption. But the evidence that policies act only with permanent income certainly complicates the problem of formulating counter-cyclical policies that act through consumption.
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I. Theory
Consider the conventional model life-cycle consumption under uncertainty: maximize E t 2 ^ r * (1 + u (c, S) ~ x, + X) under X £ r”(1 + r) ~ r (ct + t – W t + x) = ^ t-the notation used throughout the paper is:
E t = mathematical expectation conditional on all available information
t; the 3rd = subjective rate of time preference;
r = real interest rate (rg: 8), assumed constant over time; Length – T of economic life; function () for general use u = one-period, strictly concave ct = consumption, W t = earnings; T = assets apart from human capital.
Profits, W t are stochastic and are the only source of uncertainty. In each period,”the consumer chooses consumption, cv then to maximize expected utility of lifetime in the light of all available information. The consumer knows the valu3eof W t to choose ct not make any specific assumptions on the stochastic characteristics of W t except that there is an expectation of earnings conditional fu ture today information given E t W t + x in w / s particular future not assumed to be independent, W t 6nor is required to be stationary in any sense. 2
The main theoretical result, proven in the appendix, is as follows: Theorem. “Suppose that the consumer maximizes expected utility as stated above. Then u (c t + l E t = [(1 + <5) / (l + r)] u ‘(ct).
The implications of this result are presented in a series of corollary.
The corollary i. -no information available in period t beyond the level of consumption, ct aid predicts future consumption, c t i +3 in the sense of affecting valu3e expected marginal utility. In particular, income or wealth in periods t or earlier inapplicable once known c t.
Corollary 2. – The marginal utility obeys the relation of the regression, u (c t +3 i = £ 3i +1 of u (ct) h where y = (1 + <5) / (l + r) e 3i +1 is a riot true of regression, ie, E tand 3i +1 = 0.
Corollary 3. – (The utility function is quadratic, u (ct) = – E (? – Ct) 2 (where c is the level of the joy of consumption), then the regression accurately reflects consumption, ct + 3i = P the c 0 + t – e t +3 i foot 0 = c (r – <5) / (l + r). Again, no variable observed at time t or earlier will have non-zero coefficient if added to this regression.
Corollary 4. “If the utility function has constant elasticity of substitution form, u (ct) = the ~ l) /then the following statistical model describes the evolution of consumption: fr ~ + Y * = Ki _ 1 /s t + i –
2 An analysis that illuminates the behavior of consumption when income is still displayed in Yaari (1976). Other aspects are discussed by Bewley (1976).
LIFE CYCLE – PERMANENT INCOME HYPOTHESIS
Corollary 5. “Suppose that the change in marginal utility from one period to the next is small, because the interest rate is the rate ci3ose time preference and because the stochastic change is small. Then the drink itself obeys a random walk, apart from trend. 3 specifically, ct + 3, = X + ^ t + tct the ilu “(ct)+ The most top-order terms where X t [(1 + <5) / (1 + r)] rose to power of the reciprocal of the elasticity of marginal utility
/ ii Xu ‘(ct) / c t u “(ct)
The growth rate, A t exceeds one because u is negative. Can change over time if the elasticity of marginal utility depends on the level of consumption. However, it seems likely that the constancy of X t be a good approximation, at least over a decade or two. Moreover, the factor l / u “(ct) in the disturbance is of little concern in the regression work, you may enter a soft Heteroscedasticity, but not associated with the results the ordinary least squares. From this point on,et to be redefined or the incorp3orate (ct) when appropriate.
This line of reasoning that reached the simple relationship conclusi3on ct = Xc t _ + et where et is unpredictable at time t – 1, is an approximation of the stochastic behavior ci3ose consumption-cycle hypothesis under permanent income Ufe . The riot, et summarizes the impact of any new information that becomes available in period t on the welfare of the lifetime of the consumer. Their relationship to other economic variables can be considered as follows. First, assets, A v are developed according to t = (1 + r £ f) (A t– _ X _ r + W t _ x). Secondly, let H t be human capital, defined as current earnings plus the present valu3e expected future earnings: H t = £ £ r ^ 0 + r) wner of W & E t W t + t t ~ T t = W v then H t is developed according to H t = (1 + r) (H t _ x – W t _ x) + S ^ = the “( 1 + r) ~ x (E t W t + x – E t W t + l _ r). Let f] t be the second term, ie, the current system valu3e changes in expectations of future earnings occurring between t – 1 and t. Then by construction,r of E t 3i _ t = 0. However, the first term in the expression for H t can enter a complicated intertemporal dependence in its stochastic behavior, only under very special circumstances whether he wants to be a random walk. The implied stochastic equation for the total abundance is A t + H t = (1 + r) (^ 4 t _ 1 + H t – – ti on c) + ex-changes in total abundance then depends on the relationship between the new information on abundance, t] t and the induced change in consumption as measured by et Under certainty equivalence, justified by quadratic utility or by the small size of the relationship is simple et et = [1 + A / ( l + r) + • • • ++ R) ~ t (XT / / rj t 3i T_3i] ot = t This is the modified valu3e of an annual increase in abundance.
3 Grange and 1976) much stronger results this Newbold (for a similar problem but assume a normal distribution for the disturbance.
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The amendment takes account of consumer plans to do that consumption grows at the proportional excess of the rate X the rest of his life. Then the stochastic equation for the total abundance is A t + H t = (1 + r) (l – at t _ 1 (^ 4 3i _ 1 + H t – i) + Y t is a random walk with trend .
Consumers, then, process all the informationón available each period on earnings ture of the current and fu. Converting data on earnings, which can have over time large movements, reliable, human capital, which takes place in a combination of a highly-reliable partner to the realization of current earnings and an unpredictable element associated with expectations that change on future earnings. Taking into account also the financial assets accumulated past earnings, consumers determine an appropriate current level of consumption. As demonstrated at the beginning of this section, this implies that the marginal utility is developed as random walk with trend. As a result of optimization of consumers, the abundance also develops as a random walk with trend. Although it is tempting to summarize the theory saying that consumption is proportional to abundance, abundance is a random walk, so that consumption is a random walk, this is not accurate. Rather, the underlying behavior of consumers making consumption and wealth grow as random walks.
All theoretical results presented in this section rest on the assumption that consumers have faced a known, constant, real interest rate. If over time the var3ies real interest rate in a way that we know for sure in advance, the results should remain true with minor amendments, mainly, X t vary over time in this account. The importance of known variations in interest rates depends on the elasticity of substitution between present and future. If that elasticity is low, the effect would be negligible. Moreover, if the real interest rate applicable between periods i and ¿+ 1 is uncertain at the time the decision of the consumption in period t is made, then the theoretical results no longer apply. However, there is strong reason to think that it predisposes the results of statistical tests in one direction or another.
II. Tests to distinguish the rent theory of Life Cycle-Permanent alternative theories
Evidence of the stochastic implications of the hypothesis-permanent cycle of life income made in this paper that all have the form of estimating a conditional expectation, E (ct r, l5 _ xt _ x), where xt is a vector _ x of the data known at time t – 1 and then test the hypothesis that the conditional expectation is not really a o3ix t _ 1 function 4 in all cases, the expectation-conditional.
4 the nature of the hypothesis being tested and the test statistics themselves are essentially the same as in the large body of research on efficient capital markets (see Fama 1970). Sims (1978) is the statistical problem of asymptotic distribution tion of regression coefficients j vf _ this kind of regression, with conclusi3on standard formulas that are correct,
LIFE CYCLE – PERMANENT INCOME HYPOTHESIS
is linear in xt _ l5 and that the evidence is the F-test for usually exclusi3on a group of variables in a regression. Again, the regression is the appropriate statistical technique to estimate the conditional expectation, and makes no claim that the true structural relationship between consumption and its determinants is revealed by this approach.
What output cycle hypothesis of permanent income-life detect this kind of test? There are two main lines of thought about eating that contradict the hypothesis. One holds that consumers can not smooth out transitory fluctuations of consumption in excess income because of liquidity constraints and other practical considerations. Consumption is therefore too sensitive to current income consistent with the principle of cycle-permanent income life. The second maintains that a reasonable measure of permanent income is distributed as a delaylast real income, so the function of the service should relate real consumption with a delay so distributed. A general function of consumption that incorporated both ideas could leave consumption respond with a fairly large coefficient contemporary income and then have a distributed lag over past rent. Such functions of consumption are in widespread use and fit the data extremely well. But his assessment implies very substantial issue that income and consumption are determined jointly. The assessment by least squares provides no evidence whether the observed behavior is the assumption cycle permanent income-life or non-constant. The simultaneous assessment could provide evidence, but would rely on crucial assumptions Exogeneity. The regressions of consumption on the consumption delayed and delayed income can provide no evidence of Exogeneity assumptions, as this section will show.
Consider first the issue of excessive sensitivity of consumption to transitory fluctuations in income, which has been accentuated by Tobin and Dolder (1971) and Mishkin (1976). The simplest alternative hypothesis assumes that a fraction of the population consume all their disposable income simply, instead of obeying the role of cycle-permanent income consumption of life. Assume that this fraction i win a share of total income, and let the c [- IYT be your consumption. The other part of consumption, c opinion, follows the rule stated above: KC [of c “3i _ t = ‘+ st The conditional expectation of total consumption, cv given their own valu3e was delayed, and For example, two were delayed val3ues of income,kE (ct | ct UYT _ _ _ l9 t 2) = E (ct ct – U t – U t – 2) + t-i ^ ti on u c_ tt E (c) = ^ E (t ct _ 1 yt yt _ 1 _ 2) + k (ct _ 1 – IYT _ x).’s assume that if disposable income obey a univariate autoregressive process of the second order so that E (t ct t _ _ _ UYT 2) = p 1 and t – 1 + E (ct | c t _ u _ u t i-I Jt-th of p 2-2-Jt ^ ti = c + + tyyt-i-i-of Wiyt ~ ~ A * (Pi-cycle hypothesis of permanent income life will be rejected unless p 1= K and p 2 = 0, ie unless disposable income and consumption obey exactly the same stochastic process. If they do, permanent income and observed income are the same thing, and liquidity – the fraction of the population is obliged to obey the hypothesis anyway, thus confirming the hypothesis. The proposed test
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regression involving the 3i ct ct t 3i _ _ _ 2 andj 3i reject the hypothesis cycle-permanent income for life in the liquidity-liquidity model simple-bound whenever the latter is materially different from prev.
The approach of the distributed delay permanent income was first suggested by Friedman (1957, 1963) and has figured prominently in functions consumicióion since. Distributed delays are not necessarily incompatible with the hypothesis cycle-permanent income-life if the rent is due a stochastic process stable, if there is a structural relationship between innovation in income and consumption (Flavin 1977). 5 still, consumer theory presented above eliminates any additional prophetic valu3e a distributed lag of income (income excluding contemporary) in a regression containing delayed consumption. If consumers use a distributed nonoptimal delay in forming their estimates of permanent income, then this central implication of the hypothesis-cycle permanent income life is false. This case is easier to establish for the simple or delay Koyck geometric distributed, ct – an IT 5 ^ = 0 or P and P ti ct = c + a Jr assume, as before, thatt autoregressive process obeys second-order, E (yt | yt ct _ 1 _ l5? t _ 2) = i + PiJt-Piyt-2-then the conditional expectation is E 3i (c ct t ^ t -UJT-i) = P ct + i + a upiJt-P2Jt-2 ‘for the l ° ng as income is correlated series (px # 0 op 2 ^ 0)> this conditional expectation does not depend solely on 3i _ ct The approach of the distributed delay permanent income was first suggested by Friedman (1957, 1963) and has figured prominently in the consumption functions ever since. Distributed delays are not necessarily incompatible with the hypothesis cycle-permanent income-life if the rent due process estocAstico stable, if there is a structural relationship between innovation in income and consumption (Flavin 1977). 5 still, consumer theory presented above eliminates any additional prophetic valu3e a distributed lag of income (income excluding contemporary) in a regression containing delayed consumption. If consumers use a distributed nonoptimal delay in forming their estimates of permanent income, then this central implication of the hypothesis-cycle permanent income life is false. This case is easier to establish for the simple or delay Koyck geometric distributed, ct – a ti on P 5 ^ = 0 = ti yocto P c + a Jr assume, as before, that t obey an autoregressive process in Second-order, E (yt | yt ct _ 1 _ l5? t _ 2) = i + PiJt-Piyt-2-then the conditional expectation is E 3i (c ct t ^ t-UJT-i) = P ct + i + a upiJt-P2Jt-2 ‘for the l ° ng as income is correlated series(px # 0 op 2 ^ 0)> this conditional expectation does not depend solely on 3i _ ct-cycle hypothesis and permanent income life will pur3e refuted. The discussion of the specifics of the case of uncorrelated income seems unnecessary since the income is in fact highly serially correlated. With this minor qualification, the proposed test method will detect if a delay of Koyck if present and thus refute the hypothesis cycle-permanent income life.
It can be shown that the test also applies to general distributed lag model used by Modigliani (1971) and others. If the delay in the underlying structural function is nonoptimal consumption, income will have delayed additional predictive power for current consumption beyond that of delayed consumption, so the hypothesis cycle-permanent income life will be rejected. The data generated by consumers using an optimal distributed lag of current and past income in making consumption decisions will not cause rejection. This demonstrates the crucial distinction between structural models which include rent regressions contemporary evidence of this paper where the principle of evidence involves only inclusi3on delayed variables.
This section has shown that simple tests of the predictive power of variables with the exception of delayed consumption can detect departures from the hypothesis-cycle permanent income pur3e life in both directions have been suggested in prior research extensively about drinking. Excessive sensitivity to current income because of liquidity constraints and not
5 1976) arg5ues Lucas (convincingly that the stochastic process for income will shift if the rules of the policy change.
LIFE CYCLE – PERMANENT INCOME HYPOTHESIS
TABLE 1
regression results for the basic model. 1948-77
Ued to Constant Ec R2 SE DW statistic Statistic
l.ü.. 2 1.0 -1.0 -. 014 .983 (.003) .996 (.001) 1,011 (.003).000735 .00271 .0146 .9964 .9985 .9988 2.06 l.ü. .2 1.0 -1.0 -. 014 .983 (.003) .996 (.001) 1,011 (.003) .000735 .00271 .0146 .9964 .9985 .9988 2.06
1.2 1.3. 1.83 1.70 1.2 1.3. 1.83 1.70
Note. -The number in parentheses in this and subsequent regressions are standard errors.
optimal behavior will delay predictive power distributed additional income beyond the delayed of delayed consumption in a regression for current consumption. The discussion in this section focused on the possible role of laggedincome because that role is so closely associated with alternative theories of consumption. Valid tests can be performed with the variable known in period t – 1 or earlier. The additional evidence presented in the next section using additional val3ues consumption delayed and delayed val3ues price of common stock. Both variables have plausible justifications, but less closely related with the competing theories of consumption.
III. The data and results for the basic model
The most thorough research on consumption has distinguished between investment and consumption activities of consumers by investing in items that removed consumer and the addition of imputed service flowof action items for consumption. That the purposes of this paper, however, is more satisfying simply examine the consumption of nondurables and services. All the theoretical foundations of the aggregate consumption function applied to individual categories of consumption too. Drop items altogether avoids the suspicion that the results are an artifact of the procedure for imputing a service flow to the action items. The consumption data used throughout the study, then, can be defined exactly as consumption of nondurables and services in 1972 U.S. dollars of national income accounts and the proceeds divided by U.S. population. All data are quarterly.
Table 1 presents the results of fitting the basic relationship of the regression between the current marginal utility and backward predicted by the theory of cycle-permanent income pur3e life. Equations 1.1 and 1.2 are for the utility function of the constant-elasticity, with a = 0.2 and 1.0, respectively. Equation 1.3 is for the quadratic utility function exactly, or for any utility function approximately, and is a regression of consumption on their own simply valu3e was delayed and a constant. The three equations to show that the prophetic valu3e
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delayed marginal utility for the current marginal utility is extremely high, ie, the typical information that becomes available in each room, as measured by the E, has only a small impactNot for consumption or marginal utility. Of course, this is no more than a theoretical interpretation of the well known fact that consumption is highly correlated series. Ci3ose adjustment of the regressions in Table 1 is not itself confirmation of the hypothesis-cycle permanent income of life, since the hypothesis makes no prediction about the variability of permanent income and the change resulting from £. the theory is compatible with any amount of unexplained variation in the regression.
No statistical criterion for usable option among the three equations in Table 1. that the transformation of the dependent variable eliminates the simple principle of least squares. Under assumption of a normal distribution for the E “is a probability function with an additional term, the Jacobian determinant, taking account of the transformation. However, for this sample proved to be an increasing functiono There is no criterion for statistical usable option among the three equations in Table 1. that the transformation of the dependent variable eliminates the simple principle of least squares. Under assumption of a normal distribution for the E “is a probability function with an additional term, the Jacobian determinant, taking account of the transformation. However, for this sample, proved to be a function of increasing or all values, so no expert of the maximum likelihood available. This seems to reflect the operation of Corollary 5 that – the e / s are small enough that any specification of the marginal utility is essentially proportional to consumption itself, and content cash-cycle theory of permanent income life should make consumption itself develops as random walk with trend. From this point on, the paper will discuss only the equation 1.3 and its extensions to other variables.
The principal stochastic implication of the hypothesis-cycle permanent income of life is that no other variables observed in the fourth / – 1 or earlier of the can help predict the residuals of the regressions in Table 1. Before using formal statistical tests, it is useful to consider the waste themselves. The pattern of residuals is extremely similar in all three regressions, but the residuals themselves are easier to interpret for the equation 3, where units are per capita consumption in 1972 dollars. These residuals are shown in Table 2.
The standard error of the residuals at 14.6, so roughly six of the observations exceed 29.2 in magnitude. There are in fact six. Three drops in consumption, and of these, a standard date coincides with recessions: 1974:4. Milder recessions contribute five drops of less than two standard deviations: 1949:3, 1953:4, 1958:1, 1960:3, and 19704. The other major decline in consumption is associated with the Korean War, in 1950:4. Most of the drop in consumption occurred quickly, in one or two quarters. The only major exception was in the period from 1973:4 to 1975:1, when they happen straight six quarters of consecutive decline. On the side is passion, there is little consistent evidence of any systematic tendency for consumption to recover in a regular pattern after a setback. The largest single increase occurred in 1965:4. This, together with three successive increases in 1964, considers the entire increase in the tendency in relation to the consumption boom associated with prolonged mid 60s and late.
LIFE CYCLE – PERMANENT INCOME HYPOTHESIS
TABLE 2 residuals from the regression of consumption on delayed consumption, 1948-77
1948: 1956: 1964: 1972:
1 …. 5 1. . 2.8 1. … 17.8 1. .. 20.0 1 … 5 1. . 2.8 1. .. . 17.8 1. . . 20.0
2 … 8.0 2 … -10.1 2 …. 20.0 2 … 32.7 2 … 8.0 2 .. . -10.1 2 … . 20.0 2 .. . 32.7
3. . . . … -15.5 3. -6.1 3 …. 14.6 3 .. 8.4 3. . . . -15.5 3 … . -6.1 3 … . 14.6 3 .. 8.4
4 … 3.5 4 ..1.2 4 …. -4.4 4 … 21.1 4 … 3.5 4 .. 1.2 4 … . -4.4 4 .. . 21.1
1949: 1957: 1965: 1973: 1949: 1957: 1965: 1973:
1 … .. -8.6 1. -10.8 1 … 5.8 … 1 .. 8.0 1 -8.6 1 .. . -10.8 1 … 5.8 1 .. 8.0
2 …. .. -8.5 2. -6.1 .. 2 … 5.2 2. -15.6 2 …. -8.5 2 .. . -6.1 2 … 5.2 2 .. . -15.6
3 … .. -27.2 32.4 3 …. 10.2 3 .. 3.0 3 … -27.2 3 .. 2.4 3 … . 10.2 3 .. 3.0
4. . . -. 1 4 … -13.6 4. … 38.7 4. .. -32.8 4. . . -. 1 4 .. . -13.6 4. .. . 38.7 4. . . -32.8
1950: 1958: 1966: 1974: 1950: 1958: 1966: 1974:
1 … 5.6 1 … -29.1 1 .. .. -1.3 1 … -27.3 1 … 5.6 1 .. . -29.1 1 .. . . -1.3 1 .. . -27.3
2 … 23.88.3 2 … 2 .. .. 3.7 2. -23.4 2 … 23.8 2 .. 8.3 2 … 3.7 2 .. . -23.4
.. 3 … 15.5 3. 14.3 3 … _1.9 3 … -16.6 3 … 15.5 3 .. . 14.3 3 … _1.9 3 .. . -16.6
4 … .. -31.0 4. -1.9 4 …. -12.4 4 … -42.8 4 … -31.0 4 .. . -1.9 4 … . -12.4 4 .. . -42.8
1951: 1959: 1967: 1975: 1951: 1959: 1967: 1975:
1 …16.0 1 … 15.1 1 …. 10.2 1 … -5.8 1 … 16.0 1 .. . 15.1 1 … . 10.2 1 .. . -5.8
2 … -24.8 2 .. 3.8 .. 2 … 2.0 2. 25.6 2 … -24.8 2 .. 3.8 2 … 2.0 2 .. . 25.6
3 … 9.0 3 … -2.7 3 …. -2.8 3 … -21.3 3 … 9.0 3 .. . -2.7 3 … . -2.8 3 .. . -21.3
4. -6.1 .. 4 .. 1.1 4. … -7.5 4 … 94. .. -6.1 4 .. 1.1 4. .. . -7.5 4 .. .9
1952: 1960: 1968: 1976: 1952: 1960: 1968: 1976:
1 … .. -15.1 1. -5.6 1 …. 15.6 1 … . 24.4 1 … -15.1 1 .. . -5.6 1 … . 15.6 1 .. . . 24.4
2 … 18.0 2 .. 8.8 2 … 7.9 … 2 .. 8.3 2 18.0 2 .. 8.8 2 … 7.9 2 .. 8.3
.. 3 … 10.0 3. -24.3 3 …. 22.2 3 ..2.3 3 … 10.0 3 .. . -24.3 3 … . 22.2 3 .. 2.3
4 … 8.6 4 … -10.1 4 …. -8.1 4 … 30.4 4 … 8.6 4 .. . -10.1 4 … . -8.1 4 .. . 30.4
1953: 1961: 1969: 1977: 1953: 1961: 1969: 1977:
1 … -1.6 1 .. 1.8 1 …. 8 1 … -1.8 1 … -1.6 1 .. 1.8 1 … .8 1 .. . -1.8
2 … .. -1.0 2. … 10.1 2. -5.32 … -1.0 2 .. . 10.1 2 … . -5.3
3 … .. -22.1 3. -16.9 3 …. -2.4 3 … -22.1 3 .. . -16.9 3 … . -2.4
4 … .. -27.0 4. 15.8 4 .. .. 3 4 … -27.0 4 .. . 15.8 4 .. . .3
1954: 1 … -. 1 1962: 1 … -1.7 1970: 1 … 4.0 1954: 1 … -. 1 1962: 1 .. . -1.7 1970: 1 … 4.0
-2.4 2 .. 2 … … 3.4 2. -12.3 2 … -2.4 2 .. 3.4 2 … . -12.3
3 …. .. 11.9 3. . -. 8 3 …. -. 3 3 … . 11.9 3 .. . . -. 8 3 … . -. 3
4 … 7.4 4. .. 6 4 …. -21.5 4 … 7.4 4. . .6 4 … . -21.5
1955: 1 … 6.1 1963: 1 … -8.4 1971: 1. .. 1.5 1955: 1 … 6.1 1963: 1 .. . -8.4 1971: 1. .. 1.5
2 … 7.0 2 … 1.3 2 …. -2.4 2 … 7.0 2 .. . 1.3 2 … . -2.4
3 … -. 83 … … 11.7 3. -14.6 3 … -. 8 3 .. . 11.7 3 … . -14.6
4 … .. 22.3 4. -6.3 4. … -6.6 4 … 22.3 4 .. . -6.3 4. .. . -6.6
The data contain no obvious refutation of the unpredictability of the residuals of the basic model, but, just as a study of stock prices will never convince the “Chartist” tile that is trying to predict fu fu ture, the believer confirmed in regular fluctuations in consumption will not be shaken by the data only. Most powerful methods to summarize the data required.
IV. Consumption can predict its own values beyond?
The testable implication simplest pur3e life cycle – the permanent income hypothesis is that only delayed the first aid valu3e of consumption predicts the current consumption. This implication is refuted if the consumption had a defined cyclic pattern described by a differential equation of second
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or higher order. 6 smart consumers ought to be able to offset any cyclical pattern and restore the cyclical behavior of optimal consumption is not predicted by the hypothesis. The following regression test this implication by adding extra delays val3ues consumption to equation 1.3:
c t = 8.2 + 1,130 ^ ..! – 0.04 (k f^ 2+ 0,030 _ _ 3– 0.113í: f_ 4;
(8.3) (0,092) (0,142) (0,142) (0,093)
R 2 = .9988, s = 14.5, DW = 1.96.
The contribution of additional delayed val3ues is to increase the forecast accuracy of current consumption by about 10 cents per person per year. The F-statistic for the hypothesis that the coefficients of ct _ 2 £ f -3, YCF _ 4 are the zero is 1.7, lower critical point of the F-distribution of 2.7 in the 5 percent level well. Only very weak evidence against the hypothesis cycle-permanent income pur3e life appears in this regression. In particular, there is no evidence that consumption defined difference equation obeys a second-order stochastic able to generate cycles. In this respect, the consumption gap sharply from other aggregate economic measures, which typically obey the order second-order regression.
V. It can predict the consumption of disposable income?
If the rent is overdue has substantial predictive power beyond that of delayed consumption, then the hypothesis is refuted cycle-permanent income life. As discussed in Section II, this evidence would support the alternative visions that consumers are excessively sensitive to current income, or more generally, using an ad hoc, distributed late last nonpptimal of income in making consumption decisions.
Table 3 presents a variety of regressions that test the predictive power of real disposable income per capita, measured as current dollar disposable income of the national accounts divided by the implicit deflator for consumption of nondurables and services divided by the population and . Equation 3.1 shows that a single level of disposable income slowed has essentially no valu3e prophetic at all. The coefBcient of jf _ 1 is slightly negative, but this is easily explained by sampling variation only. The F-statistic for all but exclusi3on constant andthe ct _ x is 0.1, far below the critical efforts of 3.2 Fof Eq 3.9, circulated a year-long delay estimated without constraint. The first delayed valu3e disposable income has a positive coefiente mild, but this is more than offset by negative coefficients for the three longest delays. The “lasting marginal propensity to consume,” measured by the sum of salary, is actually negative, although again this could be done easily from sampling variation. The F-statistics for the common prophetic valu3e four variables delayed income is 2.0, slightly less than the 2.4 critical valu3e in the 5 percent level. Note
1970) calyx of Fame (proof similar to asset prices proof of the “weak form”.
TABLE 3 Equations linking consumption with consumption and delayed beyond the levels of real disposable income
Equation No. 2s and DW equation R F F *
3.1 C t = -16 + 1.024 c ^ i – t _ j 010 and.9988 14.7 1.71 .1 3.9
(11) (.044) (.032)
% 3.2 c t = -23 + 1,076 f t_! + • f049j _ 1-051 fj _ 2% 3.2 ct = -23 + 1,076 FT_! + • 049jf_1 – 051 jf_2
.9989 14.4 2.02 2.0 2.4
.9988 14.6 1.92 2.0 2.7 .9988 14.6 1.92 2.0 2.7
<*> (11) (.047) (.043) (.052)
3.3 c t = -25 + M3C t i + X fi> ‘ti Z& = – 077
(11) (.054) i = 1(.040)
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hypothesis that the cycle-permanent income pur3e life would be rejected if the size of the test was 10 percent or higher.
Equation 3.3 Settings delayed 12-quarter Almon to see if a long distributed lag can compete with delayed consumption as a predictor for current consumption. Again coeff3icients the sum of the delay is slightly negative, now almost significantly so. The F-statistic for the hypothesis of no contribution from the distributed delay full ci3ose income is again the critical valu3e.
The sample evidence of the relationship between consumption and income is lagging seems to say: There is a statistically marginal and numerically smallña between consumption and the very recent lev3eis disposable income. Coeff3icients The sum of the delay is slightly negative. Furthermore, no evidence at all support the view that a distributed lag over several years covering helps predict consumption. This evidence casts some doubt just assuming cycle-permanent income of life in its purest form but is absolutely destructive to a more flexible interpretation of the hypothesis, to be discussed soon.
VI. Abundance and consumption
Of the many alternative variables that might be included on the right side of a regression test the hypothesis cycle-permanent income pur3e life, some measure of abundance is one of the leading candidates. The theory and practice agree that the prevailing contemporary abundance has a strong influence on consumption, wealth long overdue is a logical variable to test. Once más the hypothesis implies that the abundance measure previous quarter should have no predictive valu3e regarding the consumption of this room. All information contained in abundance is delayed summarized delayed consumption. Quarterly data on val3ues reliable feature not available for most categoriesof feature. For an important category, however, essentially perfect data are available at any frequency, namely the market valu3e corporate action. Tests for random-walk hypothesis does not require a comprehensive wealth variable, so a test based on common prices is appropriate, although the resulting equation does not describe the structural relationship between wealth and consumption. The tests reported here are based on the comprehensive index and the poor standard of stock prices deflated by the implicit deflator for nondurables and services divided by the population. This variable will be calleds. It makes a clear statistical contribution to the prediction of current consumption:
c t = -22 + 1,012 ^ -! 0.223.T +, -! – 0.258j t^ 2+ 0,167 _ _ 3 to 0120^ _ 4
(8) (0,004) (0,051) (0,083) (0,083) (0,051)
R 2 = .9990, SE = 14.4, DW = 2.05.
The F-statistic for the hypothesis that common coeff3icients prices are delayed zero is 6.5, well above the critical valu3e of 2.4 in the 5 percent
LIFE CYCLE – PERMANENT INCOME HYPOTHESIS
level. In addition, each factor considered separately is clearly different from zero secven-test the “generally. However, the improvement in the predictive power of the regression, while statistically significant, is not numerically large. The standard error of the regression is about 20 cents per person per year smaller in this equation compared with the basic model of equation 1.3 ($ 14.40 versus $ 14.60). The stock price ofthe prophetic valu3e of Mostofthe comes from the change in price in the immediately preceding quarter. A smaller contribution is made by the change in price prior 3 quarters. Use the Almon lag technique for both ofthe lev3eis and differences in stock price could not turn up any evidence of a longer distributed lag
VII. Implications of empirical evidence
Pur3e Life-cycle hypothesis that the permanent income –ct can not be predicted by any variable dated t – 1 or earlier except ct _ x-is rejected by the data. The stock market is valuable in predicting consumption 1 quarts in the future. Most ofthe predictive power comes from the s & t -. But the data seem entirely compatible with a modification of the hypothesis that leaves its central conten3i unchanged. Suppose that consumption depends on permanent income, and that the marginal utility actually develops as random walk with trend, but that a certain portion of consumption takes time to adjust to a change in permanent income. Then the variable that is correlated with permanent income in t – 1 will help in predicting the change in consumption in period “, as part of that change is delayed response to previous changes in permanent income. They find that consumption is only weakly associated with their own past and recent val3ues immediate val3ues changes in stock prices have a modest predictive valu3e are compatible with the hypothesis that change in cycle-permanent income life .
There are still any problems in the role of consumption, it seems little reason to doubt the assumption cycle-permanent income life. Within a framework in which permanent income is a variable unnoticed while the data seems quite consistent with the hypothesis, provided a short delay between permanent income and consumption is recognized. Of course, the assumption ofthe acceptance does not yield a complete function of consumption, since it has not developed any permanent income equation. The evidence against the ad-hoc distributed lags model that relates permanent income with actual income seems fairly strong. The task of further research is the most satisfying cr3eate a model for permanent income, one that recognizes that consumers value their economic welfare in a smart way that involves looking into the future.
It is important not to treat any ofthe equations of this paper as structural links between consumption and the variables used to predict it.
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For example, Table 3 should not be read as implying that income has a negative effect on consumption. The effect of a particular change in income depends on the change in permanent income induced, and this can range anywhere from no effect to an effect of the dollar-for-dollar, depending on how the consumers evaluate the change. In any case, regressions minimize the structural relationship between the change in real income and the change in consumption because they omit the contemporary part of the relationship.
VIII. Implications for analysis and policy outlook
Low-cycle hypothesis Permanent income pur3e life, a forecast of fu ture consumption level obtained by extrapolating the historical trend today is impossible to improve. The results of this paper have implicastrong ion beyond the next drink of the rooms should be treated as exogenous variable. There’s no point in income and then relating the forecast fu ture with income, since any information available today on the future income and is incorporated in today’s permanent income. Forecasts of consumption next room can be improved slightly with current stock prices, but no further improvement can not be achieved in this manner most recent quarter.
Regarding the analysis of stabilization policy, the results of this paper go no further than supporting the view that the policy only affects consumption affects both as permanent income. In the analysis of policies that are known to leave permanent income unchanged, consumption can be treated as exogenous. In addition, only new information about taxes and other policy instruments can affect permanent income. Beyond these general issues, the policy analyst must answer the difficult question of the effect of a given policy on permanent income to predict its effect on consumption. Regression of consumption on current and past income val3ues is no valu3e anyone in answering this question.