WiGRICULTURAL ECONOMICS RESEARCH

A Journal of Economic and Statistical Research in the Department of Agriculture and Cooperating Agencies

Volume X JANUARY 1958 Number 1

The Implications of Friedman's Permanent Income Hypothesis for Demand Analysis

A Review by Marc Nerlove The measurement of income elasticities of demand for farm products, both individually and as an aggregate, is a fundamental problem which has concerned a considerable number of agricultural economists. Professor 's recent study, A Theory of the Consumption Function (3),1 investigates the relation between aggregate consump- tion and aggregate income. Though addressed to the general economist, it is of special interest to economists and statisticians engaged in the study of factors affecting the con- sumption and prices of farm products. Friedman presents a fundamentally new view of the consumption function, which he terms "the permanent income hypothesis." Cen- tral to this hypothesis is a sharp distinction between measured income, or that which is recorded for a particular short period of time, and permanent income, a longer term concept. His analysis, if correct, suggests that current methods for measuring income elasticities of demand are generally inadequate. This paper contains a summary of Friedman's position; an appraisal of its implications for the analysis of demand for in- dividual commodities; the formulation of an alternative to the permanent income hypo- thesis; and a test of their relative merits. It is hoped that this presentation will make the permanent income hypothesis more widely known and will stimulate further investi- gations in this area by agricultural economists.

The permanent income hypothesis can be sum- Implications of the pure theory of consumer be- marized in a system of three simple equations havior.—Equation (1) is Friedman's consump- (3, p. 222). Let cp and yp be undefined magni- tion function; it asserts that planned or perma- tudes which are called "permanent consumption" nent consumption (cp) is a fraction (k) of perma- and "permanent income," respectively; let c and nent income (yp) that does not depend on the size y be measured consumption and measured income; of permanent income but does depend on other and let or and yT be the difference between the variables, e. g., the interest rate (i), the ratio of measured and permanent magnitudes—what nonhuman wealth (material wealth) to income Friedman calls the "transitory" components of (w), and other factors affecting consumer tastes consumption and income—then: for current consumption versus accumulation of assets (u) 2 Friedman derives equation (1) from (1) cp= k (i, w, u) yp, (2) 11= Up-FUT, 2 One of the more important of these may be the vari- (3) C=CP±CT. ability of income. For example, farmers and small Italic numbers in parentheses refer to Literature Cited, businessmen tend to save a larger proportion of their page 13. incomes than do civil servants. • 1 the pure theory of consumer behavior as stated Essentially, what Friedman has done is to sup- in its simplest form, (3, Chapter II, pp. 7-19). pose that although "consumption" is related to This is a decided advantage as compared with "income", both variables are subject to errolik most theories of the aggregate consumption func- This is an old problem in statistics,6 but Friedmilir tion.3 The other two equations are definitional. has given it a surprising, and fruitful, new twist Permanent and transitory components of in- by giving the distinction between error and "true" come and consumption.—The real interest in the value an economic interpretation in terms of permanent income hypothesis lies, not in Fried- consumer behavior. man's formulation of the pure theory of consumer The interpretation of the permanent and tran- behavior that leads to equation (1), but rather in sitory components of either income or consumption his treatment of the relation between the unob- is slightly different, depending on whether we servable variables, cp and yp, and the variables think primarily in terms of (1) budget studies and y, which are the consumption and income we (cross-section analysis) or (2) time-series analysis actually measure. Friedman treats this relation of the aggregate consumption function. Fried- in a chapter entitled "The Permanent Income man gives the following interpretation : Hypothesis" (3, chapter III, pp. 20-37). As its The permanent component [of income] is to be in- title indicates, this chapter is the key to Fried- terpreted as reflecting the effect of those factors that man's monograph. Friedman states the central determine the consumer unit's capital value or theme as follows : wealth. . . . It is analogous to the "expected" value of a probability distribution. The transitory corn- The magnitudes termed "permanent income" and ponent is to be interpreted as reflecting all "other" "permanent consumption" that play such a critical factors, factors that are likely to be treated by the role in the theoretical analysis cannot be observed di- unit affected as "accidental" or "chance" occurrences, rectly for any individual consumer unit. The most though they may, from another point of view, be the that can be observed are actual receipts and expendi- predictable effect of specifiable forces . . . (3, pp. tures during some finite period, together, perhaps, 21-22). with some verbal statements about expectations for the future. The theoretical constructs are ex ante On this interpretation the concept of "permanent" magnitudes ; the empirical data are ex post. Yet in is closely related to that of "expected normal" order to use the theoretical analysis to interpret which I have used in several other empirical data, a correspondence must be established connectioniii between the theoretical constructs and the observed (10, 1).7 Indeed, the latter was preceded ancl■ magnitudes (3, p. 20). definitely suggested by the former. The usual way of establishing such a correspond- Two types of forces produce the transitory ence has been simply to treat current consump- component : The first is that specific to an in- tion expenditures and current income as if they dividual consumer unit. The second is not specific were the theoretical constructs. Friedman's ap- to an individual but affects all or part of the proach is different. group of consumers under consideration. For the As equations (2) and (3) indicate, Friedman sis. On several grounds a logarithmic form seems proposes the division of the measured magnitudes preferable. Friedman gives this as into two parts: the permanent component (yp or (1') log Cr—log k+log yp, Op) and the transitory component (yT or eT).4' 5 (2') log y=-log yr+log yT, (3') log c=log cr+log Cr. ° An exception is the Modigliani-Brumberg formulation, In his theoretical development, Friedman switches fre- 383-436). (7, PP. quently from the linear to the logarithmic form and back, As Friedman points out (3, p. 22), this division is but usually in his empirical applications he uses the arbitrary. At one point, Friedman generalizes his as- logarithmic form. sumption so that the observed magnitudes are divided ° See D. V. Lindley (4, pp. 218-44) for an excellent into an arbitrary number (n) of components (3, p., 186). analysis of the problem of regression when both depend- The choice of two components was made primarily on ent and independent variables are subject to error. grounds of simplicity. 7 Also Marc Nerlove, ESTIMATES OF THE ELASTICITIES OF 5 The system of equations, (1)-(3), is not perhaps the SUPPLY OF CORN, COTTON, AND WHEAT. Unpublished Ph. D. most reasonable form of the permanent income hypothe- thesis. The , Baltimore. 1956. 2 • group as a whole, the transitory factors that we . . . treat consumer units as if they regarded affect specific consumer units may tend to cancel their income and their consumption as the sum of two such components, and as if the relation between Abut by the law of large numbers, so that the aver- the permanent components is the one suggested by ge transitory component, if caused by factors of our theoretical analysis. This general approach is the first type, generally tends toward zero. On suggested by theoretical considerations, but the the other hand, transitory factors that affect all or precise line to be drawn between permanent and a large number of the members of the group do transitory components is best left to be determined by the data themselves, to be whatever seems to not tend to cancel one another. These are likely correspond to consumer behavior (3, p. 23). to be important in time-series analysis and their importance depends on the nature of the period Thus permanent income is that expected by a con- covered. Factors specific to individual consumer sumer unit as his normal income, where his ex- units are of importance primarily in the analysis pectations hold only for a finite period of the of budget data, and they depend on the nature of future. The length of this period may be called the group being studied. the economic horizon for the particular consumer. Assumptions on the relation of permanent and The concept of "permanent" is related to the transitory.—In the general form stated in equa- length of this horizon; if the horizon is short, a tions (1) to (3) (see p. 1) or (1') to (3') (see large part of any given income change will be p. 2), the permanent income hypothesis is empty : considered permanent. two additional equations have been specified but When the hypothesis is interpreted in loga- so have two additional variables. No empirical rithmic form [see equations (1') to (3' )], as- data could contradict the hypothesis as it stands. sumptions I and II should, of course, be con- Additional assumptions are therefore necessary. strued in logarithmic terms as well. The particular assumptions that Friedman makes The relation between measured consumption are as follows : and measured income.—Equations (1) to (3), plus Assumption I: The transitory components of assumptions I and II, enable Friedman to in- income and consumption are uncorrelated with one terpret the nature of the usual statistical relation- another and with the corresponding permanent ship between measured consumption and mea- components. sured income, for either time-series or cross-section Assumption II: The average transitory com- data. Suppose we compute the least-squares re- onents of consumption and income are both gression of c on y, where both c and y refer to an et observation for either (1) the same consumer unit zero.8 Friedman warns us not to interpret the perma- or (2) the same time period, depending on the nent components as corresponding to average life- nature of our data : time values : (4) c=a+by. It is tempting to interpret the permanent com- a and b are the estimated coefficients. ponents as corresponding to average lifetime values, Friedman shows that the least-squares regres- and transitory components as the difference between such lifetime averages and the measured values in a sion coefficient b may be interpreted as specific time period. Such an interpretation is not, (5) b=kPv, however, appropriate, and this for two reasons. In where P„ is the fraction of the total variance of the first place, the experience of one unit is itself but a small sample from a more extensive hypothetical income in the group (or over the period if we are universe, so there is no reason to suppose that tran- dealing with time series) contributed by the sitory components average out to zero over the unit's permanent component of income.9 As Fried- lifetime. In the second place, and more important, it man states, seems neither necessary nor desirable to decide in advance the precise meaning to be attached to "per- The regression coefficient b measures the difference manent". The distinction between permanent and in consumption associated, on the average, with a transitory is intended to interpret actual behavior : one dollar difference . . . in measured income. On our permanent income hypothesis, the size of this Assumption II is clearly unjustified for time-series difference in consumption depends on two things: data. Its chief justification for cross-section data is that it enables Friedman to explain, interpret, and predict a °To simplify the notation, the variables of which k is wide variety of empirical phenomena (3, p. 30). a function have been dropped. 3 first, how much of the difference in measured in- consideration, then the ratio of the average con- come is also a difference in permanent income, since sumption for the group to the average income only differences in permanent income are regarded as affecting consumption systematically ; second, how for the group measures k. The elasticity • much of permanent income is devoted to consump- measured consumption on measured income meas- tion. Pi, measures the first ; k, the second ; so their ures Pi,. Both parameters can be identified. If product equals b. If Py is unity, transient factors assumption II does not hold, neither Pi, nor k are either entirely absent or affect the incomes of can be measured separately; only their product all members of the group by the same amount ; a one dollar difference in measured income means can be measured. a one dollar difference in permanent income and so A similar situation arises in the application of produces a difference of k in consumption ; b is there- the permanent income hypothesis to time-series fore equal to k. If Py is zero, there are no dif- ferences in permanent income ; a one dollar difference data. As I have indicated, assumption II is un- in measured income means a one dollar difference reasonable when applied to aggregate consump- in the transitory component of income, which is tion and income over time. If assumption I only taken to be uncorrelated with consumption (by As- is made, the regression of measured aggregate sumption I) ; in consequence, this difference in measured income is associated with no systematic consumption on measured aggregate income over difference in consumption ; b is therefore zero a period of time tells us something about the (3, P. 32). product of k with 13,,, where Py measures the con- If assumption II holds and if permanent con- tribution of the permanent component to the total sumption is proportional to income, as is con- variance of income over the period in question; tinually assumed in the permanent income hypoth- it tells us nothing about k and Py separately. An esis, (5) yields an extremely simple interpreta- additional assumption or assumptions must there- tion of the regression of consumption on income. fore be introduced. Let ney be the elasticity of measured consumption A method for finding the "true" consumption on measured income as computed at the mean function from time-series data.—In his chapter, values of measured consumption and measured "Consistency of the Hypothesis with Existing income for the linear case, or as the coefficient of Evidence on the Relation between Consumption log y in the logarithmic case. Friedman shows and Income : Time Series Data," (3, pp. 115-56)dh that Friedman specifies additional assumptions approlll, (6) 'icy= PIP priate in the context of time-series analysis. That is, the income elasticity of aggregate con- Based on an examination of existing time-series sumption, as measured from budget data, meas- studies of the relation between income and con- ures not the elasticity of permanent consumption sumption, Friedman concludes that permanent in- to permanent income (the theoretically relevant come could be represented by a weighted average variables) but the proportion of the variance of of incomes for current and past years. The transi- measured income in the sample contributed by tory component of consumption is taken to be a variation in the permanent component ! On purely random error term; that is, no systematic Friedman's interpretation, therefore, the regres- relationship between the transitory components sion of measured consumption on measured in- of different time periods exists and the transitory come tells us nothing about the relation of con- components have mean zero.1° sumption to income but rather something about The particular model which Friedman con- the relation between the distributions of wealth structs to represent the relation between what and of measured income in the sample under people consider the permanent component to be consideration. and past-measured income is closely related to It should now be clear why, in dealing with Hicks' definition of the elasticity of expectations cross-section data, assumption II is an integral (1). Friedman assumes that permanent income, part of the theory, although not a necessary part. If the mean transitory components of consump- " In a later section (p. 7), it is suggested that the transitory component of consumption expenditure cannot tion and income equal zero for the sample under be so treated. 4 • yp (t), is an exponentially weighted moving aver- measured income is computed from budget data for e of past measured incomes, y(t), for time t: a group of families-the regression that has come to be called an "Engel curve"-the transitory component ar of food expenditures tends to average out, but the (7) yp(t)= a f (t-)oy (X) dX, transitory component of income does not. . . . In consequence, the elasticity of measured expenditures i1, 12 with respect to measured income reflects not only . where oc is the elasticity of expectations [consumers'] tastes and preferences but also the transitory components of income. Implications of Friedman's Hypothesis Let c f stand for the mean observed consumption on food of families with a given measured income, and Of the many implications of Friedman's per- assume that the transitory component of food ex- manent income hypothesis for the analysis of de- penditures is uncorrelated with the permanent or mand for individual commodities, we can examine transitory component of income and averages zero for the group as a whole, so that cr can be regarded only a few : (1) The effect of the type of group as the mean permanent component of food expendi- covered by the sample on income elasticities de- tures. The elasticity of Cr with respect to measured rived from cross-section data; (2) the effect of the income then is length and type of period covered on income elas- dcf dy dcf pf dye, y 13 (8) dcf y ticities derived from time-series data ; and (3) the dy Cf dye, dy ypi Cf dypf Cf dy Ypf valid way to combine income elasticities derived [where ypr represents the permanent component of from cross-section data with other time-series data income based on an economic horizon peculiar to in a demand analysis. food expenditures]." Measurement of income elasticities from cross- But, on our hypothesis, yp= /- Cp which means that section data.—Consider the planned expenditures on, or the planned quantity to be consumed of, an [if IlPt=1/P] individual item of consumption such as food. We dye, y1 dcp ky dcp y = 71y-.ypi= `Pu may expect this quantity to be related, via con- '1UPg To =7/y-Tp-I sumer tastes and preferences, to the prices (cur- so that rent and/or expected) of food and other items, nciv=?Ic or,/ n cp1/ • 15 ld to the income the family expects to receive, or The first elasticity on the right-hand side, between e permanent component of income. If current permanent food expenditures and permanent income, fith reflects the influence of tastes and preferences proper ; and expected prices are the same, we may suppose, the second, the influence of transitory factors affect- without loss of generality, that each consumer unit ing income. in a cross-section faces approximately the same It follows that the differences among groups of prices [current and/or expected]. families in the observed income elasticity of particu- Friedman describes the situation as follows : lar categories of consumption cannot be interpreted as reflecting solely the influence of differences in [A consumer unit's] . . . measured expenditures tastes or of differences in prices or similar factors on food differ from its planned expenditures because sic!] ; they of a transitory component of food expenditures, and affecting opportunities [such as income, its measured income differs from its permanent in- may [also] reflect a third set of forces, namely, dif- come because of a transitory component of income. ferences in a particular characteristic of the income When the regression of measured expenditures on "The notation in (8) is altered slightly so as to cor- " Friedman allows for the expectation of a time trend respond with that used elsewhere in this review. in permanent income. But this refinement need not con- 14 The rationale for distinguishing between permanent cern us here. components appropriate to various categories of con- " Equation (7) may be derived from the differential sumption and that appropriate to total consumption is equation given below. Although Friedman explicitly assumes that dyP the same horizon applies equally to total consumption and — =a(Y — YP)- dt its individual categories, he is in some doubt as to its In fitting his model, Friedman uses a discrete approxima- validity. As we shall see, differences in the apparent tion to equation (7), whereas, in a later section (p. 7). horizons appropriate to various categories of consumption I use a discrete form of this differential equation. Either is one of the key reasons for doubting the adequacy of approach introduces an error, the magnitude of which is Friedman's permanent income hypothesis. likely to be small. " The notation is altered from that in Friedman. • 5 distribution, the importance of transitory components penditures (for total consumption or for an in- of income (3, pp. 206-207)." dividual category of consumption) on measur If the elasticity of measured food expenditures, income tend to approximate the elasticity wit or, for that matter, expenditures on any particular respect to the permanent component of income category of consumption, with respect to measured appropriate to that group. income depends partly on the contribution of the Measurement of income elasticities from time- permanent component to the variance of measured series data.—For cross-section data, the charac- income, it follows that the income elasticity ob- teristics of the group sampled are of crucial tained from a budget study depends crucially on importance in the interpretation of income elas- the group of households covered by the sample. ticities; for income elasticities computed from For example, consider two groups, one of which time-series data, the characteristics of the period typically has highly variable incomes and the considered, particularly its length, are most im- other of which typically has stable incomes (for portant. Friedman makes this point in reference example, farmers versus civil servants) . On the to total consumption : basis of the permanent income hypothesis, we The length of the period is important because, other would expect the income elasticity for a particular things the same . . . [the contribution of the per- consumption good to be lower for the first group manent component to the variance of measured in- than for the second, even if the distribution of come], and so the observed income elasticity can be tastes, income, and the like were the same for the expected to be larger, the longer the period covered, provided that the society in question is undergoing two groups. The reason for this is simply that, a systematic secular change in income. The total for the group whose incomes are typically highly variance of [measured] income equals the variance variable, the permanent component varies much contributed by the transitory component plus the less than measured incomes; whereas, for the variance contributed by the permanent component, group whose incomes are quite stable, the varia- given our assumption that the two components are uncorrelated. The variance contributed by the tran- tion of the measured income within the group is sitory component is not systematically affected by accounted for almost entirely by the variation of lengthening the period : by definition, the transitory the permanent component. Thus we would ex- components are largely random and short-lived. pect both n„, and P„ to be smaller for the True, the variance may be larger at one time th first group than for the second. another—this is why the historical of the period are important—but there is no reason Similarly, if we compare the elasticities of ex- why it should be systematically larger or smaller for penditure on particular categories of consumption a long than for a short period. The variance con- with respect to measured income for two repre- tributed by the permanent component, on the other sentative samples, one of the urban population of hand, tends to be systematically larger, the longer the United States and the other of the total popu- the period covered, for the more widely separated two dates are, the larger will tend to be the secular lation of the United States, we might expect to difference in income between them. . . . the ratio of find the former higher than the latter, as a sample the variance contributed by the permanent component of the urban population excludes the farm popula- to the total variance [of measured income], will tion and the incomes of this population might be therefore tend to be higher, the longer the period, and expected to vary more than those of the urban to approach unity as the period is indefinitely length- ened. If secular change were the only source of group. In general, we may suppose that the more variation in the permanent component the lower limit typically stable a group's incomes the more nearly of . . . [the ratio of the variance contributed by the will an elasticity of measured consumption ex- permanent component to total variance] would be zero and this limit would tend to be approached as " This statement in qualitative form follows directly the length of the period covered approached zero. from (10). If we wish to express it in usable form Since there are other sources of variation in the no,y=n.,vp.P. permanent component [over time], all one can say is that . . . a lower limit greater than zero [will tend to we must assume, in addition to ypt=yp, that the be approached] as the length of the period approaches mean transitory components of food consumption and zero (3, pp. 125-27). total consumption equal zero. Both assumptions are questionable. The test of Friedman's hypothesis, in the Friedman finds that this expectation is well ful- section of this article beginning on page 9, appears to in- filled by the elasticities computed from regres- dicate that we cannot take the fundamental step ypr=yp. sions of measured total consumption on measured 6 income for periods of different lengths : the elas- bining cross-section and time series data." Sev- cities are systematically lower for the shorter eral recent studies of the demand for individual iperiods. With certain qualifications, this impli- commodities have attempted such combination." cation of the permanent income hypothesis may The procedure is generally to obtain an income be extended to individual categories of consump- elasticity from a cross-section sample and to as- tion : If we are willing to accept the assumptions sume that this elasticity applies, with or without underlying equation (10), then the elasticity certain minor adjustments, to the aggregates over of demand for food with respect to measured time. The income elasticity so obtained is in- income, obtained from time-series data, tends to serted into the demand function and the remain- be 17 the product of (1) the elasticity with respect ing parameters are estimated from time-series to permanent income and (2) the proportion of data. It is clear that this procedure is inconsist- the variance of measured income contributed by ent with the permanent income hypothesis. the permanent component. Thus, for example, Based on equation (10), Friedman suggests a the income elasticity computed for the period be- way to combine cross-section and time-series data tween World Wars I and II should be lower than which is consistent with the permanent income the elasticity computed for a period including hypothesis : Simply divide the income elasticity both the interwar and postwar periods.18 for a particular commodity by the income elastic- A reservation is that the assumptions on which ity of total consumption expenditures, both esti- (10) is based may not be fulfilled when we deal mated from the same budget study. In this way, with elasticities estimated from time-series. The we obtain an estimate of the elasticity of expendi- following reasons are involved : (1) The perma- tures on, or demand for, the particular commodity nent component appropriate to the particular with respect to permanent income. This estimate category of consumption under consideration may is a valid one on two assumptions only : (1) The not be the same as that appropriate to total con- same concept of permanent income appropriate to sumption. Thus, if the permanent component the particular commodity is appropriate to total appropriate to, say, food is all of measured in- consumption; and (2) the average transitory ome, the income elasticity computed for the inter- components of expenditure on, or consumption War period might be greater than, less than, or of, the commodity and of total consumption are equal to the elasticity computed for both interwar zero. An estimate of aggregate permanent income and postwar periods. (2) Systematic transitory over time may be constructed by the procedure components in the expenditure devoted to the par- which Friedman uses to estimate the consumption ticular category may occur; in general, however, function from time-series data. The resulting this might be expected to strengthen the qualita- series and the estimated elasticity with respect to tive conclusions based on the permanent income permanent incomes may be combined with other hypothesis but the quantitative relationship, (10), time-series data to obtain estimates of the other would no longer hold. parameters which appear in the demand function Combining income elasticities from cross- for the particular commodity. section data with other time-series data.—The An Alternative Hypothesis length of most economic time series is limited; A possible source of difficulty in the permanent whereas, given sufficient funds for surveys, cross- income hypothesis.—In the application of the section data are almost unlimited. It is of some permanent income hypothesis to individual cate- interest, therefore, to develop methods for corn- gories of consumption, the most important as-

17 "Tends to be" rather than "is," since the correlation sumption is that permanent income means the between prices and measured income is not taken into same thing for different categories of consump- account. " This in fact is true for meat ; see Elmer J. Working "For further discussion of the nature of this problem (14) and Marc Nerlove. THE PREDICTIVE TEST AS A TOOL and a brief survey of the literature bearing on it, see FOR RESEARCH : THE DEMAND FOR MEAT IN THE UNITED Richard J. Foote and Marc Nerlove (12). STATES. Unpublished M. A. thesis, the Johns Hopkins See, for example, (11), University, Baltimore. 1955. (12), and and Lars Jureen (18). • 7

tion and for consumption as a whole. The exact As Marshall phrases the distinction, it has to do meaning of permanent income may be inter- with the price elasticity of demand, but it is clear preted, as has been indicated, in terms of the hori- that it also applies to income. Thus, for th• zon of the consumer unit. Friedman believes that reasons Marshall suggests, a change in income there is no reason why the horizon should be the will exert its full effects on consumption only same for all individual categories of consumption after some time has elapsed. In this case, we say and some why it should differ systematically (e. g., that consumption is a function of income (and housing expenditures may be planned in terms of also possibly price) taken with a distributed a longer horizon than food expenditures). If this lag (9). is true, the concept of permanent income appli- Friedman's additional assumptions in the case cable to total consumption must be interpreted of time series analysis (see equation (7) ) show as an average of the concepts applicable to each clearly that he thinks of aggregate consumption in category (3, pp. 207, 208) . relation to income taken with a distributed lag. If both consumption and income are properly He derives this distributed lag on the basis of defined, it does not seem reasonable that the economic considerations related to the nature of horizons for different categories of consumption the transitory component of income : Any change should differ greatly from one another. Only if in income may be thought of as divided into two indivisibilities, difficulties of short-run substitu- components (just as any given income is itself tion, or various institutional factors are intro- divided into two components) . The elasticity of duced would the concept of differing horizons expectations is a measure of the proportion of the appear to be useful, but, as I have indicated else- change that is considered to be permanent. An where, it may be useful to treat this type of rigid- expression of this in difference equation form is ity differently from expectational rigidity in consumer behavior (8, 9). We thus think of (11) yp(t)—yp(t-1)=«[y(t)— expenditures for housing in terms of rental (or yp(t-1)], 0

Hum position, for example, the difficulties of the elasticity of expectations, a. Thus a should ibniding ssubstitt.utes, goo the existence ofistoclksdof dur.c- be the same for each commodity and for total ds, consumption. model can be formulated which expresses the way In addition to total consumption, the demand consumers move toward their long-run equalib- for all food and for meat are investigated. Meat rium or permanent consumption: and all food are similar commodities as compared, say, with housing or clothing, and we would not, (12) c(t)—c(t-1)=y[cp(t)—c(t-1)], therefore, expect the "horizons" appropriate to where y is the elasticity of adjustment and all these two commodities to differ greatly, although variables are expressed in logarithms.23 we might allow some difference between food and The interesting thing about this model, based meat, on the one hand, and total consumption on directly on Marshall's distinction between the the other. it short and the long runs, is that, qualitatively, Let y (t) = log of observed income during period can explain eveything that the permanent income t, hypothesis explains without introducing any dis- y p(t) = log of permanent or "expected nor- tinction between measured and permanent in- mal" income, come.24 The implications for demand analysis, c(t) = log of observed aggregate consump- however, are quite different. tion, If the income elasticities of demand for indi- qt (t) = log of the consumption of all food, vidual items are small in the short run and larger qm(t)= log of the consumption of meat, in the long run, the income elasticity of aggregate pt (t) = log of the price of food, of the price of meat.25 consumption is smaller in the short than in the p (t) = log long run. We have no reason to suppose, however, 26 For statistical purposes, these variables except for that the relation between the short- and long-run yp(t), are defined as the logarithms of : income elasticities are the same for every category for y(t), Per capita disposable personal income (Com- of consumption. Hence, the distribution of lag merce definition) deflated by the BLS con- or income need not be the same for every cate- sumer price index (1947-49=100) ; gory of consumption. The distribution of lag c(t), Per capita personal consumption expendi- tures (Commerce definition) deflated by simply appropriate to aggregate consumption is the CPI ; an average of those that apply to the individual qr(t), The Agricultural Marketing Service index of categories. per capita civilian food consumption at retail (not expenditure) ; Total civilian meat consumption per capita, Tests of the Permanent Income Hypothesis q„,(t), in pounds, excluding lard ; The Bureau of Labor Statistics index of food First test.—If Friedman's hypothesis is to pro- Pr(t), prices at retail deflated by the CPI ; vide a useful tool for the analysis of the demand P.(t), An Agricultural Marketing Service index of for individual commodities, the distribution of the retail prices of all meat excluding lard, lag should be the same for each commodity and deflated by the CPI. for similar for total consumption, or, at least, The data on observed total consumption and income commodities or groups of commodities. If we as- are not entirely appropriate for this test : the Commerce sume the distribution of lag to be generated by a definition of consumption includes many items that are model such as (11), the distribution of lag can be properly savings, and the Commerce definition of dis- summarized by the value of a single parameter, posable income excludes many items that might properly be considered as income (for example, social security taxes). Friedman has constructed series on consump- 22 For a fuller discussion see Nerlove (8) . tion and income more appropriate for work of this kind, For a derivation of equation (12), see Nerlove (9). 23 these, at the time of writing, were unavailable I have not attempted to compare quantitatively this but 24 author of this paper. The computational difficulty alternative hypothesis with Friedman's for all the data to the such series precluded their use in the he considers. I have no doubt, however, that it would of constructing prove adequate. simple test presented here. 9 • 449869-58-2

The basic equations to be estimated are the con- Regressions based on equations (16) to (20) sumption function, a demand function for all are presented in table 1. In addition to the esti- food, and a demand function for meat : mated regression coefficients, table 1 gives thigh (13) c (t) = aoo + aolYp + uo (t) square of the multiple correlation coefficient, thailir number of observations, the Durbin-Watson sta- (14) D(t) + iPf(t) + anyp (t) + (t) , tistic, the estimated or assumed elasticity of ex- (15) gm (t) = a20+ (t) aap (t) -ku2(0, pectations, and the estimated elasticity of total where uo(t), u, (t), and u2 (t) are residual terms. consumption or demand with respect to perma- It can be shown that equations (13) to (15) nent (or expected normal) income. Each regres- with the addition of an equation such as (11) , sion was run for two periods : the interwar years, which relates permanent or expected normal in- 1920-41, and the combined interwar and post- come to measured income, leads to the following war years, 1920-41 and 1948-55. system of equations : The regressions based on equation (16) indi- (16) c (t) = aooa away (t) + (1 — a)C (t— 1) + cate that the elasticity of total consumption ex- penditures with respect to income is not one as Uo (t) — (1— a) U0 (t— 1) ; suggested by the permanent income hypothesis. (17) q f (t) = a10a ai2aY (t) + (1 Tr(t — 1) + If ao, =1, as required by the permanent income anPf(t) —an (1 — a)Pf(t-1) + hypothesis, the sum of the coefficients of y (t) (t) — (1 — Ut(t— 1) ; and c ( t — 1), in the regressions based on (16), (18) q„, (t) = a20a a22aY (t) + (1 — qm(t— 1) + should equal one. Thus we can test the signifi- aziPm (t) — a21 (1 — a)p„,(t-1)+ cance of the difference between the two relevant u2(t) — (1— a) U2 (t — 1) 26 elasticities from one by testing the significance ' of the difference of the sum of the coefficients of Equations such as (16) to (18) are called the re- y (t) and c (t — 1) from one. A likelihood ratio duced equations for the system (13) to (15) .27 In test may be derived to test the null hypothesis that contrast to equations (13) to (15) , they involve the sum of the coefficients of y (t) and only observable magnitudes and may therefore c (t-1) is be estimated statistically. one. The logarithm of the likelihood ratio for the Another method, which is not generally recom- period 1920-41 is 43. For the periods 1920 41 and mended, is available for obtaining reduced equa- 1948-55, it is 12. As the value of Chi-square forilk tions for the system (13) to (15) : Simply solve one degree of freedom is 11 at the 0.001 prob-II (13) for yp (t) and substitute the result in (14) and ability level, we reject the null hypothesis and (15) ; thus conclude that the estimated elasticities of total consumption with respect to permanent income auctoo) (Inc (19) q f(t) (t) anpf+ (t) — differ significantly from one. This result, how- ao1 aoi ever, should be interpreted with care for these uo (t) reasons : (1) The use of more-or-less inappro- ao1 priate data on consumption and income may have (20) (t) =(a2o—a22am)-F c + aziPm (t) + led to the inconsistency. (2) The fact that the ao1 estimated elasticities rise when a longer period is uo (t) 28 used is consistent with the permanent income hy- U2 (t) ao1 pothesis and suggests that some transitory com- " The derivation of equations such as (16) to (18) ponent of income may be affecting the regression. from equations such as (11) and (13) to (15) is given in (3) Although the Durbin-Watson statistic does the subsection on "An indirect method for obtaining re- not indicate the presence of positive serial cor- duced equations," of Nerlove (8). relation, it is low enough to warrant caution.29 "The reader should avoid confusing these with the re- duced form equations arising in the theory of estimation both (19) and (20). In this particular instance, however, of simultaneous equations. it is plausible that such correlation is small ; hence, the a' The reason why this procedure is not generally rec- procedure, although it is not generally recommended, may ommended may be seen by examining the residual terms be applicable to this particular instance. See Nerlove (8). in (19) and (20) : since zoo(t) enters both residuals and 29 If positive serial correlation in residuals of (16) is since o(t) appears as an independent variable, one of the present, estimates of the coefficients are statistically independent variables is correlated with the residual in biased, as c(t-1) enters as an independent variable. 10 •

TABLE 1.-Demand for aggregate consumption, food, and meat based on the permanent income hypothesis: Least-squares regressions and related statistical data'.

Aggregate Food, based on equation- Meat, based on equation- consumption, equation (16) (17) (19) (18) (20) Item 1920-41 1920-41 1920-41 1920-41 1920-41 1920-41 and 1920-41 and 1920-41 and 1920-41 and 1920-41 and 1948-55 1948-55 1948-55 1948-55 1948-55

Regression coefficient for specified inde- pendent variable: y(t) 0. 729 0. 726 0. 199 0. 210 0. 351 0. 387 (. 056) (. 057) (. 030) (. 029) (. 074) (. 060) c(t) 0. 291 0. 296 0. 422 0. 554 (.028) (.016) (. 101) (.063) c(t- 1) 099 209 (.077) (.064) gi(t- 1) 182 . 266 (.128) (. 108) 1) 231 432 4..(t- (. 161) (. 117) Mt) -.065 -. 088 -. 133 -. 137 (.058) (.058) (.045) (.038) -. 475 -. 458 Pm(t) -. 470 -. 485 (.088) (.076) (.086) (.072) pf(t-1) -. 094 -. 052 (.045) (.045) p,, (t-1) -. 015 093 (.085) (.067) Constant term 315 . 122 1. 545 1. 323 1. 681 1. 682 1. 774 1. 134 2. 120 1. 855 R2 97 . 99 . 92 . 97 . 85 . 96 . 74 . 83 . 62 . 76 Number of observations_ 22 30 22 30 22 30 22 30 22 30 Durbin-Watson statis- tic, d 1. 56 1. 48 1. 86 1. 89 1. 52 2 1. 42 2. 13 2. 21 2 1. 08 3.92 /Estimate of- a 90 . 79 . 82 . 73 4. 90 4.79 . 77 . 57 4. 90 4. 79 (. 08) (. 06) C. 13) (. 11) (. 16) (. 12) The elasticity of the dependent variable with respect to per- manent income_ __ _ . 81 . 92 . 24 . 29 . 29 . 30 . 46 . 68 . 42 . 55

1 Numbers in parentheses beneath the coefficients are 3 Significant positive serial correlation. their respective standard errors. 4 Assumed. 2 Durbin-Watson test inconclusive at the 5-percent probability level.

The most interesting row of table 1 is the interwar plus postwar period in the case of meat. second from last, in which the estimates of the The only significant or inconclusive Durbin- elasticities of expectations based on the various Watson tests are also found for these regressions. regressions are presented. Although the elas- Are these differences in the elasticities of ex- ticities derived from the different equations dif- pectations among commodities and total consump- fer, depending on the length of the period, the tion significant? If they are, we have reason to differences are more marked as between com- doubt the adequacy and/or utility of Friedman's modities, especially between total consumption permanent income hypothesis as applied to in- and food, on the one hand, and meat, on the other. dividual categories of consumption. An F-test, In addition, when consumption rather than in- based on (6, pp. 100-102) , was used to test the sig- come, is used in the regressions for food and meat, nificance of the differences between the coefficients the multiple correlations are markedly lower for of c ( t-1), qt (t-1) , and qm(t-1) in the regres- the interwar period, and this is true also for the sions based on equations (16)- (18). A significant • 11 F-ratio indicates a significant difference among parameters that determine the distributions of lag. the coefficients, and, hence, among the elasticities Our basic demand equations are : of expectations for total consumption, all food, (24) cp(t) =am+ aolLY (t) + uo (t) and meat. The F-ratio for the regression using • (25) qpi(t) — + auP.,.(t) + any (t) + (t) , data for the period 1920-41 is 20, with 2 and 53 degrees of freedom; the F-ratio for the combined (26) qp,x(t)=a20+avpn, (t) a22Y (t) + /12 (t) periods 1920 41 and 1948-55 is 261, with 2 and 77 The long-run equilibrium values of aggregate degrees of freedom. Each ratio is highly sig- consumption and the quantities of total food and nificant. meat demanded cannot be observed, so equations We cannot, of course, conclude definitely on the (24) to (26) cannot be estimated. If, however, the basis of the simple, and perhaps crude, test that long-run equilibrium variables, as given by (24) to (26), are substituted in (21) to (23), we have the permanent income hypothesis is false; all we equations that contain only observable variables: can say is that it does not appear to be useful when it is applied to individual categories of con- (27) c (t)=a00-ye+awYcY (t) + (1-7 c)c(t-1) sumption.80 7 No (0 Second test.—A simpler alternative hypothesis, (28) q f(t)=--a107 fP f(t) fY (0+ based on considerations suggested by Marshall, (1 — f) qi(t-1) +7ful (t) is outlined in the previous section. If the type of (29) =a 20-y,„ + any„,p (t) + a 227 mY (t) factor suggested by Marshall is the sole cause of (1— 7„,)qm(t— 1) + 7„,u2 (t) rigidities in consumer behavior, the type of equa- Equation (27) suggests a regression of exactly tion suggested by (12) appears to be adequate to the same form as is suggested by (16) , but equa- express the relation of measured consumption for tions (28) and (29) suggest regressions that differ any particular category to permanent or long-run somewhat from those under the permanent in- equilibrium consumption. In this case, we have come hypothesis. Comparing (28) with (17) and distributed lags in both prices and income, but (29) with (18) , we see that pr (t-1) does not enter within any equation the distribution of lag is the a regression based on (28) and pm ( t-1) does not same for both price and income. In place of equa- enter a regression based on (29). The fact that tion (11), we have three equations of the same the coefficients of these variables in the regressions form as equation (12) : presented in table 1 do not differ significantly from zero or are of the wrong sign suggests that (21) c (t) — c (t-- 1) =7, [cp(t) — c (t — 1)], the alternative hypothesis may have some merit. (22) qi(t) — q f(t —1) -= f [qpf (t) —q/(t-1)], The coefficients of e (t-1), q f (t-1) and q„,(t-1), (23) q„,(t) —q„,(t-1) r---7,n[qp„,(t) —q„,(t-1)], of course, need not be the same. Regressions based where Op (t) qpf (t), and qpn,(t) are the long-run on equations (27) to (29) are presented in table 2 equilibrium values of total consumption and the for the years 1920-41 and the combined periods quantities demanded, and y c, y f and yn, are the 1920-41 and 1948-55. As can be seen, the results compare favorably with those presented in table 1. 30 A possible difficulty with the test described above is that consumers may not react to current price, just as, Conclusions according to Friedman, they do not react to current income. Models based on the assumption that consumers Friedman's recent monograph, A Theory of the react to expected normal price, a concept analogous to Consumption Function, deals with the interpreta- permanent income, may be developed. Statistical analyses tion of the statistical relation between measured based on such models, however, indicate little improve- ment over the analyses presented above. total consumption expenditures and measured in- It is also possible that, in the case of individual cate- come. Even though the explanation of total con- gories of consumption, consumers react to current price sumption expenditures is the object of Friedman's and income as well as to expected normal price and per- manent income. Models that incorporate this assumption inquiry, his approach has significant implica- are possible, and statistical analyses based on such tions for the estimation of income elasticities of models are currently underway in the Department of demand for individual commodities. Only a few Agriculture. of these implications have been explored in this 12 • TABLE 2.-Demand for aggregate consumption, food, and meat based on an alternative to the permanent income hypothesis : Least-squares regressions and related statistical data'

W Aggregate consump- Food, equation (28) Meat, equation (29) tion, equation (27) Item 1920-41 1920-41 1920-41 1920-41 and 1920-41 and 1920-41 and 1948-55 1948-55 1948-55

Regression coefficient for specified independent variable: y(t) 0. 729 0. 726 0. 217 0. 219 0. 350 0. 421 (.056) (.057) (.031) (.028) (.071) (. 056) c(t-1) . 099 209 (.077) (. 064) qi(t-1) 151 237 (. 139) (. 106) q,„(t-1) . 248 . 371 (. 127) (. 111) Pf(0 -. 155 -.142 (.042) (.036) pm(t) -. 478 -. 429 (.076) (.065) Constant term . 315 . 122 1. 563 1. 366 1. 730 1. 263 R2 . 97 . 99 . 89 . 97 . 73 . 82 Number of observations 22 30 22 30 22 30 Durbin-Watson statistic, d 1. 56 1. 48 1. 91 1. 89 2. 16 2. 04 Estimate of- 7 . 901 . 791 . 849 . 763 . 752 . 629 Long-run elasticity with respect to- Income . 81 . 92 . 26 . 29 . 47 . 67 Price -. 183 -. 186 -. 636 -. 682

Numbers in parentheses beneath the coefficients are their respective standard errors. review; many more await the reader of Fried- much weight as he does the transitory component nan's book. of income. The permanent income hypothesis is Although Friedman's permanent income hypo- a valuable contribution to demand analysis, but thesis apparently explains many things that have it will need to be supplemented in order to be puzzled demand analysts, it does not appear to be utilized effectively. This kind of thing is at once a highly useful tool in analyzing demand for in- the despair and the delight of applied research dividual commodities. The crude test presented workers : no theoretical analysis can remain un- here suggests that in order to apply Friedman's changed as it is applied to more and more data; of hypothesis we must assume that the consumer necessity, applied workers must play a fundamen- horizons appropriate to different categories of tal role in the building of theory. Professor consumption differ greatly, even for such similar Friedman is to be commended for giving us such a categories as all food and meat. fine place from which to continue his work. The permanent income hypothesis has not been Literature Cited shown to be false. What has been shown is that the transitory component of consumption is sub- (I) ARROW, KENNETH J., AND NERLOVE, MARC. 1958. A NOTE ON EXPECTATIONS AND STABILITY. ject to economic interpretation. Models based on Econometrica. April 1958. (In press.) this interpretation are more useful in the analysis (2) FOOTE, RICHARD J., AND NERLOVE, MARC. 1957. WHY APPLIED RESEARCH WORKERS ARE INTER- of demand for individual commodities than the ESTED IN PROBLEMS OF AGGREGATION. U. S. permanent income hypothesis, even though they Agr. Marketing Serv. (Processed.) (8) FRIEDMAN, MILTON. completely neglect the transitory component of 1957. A THEORY OF THE CONSUMPTION FUNCTION. income. 243 pp. Princeton, Princeton University Press. In essence, then, Friedman presents an exagger- (4) LINDLEY, D. C. 1947. REGRESSION LINES AND THE LINEAR FUNC- ated view of his hypothesis because he neglects to TIONAL RELATIONSHIP. Jour. Royal Statis. give the transitory component of consumption as Soc. Supp. 9: 218-244. • 13 MARSHALL, ALFRED. (10) NERLOVE, MARC. 1936. PRINCIPLES OF ECONOMICS. Ed. 8, 871 pp. 1956. ESTIMATES OF THE ELASTICITIES OF SUPPLY New York, The Macmillan Co. OF SELECTED AGRICULTURAL COMMODITIE MEINKEN, KENNETH W. Jour. Farm Econ. 38: 496-509. 1953. THE DEMAND AND PRICE STRUCTURE FOR OATS, (11) STONE, RICHARD. BARLEY AND SORGHUM GRAINS. U. S. Dept. 1954. THE MEASUREMENT OF CONSUMERS' EXPENDI- Agr. Tech. Bull. 1080, 102 pp. TURE AND BEHAVIOR IN THE UNITED KINGDOM, MODIGLIANI, FRANCO, AND BRUMBERG, RICHARD. 1964. "UTILITY ANALYSIS AND THE CONSUMPTION 1920-38. VOL I, 447 pp. Cambridge, Cam- FUNCTION" in POST-KEYNESIAN ECONOMICS. bridge University Press. Kenneth K. Kurihara, ed. 442, pp. New (12) TOBIN, JAMES. Brunswick, Rutgers University Press. 1950. A STATISTICAL DEMAND FUNCTION FOR FOOD IN NERLOVE, MARC. THE U. S. A. Jour. Royal Statis. Soc. Series 1957. USING DISTRIBUTED LAGS IN THE ANALYSIS OF A. 113: 113-40. DEMAND FOR AGRICULTURAL AND OTHER COM- (13) WOLD, HERMAN, AND JUREEN, LARS. MODITIES. AMS Report. (In process.) 1953. DEMAND ANALYSIS : A STUDY IN . NERLOVE, MARC. 358 pp. New York, John Wiley and Sons. 1958. DISTRIBUTED LAGS AND THE ESTIMATION OF LONG-RUN SUPPLY AND DEMAND ELASTICI- (14) WORKING, ELMER. TIES. Jour. Farm Econ. May 1958. (In 1954. DEMAND FOR MEAT. 136 pp. Chicago, In- press.) stitute of Meat Packing.

Cross-Sectional Pricing in the Market for Irrigated Land

By Edward F. Renshaw This investigation of price-determining infbuences in the market for irrigated land was motivated originally by a presumption that one way to evaluate land-investment alter- natives, such as public expenditures for irrigation, would be to compare the present price of nonirrigated land in the market with an "expected" market price after investments are made. The models were developed to aid in estimating a current market value for land that is comparable, in the value sense, to the price of such land after capital invest- ment. In an attempt to test variants of the theory that a certain proportion of the ex- pected gross receipts is capitalized into land values, that is, that land values can be estimated on the basis of gross farm income, the author has constructed both time-series and cross-sectional models. The time-series portion of the analysis was published in the May 1957 issue of the Journal of Farm Economics (4),1 "Are Land Prices Too High: A Note on Behavior in the Land Market." The cross-sectional models dealing with this problem are presented here with a unique approach and interesting methodology.

The approach used in this study to isolate expectation models 2 a few additional steps along determinants of land price is built on the premise the road to empirical application. that land value represents a capitalization of ex- pected net income. While net income to land Model 1 cannot be observed or measured easily owing to Model 1 can be classified as a conventional ex- joint ownership of agricultural factors of produc- pectation model; estimated land and water value tion, gross income, a variable that is closely corre- per acre is related directly to expected crop value lated with net income, can either be measured di- per acre, when expected crop value is a weighted rectly or estimated from acreage response. The function of estimated gross crop value in the 10 models given here are concerned essentially with preceding years. carrying the weighting principles that underlie For a more theoretical discussion of the mathematics underlying expectation models readers are referred to a Numbers in italics in parenthesis refer to Literature recent article by Marc Nerlove in the Journal of Farm Cited, page 19. Economics (3). 14 •