Testing an alternative habit persistence model.

Slottje, Daniel J.

I. Introduction

Marshall long ago noted the phenomenon of past consumption being highly correlated with current consumption. If "habit" was indeed a major determinant of current consumption behavior, then the neoclassical theory of utility maximization should take it into account. A rigorous incorporation of habit formation into consumer theory began with Gorman |12~. Pollak |21; 22; 23~ laid out the theoretical conditions that needed to be satisfied in order for "habit persistence" to be consistent with the utility maximizing model of consumer behavior.

Competent empirical work in this area was done initially by Houthakker and Taylor |14~ with subsequent studies by Manser |16~, Phlips |18; 19~, Pollak and Wales |24~, Anderson and Blundell |2~ and Blanciforti and Green |8~. These papers have focused on examining the impact of measured past consumption on current consumption. Blundell |9~ provides a comprehensive review of this literature.

The purpose of this paper is to analyze aggregate consumption behavior by constructing an alternative model of habit persistence. The usual approach in the microeconomics literature is that of Pollak which assumes the argument of the utility function is a transformation of quantities consumed. We choose an alternative tact in that the parameters of the utility function depend upon past consumption, an approach suggested by Gorman |12~ and Peston |17~. Specifically, we develop and test a model which allows us to examine the impact of past consumption behavior on the current structure of preferences. Our model differs from earlier work in that we not only allow "habit" to influence current consumption as in the aforementioned studies, but we also allow "habit" to alter the consumer's preference structure. Our model allows past ratios of expenditures on various commodity groups and lagged quantities of commodities to impact the elasticity of the marginal rate at which consumers substitute one commodity group for another. The model is presented in section two. Section three presents the empirical results of our study. The study is summarized in section four.

II. The Model

In the standard neoclassical approach, quantities of commodities appear only as arguments of the utility function and do not affect parameters. We hypothesize that past consumption impacts consumer's preference structure. That is, habit formation can be analyzed by examining changes in consumer's preferences which subsequently lead to changes in consumer demand. In order to test this hypothesis we develop a model in which past consumption behavior can have some effect on current preferences.

Basmann, Molina and Slottje |5~ presented a framework for empirically testing for preferences which depend on prices and expenditures as well as quantities. This methodology is extended here to investigate the existence of habit persistence impacts on consumer preferences as well as consumer demand. Following Phlips and Spinnewyn |20~, we assume perfect information by consumers or deterministic expectations by not explicitly modelling for uncertainty. The theory of stochastic preference changers we discuss in the section on estimation allows us to econometrically incorporate uncertainty. Furthermore, it is assumed that individuals take aggregate expenditures as given and that these expenditures affect their preferences when aggregated. Abel |1~ and Constantinides |10~ have discussed these issues in arguing for habit persistence models vis-a-vis time-separable utility models. We proceed by summarizing the methodology and developing our extension.

Let U (X;|Alpha~) be a direct utility function with continuous second partial derivatives with respect to X, where |Alpha~ designates the vector of all its parameters. Let |Mathematical Expression Omitted~ designate the marginal rate of substitution of |X.sub.n~ for |X.sub.i~ at the point X. Let ||Alpha~.sub.k~, k = 1,..., m be an observable magnitude different from X and its components. Assume that the direct utility function and all its first and second partial derivatives, |U.sub.i~ and |U.sub.ij~, are differentiable at least once at all points (X) of the budget domain with respect to each of the ||Alpha~.sub.k~. Then each of the marginal rates of substitution |Mathematical Expression Omitted~ is differentiable at every point (X) of the domain with respect to each preference-changing variable ||Alpha~.sub.k~, k = 1, 2,..., m. Following Ichimura |15~ and Tintner |25~, we interpret ||Alpha~.sub.k~ as a preference-changing variable for U (X;|Alpha~) at X, and

|Mathematical Expression Omitted~

for at least one i at (X).

We can express the effect of a change of one economic magnitude on another in terms of mathematical elasticities. Let the elasticity of the marginal rate of substitution (M.R.S.) of |X.sub.n~ for |X.sub.i~ with respect to a change in ||Alpha~.sub.k~ be defined as

|Mathematical Expression Omitted~

Recalling that

|Mathematical Expression Omitted~

where |U.sub.i~ and |U.sub.n~ are marginal utilities of |X.sub.i~ and |X.sub.n~ respectively, we can define ||Sigma~.sub.h,||Alpha~.sub.k~~ as the elasticity of the marginal utilities with respect to a preference-changing variable ||Alpha~.sub.k~:

||Sigma~.sub.h,||Alpha~.sub.k~~ = (||Alpha~.sub.k~/|U.sub.h~)(|Delta~|U.sub.h~/||Delta~||Alpha~.sub.k~) h = 1, 2,..., n and k = 1, 2,..., m. (4)

The elasticities of the M.R.S. (2.2), with respect to a change in ||Alpha~.sub.j~ are in general:

|Mathematical Expression Omitted~.

To test for the existence of habit persistence effects on consumer preferences we use a direct utility function in which past consumption can have an explicit impact on the parameters, |Alpha~, of the utility function. We specify a functional form for U (X;|Alpha~) for which the preference changing variables are a function of past period expenditures, quantities and interest rates. One such form is the Generalized Fechner-Thurstone (GFT) direct utility function. The GFT direct utility function is designed for intertemporal comparisons of consumer equilibria. Time periods are sufficiently long to allow budget constraints, i.e., prices and total expenditure to change significantly. The fundamental assumption is that periods sufficiently long for such changes to occur are also sufficiently long for significant changes of tastes to occur as well. As elsewhere in science, this kind of correlation does not entail that budget constraint changes "cause" or produce the accompanying taste changes. Consider

|Mathematical Expression Omitted~

|summation of~||Theta~.sub.i~ = |Theta~. (7)

The exponents ||Theta~.sub.i~, i = 1, 2,... n, vary from period to period. Their numerical values may be determined directly from the price and expenditure data, Basmann and Slottje |6~ describe this calculation. The ratios ||Theta~.sub.i~/||Theta~.sub.j~ are defined to be equal to |M.sub.i~/|M.sub.j~ where |M.sub.i~ represents expenditure share for good i. This condition is deductively implied by the first order conditions for the utility function given in (6) and (7).

Once the numerical values of the ||Theta~.sub.i~ have been computed for each time period, t, their variations may be modelled. To do this we specify that

||Theta~.sub.i~ = ||Theta~*.sub.i~(P, M, |Psi~)|e.sup.|u.sub.i~~,

where M is nominal income, |u.sub.i~ is a random variable and ||Psi~.sub.i~ is a systematic function of specified economic and demographic variables. We do not use this result here. We only mention it to help clarify that the GFT form is not a Cobb-Douglas form as we discuss below.

In the present article our concern is with the effects of "habit persistence" on the numerical values of the |Theta~'s. We shall specify that the systematic ||Theta~*.sub.i~ depend on lagged values of X which we denote by |Mathematical Expression Omitted~ and lagged expenditure shares |Mathematical Expression Omitted~. In this paper we specify two forms of GFT direct utility function. Specifically we utilize a constant elasticity of marginal rate of substitution (CEMRS) form and a translog form. In the next two sections we specify our estimating equations for these two forms.

CEMRS Specification

We adopt the CEMRS form, due to Basmann et al. |4~, to allow past consumption, |Mathematical Expression Omitted~, to have impact on ||Theta~.sub.i~ and thus the consumer's preference structure. This form of the CEMRS is specified as

|Mathematical Expression Omitted~

where |u.sub.i~ is the stochastic error term.

We again note that the lefthand side of (8), the numerical magnitudes of ||Theta~.sub.~, i = 1, 2,...,n can be determined directly from empirical data. The values of those functions depend only on the sample data, and can be calculated directly using a procedure described in Basmann and Slottje |6~. When this is done it is rarely the case that the |summation of~ ||Theta~.sub.i~ = |Theta~, (6), is equal or even near to unity, e.g., as would be the case if--contrary to fact--the GFT direct utility function (6) and (7) were a Cobb-Douglas static direct utility function. For some applications of the GFT direct utility function it would not create errors or mislead if one were to "normalize" the |Theta~ functions (8) so that their sum |Theta~ would be identically one for all price, quantity, and total expenditure data in the sample. The present application is not an exception. The results of interest here depend only on the ratios of ||Theta~.sub.i~/|Theta~. However, forcing the sum (7) to be identically one at all sample data points would be some trouble and gain nothing. In some other applications it would be erroneous to "normalize" the functions ||Theta~.sub.i~, see Basmann et al., |4~. Another reason for not "normalizing" the ||Theta~.sub.i~'s such that |summation of~||Theta~.sub.i~ = 1, (7), comes from Basmann's |3~ theory of serial correlation of stochastic taste changers which is used as a null hypothesis in this paper, see the discussion below equation (24). In that case the numerical values of the ||Theta~.sub.i~, i = 1, 2, ..., n, or their logarithms, are taken as dependent variables. This permits estimation of the variance and lagged covariance matrices of the stochastic taste changers, |u.sub.i~ in (8). If one were to "normalize" the ||Theta~.sub.i~'s, the estimates of those variance and covariance matrices would be changed arbitrarily. The ||Theta~.sub.i~'s appear in (12)-(14) as ratios because it simplifies estimation algorithms as will be seen below.

Now that a specification of ||Theta~.sub.i~ has been chosen, deriving the demand relations and estimating equations is straightforward. Maximization of U(|center dot~), as specified by (6), (7) and (8), subject to a budget constraint yields |Mathematical Expression Omitted~

where

|Mathematical Expression Omitted~.

Dividing the numerator and denominator of (9) by

|Mathematical Expression Omitted~

yields

|Mathematical Expression Omitted~

where |Mathematical Expression Omitted~.

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~.

To estimate (9) we assume all data are at equilibrium implying from the first order conditions, that (||Theta~.sub.i~/||Theta~.sub.n~) = (|M.sub.i~/|M.sub.n~) |3~. We take the ratio of the expenditure shares, in loglinear form: |Mathematical Expression Omitted~.

Equation (10) is the CEMRS, or constant elasticity of marginal rate of substitution, form of the GFT direct utility function (6)-(8).

While specifying habit formation in terms of |Mathematical Expression Omitted~ has been the most popular form in the literature, sometimes lagged expenditures have been used. We can define ||Theta~.sub.i~ in such a way as to derive an estimating equation which can be tested as a stochastic first order difference equation in log ||Theta~.sub.i~/||Theta~.sub.n~. In this case ||Theta~.sub.i~ is specified as

|Mathematical Expression Omitted~

where |Mathematical Expression Omitted~ represents lagged expenditures on good i.

The estimating form for this specification is

|Mathematical Expression Omitted~

where |Mathematical Expression Omitted~. This specification allows us to examine habit persistence modeled as the lagged ratio of expenditures on the various commodity groups as well as incorporate the rate of interest into the model. Since equation (12) implies a n - 1 order ordinary difference equation, our model implies habit persistence of n - 1 periods.

Translog Specification

An alternative specification of the GFT utility function yields the popular translog estimating equation. Recalling that (||Theta~.sub.i~/||Theta~.sub.n~) = (|M.sub.i~/|M.sub.n~) in equilibrium, the two alternative habit persistence specification can be stated:

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

We can define the elasticity of MRS with respect to total expenditures as

|Mathematical Expression Omitted~.

The elasticity of MRS with respect to prices for this form is

|Mathematical Expression Omitted~

Similar elasticities of MRS with respect to lagged consumption, |Mathematical Expression Omitted~, and the ratio of the lagged expenditures, |Mathematical Expression Omitted~, can be derived. For lagged consumption, |Mathematical Expression Omitted~, we have

|Mathematical Expression Omitted~

for the ratio of lagged expenditures:

|Mathematical Expression Omitted~

By specifying (13) and (14) as differences in expenditure shares we can again take advantage of Basmann's |3~ result for the stochastic disturbances. The estimating equations will be

|Mathematical Expression Omitted~

where |Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~,

and

|Mathematical Expression Omitted~

where |Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~.

By estimating (19) and (20), we can derive point estimates and confidence intervals for the parameters of (13) and (14). Since linear homogeneity in prices is assumed, then

ln |A.sub.n~ = 1/n(1 - |summation of~ln(|A.sub.i~/|A.sub.n~)) (21)

and

ln |A.sub.i~ = ln|A.sub.n~ + ln(|A.sub.i~/|A.sub.n~) (22)

To calculate |a.sub.ij~, again using the assumption of linear homogeneity in prices and that |Mathematical Expression Omitted~:

then

|Mathematical Expression Omitted~

and

|Mathematical Expression Omitted~

Point estimates |d.sub.ij~ and |s.sub.ij~ can be derived similarly. Based on these point estimates of the ln |A.sub.i~, |a.sub.ij~ and |d.sub.ij~(|s.sub.ij~), it is straightforward to calculate the residuals, the asymptotic variance covariance matrix and the standard errors for each. Thus, our estimating form can provide estimates for the translog expenditure share parameters.

Estimation Procedure

For each of these specifications we again assume a second order autoregressive process where |Mathematical Expression Omitted~ is the same AR(2) for all i. The disturbance specification is simplified and the number of inessential parameters is reduced. All of the |Rho~'s actually used in the estimation were within the region where ||Rho~.sub.1~ + ||Rho~.sub.2~ |is less than~ 1, ||Rho~.sub.2~ - ||Rho~.sub.1~ |is less than~ 1 and - 1 |is less than~ ||Rho~.sub.2~ |is less than~ 1 for all the equations, so the models discussed below were found to be stable.

Following Basmann |3~ we classify stochastic tastes changes in |u.sub.i~'s into the part that can effect the future via an autoregressive process and the part that cannot, i.e., ||Eta~.sub.ti~ = ||Rho~.sub.1~||Eta~.sub.t-1,i~ + ||Rho~.sub.2~||Eta~.sub.t-2,i~ + ||Epsilon~.sub.t~ is the same AR(2) for all i. The theory of serial correlation of the stochastic taste changers, |u.sub.ti~, in the utility function rests on two chief assumptions, Basmann |3, 199~. ASSUMPTION 1. If every stochastic taste changer |u.sub.ti~ increases or decreases by the same increment in period t, then each of the marginal rates of substitution

|Mathematical Expression Omitted~,

remains invariant (at every point of the domain of X) for all subsequent periods, t + 1, t + 2,...

ASSUMPTION 2. If there is a ceteris paribus increase in the stochastic taste changer |u.sub.tk~, then (i) all of the marginal rates of substitution for k for i, i |is not equal to~ k change in equal proportion; (ii) all other marginal rates of substitution

|Mathematical Expression Omitted~, where i |is not equal to~ k, j |is not equal to~ k, i, j = 1,...,n,

remain invariant (at every point of the domain of X) for all subsequent periods, t + 1, t + 2,...

Notice that Assumption 1 and Assumption 2 necessarily hold for period t, Basmann |3, 198~. This theory of serial correlation of stochastic taste changers is not limited in application to GFT direct utility functions. In the present application, the Assumptions 1 and 2 imply that all of the stochastic disturbances share the same serial correlogram or equivalently, spectral density function. It should be noted that uncertainty may be impacting the habit model as well. We note here that our specification allows for this possibility and is in part the reason we adopted the serial correlation theory |3~. Notice that Assumptions 1 and 2 are part of the maintained hypothesis here. By taking the ratios of the expenditures shares, the disturbance specification is simplified. In addition, the number of inessential parameters to be estimated is reduced |3, 196~.

The estimation procedure is maximum likelihood. If any of the |Mathematical Expression Omitted~ or |Mathematical Expression Omitted~ are statistically different from zero then we have detected a change in the elasticity of the MRS due to lagged quantities or ratios of expenditures lagged. We interpret these as habit persistence effects. For the translog specification, the |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~ will vary from one time period to the next. Since the |Mathematical Expression Omitted~ are not fundamental constants, but depend on constants ln |A.sub.i~, |a.sub.io~, |a.sub.ij~, |d.sub.ij~, |s.sub.ij~, interval estimates are calculated only for the ln |A.sub.i~, |a.sub.io~, |a.sub.ij~, |d.sub.ij~, |s.sub.ij~. For both the CEMRS and translog specifications, homogeneity restrictions can be tested. Homogeneity requires that |Mathematical Expression Omitted~ for the CEMRS specification. For the translog specification, homogeneity requires |Mathematical Expression Omitted~. In addition, symmetry restrictions can be tested for the translog form. Symmetry requires |Mathematical Expression Omitted~.

III. Empirical Results

To test the model specified above, price and expenditure data are required. Annual U.S. data from 1947-1983 are used throughout this study. The commodity expenditure data are constructed by the United States Department of Commerce, Bureau of Economic Analysis. The related price indices for an eleven commodity data set were provided by Richard Green, University of California (Davis), and Laura Blanciforti, United States Department of Agriculture, Washington, D.C. As the referee noted, the data requirements for this type of analysis include personal consumption expenditure data in current and constant dollars. The derivation of an implicit price index can be done by dividing current expenditures by constant dollar expenditures. Since we do not have the comprehensive national income expenditure data in constant and current dollars, we rely on Blanciforti and Green's |81~ Laspeyres-type price index. A weighted average of the appropriate subgroups was used to aggregate to a five-commodity level. If we had the underlying comprehensive data, this would not be necessary, we could add the groups together without the weighting. The data include 5 general commodity groups: 1) Food, 2) Clothing, 3) Housing, 4) Durables and 5) Medical care. We include alcohol, tobacco and food consumed at home and away in the first commodity group. The clothing group includes shoes and other outerwear. Shelter expenditures and housing maintenance are included in the housing commodity group. Transportation costs have been aggregated into the durables commodity group. The medical group includes all medical costs as well as entertainment, recreation and education expenditures. The data sources for this study are documented in Blanciforti |7~. We aggregated as we did in order to make the commodity groups as reasonable as possible in light of multicollinearity and degree of freedom problems with larger number of groups. The analysis of our statistical results begins with an examination of each of the |Mathematical Expression Omitted~ from the CEMRS model for statistical significance. This will provide evidence as to secondary utility effects from lagged quantities (previous expenditure ratios). Specifically, we can test for a significant change in the MRS between i and k when past quantities (expenditures) change. If found, this provides additional information as to the causes of the habit persistence effects. For the CEMRS model, the cause would be a change in previous quantities (previous expenditure ratios of two particular commodity groups).

The model laid out in section II above allows us to estimate what we interpret as habit persistence effects directly. Actual estimation of the model specified in equations (19) and (20) was done as noted above, with a maximum likelihood procedure that took into account first and second order autocorrelation. We can see from Tables I and II that regardless of whether we specified the CEMRS with lagged quantities of various commodities or with lagged ratios of expenditures on commodities we get statistically significant effects. We report the results for the numeraire equal to medical care. Given the symmetry of (10) one can recover other estimates if so desired.

In Table I we present the results for the case where the habit persistence is confined to lagged quantities of the various commodity groups in question. In this case we find statistically significant coefficient estimates in over half of the cases. Consumption of four of the five commodities in the previous period had a statistically significant impact on the rate at which medical care is substituted for durables. Since durable goods are frequently non-necessities, it isn't surprising to see people adjusting the rate at which durables substitute for other goods (here medical care) given their preponderance of habitual consumption. Also of interest is the fact that housing consumption in the previous period affected the marginal rates of substitution of medical care for each of the other goods. Apparently housing is an activity associated with strong habitual behavior. Since for both durables and housing we are measuring a flow of consumption, but realize these goods are purchased as a "stock" this isn't surprising. In addition liquidity constraints and large adjustment costs are expected in the consumption of durables and housing. Thus, we again must be careful about attributing to habit persistence what is in actuality due to the durable nature of the good. We also observe strong lagged effects for medical care. Food and clothing appear to be the least habitual. Since tobacco and alcohol are in the food category this is surprising and is most likely due to the aggregated nature of the goods.

In Table II we examine the impact of changes in the lagged ratios of expenditures of various commodities to medical care on the rate at which the various commodities are substituted for medical care. Intuitively, we are asking what happens to the rate at which aggregate consumers will exchange (say) medical care for clothing when the ratio at which they purchase the two goods changes. From Table II we can see that the rate at which medical care is substituted for housing decreases and is a statistically significant effect at the .01 level when the ratio of food to medical care expenditures increases. The rate at which medical care is substituted for housing seems to be impacted the most by lagged effects of the ratios of expenditures of food, housing and durables to medical care. It is noteworthy that there are fewer significant lagged parameter estimates when the lagged variable is the lagged expenditure ratio |Mathematical Expression Omitted~. In fact only the lagged dependent variables are statistically significant for three of the four regressions, suggesting habitual consumption is quite strong. Habits are based on previous relative expenditures on the goods under consideration and do not appear to be related to past consumption of other goods.

In Tables III and IV we give the implied parameter estimates for the translog specification, (20). Since the ||Omega~.sub.ij~'s estimates for the translog specification vary from year to year, we omit these estimates from the body of the paper and present these results in Appendix tables in the working paper, which is available from the authors on request. In the Appendix Tables 1-21 contained in the working paper, the results of calculating (15)-(18) (the elasticities of the marginal rates of substitution) are reported.

It is noteworthy that the translog specification implies larger elasticities in several cases and trends are evident for several of the elasticities. The elasticity of the MRS between durable consumption and medical care appears to be the most responsive to price and consumption changes during the sample period. However, in every case there has been declines in this elasticity indicating a decline in habitual consumption.

In response to changes in the ratio of past expenditure increases, the elasticity of the MRS has been largest for the "own" consumption good. This concurs with the results for the CEMRS lagged expenditure ratio form. These elasticities have declined for housing and durables suggesting a reduction in habit persistence.

From both models we find evidence of habitual consumption in nearly every category. The consumption groups which appear to be most habitual are housing and durable goods. Table V presents F-statistics for the hypothesis that none of the lagged effects are statistically different from zero. Although we find strong evidence that the habit persistence effects are pervasive throughout the alternative models, the strength of the habit persistence appears to depend on the specification of the GFT direct utility function as well as on the lagged variable's definition.

The corrected |R.sup.2~'s indicate that all of the models have good explanatory power. Since these are non-nested models, we also perform tests for non-nested hypotheses to examine the performance of lagged quantities versus expenditures. The specification test used here is presented in Davidson and MacKinnon |11~. We have two competing models, one (I) contains quantities, the other (II) expenditures. We begin by assuming I is the null, |H.sub.0~ (quantities), and calculate the statistic to test II, |H.sub.1~ (expenditures), against the null. The test is performed by taking the predicted values from II and running the first model (I) with the predicted values from II. The hypothesis is then tested that the predicted values of II belong in I. If the hypothesis is rejected then model I is rejected by II. The models are flipped around and the same procedure is used to test TABULAR DATA OMITTED TABULAR DATA OMITTED TABULAR DATA OMITTED TABULAR DATA OMITTED TABULAR DATA OMITTED model II against model I. When this test is performed we find that we cannot reject the inclusion of expenditures in the quantity equations, but we can reject the inclusion of the quantities in the expenditure equations. Thus, given the usual caveat on doing this sort of test, we find that |H.sub.1~ is accepted against |H.sub.0~, but not the other way around, so lagged expenditures are the preferred models. This result was robust across all equations.

To test each model more rigorously for habit persistence, we test homogeneity and symmetry hypotheses. Homogeneity tests were completed for each specification. Our results indicate that we can reject the homogeneity hypothesis at any reasonable significance level. The likelihood ratio test statistic had a value of 23.2595 with a probability level of 1.1237 x |10.sup.-4~ for the first CEMRS specification. The CEMRS specification with lagged ratios of expenditures rejected the homogeneity test at the 6.787 x |10.sup.-1~ level. The test statistic was 34.1976.

For the translog specifications we find homogeneity is again rejected. The lagged quantities specification's likelihood ratio test statistic had a value of 26.44 with a significance probability level of 2.57 x |10.sup.-5~. For the lagged ratio of expenditures, homogeneity was rejected at a 1.30 x |10.sup.-6~ significance probability level with a test statistic of 32.8218.

Symmetry restrictions were also rejected. For the first specification the likelihood ratio test statistic was 66.86. Under the second specification, the test statistic had a value of 149.166. With 14 degrees of freedom, the significance level was less than .0001 in both cases. Based on the homogeneity and symmetry tests we conclude habit persistence is pervasive in our models.

IV. Conclusions

This study has presented a form of intertemporal direct utility function that allows habit persistence to be incorporated into the behavioral specification. Although earlier work on habit persistence has suggested that there is a relationship between past and future consumption, our general model can specifically identify the impact of past consumption on current preferences. That is, the effect of past consumption on the elasticity of the MRS can be determined. Thus the specification is more general and also allows the habit persistence to impact preferences in a well specified manner.

Two alternative specifications were examined. One of these is similar to the popular translog form and the other implies a constant elasticity of MRS. We tested the model with aggregate U.S. data and found our hypothesis to be in excellent agreement with the data. We found evidence of habit persistence affecting preferences across all goods examined in this paper, the most pervasive being housing consumption and durable consumption. These results are not surprising due to the nature of housing and durable consumption, recalling our caveat discussed above.

We discovered not only that housing and durables are habitual consumption commodities, but in fact the past consumption of these two commodities impacts the current consumption for the other commodities as well.

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