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How Forward Looking Are Consumers? Further Evidence for the United States.



Daniel Himarios [*]

This paper extends a standard model of consumption to test for the existence of "myopic my·o·pi·a  
n.
1. A visual defect in which distant objects appear blurred because their images are focused in front of the retina rather than on it; nearsightedness. Also called short sight.

2.
" consumers. The extended model includes "rule-of-thumb" consumers as well as consumers who are assumed to solve a dynamic programming problem. The model allows this second set of consumers, however, to be "boundedly rational." For a variety of reasons, they may be unable to fully account for their future uncertain labor income. The model predicts that this inability to correctly value future resources leads to the breakdown of the simple permanent income hypothesis The permanent income hypothesis (PIH) was developed by the American economist Milton Friedman. In its simplest form, PIH states that the choices made by consumers regarding their consumption patterns are determined not by current income but by their longer-term income expectations.  and that consumption responds to predictable changes in income. Using data for the United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area.  for the period 1951u1990, the paper finds evidence of such myopic behavior.

1. Introduction

A considerable amount of research has found that the strict form of the LCuPIH (lifecycle, permanent-income hypothesis) is not supported by the data. Consumption appears to be "too sensitive" to predictable changes in income. There are several explanations in the literature for this failure, but a Keynesian "rule-of-thumb" behavior is the explanation that has received most of the attention.

Campbell and Mankiw (1990) construct a model in which a fraction of income [lambda] accrues to individuals who, following "rules of thumb," consume their current income, while the remaining (1 - [lambda]) accrues to individuals who, being extremely farsighted far·sight·ed or far-sight·ed
adj.
1. Able to see distant objects better than objects at close range; hyperopic.

2. Capable of seeing to a great distance.
, consume their permanent income. The rule-of-thumb behavior is subject to two interpretations (Shea 1995). One interpretation is that consumers are extremely "myopic." This nonoptimizing or myopic behavior implies that these consumers completely ignore their total wealth (or permanent income) when making consumption decisions. Another interpretation of the behavior of the first group of individuals is that they are liquidity constrained. These individuals have few or no real assets Real assets

Identifiable assets, such as land and buildings, equipment, patents, and trademarks, as distinguished from a financial investment.
 and have no access to capital markets. The empirical evidence from aggregate data is rather inconclusive, but evidence from more disaggregated Broken up into parts.  data lends support to the liquidity constraints A liquidity constraint in economic theory is a form of imperfection in the capital market. It causes difficulties for models based on intertemporal consumption.

Many economic models require individuals to save or borrow money from time to time.
 interpretation (Zeldes 1989a).

While the CampbelluMankiw specification, under either interpretation, generates excess sensitivity and results in an empirically more realistic consumption function, its treatment of the second group of individuals, who are assumed to consume their permanent income, is unnecessarily restrictive. As Kotlikoff, Samuelson, and Johnson (1988, p. 408) point out, "A second problem that is also routinely swept under the rug involves the implicit assumption that consumers optimize perfectly given their preferences and resources, and that they correctly value their resources." Their results, based on experimental evidence, indicate that "subjects made significant and systematic errors in their consumption choice, reflecting, in part, an overdiscounting of future income" (p. 408). This "quasi-myopic behavior" has a variety of sources, such as high computational costs, habit, self-control, lack of extreme rationality or perfect farsightedness farsightedness or hyperopia, condition in which far objects can be seen easily but there is difficulty in near vision. It is caused by a defect of refraction in which the image is focused behind the retina of the eye rather than upon it, either , short multiperiod planning horizons Planning horizon

The length of time a model or investor or plan projects into the future.
, and so on (Mariger 1986; Boskin 1988; S hefrin and Thaler THALER. The name of a coin. The thaler of Prussia and of the northern states of Germany is deemed as money of account, at the custom-house, to be of the value of sixty-nine cents. Act of May 22, 1846.
     2.
 1988; Blanchard 1997, p. 151; Lettau and Uhlig 1999, among others), which can lead to failure by consumers to fully account for their future after-tax labor income. I will show that this behavior, which is consistent with a limited degree of myopia myopia: see nearsightedness.  that might exist among those who are assumed to be extremely farsighted, can lead to excess sensitivity and the failure of the PIH PIH

prolactin-inhibitory hormone.
. Lettau and Uhlig (1999) call these consumers "boundedly rational" (p. 152). Boskin (1988) and Poterba (1988) discuss the important implications for fiscal policy resulting from such myopic behavior.

The evidence in favor of rule-of-thumb behavior in explaining consumption is too strong to ignore for empirical purposes (Dornbusch, Fischer, and Startz 1998, p. 308; Himarios 1995). Mariger (1986) argues that the failure to identify constrained and unconstrained consumers leads to models that are inherently misspecified. I will, therefore, use a specification that nests rules of thumb as a maintained hypothesis. The focus of the paper will be on the second set of consumers who are assumed to consume their permanent income, as in Campbell and Mankiw (1990). Based on the earlier discussion, I will relax this assumption and allow this set of maximizing consumers to behave in a "boundedly rational" manner.

The paper proceeds as follows. In section 2, I briefly develop an empirically tractable tractable

easy to manage; tolerable.
 consumption function and discuss the empirical implications of the model. In section 3, I discuss the data and the econometric e·con·o·met·rics  
n. (used with a sing. verb)
Application of mathematical and statistical techniques to economics in the study of problems, the analysis of data, and the development and testing of theories and models.
 methodology, and in section 4, I present the estimation results. The evidence is consistent with the existence of rule-of-thumb consumers, a result that has been documented in previous studies, and also consumers who exhibit myopia of the type suggested previously.

2. Theoretical Background

Following Campbell and Mankiw (1990), I assume two types of households. Household type 1 behaves according to according to
prep.
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

3.
 the LC-PIH. These consumers base their current consumption decisions on their lifetime resources, which consist of their financial wealth and the expected discounted value of their future after-tax labor income. A closed-form solution of this optimization problem In computer science, an optimization problem is the problem of finding the best solution from all feasible solutions. More formally, an optimization problem is a quadruple  is possible under certainty equivalence or under a quadratic quadratic, mathematical expression of the second degree in one or more unknowns (see polynomial). The general quadratic in one unknown has the form ax2+bx+c, where a, b, and c are constants and x is the variable.  utility function if income is assumed to be stochastic By guesswork; by chance; using or containing random values.

stochastic - probabilistic
. Although quadratic utility can be justified on the grounds that it is a local approximation to the consumer's true utility function, its simplicity for computational problems In theoretical computer science, a computational problem is a mathematical object representing a question that computers might want to solve. For example, "given any number x, determine whether x is prime" is a computational problem.  is offset by serious shortcomings A shortcoming is a character flaw.

Shortcomings may also be:
  • Shortcomings (SATC episode), an episode of the television series Sex and the City
, and the resulting consumption function is likely to be severely misspecified (Hayashi 1982; Zeldes 1989b; Weil 1993). A more plausible utility function, assumed both by Hayashi and Zeldes, is the constant relative risk aversion risk aversion

The tendency of investors to avoid risky investments. Thus, if two investments offer the same expected yield but have different risk characteristics, investors will choose the one with the lowest variability in returns.
 function. Yet under such preferences and stochastic labor income, no closed-form solution is p ossible.

One way, though an imperfect one, to take into account this labor income uncertainty and derive an approximate solution to the optimization problem is to allow households to discount their uncertain future labor income at a rate higher than the rate of interest (Hayashi 1982; Zeldes 1989b). The assumption that the discount rate exceeds the rate of interest is amply supported by previous evidence (Hayashi 1982; Graham and Himarios 1996, among others). The approximate solution to the type 1 consumer's optimization problem is then

[C.sub.1,t] = [alpha][(1 + r)[W.sub.t-1] + [H.sub.1,t]], (1)

where [W.sub.t-1] is the end-of-period nonhuman wealth held by these consumers (I assume that type 2 consumers hold no assets), [alpha] is the propensity to consume out of total wealth, and r is the nonstochastic real interest rate. The variable [H.sub.1,t] is the present discounted value of future after-tax labor income ([Y.sub.1,t]). If we assume that the share of after-tax labor income that accrues to these consumers is (1 - [lambda]), where [lambda] is the share of income accruing to type 2 consumers, then [H.sub.1,t] is defined as

[H.sub.1,t] = [[[sum].sup.[infty]].sub.j=0] [(1 + [mu]).sup.-j][E.sub.t][Y.sub.1,t+j] = (1 - [lambda]) [[[sum].sup.[infty]].sub.j=0] [(1 + [mu]).sup.-j][E.sub.t][Y.sub.t+j], (2)

where [E.sub.t] is the expectations operator conditional on information available in period t and [mu] is the subjective discount rate that consumers apply to their uncertain future labor income.

This specification of the consumption function assumes that individuals do not face any of the constraints mentioned previously. In order to account for this possibility, I modify the consumption function for type 1 consumers as follows:

[C.sub.1,t] = [alpha][(1 + r)[W.sub.t-1] + [gamma][H.sub.1,t]]. (3)

The parameter [gamma] [epsilon] (0, 1) measures the degree to which consumers account for their future stochastic labor income. Admittedly, this is an ad hoc For this purpose. Meaning "to this" in Latin, it refers to dealing with special situations as they occur rather than functions that are repeated on a regular basis. See ad hoc query and ad hoc mode.  specification, but it is similar in spirit to others in this line of literature on consumption and captures one plausible form of myopic behavior: Type 1 consumers respond fully to wealth that they currently see and hold but fail to fully project their future income and future tax liabilities as implied by the government's budget constraint A Budget Constraint represents the combinations of goods and services that a consumer can purchase given current prices and his income. Consumer theory uses the concepts of a budget constraint and a preference ordering to analyze consumer choices.  (Poterba and Summers 1987, p. 378). [1] This specification is also consistent with Zeldes's (1989b) formulation, although the interpretation is somewhat different. In Zeldes's formulation, the weight in front of the human wealth, ([gamma]), reflects precautionary saving behavior. His simulation results "show that current assets Current Assets

Appearing on a company's balance sheet, it represents cash, accounts receivable, inventory, marketable securities, prepaid expenses, and other assets that can be converted to cash within one year.
 (which include income just received) and nonstochastic future income receipts are optimally given much more weight than future random labor income in making the current consumption decision" (p . 295).

I assume that type 2 households do not hold any assets, they have labor income [Y.sub.2,t] and they follow rules of thumb. Their consumption function is derived trivially from their budget constraint as

[C.sub.2,t] = [Y.sub.2,t] = [lambda][Y.sub.t], (4)

where [lambda] denotes the fraction of income accruing to the type 2 households.

Aggregate consumption is the sum of consumption over the two types of households:

[C.sub.t] = [C.sub.2,t] + [C.sub.1,t] = [lambda][Y.sub.t] + [alpha][(1 + r)[W.sub.t-1] + [gamma][H.sub.1,t]]. (5)

The general form of this consumption function is similar to the one postulated pos·tu·late  
tr.v. pos·tu·lat·ed, pos·tu·lat·ing, pos·tu·lates
1. To make claim for; demand.

2. To assume or assert the truth, reality, or necessity of, especially as a basis of an argument.

3.
 by Blanchard (1997, p. 149), who calls it a more realistic description of consumption behavior. The budget constraint for type 1 households in period t is

[W.sub.t] + [C.sub.1,t] = (1 + r)[W.sub.t-1] + [Y.sub.1,t] = (1 + r)[W.sub.t-1] + (1 - [lambda])[Y.sub.t], (6)

and hence the aggregate budget constraint is given by

[W.sub.t] + [C.sub.t] = ([W.sub.t] + [C.sub.1,t]) + [C.sub.2,t] = (1 + r)[W.sub.t-1] + (1 - [lambda])[Y.sub.t] + [[lambda]Y.sub.t] = (1 + r)[W.sub.t-1] + [Y.sub.t]. (7)

In order to eliminate the unobservable human wealth variable, H, from Equation (5), I make use of the following stochastic difference equation that describes the evolution of human wealth (Hayashi 1982):

[H.sub.1,t] = (1 + [mu])[[H.sub.1,t-1] - (1 - [lambda])[Y.sub.t-1]] + [u.sub.t]. (8)

The error term [u.sub.t] is defined as

[u.sub.t] = [[[sum].sup.[infty]].sub.j=0] [(1 + [mu]).sup.-j]([E.sub.t] - [E.sub.t-1])[Y.sub.1,t+j]. (9)

This error (or surprise) term represents the revisions of expectations between t - 1 and t and is orthogonal At right angles. The term is used to describe electronic signals that appear at 90 degree angles to each other. It is also widely used to describe conditions that are contradictory, or opposite, rather than in parallel or in sync with each other.  to the information set available to households in period t - 1. It is this surprise term that leads LC-PIH consumers to revise their consumption plans.

Lagging Equation (5) once, multiplying by (1 + [mu]), subtracting from (5), and using the private sector's budget constraint (7) along with the difference equation for human wealth (8), I derive the following consumption function in terms of observable

[Delta][C.sub.t] = ([mu] - [alpha][mu] - [alpha])[C.sub.t-1] + [lambda][Y.sub.t] - [alpha]([mu] - r)[W.sub.t-1] - (1 + [mu]([[lambda](1 - [alpha][gamma]) - [alpha](1 - [gamma])[Y.sub.t-1]] + [[epsilon].sub.t], (10)

where

[[epsilon].sub.t] = [alpha][gamma](1 - [lambda])[u.sub.t]. (11)

Consider now the implications of assuming that [lambda] = 0, [mu] = r, but that consumers cannot fully discount their future after-tax labor income, that is, ([gamma] [less than] 1). Equation (10) becomes

[Delta][C.sub.t] = ([mu] - [alpha][mu] - [alpha])[C.sub.t-1] + [alpha](1 + [mu])(1 - [gamma])[Y.sub.t-1] + [[epsilon].sub.t]. (12)

It is obvious that excess sensitivity now arises because consumers are optimizing under a number of constraints that prevent them from fully discounting their future after-tax labor income or because they exhibit quasi-myopic behavior due to habit, short planning horizons, and so on.

The consumption behavior captured by Equation (10) nests some of the independent explanations that have been offered in the literature for the failure of the LC-PIH. If we assume that LC-PIH consumers fully discount their future after-tax labor income ([gamma] = 1) and that they have infinite horizons ([mu] = r) (Blanchard 1985), then Equation (10) becomes

[Delta][C.sub.t] = ([mu] - [alpha][mu] - [alpha])[C.sub.t-1] + [lambda][Y.sub.t] - [lambda](1 + [mu])(1 - [alpha])[Y.sub.t-1] + [[epsilon].sub.t]. (13)

This is the case studied by Campbell and Mankiw (1990), and in this case excess sensitivity arises from rule-of-thumb behavior. [2] If we assume that all consumers are LC-PIH consumers but allow for the possibility of finite horizons ([mu] [neq] r), then Equation (10) becomes

[Delta][C.sub.t] = ([mu] - [alpha][mu] - [alpha])[C.sub.t-1] - [alpha]([mu] - r)[W.sub.t-1] + [[epsilon].sub.t] (14)

This is the equation estimated by Evans (1988) and Graham and Himarios (1996), among others. Here excess sensitivity arises from finite horizons or precautionary saving behavior. [3] If we assume that [mu] = r, [lambda] = 0, and [gamma] = 1, then Equation (10) reduces to the familiar martingale martingale

a leather strap running from the girth to the reins or the noseband for the purpose of restricting the movements of the horse's head. There are many designs. The common ones are the standing martingale, which is attached to the noseband, and the running martingale, which
 hypothesis:

[Delta][C.sub.t] = ([mu] - [alpha][mu] - [alpha])[C.sub.t-1] = [epsilon].sub.1]. (15)

It is clear from this analysis that "excess sensitivity" can arise from a combination of rule-of-thumb behavior, whatever its causes, finite horizons, and myopic behavior of the form proposed previously and that the single separate explanations proposed in the literature might not be adequate in describing consumption behavior. Indeed, as Himarios (1995) has shown, ignoring some of these explanations results in misspecification that biases the results of testing for the other hypotheses. Equation (10) provides a useful framework for evaluating these different hypotheses controlling for data, sample period, and estimating technique.

3. The Data and Econometric Methodology

Estimation Method and Econometric Issues

Equation (10) will form the basis for testing the hypotheses discussed previously. By assumption, the error term in this equation is white noise, and it is orthogonal to the information set [I.sub.t-1]. Because current income, however, appears in the equation and [E.sub.t]([[epsilon].sub.t]/[I.sub.t] [neq] 0, one can obtain consistent estimates only by using instrumental variables. There are additional reasons that require the use of instrumental variables. For example, I have assumed that transitory TRANSITORY. That which lasts but a short time, as transitory facts that which may be laid in different places, as a transitory action.  consumption or preference shocks are zero. However, the existence of such shocks will introduce an MA(1) error in the transformed equation and make the error term correlated with variables dated t - 1 as well. Consistent estimates can be obtained by using the generalized method of moments
GMM may also mean Gaussian mixture model.
For the Thai entertainment company, see GMM Grammy.


The generalized method of moments
 estimator (GMM GMM Generalized Method of Moments (economics)
GMM Gaussian Mixture Model
GMM General Membership Meeting
GMM Good Mobile Messaging
GMM GPRS Mobility Management
GMM Global Marijuana March
GMM Genetically Modified Microorganisms
) with instruments dated t - 2 and earlier to avoid misspecification arising from time-averaging and durability. [4]

Following Campbell and Mankiw (1990), I use lagged income to divide all the variables in Equation (10) before estimation to account for the fact that both consumption and income do not follow homoscedastic linear processes in levels. An added benefit of this transformation is the induced stationarity of the right-hand-side variables. Under the LC-PIH and the alternative described by Equation (10), consumption and income and income and wealth are cointegrated (i.e., they share common stochastic trends), and therefore their ratios should be stationary (Gali Gali can refer to:
  • Gali, a town in Abkhazia, Georgia
  • Toa Gali, a hero in Lego's Bionicle storyline
  • a Tsa-la-gi (Cherokee) linking verb
 1990; Graham and Himarios l996). [5]

The real rate of return r cannot be identified from Equation (l0). [6] Rather than fixing its value, however, as some previous studies have done, one can estimate Equation (10) along with the following equation for the real after-tax rate of return:

[varphi](L)([[rho].sub.t] - r) = [[eta].sub.t], (16)

where [varphi](L) is a polynomial polynomial, mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is a0xn+a  in the lag operator In time series analysis, the lag operator or backshift operator operates on an element of a time series to produce the previous element. For example, given some time series

 and [[eta].sub.t] is a zero-mean, finite-variance white noise error term. [7] If the real after-tax rate of return for assets ([[rho].sub.t]) is stationary, then the expected real return can be estimated as its sample unconditional mean.

The Data

Following most previous studies, I measure consumption as the sum of expenditures on services and nondurables in constant 1987 dollars. I follow Campbell and Mankiw (1990) and divide this measure by 0.879, which is the mean ratio of services and nondurables consumption to total consumption over the sample period. Labor income is constructed as in Blinder and Deaton (1985) from NIPA data. The nonhuman wealth variable is an adjusted measure of the household sector's net worth constructed from Balance Sheets for the U.S. Economy. This measure is the result of adding household tangible assets Tangible Asset

An asset that has a physical form such as machinery, buildings and land.

Notes:
This is the opposite of an intangible asset such as a patent or trademark. Whether an asset is tangible or intangible isn't inherently good or bad.
 and household financial assets Financial assets

Claims on real assets.
 and subtracting household liabilities. Where feasible, market rather than book values are used. All variables are divided by population to yield per capita [Latin, By the heads or polls.] A term used in the Descent and Distribution of the estate of one who dies without a will. It means to share and share alike according to the number of individuals.  measures. The measure for the real after-tax rate of return on assets Return on assets (ROA)

Indicator of profitability. Determined by dividing net income for the past 12 months by total average assets. Result is shown as a percentage. ROA can be decomposed into return on sales (net income/sales) multiplied by asset utilization (sales/assets).
 is the ratio of after-tax corporate profits from current production to net reproducible assets Reproducible assets

A tangible asset with physical properties that can be matched or duplicated, such as a building or machinery.
 valued at replacement cost. This measure is from the April 1991 Survey of C urrent Business. The data are annual observations from 1947 to 1990. [8] The Appendix provides more information on the variables and their sources.

4. Estimation Results

I estimate the system of Equations (10) and (16) using services and nondurables as a measure of consumption for the period 1950-1990. The first three observations are used up in transformations and lagged instruments. A series of diagnostic tests indicated that the real after-tax rate of return can be adequately represented by an AR(1) process. I use the GMM technique to estimate the system of Equations (10) and variants thereof and (16). Standard errors are calculated using the Newey-West estimator. The instrument set consists of the second and third lags of all the transformed variables in the regression and a constant. The choice of the instrument set was based on evidence that weak or irrelevant instruments can have deleterious deleterious adj. harmful.  effects on the GMM estimator and that the lagged right-hand-side variables are likely to have good explanatory power, thus alleviating the problems associated with poor instrument relevance (Fuhrer füh·rer also fueh·rer  
n.
A leader, especially one exercising the powers of a tyrant.



[German, from Middle High German vüerer, from vüeren, to lead, from Old High German
, Moore, and Schuh 1995). Given that the number of instruments is greater than the n umber umber: see ocher.  of parameters to be estimated, the system of equations is overidentified. The overidentification restrictions imposed by the extra instruments, and thus the validity of the specification of the model, are tested by using the Hansen--Singleton J-test. The extra instruments also serve the purpose of improving the efficiency of the parameter estimates (Davidson and MacKinnon 1993, P. 595).

Table 1, line 1, presents the nonlinear A system in which the output is not a uniform relationship to the input.

nonlinear - (Scientific computation) A property of a system whose output is not proportional to its input.
 ordinary least squares (OLS OLS Ordinary Least Squares
OLS Online Library System
OLS Ottawa Linux Symposium
OLS Operation Lifeline Sudan
OLS Operational Linescan System
OLS Online Service
OLS Organizational Leadership and Supervision
OLS On Line Support
OLS Online System
) estimates of [gamma], [alpha], [mu] [lambda], and r as a benchmark. The estimates of [alpha], [mu], [lambda], and r have the expected sign, and their size is consistent with previous estimates. The estimate of [gamma] is considerably less than one, indicating the possibility of myopic behavior. Significance tests are not appropriate with the OLS estimator, but if the GMM estimator is successful, the OLS and GMM estimates should be of comparable magnitudes. Rows 2 through 7 present the estimates with autocorrelation Autocorrelation

The correlation of a variable with itself over successive time intervals. Sometimes called serial correlation.
 and heteroscedasticity consistent standard errors. All the estimates in row 2 have the correct sign and are statistically significant at conventional levels. The estimates are similar to the OLS estimates, indicating that the choice of the particular set of instruments is not critical to the results. The [X.sup.2] test (J-test) for the validity of the overidentifying restrictions is small and insignificant and does not provide any e vidence against the model. The estimate of [lambda]] (0.406) falls within the range estimated by Campbell and Mankiw (1990). The estimate of the discount rate ([mu]) of 8.6% exceeds the estimate of the interest rate (r) of 4.3% and this difference is statistically significant. A t-test for the difference between the two has a value of 3.17. The crucial parameter of interest ([gamma]) measuring the degree of myopic behavior is around 0.5, and it is statistically significant at the 1% level. This estimate indicates a significant degree of shortsighted short·sight·ed
adj.
1. Nearsighted; myopic.

2. Lacking foresight.



shortsight
 behavior but certainly not extreme myopia, as it is significantly greater than zero. The t-statistic for the restriction that [gamma] = 1 is 3.618 and rejects the restriction at the 1% significance level. [9] I should note that there is a complication in testing the hypotheses concerning the value of [gamma]. This parameter cannot be negative or greater than one on a priori a priori

In epistemology, knowledge that is independent of all particular experiences, as opposed to a posteriori (or empirical) knowledge, which derives from experience.
 grounds. The complication arises because the null hypotheses of zero or one lie on the boundary of the parameter space In generative art people talk about parameter space as the set of possible parameters for a generative system.

In statistics one can study the distribution of a random variable. Several models exist, the most common one being the normal distribution (or Gaussian distribution).
. [10] There is no clear solution to this problem, but Pudney and Thomas (1995, p. 375) point out that "in practice, the usual procedure for a test of this type is to examine both the conventional [X.sup.2] statistic and also separate one-sided asymptotic t-ratios for each test." One-sided t-statistics for the hypotheses [H.sub.0]: [gamma] = 0, [H.sub.a]: [gamma] [greater then] 0 and [H.sub.0]: [gamma] = 1, [H.sub.a] [gamma] [less then] 1 reject the null in both cases at the 1% significance level. The restrictions are also tested with a likelihood ratio type test constructed as C = T[(J([[beta].sup.r]) - J([[beta].sup.u])]. This test follows a [X.sup.2] distribution with degrees of freedom equal to the number of restrictions imposed. The variable T is the number of observations, while J([beta]) is the minimized value of the objective function. The superscripts r and u show this value for the restricted version and the unrestricted version, respectively. The same estimator of the covariance matrix In statistics and probability theory, the covariance matrix is a matrix of covariances between elements of a vector. It is the natural generalization to higher dimensions of the concept of the variance of a scalar-valued random variable.  is used in both the restricted and the unrestricted version to ensure that the test statistic is properly signed. The numbers in the last column indicate the value of this C-statistic for the various restrictions with the significance level at which the restriction is rejected shown in parentheses See parenthesis.

parentheses - See left parenthesis, right parenthesis.
 underneath. Rows 3 and 4 impose the restrictions [gamma] = 1 and [gamma] = 0, respectively. The restriction that households fully discount their future after-tax labor income is rejected at the 1.5% significance level, while the restriction that they completely ignore it is much more strongly rejected. The next three lines impose the restrictions that result in the different hypotheses for the failure of the PIH that I discussed previously. In all cases the restrictions are rejected. Of particular interest is the restriction in row 6, which results in the Campbell-Mankiw specification. The restriction is rejected at the 1.9% significance level when tested against a more encompassing model. The Campbell-Mankiw specification thus appears overly restrictive compared to a model that allows households to discount their future income at a rate higher than the rate of interest and to have less than perfect foresight.

Although the sample is rather small, it would still be instructive to check the sensitivity of the results to different periods. I estimated the equations for four subperiods: 1951-1981, 1956-4990, 1960-1990, and 1951-1985. The estimates for the first three periods range in value from 0.36 to 0.44, and the restriction that [gamma] = 1 can be rejected in all cases. The last period is the exception, with [gamma] taking on a value of 0.984. The restriction cannot be rejected in this case.

5. Conclusions

The evidence from the modified model that I proposed previously supports the existence of both rule-of-thumb consumers and consumers who suffer, to some degree, from myopia with regard to their future income and taxes. This quasi-myopic behavior has many sources and does not necessarily mean that consumers are not optimizing. Faced with a multitude of constraints and lack of perfect information, problems that the PIH assumes away, consumers are unable to fully account for future uncertain income and tax streams. While useful as a benchmark for analyzing a multitude of problems, the strict version of the PHI phi
n.
Symbol The 21st letter of the Greek alphabet.


PHI,
n See health information, protected.
 fails as an accurate descriptor (1) A word or phrase that identifies a document in an indexed information retrieval system.

(2) A category name used to identify data.

(operating system) descriptor
 of consumer behavior. This paper has used a rather ad hoc modification of a well-specified model to capture this quasi-myopic behavior. The challenge for future research is to develop models that incorporate the constraints mentioned previously and generate such behavior in a rigorous way. Recent models of the type investigated by Lettau and Uhlig (1999), where consumers ar e assumed to behave "boundedly rationally," may prove useful in explaining observed consumption behavior more accurately.

(*.) Department of Economics, University of Texas at Arlington For other system schools, see University of Texas System.

History
Established in 1895 as Arlington College, it was renamed Carlisle Military Academy (1902), Arlington Training School (1913), and Arlington Military Academy (1916).
, Arlington, TX 76019, USA; E-mail himarios@uta.edu.

I wish to thank two anonymous referees for helpful comments and suggestions. Any remaining errors or omissions are my own.

Received April 1998; accepted August 1999.

(1.) Lee (1991) uses the same approach to measure the extent to which consumers perceive government bonds as net wealth. His parameter [theta Theta

A measure of the rate of decline in the value of an option due to the passage of time. Theta can also be referred to as the time decay on the value of an option. If everything is held constant, then the option will lose value as time moves closer to the maturity of the option.
] [epsilon] (0, 1) is imposed ad hoc in an otherwise optimizing model.

(2.) Campbell and Mankiw follow Flavin flavin: see coenzyme.
flavin

Any of a class of organic compounds, pale yellow biological pigments that fluoresce green. They occur in compounds essential to life as coenzymes in metabolism.
 (1981) and essentially impose the restriction that [mu] = [alpha]. In this case, (1 + [mu])(1 - [alpha]) is roughly equal to one, and (13) reduces to that estimated by Campbell and Mankiw.

(3.) It is easy to substitute [W.sub.t-1] out of the equation and show that consumption responds to lagged income. Kimball and Mankiw (1989) show that [mu] [neq] [rho] is consistent with a precautionary saving motive. Haug (1996) tests Blanchard's finite horizon model with Canadian data and strongly rejects it.

(4.) The potential problems that may arise from time aggregation were investigated in Graham and Himarios (1996), who, using essentially the same data, found no evidence of biases.

(5.) Graham and Himarios (1996) eatablish cointegration between consumption and income and income and wealth for the period 1952-1991. Though the relatively small size limits the usefulness of unit root teats, I performed adjusted Dickey-Fuller and Phillips-Perron unit root tests on the ratios in the regression. These tests reject a unit root for the dependent variable and the ratio of current to lagged income at the 1% level but fail to reject it for the consumption-to-income and wealth-to-income ratios in the full sample. Even minor adjustments in the sample, however, reverse this result, and a unit root is rejected at the 5% level or better. The fragility of these results is well known, and it is common practice in such cases to use theory as a guide.

(6.) Since the equation is nonlinear only in the parameters, it can be estimated as an unrestricted linear model (Evans 1988; Graham and Himarios 1996). One can then test whether the estimated composite coefficients have the probability limits implied by the different assumptions. However, given that the model is overidentified, the underlying parameters cannot be recovered. By using a nonlinear estimator, one can get direct estimates of the parameters in question that will give a more meaningful measure of any rejection that might occur.

(7.) I wish to thank Paul Evans Paul Evans is the name of:
  • Paul Evans (athlete), British athlete who won the 1996 Chicago marathon
  • Paul Evans (basketball coach), American college basketball coach
  • Paul Evans (critic), rock reviewer for Rolling Stone magazine
 for suggesting this particular approach for identifying the after-tax rate of return on assets.

(8.) The end of the sample is dictated by the availability of some series.

(9.) Though not directly comparable, this result is consistent with the findings of Shapiro and Slemrod (1995), who conclude that 43% of the households surveyed behaved as if they were subject to myopia.

Blanchard, Olivier. 1997. Macroeconomics macroeconomics

Study of the entire economy in terms of the total amount of goods and services produced, total income earned, level of employment of productive resources, and general behaviour of prices.
. Englewood Cliffs, NJ: Prentice Hall Prentice Hall is a leading educational publisher. It is an imprint of Pearson Education, Inc., based in Upper Saddle River, New Jersey, USA. Prentice Hall publishes print and digital content for the 6-12 and higher education market. History
In 1913, law professor Dr.
.

(10.) I wish to thank an anonymous referee for pointing out this problem.

References

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Blinder, Alan S., and Angus Deaton This article is about the micro-economist. For the English comic actor and television presenter, see Angus Deayton.

Angus Stewart Deaton, born in 1945 in Scotland, is one of the most recognized micro-economists today.
. 1985. The time series consumption function revisited. Brookings Papers on Economic Activity 0:465-511.

Boskin, Michael J. 1988. Consumption, saving, and fiscal policy. American Economic Review 78:401-7.

Campbell, John Campbell, John, 1653–1728, American editor, b. Scotland. After emigrating to Boston, he was postmaster of the city from 1702 to 1718 and wrote newsletters for regular patrons.  Y., and N. Gregory Mankiw. 1990. Permanent income, current income, and consumption. Journal of Business and Economic Statistics 8:265-78.

Davidson, Russell, and James G. MacKinnon. 1993. Estimation and inference in econometrics econometrics, technique of economic analysis that expresses economic theory in terms of mathematical relationships and then tests it empirically through statistical research. . New York New York, state, United States
New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of
: Oxford University Press.

Evans, Paul. 1988. Are consumers Ricardian? Evidence for the United States. Journal of Political Economy 96:983-1004.

Dornbusch, Rudiger Dornbusch, Rudiger (1942–  ) economics educator; born in Krefeld, Germany. Educated at the University of Geneva, he came to the U.S.A. in 1967 and earned a Ph.D. at the University of Chicago in 1971. , Stanley Fischer Stanley "Stan" Fischer (Hebrew: סטנלי פישר, Arabic: ستانلي فيشر) is an economist and the current Governor of the Bank of Israel. , and Richard Startz. 1998. Macroeconomics. 7th edition. New York: McGraw-Hill.

Flavin, Marjorie A. 1981. The adjustment of consumption to changing expectations about future income. Journal of Political Economy 89:974-1009.

Fuhrer, Jeffrey C., George R. Moore, and Scott D. Schuh. 1995. Estimating the linear quadratic inventory model: Maximum likelihood versus generalized method of moments. Journal of Monetary Economics 35:115-57.

Gali, Jordi. 1990. Finite horizons, life-cycle savings, and time-series evidence on consumption. Journal of Monetary Economics 26:433-52.

Graham, Fred C., and Daniel Himarios. 1996. Consumption, wealth and finite horizons: Tests of Ricardian equivalence Ricardian equivalence, (also known as Barro-Ricardo equivalence proposition or Ricardian rent), is an economic theory which suggests that government budget deficits do not affect the total level of demand in an economy. . Economic Inquiry 34:527-44.

Haug, Alfred A. 1996. Blanchard's model of consumption: An empirical study. Journal of Business and Economic Statistics 14:169-77.

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Himarios, Daniel. 1995. Euler equation tests of Ricardian equivalence. Economics Letters Economics Letters is a scholarly peer-reviewed journal of economics that publishes concise communications (letters) that provide a means of rapid and efficient dissemination of new results, models and methods in all fields of economic research. Published by Elsevier.  48:165-71.

Kimball, Miles S., and N. Gregory Mankiw. 1989. Precautionary saving and the timing of taxes. Journal of Political Economy 97:863-79.

Kotlikoff, Lawrence J., William Samuelson, and Stephen Johnson There are several well-known people called Stephen Johnson:
  • Stephen Johnson, photographer, designer, and teacher.
  • Stephen Johnson, an American politician in Washington state
  • Stephen C. Johnson, computer scientist, mathematician and famed Unix hacker
  • Stephen L.
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Lee, Bong-Soo. 1991. Government deficits and the term structure of interest rates Term Structure of Interest Rates

A yield curve displaying the relationship between spot rates of zero-coupon securities and their term to maturity.
. Journal of Monetary Economics 27:425-43.

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Mariger, Randall. 1986. Consumption behavior and the effects of government fiscal policy. Cambridge, MA: Harvard University Press The Harvard University Press is a publishing house, a division of Harvard University, that is highly respected in academic publishing. It was established on January 13, 1913. In 2005, it published 220 new titles. .

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Pudney, Stephen, and Jonathan Thomas Jonathan Thomas (born 27 December 1982 in Pembroke) is a Welsh rugby union player who plays at flanker for the Ospreys at club level and at number 8 for Wales.

He launched his club career at Swansea RFC and played for Wales at Under 16, Under 19 and Under 21 level.
. 1995. Specification tests for the competing risks duration model: An application to unemployment duration and sectoral movement. Oxford Bulletin of Economics and Statistics 57:323-47.

Shapiro, D. Matthew, and Joel Slemrod. 1995. Consumer response to the timing of income: Evidence from a change in tax withholdings. American Economic Review 85:274-83.

Shea, John. 1995. Myopia, liquidity constraints, and aggregate consumption: A simple test. Journal of Money, Credit, and Banking 27:798-805.

Weil, Philippe. 1993. Precautionary savings and the permanent income hypothesis. Review of Economic Studies 60:367-83.

Shefrin, Hersh M., and Richard H. Thaler. 1988. The behavioral life-cycle hypothesis. Economic Inquiry 26:609-43.

Zeldes, Stephen P. 1989a. Consumption and liquidity constraints: An empirical investigation. Quarterly Journal of Economics The Quarterly Journal of Economics, or QJE, is an economics journal published by the Massachusetts Institute of Technology and edited at Harvard University's Department of Economics. Its current editors are Robert J. Barro, Edward L. Glaeser and Lawrence F. Katz.  97:305-46.

Zeldes, Stephen P. 1989b. Optimal consumption with stochastic income: Deviations from certainty equivalence. Quarterly Journal of Economics 104:275-98.
               Generalized Method of Moments (GMM) Estimates
                   of Equations (10) and (16): 1950-1990
  [alpha] [gamma]   [mu]      r    [lambda] J-test  C-test
1  0.076   0.347   0.082    0.044   0.469
  (0.028) (0.262) (0.028)  (0.006) (0.048)
2  0.071   0.471   0.086    0.043   0.406    9.221
  (0.012) (0.146) (0.013)  (0.003) (0.051)  (0.904)
3  0.043     1     0.079    0.042   0.357   15.164   5.943
  (0.009)         (0.018)  (0.003) (0.047)  (0.584) (0.015)
4  0.106     0     0.095    0.044   0.571   26.771  17.550
  (0.007)         (0.010)  (0.005) (0.032)  (0.061) (0.000)
5  0.020     1    [mu] = r  0.042   0.379   17.155   7.935
  (0.003)                  (0.003) (0.046)  (0.512) (0.019)
6  0.058     1     0.102    0.040     0     74.338  65.117
  (0.007)         (0.014)  (0.002)          (0.000) (0.000)
7  0.382   0.491  [mu] = r  0.043   0.408   15.049   5.829
  (0.013) (0.188)          (0.003) (0.051)  (0.592) (0.016)


The J-test is a test of the validity of the overidentifying restrictions with its significance level shown in parentheses. The C-test is a likelihood ratio test for the validity of the imposed restrictions. The number in parentheses underneath indicates the significance level at which the restriction is rejected. Row 1 presents the nonlinear ordering least squares (OLS) estimates. The rest of the rows are GMM estimates with autocorrelation and heteroscedasticity consistent standard errors.

Appendix

1. The consumption and income series come from the National Income and Product Accounts National Income and Product Accounts (NIPA) use double-entry accounting to report the monetary value and sources of output produced in a country and the distribution of incomes that production generates. Data are available at the national and industry level.  of the U.S. (vols. 1 and 2). Consumption is measured as expenditures on nondurable non·du·ra·ble  
adj.
Not enduring; being in a state of constant consumption: nondurable items such as paper products.

n.
A consumable item: nondurables such as food. 
 goods and services In economics, economic output is divided into physical goods and intangible services. Consumption of goods and services is assumed to produce utility (unless the "good" is a "bad"). It is often used when referring to a Goods and Services Tax.  in 1987 dollars. The after-tax labor income (Y) was constructed as follows: Let L be the sum of wages, salaries, and other labor income and I be the sum of personal interest earnings, personal dividend earnings, and rental income Noun 1. rental income - income received from rental properties
income - the financial gain (earned or unearned) accruing over a given period of time
 to persons. Then Y = L+ government transfers to persons + (L/(I + L)) times proprietors' income minus social security contributions (by employees) minus (L/(I + L)) times personal income taxes.

2. Nonhuman wealth was constructed from end-of-year data from Balance Sheets for the U.S. Economy, 1945-1992. The variable W is defined as private sector net worth minus pension fund reserves minus par value of household holdings of tax-exempt obligations and U.S. government securities plus [P.sup.*] (defined shortly) times par value of household holdings of tax-exempt obligations plus the ratio of par value of household holdings of U.S. government securities to the par value of total outstanding U.S. government securities times the market value of privately held outstanding U.S. government debt (constructed by Michael Cox The name Michael Cox could refer to:
  • Michael Cox (Academic), Professor of International Relations at the London School of Economics
  • Michael Cox, Ph.D. (Academic), Professor of Counseling and Psychology at Webster and Troy University
). The variable [P.sup.*] is a approximate market price for state and local obligations from Survey of Current Business, Current Business Statistics, Section 6: Finance, Bonds (Standard and Poors Corporation), domestic municipal bond prices per dollar of par value.

3. Per capita variables are constructed by dividing by the total population of the United States taken from Statistical Abstract of the United States The Statistical Abstract of the United States is a publication of the United States Census Bureau, an agency of the United States Department of Commerce. Published annually since 1878, the statistics describe social and economic conditions in the United States. , 1993, p. 8, Table 2.

4. Real variables, when not directly available, were constructed by dividing by the implicit price index constructed as the ratio of nominal to real expenditures on nondurable goods and services.
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