Econometric Modeling of Consumers' Expenditure in Venezuela

International Finance Discussion Papers

Number 325

June 1988

ECONOMETRIC MODELING OF CONSUMERS’ EXPENDITURE IN VENEZUELA

Julia Campos and Neil R. Ericsson

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment by a writer that he has had access to unpublished material) should be cleared with the author or authors.

ABSTRACT

Start:ing from a theoretical model with optimizing economic agents, we develop a highly parsimonious econometric model of consumers’ expenditure on hon-durab:.es and services in Venezuela for 1970-85. Disposable income, liquidity, and inflation determine expenditure in an economically sensible fashion. The empirical model is robust and has constant, well-determined parameter estimates. In specifying it, econometric methodology plays a fundamental role, and we address issues of empirical model design and evaluation, cointegration, exogeneity, policy analysis, and encompassing. Using the last concept, a large class of expectations and VAR models is found to be incompatible with the data. In particular, Hall's (1978) hypothesis (derived from the life cycle-permanent income hypothesis) that expenditure is a random walk and only predictable from its own past is

firmly rejected. The empirical model provides a clear interpretation for

why that is so.

Econometric Modeling of Consumers’ Expenditure in Venezuela

Julia Campos and Neil R. Ericsson!

1. Introduction

Model:.ng consumers’ expenditure has been a major focus of theoretical and empirical economic research over the last several decades. In spite of those efforts, considerable gaps remain between theoretical and empirical models and, among the empirical models, major disagreements exist as to the determinant:s of consumers’ expenditure. One possible cause for those gaps and disagreements is the econometric methodology adopted. Typically, an economic theory is developed, economic series corresponding to the theoretica.. constructs are found, the theoretical model is estimated with those data, and various economic hypotheses are tested on the empirical model. Wh:.le theory, choice of data, and estimation are important parts of empirical modeling, they are not sufficient to ensure that inferences based on the emp:irical model are reliable. Not infrequently, some of the hypotheses tested are rejected; cf. Hall (1978, 1987) and Hansen and Singleton (1982, 1983). If they are, little can be said about the precise causes of rejection until a satisfactory empirical model is developed. Even if they are not rejected, the theoretical model commonly entails many "auxiliary" hypotheses for the empirical model which are testable (but often untested) and whose validity is necessary for the tests of the economic hypotheses to be reliable. Such auxiliary hypotheses include innovation

disturbances, valid exogeneity assumptions, constant parameters, and the

1the views expressed in this paper are solely the responsibility of the authors and should not be interpreted as reflecting those of the Board of Governors of the Federal Reserve System, the Banco Central de Venezuela, or other members of their staffs. The authors are indebted to Angus Deaton, David Hendry, Jeroen Kremers, Jaime Marquez, and Adrian Pagan for helpful discussions:, and to Heidi Lyss for valuable research assistance. All numerical results were obtained using PC-GIVE Version 5.0; see Hendry (1987b).

ability to encompass (or account for) the results of other models. The last is necessary for any adequate empirical model: an inability to explain the properties of other models indicates the value of information contained in the other models, over and above that in the model being tested. Further, encompassing establishes an ordering across models such that an encompassing model serves as a sufficient statistic for all existing models; cf. Mizon and Richard (1986). Encompassing is particularly important when the alternative models have different economic and policy implications. In ‘spite of that, encompassing is one of the least frequently used nodel evaluation criteria. However, encompassing proves crucial in this paper for excluding certain models from being empirically viable.

Many variables might be important in determining aggregate expenditure, including disposable income, liquidity, and inflation. The degree to which each plays a role and whether or not the relationship is stable over time have substantive implications for economic policy. In developed countries, liquidity and inflation appear to play significant roles, but ones very much secondary to that of income; cf. Hall (1987), and Hendry (1983) and Bean (1986) on US and UK evidence, respectively. Liquidity and inflation may be far more important in developing countries, given their typically more skewed income and wealth distributions, volatile rates of inflation, and incomplete capital markets. Venezuela is particularly well-suited for study: it has a consistently measured and reasonably defined set of data for the last two decades; and its economic activity has varied dramatically inter alia because of the debt crisis, a fundamental change in exchange rate policy, and its role as a major participant in OPEC. The importance of these factors is a theme recurring throughout the paper.

The paper is structured as follows. Section 2 presents a simple optimizing model in which agents aim to maintain constant expenditure-income

and liquidity-income ratios but face adjustment costs. Section 3 sketches

the econometric methodology, in which model design and evaluation play central roles. Section 4 describes the data. Based on the theoretical model of Section 2, Section 5 develops a parsimonious, statistically acceptable empirical model of annual consumers’ expenditure on non-durables and services in Venezuela for 1970-85, and, in so doing, addresses issues of dynamic specification, parameter constancy, unit roots, cointegration, error-coriection, and exogeneity. Disposable income, liquidity, and inflation determine expenditure in an economically sensible fashion, with each variable doing so through several channels. In spite of the turbulence of the Venezuelan economy over the sample, the empirical model is robust and has constant, well-determined parameter estimates. In fact, the volatility of the data is crucial for giving precise estimates with limited data. Section 6 considers other theoretical and empirical models via encompassing and as alternative interpretations of the empirical model. Following the encompassing approach, a large class of expectations-based and VAR models

is found to be incompatible with the data. In particular, Hall’s (1978) hypothesis: (derived from the stochastic implications of the life cyclepermanent income hypothesis) that expenditure is a random walk and only predictable from its own past is rejected. The empirical model provides a sensible interpretation for why that is so. Further, the model’s empirical properties lend some credibility to the economic and policy implications it entails. Section 7 discusses policy implications; Section 8 concludes. The paper may appear to devote much time to econometrics relative to that spent on economics, but it is necessary, both because the central econometric issues have economic counterparts and because, without proper econometric methodology, economic inference would be far more speculative in nature and

lacking in empirical support.

2. The Economic Theory-Model.

This section develops an economic agent's optimal rule for determining consumers’ expenditure, given long-run targets for expenditure and assets and with short-run costs of adjustment. We assume ab initio that agents wish to have both expenditure and assets proportional to income in the long run. Those targets are embedded in a dynamic optimization problem with costs to being out of long-run equilibrium and to moving the control variable (expenditure) too rapidiy. The agent’s plan is the solution to that optimization, conditional on the agent's information set. Several common models are nested within that plan. Our framework generalizes upon that in Hendry and von Ungern-Sternberg (1981), and, in so doing, resolves a difficulty with their model. For the most part, we follow their notation. Starting from a multi-period utility-maximizing model with some egents facing liquidity constraints, Muellbauer and Bover (1986) derive both the proportionality targets and a similar agent plan. We prefer cost-minimization, noting the greater simplicity of derivation (cf. Blundell (1988, pp. 24-26)) and the empirical difficulties with the expect:ations terms in Muellbauer and Bover'’s formulae (see Section 6 below).

Our theory-model is a partial one in that we assume at the cutset that

some prior steady-state maximization exercise has generated the equilibrium

conditions: * wooo = KX and (2.1a) e *. A = BX , (2.1b) * * where K and B are "constants", W,. is the agent's control variable, X, is a forcing variable, AL is an end-of-period stock defined as AD = ALL tk - Wy, (2.2)

. e ey etus os and a superscript ~ denotes steady-state equilibrium. For the empirical

application below, Wee X,, and A, may be interpreted as consumers’

t’

expenditure on non-durables and services, disposable income, and liquid

assets.“ however, they could represent the permanent or anticipated components, generating certain testable hypotheses if the process generating Xx, changes within sample. Proportionality between (some form of) expenditure and income can be motivated by (e.g.) the permanent income or life-cycle hypotheses. Proportionality between assets and income may arise directly as an integral control mechanism (assets being the integral over past discrepancies between income and expenditure) or indirectly as a measure of liquidity constraints.°* Although the two rationales have different policy implications, the empirical model will provide little evidence about which is a more appropriate interpretation for Venezuela.

In light of previous studies and the analytical properties of the corresponding models, we prefer to work with the logarithms of the data rather than their levels, necessitating the following steady-state approximation to (2.2):

e

* Aa = H (x, - we

t t t) (2.3)

where H=(1+g) /B and g is the steady state growth rate of X (and so of A and W). Throughout the paper, unless otherwise noted, capital letters denoze both the generic name and the level; logs of scalars are in lower case. Defining the lag operator L as Lz.=Z,_, given an arbitrary series {z

}, the difference operator A is (1-L); hence Az =(2,-2 More

t-1): generally, Ate =(1-L") 42, . If q (or r) is undefined, it is taken to be

t

unity. For convenience, equations (2.la-b) can be re-written as:

wooo Ok 4x and (2.4a)

e t t . = b+x ; (2.4b)

a t

2 Deaton (1972) derives an explicit role for wealth in the consumption func:rion. See Salmon (1982), Nickell (1985), and Wilcox (1987) for more unif:iied treatments of the optimization problem per se.

Our analysis is a partial one also because it omits the determination of expenditure on durables. Expenditure and income could incorporate services from and the depreciation of durables; see Patterson (1985).

36n the former, see inter alia Phillips (1954, 1957), Stone (1966, 1973), and Hendry and von Ungern-Sternberg (1981); on the latter, see Pissarides (1978) and Muellbauer and Bover (1986).

Deviations from long-run targets may occur if outcomes are stochastic,

so we posit a single-period loss function qe for an agent’s plans (ap we).

- P_ 4&2 P_ ie,2 Pp. 2 qe = Ay (ay - a,) + Ao (we we) + Ag (we We 7 Pp. ee . P. e- ' 2ra(we - We) dw, Wea) 2rAs (we - We) Cw, Wey) 2-5) where ;20 (i=l,...,5). The first two terms on the RHS measure the costs

associated with plans for assets and expenditure being out of line with their steady-state values. The third term assigns costs to changing expenditure and thereby will smooth the path of adjustment. Hendry and von Ungern-Sternberg (1981) use a loss function with the first four terms, giving this justification for the fourth.

..., when the primary objectives are to attain [(2.4a) and (2.4b) |, it does not seem sensible to quadratically penalize changes in we when it is known that we has changed. Thus there is an offset te::m

[the fourth] to allow more adjustment at a given cost when we has changed than when it is constant. (p. 240, italics in the original)

Noting (2.4a), Hendry and von Ungern-Sternberg use -2A4(wh-w, 1 )Ax, as the offset term, and it reduces the cost of changing we relative to Weed when

the direction of change is the same as for the forcing variable x, (or,

t equivalently, for we). Nickell (1985, p. 120) objects to such a term by the following illustration for which \,=\,=0. If an agent were out of long-run equilibrium last period but now wenw, awe then the agent (temporarily) moves away from we even though immobility implies being at the long-run equilibrium value. One solution is the following: the agent is concerned about moving w, in the same direction that we has changed relative to the

realized value Weeq rather than the lagged equilibrium value w One

e t-1° possible offset term is -2d5 (wh -w, 4) (wE-we 4): it gives no incentive t:o

: e . P : : . change we if We=We od and so avoids Nickell's objection. For generality, we

allow both 44 and A, to be non-negative: below, we consider the effects on

the agent's decision rule of restricting either (or both) to be zero.

Two equivalent decision rules can be obtained from minimizing the expected loss function with respect to planned expenditure, one in terms of equilibrium values and the other in terms of the forcing variable. Both offer insights, so we consider each in turn. The first is obtained by setting [E(q,)/awe] equal to zero where the expectation E(+) is taken over some (for the time, arbitrary) information set TL: Denoting such an expectation of a variable by a circumflex (*) over the variable, the

decision rule is:

P A . A - “e * A ve We Meld (A4/P) (x, Xe.) + 9o(we Wey) + 93(a. 4 ae. (2.6) where y and the 9,'s are functions of the A'S: eb = (HA, + Ag + Aad - (2.7a) * ** 89 = [CgtrAs)k - AGH db I/p (2.7b) 6, = [HYA,(H™-1) + Aq + Ag + Agl/¥ (2.7c) 6, = (H'2A, + A, + As) /¥ (2.74) * 6, = (HA,)/» . (2.7e)

(6, and @, are used below.) All variables appear as expectations because the equilibrium values we and ar are functions of Xe» and x, may or may not be in Th and, depending upon the interpretation of x and w, their lagged values likewise may or may not be in TE. The first term on the RHS of (2.6)

results from Hendry and von Ungern-Sternberg’s offset term. The expression

A A

(we-we in the second term is the discrepancy between the expected

equilibrium value of We and (the expectation of) Weep the most recent A

A realized value of Wee The expression (a, y74b-p in the final term is the

extent to which the (expected) realized value of assets at the beginning of the current period is out of line with their expected equilibrium value. Thus, the latter two terms in (2.6) measure the optimal adjustments to Wy,

because of long-run disequilibria in expenditure and asset holdings. The

first term captures adjustment due to changes in the equilibrium value of

wes Substituting (2.4a) and (2.4b) into (2.6) and re-arranging gives

) A _ A _ A - A wee Wey 7 85 + 94 (x, Xe) + 92(%, 4 wep + 93(a, 4 Xp » (2.8) which is the decision rule expressed in terms of the forcing variable x.

The realized value Ww, may be stochastic and not necessarily equal to

we, We allow for that discrepancy by positing - P ~ 2 we we + UL u, NI(0,o%) (2.9)

where UL is independent of tT. and so of we? Agents make plans which are optimal conditional on the information available to them, and discrepancies between those plans and actual outcomes arise solely because of shocks outside of (and orthogonal to) that information. This efficient use of information corresponds to the statistical concept of innovation errors

entailed by conditioning; that ties economic theory to statistical

properties of a corresponding empirical model. Realized expenditures are:

A

We 7 Me. 7

A A

t In a non-stochastic steady-state with Ax=g, (2.3) implies a solution of

(W/X) = D+(A/x)? (2.11) where $=03/82>0 and D=exp{[69-(1-6,)g]/02}, linking the steady-state conditions (2.la) and (2.1b).

Although the loss function q, appears simple, several well-known models (including partial adjustment and error-correction) exist as special cases to the corresponding optimal rule for we in (2.6)-(2.8). When only

quadratic terms appear in (2.6) (i.e., A,=Ag=0), then §6,+8,=6, and (2.10)

“Te A4=0, that term vanishes and (2.6) is a partial-adjustment equation

involving long-run targets. However, when equilibrium values in (2.6) are expressed in terms of the forcing variable x, neither that new equation (nor its estimable companion) need be partial adjustment, even when Aq=0.

5 . :

The disturbance u_ also embodies the approximation error in (2.3) and mis-specification error. The bearing of such errors on empirical model design is addressed in Section 3.

A A

simplifies to eliminate (X,-X,.4)> giving a natural generalization of partial adjustment (but here, adjustment to disequilibria in both x and a). We 7 My 89 + 92(X,-w, 4) + 93(a, 4 -X,) + uo (2.12) If the asset-to-income target is also unimportant (i.e., 4,=0), the "pure" partial adjustment model is obtained. Alternatively, if only A, is zero, then @,=0 in (2.10) to give an error-correction mechanism with no integral cont:ol:

Ww 7 My 89 + 91(X,-X, 4) + 9o(X, 4-4) + ue 3 (2.13) cf. Davidson, Hendry, Srba, and Yeo (1978). Finally, if the agent’s

information set tT, is (X?,W2 4) where Z5= (Zo, - z5) for arbitrary z,

v2 5 yo then all the expectations in (2.10), (2.12), and (2.13) are actual values.

The choice of the information set, the measures of expenditure, income, and assets, and aggregation over agents and time are issues important in linking this theoretical model to an empirical model of expenditure, but a thorough treatment of them is outside this paper’s scope. Even so,

econometric methodology can help understanding these and other facets of

modeling, so it is discussed in the following section.

3. Econometric Methodology

This section discusses the interplay between economic theory and the data, and so the role of testing and design in empirical modeling. Modeling itself is viewed as an attempt to characterize data properties in simple parametric relationships which remain reasonably constant over time, account for the findings of pre-existing models, and are interpretable in the light of the subject matter (e.g., theory, institutions, historical background). Hence, econometric models are viewed as simplifications of the underlying real-world process generating the data; test statistics serve as evaluation and design criteria for these models .°

SFor general expositions and bibliographies, see Hendry and Richard (1982, 1983), Hendry (1983, 1987a), Hendry and Wallis (1984), Ericsson and Hendry (1985), and Spanos (1986).

10

The economic theory upon which an empirical model is based often contains many ceteris paribus conditions which may not hold in fact. Thus, one of the tasks of the econometrician is to choose an empirical model which both embodies the economic theory (and so permits interpretation of the model itself) and allows for the presence of any significant factors not: fully specified by the economic theory. If an empirical model fails to allow for the presence of such factors, then inference, forecasting, and policy analysis based upon it are likely to be unreliable. That argues for initially specifying a rather general empirical model.

Even so, any empirical model (including such a "general" specification) is inherently a reduced re-parameterization of the data generation process and is obtained by implicitly performing two types of operations on that process: integrating out (i.e., excluding) variables and treating one set of variables as being determined by contemporaneous values of another. Those two operations correspond to the statistical concepts of marginalizing and conditioning respectively; the former includes aggregation over agents and

time, and the latter inter alia reflects the notion of economic agents

forming plans contingent on (weakly exogenous) contemporaneous variables. Such operations necessarily entail that the "error" is a derived rather than an autonomous process, containing everything not modeled explicitly. Likewise, the parameters of the empirical model are derived, and are defined by the model's specification and the orthogonality conditions of the estimation technique. Hence, it may be possible to design an empirical model to satisfy both data-based and theory criteria.

To illustrate, consider the standard linear regression model:

Ye ~ AX, + uy t=1,...,T (3.1) where x, are the k relevant regressors and # is the (presumably constant:) parameter of economic interest. For (3.1) as an empirical model, both f and

{u,) are derived, not autonomous. For instance, for OLS, B is defined by

11

the orthogonality condition (EX, Cy, -B’x,) ]=0; t=1,...,T} and u, by

Ye ECy, IX); so the properties of both may vary according to the choice and functional form of x! For reliable inference, it is important

to evaluate whether the empirical model (3.1) satisfies the properties which its proponents claim (e.g., white noise, innovation disturbances, constant parameters). Further, it may be possible to design empirical models which have those properties and so may permit valid inference.

How well or poorly designed an empirical economic model is depends upon its ability to capture salient features of the data and to deliver reliable inference on economic issues (e.g., coefficient estimates, predictions, policy). Hence, we place considerable emphasis on a battery of test statistics which serve as criteria both for evaluating existing specifications and for designing new ones. The criteria are standard and relate to goodness-of-fit, absence of residual autocorrelation and heteroscedasticity, valid exogeneity, predictive ability, parameter constancy, the statistical and economic interpretation of estimated coefficients, the validity of a priori restrictions, and the ability of a mod2l to account for properties of alternative models. Table 1 summarizes the corresponding statistics, which are arranged by the types of information generating testable null hypotheses: the data of one’s own model, the measurement system of the data, economic theory, and the data of alternative models. Most of the model's empirical properties bear on its economic as well as statistical interpretation: four deserve particular note.

Parameter constancy is at the heart of model design, both from a stazistical and from an economic perspective. Most estimation techniques require parameter constancy for valid inference, and those that seem not to do so, still posit "meta-parameters" assumed constant over time. Since

economic systems are far from being constant, and the coefficients of

"3: milar formulae exist for more general models and estimation techniques.

lia Table 1. Evaluation/Design Criteria

Information Set Null Hypothesis Alternative Hypothesis Sources

(A) ow model’s data

(Al) relative innovation errors first-order residual Durbin and Watson (1950, 1951) past autocorrelation " " 2: q@-order residual Box and Pierce (1°70); autocorrelation Godfrey (1978), Hervey (1981, p. 173) " " 3: invalid parameter Johnston (1963, p. 126) restrictions n " 4: q@-order ARCH Engle (1982) " " 5: heteroscedasticity White (1980, p. 825), quadratic in regressors Nicholls and Pagar: (1983) " " 6: q@-order RESET Ramsey (1969) " nomnality of the 7: skewness (SK) and Jarque and Bera (1980) errors excess kurtosis (EX) (A2) relative weakly exogenous 8: invalid conditioning Sargan (1958, 198C), Engle, present regressors Hendry, and Richard (1983) (A3) relative constant parameters, 1: parameter non-constancy, Fisher (1922), Chew (1960), future adequate forecasts predictive failure Brown, Durbin, and. Evans

(1975), Hendry (1979)

(B) measurement data "impossible" predictions system admissibility of observables

(C) economic theory "implausible" coefficients, theory consistency predictions

@) altermative models’ data

(D1) relative variance relative poor fit Hendry and Richard. (1982) past dominance " variance inexplicable observed Cox (1961, 1962), encompassing error variance Pesaran (1974) " parameter significant Johnston (1963, p. 126), encompassing additional variables Mizon and Richard (1986) (D2) relative exogeneity inexplicable valid Hendry (1988) present encompassing conditioning (D3) relative forecast informative forecasts Chong and Hendry (1986) future encompassing from rival model

Note: The mumbers preceding the alternative hypotheses label the statistics in Sections 5 and 6.

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derived ("non-structural" or "reduced form") equations may alter when any of the underlying parameters or data correlations change, it is important to identify empirical models which have reasonably constant parameters and which remain interpretable when some change occurs. That puts a premium on good theory. Conversely, empirical models with constant parameterizations in spite of "structural change" elsewhere in the economy may provide the seeds of fruitful research in economic theory.

Recursive estimation of an equation provides an incisive tool for investigating parameter constancy, both through the sequence of estimated coefficient values and via the associated Chow statistics for constancy .° Again, using the standard linear regression model to illustrate, the OLS estimator of # in (3.1) is Br where:

A B. = (KEK) TRLY, (3.2) with Xx. - (x... XD’ and Y, = (yy --+¥p)'- It is-relatively simple and computationally inexpensive to obtain the entire sequence of OLS estimates (B.: teh,...,T)} starting with some initial number of observations h (h2k). Recursive estimation can generate voluminous output: T-h+l estimates of each coefficient, a standard error for each estimate, the sequence of estimated innovations (recursive residuals), and the many possible sequences of Chow statistics. Graphs can portray this information in an effective, concise manner, and we will use them to do so below. The Chow statistics also play crucial roles (a) for testing weak exogeneity indirectly through testing the conjunction of hypotheses embodied in super exogeneity and (relatedly)

(b) for testing feedback versus feedforward empirical models; cf. Engle,”

Hendry, and Richard (1983) and Hendry (1988).

Sthese tests of constancy are intimately related to tests of forecast accuracy; cf. Brown, Durbin, and Evans (1975), Hendry (1979), and Kiviet (1986). Dufour (1982) elegantly summarizes recursive techniques and their implications. vot

13

Cointegration links the economic notion of a long-run relationship between a set of variables with statistical models of those variables.” For example, in the theory-model of Section 2, the realized values of W and A need not be proportional to X, but economic forces (agent optimization) bring them back into line if they are not so. With shocks in every period, proportionality never need hold, yet agents work to absorb those shocks and W and A never drift "too far" from their equilibrium values. If x, is non-stationary (e.g., integrated of order one, I(1)), we and a, also will be

so, but some linear combination of w and a, may be stationary because

t’? Xe t

of agents’ behavior, i.e., making that set of variables co-integrated. The choice of normalization of the cointegrating vector is an unresolved issue, but both economics and the data can help. Theory may suggest which variables agents aim to control and on which ones they condition their plans, and parameter constancy in an empirical model is not invariant to normalization when the economy exhibits structural change. Cointegration implies the existence of an error-correction representation of the relevant variables, leading to the third issue, dynamic specification. Normalization and conditioning lead to the fourth issue, exogeneity.

Dynamic specification influences model design because of the statistical and economic importance of white-noise, innovation disturbances. Dynamics may appear in empirical models because the agent's optimization

explicitly dictates its presence (as in Section 2 and Nickell (1985)), “because agent behavior implies cointegrated variables and hence dynamics, because ceteris paribus conditions of the theory-model may not hold in fact, or any combination thereof. As a rule, dynamic mis-specification

invalidates inference, so dynamics cannot be safely ignored, and a general

See Engle and Granger (1987) and Hendry (1986). See Engle (1987) and Dolado and Jenkinson (1987) for recent surveys on cointegration.

14

specification (at the outset, at least) often is advisable. 1°

Weak exogeneity can occur when agents condition on information. If they use it efficiently, innovation errors are implied, raising the issue of dynamic specification. Weak exogeneity is testable, often as an implication of siper exogeneity (and so of models having constant parameters). Section 5 further discusses exogeneity in the context of the empirical model, !+

The econometric approach above contrasts with those in which the data serve only for estimating parameters of the theory-model. Estimation is an important issue, but, in itself, provides little guidance on the value or lack thereof of the empirical model obtained. An empirical model is unlikely to allow reliable statistical or economic inference, forecasting, or policy analysis unless it is "well-designed" in the sense that it does not violate either the assumptions made at the outset or the numerous

testable implications of those assumptions.

4. The Data Series and Data Transformations

In light of the modeling approach outlined in Section 3, a satisfactory empi1rical model must account for basic features of the data, and a model may be designed to do so. Conversely, an empirical model failing to account for them may be re-designed to do so better. Instead of being "data mining",

look:ng at the data can be invaluable in model construction. Further,

entire classes of models may be incompatible with observed data properties; nb. Deaton (1987). The remainder of this section describes the data, The data are annual values for Venezuela for 1968-1985 of consumers’

expenditure on non-durables and services (C), national disposable income

10566 Hendry, Pagan, and Sargan (1984) and Trivedi (1986) for extensive

discussion on theoretical aspects of dynamic specification.

lth four distinct concepts of exogeneity, namely weak, strong, super, and strict, correspond to different notions of being "determined outside the mode]. under consideration" according to the purposes of the inferences being conducted, i.e., conditional inference, prediction, policy analysis, and forecasting, respectively. For detailed discussion of these concepts, see Engle, Hendry, and Richard (1983) who build upon those in Koopmans (1950).

15

(Y), and end-of-period liquidity (L) as measured by the monetary aggregate m,.t? The unit of currency is the Bolivar (abbreviated Bs), and its value was pegged at 4-4.5 Bs/US$ until February 1983, after which time substaatial devaluation occurred under a multi-tier exchange rate system. These series are real (1968 Bolivares) per capita; the price deflator (P) is for all consumers’ expenditure. Appendix A gives details of the data and sources. Before examining the data in detail, we note several caveats. We chose to model the determinants of consumers’ expenditure on only non-durables and services so as to measure relatively homogeneous expenditure and to avoid difficulties associated with calculating the flow of services from durables. The expenditure data allow finer disaggregation, presenting an avenue for further research; cf. Palma (1976). Alternative measures of liquidity are available or feasibly constructed: an adjustment for Venezuelan holdings of liquid assets in foreign countries may improve the measure substantially although the mechanism by which such assets influence domestic expenditure is unclear. Price deflators are available for aggregate consumers’ expenditure and for its major components. Most of those series are similar, and empirically it mattered little which one was used. That is in part a consequence of the analytical properties of the theory-models and the models estimated: in the long-run, they are invariant as to whether expenditure, income, and liquidity are nominal or real, total or per capita. Because population growth is quite constant throughout the sample, the empirical results are virtually the same whether the data are aggregate or per capita. However, the population size increased by 70% from 1968 to 1985, so per

capita data are more amenable to economic interpretation.

12. use the notation (C, Y, L) to distinguish from the (potentially latent)

economic-theoretic variables (W, X, A) in Section 2.

Earlier data are available, but involve numerous and substantial re-definitions of the series, rendering them less informative. More frequent data are available, but only for some series.

16

Measurement of income raises numerous issues. .Personal: disposable income is clearly preferable to national disposable income, but data for the formei: are not available and our attempts to construct such a series have been unfruitful. Neither measure accounts for the sometimes substantial “inflation tax" from holding liquid assets. In an attempt to improve that situation, we constructed an adjusted series Y, defined as Ye CAP LL a: which nets current income of the financial loss from holding last period’s end-of-period assets in the presence of current inflation and so aims to better capture "that accrual which would leave real wealth intact"; cf. Handry and von Ungern-Sternberg (1981) 23 To provide some sense of the magnitudes involved, for 1973 (L477) and Ap, are .27 and 5.5% respectively, so Yen(1-Ap, (Ly 4/¥,) 1+¥,=-985Y, ; but by 1984 (L._4/%,) and AP, are .52 and 16.8%, with Ye only 91Y,. Adjusted and measured income differ substantially in the latter instance. | | ve

consider some basic properties of the data themselves. From Figure 1, three distinct episodes are evident in the behavior of expenditure and income. Before 1974, both grew at relatively moderate rates. Because of dramatically increased petroleum revenues, income increased by over 30% in 1974 and, through 1981, remained on a plateau at 155-170% of the level of 1968 income. From 1974, expenditure grew rapidly (but less so than income), leveling off in the late 1970's, with the expenditure to income ratio in | 1981 being virtually the same as in 1968. From 1981 to 1985, (real per capita) income plummeted at 7% per annum, but expenditure remained relatively constant. Figure 2 graphs the growth rates of expenditure and income: the levels of the series are highly correlated but not their growth

rates, and the volatility of income is notably greater than that of

13 aiso, Hendry and von Ungérn-Sternberg (1981) include a (possibly non-unit)

coefficient on -(Ap,)L to allow for scale effects in the mis-measurement of Ap and L. We would iitke to do so as well, but given the very limited number of observations and the value and extensive use of recursive estimation, we set aside that generalization for further research.

loa

Figure 1. The logs of real per capita expenditure (c) and of real per * capita income (y ) (with means adjusted).

8.058 7,989} ----- 7,919 7.849 + 7.780 | en 7,718 | |

7,648

1979 1972 1974 1976 1978 1980 1982 1984 1986 an Year

Figure 2. The growth rates of real per capita expenditure (Ac) and of real per capita income (ay").

0.324 0.267 @2lt b= ais} 0.098. | 9.042 bn a

Nomen

0.078

‘ : pereeees

972 1979 1981 1983 1985

1971 1973 1975. Year

17

expenditure, A static relationship between c and y is unlikely to generate such properties, and even a dynamic bivariate one may not.

One possible explanation for the differing responses of expenditure to income is the dramatic change in liquidity: Figure 3 graphs the (logs of) the expenditure-income:.and liquidity-income ratios. Those ratios rise by 27% and 135% over the period. Consistent with the theory in Section 2, the subsitantial increase of the latter ratio could account for the stability of expenditure in the 1980's in spite of income falling. Both ratios markedly fall in 1974 and rise in 1982-83: large changes in income are primarily responsible rather than changes in expenditure or liquidity; cf. Figure 1.

Digressing briefly, petroleum revenues are central to understanding the income process in Venezuela. Venezuela is a member of OPEC, with petroleum exports equaling approximately a quarter of GNP and accounting for roughly 90% of the value of all its exports, much of which is sold to the United States. 14 As Figure 4 shows, the nominal growth rates of national disposable income and petroleum exports (denoted Ayn and Axp) are highly correlated and, in fact, are virtually indistinguishable after accounting for their different scales. This, and the relationship between US and Venezuelan inflation noted below, play a crucial part in Section 6 when we attempt to distinguish between feedback (conditional) models as developed in Section 2 and feedforward (expectations-based) models.

Finally, consider prices. Figure 5 compares US inflation (denoted Ap’) and Venezuelan inflation (Ap). The two were similar through 1978, but, while the United States experienced moderately higher inflation after the second oil-price shock in 1979, Venezuelan inflation jumped to nearly 20%, falling during the world-wide recession in the early 1980's and sharply

increasing again in 1984. The higher inflation rates during the second half

Be ——_ Dinas

14 conversely, a large proportion of imports by Venezuela is from the United States.

17a

Figure 3. The logs of the consumption-income ratio (c-y") and of the liquidity-income ratio (2-y").

oan

1978 1972 1974 1976 1978 1988 )=—-1982 1984-1986 ear

Figure 4. The growth rates of nominal income (Ayn) and of nominal petroleum exports (Axp) (with ranges adjusted).

——— dyn 0.416

0.348 0.286 0.223 Q.162 0.098 by

0.036

1971 1973 1995, 1977 s«1979 198119831985 Year

17b

Figure 5. Venezuelan inflation (Ap) and US inflation (Ap*).

0.188

0.167 - ——— oP

197@ 1972 1974 1976 1978 1988 1982 1984 1986 Year

Figure 6. Equation (5.4): actual and fitted values for Ac.

1973 1976 1979 1982 1989

18

of the sample, combined with greater liquidity, led to the more substaritial discrepancies between Y and Y" observed above. Inflation may also affect expenditure directly, e.g., if agents have difficulty discerning relative from absolute price changes; cf. Deaton (1977). Further, the theory-meodel in Section 2 takes inflation as given, yet the constants of proportionelity B™ and K* might vary as inflation does. And, without specifying the precise timing of information availability and agents’ actions, the existing theory can not exclude short-run inhomogeneity of consumers’ expenditure with respect to prices. All three reasons imply inflation and its lags entering (2.10) additively.

Before moving to empirical model specification and testing, one more issue must be addressed: the number of observations. There are eighteen in .total, with only sixteen used in estimation. In many contexts, that number would be small and, given the relatively large number of coefficients tio be estimated, impracticably so. The absolute number of observations does restrict the complexity of the empirical model, placing a premium on both good economic theory and effective econometric methodology. However, the variability of the data as well as the number of observations determines the precision of the resulting estimates and the power of tests. For instance, the variance of the OLS estimator for (3.1) is approximately o2+[T+E(x,xt)] 7 for stationary data. Although T is small, movements in data such as c-y" and t-y" are large: fluctuations in comparable post-war US

data are an order of magnitude smaller. Such properties help account for

15

the small estimated standard errors obtained below.

5. An_Empirical Model of Consumers’ Expenditure

This section develops a conditional econometric model of Venezuelen

consumers’ expenditure on non-durables and services. It is interpretable in

5 : . Large fluctuations in the data also can reduce problems of measurement error.

19

the framework of the agent optimization problem of Section 2, with income, liquidity, and inflation all helping determine expenditure. However, since significant, economically plausible estimates are not sufficient for reliatle inferences, the remainder of the section evaluates the empirical model by the criteria discussed in Section 3, focusing on dynamic specification, parameter constancy, cointegration, and exogeneity. Encompassing is addressed in Section 6.

In order to establish a baseline innovation variance, consider the following general autoregressive distributed lag relationship for consumers’

expencliture conditional upon income, prices, and liquidity.

2 2

, = (a* 82 z (pry. .+7" D 5.1 Ce TB ait tate a? + 2 Paye-at Pea? to # MiPor + 4, +1)

1 Do, is a +1/-1 dummy for 1970-71 to account for apparent measurement errors

in consumers’ expenditure for those years; see Appendix B. With loss of

generality, we assume that (c-y*) and (h-y") are cointegrated, implying that 1-E(a., +6; )=28; and that prices enter only as inflation (i.e., Ey,~0).79 With cointegration, (5.1) can be re-written as in (5.2) below with all coefficients in (5.2) unrestricted. The assumptions imbedded in (5.1) are testable and will be tested (in part) below, but the tests available lack power because of the small sample size: even with the cointegration

restrictions imposed, (5.1) implies ten unrestricted coefficients estimated

with sixteen observations.

1 * * Ac, = a,c, 4 + ey Pi eat P ew? + 6,42 4 + ay(c-y eel * + bo(2-y ),.y + Bo + #iDor + YY (5.2)

*

16 the economic theory of Section 2 implies cointegration of (c-y ) and (£-y ), provided agents can maintain a finite variance on their realized errors.

20

This equation has the general form of the theoretical model (2.10), but contains additional lags because the theory is vague about the precise dynamic structure. The lagged rate of change of liquidity is included because the theory-model does not exclude short-run inhomogeneity of consumers’ expenditure with respect to liquidity (as with prices).

Data coherence and dynamic specification. Table 2 lists the coefficient estimates for (5.2), the associated conventional and heteroscedasticity-consistent standard errors (denoted (+) and [*] respectively; see White (1980) and Nicholls and Pagan (1983)), and diagnostic statistics, to the extent that the latter are available for such an over-parameterized model. €;(q) and n; (4,4) denote statistics which have central y?(q) and F(q,r) distributions respectively under a common null and against the jth alternative, where i is as listed on Table l.

The model in Table 2 has two notable features. First, the residual standard error is slightly above 1%: any new model will require a similar or smaller equation standard error as a necessary condition for encompassing the model in Table 2. Second, three economically sensible and statistically acceptable classes of parametric restrictions are apparent. The lagged rates of change of expenditure and of liquidity are insignificant: a single lag on each level is sufficient to capture those parts of the dynamics. The coefficients on the current and lagged growth rates of income are equal: that can be interpreted as a statistical smoothing of income in order t» extract changes which are more permanent. Changes in the growth rate of income also immediately affect the budget constraint and liquidity, so giving the coefficient on current income (or its growth rate) several interpretations. The coefficient on current inflation is approximately twice the magnitude of that on lagged inflation, and opposite in sign. Imposing that restriction implies the term Ap, +A?p, (with negative

coefficient), which is a predictor of next period's inflation, optimal if

20a

Table 2. A general autoregressive-distributed lag representation for real per capita consumers’ expenditure conditional _on incomes, prices, and liquidity.

lag i

Variable

Constant .006 (.033) - [ .027] T = 1970-1985 R? = 9743 & = 1.199% dw = 2.59 €2(2) = 3.3 ne(1,5) = .5 &7(2) = .2 Notes: 1, The dependent variable is Ac,. Even so, the equation is in

levels, not in differences, rioting the transformation of variables from the re-parameterization of (5.1) to obtain (5.2).

2. Because of the small number of degrees of freedom remaining, there are few diagnostic statistics. More statistics appear with the restricted equations (5.3) and (5.4), in which cases the validity of those statistics is conditional upon the simplifying restrictions.

21

prices vary quadratically. Economically, that might capture a smaller desired D in (2.11) in the face of higher inflation, or the aim of consumers (e.g.) to save more now in anticipation of higher inflation so as to be able to consume more closely the same amount in real terms when that higher

inflation arrives!’ Re-estimating (5.2) with those restrictions imposed

gives (5.3). Ac, = .460(A,y,/2) - .270(Ap+A?p), - 141(e-y"), 4 (047) (028) (.023) [.051] [ 024] [016] + .072(2-y"), , + 021 + .026Dg, (5.3) (.013) (.016) — ¢.007) [.010] [.011] [.001}

T = 1970-1985 R?2 = .9725 &@ = .9603% dw= 3.03 €,(3) = 6.5

n3(4,6) = .1 6(2,8) = .4 €7(2) = .5

The F-statistic , tests the restrictions which obtain (5.3) from Table 2,

and it is insignificant.

Surprisingly, the estimates in (5.3) are remarkably close to those obtained by Hendry and von Ungern-Sternberg (1981) with quarterly data for

the United Kingdom. Comparable estimates to those for the growth rate of

17 the presence of the term AptA?p (and the interpretation of it in the text)

may be viewed in several complementary ways. First, current purchases of consumer durables are one way of "saving" now for consumption later. When a higher inflation is anticipated, the budget constraint implies lower current expenditure on non-durables and services to do so. Second, because the income distribution is highly skewed in Venezuela, increasing liquidity by saving may be one of the few means available to a substantial fraction of the population for avoiding substantial negative shocks to real consumption in the face of anticipated higher inflation. That applies particularly to periods like 1978-79 and 1982-84 during which real per capita income fell: see Figure 2. Third, consumers may have difficulty distinguishing between relative and aggregate changes in prices, so inflation may induce saving; see Deaton (1977). Finally, Apt+Q?p might capture the degree to which the coefficient on (Ap, )L . in Y is different from unity, cf. Hendry ard von Ungern-Sternberg (15at, p. 247).

The term Ap+A?p does not appear to be a proxy for the interest rate, nor does the interest rate appear important in determining expenditure. The rate offered at commercial banks is statistically insignificant if added. to (5.4) below, and that result is insensitive as to whether the rate is contemporaneous and/or lagged. Further, Ap+A?p remains highly significant with the interest rate included in (5.4).

22

income and the lags of (c-y") and (2-y") are .50, -.16, and .072,+8 The implied long-run elasticity ¢ of the expenditure-income ratio with respect to the Liquidity-income ratio is .51, remarkably close to one-half and to Hendry and von Ungern-Sternberg’s estimate of .44. Because of that, and in an effort to design as parsimonious a model as possible, we re-estimated

(5.3). with ¢=.5.

A

* Ac. = 457 (Moy, /2) - .270(Ap+A2p), - —-.142[ (e-y")-.5(£-y Yet (030) (026) (.019) [.033] [.023] [.014] + 019 + .026D9, (5.4) (.004) (.007) [.004] [.001]

T= 1970-1985 R? = .9725 6 = .91608 dw=3.05 £€,(3) = 6.7 3,(5,6) = 1 mg (1,10) = .01 94(1,9) = .5 5 (8,2) = 3

ne(2,9) = .2 €,(2) = .6

The two F-statistics "34 and Ns, test the restrictions which obtain (5.4) from Table 2 and (5.3) respectively, and, in conjunction with the other

statistics, they suggest the statistical acceptability of those restrictions

on the information available. +?

Seven so, the time series and data moments of the two countries differ markedly. 19the power of these tests is quite possibly very low, although the few degrees of freedom involved are balanced to some extent by the considerable information content of each observation; cf. Section 4. Even so, the Durbin-Watson and Box-Pierce statistics provide some weak evidence of negative autocorrelation in the residuals. (Other tests for autocorrelation are not calculated by PC-GIVE for such a small sample.) Additional measurement errors of the sort described for 1970-71 in Appendix B or dynamic mis-specification could be responsible. In support of the latter, the Durbin-Watson, statistic in (5.4) falls to 2.27 when the one- and twoperiod lags on Ay, and Ap, are added; but those lags are insignificant, whether tested jointly or individually. Additional data may resolve this issue. We also note that, in their empirical model of consumers’ expenditure, Hendry and von Ungern-Sternberg (1981) detect negative autocorrelation of approximately the same magnitude as that implied by the Durbin-Watson statistic in (5.4). This class of model may imply negatively autocorrelated residuals, either due to the finite sample properties of the estimation method used or from a type of mis-specification characteristic to error-correction models with integral control; but that remains conjecture.

23

The coefficients in (5.4) have sensible values and highlight the roles of contemporaneous and lagged information. ‘In spite of income, liquidity, and prices being highly inter-correlated, the RHS variables in (5.4) are virtually orthogonal to each other, giving an economically plausible partitioning of the information set. All the economic variables may be interpreted as affecting consumers’ liquidity, and so consumers’ inclination (or ability) to spend. Income growth and inflation affect liquidity both immediately (by increasing current liquidity directly and through the inflation tax) and in the future (because of their long-run effects and because of the interpretation of Ap+A?p as a predictor of inflation). The median lag for expenditure responding to changes in income is short, under a year; but adjustment is gradual thereafter. Figure 6 shows the actual and fitted values for the rate of change in real per capita expenditure (Ac) over the sample period: 6 is less than 1%, but ¢ changes by over 4% for half the observations and by over 10% for two observations. That implies a remarkable fit relative to the observed data fluctuations.

The steady-state solution implied by (5.4) is: * * } (C/Y ) = (L/Y )°5 + exp{.135 - 3.82g - 1.90Ap) (5.5)

where g and Ap are the steady-state growth rates of income and prices. Equations (5.4) and (5.5) correspond to (2.10) and (2.11) of the theorymodel. The exponential in (5.5) is the coefficient of proportionality D in (2.11), and is a function not only of g (as postulated) but of Ap (which belonged to the host of ceteris paribus assumptions in the theory-model). The coefficients in the exponential imply that agents spend more relative to income for a given liquidity ratio when income is growing slower and/or inflation is lower. The latter implies improved future liquidity. Thus, although (5.4) is a conditional model, its particular specification gives it

and its long-run solution (5.5) a forward-looking characteristic.

24

Hquation (5.4) has a plausible economic interpretation in light of (2.10) and (2.11), is a statistically acceptable simplification of Table 2 (given our information set), and appears adequately dynamically specified, but it: must satisfy many additional conditions to be a satisfactory empirical model. These include: the estimated parameters are constant; expenditure, income, and liquidity are cointegrated; income and prices are weakly exogenous; and (5.4) encompasses all existing models. We now turn to the first three.

Parameter constancy. To investigate the constancy of the model (5.4), we adopt the recursive estimator described in Section 3. Figure 7 records

the sequences of one-step residuals (i.e., y -x,B,) and corresponding

t calculated equation standard errors (426, is shown centered on zero). The residual standard error has varied little, in spite of the dramatic fluctuations in the series themselves. The estimated coefficients also are constant: Figures 8, 9, and 10 show the sequences of estimates for the coefficients on (A2y,/2), (aptA?p),, and [(e-y)-. SLY Ie a together with plus-or-minus twice their sequentially estimated standard errors which provide an approximate 95% confidence interval. The accrual of information over time is particularly apparent for inflation, with its coefficient estimated standard error falling by two-thirds in 1979. That is not so

surprising, given the marked change in the properties of inflation in 1979;

cf. Figure 5. Finally, none of the Chow statistics for the sequences

(a) (1979, 1980, ..., 1985), (b) (1979, 1979-80, ..., 1979-85), or (c) (1979-85, 1980-85, ..., 1985) is significant at the 5% level.”° 20

In fact, no individual Chow statistic of any sequence exceeded even a third of its corresponding 5% critical value. These Chow statistics (and the other diagnostic statistics) served as design criteria, so their insignificance in part relfects our ability to design an adequate empirical model. However, (5.4) is virtually identical to Campos’s (1984) final specification using data for 1968-82 and upon which this study is based. Thus, forecasts for 1983-85 present a veritable test of the empirical model (5.4) because the data for those years were not available to Campos (1984).

24a

Figure 7. Equation (5.4): one-step residuals and the corresponding

calculated standard errors.

0.822 @. 016 @.011 8.085 -0, 008 8, G5 “0.011

—— one-step residual

0.017

1979 1988 1981 1982 1983 1984 1985 Year

Figure 8. Equation (5.4): recursive estimation of the coefficient on the

* two-year average growth rate of income (Azy¢/2).

0.648 ¢ —— coefficient estimate

0.686 On iaiiaiad coefficient estimate + 2 standard errors

“Hey et leee hehe TTD eee wecceeseessaces

0.963 0.928 0.478 0.435 8.393 0.358

1979 1988 1981 1982 1983 1984 1985 Year

24b

Figure 9. Equation (5.4): recursive estimation of the coefficient on the

inflation rate term (Ap+Adp) , .

0,069 i —— coefficient estimate

0 eeene coefficient estimate + 2 standard errors -0,136 | ‘s. “0.203 | annepenmynrteorernereeetaetana Meenas ccs -0.337 r cee genset tees eeeee eee Seeeennccees Necese . “cconcesessesusaqannnnensnnnsnesseneeteees ES 0,483 0,478

1979 1980 1981 1982 1983 =: 1984 1985 ; Year

Figure 10. Equation (5.4): recursive estimation of the coefficient on the

* * error-correction term [(c-y )-.5(2-y e-z)-

0,089

en 6.116 —— coefficient estimate

a coefficient estimate ¢ 2 standard errors -0,138

0.143 -@.157 8,170

eonccnteessetr’®

“0.188 atthe gganennnnnne nT

we . SOPTy Laer TT en he

penne ON aea saat ro

1979 1988 1981 1982 1983 1984 1985 Year

25

To evaluate further the numerical and statistical accuracy of (5.4), we estimated it using the data for 1970-80 only and calculated forecasts for the remaining five years using the sub-sample coefficient estimates but actual values of the RHS variables. As Figures 8-10 show, the sub-sample estimates are virtually those in (5.4) but have somewhat larger estimated standard errors. Figure 11 plots the actual and forecast values of Ac for 1981-85 with 95% confidence intervals for each forecast. Figure 12 plots the actual and fitted values of Ac through 1980, with actual and forecast values thereafter. Actual values lie well within the confidence intervals, and the fit of the model (as measured by &) improves slightly with the additional data. In brief, the conditional formulation (5.4) both fits well and is remarkably constant over a turbulent decade and a half of the Venezuelan economy.

Cointegration. In testing for the existence of cointegration, it is necessary to establish first that the individual series are I(1) and then that there exists some non-trivial function of them which is I1(0). The most common approach is to test for a unit root in the univariate representations of the individual series and then in the least-squares linear combination. Table 3 lists the values of the Sargan-Bhargava (Durbin-Watson) statistic and the augmented Dickey-Fuller statistic (ADF) for the logs of expenditure, income, liquidity, prices, and the expenditure-income and liquidity-income ratios. No tests reject the hypothesis of a unit root at the 5% level although the power of these tests is low for a sample size of sixteen and a root close to unity (e.g., .8).2+ The Engle-Granger static cointegration

regression for expenditure, income, and liquidity is:

lef, Evans and Savin (1981), Dickey and Fuller (1979, 1981), and Sargan and Bhargava (1983).

Note also that I(0) series with structural breaks can look like I(1) series: for Venezuela, the former may more appropriately describe the data.

25a

Figure 11. Equation (5.4) estimated over 1970-80: actual and forecast values

of Ac for 1981-85, and 95% confidence bands for the forecasts.

0.087 - ——— actual dc

9.063 bo forecast dc 95% confidence band 4 for forecast

4,839 @.@15 -@, 00? “0.031 0.055 0,879

1982 1983 1984 1985 Year

Figure 12. Equation (5.4) estimated over 1970-80: actual, fitted, and

forecast values of Ac.

@. 116 — actual ac a ¢-forecast period-+

é

|

i]

- ¢ . S |

0.892 fitted ae fe | —— actual dc !

0.069 | ecnn- forecast Ac

0,045) a “ee aX / NS

-0, 001 9,025 + I -0,048

1973 1976 1982 1985

Year

25b

Table 3. Univariate statistics for testing unit roots.

Variable ADF(0)

Notes: 1. The variables Ys 6) and Ys 7) are the residuals from equations (5.6) and (5.7):"° .

* * * 2. The variable ecm is (c-y yer SCA -¥,)- Lagged 2 is used here and in (5.6) and (5.7) because it méasures end-of-period liquidity.

3. The Durbin-Watson (dw), Dickey-Fuller (ADF(0)), and augmented Dickey-Fuller (ADF(1)) statistics are calculated over the maximum number of observations available: 1968-85, 1969-85, and 1970-85, respectively.

26

A

Cc =

t .362

+ 4,45

082, + (5.6)

t-1

T = 1968-1985 R?2 = .9658 G6 = 3.549% dw = 2.01 ADF(0O) = -3.89

ADF(1) = -3.26 The Sargan-Bhargava statistic is at the upper end of the inconclusive region (albeit offering no evidence against white-noise residuals as well), and the Dickey-Fuller statistics are significant at about the 5% level. However, the theory-model in Section 2 is in terms of the expenditure-income

and liquidity-income ratios, suggesting a second cointegration regression.

“x * (c-y ye = -26(2, 4 -Y_) . 36 (5.7)

T = 1968-1985 R2 = .4077 G = 11.368 dw-= .37 ADF(O) = -1.28 ADF(1) = -1.43 None of the test statistics in (5.7) provides much evidence in favor of cointegration although their power to do so is minimal. One alternative to these univariate methods is to estimate the

conditional error-correction mechanism for c

t and test the significance of

the error-correction term therein. Monte Carlo results in Banerjee, Dolado, Hendry, and Smith (1986) suggest that the size of the test based on the t-ratio of the error-correction term is approximately correct for the 5% level and that this test is much more powerful than the Sargan-Bhargava

test. That follows because the Sargan-Bhargava and Dickey-Fuller statistics

for (e.g.) (5.7) impose and cointegrated series tests remain consistent power.

Conversely, the

inhomogeneity, so tests

*

short-run as well as long-run homogeneity on (c-y ), need not be short-run homogeneous. Those univariate even with short-run inhomogeneity, but they can lose

error-correction model allows for short-run

using the t-ratio of the error-correction term may

* be more powerful. To wit, the highly significant estimate on (Agy,/2) in

(5.4) implies substantial short-run inhomogeneity of expenditure with

respect to income, and the t-ratio on the error-correction term is -7.6.

27

Further, Banerjee et al. (1986) show that, in finite samples, the static

estimator of the cointegrating vector can be badly biased towards zero relative to the corresponding estimator in the error-correction model, particularly when R? is small in the static regression. In (5.7), R? is only .41, and the static and dynamic estimates of the cointegrating vector are .26 and .51, respectively, in line with those finite sample results. Thus, although these results on cointegration are qualified, the disparixies between the static and dynamic regressions are in line with existing finite

sample evidence for highly dynamic cointegrated variables and argues for

D) full dynamic modeling, both to achieve greater power and to reduce bias." Exogeneity. One important, testable assumption is the weak exogeneity

of income and prices, i.e., the validity of conditioning upon them for statistical inference (estimation and testing). We test for weak exogeneity both by estimating (5.4) by instrumental variables and comparing those results with (5.4), and by constructing marginal models for income and inflation which are non-constant over time, from which it follows that income and inflation are super exogenous (and hence weakly exogenous) for the parameters in (5.4).

Given the marked dependence of the Venezuelan economy on the United States for manufactured goods and on petroleum exports for the purchase of those goods, we selected APL 1 APL 9» AXP. 1) and Ac. 4 as instruments for

(Azy,/2) and (Ap+A?p) ,. The results are in (5.8).

AE, = — -425(Agy,/2) = .353(ApHA2P), = .155[(c-y")-.5¢2-y*)], (053) (.080) (029) . + .025 + .027D9, (5 8)

(.007) (.009) T = 1970-1985 o@ = 1.2878 (3) = 5.1 94(1,9) = .2

75(8,2) = .5 E7(2) = .2 €,(2) = .4

2216 (5.4) is estimated by Engle and Granger's two-step procedure in which

the residuals from (5.7) replace the error-correction term in (5.4), very similar parameter estimates result, but 6 increases to 1.152%.

28

Sargan’s (1958) statistic €, does not reject the validity of the instruments. Additionally, the estimated coefficients are negligibly different from those in (5.4) and the estimated standard errors are somewhat larger, as would be expected if (5.4) were well-specified with no simultaneity bias. Similar results obtain for other instrumental variables. Super exogeneity requires both weak exogeneity and structural invariance, so finding super exogeneity implies weak exogeneity. Demonstrating super exogeneity relies on showing that the parameters of the conditional »process remain constant even though the marginal process

changes. The precise justification of this test for super exogeneity

requires a subtle argument, cf. Richard (1980), Engle et al. (1983), Engle

and Hendry (1985), and Hendry (1988). Even so, the nature of the argument is well-illustrated with the following simple expectations-based model in which x and y, are simultaneously determined. This model also lays the foundation for testing feedback versus feedforward models in Section 6 and refines the links between parameter constancy and super exogeneity. Suppose that the correct specification for Ye is in terms of the

expectation of x, given z rather than x, itself, e.g.,

t’ t

Ye BrE(x,12,) + ue (5.9) with

x = E(x, 12.) + ov (5.10) where E(z,u,)=0 and E(x, 12,)*0 by assumption, E(zZ,v,)=0 by construction, and B (not necessarily equal to # in (3.1)) is the parameter of interest .27 By

substitution,

Ye = Bix, + (u, - pty.) (5.11)

23 : : : : The variables x and u here are not necessarily equivalent to the variables

in Section 2 designated by the same letters.

29

Instrumental variables estimation of (5.11) using the instrument Ze is * consistent for 8 because Z, is uncorrelated with the composite error term. *

However, the OLS estimator for (5.11) generally is not consistent for B :

- Ax * -1 * *

= . = ' . '

B =. plim gp Bp + (E(x, x1) ] [E(v,u.) E(v vib J (5.12)

from the standard formulae for simultaneity bias; see Bronfenbrerner (1953).

For ease of illustration, suppose that x, is generated as an AR(]1):

t X= PoXe.y + VE ve 7 NI(0,02) t=1,...T)> (5.13a) XT PX tM vu NI(0,0?) t=Tot+1l,...,T (5.13b) where x is univariate and pg may not equal p,. If po=p,=p and E(v,u,)=0, (5.12) simplifies to

Bo = Bp - (1-62) (5.14) for |p|<l and px0. Consistent estimation of B° in (5.9) requires: information additional to Xe itself (e.g., knowing that z, enters (5.10)).

Efficient estimation requires modeling the process for x, in full. That is,

t * x is not sufficient information for conducting inference about # : hence x, * A cannot be weakly exogenous for Bf 24 Conversely, x, (=E(x, 12,)) may be

* A weakly exogenous for f ; but x, is unobservable, which necessitat:es knowing

* something about the process for x,_ in order to conduct inference about £6 .

t In terms of "textbook econometrics", OLS estimation of (5.11.) is inconsistent for the underlying constant parameter of interest B. and, instead, plim Bt is a function of both B and the parameters of the process for Xi. OB, B = plim at = B(B’.p) when x is AR(1). Hence, the OLS estimate will vary as the parameters of the marginal process do: the Lucas critique applies. Conversely, establishing that pp¥p, (or more generally, that the parameters of the process for x, change) and that 6 in “3.1) is

nevertheless constant over [1,T] shows that x_ is super exogenous for #.

t

24this is true even though the marginal process for x, may involve lags of

x, and no other variables. Strict exogeneity of x is neither sufficient nor necessary for its weak exogeneity.

30

Technically speaking, in that case, the parameters of interest B are invariant to those changes in the marginal process for X- The constancy of the parameters in (5.4) has already been established; it remains to show that marginal processes for prices and income are non-constant.

The marginal processes for inflation and income are simple: Venezuelan prices depeid upon US prices and income depends upon petroleum exports. As follows immediately from Section 6 below, it is not necessary to test the constancy of fully specified marginal processes: it suffices that a marginal

process be non-constant. Estimating over 1968-78, we obtain:

(ppt), = .681(p-p*),- 1.21 (5.15) (.093) (.35) [.109] [.41]

= 1958-1978 R? = .8563 G&G = .9533% dw = 1.66 n1(7,9) = 33.7

ng(2,7) = 1.0 75(2,6) = .4 (1,8) = 5.2 €,(2) =1.0.

The model appears reasonably well-specified within sample, with neither short-run nor long-run homogeneity between Venezuelan and US prices rejected.” However, the model exhibits substantial predictive failure over the remainder of the sample, as is evident from the one-step residuals and their standard errors in Figure 13 and from n, in (5.15). If Venezuelan inflation is modeled as an AR(1) process, similar results obtain.

For noninal income, the marginal process is the error-correction model:

A

Ayn, = .134Axp + .407A(xp,-yn, ,) + .284(xp-yn) + .476 (5.16) t= 033) = + ¢.026) FE) 60675 t-1 (1088) [029] [.017] [ 048] [.065]

= 1970-1985 R? = .9581 G = 2.618% dw=1.14 m1,(1,7) = 8.2 M1,(1,7) = 8.8 9 93(2,10) = 1.6 94(1,10) = .5 &,(2) = .4 In (5.16), income has a long-run elasticity of unity with respect to

petroleum exports and a median lag of under a year. However, the parameters

2SNote that (5.15) is equivalent to the model in which Py equals Py plus a constant andi error, and the error is AR(1).

30a

Figure 13. Equation (5.15): one-step residuals and the corresponding

calculated standard errors.

8.076 afew 0.056 " 8.037 8.018

0.000

0,013

0,039

-0.058

1979 1988 1981 1982 1983 1984 1985 Year

Figure 14. Equation (5.16) estimated over 1970-80: actual and forecast values of Ayn for 1981-85, and 95% confidence bands for the forecasts.

8.257 —— actual dyn ; 95% confidence --+

Q.202 fF forecast dyn hand of forecast

0.187 8.153 @.118 @. 683 @. 448 8,813

1982 1983 1984 1985 Year

31

in (5.16) are non-constant: for (5.16) estimated over 1970-80, the one-period Chow statistics for 1982 and 1983 (m1, and 114) are highly significant. Figure 14 plots actual and forecast values with 95% confidence bands for the forecasts: 1982 and 1983 are significant outliers.

To summarize, the marginal processes for prices and income are non-constant over the sample period yet the empirical model (5.4) of

expend:.ture conditional on observed prices and income has constant

parameters “6 Thus, the parameters in (5.4) (and so the parameters of

interest) are invariant to the class of interventions which occurred in 27

sample; prices and income are super exogenous for those parameters. Super exogeneity has further ramifications. Because (5.15) and (5.16) have non-constant parameters, constancy of (5.4) implies that a broad class of expectations-based empirical models for expenditure cannot have a constant parameterization. This result, developed by Hendry (1988), is the

focus of Section 6 on encompassing.

6. Encompassing, Alternative Models, and Alternative Interpretations Encompassing, one of the primary criteria listed in Table 1, is loosely speaking the ability of one model to account for the results of another

model. Omitted variables bias in linear models is a good example: the less

equation (5.4) is a nonlinear function of p, and Ayn, in (5.15) and (5.16). Those variables proved simpler to model than kp and Ay,, which appear directly in (5.4). That does not affect the disctission on exogeneity. 27 sust what the parameters of interest are is fundamental to any econometric investigation. Unfortunately, the notion of parameters of interest is taken for granted (and perhaps lost) in the standard textbook approach to exogenzity. Economic theory determines in part what are parameters of interest, e.g., ¢ and {@,} for the model in Section 2. Also, the empirical statistical properties of the estimated coefficients play a role, e.g., statistically constant coefficients generally are of more economic interest than non-constant ones when using data from an economy in which structural change and changing data moments are typical. The reason for the latter is economic interest in underlying ("structural") parameters. Structural invariance is a principal link between those economic-theoretic and statistical concepts; cf. Lucas (1976) and Engle et al. (1983).

32

restrictive (and, by assumption, correct) model predicts that the rest:ricted model has biased coefficient estimates given by the standard formula. Encompassing applies to non-nested and nonlinear hypotheses as well, and to virtually any characteristic of a model (e.g., forecasts, error variances, autocorrelation in residuals, parameter non-constancy); cf. Mizon and Richard (1986). However, we are unaware of any alternative data-coherent empirical models for Venezuelan consumers’ expenditure on recent data;

cf. Appendix C. That does not leave encompassing as a (temporarily) vacuous criterion. First, by construction, (5.4) necessarily encompasses any empirical model nested in the model on Table 2. Second, because variance dominance is a necessary condition for variance and parameter encompassing, any new model must have an error variance of under .9% to encompass (5.4). Finally, because (5.15) and (5.16) are not constant but (5.4) is, broad classes of empirical models cannot encompass (5.4), even in principle. The remainder of this section investigates that last implication for constant-parameter expectations-based empirical models in general, for Hall's variant of the life cycle-permanent income hypothesis in particular, and for vector autoregressions (VARs).

To clarify why expectations-based empirical models cannot encompass (5.4), again consider the linear conditional model (3.1). Suppose that Ze is a valid instrumental variable for (3.1) and (3.1) holds (i.e., 6 is the parameter of interest). Instrumental variable estimation of (3.1) using zy is consistent for B:

E(y, Iz.) = BECK I2,) (6.1) Thus, the conditional model (3.1) has an expectations interpretation. The converse, that expectations models have a conditional interpretation, is not true when the process for Xe changes and "conditional" means conditional upon observed x, As shown in Section 5, if the expectations model (5.9)

holds, then

33

E(y, 1X) = Bix, (6.2) where B = B(B’.p): B varies as p varies, even when B. is constant. Conversely, if empirically p varies but B does not, the data cannot sustain the expectations interpretation (5.9) with B constant. That adds a twist to the empirical demonstration of super exogeneity. Stated more generally (and non-technically):

Proposition. If an empirical model for y, conditional upon X has constant parameters, and a marginal process for X involves Z, and has parameters which change over time, then the data are not compatible with any expectations model for Ye with a set of constant parameters and for which the expectation of x depends upon Zee See Hendry (1988) .28

One might object that the proposition is dependent upon the particular estimated marginal process for x,- Surprisingly, the proposition holds for all marginal processes for X10 long as they include z,- For instance, for Ze Xey and pop, as in (5.13a-b), the proposition holds for all marginal processes for x, which include X,.1: The proof, given in Hendry (1988), is both ingenious and remarkably simple. If the marginal process

for x based on some variable(s) z, changes but extending the information

set to include we (say) makes the marginal process for x constant, then the

t

process for w, conditional on Zz, must change. Hence the "joint" marginal

* process for Zp =(Z iw.) is non-constant as well. By assumption, * * = , E(y,12,) B'E(x, |Z.) (6.3) ta . : : . * so the proposition with Ze applies with z, re-interpreted as Zhe

Again, the AR(1) process for x is illuminating. Suppose Po¥P; in

(5.13) but the "true" process for X, requires some additional variable we!

28 cimilar results apply when future values of x appear in expectations, but

the details have not been completely worked out.

In practice, we do not know for certain whether or not a parameter is constant, so the empirical statements in the text are qualified by the properzies of the statistics for testing parameter constancy.

34

* * * x PX 4 + 7 we + ve ve NI(0,03) t=1,...T (6.4)

* Vv t-lt

time or they are constant. If they vary, the proposition clearly holds. If

where E(x ')=0 and E(w,v,')=0 by construction. Either (p",1) vary over they are constant, the marginal process for we must have changed; otherwise, Ps could not have changed in (5.13), noting the formula for omitted variable bias when excluding wy, from (6.4) to obtain (5.13). That implies that the marginal process for (x5) must have changed, so the proposition holds. 2? The relevance of the proposition for the empirical results in Section 5 is the following. No empirical expectations-based model for Venezuelan consumers’ expenditure on non-durables and services with ye and p endc genous can encompass (5.4) if it includes any of APL AP, 1? or (xp, , XP? ¥Pe_o> Y8p_1) yn, 9) in the set of information for formirg expectations about y, and Py: In particular, it could not account for why the coefficient estimates in (5.4) are constant. Given the institutional structure of the Venezuelan economy, at least one of those variables almost invariably is an important determinant of vy, or P,: hence expectations models for consumers’ expenditure in Venezuela are unlikely to be consistent with the data. °° However, even though a given expectations model is likely to be significantly mis-specified, (5.4) may be unable to encompass it: if so, that would indicate scope for improving (5.4) and might suggest how to do so. Such an encompassing test requires explicit specification of an

expectations model and, until one exists or until other evidence is brought

to light, (5.4) appears to be congruent with the data (see Hendry and

290... : . . Similar arguments apply for changes in equation error variances.

30this raises the question of why agents would use (condition upon) relatively simple functions of the data (including those of the forcing variables) rather than on the process of the forcing variables. One reason may be that, in a world with frequently and rapidly changing regimes of the forcing variables, data functions may provide relatively efficient and reliable predictions (or measures of) the underlying latent variables without the informational costs attendant to modeling the process of the forcing variables and the changes of that process.

35

Richard (1982, 1983)). We do not conclude that (5.4) is the "true" structural relationship, but its properties indicate its usefulness for inference and policy analysis, and it can serve as the basis for a progressive research strategy in which newer models encompass previous ones and account for additional as-yet-unexplained features of the data.

The life cycle-permanent income hypothesis is an important expectations-based model of consumers’ behavior. Hall (1978) derives some statistical implications of that hypothesis, among which are: only the first lag of expenditure helps predict current expenditure and, conditional on that: lag of expenditure, lagged disposable income offers no more predictive power, i.e., income does not Granger-cause expenditure. Estimating an AR(2)

process for Cy yields:

c. = 1.16c - .26¢ + .78 (6.5) t Ca7yth — ciasy®2% (54) [125] [.25] - [.51]

T = 1970-1985 R2 = .9313 6 = 4.4983 dw=1.82 ADF(1) = -1.42 Although the t-statistic for Cho is -1.03 and insignificant by standard measures, two other features of (6.5) may invalidate that inference: the one-step Chow statistics for 1979 and 1984 of the AR(1) process for c, indicate parameter non-constancy, and the Dickey-Fuller statistic for a unit

root in (6.5) is "insignificant". Even ignoring these issues, deleting Cho

and adding two lags of income gives:

A

* * c = .88c + .32y - .23y + .20 (6.6) t Cisyt) Coy 2 ey 2.47) [.15] [.05] (.12) [.39]

T = 1970-1985 R?2 = .9619 6G = 3.485% dw= 2.39 3(2,12) = 5.7 where n, tests for the significance of (ep a) and has a 95% nominal critical value of 3.89. Lagged income is highly significant, rejecting the second implication of the life cycle-permanent income hypothesis. That may not be surprising for Venezuela, given its income distribution, financial

institutions, and the importance of liquidity in (5.4). However, the life

36

cycle-permanent income hypothesis is a widely espoused theory of consumer behavior, so testing its implications bears some merit. ?+ At a more general level, the results above on feedback versus feedforward models apply to (and reject) the life cycle-permanent income hypothesis because the latter is an expectations model and lagged inflation and petroleum revenues are not excluded from the information set for forming expectations in that model.

VARs are another common approach to modeling economic time series. Forecasting ability is a primary claimed advantage of VARs over other classes of models: even the proponents of VARs admit that the parameters estimated lack specific economic interpretation because they are reduced-form; see Sims (1987). For economies with structural change, VARs may no longer forecast well. For instance, the bivariate vector autoregressive representation of (YerX) from (3.1) and (5.13) is:

Ye = Xe, + (u,+Av,) (6. 7a)

Xe PGR oF Ve (6. 7b) where m=p;B. As Ps changes, so will the VAR coefficients (m5 2P3), and the entire VAR will manifest predictive failure; cf. Hendry (1979). Nonetheless, it may be difficult to detect parameter non-constancy because the error variance in (6.7a) is larger than that in (3.1) and because VARs

tend to be heavily over-parameterized, >“

31... . cogs . sees Finite sample properties of statistics for testing "excess sensitivity"

(e.g., nz) have been widely discussed; cf. Banerjee and Dolado (1987) and Stock and West (1988). In (6.6), lagged income remains significant if a unit coefficient is imposed on lagged expenditure and/or if expenditure enters as a lagged rate of change only. Contrasting with Mankiw and Shapiro's (1985) Monte Carlo results, lagged income is insignificant if income appears at only one lag and a unit coefficient is imposed on lagged expenditure. Inclusion of Dy), does not affect these results.

Parameter non-constancy (likely for 1981 and 1985) may compromise

"classical" inferential procedures such as those which Hall uses. See also Davidson and Hendry (1981).

32: quations (5.4), (5.15), and (5.16) jointly imply that a VAR representation of expenditure such as (6.6) should have non-constant coefficients. Even though the residual variance in (6.6) is over fourteen times that in (5.4), the l-step Chow statistics for (6.6) point to predictive failure in 1981 and 1985.

37

Factorization of a VAR into conditional and marginal models may mean more. straightforward economic modeling of the time series. If the factiorization implies super exogeneity, the conditional density may be amenable to a relatively parsimonious specification, as in (5.4). When the factorization corresponds to agents conditioning on outcomes from a marginal process, the marginal model (as well as the conditional one) may have an economic interpretation, thereby permitting easier modeling of the structural break(s) in the marginal model.>° The approach in Section 5 is similar to that with VARs in that both allow a general dynamic specification initially. It differs from the latter in its emphasis on model evaluation and design, economically interpretable parameters of interest, and (relatedly) parsimony of the final specification and parameter constancy.

Having found (5.4) to be a tentatively adequate and economically interpretable characterization of the data, and having set aside a large

class of alternative models, we turn to policy implications.

7. Policy Implications

Statistically valid policy analysis of an empirical model requires super exogeneity, i.e., that the parameters of interest # are invariant to a given class of interventions (changes) in the process for Xe Section 5 demonstrates the super exogeneity of income and prices for the parameters in (5.4) with respect to the sorts of structural breaks and policy rule changes which occurred in sample. Before considering the policy implications of (5.4), some discussion of the Lucas critique is required.

The Lucas critique has been confirmed often in the empirical

literature. It is less well-known that the Lucas critique can be refuted:

Her.dry (1988) implies refutability. In particular, the empirical model

33, wbrano, Pierse, and Richard (1986) illustrate this well for the

determination of money and interest rates in the United Kingdom, where the introduction of Competition and Credit Control in 1971 provided the break.

38

(5.4) refutes the Lucas critique for the class of regime changes and policy rule switches which occurred in sample. Obviously, but non-trivially, the data are uninformative for classes of interventions which did not occur. For instance, (5.4) might not have constant parameters if the personal income tax rate increased to 100%. Refutation of the Lucas critique is tempered because economic agents can modify their own behavior.

Given these caveats, (5.4) has the following policy implications. Foremost, government policy does have the potential to influence the path of real variables: that follows because (5.4) has a constant parameterization in spite of structural change within sample. In so far as government actions affect income, liquidity, and inflation, the government can (and will) affect consumers’ expenditure. The dependence of income on petroleum exports (and on imports of manufactured goods) is clear: it had dramatic repercussions for the economy, both positively and negatively (e.g., 19724 and 1982-83). Thus, diversification of exports and expansion of the domestic manufacturing industry could reduce the potential volatility of consumers’ expenditure. Price (or wage and price) policies and policies influencing real income growth and liquidity could affect both current ard equilibrium expenditure through (Ap+A?p),, (Azy,/2), Ye itself (which is Ye APL? 4p y)> and the error-correction term (which depends upon lagged y and 2) .>4 To the extent that agents are liquidity-constrained, expansionary government fiscal policy may relax that constraint if trade-offs in utility exist between consumption of private and public goods; cf. Rossi (1988). A more detailed discussion of the policy implications of (5.4) requires specifying the policy at hand and analyzing the mechanism by which it

influences prices, income, liquidity, and other economic variables.

4 . . . However, price polices might not, to the extent that they implied rationing.

39

8. Concluding Remarks

This paper starts with a simple optimizing model in which economic agents aim to maintain constant expenditure-income and liquidity-income ratios but face adjustment costs. That theoretical model provides the basis for constructing a parsimonious, statistically adequate econometric model of consumers’ expenditure on non-durables and services in Venezuela.

Disposable income, liquidity, and inflation help determine expenditure, with all variables doing so through several economically sensible channels. To the model's benefit, its parameters are constant in spite of structural change in the economy: that evidence also excludes a large class of expectations and VAR models from being empirically viable. Rather than being the econometrician’s bane, structural change proves invaluable for sorting through alternative models. The structure of the consumption function has numerous implications for economic forecasting and policy.

At another level, this paper illustrates an econometric methodology which appears promising for evaluating empirical models, designing them to have desirable statistical and economic properties, and improving the chances of reliable inference. The methodology applies equally to other classes of models: selecting a conditional model was an empirical issue, not one of principle. Further, the methodology provides means for resolving conflicts between competing empirical explanations of the same phenomena,

thereby focusing empirical analysis into a progressive research strategy.

40

Appendix A. Data Definitions

VARIABLE DEFINITION SOURCE

ABT Gasto de consumo final de los hogares en el mercado A.G.N. interno: alimentos, bebidas y tabaco III-5 [Consumers’ expenditure on food, drink and tobacco]

C Real per capita consumers’ expenditure on non-durables and services ( = [ABT+OT+SD+S]/[P*N] )

(1968 Bolfvares per capita) [Gasto real per capita de consumo en bienes no durables _y servicios]

Doi A dummy variable for mis-measurement on consumers’ See expenditure: +l for 1970, -1 for 1971, 0 otherwise App. B

L Liquidez monetaria (M2) = monedas + billetes + depédsitos B.M.

a la vista + depdsitos de ahorro + depdsitos a plazo III.2.1 (end-of-year)

[Monetary aggregate M. = coins + bills + sight deposits (checking) + savings deposits + time deposits (CDs) ]

N Population (mid-year estimates in millions) I.F.S [Poblacién] 99Z

OT Gasto de consumo final de los hogares en el mercado A.C.N interno: otros bienes no durables III-5 [Consumers’ expenditure on other non-durables]

P Indice de precios al consumidor para el area metropolitana B.M. de Caracas; indice general (diciembre, 1968=1.00) III.4.6 [Consumer price index for the Caracas metropolitan area,

December values]

pt Consumer price index for the United States (1980=1.00) I.F.S. {Indice de precios al consumidor para los EE.UU.] 64.

Ss Gasto de consumo final de los hogares en el mercado A.C.N. interno: servicios IJI-5 [Consumers’ expenditure on services]

SD Gasto de consumo final de los hogares en el mercado A.C.N interno: bienes semidurables ITI-5 [Consumers' expenditure on "semi-durables"]

XP Petroleum exports I.F.S [Exportaciones de petréleo] 7OA

Y Real per capita national disposable income ( = YN/[P*N] ) - [Ingreso nacional disponible, real per capita]

*

Y Real per capita national disposable income, adjusted for See the inflation tax on liquid assets text [Ingreso nacional disponible, real per capita]

YN Ingreso nacional disponible

[National disposable income]

41

Sources. The data sources are: A.C.N., Anuario de Cuentas Nacionales (Annual Report of the National Accounts); B.M., Boletf{n Mensual (Monthly

Bulletin); and I.F.S., International Financial Statistics 1987 Yearbook.

The first two are publications of the Banco Central de Venezuela (Caracas, Venezuela) and the last is published by the International Monetary Fund (Washington, D.C.). Data from the A.C.N. are from the 1982 volume, with extensions and revisions to the data from subsequent issues; data from the B.M. are from various issues. The number below a source indicates the relevant table (for A.C.N. and B.M.) or line in the corresponding country table (for I.F.S.). The definition as it appears in the source is given first. An English (or Spanish) translation appears in brackets.

Units. Unless otherwise noted, all published data are annual, and nominal in millions of Bolfvares.

Adjustments. Population data before 1975 is rescaled to account for a re-definition in 1975; cf. International Financial Statistics 1984 Yearbook.

Acknowledgments. We are grateful to Mireya de Cabré, Angel Lucenti, David Mendoza and Trino Valerio for their help in finding and interpreting

the data.

Appendix B. Data Measurement

This appendix records several caveats about the principal series analyzed in the text.

Consumers’ expenditure (C) is final expenditure in the domestic market by households and non-profit institutions. It includes purchases in the domestic market by non-residents and excludes those by residents in the foreign market. In 1974, the former were at most 2% and the latter at most 8% of final expenditure in the domestic market.

There appear to be measurement errors in C for 1970 and 1971: Figures B.1, B.2, and B.3 graph the logs of nominal, real, and real per capita

expenditure for 1968-1973. We have found no economic or institutional

4la

Figure B.1. The log of nominal consumers’ expenditure (ctptn) for 1968-73.

10.37

—— ctptn 18.31 18.25 10.20 10.14 10.89

10.3 9.97

1969 1970 1971 1972 1973 Year

Figure B.2. The log of real consumers’ expenditure (ctn) for 1968-73.

1969 1976 1971 1972 1973 Year

41b

Figure B.3. The log of real per capita consumers’ expenditure (c) for 1968-73.

7,704 7,689 7,675 7,661

7.647 7,633 7,619 7,604

1969 1978 1971 1972 1973 Year

Figure B.4. Equation (B.1): scaled residuals from the error-correction

equation (5.4) without Do.

—— scaled residual

1.356 0.885 ¢ 9.414

-9,056

-9,527

-0,998

~1,469

1973 1976 1979 1982 1985 Year

42

explanations of the unusual movements in 1970-71. Estimation of (5.4) without Dj, results in virtually identical estimates of the remaining coefficients (see (B.1) below), but larger estimated standard errors and Co. That is consistent with measurement errors on expenditure which are nearly

orthogonal to the RHS variables in (B.1).

A

Ac, = 451(Agy¢/2) - .262(Ap+Ap), - 139[ (e-y")-.5(L-¥ I], (046) (039) (.028) [ .032] [.025] [041] + .019 (B.1) (006) [010]

T = 1970-1985 R? = .9317) @ = 1.38168 dw=2.92 €&,(3) =17.1

ng(1,10) = 3.96 5(6,5) = 4.41 6(2,10) = .4 €,(2) =.1

Figure B.4 graphs the scaled residuals from (B.1): those for 1970 and 1971 are opposite in sign and nearly equal in magnitude, and all other res‘iduals are considerably smaller. Figure B.5 plots the one-step residuals with

calculated equation standard error bands. Those bands narrow over time,

indicative of the relatively large outliers early on in the sample.

One explanation of these anomalies is a minor re-definition of the expenditure series in 1971. Another is an over-estimate of expenditure in 1970 and a compensating under-estimate in 1971. Both are plausible and, until we have additional evidence, we adopt the latter model, capturing the effect on C with the dummy Dj,.

National disposable income (Y) is not the best measure of income conceivable; personal disposable income would be better, but it is not available. In particular, national disposable income includes profits of the petroleum industry, but those profits should not affect consumers’ expenditure directly. Those profits were unusually high in 1973 and low in 1982-3: that may be responsible for (5.4) over-predicting in 1973 and

under-predicting in 1982-3; cf. Figure 6.

42a

Figure B.5. Equation (B.1): one-step residuals and the corresponding

calculated standard errors.

BG87 pre seeeetetteteeee

9.a2g + ——— one-step residual rete ssscseeeneseceeeensstettsensna. A

@.@18 - ----- Qt ar

8,609 a

0.008 F- Z* = a

-@, 009

“8.019

a

cecaneggenmeaeatenscoenes envattecssccaceranscgoosemeed esos peece aogguowennre®

eee pennscgteneontrepene ee nee® ee

1979 1988 1981 1982 1983 1984 1985 Year

43

The consumer price index (P) is for the Caracas metropolitan area only, so it does not reflect regional variations in prices. The index is for all expenditure, both durable and non-durable. Although the index may be well-suited for deflating expenditure of non-durables and services foi our econometric analysis, the price of durable relative to non-durable goods also could be important, especially if (Apt+A?p), in (5.4) is interpreized as in Deaton (1977). The index is sensitive to the particular basket of goods used in its calculation and to the presence of price controls (which are common in Venezuela and have existed in varying degrees).

Liquid assets (L) are measured by the monetary aggregate M, and include holdings by both the personal and commercial sectors (but not the government and excluding financial institutions [las Sociedades Financieras]). ‘They exclude holdings in Savings and Loans Associations ([Cédulas Hipoteca:ias] ; very liquid) and holdings abroad. The latter increased dramatically over the sample because of capital flight. While accounting for capital flight may be important, it is not immediately obvious how (e.g.) Venezuelan assets in dollar accounts in the U.S. affect expenditures in Venezuela.

Appendix C. Encompassing, and Previous Empirical Models of Consumers’

Expenditure in Venezuela

In contrast to most industrialized countries, little empirical research exists on consumer behavior in Venezuela. Belandria (1971) analyzes the’ demand for various goods with cross-section data from three cities (Barinas, Mérida, and San Cristébal). He estimates three equations using income and either total expenditure or prices, and finds those variables significant. He rejects the hypotheses that corresponding coefficients are equal for the three cities. Lépez (1972) estimates a subset of Zellner’s (1957) equations and tests for habit formation, inertia, and the importance of liquid assets and of past levels of expenditure. Lépez finds that (i) including lagged

expenditure as an explanatory variable reduces the estimated marginal

44

propensity to consume and increases the latter’s standard error, (ii) the coefficient of liquid assets is very high (much more so than Zellner’s), and (iii) the marginal propensity to consume typically is negative when estimated by indirect least squares. Palma (1976) builds a model of the Venezuelan economy which explains inter alia total consumers’ expenditure, expenditure on food, beverages and tobacco, and expenditure on other non-durables and services for 1950-69. He finds that both liquidity and (a constructed series of) personal disposable income are important as explanatory variables. Musgrove (197*) examines cross-section data from a household budget survey to finds that total expenditure and family structure (number of members, age and sex) have a significant effect on expenditure. Finally, Villoria (1983) estimates several equations for total consumption in terms of current and lagged national income, lagged consumption and liquidity.

These studies use data over periods different from ours and gathered on

different accounting principles.” Even so, Davidson et_al. (1978) were

successful in resolving similar issues in their analysis of different models of consumers’ expenditure in the United Kingdom. Palma's (1976) data are perhaps closest to ours so, at a minimum, we plan to re-estimate (5.4) with

his data and test if either his model or (5.4) can encompass the other.

tn 1970, the Central Bank of Venezuela (which produces much of the Venezuelan economic data) adopted the then new United Nations system of national accounts; it has published data from 1968 according to those methods. Of the authors mentioned above, only Villoria uses time series under that system, and he considers total expenditure rather than expenditure on non-durables and services. Given the marked differences in the time-series behavior of expenditure on durables in comparison to that of non-durables and services, we chose to analyze the more disaggregated series. Encompassing his results is feasible with a model of durable expenditure in addition to one for non-durables and services.

45

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51

International Finance Discussion Papers

IFDP NUMBER TITLES AUTHOR. (s) 1988

325 Econometric Modeling of Consumers’ Julia Campos Expenditure in Venezuela Neil R. Ericsson

324 Income and Price Elasticities of Foreign Jaime Marquez Trade Flows: Econometric Estimation and Analysis of the US Trade Deficit

323 Money, Interest, and Capital ina Wilbur John Coleman II Cash-in-Advance Economy

322 The Simultaneous Equations Model with Richard Harmon Generalized Autoregressive Conditional Heteroskedasticity: The SEM-GARCH Model

321 Adjustment Costs and International Trade Joseph E. Gagnon Dynamics

320 The Capital Flight "Problem" David B. Gordon

Ross Levine 1987

319 Modeling Investment Income and Other William Helkie Services in the U.S. International Lois Stek..er Transactions Accounts

318 Improving the Forecast Accuracy of B. Dianne Pauls Provisional Data: An Application of the Kalman Filter to Retail Sales Estimates

317 Monte Carlo Methodology and the Finite Neil R. Exicsson Sample Properties of Statistics for Testing Nested and Non-Nested Hypotheses

316 The U.S. External Deficit: Its Causes Peter Hooper and Persistence Catherine L. Mann

315 Debt Conversions: Economic Issues for Lewis S. Alexander Heavily Indebted Developing Countries

314 Exchange Rate Regimes and Macroeconomic David H. Howard Stabilization in a Developing Country

313 Monetary Policy in Taiwan, China Robert F. Emery

Please address requests for copies to International Finance Discussion

Papers, Division of International Finance, Stop 24, Board of Governors of the

Federal Reserve System, Washington, D.C.

20551.

IFDP NUMBER

312

311 310

309 308 307 306

305

304

303

302

301 300

299

52

International Finance Discussion Papers

TITLES The Pricing of Forward Exchange Rates

Realignment of the Yen-Dollar Exchange Rate: Aspects of the Adjustment Process in Japan

The Effect of Multilateral Trade Clearinghouses on the Demand for Irternational Reserves

Protection and Retaliation: the Rules of the Game

Changing International Duopoly with Tariffs

A Simple Simulation Model of International Benk Lending

A Reassessment of Measures of the Dollar's Effective Exchange Value

Macroeconomic Instability of the Less Developed Country Economy when Bank Credit is Rationed

The U.S. External Deficit in the 1980s: An Empirical Analysis

An Analogue Model of Phase-Averaging Procedures

A Model of Exchange Rate Pass-Through

The Out-of-Sample Forecasting Performance of Exchange Rate Models When Coefficients are Allowed to Change

Financial Concentration and Development: An Empirical Analysis of the Venezuelan Case

Deposit Insurance Assessments on Deposits az Foreign Branches of U.S. Banks

AUTHOR (s)

Ross Levine Bonnie E. Loopesko

Robert E. Johnson

Ellen E. Meade

Catherine L. Mann

Eric O'N. Fisher

Charles A. Wilson

Henry S. Terrell Robert S. Dohner

B. Dianne Pauls William L. Helkie

David F. Spigelman

William L. Helkie Peter Hooper

Julia Campos

Neil R. Ericsson David F. Hendry Eric O’N. Fisher Garry J. Schinasi

P.A.V.B. Swamy

Jaime Marquez Janice Shack-Marquez

Jeffrey C. Marquardt