A note on the aggregation of slack and shortage in centrally planned economies

Economics of Planning 23: 193-207, 1990. �9 1990 Kluwer Academic Publishers. Printed in the Netherlands.

A Note on the Aggregation of Slack and Shortage in Centrally Planned Economies*

TSANG SHU-KI Dept. of Economics, Hong Kong Baptist College

Abstract

This note attempts to identify the key methodological problems that remain unsolved in the controversy about the aggregation of slack and shortage in disequilibrium econometric models of centrally planned economies (CPEs). The procedure of 'smoothing by aggregation' implemented by Burkett (1988) is critically reviewed and found wanting, despite possible attribution to Kornai (1980), for justification. We argue that the procedure neglects the problems of resource immobility and hoarding that have prevailed in CPEs. Even from a neo-Keynesian perspective, it is at odds with a rigorous microeconomics of rationing that takes into full account the substitution and income effects of spillovers. One important issue is that saving may actually be reduced because of a tightening of the ration. These considerations throw serious doubt on the validity of the smooth trade-off between slack and shortage that forms the basis for econometric estimation and lead to concern that the Walrasian configuration cannot be identified from the estimation results.

I. Introduction

Under a situation characterized by the coexistence of shortage and slack in different micro markets, a feature of the centrally planned economies (CPEs) which few would deny, the aggregation of micro information into macro measurements of a whole market or the whole economy becomes problematical. A heated controversy on the issue of aggregation was initiated by Kornai's (1980, 1982) criticisms of the Portes-Winter (P-W) 'canonical model' of the consumption market for East European CPEs (1978, 1980), which makes use of 'the minimum condition' that the observed aggregate quantity represents the minimum of aggregate supply and demand. Surprisingly, despite considerable amount of exchanged antagonism (Kornai, 1982; Podkaminer, 1989; Kemme, 1989; Portes, 1989), some of the central issues have not yet been clarified by either side. On the basis of the major developments in theory and applied

*I wish to thank Michael Artis, Paul Madden, Bernard Waiters and two anonymous referees for useful comments, suggestions and criticisms. The issues reviewed in this note are admittedly controversial and I am solely responsible for all interpretations, opinions and errors.

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research related to the controversy, this note attempts to identify the key problems that remain unsolved.

One important point that we should keep in mind is that the validity of any aggregation procedure depends on the condition that Jt does not neglect, distort or obliterate important information on the micro markets that is needed for a meaningful understanding of the economy and the subsequent derivation of optimal policies.

2. Smoothing by aggregation

P-W and their associates have been aware of the aggregation problem from the beginning. In fact, P-W drew attention to it in their 1980 article. The way that they claim can overcome the problem, which they have not themselves implemented, is to use the 'smoothing by aggregation' technique, which draws on the literature in labour economics (Gordon, 1967; Hansen, 1970; Medoff, 1983). In a recent review, Portes (1989) summar- izes his response to the critics in the following way:

One internally consistent way of approaching the problem in our context is 'smoothing by aggregation', whose lengthy pedigree is sketched by Muellbauer (1978). If we aggregate over many micro labour markets, for example, some in excess supply and some in excess demand, we find that total demand is the sum of employment and vacancies, total supply is the sum of employment and unemployment, so total excess deman d equals vacancies minus unemployment; as the real wage rises, aggreg~ate excess demand falls in a continuous manner, with a smooth unemployment-vacancies trade-off. Aggregate employment will always lie to the left of the wedge formed by the aggregate demand and supply curves. . . Note that the larger the elasticities of substitution, and hence the stronger is forced substitution, the closer will observed aggregate behaviour approximate the underlying aggregate demand and supply curves which would be observed in full Walrasian equilibrium, and consequently the more suitable is the discrete-switching, min-condition empirical model (p. 33, our emphases).

Central in this methodology appears to be the assumption that the items in question respond in a similar manner to a change in the driving macroeconomic variable. So if the real wage rises, demand for labour in all micro markets would fall. In that case, a smooth trade-off between slack and shortage may be obtained.

Burkett (1988) has made use of such an approach in a pioneering piece of empirical econometrics. He gives a vivid picture of the aggregation process:

A NOTE ON THE AGGREGATION OF SLACK AND SHORTAGE 195

Suppose that initially excess supply, of varying intensity, can be found in most submarkets. Consider the effects of successive, uniform increases in demand in all submarkets. The first increase in demand reduces excess supply in the many submarkets where it existed, elimi- nates excess supply and creates excess demand in the few submarkets where only a little excess supply had existed, and increases excess demand in the submarkets where it already existed. This first increase in demand, therefore, greatly reduces gross aggregate excess supply (qs - q a ) / q s , but only slightly increases gross aggregate excess demand (qd -- q, ,) /qd" AS the number of submarkets in excess supply falls and that in excess demand rises, successive increases in demand will have less effect on ( q s - q , , ) / q , , and more on ( q a - q a ) / q d . Thus if (qs - q , ) / q , is plotted against (qd -- q a ) / q d , the result is a curve that is negatively sloped, convex to the origin, and approximates a rectangular h y p e r b o l a . . . (p. 494).

where qs, qd and qa represent aggregate supply, aggregate demand and observed quantity respectively. These long quotations are necessary because there has been considerable confusion on what is assumed and achieved by the technique of smoothing by aggregation advocated by the P - W school. The rectangular hyperbola that Burket t relies on is directly related to the curve that Portes (!,989) refers to, which lies to the left of the wedge of the aggregate supply and demand curves in a price-quantity space. Ironically, in his attempts to contrast the characteristics of 'resource-constrained' economies with those of 'demand-constrained' economies, Kornai (1980, Figure 11-3) has depicted a similar trade-off between slack and shortage for the labour markets in the CPEs. 1

The hyperbola can be written as:

(( qd -- q a ) / q d ) ( ( qs -- q a ) / q s ) = g . z (1)

where g is a coefficient of the slope and z is the shifting parameter which can be assumed to be constant in the short run and therefore set to, say, unity. Assuming linear, deterministic demand and supply functions:

q d = a ' x and q s = f l ' Y

the estimable stochastic equation for the model will be:

q = (oe'x + f l ' y ) / 2 - ( ( ( a ' x + f l ' y ) 2 ) / 4 - (1 - g ) a ' x f l ' y ) 1/2 + u (2)

after adding the error term u. Note that if g---0, qa = min(qs, qd)" SO a test of g = 0 is a test of the validity of the canonical discrete-switching model. Burket t (1988) estimates variations of Equat ion (2) for the aggregate consumption goods market in five East European CPEs. He

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finds good fit and fails to reject the hypothesis of g = 0 in all cases, thus vindicating the canonical model against Kornai 's criticisms which are related to the aggregation problem. 2

Burkett 's formulation of the demand function also addresses another objection raised by Kornai concerning discouraged consumers and forced saving, which would be a possible outcome of the coexistence of shortage and slack. Some of the consumers in CPEs may be utterly discouraged by the persistent shortage of the good they want and yet they still do not want to substitute into the poor-quality goods which are being accumulated in the warehouses. In the end, they have to give up the shopping effort and are forced to save. Therefore , the observed transactions would not reveal their true preferences. To deal with this problem, Burket t uses an error-correction form of the P - W function:

C D t - Ct_ 1 = a 2 D Y D t + (1 + a l ) ( Y D t _ 1 - Ct_~) (3)

where C D represents household consumption demand, C actual consumption, Y D disposable income, and D Y D the change in Y D from the last period. Equation (3) can be rewritten as:

C D , = a 2 Y D ` + (1 + a 1 - a 2 ) Y D , _ 1 - OllCt_ 1 (4)

Provided that o/1 is negative, the smaller C t _ 1 is, the smaller C D , must be. Thus frustrated demand in the last period would dampen current period consumption and increase saving. If the effects of past shortage are transmitted to present consumer demand o n l y through lagged consumption, current potential demand C D P , will be a relatively accurate measure of how strong consumer demand would have been had shortages never occurred:

C D P t = a 2 Y D t + (1 + a I - % ) Y D , 1 - - ~ -~- u t - 1 ) (5)

As shown by Burkett , as long as a 1 is greater than - 1 , C D P can be i terated by making an assumption about its relationship with the estimated value of C D in the base year.

3. Resource immobility, hoarding, rationing, spillovers and excess saving

Burkett 's innovations, though stimulating, still have not adequately addressed the problems of the co-existence of slack and shortage and their interaction in a disequilibrium context. Despite possible attribution to Kornai for the conception of the rectangular-hyperbolic trade-off between slack and shortage, the validity of using the trade-off as an aggregation tool in CPEs is in serious doubt. Even if the hyperbolic relationship is an


appropriate specification of the aggregate labour market in a market economy because of the relative homogenei ty of labour (structural and frictional unemployment notwithstanding), one would have strong re- servations about its adoption in aggregating over submarkets of factors of production in CPEs. The supply behaviour of most factors across different micro markets is difficult to gauge. Their effective supplies often depend on various structural constraints (e.g. whether they are in the bott leneck sectors or not). Moreover , as objects of hoarding, they are notoriously immobile. Under a situation of resource immobility, the relationship between the observed aggregate and the structural distribution of slack and shortage is anything but well-behaved and smooth. Deng and Luo (1987) have emphasized the importance of this. 3 Given the institutional reality of the CPEs, it is difficult to conceive that the demand for factors of production in all submarkets would fall in a uniform manner as their real prices rise. Demand for them in some, though not necessarily all, submarkets may indeed increase because of intensified hoarding. 4

Even if we restrict our attention to the submarkets for consumption goods, hoarding would still be a major obstacle to the successful realiza- tion of a smooth aggregate 1Lrade-off between slack and shortage. While hoarding may be concentrated on essentials or expensive items, it is obviously not technically viable in the case of perish,able items such as non-processed food, which forms an important part of the daily meals for most of the population in a CPE like China. Some of the consumption goods (e.g. expensive durables, imported brands etc.) are channelled only to officials and the elite and not accessible to the general public, so their supply and demand may not be price-sensitive at all. Moreover , not all parties can or have the same ability to hoard. In general, those closer to the administrative authorities and having larger amounts of resources under their control can afford to hoard more. Overall, it seems therefore that the burden of proof should fall on those economists who assert that the submarkets of consumption goods in a typical CPE would respond in a uniform manner to changes in a macroeconomic driving variable such as the consumer price index.

Resource immobility and hoarding aside, there are also other theoretical difficulties even if we adopt a more neo-Keynesian (and less in- stitutionalist) line of thinking. A key point to note is that both Burket t (1988) and Portes (1989) argue that the larger the elasticities of substitution between different micro markets, the closer would the rectangular hyperbola approximate the wedge formed by the aggregate supply and demand curves. On the surface, this is easy to see. When, for example, the real wage is falling, demand for labour in all submarkets is supposed to rise. If frustrated demands in rationed markets can be more readily compensated by substitutes in other unrat ioned markets, the observed aggregate trade volume will certainly increase, pushing the rectangular hyperbola closer to the wedge.

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Hence, even accepting the postulate of uniform responses to macroeconomic disturbances, the 'second round' of spillover effects across micro markets (e.g. those of ' forced substitution' that Portes mentions in the above quote) has to be taken care of. One way to rationalize the postulated process is therefore to draw on the economics of rationing, as Portes (1989) readily agrees, and to link the change in the consumer price index implicitly to the change in the quantity rationed, s From this perspective, the smooth trade-off between slack and shortage and its approximation of the wedge hinge on a close statistical relationship between aggregate excess demand and the number of micro markets in which rationing takes place. Moreover , aggregate excess demand must be positively correlated with excess saving. So as aggregate excess demand increases, more and more micro markets will switch to a regime of rationing in an orderly manner. Because a portion of the frustrated demands would be channelled into excess saving, the increases in effective demands in other unrationed markets would be damped. A smooth hyperbolic curve of observed aggregate trade to the left of the wedge formed by the notional aggregate supply and demand curves may thus be obtained.

In that case, the postulated process has to be based on the assumption that in a situation where some submarkets of consumption goods move (move deeper) into a state of excess demand and rationing in them begins (tightens), the substitution effect always dominates the income effect and that saving is a net substitute for the rationed goods. So the following two results will obtain as rationing begins (tightens): (1) excess saving will increase; and (2) excess demand in one submarket will generate orderly spillover effects on other submarkets. When these conditions hold and assuming a very large number of submarkets, aggregate excess demand will be directly correlated with the amount of excess saving and with the number of submarkets in excess demand through appropriate assumptions about the probability distribution of shortage and slack and that of spillovers over the submarkets (Martin, 1985).6 The procedure of deriving the rectangular hyperbola to the left of the wedge may hence be legitimate.

Unfortunately, these two assumptions, though intuitively plausible, are not necessarily correct. Latham (1980) has shown that, in a disequilibrium context, the Tobin-Houthakker conjecture that the reduction in the ration of one good will increase the consumption of unrationed substitutes and diminish the demand for unrationed complements may not hold, largely because of the income effect which has been neglected. A more general case can be demonstrated by a household utility maximiza- tion model which Naughton (1986) presents, 7 drawing on the arguments of Neary and Roberts (1980). Suppose the representative household faces a vector of unrat ioned goods, x 1 and a vector of rationed goods, Xz, both of which enter into its utility function. Neary and Roberts (1980) have


shown that there exists a set of 'virtual' prices P2, which when combined with exiting Pl would cause the household to purchase the same bundle of goods that it actually does buy under rationing. So the compensated demand functions for x 1 and x 2 can be written. Using the duality technique in demand analysis, the analogue to a normal Slutsky equation can be derived, which shows the derivative of x I with respect to x 2 (dXl /dX2) . Since x 2 is rationed, the derivative can be interpreted as the effect of the relaxation of the ration. In Naughton's words, the Slutsky equation shows

that the relaxation of the ration has a substitution effect, reducing demand for substitutes and increasing demand for complements; and an income effect increasing demand for normal goods. Conversely, a tightening of the ration increases demand for substitutes, but has an income effect which reduces demand for normal goods. (1986, p. 94)

The mental experiment of increasing (reducing) the number of submarkets in excess demand successively, from which the rectangular- hyperbolic relationship generated through smoothing by aggregation may be derived, is similar to that of depicting a continuous tightening (relaxation) of overall rationing in a Neary-Roberts-Naughton n-good model. If the Tobin-Houthakker conjecture does not hold over many micro markets, it would be doubtful whether a smooth trade-off between slack and shortage could be obtained as assumptions about well-behaved probability distributions flounder. Latham (1980) does not directly address the problem of saving and its impact on effective demand. Taking these important considerations into account explicitly, further doubts would arise concerning the technique of smoothing by aggregation. The utility that the representative household obtains from income will decline as the ration tightens. To minimize the decrease in utility, the household may be forced to spend more on some unrat ioned goods and hence save less overall. This result is highly probable if saving is a normal good (not to mention luxury good, as most economists believe) and the income effect turns out to be large. A typical example would be the case of the dual system under which a portion of the same category of food is rat ioned while the remaining is not. When a deterioration of shortage in the rationed submarket occurs, a higher total cash outlay for food may result as the household is forced to buy more food in the unrat ioned submarket to maximize utility. Naughton (1986) cites some relevant elasticities in developing economies calculated by Llueh et al. (1977) to support such a possibility:

Lluch et al. (p. 82) have calculated the elasticity of saving with respect to the price of food. They derive a significant negative number, larger in absolute value for low-income countries (ranging from -2 .93 for Korea to - 0 . 22 for Sweden). If the virtual prices of Neary and Roberts

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are in the same range as the price increases recorded by Lluch, we can interpret these results as indicating that a tightened ration for some categories of food will decrease saving. Due to the nature of the elasticities involved, this result is more likely to hold for low-income countries, and when the rationed goods is a 'necessity' rather than a luxury. (p. 95)

After spending a large amount of money on food through desaving, consumers may limit or increase further purchases in other submarkets, rationed or not. In that process, an initial tightening of the r~tion in some submarkets could generate disproportionate and irregular effects on other submarkets. The Latham phenomena may indeed take place in many of the latter.

Naughton (1986, pp. 95-99) also presents a simple intertemporal model in which demand depends on future expectations about shortage. From that angle, it is even easier to see why a tightening in the ration would reduce saving: that would happen simply if expectations are extrapolative. 8 Positive hoarding will take place and we are back to the problems discussed early in this section. Under those circumstances, one could even argue that it may be possible for effective demand to exceed notional demand at the aggregate level.

Overall, there seem to be few theoretical reasons for the pattern of 'successive, uniform increases in demand in all submarkets ' that Burket t perceives to take place in the CPEs and the close statistical relationship between aggregate excess demand (supply) and the number of submarkets in excess demand (supply) may not exist at all.

Burket t (1988) has at tempted to address the problem of forced saving through the specifications of the demand function in the form of Equation (4). Even this procedure, however, still leaves room for criticism. Burket t was the first one to grant this:

However , if the effects of past shortage on present consumer demand are transmitted through channels other than lagged consumption, then C D P may be an inaccurate measure of how strong consumer demand would have been had shortage never occurred. Thus we cannot hope that calculation of C D P will fully answer Kornai 's second objection. (p. 495)

In a related footnote , Burket t also admits that

Kornai 's concept of shortage is broad enough to embrace forced saving, forced spending, and forced substitution. The concept of shortage in this article embraces only forced saving. (p. 503).

Burket t apparently realizes that the various phenomena of forced substi-


tution (forced saving being a special case: with saving as the substitute) have not been addressed adequately by the formulation of the rectangular hyperbola. His research strategy seems to be this: first abstract from the phenomena and derive the hyperbola; then add in further specifications to cater for them. His 1988 article however deals only with forced saving, not the more general problem of forced substitution. Equation (4) is, moreover, macroeconomic and extraneous in nature, and its foundation in the microeconomics of rationing has not been clearly established.

4. The model of Gourieroux and Laroque

To adequately deal with the problems of aggregation, it appears that there is little escape from directly modelling the degree of substitutability between consumption goods and the spillover effects, as Kemme (1989) insists. Gourieroux and Laroque (1985) have pioneered such an attempt in an abstract quantity rationing model, which extends the works of Laroque (1981) and Schulz (1983). They have derived exactly the same rectangular hyperbola as that theorized by Portes and Burkett (p. 691). However, other than the heavy informational requirements that have to be met in order that their model can be estimated econometrically (including knowledge about the proportions of submarkets in excess demand and in excess supply), a point which they admit (p. 693), their results are based on some specific assumptions which are unlikely to be realistic characterizations of the circumstances in the CPEs. To be fair, they do not seem to intend them to be.

They assume two types of economic agent: s, who buys (sells) various commodities o) in the set of markets /2 simultaneously and so generates the spillover effects; and a, who specializes in one commodity and operates in a single market. This implies a rationing scheme that allocates the ration between the two types. The relative prices of all commodities in 12 are fixed. In order to obtain analytical results, they restrict themselves to linear spillover effects. More specifically, they assume that effective demands (after taking into account the effects of substitution and spillover) are linear in the ration x x of the subset of goods (X). As they make it clear, that would be the case 'if and only if (effective demand) is linear in income, i.e. the Engel curves are straight lines in some region of the commodity space' (p. 684). Moreover, they assume that the coefficient of the spillover term in the effective demand function c(~-) = a / ( 1 - a n ) with 0 ~ < c t < l , where a is a real number and 7r the proportion of markets constrained on the demand side. As they point out, such demand curves can be derived from additive utility functions of the 'Bergson family' described by Pollak (1971).

On the basis of such restrictions and the other assumptions of continui- ty of effective demands, symmetry of commodities and the equality of

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effective and competitive demands in the case that the agent is uncon- strained, Gourieroux and Laroque subsequently arrive at their theorem 3.1 which states that there exists a unique aggregate exchange equilibrium consistent with quantity rationing (p. 688). Through a comparative statics exercise which assumes an excess demand function that is linear in the difference between the actual and the equilibrium price levels (p. 690), they derive the rectangular hyperbola to the left of the wedge (actually below the wedge as they put price on the horizontal axis and quantity on the vertical). They admit that the uniqueness result is not surprising and the following elaboration is very revealing for our purpose:

In fact, when the demanders of type s are forced to reduce their total purchases by 1 on the markets w in X, a fraction (1 - a ) / ( 1 - ~ r ) is saved in money, the rest a(1 - ~-)/(1 - ~ r ) being spent on the markets in J2]X ( ~ / ( 1 - ~ T r ) on each individual market o) in DIX ). Since (1 - o 0 / ( 1 - air) is strictly positive and smaller than one, we are in the favourable case, characterized in the standard macroeconomic model by a marginal propensity to spend income between 0 and 1 . . . (pp. 688-89).

So by construction, any tightening of the ration automatically leads to an increased saving which amounts to a fraction of the total decrease in purchases on the rationed goods. This model therefore does not entertain the case of the income effect dominating the substitution effect and the possibility of reduced saving which we have discussed above.

5. A few words on implicat ions

The failure to address adequately the phenomena of hoarding, rationing and forced substitution in CPEs may give rise to serious problems of identification, particularly when we are concerned with devising optimal policy. A key objective of disequilibrium modelling, as stated by Portes (1989), is to unravel ' the underlying aggregate curves which would be observed in full Walrasian equilibrium'. Unless we model those compli- cated phenomena that we have discussed appropriately, it may not be possible to work from observed aggregate behaviour back to the 'Wal- rasian equilibrium' configurations. Podkaminer (1989) argues that in a rationing situation, the true notional supply and demand functions cannot be identified by econometric models using the minimum condition. Ironically, he uses utility functions belonging to the 'Bergson family' (Katzner, 1970, chapter 2) in his demonstrative examples. While these examples may or may not be adequate in revealing the fallacy of the minimum condition in the discrete switching model, they do not directly deal with the continuous version of Burkett 's . Podkaminer includes

A N O T E ON T H E A G G R E G A T I O N OF SLACK AND S H O R T A G E 203

quantities of goods consumed (q) , leisure (L) and the stock of savings (s) as arguments in the following type of log-linear Cobb-Douglas utility functions with equal exponents that sum to one:

U(q, L, s) = In q / + In L + Ins N

where N = k + 2. The household would maximize utility subject to a typical budget constraint. The problem is that under such a construction, any tightening of the ration on any qi or upward restriction on L will necessarily have a positive effect on s as frustrated demand looks for substitutes. In an additive utility function like this, saving is a net substitute for consumption. The possibility of saving being reduced as a result of the tightening of the ration on consumption goods is therefore excluded in Podkaminer 's (1989) examples. 9

The question of identifiability will certainly arouse further controversy in the future. One of the main tasks for the critics of the Portes-Winter- Burket t line of research is to formalize models of consumer behaviour under rationing which demonstrate the non-correlation among the severi- ty of rationing, the amount of excess saving and the proportion of micro markets that are in excess demand, at a level of analytical rigour comparable to that of Gourieroux and Laroque (1985). Works of such kind have yet to be published by members of Kornai 's camp. In any case, the implications for failing to work back from empirical observations to the Walrasian notional supply and demand functions can be serious as far as policy formulation is concerned. A possible dilemma is graphically presented in Fig. 1.

Point E in Fig. 1 represents the Walrasian equilibrium in a two-good case, given the indifference map of the representative household. Sup- pose that initially, q2 was rationed but ql was not. However , after a round of forced substitution, even q~ becomes rationed. The typical example that the East European economists like to quote is: 'If consumers could not buy the cars they want, they will spend more at the butcher 's . ' It is possible that as a result of forced substitution, demand for qt may even rise above the level of its notional demand. Lines AC and BD in Fig. 1 depict the quantity constraints in the two markets, both of which are now binding. Unless we model and estimate the spillover effects among the goods properly, there is no way for us to infer from the observed point M directly back to the Walrasian E. Indiscriminate employment of the minimum condition and superficial acceptance of evidence of rationing as an indication that the short-side rule applies would lead to the wrong policy mix. Suppose ql represents a vector of necessities and q2 luxury goods. For reasons that Podkaminer (1986) discussed for Poland, the government under resource constraints may decide to relax the ration on ql but tighten that on q2, moving the economy to the wrong direction and generating serious supply-side repercussions. Optimal policy actually calls

D

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qa

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qi B

Fig. 1. Rationing and the structure of disequilibria.

for the relaxation of the constraint on q2 but further restriction of the 10 supply of ql.

This points to the importance of analyzing the structure of disequilibria in the CPEs, as emphasized by Podkaminer (1986, 1989). The P-W model and the Burkett version have concentrated on measuring 'aggregate slack and shortage'. While that type of findings may generate useful understanding of the CPEs, it is by no means enough. Moreover, because important information is hidden or lost in the process of 'smoothing', any results that emerge could be misleading.

Notes

1. The only major difference with the labour markets in demand-constrained market economies is that shortage dominates slack in the resource-constrained CPEs, so that the 'normal state' would be located near the upper, instead of the lower, end of the hyperbola in a labour shortage-unemployment space (Kornai, 1980, p. 250).

2. I have applied the Burkett model to a study of the aggregate consumption goods market in China for the period of 1955-87 (Tsang, 1989), modifying and extending the work of Portes and Santorum (1987). Again, I failed to reject the hypothesis of g = 0,

3. It can also be argued that the responses of economic units in a CPE like China to changes in macroeconomic variables are likely to be asymmetrical. When, for example, the price level rises, demand would decrease only slightly or not at all. If it falls, however, demand would increase significantly. On the supply side, even when the price level falls, enterprises would not want to cut production. They would rather hoard the redundant inventories and factors of production. On the other hand, if product prices


rise, they would strive to increase supply markedly and procure a much larger amount of factors of production. This asymmetry in behaviour is mutually reinforcing with the phenomenon of stock immobility. Idle resources will be accumulated in the economy, resulting in a widening gap between notional and effective supply. It would therefore be difficult to infer from observed transactions back to the underlying notional schedules, unless these problems are adequately addressed.

4. By adding a hoarding function to a cobweb model, Chen and Wang (1989) have given an interesting analysis of the relationship between the price level and different hoarding propensites in a typical CPE at the aggregate level. Various forms of positive and negative feedback effects are identified. They also extend the model to incorporate 'profiteering' ('reselling') activities in a dual system, where a portion of the goods in the planned sector is transferred (legally or otherwise) to the free markets to fetch higher prices. One of the major findings is that the actual quantity traded depends not only on the price level and the price elasticities of supply and demand, but also on the relative size of the planned sector as well as the forms of hoarding and profiteering activities.

5. It is of course possible to derive the hyperbolic relationship in the context of a rationing model. See the following section on the model of Gourieroux and Laroque.

6. Martin (1985) does not address the issue of saving explicitly. He compares three definitions of effective demands under rationing: those by Clower (1965), Benassy (1975) and Ito (1980). Although the three functions are 'observationally equivalent' in the discrete switching model as they all assume proportional responses to frustrated demands, they imply different amounts of aggregate trade in the continuous model. Martin (1985) finds the Benassy formulation most satisfactory, under which economic agents respond if their effective demands cannot be realized and the spillover is proportional to the difference between effective demands and actual trades.

7. It should immediately be pointed out that Naughton's (I986) intention was to show that Portes and Winter accepted the conclusion of excess saving, and hence stortage, in the CPEs too easi ly- a proposition just opposite to Kornai's. Nevertheless, his analysis throws insights on the aggregation problem.

8. Although in that case it would not be easy to distinguish between voluntary and forced saving (desaving). One could argue that the intertemporal transfer of purchasing power is 'voluntary'.

9. Podkaminer (1982, 1988) himself has of course developed a general disequilibrium methodology which, by comparing vectors of prices and quantities of a CPE (Poland) with those of another economy regarded as in equilibrium, aims at overcoming the problem of identifiability.

10. In this example, of course, if the government in the CPE could afford it, indiscriminate loosening of both rationing schemes would result in an eventual return to the Walrasian E. This shows how difficult it is to construct illustrative examples to serve one's precise purposes. The constraint on ql would in due course become non-binding as substitution back into q2 continuously takes place. So the dynamic path back to the point E would first take a northeastern and then a northwestern route. I am grateful to Paul Madden for pointing this out to me clearly. Nevertheless, time in economics is seldom long enough and the initial flight towards the northeastern direction could be dangerous as it may send out wrong signals to the planners and various suppliers and demanders, e.g. the planners may then attempt to change the relative price ratio in the wrong direction.

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Documents

A note on the aggregation of slack and shortage in centrally planned economies