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Barrett proposes that objective food price risk differs between rural and urban areas of infrastructure-poor economies characterised by spatially concentrated patterns of foodgrains storage. This difference implies an urban bias having adverse welfare effects for peasants who seasonally switch between net food seller and net food buyer positions.

This article considers the proposition that objective food price risk' is experienced differently in rural and urban areas of economies characterised by spatially concentrated patterns of foodgrains storage. The principal finding is that in infrastructure-poor countries rural and urban price distributions predictably diverge in such a way that rural residents face greater objective food price risk than do urban residents. Since greater risk exposure reduces the welfare of risk-averse individuals, the geography of food prices has adverse welfare effects on the rural peasantry. This suggests an important dimension to urban bias thus far ignored, with potentially actionable policy remedies having relatively minimal distortions to the rest of the food economy.

If bulk commercial storage of storable food commodities such as basic grains is concentrated in urban areas, as is common in low-income economies for reasons discussed in section II, grain may flow from rural to urban areas in the immediate post-harvest period but reverse direction as the harvest approaches again and rural farm households exhaust stocks and become food buyers. While no one, to my knowledge, has employed intranational trade volume data to prove this phenomenon, many analysts claim the existence of interseasonal flow reversals in low-income agriculture [Timmer, 1974; Southworth, Jones and Pearson, 1979; Unnevehr, 1985; Elz, 1987; Loveridge, 1991; Harriss-White, 1995]. As I document in section III, the empirical evidence from Madagascar supports the hypothesis of urban storage concentration and interseasonal flow reversal. The impact of such flow reversals on the variance and skewness of rural and urban food price distributions has thus far been ignored. In other words, the effect of the food marketing system on the geography of risk bearing has been overlooked. But if the higher-order moments (that is, variance, skewness) of food price distributions faced by particular subpopulations systematically exceed those faced by others, this alone will generate important welfare differences between risk-averse agents.

One can usefully distinguish between three distinct subpopulations in low-income economies. First, there are year-round net food buyers, a group including all nonproducers of food, and thus most urban residents and the landless poor of rural areas. Second, there are year-round net food sellers, mainly large commercial farmers. Finally, there is a class of peasants who predictably switch between net seller and net buyer positions over the course of the agricultural calendar, selling in the immediate post-harvest period and buying in the pre-harvest `hungry season'. Recent research indicates that a large proportion of farmers engage in such seasonal switching of exchange relations - from seller to purchaser, then back again [Ellsworth and Shapiro, 1989]. Indeed in Africa, a substantial proportion of food producers are net food buyers in aggregate [Weber et al., 1988; Barrett and Dorosh, forthcoming]. It is this latter group, whose preferences over the moments of food price distributions vary seasonally,2 that shoulders the burden of the geography of food marketing in infrastructure-poor countries, and I follow the literature on urban bias [Lipton, 1977; Bates, 1981] in focusing primarily on this peasant class.

The above points are developed over four sections. Section I briefly reviews the economic theory of preferences over uncertain prices, including the concept of stochastic dominance, which is applied in section III. Section II presents (informally) a theoretical explanation of rural-urban differences in food price distributions. Section III offers corroborating empirical evidence from rice in Madagascar. Section IV draws out a few policy and research implications. In particular, examination of intranational and interseasonal price distributions demonstrates the inferential hazards of averaging prices across space, time, or both. Moreover, spatially and temporally divergent food price distributions point to the centrality of marketing infrastructure to the alleviation of food insecurity and rural poverty obstacles to development. These also raise issues of econometric methodology for food policy analysts, which are discussed in the concluding section.

I. PREFERENCES AND STOCHASTIC PRICES

Because all people consume food, but only some buy or sell it (or both), food prices affect the welfare of everyone, but not in identical ways. Those who sell food enjoy welfare gains from higher expected food prices, while those who purchase food prefer lower mean prices. This follows directly from Roy's Identity.3 Moreover, since people consume food over many periods and food production involves biological lags, food prices are inevitably subject to considerable temporal uncertainty. Except under the rare circumstances when the strong assumption of agent risk neutrality is defensible, one must thus consider as well agents' preferences with respect to moments beyond the mean (for example, variance, skewness). Any form of risk aversion implies a preference for low variability in real income, and thus in prices.4 Agents' qualitative preferences with respect to skewness, however, vary across agents according to their net buyer/seller position. Purchasers are harmed by the extraordinary price rises that yield positive skewness in price series, while sellers lose from sharp price drops associated with negative skewness [Menezes, Geiss and Tressler, 1980]. Fortunately for sellers, a workably competitive storage market tends to ensure positive skewness in commodity prices series [Williams and Wright, 1991; Deaton and Laroque, 1992]. Net sellers thus prefer high means, low variance and positive skewness, while net buyers desire low means, low variance and negative skewness in food price series.

Based on this rather parsimonious description of agents' preferences, one can rank order price distributions' welfare effects using the concept of stochastic dominance. Stochastic dominance is an especially useful method of risk analysis under the expected utility hypothesis when one has incomplete information about agents' preferences [Anderson, Dillon and Hardaker, 1977; Whitmore and Findlay, 1978]. The basic intuition behind stochastic dominance is that individuals can order their preferences among alternative, stochastic variables just as they order preferences among goods and services in basic consumer theory. Simply put, people prefer gambles having the lowest probability of the least desirable outcomes and relatively high probability of the most desirable outcomes. More formally, if a net seller's utility is increasing in income, he will unambiguously prefer the urban price distribution, u(p), to the rural one, r(p), if and only if

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In words, if the cumulative mass function for the discrete distribution r(p) lies everywhere to the left of the cumulative mass function for the discrete distribution u(p), u(p) offers everywhere better (that is, higher) prices to the net seller. If this condition holds, u(p) is said to first-degree stochastic dominate (FDSD) r(p). Conversely for a net buyer, Only then does u(p) present everywhere better (that is, lower) prices than r(p) to the net buyer. The reversed ordering between sellers and buyers reflects their divergent preferences over means and skewness in price distributions.

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FDSD often proves insufficient to generate an unambiguous preference ordering between stochastic variables. But if one is willing to impose a bit more structure on agents' preferences, specifically risk aversion, then a more powerful concept, second-degree stochastic dominance (SDSD), becomes available. Using the earlier FDSD results, a risk averse net seller will prefer u(p) to r(p) if and only if In words, SDSD measures the area under the FDSD curve, thereby allowing large differences between distributions under adverse draws to offset small reversals under more favorable draws. In this important sense SDSD captures the essence of downside risk aversion, the notion that people are averse above all to adverse shocks.

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Again, the necessary and sufficient condition for a net buyer is the converse of that for a net seller due to opposite preferences over the mean and skewness of the stochastic variable. As will become apparent in section II, SDSD provides an appropriate test of the hypothesis that the urban price distribution welfare dominates the rural price distribution, in particular for risk-averse peasants who seasonally switch between net seller and net buyer positions. The next task is to establish that regional price series are indeed distinct stochastic variables with differences worth considering seriously.

II. SUPERVARIABILITY AND SUPERSKEWNESS IN RURAL FOOD PRICES

Rural smallholders with seasonally-varying preferences over the moments of food price distributions systematically suffer from the geography of agricultural marketing prevailing in many low-income countries. First, they tend to receive lower mean sales prices over the course of the year than do other food sellers. Peri-urban farmers enjoy higher prices during the postharvest period when rural smallholders sell, while the rural large farmers are more likely to sell during the pre-harvest price peaks when smallholders become purchasers. Second, assuming identical price risk aversion across agents, rural smallholders face greater welfare-reducing price variability than their urban brethren. Third, while rural large farmers often sell during the hungry season, thereby benefiting from positive skewness in prices, smallholders are usually hungry season food buyers. Moreover, rural purchasers face more sharply positive hungry season food price skewness than do urban buyers. These propositions with respect to mean, variance and skewness derive from the concepts of interseasonal and intraseasonal supervariability and superskewness in rural food prices, introduced next.

Bulk grains storage for commercial sale is often concentrated in urban areas of developing economies.5 There are multiple reasons for this. Greater population density and higher per capita incomes concentrate purchasing power, and thus commercial demand, in urban areas. Given non-trivial risks of logistical bottlenecks in transshipment due to poor infrastructure, traders often prefer to store nearer final markets, even paying a `convenience yield' to do so [Working, 1949; Brennan, 1958]6Moreover, Hotelling's [1929] classic work on spatial competition suggests marketing is generally even moregeographicallv concentrated than demand. Rural-urban infrastructure differences magnify this tendency toward spatially concentrated marketing. The effect of low rural electrification rates, poor rural roads maintenance, unreliable rural communications, and sparse, illiquid rural financial networks is transactions and capital costs that are generally higher in rural areas, feeding the spatial concentration of food marketing. Higher rural operating costs demand a higher rate of return to rural commercial storage (that is, interseasonal price variation). Moreover, interseasonal storage is unusually dependent on commercial credit, but storage sites have collateral value to creditors only in (urban) areas where they can be leased or sold to other firms needing storage space in the event of foreclosure. The collateralisation requirements of commercial credit thus contribute as well to urban concentration in grain storage capacity. While commercial grain storage is by no means always concentrated in urban areas, it is a common phenomenon consistent with economic theory in infrastructure-poor settings, like the Malagasy case explored in section III.

If storage is predominantly urban and if a sizeable sub-population in rural, producing areas demand food through commercial markets in the preharvest 'hungry' season, then there will generally be seasonal flow reversals. Such reversals are the natural byproduct of intermarket arbitrage when demand or supply conditions, or both, are dynamic. In the stylised low-income economy of this section, rural food supplies peak immediately post-harvest, when rural commercial demand for food is relatively weak since farm households can self-provide. As the months pass, however, and farm households draw down or exhaust their own stocks, rural commercial demand grows. In the meantime, if interseasonal storage capacity is concentrated in urban areas, rural food supplies diminish over time. The net effect of these dynamic shifts in regional aggregate demand and supply schedules is that the producing zone exhibits season-specific excess demand and thus becomes a seasonal net importer of food from the very urban areas it supplies in the post-harvest period. Moreover, even if urban areas cannot supply rural areas from interseasonal stocks, if cities are the principal international ports of entry and the nation is a net food importer, urban-rural flows will still occur, instead from the transshipment of current imports. This phenomenon of seasonal flow reversals thus results from urban concentration of storage, including of imported transactional stocks, and from seasonal net demand in producing areas. These distressingly common characteristics of low-income economies result from the poor quality of rural infrastructure and food production technologies, both of which are evident in Madagascar, as section III explains.

Just as the geography of food storage and marketing has a sound basis in economic theory, so does this geography have implications for rural and urban food price distributions. First, mean rural food prices are below mean urban prices in the immediate post-harvest period, but increase more rapidly as the year progresses, eventually exceeding mean urban prices during the pre-harvest hungry season, before the cycle recommences with the next harvest. These patterns are the byproduct of basic spatial equilibrium principles under seasonal flow reversals [Takayama and Judge, 1971]. Since rural seasonal prices exhibit lower minima and higher maxima than urban seasonal prices, one might classify this phenomenon `interseasonal supervariability' in rural food prices, where the prefix `super-' indicates the ordinal ranking of rural measures against an urban base.

Second, the same conditions that generate a concentration of interseasonal grains storage in urban areas - higher costs and lower and less concentrated demand - also serve to thin rural markets, especially in the hungry season. The fewer the participants, the less elastic is aggregate demand and supply. Because storage is more distant from rural markets, lag times in response by arbitraging intermediaries tend to be greater, fuelling price variability. Moreover, if small market size and some minimum efficient scale to commercial storage result in high concentration ratios, incumbent rural middlemen with market power might rationally stimulate food price volatility to discourage entry [Newbery, 1978; Hollander, 1994]. Whether due to market thinness, lagged trader response, intermediary market power, or some combination, rural food price variability may be greater not only interseasonally, but also intraseasonally, especially in the hungry season. For consistency's sake, label this hypothesis `intraseasonal supervariability' in rural food prices.

Finally, the non-negativity constraint inherent to grains storage implies asymmetry in storable commodities' price distributions [Williams and Wright, 1991; Deaton and Laroque, 1992]. Real food price data generally exhibit flat ranges punctuated by upward spikes that tend to emerge and dissipate rapidly. However, the regional differences in transactions costs and communications efficiency that facilitate urban concentration of commercial food storage also inhibit rapid response by arbitragers that might mitigate the duration and intensity of upward price spikes in rural areas, which are of course most likely during the hungry season. As a result, the positive skewness of prices is likely to be greatest in rural areas during the hungry season. Call this hypothesised phenomenon hungry season 'superskewness' in rural food prices. Figure 1 depicts these three hypothesised phenomena-interseasonal and intraseasonal supervariability and hungry season superskewness. Interseasonal supervariability is evident in the steeper slope of the rural conditional expectation function. Comparison of the rural and urban conditional price distributions reveals intraseasonal supervariability and hungry season superskewness. If true, these hypothesised phenomena imply a strong urban bias in the distribution of objective price risk in low-income economies.

Strictly speaking, interseasonal supervariability need not represent any risk, for if each period's price distribution is degenerate (that is, variance equals zero) one can forecast intertemporal price patterns perfectly. The issue is instead individuals' ability to smooth consumption optimally through savings, credit, or insurance. Interseasonal variation in food prices, especially when negatively correlated with nominal income, induces savings and borrowing to smooth consumption [Deaton, 1990]. If interseasonal food price variability is greatest in rural areas, the need for financial intermediation is likewise greatest in rural regions. Although considerable evidence exists that consumption smoothing occurs through savings or state-contingent contracts [Deaton, 1992; Paxson,1993; Udry, 1994], rural financial networks are notoriously underdeveloped relative to urban networks. No comparative empirical evidence exists, but it seems likely that greater demand for intertemporal transactions due to interseasonal supervariability conspires with tighter rural financing constraints to inhibit rural consumption smoothing, relative to that of urbanites. If this is true, the geography of agricultural marketing and finance jointly impose welfare costs on rural residents not borne by their urban counterparts.7

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Intraseasonal supervariability implies that a price risk-averse agent would prefer to face the urban price series than its contemporaneous rural counterpart. Unless the urban mean is substantially lower when such an agent is selling or higher when the agent is buying - which will not be the case under interseasonal supervariability in rural prices - the urban price series is welfare-superior in a (second degree) stochastic dominance sense. Similar results obtain with respect to hungry season superskewness if a downside risk averse agent 8 purchases food: s/he would uniformly prefer to face the urban food price distribution than the rural distribution, assuming equal mean and variance. Note that large farmers with net sales of food in all periods gain from positive skewness in food prices; this represents upside welfare risk to sellers. But positive skewness in price is unattractive to downside risk averse smallholders who are seasonal net buyers. Hungry season superskewness in rural food prices may thus imply welfare differences between wealthy (all-season net seller) and poor (hungry season net buyer) farmers, as well as between urban and rural net food buyers.

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In summary, the three detailed hypotheses about spatial differences in objective price risk are that for the distinct rural and urban conditional price distributions, rn(p) and u,(p), respectively, where sigma^sup i^ is the i^sup th^ central moment of the price distribution (that is, sigma^ sup 2^ is variance, sigma^ sup i^ is skewness), subscript t indicates a distribution conditional on time period, and H is the set of hungry season months. These differences in objective price risk are hypothesised to adversely affect the welfare of peasants who seasonally switch between net seller and net buyer positions as measurable using the concept of second degree stochastic dominance introduced in section I.

III RURAL-URBAN RICE PRICE DISTRIBUTIONS IN MADAGASCAR

The hypotheses of interseasonal and intraseasonal supervariability and hungry season superskewness in rural food prices and welfare differences across subpopulations are tested using regional rice price data from Madagascar. This is not meant as a definitive set of statistical tests, but merely an empirical corroboration of the plausibility of the concepts mapped out above.

Rice is the staple food throughout Madagascar, comprising more than half of all cultivated land [MPARA/FAO, 1988], and about 55 per cent of per capita daily calorie and protein supplies [FAO, 1984]. Although rice production is the nation's main economic activity, an estimated 63 per cent of Malagasy rice producers are net rice buyers; indeed, the rice producing sector is (astonishingly) a net importer of rice [Barrett and Dorosh, forthcoming]. A major reason for this is that Malagasy rice yields are low, at 2.11 metric tons per hectare in 1990-92 against a world average of 3.55 [FAO, 1992]. Until 1970 Madagascar was a net rice exporter, but production stagnated and demand increased sharply in the face of rapid population growth. Rice imports reached 25 per cent of total availability in 1982 before declining to under ten per cent in the 1990s.

Both private and public agricultural marketing networks are designed around the movement of paddy or processed rice, predominantly in hulled form [Abt Associates, 1991], with 50-75 percent of national commercial grains storage concentrated in just three urban areas: the capital city, Antananarivo, and the port cities of Toamasina and Mahajanga [Cabinet Fivoarana, 1989].9 The high concentration of grains storage capacity follows from the reasons outlined in section II. While only 21 per cent of the 1985 population lived in cities [MPARA/FAO, 1980] mean household incomes in those three cities was more than 70 per cent higher than mean rural incomes [BDE, 1987], and urban demand likely accounts for more than 90 per cent of commercial rice sales [World Bank, 1989; Barrett and Dorosh, forthcoming]. Madagascar's transportation network is a shambles, heavily oriented toward domestic air transportation rather than ground movement by either rail or truck.'10 All flights and most rail or road traffic must pass through Antananarivo, while Mahajanga and Toamasino accounted for 69 and 73 per cent of coastal shipping and international import volumes, respectively, in 1986 [BDE, 1988]. Concentrated commercial demand and infrastructure foster heavy concentration of commercial grains storage in just three cities, and the nation's grain imports pass through these cities, whether or not they are stored interseasonally. Thus seasonal market demand in rural areas caused by low yields is met by rice supplies from interseasonal storage in urban areas or imports that pass through the cities. This produces seasonal flow reversals in Madagascar, a phenomenon noted by most observers of Malagasy agriculture [Abt Associates, 1991; Barrett, 1995b].11 The human and physical geography of rice marketing in the peasant-farming dominated economy of Madagascar thus fits well the stylisations of section II.

The data are monthly retail-level observations, January 1983 to December 1991, of nominal hulled rice prices from Madagascar's 17 agricultural enumeration regions. Barrett [1994] explains the data in detail. For each regional series, year-specific seasonal indexes, si,, were computed using the ratio-to-moving average method.12 This removes the trend and cyclical variation from the regional time series, leaving just the seasonal and stochastic components, thereby accomodating demand and supply shocks associated with region-specific economic cycles and inflation patterns, so one need not impose national indicators across a range of demonstrably heterogeneous subeconomies."

Since the hypotheses to be tested compare the moments of rural and urban price series, I next group the specific seasonals geographically and calculate the empirical moments of seasonally disaggregated group frequency distributions. The urban group comprises the three metropolitan regions with most of the nation's commercial grains storage capacity (Antananarivo, Mahajanga, Toamasina). The other 14 regions constitute the rural group. Figure 2 shows the location of the three urban regions (numbers 1, 7, and 10) in a belt across the north-central part of the island.

The rural and urban regional price distributions are similarly centred. Sample mean panseasonal price in the two groups differs by less than one per cent, a statistically insignificant amount. The peak of Madagascar's rice harvest runs from mid-March to late June. The soudure?re (hungry season) runs November through early March. Six bi-monthly distributions were constructed for each areal grouping.14

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The computed empirical moments of Madagascar's urban and rural bimonthly rice price distributions support hypotheses (1) - (3), stated at the end of section II. Table I reveals interseasonal supervariability evident in the greater range of rural seasonal means (87.3-110.8) than urban seasonal means (90.4-109.8), as well as in the higher variance and coefficient of variation of panseasonal rural prices. Average interseasonal returns to storage are 25 per cent higher in rural areas than urban, much of which is likely attributable to spatial differences in financial and physical storage costs. Intra-seasonal supervariability appears in the higher coefficients of variation for each bi-monthly rural price distribution, and in rural variance greater than urban variance in all periods except the peak harvest months of May-June, when rural markets are flush with intermediaries. Hungry season superskewness is apparent in the substantially greater positive relative skewness in rural prices during the peak of the hungry season, November-February. Most of these differences are statistically significant at the 5 per cent level. Since the difference in rural and urban panseasonal means is less than one per cent, the essential difference between the rural and urban rice price distributions is the greater objective price risk faced by rural inhabitants.

The welfare effects of this greater objective price risk exposure of peasants can be demonstrated most unambiguously through stochastic dominance testing of the general hypothesis that risk-averse peasants are worse off facing the rural price distribution than if they could face the urban price distribution. Tests of the panseasonal distributions (that is, pooling all months' observations together) reveal neither first nor second degree stochastic dominance between the rural and urban distributions, for either net buyers or net sellers15 This demonstrates that there is no unconditional preference ordering of rural and urban food price distributions for pure buyers or sellers, due above all to seasonal flow reversals in the marketing channel.

However, the focus of this article is the peasant population, many of whom switch seasonally between net seller and net buyer positions. Andrianarijaona's [1985] survey of 692 central highlands farmers found that 79 per cent of producers bought rice for at least four months in the 1984-85 crop year. Almost 90 per cent were net rice buyers in January-February, but that number fell to only 20 per cent by April.' 16 If we thus assume that Malagasy peasants are net rice sellers from the beginning of the harvest in March, and that they are net buyers for at least the last two months of the hungry season (January-February), the data indeed indicate ut(p) dominates rt(p) in a second-degree stochastic sense. Figures 3 and 4 show this for two illustrative plots of the rural and urban conditional cumulative mass functions: the hungry season period of January-February (Figure 3) and the post-harvest period of May-June (Figure 4). Figure 3 shows multiple crossings of the rural and urban rice price distributions, hence the need for SDSD analysis. Note that the rural distribution yields lower probability of a low price and especially, a higher probability of a high price, or superskewness, during the hungry season. Figure 4 suggests the urban distribution nearly stochastically dominates the rural distribution in a first degree sense. Formally, D^ sup 2^(pj I t) > 0 \forall p; for t=JAN-FEB and D^ sup ns^ (pj I t) > 0 V\forall pj for t=MAR-APR, MAY-JUN, and JUL-AUG. So only during the last four months of the calendar year, during the transition from the post-harvest period to the hungry season, do urban rice price series not stochastically dominate rural rice price series for risk-averse peasants.

IV. IMPLICATIONS FOR POLICY AND RESEARCH

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Poor infrastructure and food production technologies in many low-income economies yield a geography of agricultural marketing that imposes greater objective food price risk on rural residents than on city-dwellers. Peasants who seasonally switch between net food seller and net food buyer positions are particularly disadvantaged by the price distributions that follow naturally from food marketing patterns in infrastructure-poor economies. Because food price distributions have predictable spatial and temporal patterns, disaggregation across both space and time is thus essential to careful food price analysis. Price data averaged over space and time (for example, annual national averages) may mask trends of substantial importance to policy design and research on agricultural marketing and production, food security, and poverty.

These results have clear policy implications. High gross rates of return to commercial storage often reflect high real transaction costs that are inversely related to the quality of human and physical infrastructure. Even in competitive rural markets, interseasonal and intraseasonal supervariability and hungry season superskewness of rural food prices emerge naturally where infrastructure is poor, both because rural costs are higher and because poor rural infrastructure induces commercial grains storage nearer to markets than to producing regions. This impacts adversely on the welfare and food security of credit-constrained sub-populations, a group increasingly recognised as numerous in low-income countries. While government controls on marketing margins cannot rectify the problem [Unnevehr 19851, redressal of the root geographic cause of these phenomena may generate substantial social returns. Research suggests rural public works projects have important effects on demand, supply, and food prices when interseasonal flow reversals stem from physical infrastructure deficiencies, with generally favourable consequences for rural consumption, employment, investment, and agricultural production [Ahmed and Donovan, 1992]. Indeed, rural infrastructure improvements that eliminate prospective logistical bottlenecks to interregional trade should largely eliminate seasonal flow reversals by inducing commercial storage nearer producers than final markets. Countries like Madagascar17 are not yet to this point.

The present findings add to the evidence that rural infrastructure investment can have important positive direct welfare effects on poor peasant populations. Moreover, positive indirect effects may be considerable, as well, in that higher risk generally leads to lower rates of private investment, creating a sort of vicious circle wherein lower private investment in marketing infrastructure leads to high price variability which further discourages market development. The prospective `crowding in' effects of public investment in rural communications, transport, and utilities networks might thus operate, not just by increasing expected returns to private investment, but by dampening the variability of returns to investment as well by dampening price risk. Since investment tends to be an important leading variable in employment creation, and rural labour markets are an important component of the portfolio of income-generating activities for rural peasants, not to mention landless rural subpopulations, rural infrastructure provision may have important indirect welfare effects as well through improving investment incentives.

Yield improvements in smallholder food production could likewise stem seasonal flow reversals, and their risk-bearing consequences for peasants, by eliminating seasonal net commercial demand from producing regions. However, given continued rapid population growth in low-income agrarian economies, it may be difficult to generate per capita food output gains sufficient to eliminate seasonal rural food imports in the near future.

There are two econometric implications also worth considering. Much attention has been paid to the relationship between food quality and expenditures, both by those striving for accurate estimation of price elasticities [Deaton, 1988] and those concerned about the effect of income growth or transfers on nutrient intake levels [Pitt, 1983; Behrman and Deolalikar, 1987]. Cross-sectional expenditure surveys typically gather recall data from clusters of households. While spatial variation in prices (due to transportation costs, for example) is admitted, within-cluster variation in unit values (expenditures divided by physical quantities) is generally attributed to measurement error and variation in the quality of food purchases. Imputed quality variation might be substantially overstated. Where recall periods are more than just a matter of days, there may be substantial temporal variation in price as well. Since wealthier agricultural households generally wait longer after harvest before entering the market as food purchasers, and because food prices rise from harvest due to storage costs, there may be a genuine positive correlation in rural expenditure surveys between wealth or income and average food prices that is unrelated to any differences in the quality of food purchased. Attribution of within-cluster price variability to quality differences may thus bias estimates of the relationship between income and food quality upwards, thereby biasing `quality-adjusted' estimates of the income elasticity of nutrient demand downwards.

Finally, recent advances in time-series analysis have admitted modelling autocorrelated heteroskedasticity in commodity price estimation using ARCH/GARCH techniques [Aradhyula and Holt, 1988; Holt and Aradhyula, 1990; Jayne and Myers, 1994; Barrett, 1995b]. Table 1 suggests (and Barrett [1995b] confirms) autoregressive heteroskedasticity's presence in food price series from Madagascar. This is likely a widespread phenomenon to which development researchers should give more attention, especially those concerned with agricultural price and marketing policy. Moreover, the evidence here suggests that generalisation to conditional skewness would be fruitful as well, in that there seems to be a dynamic dimension to skewness that existing methods do not capture well. This is especially important if downside risk-aversion matters to economic agents and is routinely addressed through government interventions to defend price bands, ceilings, and floors. Recent advances in generalising autocorrelation across the moments of stochastic distributions [Hansen, 1994] might thus be of interest to development researchers exploring the welfare consequences of food price policies.

final version received November 1995

[Reference]

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Andrianarijaona, M.E., 1985, `Enquete Socio-Economique Dans la Region d'AmbohibaryManjakandriana', Memoire de stage, University of Antananarivo.

Aradhyula, S.V. and M.T. Holt, 1988, `GARCH Time-Series Models: An Application to Retail Livestock Prices', Western Journal of Agricultural Economics, Vol.13, No.4, pp.365-74. Banque des Donnees de l'Etat, 1987, Enquete Sur les Budgets des Menages: Depenses/Centres

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[Author Affiliation]

The author is an assistant professor in the Department of Economics, Utah State University, Logan, UT 84322-3530 USA. The financial support of the Institute for the Study of World Politics, the Social Science Research Council and the Utah Agricultural Experiment Station is gratefully acknowledged. Approved as UAES journal paper number 4843. This work has benefited considerably from conversations with Jean-Paul Chavas, Michael Carter and Matt Holt and the comments of DeeVon Bailey, an anonymous referee and participants at the 1995 annual meeting of the American Agricultural Economics Association. All remaining errors are the author's.