Modelling the maize marketed surplus behaviour under risk and time preference conditions: The case of Zvimba and Mokonde districts of Zimbabwe

Abstract The Heckman sample selection technique was applied in modelling the households’ maize marketed surplus decision under risk and time preference assumption. We assumed that maize returns depend on farmers’ market selection choices. We then applied the sample selection model to explain why maize surplus households shunned the uncertain, high-return state-owned Grain Marketing Board (GMB), with delayed payment system in favour of the more certain, low-return private buyer market, with immediate payment system. In the process, we tested whether the marketed surplus decisions followed a sequential or simultaneous decision process. Using survey data collected from 433 households from Zvimba and Makonde districts, the results confirmed that households followed a sequential decision process when selling through the private buyer market and a simultaneous decision process when selling through the GMB market. These findings implied two things; firstly maize surplus households could exercise some bargaining power in the private buyer market even if they got less. Secondly, in the presence of uncertainty and payment delays, high-return incentive offered through government parastatals may not be sufficient to attract maize surplus, as households may not sufficiently respond, due to risk aversion attitude and time impatient behaviour.


Introduction
This paper applied the Heckman sample selection technique to unpack the paradox of maize marketed surplus behaviour in Zimbabwe, under risk and time preference assumptions. Its main objective was to provide an explanation as to why maize surplus households in Zvimba and Makonde district exhibited a seemingly confusing, conflicting and myopic marketing channel selection choice behaviour (Adamkovic & Martoncik, 2017;Mani et al., 2013) that was inconsistent with both household long-run income optimisation behaviour and the government's maize marketing policy imperative of guaranteeing better prices to the farmers. This therefore, motivated this paper to explore the Zimbabwean maize surplus marketing puzzle, where households decided to sell their maize crop at the farm gate, to intermediaries at very low prices, instead of selling to the formal state-owned GMB market at higher prices (Fafchamps & Vargas Hill, 2005;Kamoyo & Makochekanwa, 2018). In addition, the same maize farmers succumbed to the "sell low, buy high" or "the distress sale" phenomenon, in which they sold their maize soon after harvest when prices were very low and buy it again in future after prices have gone up (Stephens & Barrett, 2011;Sahu et al., 2004). This market participation behaviour exhibited a "seemingly irrational" decision that generates farm household income losses, hence the need for a rigorous empirical enquiry that explain the causes of this behaviour, so as to inform appropriate interventions.

The Zimbabwean smallholder maize market
The Zimbabwean maize marketing system was too complex and dualistic in nature, thereby causing a serious marketing channel selection choice dilemma. Under the system, the private buyer market co-existed with a formal state-owned GMB market. These two markets were characterised by serious price disparities and varying payment terms that signalled different risk and payment delay lengths (Jayne et al., 2005;Kamoyo & Makochekanwa, 2018;Scoones et al., 2011). On one hand, the formal state-owned GMB market offered a high support price of $390 per tonnes. However, the payment dates were delayed and uncertain. Farmers' could spend two years without receiving payment for their deliveries. On the other hand, was the private buyer market comprised of both registered and unregistered buyers who offered spot payment for delivery, though at very low prices that ranged between $200 and $300 per tonnes (AMA, 2013). In addition, the private buyer market was largely informal and based on traditional marketing systems of barter exchange of maize for groceries, using 20 litre buckets for transaction (Moyo, 2011;Taylor et al., 2008). In this market setup, maize surplus households had to make a hard choice between accepting a low return, safe marketing option, or high return but risky and delayed marketing option.
The puzzling aspect was that maize surplus farmers preferred a low return farm gate marketing option, whilst shunning a high return formal state-owned GMB marketing option. Explaining this "seemingly irrational" market participation behaviour has been the burden of many scholars, who for the past, proposed various factors, but giving little attention to the role played by risk aversion and time preference factors in shaping such marketed surplus behaviour among smallholder farmers. Simtowe and De Groote (2021), Stephens andBarrett, (2011), andSahu et al. (2004), emphasised on the effect of household liquidity constraints on marketing channel selection choices. Sibande et al. (2017), and Barrett (2008) associated such behaviour to market access barriers such as poor infrastructure, high transaction costs of marketing, insufficient productive assets endowment, and information asymmetry, among others. Recent studies that incorporated risk aversion attitude and time preferences like Girma et al. (2023), Sarwosri and Mußhoff (2020) were confined to production decision, with little focus on marketed surplus decisions.

Research originality
Unlike these previous studies, this paper incorporates the role of farmers' risk and time preference factors in shaping the marketed surplus decision, thereby filling a literature gap that was overlooked before. Knowledge on this area uniquely contributes to literature that supports government food marketing policy formulation in developing countries (Montalbanoa, Pietrellib and Salvaticic, 2018). An understanding of how risk aversion and time preference factors affect smallholder farmers' marketing policy response behaviour is important in the crafting of policy interventions.
This study was done in Zvimba and Makonde districts of Zimbabwe, where nothing was done to uncover market participation behaviour, under risk and time preference assumptions. The two districts are in agro-ecological region II, with good soils and rainfall pattern that are suitable for maize crop farming. Unfortunately, the market participation decisions in these two districts and the rest of Zimbabwe are still masked by many inhibiting factors. Maize farmers are still confined in a state of vulnerability, characterised by risk avoidance and short-run temptations, which led them to forgo high rewarding income markets. This market participation behaviour is a serious concern that perpetuates a wave of low marketed surplus and persistent food deficits (De Jenvry & Sadoulet, 2006;De Jenvry et al., 1991;Eriksson, 1993;Kapuya et al., 2013;Muchapondwa, 2009). Yet, little was done from the scholarly side to establish the impact of risk and time preference behaviour on marketed surplus decisions. This paper, therefore answers two main research questions linked to the smallholder farmers' "seemingly irrational", marketed surplus behaviour. Firstly, it applied the risk aversion and time preference factors to unravel why maize surplus households shun the high-return, formal stateowned GMB market in favour of the low-return, private buyer market (Kamoyo & Makochekanwa, 2018). Secondly, using the sequential or simultaneous decision modelling, the paper provided answers to why the state-owned GMB marketing channel failed to attract smallholder marketed surplus, despite it paying comparatively higher price than the private buyer marketing channel. This last objective arises because the government's extensive involvement in maize marketing through the GMB proved to be unpopular with smallholder farmers; hence, the need to generate new knowledge on smallholder marketed surplus behaviour. This knowledge can help to shape the future of grain marketing policy in Zimbabwe and other developing countries. It is useful in the development of right agricultural marketing policies that activate market incentive systems and increase the marketed surplus, so as to make agricultural markets work for the poor (OECD, 2007).

Literature review
The smallholder marketed surplus behavioural theory can be traced back to Scott (1966)'s socalled irrational "obsolete anti-market mentality" hypothesis. The theory is based on the premise that, in the presence of market failure, smallholder farmers' production decisions are not marketoriented, thus they generate inadequate marketed surplus. Their agricultural decisions can be contextualised based on the non-separability or simultaneity in farm production and consumption decisions (De Jenvry & Sadoulet, 2006). This scenario is synonymous to zero marketed surplus because production is deemed to be purely for auto-consumption. However, contrary to the "antimarket mentality", the recursive models affirm that agricultural households in developing countries are semi-commercial. They produce partly for consumption and partly for the market (Singh et al., 1986). In that regard, markets and prices plays a very critical role in household production and marketing decisions (La Fave & Thomas, 2016).
The recursive models for farm household decisions generated a lot of interest among scholars, who sought to explain the market participation behaviour. Market participation decisions, which encompasses the marketed surplus decisions play a central role in the reconfiguration of subsistence farming to commercial and profitable agricultural enterprise (Barrett, 2008;Melkani et al., 2019). The first breakthroughs on agricultural marketed surplus decisions and supply response were done by Krishna (1961), Behrman (1966), Ghatak (1975), Griffin (1979) and Jabbar (2010). These researches were centred on market access barriers that inhibit smallholder farmers from accessing high return formal agricultural markets for their surplus grain. All these studies were much celebrated, however, they offered little attention on the role played by farm households risk aversion attitude and time preference structures in influencing marketed surplus decisions. Limited effort was made to incorporate risk and time preference factors in modelling household marketed surplus decisions (Grover et al., 2012;Malchow-Moller, 2002).
There is strong empirical literature confirming that economic choices and agricultural household marketing decisions are strongly influenced by the producer's risk aversion attitude (Finkelshtain & Chalfant, 1991;Franken et al., 2014;Pope & Just, 1991) and time preference factor (Hardisty et al., 2013;Malchow-Moller, 2002). In general, marketed surplus households face multivariate risk due to price randomness, weather fluctuations and natural disasters (Finkelshtain & Chalfant, 1991) and most of their decisions involves delayed outcomes with regard to future income options and conditions (Malchow-Moller, 2002). Risk aversion attitude and time preference as widely applied in economic decision modelling (see Andersen et al., 2008;Malchow-Moller, 2002;Meier & Sprenger, 2010) shape households' response to uncertainty and payment delays in economic transactions (Saitone et al., 2018), which in turn is a critical factor towards efficiency loss and "poverty traps" for peasant-based households (Mendola, 2007). Modelling the farm household's complex choice selection behaviour under these conditions of uncertainty and time preferences has been a subject of interest among behavioural economist. They applied the expected utility theory and the safety first models to clarify the seemingly short-sighted marketing channel selection behaviour (Hardisty et al., 2013).

Expected utility theory and the safety first models
One way to conceptualise the "seemingly irrational" marketed surplus choice behaviour of smallholder farmers, is to analyse them based on the expected utility maximisation theory, instead of the profit maximisation theory (Mendola, 2007). These farmers are assumed to follow the von Neumann-Morgenstern expected utility theory (Levin, 2006). According to the expected utility theory, economic agents make decisions that maximises their expected utility, instead of expected returns by avoiding unsafe income options. Such that, given two income options, a delayed highreturn, high-risk option and an immediate low-return, low-risk option, a risk averse and time impatient farmer is better off given the small immediate amount with certainty rather than risking in a future uncertain gamble (Mendola, 2007). Thus they get into "a feeling of vulnerability" by prioritising a safe and conservative option, even if it pays less, thereby resulting in efficiency loss and "poverty traps" (Kanbur & Squire, 2001;Mendola, 2007). Empirical literature confirms that in the presence of risk and deferred agricultural payments, subsistence households will forgo high return production and marketing options for greater self-protection and disaster avoidance (Domingo, et. al, 2015;Mendola, 2007). Findings by Gloede et al, (2012) confirms that, in Thailand and Vietnam household's degree of risk aversion strongly influenced poverty continuity and vulnerability. Similarly, findings by Humphrey and Verschoor (2004), and Yesuf and Bluffstone (2009), confirmed that selection of low income options was closely related to high risk aversion and high discount rates.
If we analyse the expected utility maximisation theory within the context of time preferences, it offers quite appealing conclusions. First, the time preference variable recognises that agricultural marketing decisions involve some options with immediate payoffs and others with deferred payoffs, thereby factoring in the importance of time discounting in modelling farm household market decisions that involves monetary rewards. Second, it helps to explain why poor smallholder farmers reflects a "seemingly" short-sighted, sub-optimal market selection choices, by strongly discounting or devaluing monetary reward from deferred marketing channels, in favour of monetary rewards from immediate marketing channels (Hardisty et al., 2013). In other words, the poor succumb to short-run temptation at the expense of long-run optimisation (Hardisty et al., 2013;Kovacs et al., 2021). Poor households are time impatient and they exhibit present-bias behaviour, to the extent that they forgo long-run income gains in order to satisfying immediate cash needs (Simtowe & De Groote, 2021). Their desire for immediate cash gratification curtails their ability to access high income options for the future (Kovacs et al., 2021). In that regard, if the poor are given two marketing channel options, one with a "larger-later" financial reward and the other with a "smaller-sooner" financial reward, they are more likely to choose a marketing option with "smaller-sooner" financial reward (Hardisty et al., 2013). This is because poor farmers are more time impatient than the non-poor farmers, they have higher discount rate than the non-poor (Tanaka et al., 2010).
There is abundant literature positioning the expected utility maximisation and safety first theories as the backbone of many farmers' risk and time preference behavioural studies (Mendola, 2007;Levin, 2006;Andreoni et al., 2015). These theories are important in explaining why smallholder farmers may choose to sell at the farm gate at lower prices instead of selling at formal markets at higher prices (Melkani et al., 2019). Based on the utility maximisation behaviour and safety first models, Fafchamps and Hill (2005) and Mendola (2007) explained that, the propensity to sell at a high return formal market instead of a low return farm gate, increases with the farmers' wealth, access to infrastructure and better information. Similarly, Muamba (2011), Takeshima and Nelson (2012) emphasised on the existence of market imperfections as the reason behind farmers' preference towards selling at low return farm gate, instead of selling at formal markets. Although evidence from previous literature is mixed and varied, limited work was done on linking risk aversion attitude and time preferences on marketing channel choice decisions.
Based on Hardisty et al. (2013), the marketing choice options facing surplus households in Zvimba and Makonde districts can be viewed within the context of two reward options, with the state-owned GMB marketing option offering a more risky, "larger-later payment" and the private buyer market offering a less risky "smaller-sooner payment". Maize surplus farmers had to choose either to be time impatient by accepting a low-return, low-risk, "small-sooner payment" from the private-buyer market or being time patient by waiting for a high-return, high-risk "larger-later payment" from the stateowned GMB market. As such, time impatient households, who dislike risk, would select the more safe marketing options (from the private buyer market) with low returns (Mendola, 2007), thereby succumbing to "short-run temptation", whereas time patient households, who are less risk-averse would opt for the high-return, delayed state-owned GMB market, thereby attaining "long-run optimisation" (Hardisty et al., 2013). Such households' marketing channel choice decisions have serious income implications and would determine the households' future agricultural growth prospects, as well as the marketed surplus level. The section below explains the size of the marketed surplus.

Marketed surplus and market participation
Some households sell part of their output and others purchase the same crop they also produce, whereas others are self-sufficient and do not participate in the market (Key et al., 2000). If in semicommercial households, food crop produced is partly consumed and partly marketed, then, the size of the marketed surplus M s is the difference between the household maize supply or production level S q : ð Þ and the internal demand function D q : ð Þ. Household internal maize demand D q : ð Þ is driven by the family's own consumption, precautionary and speculative needs (Renkow, 1990). Households may hold additional precautionary maize inventories for safety reasons, to cater for unanticipated future food shortage. They may also hold additional food grain for speculative reasons in anticipation of seasonal price fluctuations. Last, maize inventory can also be kept for social functions or gifts to the extended families and friends (Ibid 1990).
If marketed surplus is jointly influenced by production and demand factors (Strauss, 1984), equation (1) will therefore, holds. The equation expresses marketed surplus as the difference between household maize production levels S q : ð Þ and internal maize demand D q : ð Þ.
The household crop production factors or supply function S q can be expressed as a function of the price vector p and the production characteristic vector z q that in turn, are determined by the production costs and technology. equation (2) represents the household supply function.
where the household demand function D q : ð Þ is expressed by equation (3); where z c , is the household characteristic vector that affects demand preferences. It may include aspects like household size, future expectations and availability of other consumption options. The internal demand preferences also depends on the household profit function f : ð Þ. If profits are high, the opportunity cost of holding maize inventories is high. Therefore, households are tempted to reduce the inventories kept for consumption, precautionary and speculative purposes, thereby increasing the size of the marketed surplus (Renkow, 1990). The profit function f : ð Þ depends on the price vector p facing the household and the production characteristic vector z q . In the demand function A i is the exogenous income sources, which also affect demand preferences.
Modelling subsistence farmers' marketed surplus is complicated by households' structural heterogeneity and trichotomy state (Goetz, 1992). We can illustrate the farming household's marketed surplus trichotomy state, as a net seller or a net buyer and or autarkic using equation (1). The household will participate in the maize market as a net seller, if the marketed surplus is positive as shown by Equation (4) The marketed surplus is positive if production levels exceed household food requirements such that S q : ð Þ>D q : ð Þ. On the other hand, if the marketed surplus is negative, the household will participate in the maize market as a net buyer. The household's maize supply will be less than the demand needs such that S q : ð Þ>D q : ð Þ as presented in equation (5).
Last, the household may decide not to participate on the market if its food supply is just sufficient to meet its internal demand needs, such that S q : ð Þ ¼ D q : ð Þ. As a result, the condition illustrated by equation (6) is satisfied The price elasticity of the marketed surplus, using equation (1), can therefore be given as This will give the wedge between household production and demand elasticities, weighted by the value of the marketed surplus. Theoretically, the elasticity of the marketed surplus with respect to own price can be negative if change in domestic demand exceed change in production. This is caused by a higher income elasticity of demand for food and an inelastic supply response caused by supply side constraints emanating from production factors.

Conceptualise marketed surplus decision under risk and time preference
The next step will be to explain how the households arrive at the marketing channel selection choice given the marketed surplus, and the household's risk aversion and time preferences conditions. The marketed surplus decision can be analysed by borrowing from Renkow (1990), Finkelshtain and Chalfant (1991), Holt and Laury (2002) and, Kapteyn and Teppa (2011). These studies made useful contribution in the analysis of farm household agricultural decisions in the presence of risk and time preference factors. The new conceptual framework was based on the utility maximisation assumption, which entails that, high risk averse and time impatient households are less willing to select options that are risky and delayed, even if they are highly profitability (Andreoni et al., 2015;Clot et al., 2016;Tanaka et al., 2010).
If U � A and U � B are the unobserved utility levels associated with marketing channel A and marketing channel B respectively, then marketing channel A is selected if its utility exceeds that of channel B, such that the condition U � A >U � B is satisfied (Greene, 2003). The random utility model represented by these utilities can be expressed as depended on the set of explanatory variables X and parameters β as in equation (8) below (de Brauw & Eozenou, 2011).
where X is a vector of explanatory variables that include household specific characteristics like risk aversions attitude, and time preference factors (Greene, 2003). After marketing channel selection decision, it is important to establish whether the participation decision made followed a simultaneous or sequential process.

Simultaneous or sequential marketed surplus decisions
Under a dualistic market condition, market participation is viewed as a multi-staged phenomenon that embodies two decision processes (Bellemare & Barrett, 2006;Goetz, 1992) involving the discrete and continuous choices that can be completed simultaneously or sequentially. Figure 1 illustrates the multi-staged marketed surplus decision process followed by households as explained by Abu et al. (2016).
At the initial stage, the sampled household make a discrete decision on whether to participate or not to participate in the maize market. If it chooses to participate, it would then make another decision on whether to participate as a buyer or as a seller. If it chooses to participate as a seller, the next step would be to decide on which market to participate in between the state-owned GMB market and the private buyer market? Finally, the household will make a continuous decision on the quantity to sell. The thrust of this paper is centred on the last two stages that involve making a discrete choice decision on which market between the state-owned GMB market and the private buyer market to participate in and the continuous decision on what quantity to sell to the selected market?
The question is on whether the net selling households will complete the two decision tasks sequentially or simultaneously. If a sequential process is followed, the seller would search for market information first and compare different markets before deciding on the quantity (Goetz, 1992). A sequential decision process gives the farmers some degree of bargaining power because delivery is done after the seller has secured all the decision information. Marketed surplus is therefore, responsive to changes in market incentives. If simultaneous decisions are made, farmers lack the bargaining power because they pre-commit a given quantity to the market before acquiring relevant decision information (Bellemare & Barrett, 2006). In this case, the seller will only realise both price information and trading terms while at the chosen market, thus limiting the seller's flexibility in bargaining and negotiating the trading terms. This would make marketed surplus and supply in general inelastic with respect to market information. Evidence obtained by  Goetz (1992) in Southern Senegal and Bellemare and Barrett (2006) in Ethiopia and Kenya supported the sequential decision processes, suggesting that farmers may possess some degree of market power with respect to the buyers. However, these findings may not be universally applied. As such, conclusions need to be made on case by case basis, hence the need for further studies.

Methodology
A survey of 433 maize farmers in Makonde and Zvimba districts of Zimbabwe was conducted in 2016 using a comprehensive questionnaire distributed through Agricultural Extension Officers. The questionnaire covered data on farmers' marketing choices between the state-owned GMB and the private buyer market, household characteristics like age of household head, household size, land size, maize output, marketed surplus, household maize consumption requirements, maize price received per ton, aggregate household income levels, expenditure levels, value of inputs used and income from other crops. The dummy variable for truck ownership status was used to proxy the effects of transportation costs. Costs were assumed to be low for households with a truck.
Given that farmers were faced with a two stage decision process that may lead to sample selection problem or self-selection problem, using the OLS estimates to determine the market participation choices and the size of the marketed surplus will yield inaccurate estimates due to the presence of selectivity bias (Goetz, 1992). Estimation of the causal effect can only be done after correcting for the selection bias (Toomet & Henningsen, 2008). Selection bias arises because those who decide not to participate in the market will not be considered in the second-stage market choice model. As such a "univariate probit model would introduce sample selection bias since farmers would self-select into treatment" (Abu et al., 2016). Based on Goetz (1992) and Heckman (1979) this selection bias can be corrected by applying the Heckman sample selection model that endogenously switched households into alternative market participation states, either as sellers to the state owned GMB market or private buyer market. Singbo et al. (2021) solved a similar problem on selection bias by applying, the triple-hurdle model that controls for both selection bias and endogeneity between market participation and technology adoption.
Given that the problem faced by maize surplus farmers was a two decision process that involved determining the discrete marketing channel choice and the continuous quantity decision, the Heckman two step procedure was ideal in establishing whether the two decisions were made simultaneously or sequentially. A simultaneous decision will mean inelastic marketed surplus while sequential decision process implies an elastic or responsive marketed surplus. The general Heckman' sample selection model was specified by the structural process as in equations (1) and (2) based on (Toomet & Henningsen, 2008).
equation (1) is the selection equation for the market choice decision. The household will have a discrete choice on which market to participate in between the GMB and private buyer market. Y p is the discrete decision variable for participation choice, it assumes that; X p is a vector of explanatory variables for the selection equations. equation (2) is the outcome equation, it estimate the second stage for quantity determination after the farmer decides on which market to participate in. Y qs is the continuous decisions variable for the marketed surplus sold either to GMB or private buyer market. This marketed surplus is only observable if the household chooses the market to participate in. The decision on which market to participate in is based on the unobserved utilities derived from each marketing channel.
If U � GMB and U � pvt are the utility levels associated with GMB marketing option and private buyer market respectively, then ΔU � ¼ U � GMB À U � pvt is the latent variable for the utility difference that depends on the set of explanatory variables X and parameters ρ; β (de Brauw & Eozenou, 2011). This can be expressed as a function of the explanatory variables as given by equation (8) U This is equivalent to estimating the binary choice model in equation (9) y where y GMB ¼ 1½y � >0� and y GMB represented the choice of GMB marketing option. The error term ε is normally distributed with variance 1 and identically and independently distributed.
The same marketed surplus was obtained as the difference between the gross maize sales and the buyback quantity before the next harvest. 1 Subsistence households sometimes sell their maize soon after harvesting only to buyback the food grain before the next harvesting season, implying that what they sold is not marketable surplus. To obtain the net marketed surplus, the quantity buyback was deducted from the quantity sold. 2 In Alam and Afruz (2002), marketable surplus was treated as the difference between household production and consumption demand, whereas in this case, we used household inventory demand and not consumption demand. Marketed surplus was given as the difference between total production output and maize inventory stocks kept for consumption, precautionary, speculative and social related functions.
In the outcome equation, X q is a vector of the explanatory variables that determines the marketed surplus. Previous studies on marketed surplus focused on price levels, output, income and other non-price factors such as household characteristics as the explanatory variables. This study added individual risk aversion attitude and time preference 3 factors as new explanatory variables. It borrowed the concept from Harrison et al. (2002), Andersen et al. (2008), Andreoni et al., (2015), Hardisty et al. (2013), Tanaka et al. (2010), Eil (2011) who incorporated farmer's time preference and risk aversion attitude in production and input allocation decisions. The data on farmers' risk aversion coefficients and the discount rates, as well as the estimation procedures were borrowed from our previous paper Kamoyo and Makochekanwa (2018).
The first step was to estimate the selection equation (1) by probit and generate the inverse Mill's ratio or the non-selection hazard rate, specified as by Equation (4) λ : Where ϕ : ð Þ is the standard normal density function for the probability of the farmer selecting the preferred marketing option and Φ : ð Þ is the cumulative distribution function of the probability of a farmer choosing to participate in the maize market. The inverse Mill's ratio is included in equation (2) which was estimated by ordinary least square (OLS) as the additional regressor. In that regard, the selection problem can be understood as the omitted variable problem, with λ : ð Þas the omitted variable (Toomet & Henningsen, 2008). Table 1 shows the summary statistics by marketing channel. The average maize marketed through the state-owned GMB is 57 tons which is 7 times higher than the 8 tons sold through the private buyer market. The difference is statistically significant at less than 1% level suggesting that access  to the high value state-owned GMB market was mainly attained by those with adequate productive capacity. These findings were consistent with Simtowe and De Groote (2021) that land size positively affected marketed surplus choices. It is therefore, evidenced that those who sold through the state-owned GMB market had large land sizes which averaged 42 hectares, compared to 12 hectares for those who sold through the private buyer market. The land holding determines productive asset endowment and as per expectation those who sold through the GMB market have had better land asset endowment. They were also characterised by high input intensity, with an average value of $4367 compared to $701 for those who sold through the private buyer market. Those who sold through the private buyer market were more risk averse than those who sold through the state-owned GMB and their discount rate was higher as well. This suggests the low return private buyer market was mainly accessed by the more impatient and high risk averse households.

Results
On average, the maize income for those who sold through GMB was $10664 compared to $1224 for those who sold through the private buyer market. Evidence drawn from the study suggests that maize is the major income earner in the two districts of Makonde and Zvimba. It constituted 66% of total household income for those who sold through GMB and 71% for those who sold through the private buyer market. Table 1 also shows that farmers who sold through the GMB marketing channel have had well-diversified crop income sources. It is also evidenced from the survey that 12% of the farmers entered the maize market as net buyers and 82.2% entered as net sellers, implying that 5.8% of the households were under autarky, as they neither participated in the maize market as buyers nor sellers.

The market participation choices
Table 2 presents factors that influenced farmers' discrete choice decision on participating in the private buyer market given the state-owned GMB market and the continuous decision on the quantity to be sold on the private buyer market. Model 1 shows the probit estimation results for the discrete private buyer marketing channel choice decision without controlling for selectivity bias. According to the model, the probability of a farmer choosing to sell through the private buyer market decreases significantly with land size, price difference between the GMB and private buyer market and it also decreases with the employment status of the household head. The same probability increases with the farmer's discount rate. However, these results may not be trusted due to the suspected presence of selectivity bias. The probit model was then used to compute the inverse mills ratio, which then determined whether selectivity bias is present or not. The Inverse Mill's Ratio indicates the probability that a farmer decides to sell to the private buyer market over the cumulative probability of the farmer's decision to participate in maize market.
The computed inverse mills ratio λ ð Þ was included in the OLS regression model for the output represented by model Model 2 to check for the presence of selectivity bias. Like studies conducted by Goetz (1992), Key et al. (2000) and Bellemare and Barrett (2006), Abu et al. (2016) there was evidence for selectivity bias. The coefficient for the inverse mills ratio was found to be negative and significant at less than 1%, indicating the existence of negative selection bias, implying that using the probit model will understate the size of the estimated coefficients. Therefore, it was appropriate to correct for selection bias by estimating the Heckman sample selection model represented by results on equations (3), (4) and (5). Equation (4) is the selection equation which shows the results for the discrete choice decision for market participation choice. Whereas equation (3), is the outcome equation for the continuous quantity decision after the farmer decide to sell to the private buyer market and last equation (5) is showing the inverse mills ratio for the Heckman selection model.
The inverse mills ratio for the Heckman selection model was found to be significant, supporting the presence of the downwards selection bias. When comparing the uncorrected model (1) and the corrected models (3) and (4), it is clear that, the coefficients for the corrected models did not only increase in size but they also changed in terms of significance after correcting for selectivity bias.  The coefficient for marketable surplus is now positive and significant on the selection model and it is negative and significant on the outcome equation.
Price difference was found to be negative and significant on both the selection equation and the outcome equation. The discount rate was found to be positive in both the selection and outcome equation. However, it was only significant in affecting the market selection decision and was insignificant in affecting the quantity decision on the outcome equation. Risk aversion was positive and significant in affecting the market selection decision and it has a negative significant effect in affecting the quantity decision. Poverty status was positive but insignificant in affecting the marketing choice decision. While employment status of the household head was significant in the probit estimation in equation (1), after correcting for selectivity bias the effect was no longer significant. Other factors like input intensity, land size and age were not significant in affecting the market selection decision.
The marginal effects after the Heckman estimation confirms that a one unit increase in the logarithm of the difference between GMB price and private buyer prices decreases the probability that the farmers would sell to the private buyer market by 1.3%. While a one unit increase in the logarithm of the marketable surplus will increase the probability of selling to private buyer market by 1.784%. For every one unit increase in the discount rate, the probability that the farmer would sell to private buyer market increases by 1.034%. Similarly, every one unit increase in the risk aversion, increases the probability that the farmer would sell to private buyer market by 0.65%. Therefore, there is sufficient evidence that risk aversion and time preferences play a significant role in explaining the market participation decision for farmers even if selection bias is controlled for.

Marketed surplus decision for state-owned GMB market
When the test above was repeated for the state-owned GMB market, evidence obtained failed to support a sequential process when making both the discrete choice and the continuous quantity decisions. The inverse mills ratio for the state-owned GMB market was found to be insignificant, confirming the absence of selection bias in both the discrete and continuous marketing choice decisions regarding the GMB marketing channel. In the absence of selection bias, the probit and OLS regression analysis provides better estimates than the Heckman sample selection procedure. The results for the probit and OLS estimation are presented on Tables 3 and 4, respectively. The probit results represent the discrete selection choice decision and the OLS results represent the continuous quantity decision.
The coefficient for the size of the marketable surplus was found to positive and significant as per theoretical expectations. The results imply that the log ratio of a farmer choosing the GMB marketing channel increases with the size of the marketable surplus. The coefficient of 0.265, for the marketed surplus on the marginal effect model, implies that, when the logarithm of marketable surplus increases by a unit the probability of a farmer selling to the GMB market increases by 0.265%. More interesting the coefficient for per capita income was found to be positive and significant, indicating that the probability of observing a farmer choosing GMB increases with household per capita income. The coefficient of 0.0935 for per capita income on the marginal effect model implies that if the log of household per capita income increases by a unit, the probability of observing a farmer selling to GMB increases by 0.0935%.
The coefficient for price differences between the GMB marketing channel and the private buyer market was also found to be positive and significant as expected from the theory. Given that the GMB market offered a higher price compared to private buyer market and that the price was fixed, an increase in the price difference is only possible if the private buyers offered to lower their prices, thereby widening the price gap. It therefore follows that, as the private buyers continue to lower their price offer, the probability of observing a farmer selecting GMB market increases. The results also confirmed that, the age of household head has a significant positive effect on the probability of a farmer selecting the GMB marketing channel. As age increases, the probability of a farmer selecting GMB increases. However, the fact that the coefficient for age squared is negative and significant implies that there is a certain age limit at which a continued increase in age will begin to have a negative effect on the probability of a farmer choosing GMB marketing channel.
Of interest are the coefficients of the risk aversion attitude and time preference. The results corroborate those found by Nigussie et al. (2020) and Senapati (2020) that risk aversion attitude and individual discount rate influences farmers' behaviour. Risk aversion was found to be significant and negative. The more risk averse farmers are less likely to select the GMB marketing channel. Based on the marginal effect, a unit increase in the risk aversion is likely to decrease the probability of a farmer selling to GMB by 0.0771%. On the same note, the coefficient for discount rate was found to be negative and significant, implying that the probability of a farmer choosing the GMB market decreases with the farmer's discount factor. In that regard, poor farmers who are more impatient are likely to highly discount their future cash flows, as such they are unlikely to choose GMB marketing channel due to its delay in payments. The coefficient for poverty status was significant and negative as expected from the theory. For every poor farmer observed, the log ratio that the farmer will sell to GMB decreases by 0.1%.
Variables for asset endowment like land size, truck ownership and tractor ownership were found to be insignificant in influencing the marketing channel selection decision, although the signs were positive as expected from theory. Since truck ownership was used to proxy trade costs, with the assumption that ownership of a truck reduces transportation costs, it therefore follows that, transportation costs were not significant in explaining marketing channel selection choice. Similarly, the coefficient for distance to nearest town as a proxy variable for remoteness was found to be insignificant. Remoteness determines the trade costs. Places that are located far away from the urban centre are very costly to access and as a result the trade costs are relatively higher. These findings imply that trade costs were not significant factors in determining the marketing Standard errors in parentheses *** p < 0.01, ** p < 0.05, * p < 0.1 choice decision, especially given that the new marketing arrangement is characterised by both GMB and private buyers operating community-based purchasing system.
The marketed surplus to the state-owned GMB was found to be significant and positively related to the size of the household's marketable surplus and land size. Similar to Abu et al. (2016), both age of household head and price effect were found to have a positive effect the size of the marketed surplus. The square of age has a negative effect as expected from theory. As age continue to increase, its effect on marketed surplus decrease. It was also found to be negatively related to the discount rate and to the square of the age of the household head. The coefficient for risk aversion was negative and insignificant. Factors like poverty status, employment status of the household head, tractor ownership and input intensity, were found to be insignificant in determining the size of the marketed surplus to the GMB market.

Discussion of results
The study confirmed a simultaneous decisions process when farmers chose to sell to the stateowned GMB market and sequential decision process when farmers chose to sell to the private buyer market. These findings reflect the fundamental differences in the nature of pricing systems in the two different markets. The state-owned GMB market failed to support the sequential process because the price is predetermined, since it is pegged by the government. In accordance with Bellemare and Barrett (2006), farmers cannot bargain, therefore, they cannot follow a sequential decision process. This because the process of searching for price information is virtually absent, hence no room for negotiation.
Second, when the price is pre-announced and fixed, the farmers do not have any power to bargain for a change in price or the trading terms because these two variables are predetermined. As a result, farmers will simultaneously arrive at both the discrete marketing channel decision and the continuous quantity decision, since price information is known beforehand. The outcome is likely to differ when the farmers decided to sell to the private buyer market where price and trading terms are random. Under price randomness, the farmers are likely to follow a sequential decision process as they need to search for Standard errors in parentheses *** p < 0.01, ** p < 0.05, * p < 0.1 marketing information first before arriving at the quantity decision. It, therefore, follows that marketed surplus will vary depending on the prevailing market incentives.
The evidence for sequential decision process under the private buyer market supports the principle of the recursive models. If farmers follows a sequential marketing decision process, there is high possibility that marketed surplus is largely influenced by the prevailing marketing conditions. As such, if farmers are impressed by the market price and transaction terms, they may choose to reduce their maize inventory holding and increase on the size of the marketed surplus. If the market is not providing attractive prices and buying terms, households may decide to increase on their maize holdings for social functions, speculative and pre-cautionary reasons, thus reducing the size of the marketed surplus. Despite the fact that the degree of market participation by smallholder farmers is still limited, with the size of marketed surplus still very small, evidence for the existence of sequential marketing decision process suggests that the level of marketed surplus in the private buyer market can be increased if marketing conditions in the private buyer market are attractive.
Beside the aspect of the sequential decision process, the results also confirmed that farmer's specific factors like risk aversion attitude, time preference factors, age of household head and farm productivity levels are key determinants of both the discrete choice decision for marketing channel choice and the continuous decision for the quantity of the marketed surplus in any of the selected channel. It was also noted that although the price variable was very important in determining market selection decision and the marketed surplus level, GMB's uncertainty and payment delays neutralised the high-return incentive effect for the risk-averse and time-impatient poor households who preferred the immediate small return with certainty from the private buyers. Poverty status was therefore, found to have a significant negative effect on the decision to sell to the state-owned GMB market and have no significant effect on the decision to sell to the private buyer market.
Comparing results from Table II shows and Table III, the size of the marketed surplus to the two marketing channels was found to be influenced by the price differences between the state-owned GMB market and the private buyer market in two opposite ways. If there is a convergence in the two prices, the price difference falls and the size of the marketed surplus to the private buyer market increases as shown on Table II. On the other hand, a decrease in the price difference reduces the size of the marketed surplus to the state-owned GMB market.

Conclusions and recommendations
The study reveals that risk aversion and time preference factors have significant effect on both the discrete choice decision and the continuous decision. On the discrete choice decision, the findings confirm that for every one unit increase in the discount rate, the probability that the farmer would sell to private buyer market increases by 1.034%. Similarly, every one unit increase in the risk aversion, increases the probability that the farmer would sell to private buyer market by 0.65%. Whereas, the same one unit increase in risk aversion decrease the probability of a farmer selling to GMB by 0.0771%. On the continuous decision, a unit increase in discount decreases marketed surplus to the GMB by −0.967%, whilst it increase marketed surplus to the private buyer market by 1.034%.
The findings also confirmed that farmers follow a sequential decision process only when deciding to sell to private buyer market and a simultaneous decision when selling to GMB market. Considered together, these findings imply that grain market reforms that reduce GMB payment delays and risk are very are very critical in increasing the marketed surplus to the high return state owned GMB.
This recommendation opens future research gaps that explore the prospects of introducing commodities exchange market that can resolve the problems associated with government controlled prices. Such markets may allow some flexibility in price and payment terms determinations, a factor that is lacking in the current GMB market. Since risk aversion and time preference factors were found to play a very significant role in influencing both the marketing channel selection choice decisions and the continuous marketed surplus decision, it is recommended that, government should develop markets for risk transfer and maturity transformation. These markets will help the risk averse and time impatient farmers to participate in high return GMB market which is characterised by high risk and delayed payment terms. Notes 1. Marketable surplus as differentiated from marketed surplus (MS) is given as Total Production (TMP) less total food requirements (TMR) which includes family consumption requirements, farm retained seeds, payment for labour, social and religious functions. MS=TMP-TMR. So the marketed surplus can either be less than or equal to marketable surplus. Expectations are that if market access conditions improve with better buying terms and prices farmers can increase the size of the marketed surplus from the available marketable surplus. In other word maize farmers may not need to sell every maize grain that is marketable, but their decision depends on prevailing market conditions. 2. Y qs =G-B the net marketed surplus is the difference between the quantity sold (G) and the quantity bought (B) by the household before the harvest season to supplement food deficit (Alam & Afruz, 2002). 3. Notes on the procedures followed in estimating the individual risk aversion and discount rate for time preferences are available upon request. Readers can also refer to a paper by Kamoyo and Makochekanwa (2018) that provide adequate details on how the risk aversion and discount rates were estimated.