GIS use of Land Use/Land Cover layers and historical data for water losses indices

The population growth and/or its use and development of the land is a continuous preoccupation of the decision factors regarding the water supply system in general and the development of the potable water distribution networks in particular. This issue is even more critical especially in the areas of big cities and important urban growing. As the urbanization of land outgrows the existing water supply systems, one of the possible solutions is to expand the water distribution network in order to cover this urban growth. The present paper analyses further the possibilities to define and use certain indices of urban development together with water loss indices in order to determine trends or issues related with the provision of water supply services and connectivity.

Introduction
Drinking water infrastructure is one of the most important infrastructures that should be considered besides transportation in analyzing the needs and the constraints for the recently developed urban areas and a city's urban growth. The problem for the water supply infrastructure arises from the further growth of the urban areas, away from the crowded town centers and the variations in population density and the water distribution adjustments, which are induced by this trend and their implications on the water loss volume.
Romania, an EU member country has a water supply network of more than 79000 km of distribution mains and service laterals as recorded in 2016 [1], many of them in service for longer than 40 years [2]. Leakage rates and water loss through pipelines varies significantly, but there are some possibilities of estimation as exemplified in a study [3] over the data in four countries on two continents which shows that the distribution of burst frequencies across the water supply network follow the Pareto principle, about 80% of the distribution network experiencing less than 2 failures/km/year, only 1% of the network breaking at a frequency of 4 failures/km/year or more.
On this account, the length of the pipes was taken into consideration as an important indicator to be used in our analysis presented further in this paper.

Data and methods used in GIS analysis for water losses in Bucharest case study
Bucharest is the largest city of Romania and its capital. Next, we present the case study on the urban growth and population dynamics of the Bucharest metropolitan area and the indicators which may be affected or affect the drinking water infrastructure.
The study at such a complex level as a metropolitan area implied the use of a variety of data sources, not only from multiple domains and in different forms and formats but also from several periods of time. There were three main categories of datasets which were identified, obtained or produced and then used in our analysis.
The first set used for the analysis is the GIS dataset containing the Land Use/Land Cover Classes which can be obtained from the classification of different time series of satellite imagery. For this dataset, we propose the use of the following four major types of consumers which influence the water consumption indicator: -Economic consumers (both industrial and commercial) which means that they are big consumers -High density residential consumers (tall residential or office buildings) which means a big number of connections/area -Medium density consumers (individual houses) which means a smaller number of connections/area with reduced consume of potable water -Low density consumer (recently urbanized individual houses with bigger parcels) which means a potential of an increased consume for the summer garden watering with potable water The four types of consumers presented above can be then identified in the various satellite images available from different governmental agencies such as USGS or ESA, since they are recently accessible at low or no cost, for different periods. The identification of the mentioned consumer categories is possible as for the large scale such as the city scale or the metropolitan area scale the four types of consumer areas exhibit certain shapes and distinctive spatial arrangements recognizable in the Land Use and Land Cover patterns.
The second dataset that we found suitable for our analysis is the one containing the historical values for the water loss indices available for the current water supply and distribution system: real losses/network length/day; real losses/connection/day and water losses/capita/day. These data are specific data usually collected and recorded by the water companies.
The last set of data usable in these type of analyses is the one containing additional but suggestive information such as the historical recordings of the statistical data regarding the population and demographics (e.g. the Census data); the distribution of population/square km; utility companies' reports and archives; urban area maps, water network maps etc.
In the context presented above, our study covers the case of Bucharest making use of all the data available for such a complex analysis, and attempts to find the key factors and indicators that, in general, impact the drinking water networks on the operational level and regarding the water loss implications on infrastructure.

Classes
HiRes MedRes LowRes MedComInd Full name High residential Medium residential Low residential Medium commercial or industrial

Classes defined as
High-rise residential units but less dense builtup with or without green space between them, medium needs of water due to the many stories.
Low-rise residential units but very dense built-up with or without very small courtyards, reduced needs of water.
Low-rise rural residential units but less dense builtup with large gardens, needs of water especially for gardens.
Low-rise to medium-rise commercial or industrial units but with large impervious surfaces, greenhouses, very high needs of water.
For Bucharest and the urbanized area surrounding it, the four major types of consumers are specified above, in Table 1, and were determined based on the specificity of the Land Use and Land Cover classes identified for this particular city.
Next, the evolution of the area of the four types of Land Use and Land Cover for the Bucharest metropolitan area was calculated with the help of the vector polygons obtained from the classification of the Landsat satellite images over four decades in time. The areas of these surfaces could then be calculated and correlated with the statistical values recorded as close as possible to the same periods of time and also correlated with the water mains coverage extracted from the additional datasets [1], [4], [5]. The water company in Bucharest, Apa Nova Bucharest, a private operator part of the Veolia group, provided all the data needed for the second set of data in our study, as presented in Figure 2, 3 and 4.   The third dataset assembled for Bucharest case was constructed by consulting historical archives of the various statistical recordings or reports [6], [7], the main indicators which were isolated from this massive amount of data being those which could be correlated with the actual water loss indicators, such as pipe lengths, population, urbanized area, connection etc. They are presented in Table 2:

Results and discussions
The option of extending the present system over the areas of urban growth is analyzed and the net value of expansion taken into consideration is the Land Use and Land Cover area calculated in ArcGIS for the entire built-up area, but without taking into account the open space inside the city. As it can be shown in Table 3, the city boundary is much larger than the actual built-up space inside, including many parks and open space. As we were interested rather in the connection number which takes place on the built-up space, this seems to be a better suited indicator. Thus, the extension of the water distribution system can vary between 165 km and 215 km of new mains, while the losses can vary between 59,600 l/day and 9200 l/day, taking into consideration the historical values. To conclude, it is important to emphasize that statistical data cannot be satisfactory used without GIS and spatial information, this is why the GIS layers obtained from the Land Use and Land cover classes, together with the statistical and water loss data can add valuable information in the process of decision making.


extfieldsofstudy:
Economics
Political Science

text:
A Model of Presidential Debates

Presidential debates are viewed as providing an important public good by revealing information on candidates to voters. We consider an endogenous model of presidential debates in which an incumbent and a challenger (who is privately informed about her own quality) publicly announce whether they are willing to participate in a public debate, taking into account that a voter's choice of candidate depends on her beliefs regarding the candidates' qualities and on the state of nature.It is found that in equilibrium a debate occurs or does not occur independently of the challenger's quality and therefore the candidates' announcements are uninformative. This is because opting-out is perceived to be worse than losing a debate and therefore the challenger never refuses to participate.

Introduction
In US presidential elections, debates between the candidates are major media events. Even the least watched debate had an audience share of about 30 percent (Erikson and Wlezien, 2012). 1 The debates may or may not have a significant effect on voters (for evidence supporting the former view, see Geer, 1988;Bidwell et al., 2019;Brierley et al., 2020; for evidence supporting the latter view, see Abramowitz, 1978;Miller and MacKuen, 1979;Lanoue, 1991). Erikson and Wlezien (2012) point out that although there is some anecdotal evidence regarding presidential debates, their effect on voter behavior is hard to measure and therefore remains an open question.
Furthermore, while in some countries, such as the US, debates are regularly held, in others, such as Israel, they are rare. 2 In particular, candidates are usually not obligated to participate in a debate and they take place only if both candidates agree to do so. In light of the aforementioned measurement difficulties, it would appear that a theoretical model is called for. In what follows, we build a game theoretic model that is, to the best of our knowledge, the first to evaluate the interactions between candidates and voters in presidential debates (although it may also apply in other contexts). 2 In Israel, one-on-one debates between the two leading candidates for prime minister were held regularly only between 1977 and 1996. Even in the US, presidential debates were not held between 1964 and 1972. 3 We essentially attempt to answer two important questions: 1) Under what conditions are debates held? and 2) Are they informative or noisy?
Specifically, we consider a model in which an incumbent and a challenger (who is privately informed about her own quality) are running for president.
Before the elections are held, each candidate publicly announces whether she is willing to participate in a debate, in which the winner-from the voters' perspective-is stochastically determined according to the candidates' qualities. On Election Day, the (median) voter's choice of whom to vote for depends on the candidate's expected qualities and on nature, which is a random variable realized on Election Day.
We show that the game's equilibrium is independent of the challenger's quality. In particular, there exists a unique equilibrium in pure strategies in which the challenger always announces that she is willing to participate in a debate, whereas the incumbent's announcement depends on other fundamentals in the model. This can be viewed as "the dictatorship of the incumbent." Specifically, under reasonable conditions, the incumbent chooses to participate in a debate when her quality is low and not to participate when her quality is high. On the other hand, the challenger chooses to participate in a debate even when defeat is certain and, more generally, a challenger who participates and loses is always perceived to be a stronger candidate than one who opt-outs. This is because although beliefs about a candidate's quality are downgraded after a loss, the lower bound on these beliefs is still higher than the upper bound in the case that the 4 challenger had opted-out. The results correspond to what is commonly observed in elections, namely that strong incumbents often choose to avoid debates. 3 Given this behavior, the candidates' announcements are uninformative since no new information about the challenger's quality is revealed. However, if a debate is held, and depending on the shape of the probability distribution of the challenger's quality, the debate can be either informative or noisy. Furthermore, under reasonable conditions, the announcements made by the candidates are shown to be independent of the sequence in which they are made, and every sequence satisfies Perfect Bayesian Equilibrium when it is endogenously determined.
The paper proceeds as follows: In the remainder of this section, we review the related literature. Section 2 describes the model and section 3 presents the results. In section 4 the results are generalized to a game in which the sequence of announcements is endogenously determined. Section 5 concludes.

Review of the literature
The current model brings together two strands of the literature: information transmission and the effect of the media on voters in the context of a political campaign. More specifically, in the static version of our model, the problem of the incumbent can be viewed as a Bayesian persuasion problem (Kamenica 5 and Gentzkow, 2011). The incumbent who can be viewed as the sender shares the same prior with the voter who can be viewed as the receiver. She chooses the action that transmits a signal to the voter that maximizes her probability of being reelected. 4 Our result that the challenger's choice of whether or not to participate is not informative is related to the seminal paper of Grossman (1981) who shows that when a monopoly cannot reveal the quality of its product but can offer warranties against bad outcomes, then it will always offer a full warranty, regardless of the quality of the product. Therefore, in equilibrium the quality of the product is unrevealed. Note that apart from the context being different, in our model the choice of whether to participate in a debate transmits two different and sequential signals (the choice whether to participate followed by the outcome of the debate, if it occurs). As noted, the 4 A related study of competition between multiple senders in the context of Bayesian persuasion is Gentzkow and Kamenica (2017). Another is Gul and Pesendorfer (2012) who consider two rival parties that provide costly information to a voter who then chooses between them.
6 key intuition behind our result is directly attributable to this sequential structure. 5 A presidential debate is a major media event and therefore our paper is also related to the large empirical literature on the effect of the media on voters. In this literature, researchers have examined various aspects of effect and have arrived at differing conclusions. For instance, DellaVigna and Kaplan (2007) find that Fox news has a significant effect on voters. Gerber et al. (2011) find that televised campaign ads have a strong but short-lived effect on voter's preferences, while Spenkuch and Toniatti (2015) find that ads have no impact on turnout but do have a significant effect on voting. In the context of political debates, evidence appears to be mixed (as mentioned above).
However, more recent studies show that debates are important. In particular, 5 Note that a presidential debate is modeled here as a contest (see Dixit, 1987;Konrad, 2009). However, unlike the usual contest models, we assume that the outcome of a debate depends only on players' qualities rather than their effort. Although participating in a debate certainly requires a certain amount of effort, we nevertheless posit that the effort invested and its effect on the debate's outcome are of marginal importance and moreover the outcome is primarily determined by the candidates' inherent abilities. For studies that analyze how information about contestants is inferred from the contest outcome, see Krähmer (2007) and Noe (2020). For a recent study on signaling in contests, see Denter et al. (2018). where information on candidates is scarce. They concluded that political debates have a significant effect on voter opinion and therefore can also trigger a chain of events, such as an increase in campaign spending.
Moreover, using a unique data set, Brierley et al. (2020) shows that debates have a strong effect on partisan voters.
Our main contribution to the existing literature is the analysis of presidential debates from a rational point of view, and although the analysis does not consider specific aspects of a debate, such as the appearance and verbal skills of the candidates, 6 it does help to understand the nature of a debate by demonstrating that the choice to participate is more important than the debate itself.

The Model
Two candidates, an incumbent and a challenger, are running for president.
The incumbent's quality is commonly known to be (∈ (0, 1]) while the challenger's quality, q, is a random variable with a probability distribution p over the interval [0,∞) with mean > 0. The actual value of q, (∈ [0,∞)) is private information known only to the challenger until it is learned by all after Election Day. Since the incumbent has already served as president while the challenger has not, we assume that there is more information available on the incumbent (which may not necessarily be the case). Furthermore, we restrict qI 6 Lawson et al. (2010) examines this effect. 8 to be bounded from above in order to assign a positive probability to the case in which the challenger's quality is higher than that of the incumbent. 7 Before Election Day, each candidate publicly and simultaneously announces whether she is willing to participate in a debate (P) or not (NP), where the probability of the challenger winning the debate is ( , ) and that of the incumbent is 1 − ( , )), where satisfies the usual properties: 8 A debate is held only when both candidates announce P.
7 In principle, qI can be bounded from above by any real positive number and the specific assumption of a boundary of 1 is made without loss of generality.
8 Note that the constraints on with respect to qC are tighter than those on with respect to qI. Therefore, we do not require anonymity. 9

The voter
There is one voter. In the case that a debate is not held, she observes the candidate's announcements before the elections. In the case that a debate is held, she observes who won the debate. 9 If we define ̅ to be the expected value of q on Election Day, then the voter chooses the challenger when ̅ − > , where (∈ ), which represents nature, is a random variable independent of q with a commonly known cumulative distribution G that is realized on Election Day (before the voter chooses a candidate). Note that can be viewed as a measure of the match-from the voters' perspective-between the incumbent and the state of nature. 10 For instance, if a natural disaster takes place in the time between the debate and the elections and the voter has determined the expected quality of the challenger to be equal to that of the incumbent, then the voter may vote for the more experienced candidate (corresponding to the case in which the realization of ε is positive). More generally, a candidate usually has characteristics other than quality that may give her an advantage in certain scenarios. Note that the voter only cares about the expectation of the challenger's quality (not about its distribution) and therefore she is riskneutral.
After the announcements are made and the debate is held (or not), and before ε is realized, the probability of the challenger winning the election is therefore ( ̅ -). 11

Timeline
In view of the above, the timeline of the model is as follows:

Candidates
Each candidate maximizes her expected probability of winning the election.
We assume that a candidate is indifferent between winning with a certain probability and winning with an expected probability equal in value.
Therefore, both the voter and the candidates are risk-neutral. In the remainder of this section, we describe each candidate's problem and add some notation that will be useful in the remainder of the analysis. Let p(q')│w be the probability that the challenger's quality is q' in the case that a debate was held and she won, and let it be p(q')│l in the case that a debate was held and she lost, for all ′ ∈ [0,∞). Also, let ̅ ≡ | if the challenger won and let ̅ ≡ | if she lost. It then follows that: Given the incumbent's announcement, the challenger makes the announcement that maximizes [ | ]. Formally, given the incumbent's announcement, the challenger's maximization problem is: The incumbent. Let be the challenger's expected probability of winning the election from the incumbent's perspective (since she does not observe the challenger 's quality) after announcements are made and before the debate is held (or before Election Day in the case that the debate is not held).
In the case that both candidates announce P, let ≡ | . 13 Otherwise, by definition, 13 It is shown later that | is identical to (6).
Given the challenger's announcement, the incumbent makes the announcement that maximizes her expected probability of winning the election, i.e., 1 − , which therefore minimizes . Formally, given the challenger's announcement, the incumbent's minimization problem is: (4) min announcement∈{ , } .
We now proceed to the analysis of the model's results.

Mandatory participation in the debate
It is useful at this point to consider the case in which participation in the debate is mandatory (i.e., neither of the players needs to make a decision).
We add the lower index m to all notations in this subsection. For instance, | is the challenger's expected quality given that she wins the debate, and | is her expected quality given that she loses. 14 It follows that: We now present a technical lemma that will be useful in the remainder of the analysis. All proofs appear in the appendix. We now proceed to analyze the equilibrium of the original game.

Equilibrium
Notice that the voter and the incumbent share the same information set and therefore the incumbent's announcement cannot reveal information to the voter. Regarding the challenger's announcement, if the incumbent announces P, then the challenger's announcement is decisive (i.e., her announcement determines whether or not a debate will be held) and therefore it may reveal information to the voter, since it is made given a specific qC that is privately known to the challenger. Otherwise (i.e. in the case that the incumbent announces NP), the announcement made by the challenger is not decisive and therefore does not reveal information. We can therefore state the following: Fact 1 Given that the incumbent announces NP, the probability distribution of q remains p and therefore | = | = .
Furthermore, we can state the following lemma:

Lemma 2 If the incumbent announces P, then so does the challenger.
The key intuition behind Lemma 2 is that given the incumbent's announcement of P, an announcement of NP by the challenger implies that her quality is lower than if she had announced P and therefore the challenger always responds to P by also announcing P.
To see this, consider the following: Assuming that some challengers respond with P and others with NP and given that (( | ) − ) is independent of qC while [ | ]| is continuous in qC, there must exist a challenger who is indifferent between P and NP, and since [ | ]| is monotonically increasing in qC all challengers who are stronger than this one will respond with P while weaker ones will respond with NP; however, in that case, the weaker ones will mimic the behavior of the stronger ones in order to be viewed as strong. This implies that the challenger's strategy can be consistent with beliefs only in a pooling equilibrium in which all challengers behave identically.
There are two additional and important points that should be clarified regarding the challenger's behavior. First, a belief that the challenger always responds to P with NP is not consistent with the challenger's strategy. To see this, assume that this is indeed the case. Then, the probability distribution of q remains p when the challenger chooses NP. However, since [ | ]| is monotonically increasing in qC, after a challenger deviates and responds to P with P, the updated beliefs about this challenger's quality must be such that either the probability distribution of q remains p or the left tail is truncated; either way, given these beliefs an extremely strong challenger prefers to respond to P with P, which is inconsistent with the initial belief that a challenger always responds to P with NP.
The second important point is that according to Lemma 2 the probability distribution of q remains p when the challenger responds to P with P. But what happens if she deviates and responds with NP instead? Then, by the same reasoning as above, the updated beliefs about this challenger's quality are such that the probability distribution of q remains p or the right tail is truncated. Either way, given these beliefs an extremely strong challenger will prefer to respond to P with P and therefore she is not the challenger who deviates by choosing NP, implying that there is a separating equilibrium and, as noted above, this is impossible.
Finally, note that Fact 1 together with Lemma 2 implies that, in all possible equilibria, the probability distribution of q remains p after announcements are made, and therefore the candidates' announcements are uninformative.
We are now in a position to characterize the game's equilibria.

Proposition 1
The unique Bayesian equilibrium of the presidential debate game is as follows: Proposition 1 implies that the equilibrium outcome is independent of the challenger's quality (i.e., qC) and at the same time coincides with the incumbent's preferences. The challenger always announces P, and the choice of the incumbent, who makes the announcement that maximizes her expected winning probability in the election, is therefore always decisive.
Note that the effect of the incumbent's quality on the equilibrium outcome depends on the probability distribution of ε. In particular, in the case that ε has a unimodal probability distribution, G is convex up to a certain point on the X-axis, after which it becomes concave. Therefore, since the interval [( | ) − , ( | ) − ] "moves right" on the X-axis when qI decreases, by Lemma 1ii a decrease in the incumbent's quality can induce her to participate in the debate. For example, when ε has a normal distribution and goes to zero, this interval sits on the positive side of the X-axis where G 16 Specifically, the incumbent announces NP and the challenger announces P.
is concave and therefore the incumbent announces P. It follows that a highquality incumbent prefers to avoid a risky debate, while a low-quality incumbent may take her chances and participate.
There is some anecdotal evidence to support this result. For example, the first presidential debate in US history between the two leading candidates was held in 1960, while there were no debates in the subsequent three elections between 1964and 1972. In particular, in 1964 Johnson refused to participate in a debate and eventually won the election nonetheless. In 1968, Johnson did not run again and therefore the race was between two challengers, one of whom was Richard Nixon who won the election that year. In 1972, Nixon refused to participate in a debate and again won the election. Therefore, in the only two cases in US history in which the incumbent refused to participate he was later reelected.
In Israel, incumbent Prime Minister "Bibi" Netanyahu, who was clearly the favorite in the 2015 election and indeed won it, refused to participate in a debate against the challengers (eventually a debate was held between most of the challengers but without Netanyahu). In fact, Netanyahu participated in only one debate, which took place prior to the 1996 election in which he was 19 first elected prime minister. He did not agree to participate in any debates subsequent to that one. 17 Table 1 summarizes the expected probabilities of winning for the incumbent and the challenger, given the information available to them: Table 1 Incumbent/ Challenger announce P announce NP Each cell in the matrix contains the pair: 1 − and [ | ]. 18

Information analysis
In this section, we derive the sufficient conditions for a debate to be either informative or noisy.
Formally, we define a debate as informative (noisy)  20 debate is held, if a candidate's expected probability of winning the election is the best available predictor of the corresponding probability in the case that qC is commonly known, then the debate is considered to be informative.
Otherwise, it is noisy. 19 In Lemma 3, we derive sufficient conditions for a debate to be either informative or noisy.

Lemma 3 (i) A debate is informative if qC is sufficiently far away from . (ii) A debate is noisy if qC is in the neighborhood of , and is sufficiently small or large.
Given that qC is unobservable, Lemma 3 implies that whether a debate is expected to be informative or noisy depends on the shape of the (commonly known) probability distribution of the challenger's quality. In particular, a debate is expected to be informative when voting for the challenger may look like a risky gamble, since it is most likely that she is either weak or strong.
Alternatively, a debate is expected to be noisy when it is likely that the challenger is a weak candidate (or a strong one).

Endogenous sequence of announcements
In this section, we allow for the sequence of announcements to be endogenously determined. In particular, the candidates first agree on the order of the announcements, and then each candidate makes her announcement in the agreed-upon order. This leads to the following proposition: Proposition 2 If the sequence of announcements is endogenously determined, then there exist Perfect Bayesian equilibria that are characterized as follows: The probability distribution of q is believed to be p after the sequence of announcements has been agreed upon, regardless of which sequence that is.
(ii) Any sequence of announcements satisfies Perfect Bayesian Equilibrium.
(iii) The candidates' announcements are the same as in Proposition 1. 20 Note that in the equilibria described in Proposition 2, the candidates' expected probability of winning the election, the information available on Election Day and whether or not a debate will be held are all independent of the sequence of the announcements. The intuition behind this result is as 20 Note that there are multiple pairs of announcements that satisfy a Perfect Bayesian Equilibrium when a debate is not held. In particular, any pair of announcements except (P,P) satisfies a Perfect Bayesian Equilibrium when the challenger makes the first announcement, and both (NP,NP) and (NP,P) satisfy a Perfect Bayesian equilibrium when the incumbent makes the first announcement.

22
follows: Let the sequence of announcements be exogenously determined.
Since the preferences of the incumbent are commonly known, the challenger's announcement is decisive and therefore she cannot avoid a debate without being considered to be a weak candidate even when moving first.
Furthermore, given that the challenger's expected probability of winning is the same for all sequences, if it is believed that the probability distribution of q remains p after the sequence has been agreed upon, then those beliefs are consistent with a challenger's strategy of approving any sequence of announcements that is proposed.
Note that, in principle, the challenger's approval or disapproval of a particular sequence of announcements can in itself be informative, which implies that the characterization in Proposition 2 may not be unique. In particular, there may be other equilibria, in which for at least one sequence of announcements the probability distribution of q is believed to differ from p after the sequence has been agreed upon, which may lead to a completely different equilibrium characterization.

Conclusion
We consider a model of presidential debates with private information, which may be applicable in other contexts in which two individuals with conflicting interests decide whether to participate in some type of competition, taking into account that both the competition itself and their choice of whether to participate may reveal information about their qualities to an external 23 decision maker. The results shed light on these situations, and in particular on the mutual effects between voters and candidates in presidential debates, by showing that the choice of whether to participate in a debate is uninformative since opting-out is not an option for the challenger.

Appendix:
Proof of Lemma 1i: Given that the debate is mandatory, by Bayes' rule: Therefore: . By (7) and (8), By (1), (5) and (12) Proof of Lemma 1ii: Substituting (9) and (10) into (6) results in: , for each q smaller than ̂, the decrease in ( )| relative to ( ) must be fully compensated for by an increase in ( )| relative to ( ) for at least one value of q greater than ̂. A similar argument applies to ( )| . Therefore, where by definition, However, it can be shown by contradiction that q* does not exist: Assume for now that there exists * ∈ [0,∞). Since it is commonly known that

22
To see this, assume that the incumbent announces P. If the challenger announces NP, then | and therefore also (( | ) − ) are both uniquely determined regardless of qC, while if the challenger announces P, then | and | are both uniquely determined and therefore given (1) and (2), [ | ]| is increasing in qC.
the challenger's response to P will be P iff ∈ [ * ,∞), 23 | > * , | > * and | ≤ * , and therefore, by (2) Assume that the challenger always responds to P with NP. Given that [ | ]| is increasing in qC and ( | ) is independent of qC, if a challenger deviates and responds to P with P, then the quality of this challenger is believed to be ae least q≥0. Moreover, by (1) and (2), when → ∞, [ | ]| → (( | ) − ), where | > = ̅| for any q≥0 24 and therefore, given that G is monotonically increasing in ̅ , (( | ) − ) > (( | ) − ), which implies that there exists a sufficiently large q'' above which [ | ]| > (( | ) − ) for all ≥ ′′ and therefore a challenger with quality greater q'' deviates and responds to P with P, a contradiction. Now assume that the challenger always responds to P with P. Given that [ | ]| is increasing in qC and ( | ) is independent of qC, if a challenger deviates by responding to P with NP, then the quality of this which implies that | < and therefore the incumbent's best reply to the challenger's announcement of NP is to announce P. QED Proof of Lemma 3i: By (1) and (2)


INCIDENCE OF SHORT TERM PRIVATE CAPITAL OUTFLOW: EMPIRICAL ANALYSIS IN NIGERIA

JEL Classification: C01; C22; E52; E60; F32. Over the years, the rising uncertainty in macroeconomic policy environment coupled with the prevailing uncertain non-economic factors like political instability, corruption, poor governance, civic conflicts and property right is perceived to be having contributing factors on short term private capital outflow in Nigeria. The study investigated the incidence of short term private capital outflow in Nigeria where a combination of the push factors and portfolio risk theories were adopted in the study for the period 2013/March – 2018/May using the fully modified OLS technique. The longrun and short-run results show that uncertainty of macroeconomic policy environment such as inflation-price instability, real exchange rate volatility and lack of confidence on domestic stock market enhanced the increasing level of short term private capital outflow in Nigeria. The study recommends that authority should adopt more progrowth policies that can ensure and maintain sound domestic macroeconomic policies to stem short term private capital outflow and that stock market authority should ensure accountability and transparency to strengthen the interest of domestic investors if they want to reduce the outflow of domestic capital.

INTRODUCTION
It had been reiterated that short term private capital outflow is associated with risk diversification motive in term of relative risk incentives which arises due to factors associated with the relative riskiness of the domestic economy and return differential incentives accompanying macroeconomic environment adversely such limit the risk adjusted returns to domestic assets (Sheets, 1995) while Eryar (2005) argues that capital outflow seems to be as a result of confidence lost in overall economy. This indicates that residents of a country consider the macroeconomic instability as a threat to holding of domestic assets, such lead to switch to foreign assets so as to protect the value of their assets from any sudden changes. These sudden changes can be in the form of a freeze on assets in the banking system or a postponement of interest payments on public debts. Ajayi (1992) argues further that capital flight is associated with an expectation of currency appreciation; such will encourage domestic wealth owners to shift assets converting into foreign wealth and currencies. The implication of this argument is that exchange rate can exert either negative or positive impact on capital flight depending on residents' expectation of future currency value.
According to Reilly and Brown (2012) investors in pursuance of optimal investment portfolio unavoidably become risk-averse selecting assets with the lowest risk in the list of options open to them. Portfolio investment is hinged on the framework of risk return trade-off, as higher return on investment is accompanied by higher level of risk (Moreno-Vozmediano et al., 2007). There are the factors driving domestic capital out whereby the content and direction of present and future macroeconomic policies are uncertain and/or volatile, domestic investors will be unsure about the effect of these macroeconomic volatilities or uncertainties on the value of their assets locally. This vulnerability may motivate them to pull back their investments from the economy and invest in foreign assets instead (Meade, 1951); (David and Ampah, 2018). These outflows are inherently related to welfare losses especially, developing countries where they are unable to cover their investment, import and government budgetary requirements or service their liabilities. Thus, any systematic capital outflows represent a great constraint on their economic development potential (Collier et al., 2001).
In the literature, Short term private capital outflow has been conceptualized to mean investment in financial assets such as shares, stocks, debt instruments, mutual fund etc. with varying risk and returns (Myles, 2003;Levišauskait, 2010) which flow out of one country into another country, there are few of empirical studies with regards to determinants of capital outflow or capital flight in Nigeria such as Lawanson (2007); Ayadi (2008); Oluwaseyi (2017) in which a number of measures had been identified to capture capital outflow or capital flight such as residual method, Dooley method, hot money and asset method. Each method of measure has some drawbacks, due to lack of consensus with respect to appropriate measure for capital outflows, such makes this study to distinguish itself by identifying the dimensions of the domestic uncertainty at the macroeconomic level by assessing the effect of each dimension on short term private capital outflow instead of adopting any of the conventional measure of capturing capital flight aforementioned in Nigeria.

LITERATURE REVIEW
One fundamental question in domestic private capital outflow/capital flight literature that has preoccupied policy makers is why economies suffer domestic private capital out flow/ capital flight. One leading key factor receiving considerable attention is the effect of macroeconomic uncertainty in the domestic private capital outflow process. Studies like Nyoni (2000); Forson et al. (2017); Liew et al. (2016); Lawanson (2007); Ayadi (2008); Le and Zak (2006); Boyce and Ndikumana (2001); Victor (2004) have studied the effects of macroeconomic uncertainty on domestic capital outflows. Some of these studies are time series based while others are both time series and crosssection based (panel data analysis).
Based on time series analysis, for instance, Nyoni (2000) conducts a study by analyzing the macroeconomic impact and political shock on capital outflow on Tanzania using time series between 1973 and 1992. The study concluded that lagged capital outflow, real growth rates, interest rate and exchange rate differentials significantly impacted on a capital flight while political shock had no statistically significant impact on capital flight. Lawanson (2007) states in his study on capital flight from Nigeria based on portfolio choice approach using data from 1970-2001, found that GDP growth rate has a negative significant effect on capital flight in the shortrun. The results also revealed that higher external debt-GDP ratio, increase in real interest rate differential and an increase in inflation rate drive capital flight in Nigeria. Ayadi (2008) agrees with Lawanson (2007) where Ayadi (2008) investigates an analysis of capital flight in Nigeria. The study found the validity of the portfolio theory which postulates how risk-averse investors can build portfolios in order to optimize or maximize expected returns given a level of market risk. The study revealed that capital flight is caused by the interest rates differential both in the short and in the long run. In addition, exchange rate depreciation significantly increases capital outflow in Nigeria.
Output growth has negative and significant in the short-run. These findings are validated by Oluwaseyi (2017) that there is a negative relationship between economic growth and capital outflow or capital flight. The results also depict that a positive and significant relationship exists between capital flight and interest rates differential, explaining that the higher risk-adjusted returns abroad influence domestic capital flight.
According to a similar study in Ghana, Forson et al. (2017) finds that the long-run and short-run real GDP growth rate, higher domestic real interest rate over foreign interest rate, financial development, good governance and strong property rights reduce capital outflow, while external debt to GDP leads to increase in capital flight in Ghana. However, lagged external debt to GDP and lagged financial development had a negative and positive effect respectively in the short-run. Contrary to this study, Liew et al. (2016) posit that in Malaysia that political risk and financial crises are positively related to capital flight in Malaysia while FDI, external debt and stock market have a negative impact on capital flight. Alam and Quazi (2003) confirms that corporate income taxes, higher real interest rate differentials and lower GDP growth rates, proved to be significant but political instability was the most important factor affecting capital flight determinants of capital outflow was examined on Bangladesh using ARDL model. Levin et al. (2000) argue that panel data analysis better capture the complexity of heterogeneity inherent in each individual country Since panel data provides time series on each cross section unit in a group,. Le and Zak (2006) presented a portfolio choice model that relates capital outflow to return differentials, risk aversion, and three types of risk: economic risk, political instability, and policy variability. In their estimation for a panel of forty-five developing countries over sixteen years, all three types of risk had a statistically significant impact on capital outflow and political instability was the most important factor associated with capital flight. Hermes and Lensink (2000) argue that uncertainty with respect to government policies perceived by domestic wealth holders has its influence on capital flight in less developing countries. The outcomes of investigation support the view that policy uncertainty stimulates capital flight. It has been identified that if the content and direction of current and future public policies are uncertain and/or unstable, domestic investors will also be uncertain about the impact of these policies on the real value of domestically held assets in the future. Policy uncertainty measured by uncertainty of budget deficits, tax payments, government consumption and real interest rates appears to have a statistically significant positive impact on capital flight. In support of Hermes and Lensink (2000) position, David and Ampah (2018) examines whether macroeconomic volatilities as perceived by domestic investors in the subregion have any influence on these outflows taking some selected heavily indebted poor countries (HIPC) and dataset for the period 1990 to 2012 employing GARCH model and Panel ARDL model. The outcomes reflect the current situation in the sub-region which supports the view that domestic investors will withdraw their investments and other financial holdings from the domestic economy if they perceived present and future government policies to be volatile. Victor (2004) formulated the hypothesis that inflation has a positive additional impact on post-war capital flight flows where a study was conducted on 77 developing countries between 1971 and 2000 using panel data. The outcome of the results consistently support the hypothesis that post-war, inflation exacerbates annual capital flight flows by about 0.005 to 0.001 percentage points of GDP. He further concluded that low inflation helps in dampening capital flight in post-conflict economies. Cuddington (1986) verifies the relationship between capital flight and a number of macroeconomic variables in 7 Latin American countries. His results showed that interest rate differentials, external debt flows, lagged capital flight, inflation and exchange rates significantly accounted for capital flight in those countries. Studies like Boyce (1992) confirmed Cuddington (1986) on the contribution of external debt, budget deficits, and interest rates in the determination of capital flight. Collier et al. (2001) and Ndikumana and Boyce (2003) used M2/GDP and M3/GDP respectively as a measure to financial development and found that financial development is insignificant in determining capital flight in Sub-Sahara Africa. These findings contradict (Raheem, 2015) who re-examined determinants of capital flight using twenty-eight Sub-Sahara Africa countries and found that M2/GDP has a positive and significant coefficient. The inconclusiveness in the need to have a proper understanding of macroeconomic factors influencing each of the various forms of capital outflow or capital flight than using a conventional method of measuring capital outflow or capital flight. Such can lead to a proper course for policy which will be clearly suggestive.

MODEL SPECIFICATION AND ESTIMATION METHOD
With regard to theoretical explanation of short term private capital outflow, Markowitz (1952) argued in his portfolio choice model that economic agents send their capital abroad to invest in a portfolio that maximizes the expected utility of their wealth. To examine uncertainty surrounding current and future direction of macroeconomic policies have any impact on short term private capital outflows in Nigeria, this paper draws on a similar model by Le and Zak (2006); David and Ampah (2018) and Hermes and Lensink (2000) and estimate a dynamic time series data model where short term private capital outflow is a function of macroeconomic policy environment and control variables as: Where Co is short term private capital outflow, M represents macroeconomic policy environment, X is a vector of control variables and is the error term.
are the coefficients of CO, M and X respectively. This study considers inflation rate (inf), exchange rate volatility(vex), interest rate differentials(i-i_) and stock exchange development (stmk) as macroeconomic policy environment. Also, financial development (fd), gross domestic product (gdp), short term private capital inflow (cif) and internal debt (dt) and governance (gov) are chosen as the control variables for the study. These variables are chosen as a result of carefully examining the theoretical and empirical literature. Therefore M and X can be re-written as:

DATA REQUIREMENT AND SOURCES
In order to investigate the incidence of short term capital outflow on the Nigerian economy, monthly time series data for econometric analysis are employed in this study. The variables used are defined and described below and sources are also stated in Table 1.

Variables
Definition and description of the variables Sources Short term private capital outflow It is captured by outflow of foreign portfolio investment from abroad. It is adopted due to lack of data on short term capital outflows in Nigeria.

Nigeria Stock Exchange
Short term private capital inflow It is captured by inflows of foreign portfolio investment into Nigeria. it is adopted due to lack of data on short term capital inflows in Nigeria. it is captured as quality of institution and was proxy by a dummy characterized by 1 for month of an increase in short term capital outflow and 0 when short term private capital outflow fall.
Author's estimation Domestic debts stock It is captured by total domestic debt stock in the economy. Central Bank of Nigeria Note: some of the data series only annual and quarterly values are available not monthly from for these and it they are used in that form, it will lead to degree of freedom problem in the analysis to over come that problem, monthly series were generated for growth rate and domestic debt stock using interpolation method. For details see Schlegel et al. (2012). On the interpolation of data with normally distributed uncertainty for visualization (Box and Jenkins, 1970). Table 2 exhibits the outcome of the Eagle-Granger single equation cointegration test which confirms the existence of a cointegrating vector. As to the tests themselves, the eagle-granger tau-statistic (t-statistic) and

EMPIRICAL FINDINGS
normalized auto-correlation coefficient (z-statistic) both reject the null hypothesis of no cointegration (unit root in the residuals) at the five percent significance level. Given the small sample size of the probabilities and critical values, there is evidence of three cointegrating equation at the five percent significance level using the tau-statistic (t-statistic) and evidence of four cointegrating equation at the five percent significance level using the z-statistics. It implies that they both rejected the null hypothesis of no cointegration among the variables at the five percent significance level. On balance, using the tau-statistic (t-statistic) the evidence clearly suggests that logcof, logcif and logcm are cointegrated and also logcof, logcif and logcm are cointegrated using z-statistic. It means that there exists a long run relationship or cointegration between short term private capital outflows and some macroeconomic parameters.

Short Run Estimate of Incidence of Short Term Private Capital Outflow
Having established that the variables are stationary and exhibit long-run cointegration, we now estimate the short run and long-run impacts of the macroeconomic instability or factors on short term private capital outflow indices in Nigeria using the fully modified ordinary least squares (FMOLS) estimator. The result of the short-run analysis is presented in Table 3. This is reflected through the error correction model (ECM) estimation which is reflected through the coefficient of the short run elasticity estimated and long run elasticity estimated i.e. the co-integration relationship between the dependent variable and the regressors Having examined the co-integrating relationship, the Eagle-Granger cointegration test implies that our study can generate error term of co-integrating equation which captures both the long and short run dynamics of the impact of macroeconomic factors on short term private capital outflow in Nigeria between 2013/March and 2018/ May periods.
The result from the FMOLS estimates showed a high level of precision and accuracy given the statistical components; the explanatory variables in terms of their explanatory power (adjusted R 2 ) explained 0.84 variation in short term private capital outflow in short run estimate. The long-run variance of 0.030086 was less than unit which indicated that the estimators of the model had minimum variance and hence, efficient, sufficient and best linear and unbiased. Finally, the ECM result from the short-run estimates is negative and significant (t = -4.75 and probability= 0.0000). This implies that if disequilibrium or temporary changes occur to the selected variables, there will always be a convergence back to equilibrium. Although the speed of adjustment is very moderate at 0.55%, however, the result confirms the existence of a long-run equilibrium among the selected variables.
The results of the fully modified OLS (FMOLS) estimate revealed that increase in macroeconomic policy uncertainties such as inflation, real effective exchange rate volatility, interest rate differential and and stock exchange development had significant effect in promoting the level of short run private capital outflow in Nigeria.
Drawing specific inferences from the short-run coefficient estimates, Table 3 shows the impact of macroeconomic policies or macroeconomic factors on short term private capital outflow in Nigeria. It is evident from the result that first lag of inflation, real effective exchange rate volatility, economic growth, stock market development, and current interest rate differential variables were positively related to short term private capital outflow. A percent increase in first lag of inflation, real effective exchange rate volatility, economic growth, stock market development and current interest rate differential would, other things being equal, result to 10.9%, 0.03%, 1.01%, 0.62% and 0.89% increases in short term private capital outflow respectively. The implication of this result is that an increase in each of these regressors triggers short term private capital outflow to increase at the detriment of the economy.
Moreover, with the values of the t-statistic and probabilities, first lag of inflation, real effective exchange rate, economic growth, stock market development and current interest rate differential were the variables that were statistically significant in determining short term private capital outflow. While the variables like governance, financial development, short term private capital inflow, first lag of interest rate differential, first lag of domestic debt and previous short term private capital outflow were negatively related to short term private capital outflow.
It suggests that a percent increase in aforementioned variables will reduce short term private capital outflow by 0.4%, 0.42%, 0.06%, 0.91%, 0.35% and 0.14% respectively. With regard to values of t-statistic and probabilities, governance, past short term private capital inflow, first lag of interest rate differential, first lag of domestic debt and past short term private capital outflow were statistically significant in the determination of short term private capital outflow except financial development which is significantly related to short term private capital outflow.
The estimated result presented in Table 4

Discussion of Findings
Increase in macroeconomic instability motivates the rise in short term private capital outflow which can heighten the danger of growth depression in the economy. Persistent instability in inflation rate triggers a continuous rise in the short term private capital outflow in Nigeria. Uncertainty around price level will mean a higher cost of investing in the country and also show that the portfolio behaviour of private wealth holders is influenced by inflationary tax. In addition, real exchange volatility has positive and significant relationship with short term private capital outflow. It implies that exchange rate volatility further compounded the level of short term private capital outflow. Continuous distortion of exchange rate result in the fall of the value of assets invested or profit expected to be generated. This perceived reduction in the asset value or profit may encourage investors rather shift their resources abroad.
The finding reveals the positive and significant relationship between interest rate differential and short term private capital outflow in Nigeria indicating that increase in real interest rate differential induces the proportion of private real wealth held abroad. This confirms the rational behaviour of private wealth holders to take advantage of relative returns on investments. Stock market development was included among the variables of study which was expected to have effects on investors' decisions. Development of stock market is a sigh of higher than expected current wealth which is a boost to investors' confidence to make more investment. Surprisingly, our findings disclosed positive relationship between stock market development and short term private capital outflow. It indicates that there is little investors' confidence to own more domestic stock and retain their domestic portfolio which in turn further motivates short term private capital outflows Economic growth and short term private capital outflow are positive and statistically significant signifying that as gross domestic product increase, short term private capital outflow tends to trigger further. It is expected that higher economic growth is an indication of higher expected returns on investment and saving. It is contrary to existing studies carried out by Lawanson (2007) on capital outflow in Nigeria.
Empirical finding revealed that a period lagged of domestic debt stock significantly motivates short term private capital outflow. It indicates that domestic investors or private wealth holders may consider the acquisition of government debt instruments as an investment opportunity with relative assurance of returns. Chipalkatti and Rishi (2001) argued that when the debt level is lower, the economy is actually suffering from lesser resources and this indicates that the capacity for the economy to grow has shrunk.such can further have adverse effect on the local economic condition which can lead to greater capital outflows.
Our finding further reveals that current Short term private capital outflow had inverse and significant relationship with both first lag of short term private capital inflow and even itself. It implies that higher level of short term private capital inflow indicates that the country has investment climate perspective. Such is expected to lessen short term private capital outflow as the investment at home offers more attractive and lucrative return as compared to investment abroad. Governance, which was used to explore the quality of institution on short term private capital outflow is negative statistically significant at five percent significance level. The results explain that improvement in governance in Nigeria can reduce short term private capital outflow in both short run and the long-run. This is because good governance has been seen as a pre-requisite for politically stable environment which is friendly for domestic investment. Therefore, this finding suggests that good governance in Nigeria will be a driver of reducing short term private capital outflow.
Finally, there is evidence that financial development showed a negative impact on short term private capital outflow as theory predicted that financial development boosts investor confidence in the economy and expected to decrease the amount of short term capital outflow but it is statistically insignificant in Nigeria.

CONCLUSION
This study had been concerned with the incidence of capital flight in Nigeria. The outcome from the study indicated the sensitivity of overall outcome to model specification. One result that stood out in the exercise was uncertain structural policy (stock market development) and unstable stabilization policies (inflation-price instability and real exchange rate volatility) were a short run and long run important determinants of short term private capital outflow in Nigeria. The course for policy was clearly suggestive i.e. there is a need for intensified efforts towards ensuring and maintaining sound domestic macroeconomic policy to stem capital outflow in Nigeria and more so, Nigerian capital market should ensure that in the area of domestic investors' protection and confidence, infrastructural development, and accounting disclosure requirements are maintained and sustained.
In conclusion, it should be noted that the study was only concerned with the economic aspect of short term private capital outflow and did not capture non-economic aspect like political factors, corruption, civic right, that might have played significant roles.
Funding: This study received no specific financial support.


Performance of Yam Marketing in Yewa Division of Ogun State, Nigeria

Nigeria’s socio-economic history and development has been very closely tied to its agricultural sector Egbuna, [1]. Agriculture holds the key to rural development, poverty alleviation and overall economic development Oluwafemi [2]. The sector accounted for about 31-42% of Gross Domestic Product (GDP) between the year 2005 and 2008. In addition, it provides paid and selfemployment for over 70% of the nation’s population (Nigerian Export Promotion Council NEPC [3]. The Food Crop Sub-sector (with maize, sorghum, millet, rice, yam, cocoyam and cassava as the main food crops grown in the country) contributed about 28% to GDP representing about 75-76% of the share of the agricultural sector’s contribution to GDP CBN [4]. Agriculture belongs to the real sector of Nigerian economy and it is characterized by multitude of small-scale farmers scattered over wide expanse of land area, with small holdings ranging from 0.05 – 3.0 hectares per farm land, rudimentary farm systems, low capitalization and low yield per hectare Okoedo-Okojie and Okwuokenye [5]. Root and tuber crops comprise crop covering several genera. They are staple food crops, being the source of daily carbohydrate intake for the large populace of the world. The term root and tuber crop refers to any growing plant that store edible materials in the subterranean root, corm or tuber Toluwase and Sekumade [6]. Yam is a member of this important class of food. Yams (Dioscorea spp) are annual or perennial tuber-bearing and climbing plants with over 60 species out of which six are economically important in terms of food and medicine.

Introduction
Nigeria's socio-economic history and development has been very closely tied to its agricultural sector Egbuna, [1]. Agriculture holds the key to rural development, poverty alleviation and overall economic development Oluwafemi [2]. The sector accounted for about 31-42% of Gross Domestic Product (GDP) between the year 2005 and 2008. In addition, it provides paid and selfemployment for over 70% of the nation's population (Nigerian Export Promotion Council NEPC [3]. The Food Crop Sub-sector (with maize, sorghum, millet, rice, yam, cocoyam and cassava as the main food crops grown in the country) contributed about 28% to GDP representing about 75-76% of the share of the agricultural sector's contribution to GDP CBN [4]. Agriculture belongs to the real sector of Nigerian economy and it is characterized by multitude of small-scale farmers scattered over wide expanse of land area, with small holdings ranging from 0.05 -3.0 hectares per farm land, rudimentary farm systems, low capitalization and low yield per hectare Okoedo-Okojie and Okwuokenye [5]. Root and tuber crops comprise crop covering several genera. They are staple food crops, being the source of daily carbohydrate intake for the large populace of the world. The term root and tuber crop refers to any growing plant that store edible materials in the subterranean root, corm or tuber Toluwase and Sekumade [6]. Yam is a member of this important class of food. Yams (Dioscorea spp) are annual or perennial tuber-bearing and climbing plants with over 60 species out of which six are economically important in terms of food and medicine.
Yam belongs to the genus "Dioscorea" and family "Dioscoreaceae". It is an important tuber crop of the tropics. Yam is a tropical crop with many species, which originated from South East Asia and was brought to West Africa in the 16th century Toluwase and Sekumade [6]. Yam is an important food crop especially in the yam zone of West Africa, comprising Cameroon, Nigeria, Benin, Togo, Ghana and Cote de 'vore. This zone produces more than 90% of the total world production, estimated at 20 -25 million tons per year Adeniji et al. [7]. Nigeria is noted to be a leading World producer of yam FAO [8].
The report noted that out of the World production of over 30 million tonnes per annum, Nigeria produces about 25 million tones. It is one of the principal tuber crops in the Nigeria economy, in terms of land under cultivation and in the volume and value of production Bamire and Amujoyegbe [9]. Agronomically, yam can be grown from whole tuber, seed yam or micro-sett IITA [10]. The report (IITA 2005) showed that use of micro-sett (small pieces of yam cut from "mother seed yams") under plastic mulch could increase the multiplication rate tenfold over conventional system. Okwuokenye and Onemolease [11] noted that on the part of profitability that yam production is very profitable and that more marketers can still enter the market and still make profit. A wholesaler is an intermediary entity (person or enterprise) in the distribution channel whose role is to buy in bulk and sell to resellers (also known as retailers) rather than to consumers. Wholesalers obtain large quantities of products from producers, may store them, and may break them down into cases or sets and other smaller units more convenient for retailers to buy; this process is best described as "breaking bulk".
Marketing is defined as a process of satisfying human needs by bringing products to people in the proper form and at a proper time and place. Marketing has economic value because it gives form, time, place, utility to products and services. The marketing of agricultural products begins at the farm when the farmer harvests his products. The product when it is harvested cannot usually go directly to the consumers. Firstly, it is likely to be located some distance from the place of consumption in regular and continuous manner throughout the year. Secondly, storage is required to adjust supply to meet demand. Thirdly, a product when it has been harvested is rarely in a form acceptable to consumers. Therefore, it must be sorted, cleared and processed in various ways and must be presented to the consumer in convenient quality and quantities for sale. Finally the farmer expects payment when his produce leaves his possession, and hence some financial arrangements must be made to cover all the various stages until the retailer sells the products to the final consumer. Marketing covers all business functions including production and in its broadest sense, it also covers production decision. So it can be argued that in farming such decision as the variety of crops to grow or the breed of animal to keep are marketing decisions. The primary role of an integrated marketing system is to add form, place, time and possession utility, so that the subjective satisfaction of consumers is maximized.
Marketing generally entails the movement of goods (agricultural products) from on producer to the final consumer, a route that is often linked with middlemen of which the retailer is one Okoedo-Okojie and Okwuokenye [12]. Wholesale marketing involves buying in large quantities from the farmers and selling in small quantity to the retailers and final consumers Kotler [13].
He asserted that the retailer's sales volume comes primarily from wholesalers. To improve on the wholesale marketing of yam would demand an understanding of the marketing function and cost. Okoedo-Okojie and Okwuokenye [12] asserted that whatever affects marketing functions and cost will ultimately affect the agricultural development process and socioeconomic wellbeing of the citizenry. This is because too high a cost will limit customer's ability to buy and this will eventually limit agricultural production (yam inclusive). Despite the benefits derived from yam production, it is realized that it has earned little attention from scientific research compared to other food crops. This situation has not only affected the production but also the marketing of yam Okwuokenye and Onemolease [14]. This study therefore seeks to bridge the gap so that a drastic increase in production and wholesale marketing of the product can be achieved.
Markets are prerequisites for enhancing agro-based economic growth and increasing rural incomes in the medium term particularly for the rural poor households. Subsistence food crop production cannot improve rural incomes without marketoriented production systems. These require the intensification of agricultural production systems, increased commercialization and specialization in higher-value crops. And these must be built upon the establishment of efficient and well-functioning markets and trade systems-ones that keep transaction costs low, minimize risk, extend information to all players and that do not either exclude or work contrary to the interests of the poor-especially those living in areas of marginal productivity and weak infrastructure. Food marketing is a very important but rather neglected aspect of agricultural development. In developing countries, more emphasis is usually placed on policies to increase food production with little or no consideration on how to distribute the food produced efficiently and in a manner that will enhance increased productivity. Food marketing is a very important but rather neglected aspect of agricultural development. In developing countries, more emphasis is usually placed on policies to increase food production with little or no consideration on how to distribute the food produced efficiently and in a manner that will enhance increased productivity Robert et al. [15].

Objectives of the study
The broad objective is to study the performance of yam marketing in Yewa Division of Ogun State, Nigeria. The specific objectives are to examine the cost and return structure of yam marketing and estimate the marketing margin and efficiency of yam in the study area.

Study Area
The Yewa Division of Ogun State was used as study area. The marginalization of Yewa in Ogun State is crystal clear from its inability to occupy the State Government House the moment the State was created in 1976 and beyond. While other regions within the State have been to the apex position and even recycling it. Traditionally speaking, Ogun State is divided into four; Egba, Ijebu,

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Remo and Yewa respectively. But into three for administrative purposes as enshrined in the country Constitution, these divisions are Ogun Central Senatorial District mainly made up of Egba with six LGAs, Ogun East Senatorial District with Ijebu and Remo with nine LGAs and Ogun West Senatorial District comprises of Yewa with five LGAs Lamidi and Ogunkunle [16]. Yewa formerly Egbado is made up of seven different tribes which was the main reason the cover name of the region was changed in 1995 to Yewa. Even at that, Awori one of the tribe in the region failed to agree with the problem created by the 20 th century scholars by classifying her as Yewa, rather see herself as a unique entity within the region with link to the Egbas. It was all these factors that would later affect the socio-economic and political development of the region despite its closeness to the international borderline Olusegun [17] (Figure 1).

Sources and Methods of Data Collection
Both primary and secondary data were used for the study. The primary data were collected through the use of well-structured (pre-tested) questionnaire, while the secondary data were obtained from published journals, books, internet, periodicals, government official websites and other relevant sources.

Sampling Techniques
A two-stage sampling technique was employed in this study to select a cross section of 120 yam marketers in the areas. Two (2) Local Government Areas were randomly selected out of five (5) Local Government Areas that make up Yewa Division of Ogun State. Five (5) markets were purposively selected from each of the LGAs making a total of ten (10) markets. Twelve (12) yam marketers were selected in each market making a total of one hundred and twenty (120) marketers in the study area.

Methods of Data Analysis
The data obtained from this study were analyzed using both descriptive and inferential analytical techniques. Descriptive statistical tools (such as frequency distribution tables and percentages, charts, measures of central tendency and proportions) were used to describe the socio-economic characteriswtics of the respondents. While, inferential statistics (such as Budgetary Analysis and Marketing Efficiency models) were used to examine cost-return structure of the respondents and marketing efficiency of the yam marketers. frequency distribution tables and percentages, charts, measures of central tendency and proportions.

Cost and Return Structure Analysis of Yam Marketing
Budgetary analysis was used to estimate the cost and return structure of yam marketing in the study area. The Net Income (NI) was obtained thus:

MM = Total Marketing Margin
According to Abdou (2004), the marketing efficiency estimates marketing margins as representing the difference between purchasing and selling prices of marketers compared to the real marketing costs. A positive sign estimates would justify application of such services, making it efficient, and a negative estimate would indicate otherwise (Table 1).

Results and Discussion
Results of socio-economic characteristics of the yam marketers in the study area are presented below. The ability of the marketers to take advantage of emerging opportunities that could improve marketing efficiency and profitability could be influenced by their age. The age distribution of respondents as presented in Table 1 indicates that 69.1% of the yam marketers are between ages 31 and 50, while 6.7% of them are above 60 years, meaning that most yam marketers in the study area are in their middle age. The average age was estimated at 41 years. An economic active age that can make positive contribution to agricultural production which may translate to improved profitability of yam marketing. It is necessary to describe the sex of the respondents for possible inference and generalization on how it relates to yam marketing. The finding revealed that majority (65.8%) of the respondents was females. This showed that yam marketing seems solely a female business in the area, which confirms Oladapo et al. [19] and Okoedo-Okojie and Okwuokenye [12], but shows difference with Okwuokenye and Onemolease [11] that reported mixed distribution in equal proportions in their various studies. The relative sole distribution may be as a result of social barriers. Marital status is expected to influence respondents' level of responsibilities which could have positive or negative influence on their disposition to economic activities including the yam marketing. It was revealed in Table 1 that 85.8% of the yam marketers are married, 3.3% were observed as single, while 9.2% of are widows. The result shows that most of the yam marketers in the study area are married and therefore yam marketing would serve as a means to meet the needs of the family.
Education is of great importance in decision making. It can indirectly influence the respondents' understanding of marketing dynamics and ways to maximize gains. Finding revealed that 51.7% of the yam marketers had non-formal education; 34.2% had primary education, 13.3% had secondary education, while 0.8% had secondary education. This result reveals that majority of yam marketers in the study area do not have formal education. Notably, formal education is an essential tool for the adoption of effective communication system that encourages increase in the marketing of any agricultural produce. Thus, with low level of literacy in the study area, yam marketers would hardly adopt new marketing strategy which could improve their levels of profits ceteris paribus. Analysis of the religion of the respondents revealed that majority (53.3%) of the yam marketers practiced Islam as religion while 45% of them were Christian and only 1.7% did not practice Christianity and Muslim. Substantial percentages of the two dominant religions are well represented in the study area. Experience is an important determinant of efficiency and perhaps profitability. The study further revealed that majority (53.3%) of the yam marketers have been in the business for about 10years while 29.2% of the yam marketers have been in the business within 11 to 20years, 15% of the yam marketers have been in the business within 21 to 30years and the remaining 2.5% of the yam marketers have been in the business above 30years. The average experience of wholesalers was determined at 14 years and 6 months. This shows that the managerial ability of the marketers can be inferred to be reasonably good.
Household size may determine the family Labour at the disposal of a yam marketer. In terms of the household size distribution of the yam marketers, the results indicate that 21.7% of the yam marketers had household size of between 1 and 4 inhabitants, with 76.6% belonging to the household size of between 5 and 8 persons. The relative size of the household implies availability of Labour which could be an opportunity for the yam business. Data showed the percentage distribution of respondents by membership of marketing association. The result showed that majority of the respondents (90.8%) subscribed to the membership of marketing association, whereas 9.2% did not subscribe to the membership of marketing association. Those involved in Marketing Association did so because of easy access to extension services, market and credit facilities.  Table 2. The yam marketers incurred several costs in the course of marketing. These costs were variable costs. The variable costs were expenses on cost of yams, transportation, market space, storage facilities, and labour employed, while the fixed costs include rent on shop/land and depreciation costs of heaps, basket, interest on loan, etc. Yam marketers in the study area spent N91,233.37 on variable cost items, representing 90.73% of the total cost of marketing. Out of this percentage, cost of yams accounted for 64.42%, transportation 4.98%, market space 10.02%, storage facilities 2.51%, labour 4.97% and the other variable cost item incurred was 3.82%. In all, an average of N100,550.04 were expenses the marketers incurred. Further result of the analysis in Table 2 generated positive gross margin and net income values of N75,808.30 and N66,491.63, to prove yam marketing enterprise profitable in the study area ( Table 2). Benefit Cost Ratio (BCR) was greater than one. This ratio is one of the concepts of discount method of project evaluation. As a rule of thumb, any business with benefit cost ratio greater than one, equal to one or less than one indicates profit, break-even or loss respectively Olagunju et al. [20]. Since the ratio (BCR = 1.66). It implies that yam marketing in the study area is profitable. The Profitability index, return on investment, Operating ratio and Return on variable cost were computed as 0.40, 0.66, 0.55 and 1.83 respectively. The PI, RRI, RRVC and OR were all favorable. Return on investment was 0.66, implying that the marketers' returned N0.66 for every N1.00 invested in the business. This implies that yam marketing in Yewa Division of Ogun State is a profitable business. Table 3 presents the marketing margin and the marketing efficiency of yam marketing in Yewa Division of Ogun State. The marketing margin was estimated at N554.10. The marketing efficiency (ME) was estimated at 1.51. The ME estimates was above 1 indicating that the market is highly efficient. Marketing efficiency ranges from zero (0) to infinity. Scarborough et al. [21], noted that if marketing efficiency is less than 1, it indicates inefficient market whereas if the marketing efficiency is greater than 1 there is excess profit. A market that is efficient does not only bring sellers and buyers together, it enables entrepreneurs to take advantage of opportunities, to innovate and improve in response to demand and price changes ( Table 3). Source: Data analysis, 2018.

Problems Militating against Yam Marketing in the Study Area
The results of Figure 1 showed that the respondents considered bad roads (45%) and poor storage (45%) as a major constraint and it ranked first among the identified constraints. This was because yam is heavy and fragile, so transporting it can be difficult on a bad road. It is often transported manually using head pans or baskets. Credit sales and Poor and instable price of yam (40.0%) was also considered a problem. Other problems include, lack of capital, high purchase price, poor sales, too many traders, too many market levies, high cost of transportation and risk of accident or robbery ( Figure 2).

Conclusion
The conclusions of the study are that the yam marketers were mainly females who are still in their prime, married and considerably illiterate. Cost of buying yam constituted the main cost of operation. In terms of profitability, yam marketing was highly profitable in the study area with returns that could comfortably offset the cost of capital. The yam market was very efficient with good marketing margin. The problems militating against yam marketing were numerous but the main constraints facing them include bad roads, poor storage, credit sales and Poor and instable price of yam.