Article

# Investment and the Dynamic Cost of Income Uncertainty: the Case of Diminishing Expectations in Agriculture

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## Abstract

This paper studies optimal investment and the dynamic cost of income uncertainty, applying a stochastic programming approach. The motivation is given by a case study in Finnish agriculture. Investment decision is modelled as a Markov decision process, extended to account for risk. A numerical framework for studying the dynamic uncertainty cost is presented, modifying the classical expected value of perfect information to a dynamic setting. The uncertainty cost depends on the volatility of income; e.g. with stationary income, the dynamic uncertainty cost corresponds to a dynamic option value of postponing investment. The numerical investment model also yields the optimal investment behavior of a representative farm. The model can be applied e.g. in planning investment subsidies for maintaining target investments. In the case study, the investment decision is sensitive to risk.

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... The dynamic uncertainty cost as formalized in (10) can be decomposed into a quantity cost (lower expected investment) and a value loss (reduced expected value of investment). Following (Heikkinen and Pietola, 2006) let Pr t denote the probability of investment at time t when the state r t is observed, and let Pr 0 t denote the corresponding probability with expected value maximization (Model 2). Assuming Pr t > 0, define the unit value of investment at time t, v 1 (t), in Model 1 as v 1 ðtÞ ¼ E½y t ðI Ã t Þ Pr t I a and assuming Pr 0 t > 0 define the unit value in Model 2 as v 2 ðtÞ ¼ E½y t ðEðr t jr tÀ1 Þ; I ÃÃ t Þ Pr 0 t I a : ...
... Author's personal copy the dynamic EVPI(t) in (10) can be decomposed into a value loss and a quantity loss component (Heikkinen and Pietola, 2006): (11). An aggregate dynamic uncertainty cost EVPI D can be defined as the difference E½f ðfI Ã t g; fr t gÞ À E½f ðfI ÃÃ t g; fr t gÞ. ...
Article
This paper studies optimal investment decision in agriculture under diminishing income expectations. The goal is to study the cost of income uncertainty and its implications to the efficiency of investment subsidies. Investment decision is modelled as a Markov decision process, extended to account for risk. Applying a stochastic programming approach, the cost of imperfect information is evaluated as the difference between the profitability of investment under stable income and under uncertain income. Computational experiments demonstrate that the cost of imperfect information can be high, deteriorating the efficiency of investment subsidies. Also, examples suggest that the optimal timing of the investment can be sensitive to risk.
... Likewise, different programming variations are made to address studied problems better. As presented in(Heikkinen and Pietola, 2009), by modifying the classical expected value of perfect information (a standard metric of the value of information in decision theory) to a dynamic setting, it is possible to study the dynamic uncertain cost for an investment farm decision problem.Janová (2012) proposed a SP optimization model based on mean variance theory for a crop planning optimization problem. 7 ...
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Given the evolution in the agricultural sector and the new challenges it faces, managing agricultural supply chains efficiently has become an attractive topic for researchers and practitioners. Against this background, the integration of uncertain aspects has continuously gained importance for managerial decision making since it can lead to an increase in efficiency, responsiveness, business integration, and ultimately in market competitiveness. In order to capture appropriately the uncertain conjuncture of most agricultural real-life applications, an increasing amount of research effort is specially dedicated to treating uncertainty. In particular, quantitative modelling approaches have found extensive use in agricultural supply chain management. This paper provides an overview of the latest advances and developments in the application of operations research methodologies to handling uncertainty occurring in the agricultural supply chain management problems. It seeks to: (i) offer a representative overview of the predominant research topics, (ii) highlight the most pertinent and widely used frameworks, and (iii) discuss the emergence of new operations research advances in the agricultural sector. The broad spectrum of reviewed contributions is classified and presented with respect to three most relevant discerned features: uncertainty modelling types, programming approaches, and functional application areas. Ultimately, main review findings are pointed out and future research directions which emerge are suggested.
... These risks and uncertainties are the results of fierce business competition with continuously changing market economy and/or unexpected events during project execution. As a result, recent research in investment decision-making is driving a paradigm shift, integrating new techniques with existing methods to develop a robust decision-making process (Heikkinen and Pietola, 2009). ...
... Foulds and Foulds (2006) proposed a probabilistic dynamic programming model for operations scheduling. Heikkinen and Pietola (2009) modelled the investment decision problem as a Markov decision process (MDP) and they used stochastic programming approaches to make optimal decisions. They presented dynamic uncertainty cost with the modification of the classical expected value of perfect information to a dynamic setting. ...
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In multi-stage project investment decision-making with uncertainty, risk mitigation plays a vital role. The return on investment (ROI) that will be realised in making a particular decision quite often carries a high degree of uncertainty, with an increased number of competing investors entering to the market every day. In this research, our objective is to develop a technique for a multi-stage project investment decision problem that deals with uncertainty in ROI and complex interrelated state transition dynamics. We do this by formulating our problem as an infinite horizon stochastic dynamic programming (IHSDP) problem and solve it to maximise the total return over an infinite time horizon. We have implemented our solution to the project investment decision problem in a simple case study using three well-known stochastic dynamic programming algorithms. Our simulation results show that the IHSDP algorithms are useful in making optimum investment decisions in an uncertain business environment.
... This is related to the recognition that agricultural production is often a lengthy process requiring ongoing investments that may not produce expected returns for a prolonged period, thereby being highly sensitive to market risks. Research on investment in agrifood businesses shows extensive impacts as a consequence of uncertainties in investment decisions ( Heikkinen & Pietola, 2009 ). Investment in the food supply chain, from farmers to food-providing services, can also be dampened and discouraged by volatile prices. ...
... However, without stable farm revenue, investment cannot be improved. Research on investment in agri-food businesses shows extensive impacts of uncertainties on investment decisions ( Heikkinen & Pietola, 2009 ). A study by Lagerkvist (2005) reports effects from policy uncertainty on investment in the agriculture industry, while according to Bo and Lensink (2005) econometric evidence supports a nonlinear uncertainty-investment relation. ...
Article
This study examines how managing risk by introducing commodity price insurances may improve the likelihood of increased investment in agri-food supply chains. A model is introduced which shows how insurance products on index prices can reduce the uncertainty of the impact of investment, and also how lower investment can generate the same impact as a higher investment. To show our results, we use two different frameworks which include total profit (Pareto optimal) and Stackelberg game setups. The results demonstrate that in both frameworks the investment will have a greater impact when an insurance product is present. By implication, the study presents an encouraging message to the insurance industry to introduce products to secure supply chain actors’ revenue leading to an increase in investment rate. Consequently, the study offers insight into how the role of traditional government subsidies for protecting farmers, particularly the small to medium-sized farms, may be revisited by replacing some of the existing subsidisation policies with revenue insurance.
... Extending the decision-making unit from the farm to the household, including on-and off-farm resource allocation and including investment variables, can also improve the decision-making process (Viaggi et al., 2010b). While many studies ignore transaction costs and investment dynamics, several studies showed their importance for the adoption of alternative activities and resulting impacts of policies (Bartolini et al., 2007a;Bartolini et al., 2007b;Heikkinen and Pietola, 2009;Peerlings and Polman, 2008;Viaggi et al., 2010a) and to convert to alternative types of farming (Acs et al., 2009;Acs et al., 2007). ...
... These risks and uncertainties are the results of huge business competition and vibrant market economy. As a result, recent research in investment decision making is undergoing a paradigm shift with much integration of new techniques with existing methods to develop robust decision making processes [Heikkinen et al. (2009)]. ...
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... -Moghaddam (2010), Albareda-Sambola et al. (2011), Kavadias and Chao (2008), Wang et al. (2010), Triki et al. (2005), Li and Zabinsky (2011), Sodhi and Tang (2009), Geng et al. (2009), Al-Othman et al. (2008), Zhou and Liu (2003), MirHassani et al. (2000), Wang et al. (2008), Ma et al. (2010), Lin et al. (2011), Santoso et al. (2005), Li and Tirupati (1995), Domenica et al. (2007), Guan and Philpott (2011), El-Sayed et al. (2010), Schutz et al. (2009), Peidro et al. (2009), Longinidis and Georgiadis (2011),Louveaux and Thisse (1985),Yang (2009) andList et al. (2003) Health, pharmaceutical research and development, epidemic model; vaccination, emergencyTanner et al. (2008),Tanner and Ntaimo (2010),Colvin and Maravelias (2008), Chang et al. (2007 andMin and Yih (2010) Economic planning, investment, trade, banking, insurance, and financeHagigi et al. (1990),Sengupta (1982),Fang et al. (2008),Topaloglou et al. (2002Topaloglou et al. ( , 2008,Hibiki (2006),Heikkinen and Pietola (2009), Infanger (2008), Hoyland and Wallace(2008), Luo et al. (2007), Bertocchi et al. (2008), de Lange et al. (2004), Tokat et al. (2003), Kouwenberg (2001), Osorio et al. (2004), Mulvey and Shetty (2004), Board and Sutcliffe ...
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... -Moghaddam (2010), Albareda-Sambola et al. (2011), Kavadias and Chao (2008), Wang et al. (2010), Triki et al. (2005), Li and Zabinsky (2011), Sodhi and Tang (2009), Geng et al. (2009), Al-Othman et al. (2008), Zhou and Liu (2003), MirHassani et al. (2000), Wang et al. (2008), Ma et al. (2010), Lin et al. (2011), Santoso et al. (2005), Li and Tirupati (1995), Domenica et al. (2007), Guan and Philpott (2011), El-Sayed et al. (2010), Schutz et al. (2009), Peidro et al. (2009), Longinidis and Georgiadis (2011),Louveaux and Thisse (1985),Yang (2009) andList et al. (2003) Health, pharmaceutical research and development, epidemic model; vaccination, emergencyTanner et al. (2008),Tanner and Ntaimo (2010),Colvin and Maravelias (2008), Chang et al. (2007 andMin and Yih (2010) Economic planning, investment, trade, banking, insurance, and financeHagigi et al. (1990),Sengupta (1982),Fang et al. (2008),Topaloglou et al. (2002Topaloglou et al. ( , 2008,Hibiki (2006),Heikkinen and Pietola (2009), Infanger (2008), Hoyland and Wallace(2008), Luo et al. (2007), Bertocchi et al. (2008), de Lange et al. (2004), Tokat et al. (2003), Kouwenberg (2001), Osorio et al. (2004), Mulvey and Shetty (2004), Board and Sutcliffe ...
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Transportation and logistics systems are characterised by their highly dynamic structures along with numerous interconnected processes. The natures of these systems involve various levels of resource allocation decisions where usually it is not always possible to execute these decisions in the field on time at the best possible way because of the unpredictable factors in plans. By considering the uncertain operational environment, this paper explores the uncertainty issue within operational systems and deals with the problem of allocating resources to maximise expected total profit and minimise inefficiencies under uncertainty. The aim is to design, develop, visualise, and effectively deal with a more realistic model to satisfy uncertain demand nodes by leaving minimal or no unsatisfied zones within an operational environment at seaports, transportation, logistics and supply chain systems. A representative optimisation model, which is developed to address the uncertainty issue, has been solved by using an optimisation algorithm. The results show that operational plans without the utilisation of uncertainty models could have negative impacts, including increased emissions, negative environmental effects, along with higher costs to organisations.
... Another stream of research develops a refinement of the basic profit-maximising model in the direction of accounting for uncertainty. Examples are provided by the Real Option Approach (Pyndick, 1991), or by Stochastic programming (Heikkinen and Pietola, 2009). ...
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We examine the investment-uncertainty relationship for a panel of Dutch non-financial firms. The system generalized method of moments (GMM) estimates suggest that the effect of uncertainty on investment is nonlinear: for low levels of uncertainty an increase in uncertainty has a positive effect on investment, while for high levels of uncertainty an increase in uncertainty lowers investment. This result is in line with a number of theoretical studies, but has never been documented empirically. Copyright (c) The London School of Economics and Political Science 2005.
Investment and the Dynamic Cost of Income Uncertainty: the Case of Diminishing Expectations in Agri-culture. MTT Discussion Paper 5, 2006 (previous version also in proc
• T Heikkinen
• K Pietola
Heikkinen, T., Pietola, K., 2006. Investment and the Dynamic Cost of Income Uncertainty: the Case of Diminishing Expectations in Agri-culture. MTT Discussion Paper 5, 2006 (previous version also in proc. ERSA 2006, Volos).
A Stochastic Dynamic Programming Model of Direct Subsidy Payments and Agricultural Investment. Presentation at the Joint Annual Meetings of the American Agricultural Economics Association and Canadian Agricultural Economics Society
• J Vercammen
Vercammen, J., 2003. A Stochastic Dynamic Programming Model of Direct Subsidy Payments and Agricultural Investment. Presentation at the Joint Annual Meetings of the American Agricultural Economics Association and Canadian Agricultural Economics Society. Montreal.
Introduction to Stochastic Programming Springer Series in Opereations Research Is the investment-uncertainty relationship nonlinear? an empirical analysis for the netherlands
• J Birge
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Birge, J., Louveaux, F., 1997. Introduction to Stochastic Programming. Springer Series in Opereations Research. Bo, H., Lensink, R., 2005. Is the investment-uncertainty relationship nonlinear? an empirical analysis for the netherlands. Economica 72, 307–331.
Can Grater Uncertainty Hasten Investment. Working Paper Taloustohtori (in Finnish)
• R Mason
• H Weeds
Mason, R., Weeds, H., 2005. Can Grater Uncertainty Hasten Investment. Working Paper, Department of Economics, University of Southampton. MTT, 2007. Taloustohtori (in Finnish). www.mtt.fi/kannattavuu-skirjanpito.
The Effect of Decoupling CAP-subsidies on Profitability of Livestock Bilding Investments'. In "CAP-uudistus Suomen maataludessa
• P Uusitalo
• A.-M Heikkilä
• K Pietola
[Uusitalo et al.2004] Uusitalo, P., A.-M. Heikkilä, and K. Pietola: 2004, 'The Effect of Decoupling CAP-subsidies on Profitability of Livestock Bilding Investments'. In "CAP-uudistus Suomen maataludessa", H. Lehtonen ed. (in Finnish, attachments available upon request).
Compecon Toolbox for Matlab
• P Fackler