metadata: authors: 0: author: Gouel,Christophe
1: author: Gautam,Madhur
2: author: Martin,Colleen J.
count: India
docna: 0: docna: Managing food price volatility in a large
            open country : the case of wheat in India
docty: Policy Research Working Paper
subtopic: Disability,Trade Policy,Services & Transfers to Poor,International Trade and Trade Rules,Rules of Origin,Economic Assistance,Access of Poor to Social Services,Macroeconomic Management,Trade and Multilateral Issues
teratopic: Finance and Financial Sector Development,Macroeconomics and Economic Growth,Private Sector Development,International Economics and Trade
abstracts: cdata!: India has pursued an active food
            security policy for many years, using a combination of trade
            policy interventions, public distribution of food staples,
            and assistance to farmers through minimum support prices
            defended by public stocks. This policy has been quite
            successful in stabilizing staple food prices, but at a high
            cost, and with potential risks of unmanageable stock
            accumulation. Based on a rational expectations storage model
            representing the Indian wheat market and its relation to the
            rest of the world, this paper analyzes the cost and welfare
            implications of this policy and unpacks the contribution of
            its different elements. To analyze alternative policies,
            social welfare is assumed to include an objective of price
            stabilization and optimal policies corresponding to this
            objective are assessed. Considering fully optimal policies
            under commitment as well as optimal simple rules, it is
            shown that adopting simple rules can achieve most of the
            gains from fully optimal policies, with both potentially
            allowing for lower stockholding levels and costs.
geo_reg_key: 517191,517212,517198
repnme: repnme: Managing food price volatility in a large
            open country : the case of wheat in India
display_title: Managing food price volatility in a
            large open country : the case of wheat in India
listing_relative_url: /research/2016/02/25860944/managing-food-price-volatility-large-open-country-case-wheat-india
topicv3: Price Volatility m1326059 1150,Trade m1326924 698,Social Assistance m1327201 1466,Trade Policy and Integration m1327407 775,Trade Policy m1327640 776
publishtoextweb_dt: 2016-02-02T00:00:00Z
historic_topic: Finance and Financial Sector Development,Macroeconomics and Economic Growth,Private Sector Development,International Economics and Trade
no_of_pages: 46
author_keys: 0: author_key: 1170456
1: author_key: 95255
2: author_key: 96573
model_extractions: WPS7551 Policy Research Working Paper 7551 Managing Food Price Volatility in a Large Open Country The Case of Wheat in India _Christophe Gouel Madhur Gautam Will J. Martin_ Agriculture Global Practice Group February 2016
Policy Research Working Paper 7551

# **Abstract**

India has pursued an active food security policy for many years, using a combination of trade policy interventions, public distribution of food staples, and assistance to farmers through minimum support prices defended by public stocks. This policy has been quite successful in stabilizing staple food prices, but at a high cost, and with potential risks of unmanageable stock accumulation. Based on a rational expectations storage model representing the Indian wheat market and its relation to the rest of the world, this paper analyzes the cost and welfare implications of this policy and unpacks the contribution of its different elements. To analyze alternative policies, social welfare is assumed to include an objective of price stabilization and optimal policies corresponding to this objective are assessed. Considering fully optimal policies under commitment as well as optimal simple rules, it is shown that adopting simple rules can achieve most of the gains from fully optimal policies, with both potentially allowing for lower stockholding levels and costs.

This paper is a product of the Agriculture Global Practice Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at mgautam@ worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Managing Food Price Volatility in a Large Open Country: The Case of Wheat in India**

**Christophe Gouel**<sup>**1**</sup> **Madhur Gautam**<sup>**2**</sup> **Will J. Martin**<sup>**3**</sup>

_JEL classification:_ F13, O13, Q11, Q17, Q18 _._

> 1 INRA, Économie Publique, and CEPII (christophe.gouel@grignon.inra.fr)

> 2 World Bank, Agriculture Global Practice, The World Bank (Mgautam@worldbank.org).

> 3 International Food Policy Research Institute (IFPRI) (w.martin@cgiar.org).

A revised version of this paper has been accepted for publication in Oxford Economic Papers.
# **Acknowledgements**

This work was supported by the World Bank Knowledge for Change Program [TF010230]; by the South Asia Food and Nutrition Security Initiative [SAFANSI] managed by the World Bank with contributions from the Governments of United Kingdom and Australia; the European Union’s Seventh Framework Programme FP7/2007–2011 [290693 FOODSECURE to C.G.] and the CGIAR Research Program on Policies, Institutions, and Markets.

The authors gratefully acknowledge the feedback and comments from Prachi Mishra (Senior Economist) and her team at the Office of the Economic Adviser, Ministry of Finance, Government of India. The study has benefited from feedback and comments from the participants at the Indian Econometric Society Meetings in Mumbai, in December 2013, and the Food Price Volatility Workshop organized by the Global Development Network, the IMF, and the OCP Policy Center at Rabat, Morocco, in February, 2014, where preliminary model results were presented. The authors also benefited from feedback from Brian Wright, Sergiy Zorya, and Julian Lampietti, and from discussions and inputs from Donald Larson and Maros Ivanic.

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# **Summary**

India has pursued an active food security policy for many years using a combination of trade policy interventions, public distribution of food staples, and assistance to farmers through minimum support prices defended by public stocks. This policy has been quite successful in stabilizing staple food prices, but stabilization has come at a high cost, raising concerns whether the costs exceed the associated benefits. Further, it carries the risk of accumulating unmanageably large stocks, even as food prices remain high, as has been the case in recent years with stocks far exceeding the established norms for buffer stocks and strategic reserves.

To analyze the welfare and cost implications of the current policies, this study relies on a rational expectations storage-trade model to represent India’s wheat market and its relations with the rest of the world. The model helps evaluate the current policies for managing wheat price volatility in India and consider alternative stabilization policies. Representing current policies is a challenge, however, because they appear to be highly discretionary. To capture their essence, they have been represented as simple rules, defined as functions of world and domestic conditions. The alternative stabilization policies are derived from the maximization of a social welfare function that includes a motivation for price stability. The model developed in this study contains two innovations for developing price stabilization policies: It designs optimal price stabilization policies for a large-country case, and it considers simple rules for stabilization and demonstrates how closely their effects can approximate those of a fully optimal policy.

The current policies pursued by India are costly for two reasons: trade and storage policies are not well coordinated, and in the absence of clearly defined rules for the release of stocks (other than for the public distribution system), the storage policy effectively translates to a buy-and-hold strategy. Large stock levels are held for long periods, and procurement continues regardless of the current level of stocks. But stock releases, beyond the public distribution system releases, are insufficient to dampen domestic price rises or keep stock levels in check. Instead, the government has occasionally had to dispose of wheat stocks on the world market.

Another key policy consideration is the cost of public grain storage. The current costs, declared by the Food Corporation of India, are four times higher than long-run costs estimated for other countries by the World Bank and Food and Agriculture Organization (FAO) (2012). Such high costs make it extremely difficult to justify public storage in India on economic grounds, as it would be much less costly to rely on domestic private storage or on world trade and storage abroad. For that reason, the alternative policies considered here are based on providing sufficient incentives to induce more cost-efficient private stock holders, or a lower-cost public storage agency, to store grains in a socially optimal way.

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The model is used to identify the levels of storage and trade under an optimal policy maximizing total welfare. But since a fully optimal policy is state-dependent and may be difficult to implement, more practical policy guidance may be obtained using some optimal simple rules for stabilization. These are simple pre-determined rules of public policy whose parameters are chosen to maximize the same welfare function. Two simple rules considered are a constant subsidy to private storage (as storage policy) and tariffs defined by an isoelastic function of border price (as trade policy). A notable result from the model is that the optimal simple rules achieve welfare gains approaching those obtained by implementing a fully optimal policy. Under simple policy rules, private storage is incentivized to exceed a storage level above the competitive level. Since private storage reacts in appropriate ways to price behavior, it combines well with the trade policy, a result that is extremely difficult to achieve with a price-band program (or its variants).

Two main messages emerge from the analysis in this paper. One is that the broad approach adopted by India to manage price volatility, using a combination of trade and storage policies, is logical for a large country with large gaps between import costs and export prices. The second is that, using this combination of policies with some modifications, India could significantly improve its total welfare and reduce its costs (primarily storage costs). Price stabilization policies are generally not regarded as first-best policies, as they do not directly target the underlying market failures, which are often thought to be related to the economic agents’ lack of capacity to cope with shocks. Yet price stabilization policies hold considerable appeal for many policy makers given their strong dislike for price instability and the fact that certain market failures may prevent the first-best policy options from achieving their goals. Considering these factors, it is important to identify better policies to achieve price stability.

In India, given the current circumstances, it appears that significant cost savings (through a combination of storage and trade costs) could be made without any significant net loss in real income through a less insulating trade policy implemented in conjunction with storage rules that lead to stock levels similar to, but above, competitive storage levels. These gains are predicated on efficient storage, however. The current public costs of storage appear to be extremely high and make it difficult to justify any level of public storage in the country without significant overall loss in welfare.

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# **1 Introduction**

India has aggressively pursued food security for many years. For India’s policy makers, the prices of staple foods—particularly wheat and rice—raise major concerns. To protect poor consumers from high prices, and to lower the cost of food in normal times, a Public Distribution System (PDS) provides food to low-income consumers at concessional prices. To protect producers from low prices, a pre-announced Minimum Support Price (MSP) places an effective floor on domestic prices, defended by the government’s accumulation of staple food stocks. India also pursues an active trade policy to insulate the domestic market from fluctuations in world prices of these staples. Together, these policies have been quite successful in stabilizing domestic prices, but concern is growing over the policies’ mounting costs, potential inefficiencies, and the stark juxtaposition of large and growing public stocks with rising food prices (Basu 2011).

Concern about food prices is common in countries with many poor people who are vulnerable to price spikes or price slumps. In that context, policy makers often favor policies that reduce the volatility of staple food prices. Such policies have been especially prevalent since the 2007/08 world food crisis, which highlighted the potential instability in world food markets (Demeke, Pangrazio, and Maetz 2009; Gouel 2014).

This study looks at alternatives to address some of the challenges facing policy makers in these situations. Based on the assumption that policy makers seek to maximize social welfare, and specifically taking into account their dislike for price volatility, this study assesses current policies for wheat in India and then examines alternatives. The analysis relies on a rational expectations model of storage and trade that represents two regions—India and the rest of the world—and their interaction on the wheat market. The economic agents in the model include producers, consumers, and holders of stocks. Producers base their planting decisions on expected prices at harvest time. Stock holders make decisions on how much to store from one year to the next based on the price they expect next year, the price of grain this year, and the cost of storage. International trade is represented by spatial arbitrage conditions. Current policies are incorporated by identifying patterns that enable them to be represented as simple rules, defined as functions of world and domestic conditions. The model is calibrated using 2012 data on India’s wheat market and solved numerically.

Alternative stabilization policies are designed based on the maximization of a social welfare function that includes a quadratic loss function in prices. In addition to a fully optimal policy, which gives welfare-maximizing levels of storage and trade in all situations, the use of simple rules of intervention is also considered. Past research suggests that simple rules might yield a large share of the benefits of an optimal policy (Gouel 2013c) while being easier to design and to 5
implement. The simple rules considered are a constant subsidy to private storage and trade tariffs defined by an isoelastic function of the border price.

A final issue addressed in the study is the cost of public storage in India, which appears to be much higher than in other countries. With such high costs, public storage is extremely difficult to justify on economic grounds. It would be far less costly to rely on domestic private storage or on world trade and storage abroad.

Beyond the analysis of current and alternative policies for wheat in India, this study contributes to the literature on the design of food price stabilization policies (Gouel 2013a, 2013c; Gouel and Jean 2015). It augments the modeling undertaken for previous studies by considering the case of a large country. Modeling a large-country case makes it possible to assess the effect of countercyclical policies on the world market, a very contentious issue since the 2007/08 spikes in food prices, which were partially precipitated by widespread use of export restrictions (Martin and Anderson 2012). A second contribution of this study is that it confirms, for an open-economy setting, Gouel's (2013c) results that optimal simple rules can achieve welfare gains close to those from fully optimal rules. Optimal simple rules are found to be slightly less successful in an open economy setting compared to a closed economy setting, however, because they do not exploit the country’s market power as do fully optimal policies.

Two main messages emerge from the analysis in this paper. One is that the broad approach adopted by India, using a combination of trade and storage policies, is appropriate when the welfare measure is extended to account for a preference for food price stability. The second is that, using this combination of policies with some modifications, India could significantly improve its total welfare and reduce its costs (primarily storage costs). Price stabilization policies are generally not regarded as first-best policies as they do not directly target the underlying market failures, which are often thought to be related to the economic agents’ lack of capacity to cope with shocks. Yet price stabilization policies hold considerable appeal for many policy makers given their strong dislike for price instability and the fact that certain market failures may prevent the first-best policy options from achieving their goals. Considering these factors, it is important to identify better policies to achieve price stability.

In India, given the current circumstances, it appears that significant cost savings (through a combination of storage and trade costs) could be made without any significant net loss in pure welfare (defined as the sum of producers or consumers surplus) through a less insulating trade policy implemented in conjunction with storage rules that are similar to, but above, competitive storage levels. These gains are predicated on efficient storage, however. The current public costs 6
of storage are extremely high and make it difficult to justify any level of public storage in the country without significant overall loss in welfare.

The outline of this paper is as follows. After the main features of India’s wheat market are outlined in Section 2, Section 3 develops the model representing India’s wheat market and its relation to the world market. A representation of welfare in this framework is proposed, taking into account the observed preference for food price stability (Section 4). A core assumption is that the cost of risk to policy makers rises more than proportionately with deviations from the mean price. Section 5 begins by considering the mathematical representation of current policies and the design of alternative stabilization policies. The objective function and the structure of the model make it possible to identify a set of optimal policies that minimize the costs of any given degree of volatility. Simple rules of intervention are considered as well. Section 6 develops a numerical calibration for the model and presents the numerical results. Section 7 presents the conclusions.

# **2 India’s wheat market**

India has undergone a major transformation since the 1960s, from being a highly insecure food importer to a consistent net-exporter of agricultural products (Gulati, Jain, and Hoda 2013), and from a policy framework that discriminated against agriculture to a relatively more neutral domestic policy regime (Pursell, Gulati, and Gupta 2009). The evolution of India’s wheat market reflects this profound transformation—from being a chronic food-aid recipient to an often substantial net-exporter (Figure 1, left panel).

**Figure 1: Wheat trade and stock levels in India**

<!-- Start of picture text --> Stock level<br>Stock-to-use ratio<br>1960 1970 1980 1990 2000 2010 1960 1970 1980 1990 2000 2010<br>Market year Market year<br>Source: USDA 2013.<br>25<br>45.5<br>5<br>20<br>36.4<br>15<br>27.3<br>0<br>10<br>18.2<br>Net trade (X-M, million ton) -5 Beginning stocks (million ton) 5 9.1<br>0 0<br><!-- End of picture text --> 7
Traditionally India has sought to achieve food security through actions to ensure that food is available and accessible. Policy has focused on an aggressive drive toward self-sufficiency in food grains, encompassing comprehensive support to farmers through the introduction of improved varieties and inputs; rapid expansion of irrigated area; subsidies of various inputs; efforts to maintain relatively stable producer prices; and management of the long-run relationship between domestic and world prices.

Protecting poor consumers through stable market prices and access to subsidized food has been another major feature of India’s food policy. Aside from these interventions, for decades the government has maintained public stocks of food grains to buffer against production shocks, assist in maintaining national food self-sufficiency, stabilize food prices, and supply the PDS. These policies are supplemented with highly interventionist trade policies that rely on a combination of tariffs and periodic quantitative restrictions.

These policies have been highly successful in stabilizing both production and prices. Irrigation expansion in particular has been a major contributor to wheat production stability, with over 90 percent of wheat cultivated now on irrigated land (Figure 2). The reduction in production variability is even more impressive considering output now is almost four times the level in 1970.<sup>4</sup>

**Figure 2: Stability of Wheat production and irrigation expansion**

<!-- Start of picture text --> 0.25 100<br>0.2 80<br>0.15 60<br>0.1 40<br>0.05 20<br>0 0<br>Output Variability (5 year rolling Std. Dev. ‐ left axis)<br>1950‐51 1953‐54 1956‐57 1959‐60 1962‐63 1965‐66 1968‐69 1971‐72 1974‐75 1977‐78 1980‐81 1983‐84 1986‐87 1989‐90 1992‐93 1995‐96 1998‐99 2001‐02 2004‐05 2007‐08 2010‐11*<br><!-- End of picture text --> _Source:_ Authors using data from Directorate of Economics and Statistics, Dept. of Agric. and Cooperation With higher and more stable output, the government is compelled to procure increasing volumes of wheat at the pre-announced MSP. It acquires wheat early in the marketing season and then uses the accumulated stocks throughout the year to supply the PDS. Since the quantities

> 4 It is important to note that while production shocks, driven by the vagaries of the monsoons, are a fact of life in India, the largest production decline since 1950-51 was in 2002-03 at 7.01 million tons in absolute terms and 10% in relative terms from the production level of the previous year.  In terms of rainfall, 1972 and 2009 had the worst monsoon years over the past 110 years, each experiencing 22% less rainfall than the 110 year average. Yet wheat production fell in 1972 by only 1.7% but grew marginally (0.02% or 0.1 million tons) in 2009.

8
procured at the minimum price may exceed the needs of the PDS, it is necessary at times to dispose of excess stocks. These releases are made on a discretionary basis, however, and as Basu (2011) explains, an emphasis on selling the stored grains at prices that cover the purchasing price and storage costs frequently makes it impossible to dispose of stocks in this way. Basu also notes that releases often fail to occur in periods of high prices. On occasion, the excessive accumulation of stocks requires the government to export its stocks, including by writing down the price, as reportedly done in 2002–03 (Ganesh-Kumar et al. 2012).

From 2007, during several years of high world prices, India used trade barriers to restrict grain exports and keep domestic prices down. The net outcome of these actions, together with public procurement, has been a substantial rise in stocks (Figure 1, right panel). The trade policy measures pushed domestic prices down relative to world prices, making the MSP the effective market price and requiring increases in stocks to support this price. Trade and stockholding policies appear to have been working against each other during this period, with trade policies holding down domestic prices while stock accumulation in support of the MSP drove them up.

# **3 Core model: The laissez-faire situation**

A rational expectations two-country storage-trade model (similar to Larson et al. 2014 and following the first development of a storage trade model by Williams and Wright 1991, Ch. 9) is used to model the market for wheat in the absence of any intervention—a context in which behavior does not follow from government decisions but from the economic responses of decentralized firms and consumers. It is a partial equilibrium model, representing the behavior in each country of competing stock holders, producers, and consumers. This model is a departure from previous studies on India (such as Srinivasan and Jha 2001) in that it represents the rest of the world (RoW) not as an exogenous price process but as a single large “country” with its own demand and stochastic supply. This specification is important for two reasons. First, a storage model is a better representation of world price dynamics than any simple dynamic process (Cafiero et al. 2011). Second, although the policy response of the RoW is not modeled, important feedback effects between India’s food policy and the behavior of the RoW take place through the reactions of private stock holders and producers in India and abroad. These effects can be accounted for only if all agents are explicitly represented. With respect to the RoW, India represents a large share of the market, so India’s stabilization policies affect the world market.

Regions RoW and India are indicated by the subscript �∈��, ��. Producers make their production choices and pay for inputs one period before bringing output to market. However, actual production is uncertain. The difference between planned and actual production is a random 9
<!-- Start of picture text --> tlt-+1 = 6E, (Pri ets1) — Y" (AL),<br><!-- End of picture text --> (Hf) Et41 4 Ht Et t+1 <!-- Start of picture text --> t<br><!-- End of picture text --> OE, (Piy1€f41) = 0" (A).

S20 L PP +k" —6E,Pi,, = 0, gr xX" kt’ Xi >0 LP? +6,, => PP fors #1, r 6,5 rs At Ay = St_y + Alef A, + Xf =D" (Pf) +S, 4+ Xf fors #r. D" (Pr) = dTMPr”TM dTM >0 a’>0 L
wr' (AY) =a" +b’ At a” bb >0 {Az} {PIS}, Hi, XT} r € {i,w}.

We To ~~pte~~ rqyr r rygr ~~bY Ar”~~ rer Yr r\cr rT CS = fp D(p)dp = [dp*** (1+ ah = a PH" — PM) (1 +) P
Costt wy ~~pyre~~ _ ~~brHy?~~ = —d" ~~+~~ PEAY — a Hy ~~~*~~~ (ke" + PES — Cost Costi = Costi® + Cost?” ital ey) . _P} - ._. b'Ht . , . KK, x, wi = —d! ~~+~~ PiAt — aH ~~-—\~~ — (k! + PE)Si — Cost; —— ~~(P~~ i — PY’ K2=0 P!

pi K y(R —v)D'(P*)/P! y R Vv K K
## **_4.3 Cost of the PDS_**

The cost of the PDS is assessed here as the direct cost of the subsidies in the PDS, measured as the difference between the open-market price at the time and the subsidized price at which grains are released through India’s Fair Price Shops. This cost abstracts from the direct costs of the scheme, such as administrative costs, costs of transport to final consumers, or any costs associated with leakages or fraud—all of which are outside the scope of the model used. The cash flow of the PDS subsidies is equal to the distributed volumes times the difference between market and subsidized prices: where the different categories of households benefiting from the PDS—households above the poverty line (APL), below the poverty line (BPL), and the “poorest of the poor” households receiving grain subsidized under the Antyodaya Anna Yojana (AAY) scheme—are indexed by �∈����, ���, ����; �� is the distributed volume; and ����� the subsidized price. Consistent with the modeling of stock releases in Section 5.1.1, �� are assumed to be constant and sum to Θ, the total volume released through the PDS. The values can be found in Table 1.

**Table 1. Values used to assess the cost of subsidies in the PDS**

||**Above thepoverty line**|**Below thepoverty line**|**Antyodaya Anna Yojana**|
|---|---|---|---|
|**Subsidized**<br>**price,**<br>��<br>���|6,100|4,150|2,000|
|**(Rs/t)**||||
|**Share of volume released,**<br>�� **(% of**�**)**|51|32|17|

_Source:_ Food Corporation of India.

The measured costs of the PDS do not appear in the national welfare measure, since it is considered to be a pure transfer that does not affect the overall economic welfare measure used in this representative-agent model. Clearly, the targeted nature of this intervention may result in a substantial increase in social welfare if the social welfare function attributes greater marginal utility of income to the beneficiaries relative to those paying the costs of the scheme.

# **5 Price stabilization policies**

This section begins by incorporating India’s current wheat policies in the analytical model. As noted, these policies target the three main channels for price stabilization—production, storage and trade. Next, the derivation of optimal price stabilization polices is outlined, followed by proposals for some optimal simple rules that might serve as a more realistic, practical policy alternatives.

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The social welfare outcomes under the optimal simple rules are then compared to those under the fully optimal policies to test how well they perform.

# **_5.1 India’s current wheat policies_**

India’s current trade and storage policies are adjusted regularly at the discretion of the government, depending on prevailing market conditions and policy makers’ assessment of which changes are required. To analyze the effects of these policies, they are represented in the laissez-faire model as rules that respond to the market context. The model is designed to capture the indicative impacts of current policies rather than to provide precise figures. The following sections describe how the main structural characteristics of current policies are incorporated into the model.

# 5.1.1 Storage policy and the PDS

Public stocks are built up largely through purchases at the announced MSP. For simplicity, and given that the model focuses on price volatility stemming from production shocks (domestic and foreign), the MSP is assumed to be constant and equal to the steady-state price, which is the price in the absence of shocks—that is, under normal harvest and demand conditions. In the model, the MSP therefore plays the role of a floor price that the government defends through public storage. Public stock accumulation, Δ�<sup>��</sup> , is governed by The critical influence on the market is the difference between government stock purchases, Δ����, and releases under the PDS, Δ����. Accounting for public stock purchases and releases, the Indian market clearing equation is adjusted as follows with respect to the laissez-faire model: Volume released for the PDS, denoted Θ, is assumed to be constant and, based on data from the previous decade, equal to 12 million tons per year. The model allows for the possibility that existing public stocks ���� �Δ����� may not always be sufficient to cover the quantities required for the PDS. If procurement at MSP is not enough to supply the PDS, the remaining quantities are assumed to come from open-market purchases. Such purchases need not be represented here, because they are analogous to a transfer operated by the government. Stock releases therefore obey the following equation: Because releases for the PDS are not state-contingent and the MSP tends to be set at a high level, procurement levels are often high relative to requirements. Without a policy for systematic 14
xs® xs° = max(0,S¢ + Asét — as&- — §4), SG AW +xXi+x5° = DY(PY) +5" +X _ St = Sty + ASE, — ASE, — XPG t Costi® =k! (Sf + ASE — asé~ — x5") +P!(AS&* — ASE-) —X$°(PY — iy).
<!-- Start of picture text --> (1 +7)<br>M_ Ww B<br>xX _ Ww B<br>Tf = ay (P} _ Oiw)<br>TTM TX B<br>1+<br>Xv >0 1 (PY +6,)TM = Pi<br>Xi>0 1 Pi = (PY -Oiw)TX<br>CostyTM” = (TX — 1)Xi (PY - Oy)<br>—(TH" — 1)X (PY + Oyi).<br><!-- End of picture text -->
CosttTM = Xi(Oiy + Pi — P}”) + XP (Owi + P” — PD.

00 Atal igi2 ~~——~~ — (k' + P})S} — Cost, Ey) 6 —d' ~~+~~ Pit — a'H} —- t=0 K.. _. _ <u>—(P; _</u> ny}
probability of stockouts and collapse when stocks reach unmanageable levels is very high (for additional discussion of this issue, see Wright 2011 and Gouel 2013c).

Previous studies (Gouel 2013c; Gouel and Jean 2015) have found that optimal storage policies tend to behave similarly to a competitive storage rule. Building on the idea that private stock holders are good at reacting to evolving economic situations but may provide too little stabilization in the absence of intervention, the prospects for a very simple policy to encourage more private storage (specifically, a constant subsidy to private storage in India) are considered here. Such a subsidy should increase stock levels, which in turn would stabilize prices. As noted, the resulting storage rule could also be implemented through public stocks. Accounting for the constant subsidy �, the stock holders’ arbitrage equation (3) becomes for India To facilitate the interpretation of results, the subsidy is expressed as a percentage of physical storage costs �<sup>�</sup> . In this case, the public costs of storage are defined by In the absence of an upper bound on stock levels, a necessary condition for a stationary rational expectations equilibrium to exist is for storage to be costly. For instance, if price stays constant (that is, at a steady state), storage should not be profitable and so should not take place, which can be stated using equation (26) as This value will be used in the welfare maximization as an upper bound on � to ensure convergence to a stationary equilibrium.

Trade policies are assumed to be set following the rule in current use, indicated in equations (19) and (20). However, �, the elasticity of border protection with respect to border price, will be chosen to maximize welfare.

Taking into account the public costs defined by equations (23) and (27), the optimal simple rules are the rules defined by the parameters � and � that maximize 18
00 Ata! i i2 Eo bf gi ~~ve~~ PiAt —a'H! ~~bite~~ al Pils! — Cost! ~~Uta~~ t Prat t ~~-——~~ —— [k'(1 — ¢) + PES?— Cost; t=0 K.. _. ~~Fr~~ ay} <!-- Start of picture text -->
|<br>|<br>|<br>OO<br>|<br>OO<br><!-- End of picture text -->
below the fob price. To reflect the fact that on average India is more likely to export rather than to import, the steady-state price is calibrated closer to the fob price than the cif price.

Based on detrended production, the random component of wheat production is estimated to have a standard deviation of 0.035 in both regions, and to be independent across time and space. The equality of production variability between the RoW composite and the single country of India is unusual and likely reflects the diversity of production regions within India and the fact that almost all of India’s wheat is grown under irrigation. In general, the volatility of output would be expected to be much higher for an individual country than for the RoW composite, because of the low correlations between the outputs of different countries.

Annual interest rates are assumed to be the same for each region, at 5%. Choosing appropriate storage costs is important, as this variable significantly affects the results. For private stock holders in India and in the RoW, per unit storage charges are assumed to be US$ 22.40 per ton, based on estimates of worldwide benchmark private sector costs from a recent World Bank study (World Bank and FAO 2012).<sup>7</sup> Combined with the opportunity cost of the grain, this physical storage cost entails an overall storage cost at steady state of 17.5% of India’s domestic price. Public storage costs in India appear to be much higher, at around US$ 87 per ton,<sup>8</sup> but these costs are likely to be underestimated because they neglect the cost of storage losses. Anecdotal evidence appears to indicate that such losses are large because storage conditions are inadequate,<sup>9</sup> but the actual rate at which stocks deteriorate is unknown. For private storage costs, following (29), the maximum storage subsidy compatible with a stable steady state is equal to 1.4. Similarly, for public storage costs of US$ 87 per ton, the maximum subsidy is 1.1.

7 Private storage costs in India are competitive relative to the global benchmark used here. Estimates of storage costs from National Bulk Handling Corporation, a private entity, are equivalent to about US$16 per ton in general, but a bit higher at about $19.2 in the National Capital Region or port locations (Anil Choudhary, Managing Director and CEO, _personal communication)_ . Data from IFC from recent modern grain silos projects indicate a cost of storage at about US$ 19.75 per ton in Punjab, where the private developer of storage provides land, and $11.5 per ton in Madhya Pradesh, where land is provided by the government. The Food Corporation of India has fixed ceiling rates for storage rental from private providers under the “Private Entrepreneurs Guarantee” (PEG) scheme at Rs 4.78 per quintal per month, which translates to only US$ 9.56 per ton (see Department of Food and Public Distribution website at http://dfpd.nic.in/?q=node/34). Finally, the base storage rental rates established by the Central Warehousing Corporation for private sector bidding for wheat storage under normal access conditions (that is flat terrain with easy access such as may be expected in the national capital region) are about US$ 18 per ton (see http://www.cewacor.nic.in/Docs/commodity_tariff_2013-14.pdf).

8 The economic cost of the Food Corporation of India available at http://fciweb.nic.in/finances/view/9, accessed May 12, 2014. For the financial year 2012/13, the annual rate of buffer stock carrying cost is estimated to be Rs 4,744.6 per ton. The average exchange rate from April to March was 54.35 Rs/US$, which leads to an annual storage cost of US$ 87.3 per ton.

9 “As crops rot, millions go hungry in India,” Reuters, July 1, 2012; “2,400 MT wheat rotting in govt granaries for past 2 years,” The Times of India, May 7, 2013.

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Indian import costs are based on international trade costs and port charges from Pursell, Gulati, and Gupta (2009). For export costs, the port charges are the same as for imports, but international trade costs are assumed to be smaller (2/5), as India exports wheat to less distant countries than those from which it sources its imports (Pursell, Gulati, and Gupta 2009 do not provide information on export costs). These trade costs exclude domestic transport costs. The exchange rate plays no role in the model; it serves only to present the results and is set at Rs 50 Rs per US$ 1, which is the exchange rate that prevailed in early 2012.

The selection of appropriate elasticities is challenging—the literature is uncertain on this point—but crucial, as they drive many results. The literature on commodity price dynamics, which implies relatively low demand elasticities (Cafiero et al. 2011; Roberts and Schlenker 2013), puts the RoW demand elasticity at –0.12. An elasticity this low is unlikely to be valid for a lowermiddle-income country such as India, however, where demand for this staple food is expected to be more elastic than the world average (Muhammad, Seale, and Regmi 2011). Based on recent estimates by Kumar et al. (2011), a price elasticity of –0.3 was ultimately selected.

The supply elasticity at steady state is 0.2, in line with the commonly used supply elasticity for wheat. The combination of this elasticity and of target values of price and production at steady state makes it possible to determine �<sup>�</sup> and �<sup>�</sup> . The rational expectations storage model is approximated numerically (see Annex 3 for details).

To evaluate social welfare and to design optimal policies, a weight is assigned to wheat price volatility in the social welfare function. No ready source of information is available for this policy parameter. As explained in Section 4.2, the parameter characterizing the social preference for price stability, �, could be interpreted as a second-order approximation of the equivalent variation for a risk-averse consumer, reflecting income and risk-aversion effects. This interpretation is used to guide the choice of relevant values, and consumers are assumed to spend 10% of their income on wheat. The steady-state values are used as the reference levels for demand and price. In seeking to define optimal policies, several values will be considered for � to illustrate how policies vary when different welfare weights are assigned to price volatility. The difference between the parameters of relative risk aversion and income elasticity (���) are varied from 0 to 12. In unpacking current policies (6.2) and exploring fully optimal policies (6.3), the analysis retains ����6.

# **_6.2 Unpacking current policies_**

This section characterizes the effects of the current storage and trade policies described in Section 5.1. Three scenarios are considered as alternatives to laissez-faire: a scenario with storage policy alone, a scenario with trade policy alone, and a scenario combining both policies. These 21
policy experiments make it possible to unpack the contribution of each policy. The experiment relying only on storage policy assumes that India liberalizes its wheat trade, including the use of export subsidies to dispose of excess stocks. Similarly, the trade policy assumption implies no public storage.

In interpreting the results that follow, a word of caution is in order regarding the limitations of rational expectations storage models with respect to what they aim to represent and how well they achieve that aim. First, the only motivation for private storage assumed here is intertemporal arbitrage. While that is an important motive per se, it excludes many other important transactional or precautionary motives that could explain much actual stock-holding behavior (Williams 1986). Given that trade is instantaneous in the model, there is also no reason to accumulate stocks to account for time to ship (Coleman 2009). These motivations are quantitatively important, as evidenced by historical stock data. A purely speculative motive would allow for regular stockouts, while at the world level the stock-to-use ratio never decreases much below 20%. Because of this focus on one motive for storage, the simulated statistics on private stock levels are likely to underestimate real storage. Second, stabilization policies are represented as free of any flaws (except potentially in their design): The policies perfectly follow the decided rules without any delay or discretionary political interventions. Such a perfect representation of India’s wheat policies is likely to overestimate the achievable price stabilization. Third, for the sake of tractability, the model focuses on two main sources of price volatility: production shocks in India and in the RoW. This focus excludes other sources of volatility such as shocks to exchange rates, and prices of oil and other agricultural commodities. Overall, the model aims to capture the most important types of spatial and intertemporal arbitrage, but the inherent complexity of this issue implies that the model should not be considered a forecasting tool but rather a means of quantitatively illustrating the consequences of each policy option.

Table 3 presents the effects of the various instruments of current policy on the asymptotic distribution of the model.<sup>10</sup> Storage and trade policies alone provide similar levels of price stabilization, with storage decreasing the coefficient of variation a little more than trade policy. The ability of storage to achieve such price stability in an open economy comes from the fact that India’s domestic price is often between the fob and cif margins. This assessment is confirmed by the fact that world price volatility is little affected by a storage-only policy. The fundamental difference between the stability provided by trade and storage concerns extreme prices. The storage policy truncates low prices almost perfectly, but it cannot prevent all price spikes and does little to reduce the occurrence of high prices. The explanation for this outcome lies with the rule

> 10 See Annex 3 for details about the simulation method.

22
governing the storage policy. The policy is not designed to operate as a price band, with stocks released to prevent high prices; rather, stocks are released in a fixed amount every period to supply the PDS. In contrast, the trade policy mostly truncates high domestic prices. Together both policies are extremely effective in stabilizing the domestic price, because of the complementarity between the instruments. Trade policy prevents public stocks from being exported when the world price spikes, preventing any leakage from the operation of the storage policy to the world market.

**Table 3. Unpacking current policies, statistics (quantities in million tons)**

|**Variables**|**Laissez‐faire**|**Tradepolicy**|**Storage policy**|**Both instruments**|
|---|---|---|---|---|
|**Indiaprice(Rs/t)**|||||
|**Mean**|9,809|9,527|9,882|9,486|
|**CV(%)**|14.39|10.68|10.12|3.13|
|**Quantile 10%**|8,223|8,307|9,417|9,417|
|**Quantile 90%**|11,544|10,910|11,085|9,417|
|**RoWprice(US$/t)**|||||
|**Mean**|200.5|202.3|199.7|202.5|
|**CV(%)**|20.70|23.99|19.57|23.28|
|**Quantile 10%**|160.2|160.2|159.8|160.3|
|**Quantile 90%**|258.8|269.2|251.6|272.3|
|**India demand**|||||
|**Mean**|85.77|86.39|85.41|86.33|
|**CV(%)**|3.98|3.11|2.58|0.84|
|**Mean Indiaproduction**|87.13|86.66|87.37|86.62|
|**Mean India storage **|||||
|**Private**|0.10|0.02|0.00|0.00|
|**Public**|||4.21|10.38|
|**Mean RoWprivate storage **|4.05|4.78|3.69|4.75|
|**Mean exports**|1.38|0.27|1.96|0.18|
|**Mean imports**|0.02|0.00|0.01|0.00|

The policies have little effect on India’s wheat production. Since producers are assumed to be risk neutral in their behavior and their marginal cost linear in the production level, their production decisions depend not on price volatility but on the expectations of prices times the yield shock (equation (2)), which vary little between the policies considered, as evidenced by the mean price changes.<sup>11</sup> Under all scenarios, the model allows for the possibility of competitive domestic storage in India. In practice, stock holders find few profit opportunities under scenarios that include active trade and storage stabilization policies, since these policies rarely allow speculators to cover their costs. A significant level of private storage arises only when both storage and trade policies are

> 11 This result is confirmed in a context of risk-averse producers; see Annex 4. India’s wheat production is largely unaffected by the stabilization policies, unless producers are assumed to have a very high level of risk aversion.

23
removed. These policies do have an effect on private storage in the RoW, however. By increasing world price volatility, the trade policy option increases the profit opportunities from speculation and raises the mean stock level. The storage policy crowds out part of foreign storage, as it diminishes world price volatility slightly. The combination of the two policies is dominated by the effects of the trade policy and storage increases worldwide.

Public stocks reach a much higher level when storage policy is combined with trade policy. This outcome is explained by the high degree of insulation permitted by trade policy. Combined with a trade policy of this type, public stock accumulation is almost perfectly insensitive to foreign availability, since the foreign price does not influence the domestic price. Storage releases for the PDS are constant and do not differ across scenarios. Only the releases for direct export to dispose of excessive stocks differ, as they are not allowed in the storage-only policy. For that reason, differences in average stock levels are explained by the levels of stock accumulation. Without trade policy, Indian domestic prices are often driven above the intervention price (equal to the steady-state price) by foreign demand. Counter-cyclical adjustments of trade policies prevent this from happening and trigger frequent public storage interventions to defend the MSP. In this situation, which is not far from that of a closed economy, defending a floor price equal to the steady-state price is sure to lead to very large stocks.

These differences in stock levels translate to large differences in government outlays. The discounted average cost of a storage policy alone is US$ 382 million, while it is US$ 874 million when combined with trade policy (Table 4). Table 4 also displays the 5<sup>th</sup> and 95<sup>th</sup> percentiles of the corresponding annual cash flow. The cash flow for the storage policy is alternatively positive or negative depending on changes in stock levels. In both situations, 5% of the time, the accumulation of public stocks costs more than US$ 2,021 million. The storage policy is much more costly than the trade policy. On average, trade subsidies are compensated by taxes, and trade is so much reduced by these interventions that actual outlays are low.

The cost of the PDS subsidy revolves around US$ 1,150 million but varies considerably with the domestic price. Price stabilization policies clearly help to stabilize costs of the PDS; in the absence of these policies, the cost of the PDS could increase two-fold from one year to the next.

Table 4 also decomposes the welfare results for each component. Welfare components are expressed as deviations from laissez-faire and normalized as a percentage of the steady-state value of consumption of the corresponding country. Notably, when both policies are combined, storage costs reach on average 3.7 percent of the commodity budget share. Without retaining a very high weight given to food price stability, this cost is likely to exceed gains from lower price instability.

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**Table 4. Welfare changes and public cost of current policies**

|**Variable**|**Laissez‐fa**|**ire**<br>**Tradepolicy**|**Storage policy**|**Both instruments**|
|---|---|---|---|---|
|||**_Welfare changes asper_**|**_centage of consumpti_**|**_on value_**|
|**India welfare**|||||
|**Consumers' surplus**||2.43|‐1.34|2.14|
|**Producers' surplus**||‐2.65|1.42|‐2.22|
|**Total cost**||0.08|‐2.18|‐3.62|
|**Storage cost**<sup>**a**</sup>||0.00|‐2.18|‐3.74|
|**Trade cost**||0.08|0.00|0.13|
|**Cost of volatility (for**<br>�����**)**||0.39|0.31|0.66|
|**Total welfare**||0.24|‐1.80|‐3.04|
|**RoW welfare**||‐0.01|0.01|‐0.01|
|||**_Cost of thepolicies on the as_**|**_ymptotic distribution_**|**_(million US$)_**|
|**Storage policy**|||||
|**Mean**|0|0|382|874|
|**Quantile 5%**|0|0|‐1,322|‐595|
|**Quantile 95%**|0|0|2,021|2,659|
|**Tradepolicy**|||||
|**Mean**|0|‐13|0|‐26|
|**Quantile 5%**|0|‐72|0|‐160|
|**Quantile 95%**|0|6|0|64|
|**PDS subsidy**|||||
|**Mean**|1,201|1,140|1,225|1,131|
|**CV**|28.50|21.37|19.46|6.31|
|**Quantile 5%**|777|801|1,084|1,101|
|**Quantile 95%**|1,820|1,594|1,715|1,227|

a Using public storage costs.

Before analyzing optimal policies, it is important to understand the behavior of private stock holders in laissez-faire, as the simple rules consist of incentivizing them to store more. The first panel of Figure 3 represents the storage rules that are applied depending on the availability of wheat in the RoW. To facilitate interpretation, the five values of RoW availability selected correspond to 95%, 100%, 105%, 110%, and 115% of steady-state availability. For a RoW availability that is 5% less than normal (560 million tons), nothing is stored in India, because global scarcity drives the price too high to make storage profitable. Some private storage occurs when RoW availability is at the steady-state level (590), but the marginal propensity to store (out of domestic availability) in this situation is between 0.36 and 0.50, which is much lower than for higher availability. This result is explained by the coexistence of private storage and exports. When domestic availability increases, it is either exported, consumed, or stored. At a higher level of RoW availability (619—678), there is no competition with exports, so the marginal propensity to store is higher. Private storage in India reacts nonlinearly to RoW availability. Starting from low RoW availability, Indian stocks tend to increase with global availability. When RoW availability is 25
plentiful, the additional availability translates into additional RoW stocks, which depress expected prices and thus storage in India. It is interesting to note that storage becomes positive for levels of domestic wheat availability around 90 million tons, significantly above the steady state equal to 86.51.

**Figure 3. Storage rules followed by Indian private stock holders in the laissez-faire model and under simple rules for various levels of availability in the rest of the world**

<!-- Start of picture text --> 560 Laissez-faire Simple rules, R  =0 Simple rules, R  =3<br>590<br>619<br>649<br>678<br>80 85 90 95 10 0 105 80 85 90 95 100 105 80 85 90 95 100 105<br>Simple rules, R  =6 Simple rules, R  =9 Simple rules, R  =12<br>80 85 90 95 100 105 80 85 90 95 100 105 80 85 90 95 100 105<br>Availability in India (million ton)<br>10 10 10<br>8 8 8<br>6 6 6<br>4 4 4<br>2 2 2<br>0 0 0<br>10 10 10<br>8 8 8<br>Stock levels in India (million ton) 6 6 6<br>4 4 4<br>2 2 2<br>0 0 0<br><!-- End of picture text --> In contrast, for a given level of domestic availability, public stocks accumulate much more than private stocks (not displayed in Figure 3). When the domestic price reaches the MSP, the government is compelled to buy all the wheat offered for procurement. In consequence, the marginal propensity to store is equal to one until stocks reach the threshold that triggers exports from public stocks, while in laissez-faire the marginal propensity of private stock holders to store does not exceed 0.8. Since public stock accumulation is only a function of domestic availability and does not depend on previously accumulated stock, except for the direct exports, such a storage policy would be explosive: Public stocks would grow infinitely.

It is also worth noting that since the trade policy insulates the domestic market from the RoW, public stock accumulation mostly reacts to domestic and not worldwide availability. One 26
consequence is that a large accumulation of public stocks may coexist with export restrictions, which could be interpreted as the simultaneous application of both the brake and the accelerator— the price is lowered by the export restrictions and raised by the stock accumulation. This combination is not problematic in itself, however, because it can arise as an outcome of optimal trade and storage policies (Gouel and Jean 2015). In the Gouel and Jean framework of a small economy, this combination occurs at medium world price levels because stock accumulation does not increase the domestic price when the country is exporting, and the subsequent release of stocks will cause prices to fall in periods of scarcity.

In the present framework, however, the combination of export restrictions and stock accumulation is more likely to create problems. Insulated from the world price, stock accumulation does not respond to global market conditions, allowing stocks to accumulate even as the price spikes in the RoW. In addition, in the absence of effective release rules, the accumulation of stocks does not guarantee more stable future prices.

# **_6.3 Optimal policy versus simple rules_**

This section compares outcomes under the laissez-faire model, the application of an optimal policy, and the use of optimal simple rules. Because the costs of public storage are very high in India, it is challenging to find a role for storage in an optimal stabilization policy. Here it is assumed that grain is stored by private agents, and the precise stock level is optimally decided. The issue of optimal storage at a high public cost is left for discussion in Section 6.4.

Total welfare gains for India under the optimal policy represent 0.46% of the value of steadystate wheat consumption in India (Table 5). When compared with the optimal policy, the optimal simple rules prove to be very good, achieving 86% of the welfare gains of the optimal policy. One important difference between the results of these policies is that under the optimal policy, the coefficient of variation of price in India is almost four percentage points lower than under simple rules, despite similar stock levels.

Under simple rules, private storage is incentivized by a constant subsidy equal to 97% of physical storage costs. Under optimal policy, the government controls storage, but it is possible to determine the state-contingent subsidy that would make private stock holders behave similarly to the optimal policy. The optimal state-contingent subsidy would be above 100%, close to steady state, but could fall below 97% when availability in India falls below steady state. The subsidy decreases with domestic or foreign availability, because in a context of scarcity it is better to let producers increase the production level than to incentivize stockpiling.

27
**Table 5. Optimal policy versus simple rules for** ����� **(quantities in million tons)**

|**Variable**|**Laissez‐faire**|**Optimalpolicy**|**Simple rules**|
|---|---|---|---|
|**_India_**||||
|Meanprice(Rs/t)|9,809|9,544|9,583|
|Price CV(%)|14.39|4.78|8.53|
|Mean stock|0.10|0.95|0.95|
|Mean exports|1.38|0.85|0.62|
|Mean imports|0.02|0.32|0.00|
|**_RoW_**||||
|Meanprice(US$/t)|200.5|201.9|201.7|
|Price CV(%)|20.70|22.69|22.48|
|**_India welfare_**||||
|Consumers' surplus||1.66|1.70|
|Producers' surplus||‐1.79|‐1.84|
|Total cost||0.02|0.05|
|Storage cost||‐0.09|‐0.12|
|Trade cost||0.11|0.17|
|Cost of volatility||0.57|0.49|
|Total welfare||0.46|0.40|
|**_RoW welfare_**||**_‐0.01_**|**_‐0.01_**|

The simple-rules trade policy is counter-cyclical to border price, with an optimal constant elasticity of –0.49, and adjusts similarly for exports and for imports. Compared to the laissez-faire arrangement, the simple-rules trade policy has a strong anti-trade bias, significantly reducing exports and imports. The optimal trade policy does not restrict trade as much; it reduces exports but increases imports. By design, the optimal trade policy is a function of both world and domestic availability, not just world price, as under the simple-rules policy. In consequence, instead of just insulating India from the world market, the optimal policy exploits the world market to increase domestic stability, resulting in increased imports. With this policy, imports may be subsidized to decrease the domestic price when domestic availability is low, whereas imports are subsidized under the simple-rules policy only when the world price spikes.

Despite these limitations, the simple-rules policy does very well, achieving almost all of the welfare gains offered by the optimal policy. The good performance of the simple rules is not limited to the specific value of �. Table 6 shows that for other positive weights given to price stability in the welfare function, simple rules achieve a high share of the gains from the optimal policy. Since policies under simple rules are easier to analyze and to implement than optimal policies, the remaining discussion will focus on the simple-rules policies.

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**Table 6. Optimal simple rules when private agents hold stocks (quantities in million tons)**

||||**_R‐ν_**<br>|||
|---|---|---|---|---|---|
|Variables|0|3|6|9|12|
|Insulationparameter���|‐0.17|‐0.41|‐0.49|‐0.53|‐0.55|
|Storage subsidy ���|0.02|0.72|0.97|1.08|1.15|
|Share of welfare achieved by optimal<br>simple rules(%)|77.8|85.8|86.3|86.1|85.7|
|**_India_**||||||
|Meanprice(Rs/t)|9,728|9,614|9,583|9,570|9,564|
|Price CV(%)|12.77|9.91|8.53|7.76|7.16|
|Pricequantile 10%|8,232|8,632|8,818|8,906|8,972|
|Pricequantile 90%|11,343|10,954|10,769|10,644|10,544|
|Mean stock|0.08|0.48|0.95|1.31|1.68|
|Mean exports|1.09|0.73|0.62|0.56|0.53|
|Mean imports|0.01|0.00|0.00|0.00|0.00|
|**_RoW_**<br>||||||
|Meanprice(US$/t)|201.0|201.5|201.7|201.9|202.0|
|Price CV(%)|21.40|22.25|22.48|22.59|22.62|
|Mean stock|4.21|4.44|4.47|4.48|4.49|
|**_India welfare_**||||||
|Consumers' surplus|0.64|1.53|1.70|1.77|1.80|
|Producers' surplus|‐0.72|‐1.68|‐1.84|‐1.91|‐1.94|
|Total cost|0.10|0.11|0.05|0.01|‐0.04|
|Storage cost|0.00|‐0.05|‐0.12|‐0.17|‐0.22|
|Trade cost|0.10|0.16|0.17|0.18|0.18|
|Cost of volatility|0.00|0.21|0.49|0.79|1.10|
|Total welfare|0.02|0.17|0.40|0.66|0.92|

# **_6.4 Optimal simple rules of stabilization_**

The optimal simple storage policy allows for two interpretations. In the most obvious one, government provides incentives to private stock holders through the constant subsidy. Another interpretation is that the optimal storage subsidy also provides a storage rule that could be implemented by a public authority such as the Food Corporation of India, although (as noted in the calibration) storage costs are much higher for public than for private storage. For that reason, optimal storage will differ depending on whether it is undertaken by the private sector or by a public agency. The following sections seek to determine the optimal policies for both configurations, but the emphasis is on privately operated storage, given that it is much more costeffective.

# 6.4.1 Storage by private stock holders

For ����0, no weight is assigned to price volatility in social welfare. This choice does not imply that the optimal policy is free trade, because India can improve its social welfare by manipulating its terms of trade. For the trade policy, the chosen simple rule is not particularly 29
suited to maximize welfare by manipulating the terms of trade. Export or import subsidies would not make sense, because both lead to a deterioration in the terms of trade. Following Bagwell and Staiger (1990), a trade policy aimed at exploiting the terms of trade should be based on the potential trade volume, and thus on the difference between Indian and RoW availability, rather than on RoW price. Although the simple rules are not designed to take into account the motivation for terms-oftrade manipulation, trade interventions are not negligible when price volatility is unweighted (see Table 6, first column). The optimal elasticity of border protection (�) is –0.17, which already reduces price volatility from 14.39% in laissez-faire to 12.77%. The optimal storage subsidy (�) is low, equal to 2% of physical storage cost. One interpretation for this non-zero storage subsidy is that an increased storage level could lead to more exports and so to larger potential gains from terms-of-trade manipulation.

When a positive weight is given to price stability in India’s social welfare function, the optimal simple rules provide significant price stability. The two parameters that characterize the rules, � and �, increase significantly for the initial departures from a zero weight on volatility, but they progressively flatten as the risk weight is further increased. It follows from their limited progression that price volatility decreases only slightly once ��� exceeds 9. The implications are shown by calculating the cost of the policy and the welfare gains from price stabilization. The mean stock level and the cost of storage increase linearly with the preference for price stability (Table 6), while price volatility decreases at a much slower rate. The effect of storage policy on price stability decreases with existing stock levels, because stocks have to be held for longer and to be bought at higher prices.

From the observation of the 10% and 90% quantiles, the price stabilization achieved by the optimal simple rules appears to provide some protection from very low and very high prices. In laissez-faire, the 10% price quantile is equal to 87.3% of the steady-state price, while under optimal simple rules, for ����6, it is equal to 93.6% of the steady-state price. Such a policy will provide farmers significant protection from low prices.

The average stock levels for India in Table 6 are low relative to current stock levels. However, it is important to remember that these stock levels are end-of-year stock levels, rather than the within-year stocks that are frequently discussed. The stock level of 1.68 million tons for the highest level of stabilization appears comparable with the norm of 4 million tons for buffer stocks of grain recommended in the 2003 technical report (Chand and Birthal 2011, p. 4), assuming that this buffer stock is around two-thirds rice and one-third wheat. Within year stock levels are predominantly working stocks, rather than the buffer or reserve stocks that are considered in the annual model used in this paper. The results from the model might be expected to be below those generated by 30
norms for buffer stocks based on observed crop yield shortfalls, such as those derived by Chand and Birthal, because the policy considered here uses trade as well as storage policies to manage price volatility.

Figure 3 permits a comparison of storage behavior under laissez-faire and optimal simple rules. Each panel of the figure represents the private storage rules for various levels of availability in the rest of the world. Overall storage behavior is identical under optimal simple rules and laissez-faire, but the simple rules affect the stockout limits, the marginal propensity to store, and the reaction to world price. As shown in Table 6, in the absence of preference for price stability (top-middle panel of Figure 3), stock levels decrease slightly because the price stabilization coming from trade policy interventions is not compensated by a significant storage subsidy. With preference for price stability, the stockout limits (defined as the levels of domestic availability at which all private stocks are sold) decrease when � increases. In laissez-faire, the stockout limit is close to 90 million tons, while for ����12 it is close to the steady-state consumption level of 86.51 million tons. In that case, private stock holders start accumulating stocks as soon as normal consumption is satisfied, while in the absence of public intervention storage starts at a much higher level of availability.

The second effect of optimal simple rules is that they tend to increase the marginal propensity to store out of domestic availability. The storage curves are also much less influenced by RoW availability in the presence of public intervention. The increased marginal propensity to store is explained by the storage subsidy, while the decreased sensitivity to world price is explained by the trade policy interventions. Since those interventions insulate India from RoW price changes, domestic storage tends be less sensitive to foreign conditions. This point is also clear in the topright panel for ����3. When RoW availability is equal to 590 million tons, India exports for high domestic availability, as reflected in the storage rule that has a lower marginal propensity to store than for higher RoW availability. Under simple rules, however, the marginal propensity to store while exporting is much higher than it is under laissez-faire as a result of the trade policy interventions.

One consequence of the optimal simple rules is a shift in the distribution of domestic availability to the right (see Figure 4, left panel) relative to the situation under laissez-faire. Not only does the average level of availability rise but the distribution becomes more dispersed, with a higher probability of availability outcomes above the mean. These changes in availability help to stabilize domestic prices as reflected in the concentration of its density around the mean (Figure 4, right panel). The combined policy reduces the probability of both high and low price outcomes 31
but is more effective in managing the low price shocks (which can be fully absorbed using storage alone) than in reducing high price shocks (for which trade policy is more effective).

**Figure 4. Asymptotic densities of availability and price in India under laissez-faire and optimal simple rules**

<!-- Start of picture text --> Laissez faire Laissez faire<br>Optimal simple rules - R-v=6 Optimal simple rules - R-v=6<br>Optimal simple rules - R-v=12 Optimal simple rules - R-v=12<br>75 80 85 90 95 100 8000 9000 10000 11000 12000 13000 14000<br>Availability (million tons) Price (Rs/t)<br>0.0020<br>0.12<br>0.10 0.0015<br>0.08<br>Density 0.06 Density 0.0010<br>0.04<br>0.0005<br>0.02<br>0.00 0.0000<br><!-- End of picture text --> To illustrate the complementarity between the two instruments, Table 7 displays statistics on Indian prices and the parameters of the policy rules when instruments are optimized separately. The price stability achieved by using the policy instruments separately is much lower than when they are combined. The optimal coefficient of insulation from world price � is very close to its value when combined with storage. This is not the case for the subsidy to private storage, which is lower than when combined with trade policy. This lower value can be explained by two things.

**Table 7. Optimal simple rules when instruments are considered separately**

||||**_R‐ν_**<br>|||
|---|---|---|---|---|---|
|**Variables**|**0**|**3**|**6**|**9**|**12**|
|||**_Optimal_**<br>|**_tradepolicy (wh_**<br>|**_en_**���**_)_**<br>||
|Insulationparameter���|‐0.17|‐0.40|‐0.48|‐0.52|‐0.56|
|Indiaprice||||||
|Mean(Rs/t)|9,728|9,631|9,602|9,587|9,575|
|CV(%)|12.79|11.24|10.92|10.79|10.71|
|RoWprice||||||
|Mean(US$/t)|201.0|201.6|201.8|201.9|201.9|
|CV(%)|21.40|22.40|22.75|22.95|23.13|
|||**_Optimal st_**<br>|**_orage policy (w _**<br>|**_hen_**���**_)_**<br>||
|Storage subsidy ���|‐0.09|0.49|0.73|0.85|0.93|
|Indiaprice||||||
|Mean(Rs/t)|9,809|9,802|9,805|9,815|9,823|
|CV(%)|14.46|13.61|12.85|12.28|11.85|
|RoWprice||||||
|Mean(US$/t)|200.5|200.3|200.2|200.1|200.1|
|CV(%)|20.72|20.56|20.41|20.27|20.16|

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First, by reducing domestic price volatility, the trade policy reduces the incentives for private storage; these lower incentives are compensated by the subsidy to storage when both instruments are used, but this compensation is not needed when using storage policy alone. Second, the benefits from the storage policy leak to the world market without trade policy, reducing the benefits compared to those from a combined intervention.

# 6.4.2 Storage by a public agency

If the agent receiving the storage subsidy is a public agency, the results are very different. The combination of a storage cost of US$ 87 per ton and a 5% interest rate implies at steady state an overall cost to store for one year equal to 53.5% of the price. A private stock holder with these high costs would not carry any stocks in laissez-faire in the absence of a storage subsidy. Indeed, it is not possible to break even with such high storage costs.

In this scenario, results depend on maintaining the assumption that private stock holders are authorized to operate (without subsidy) alongside the public agency. If they are authorized to operate, it is optimal to not subsidize public storage, and the results are identical to the results obtained from the optimal trade policy alone in Table 7. In the absence of private stock holders, it is optimal to subsidize storage, but the overall level of storage remains very small because its high cost discourages its use as a policy instrument (Table 8)—even with significant storage subsidies (between 60% and 77% of storage cost). These subsidies are just sufficient to make public storage profitable but not to induce a significant level of storage. With such high storage costs, it is better for India to rely on trade and private storage abroad than on domestic public storage.

Since it is difficult to economically justify public storage at the current high costs, Table 8, also considers what optimal rules would be if public costs were lower at $40 per ton, that is between private storage costs and current public costs. Albeit high, costs at US$ 40 per ton are low enough to justify a significant level of public storage when a sufficient weight is given to price volatility. The amount of storage subsidy is significant, as it covers almost all storage costs, but the insulation parameters are not significantly affected by the change in public storage costs.

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## **Table 8. Optimal simple rules when stocks are managed by a public agency and private storage is prohibited**

||||**_R‐ν_**<br>|||
|---|---|---|---|---|---|
|**Variables**|**0**|**3**|**6**|**9**|**12**|
|||Public stor<br>|age cost of US$|87per ton<br>||
|Insulationparameter���|‐0.17|‐0.40|‐0.48|‐0.54|‐0.57|
|Storage subsidy ���|0.60|0.62|0.69|0.77|0.77|
|Indiaprice||||||
|Mean(Rs/t)|9,730|9,633|9,601|9,581|9,573|
|CV(%)|13.03|11.42|11.00|10.69|10.62|
|RoWprice||||||
|Mean(US$/t)|201.0|201.6|201.8|201.9|202.0|
|CV(%)|21.43|22.41|22.78|23.02|23.15|
|Mean India stock(million tons)|0.01|0.01|0.02|0.06|0.06|
|||Public stor<br>|age cost of US$|40per ton<br>||
|Insulationparameter���|‐0.17|‐0.40|‐0.49|‐0.54|‐0.56|
|Storage subsidy ���|0.14|0.48|0.83|0.93|1.00|
|Indiaprice||||||
|Mean(Rs/t)|9,730|9,630|9,585|9,563|9,554|
|CV(%)|13.03|11.18|9.71|8.89|8.22|
|RoWprice||||||
|Mean(US$/t)|201.0|201.6|201.7|201.8|201.9|
|CV(%)|21.43|22.41|22.62|22.78|22.84|
|Mean India stock(million tons)|0.01|0.06|0.42|0.69|0.99|

# **7 Conclusions**

The analysis presented here has relied on a rational expectations storage-trade model to represent current policies for managing wheat price volatility in India and propose alternative stabilization policies. Representing current policies is a challenge, because they appear to be highly discretionary. To capture their essence, they have been represented as simple rules, defined as functions of world and domestic conditions. The alternative stabilization policies are derived from the maximization of a social welfare function that includes a motivation for price stability. The treatment of alternative policies contains two innovations for developing price stabilization policies: It designs optimal price stabilization policies for a large-country case, and it considers simple rules for stabilization and demonstrates how closely their effects can approximate those of a fully optimal policy.

India’s policies have been very effective in stabilizing the domestic wheat price, but their high costs raise concerns about whether the costs are exceeding the benefits. The current policy is costly for two main reasons: Trade and storage policy are not coordinated, and the storage policy appears to follow a buy-and-hold strategy. Large stock levels are held for long periods, but stock releases 34
are insufficient to dampen domestic price rises; instead, the government has occasionally had to dispose of wheat stocks on the world market.

Another key food policy issue for India is the cost of public grain storage. The current costs, declared by the Food Corporation of India, are four times higher than long-run costs estimated for other countries by the World Bank and Food and Agriculture Organization (FAO) (2012). Such high costs make it extremely difficult to justify public storage in India on economic grounds, as it would be much less costly to rely on domestic private storage or on world trade and storage abroad. For that reason, the alternative policies considered here are based on providing sufficient incentives to induce the more cost-efficient private stock holders to store grains in a socially optimal way.

The fully optimal policy determines the levels of storage and trade that maximize total welfare, whereas the optimal simple rules of stabilization adjust the parameters from predetermined rules in optimizing the welfare function. These simple rules are a constant subsidy to private storage (as storage policy) and tariffs defined by an isoelastic function of border price (as trade policy). A notable result from the model is that the optimal simple rules achieve welfare gains approaching those obtained by implementing a fully optimal policy. Under simple policy rules, private storage is incentivized to exceed a storage level above the competitive level. Since private storage reacts in appropriate ways to price behavior, it combines well with the trade policy, a result that is extremely difficult to achieve with a price-band program (or its variants).

One important conclusion of the analysis is that the broad approach adopted by India to manage price volatility, of using a combination of trade and storage policies, is logical for a large country with large gaps between import costs and export prices. A second important conclusion is that this combination of policies could be fine-tuned to significantly increase India’s total welfare and significantly reduce its storage costs by adopting a more rules-based food policy. As price stabilization policies do not directly target the underlying market failures, which are often thought to be related to the economic agents’ lack of capacity to cope with shocks (Gouel 2014), they are not regarded as first-best policies. Yet price stabilization policies hold considerable appeal for many policy makers who have clearly exhibited a dislike for price volatility, and certain market failures may prevent the first-best policy options from achieving their goals.

If price stabilization policies are to be used, however, it is important to identify how best to use them. In India, given the current circumstances, significant cost savings (through a combination of storage and trade costs) could be made without any significant net loss in real income through a less insulating trade policy implemented in conjunction with storage rules that lead to stock levels similar to, but above, competitive storage levels. These gains are predicated on 35
efficient private sector storage, however. The current public costs of storage appear to be extremely high and make it difficult to justify any level of public storage in the country without significant overall loss in welfare.

A final consideration is that this work has neglected the rest of the world’s reaction to India’s wheat policies, although that reaction may not be without consequence. The recent food crisis (and prior crises) demonstrated that when one country institutes trade policies to insulate from the world market, the desire of other countries to use insulating policies is reinforced, and the overall effectiveness of such policies is attenuated (Martin and Anderson 2012; Anderson, Ivanic, and Martin 2014). By definition this collective action problem cannot be solved by one country alone, but the problem may nevertheless matter for the design of an individual country’s policies. If the effectiveness of trade policies is limited by partners’ reactions, the implication is that storage policy may play a more important role in domestic price stabilization than was found in this analysis.

36