Jeroen Hinloopen
email: j.hinloopen@uva.nl.

Charles Van Marrewijk
email: vanmarrewijk@few.eur.nl

Factor Movements and International Business < F -International Economics, F11 -Neoclassical Models of Trade < F1 -Trade < F -International Economics, D43 -Oligopoly and Other Forms of Market Imperfection < D4 -Market Structure and Pricing < D -Microeconomics

Keywords: Balassa index, Hillman condition, comparative advantage Balassa index, Hillman condition, comparative advantage JEL codes: C81, D43, F11, F20

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Introduction

The concept of 'revealed' comparative advantage (RCA), introduced by [START_REF] Liesner | The European Common Market and British industry[END_REF] but refined and popularized by [START_REF] Balassa | Trade liberalization and 'revealed' comparative advantage[END_REF] with his concomitant index, is widely used empirically to identify structural trade-related patterns across countries. It is the starting point for [START_REF] Peterson | Export shares and revealed comparative advantage. A study of international travel[END_REF] analysis of the export performance in travel services; [START_REF] Porter | The competitive advantage of nations[END_REF] uses it to identify strong sectoral clusters; it is the basis for Amiti's (1999) analysis of specialization patterns in Europe; [START_REF] Bojnec | Trade and revealed comparative advantage measures: regional and central and east European agricultural trade[END_REF] employs it for his study of Central and Eastern European agricultural trade; [START_REF] Fertö | Revealed comparative advantage and competitiveness in Hungarian Agri-food sectors[END_REF] use it to analyze the competitiveness of Hungarian agri-food sectors; [START_REF] Hinloopen | Dynamics of Chinese comparative advantage[END_REF] use it to analyze the dynamics of Chinese comparative advantage; and [START_REF] Svaleryd | Financial markets, the pattern of industrial specialization and comparative advantage: evidence from OECD countries[END_REF] examine to what extent a related index value is instrumental for explaining a country's level of financial development. The dynamics of (the distribution of) the Balassa index as such are considered in Proudman andRedding (1998, 2000) and [START_REF] Hinloopen | On the empirical distribution of the Balassa index[END_REF]. [START_REF] Balassa | Trade liberalization and 'revealed' comparative advantage[END_REF] in fact proposes two measures, one based on relative export shares (the one labelled "Balassa-index" throughout the remainder of this paper) and one using export-import ratios. Meanwhile both indices have been discussed in detail (for an overview of the discussions on measuring RCA see [START_REF] Webster | Some issues on the measurement of comparative advantage[END_REF] and the prevailing concensus is that proper measures of export performance should be based on relative export shares. First, trade interventions could compromise the effectiveness of the export-import measure as import data reflect trade restrictions more readily. [START_REF] Balassa | Revealed' comparative advantage revisited: an analysis of relative export shares of the industrial countries, 1953-1971[END_REF] therefore shied away from its use, focusing only on the measure using relative export shares. Second, in the modern 'new trade' era a problem of the use of net export data is the difficulty with which they can identify succesful intra-industry trade clusters. These are readily identified when using relative export shares. Third, and most importantly, a solid theoretical foundation for the Balassa index is provided by [START_REF] Hillman | Observations on the relation between 'revealed comparative advantage' and comparative advantage as indicated by pre-trade relative prices[END_REF].

He diagrammatically develops a necessary and sufficient condition for the correspondence between the Balassa index and pre-trade relative prices in cross-country sector comparisons, the so-called Hillman condition. As Hillman notes (1980, p. 320): "Whether this condition obtains is a matter for empirical investigation". It is precisely that question which we answer in this paper.

Because the Hillman condition can be easily verified empirically it is rather surprising that it is ignored by the large majority of empirical studies on revealed comparative advantage that have appeared since. The only empirical investigation to date of the Hillman condition as such is the study of [START_REF] Marchese | Monotonicity of indices of 'revealed' comparative advantage: empirical evidence on Hillman's condition[END_REF], who analyze the exports of 118 developing F o r P e e r R e v i e w 3 countries at the 1-, 3-, 4-, and 5-digit level of sector aggregation. They conclude that in the year 1985 (the only year considered in their study) the Hillman condition does not hold for about 9.5 percent of the value of exports of their group of developing countries. The only empirical study into comparative advantage that we are aware of that explicitly mentions to include only those sectors that meet the Hillman condition is [START_REF] Hinloopen | On the empirical distribution of the Balassa index[END_REF]. They find that the Hillman condition does not hold for about 0.5 percent of the number of observations in their sample, which corresponds to about 7.0 percent of the value of exports.

In this paper the empirical relevance of the Hillman condition is thoroughly investigated using a comprehensive dataset consisting of annual recordings on bilateral trade flows for 747 4-digit sectors, 165 countries, and 28 years, yielding a total of slightly less than 18.4 million positive observations (indeed, not every possbile bilateral trade flow actually ocurred; see also [START_REF] Feenstra | World trade flows; 1980 -1997[END_REF]. This dataset allows for an investigation of the Hillman index for virtually all countries of the world, over an extended period of time, and for four different levels of sector aggregation (Appendix A contains a description of the dataset). The empirical relevance of the Hillman condition can thus be established.

As the dataset represents a large part of recent international trade flows the empirical findings are presented as stylized facts. Among these are the observation that violations of the Hillman condition are small as a share of the number of observations, but often represent a disproportionally large value of trade. Including these observations in studies into (the dynamics of) revealed comparative advantage could thus yield quite inaccurate inferences. Further, two periods can be distinguished as to the severity with which the Hillman condition is violated. From 1970 through 1984 violations happen relatively frequently and they represent a significant fraction of the value of total trade, while from 1985 onwards violations hardly ever occur and represent an insignificant fraction of total trade value. Hence 1985, the year analyzed by [START_REF] Marchese | Monotonicity of indices of 'revealed' comparative advantage: empirical evidence on Hillman's condition[END_REF], is not representative for the extent to which violations of the Hillman condition are empirically relevant. Also, violations do not occur randomly across sectors or countries. They occur foremost in sectors producing primary products or that are natural-resource intensive, and in countries located in Africa, the Middle East, Central and Eastern Europe, and Latin America. The exclusive focus of [START_REF] Marchese | Monotonicity of indices of 'revealed' comparative advantage: empirical evidence on Hillman's condition[END_REF] on a group of developing countries is, again, not representative for the empirical relevance of the Hillman condition.

The Balassa index and the Hillman condition

Since it is hard to gauge the importance of a sector without a frame of reference, [START_REF] Balassa | Trade liberalization and 'revealed' comparative advantage[END_REF] introduced normalized export shares as an indicator of revealed comparative advantage:

(1)

J j I i X X X X BI t j t t i j t i j t i = , , , , ,
, where j t i X , are country i's exports in sector j during period t, I is a group of reference countries, J is the bundle of potential export products,

= i j t i j t X X , , = j j t i t i X X , ,
, and

= i j j t i t X X , . If 1 , > j t i

BI

country i is said to have a revealed comparative advantage in the production of commodity j in time period t as its export share for product j is larger than the concomitant export share in the group of reference countries I. This group may vary, as indeed it does in the studies referred to in the introduction, and is most often determined by the largest set of reference countries for which reliable data are available. [START_REF] Hillman | Observations on the relation between 'revealed comparative advantage' and comparative advantage as indicated by pre-trade relative prices[END_REF] examines the correspondence between the Balassa index and pre-trade relative prices in cross-country comparisons for a specific sector under homothetic preferences by forming a Hicksian composite commodity for all other sectors. More specifically, the question he for scaling a country's exports by a measure of its (sector) size. In particular, the Hillman condition states that:

(2)

> t t i t i j t i j t j t i X X X X X X , , , , 1 1 .
Condition (2) must be met for the value of the Balassa index (1) to be in concordance with pretrade relative prices. Note that the Hillman condition (2) consists of three parts that all have a distinct economic interpretation:

market share, as measured by

j t j t i X X ,
, that is, the share of a country's exports in a particular sector relative to the total exports in that sector of the group of reference countries; degree of export specialization, as measured by

t i j t i X X , ,
, that is, the share of a country's exports in a particular sector relative to that country's total exports; country size, as measured by

t t i X X ,
, that is, the share of a country's total exports relative to total exports of the group of reference countries.

As [START_REF] Hillman | Observations on the relation between 'revealed comparative advantage' and comparative advantage as indicated by pre-trade relative prices[END_REF] notes, violations of (2) readily obtain in case a country exports one commodity only (in which case

t i j t i X X , , =
and the degree of export specialization is equal to one)

or when a country is the sole supplier of a particular product (in which case j t j t i X X = , and the market share is equal to one). In general, the Hillman condition is violated if a country has a significantly high market share in the supply of the particular commodity in combination with a 'high enough' degree of export specialization. Figure 1 divides the market share -export specialization space into two sub-areas, indicating whether the Hillman condition is violated or not, for an infinitely small country size. For larger country sizes the dividing line shifts clockwise outwards (see Figure A.1 in the Appendix for a three dimensional image), indicating that the Hillman condition is somewhat less stringent for large countries. In case of violations an increase in a country's exports in a particular sector increases this sector's export share in world trade more than that it increases the sector's national export share. As a result the Balassa index drops in value, which contradicts the notion of revealed comparative advantage.

(world) market shares, they find trade flows violating the Hillman condition to represent a higher percentage of total trade (9.5%) than reported here (for the sample year considered by Marchese and Nadal de Simone (1989) these percentages are, 1.67, 1.23, 0.68, and 0.04, at, respectively, the 1-, 2-, 3-, and 4digit level of sector aggregation; see also Stylized Fact 10 below). On the other hand, Hinloopen and van [START_REF] Hinloopen | On the empirical distribution of the Balassa index[END_REF] consider EU countries only, also as the group of reference countries, thereby generating relatively large export market shares. Violations of the Hillman condition are thus also more likely, ceteris paribus. These violations represent 7% of total trade in their sample compared to the 3.4% recorded here for the same level of sector aggregation (see also Stylized fact 1 below).

Data aggregation

Before discussing in detail the characteristics of all observations violating the Hillman condition, the impact of sector aggregation on the Hillman condition being violated or not needs to be addressed. At lower levels of aggregation, where more sectors are identified, it becomes "easier" in principle for a country to realize a large market share in a specific sector. This tends to increase the likelihood that the Hillman condition is violated. On the other hand, the degree of export specialization falls at lower levels of aggregation, which tends to decrease the likelihood of violation. The net result of these two forces rules the likelihood of violating the Hillman condition in relation to data aggregation. Table 1 summarizes the violations of the Hillman condition for different levels of data aggregation. As a share of the number of observations, the violations are virtually insignificant; as a share of the value of total exports, the violations are substantial. These findings suggest that in practice violations of the Hillman condition do not happen often, but when they do occur they usually involve (very) large trade flows. These observations lead to the first empirical regularity: Table 1 also shows that sector aggregation matters. The average market share of violation cases increases with more refined sector definitions, while at the same time both average export specialization and, to a lesser extend, country size decrease. Although an increasing market share and a decreasing country size enhance the probability of violation, going through the 1-, 2-, 3-, and 4-digit sector aggregations shows that these effects are on average more than corrected for by the concomitant reduction in export specializations. That is:

Stylized fact 2 The higher is the degree of sector aggregation, the higher is the probability that the Hillman condition is violated.

At the same time, the value of total trade involved in the violation cases is about the same for the 1-, 2-, and 3-digit levels of sector aggregation. The reduction in trade value represented by all observations violating the Hillman condition at the 4-digit sector aggregation level is attributable to the reduced coverage of total trade. Accordingly:

Stylized fact 3 The value of trade represented by all cases violating the Hillman condition is

hardly affected by the level of sector aggregation.

Stylized Fact 1 indicates that the set of observations violating the Hillman condition represents a substantial part of total trade. In 2002 1% of total trade corresponded to about US $ 80 billion (World Bank, 2004). Stylized Fact 3 reveals that this value is hardly affected by the level of sector aggregation; no matter at which level of sector aggregation revealed comparative advantage is examined, the group of observations violating the Hillman condition remains equally important as to the value of trade they represent. Checking for the validity of the Hillman condition and dismissing those observations not passing the test thus seems to be an obvious routine to be used under all circumstances.

An obvious stylized fact would be the classification of violations along the "market share" and "export specialisation" component of the Hillman condition. 6 However, no objective measures exist to classify an observation as representing a too large market share and/or a too high degree 6 Violations are never related to country size as these are small in all cases. of export specialisation. Yet some insights along these components are illustrative. Table 1 therefore identifies all violations along these two components whereby a market share of 50 percent or more is taken to be decisive. That is, if the Hillman condition is violated and the related market share exceeds 50 percent it is attributed to a too large market share. In all other cases the violation is attributed to a too high degree of export specialization.

Classified in this way almost all violations at the 1-, 2-, and 3-digit level of data aggregation are attributed to a too high degree of export specialization, indicating that the country in question is exporting virtually only one commodity at that level of aggregation. On the other hand, at the 4digit level of data aggregation a substantial share (23 percent) of the violations is attributed to a too large market share. Given that at lower levels of data aggregation more narrowly defined markets are identified, this classification is in line with expectations.

Finally, the reduction in coverage of total trade at the 4-digit level of sector aggregation is due to yet another problem: erroneous trade flow classifications. Indeed, erroneous data aggregation is a problem in applied research if it remains unnoticed. For empirical studies into revealed comparative advantage, the Hillman condition appears to be an effective screening device for detecting these errors.

Data classification

An important advantage of analyzing trade flows in general and comparative advantage in particular at lower, more detailed levels of aggregation is the increased coherence and homogeneity of the specific markets analyzed, and therefore the more precise identification of revealed comparative advantage. An important disadvantage is that some part of all trade is not specified at lower levels of aggregation, such that a lower share of total trade is represented by the data. Table 1 shows that it is especially relevant here at the 4-digit level of sector aggregation, which represents only some 60% of total trade.

Identifying and subsequently ignoring the remaining 40% is important however. At the 4-digit level raw data could contain trade flows effectively classified at the 3-digit level. For the dataset used here this occurs, for instance, for category 752X 'automatic data processing machines & units thereof' which could refer to trade flows in any of the more detailed true 4-digit SITC categories 7521, 7522, 7523, 7524, 7525 or 7528, as the "X" refers to "unallocated products in SITC group 752" (Feenstra, 2000, p.5). On the other hand, category 752A stands for 10 combinations of "two or more SITC Revision 2 codes" that have been "rolled up" in order to create a commodity classification that is usable for all countries included in the dataset (Feenstra, 2000, p.5). It means that for some countries some export flows reported within a 4-digit industry beginning its code with 752 have been combined such that they match with the 3-digit classification 752, as the country's industry description at the 4-digit level does not match with the SITC listing. The "4-digit" industries 752A and 752X thus contain observations that are effectively aggregates at the 3-digit level. Similar problems apply to data classifications at the 2digit and 3-digit levels of aggregation. In all these cases export flows are inflated, possibly to a very large extent, yielding artificially high values of the Balassa index.7

For illustrative purposes, the Hillman condition is re-examined for all countries, sectors, and years at the 3-digit level, this time including the 1-digit and 2-digit 'aggregates' that are reported at the 3-digit level in the raw data. This yields in total 188 violations of the Hillman condition (compared to 88 violations in case only 'true' 3-digit sectors are considered), 108 of which are attributable to erroneous data classification. These are listed in Table 2. Hillman condition for all remaining sectors, whereby it is important to include for total country trade flows observations that are exclusively recorded at higher levels of sector aggregation in order not to underestimate these cumulative values.

All calculations of the remainder of this paper are performed only at the appropriate level of sector aggregation, whereby a country's true total trade flows in any given year are used, thus including trade flows classified exclusively at higher levels of aggregation. The same then applies for the calculation of total world trade.

Empirical violations of the Hillman condition

For all 165 sample countries the Hillman condition is verified for all 28 sample years at the four different levels of sector aggregation. In what follows, the concomitant empirical regularities are ordered along three dimensions: time (Subsection 5.1), sectors (Subsection 5.2), and countries (Subsection 5.3). Of foremost importance here are the two oil crises of the seventies. These shocks gave rise to such drastic price movements that related market shares (in value) increased thereby challenging the validity of the Hillman condition. In the period 1970 -1984 violations of the Hillman condition occurred primarily for oil-related exports.

Empirical violations of the Hillman condition over time

Empirical violations of the Hillman condition across sectors

At the 1-digit level of sector aggregation violations of the Hillman condition occur in two sectors only: "Food and live animals chiefly for food" (SITC code 0), and "Mineral fuels, lubricants and related materials" (SITC code 3). Going from this 1-digit level to the 2-digit level of sector aggregation the "non-ferrous metals" sector (SITC code 68) joins the group of violating sectors.

At the 3-digit level four additional sectors are included: "Fertilizers, crude" (SITC code 271), "Radio-active and associated materials" (SITC code 286), "Copper" (SITC code 524), and "Ships, boats and floating structures"(SITC code 793). The latter two sectors leave the basket of violators again if sectors are considered at the 4-digit level of aggregation.

It thus appears that more detailed sector definitions encompass the group of sectors violating the Hillman condition at higher levels of sector aggregation (the narrowing scope of violating sectors when going from the 3-digit level of sector aggregation to the 4-digit level is related to the concomitant reduction in trade flow coverage). At the same time, at lower levels of sector aggregation violations occur in sectors that are not identified as violators at higher sector aggregation levels. Accordingly:

Stylized fact 7

The correlation between sectors violating the Hillman condition across levels of sector aggregation is asymmetric; violations at lower levels of sector aggregation are likely to occur at higher levels as well, while violations at higher levels of sector aggregation need not occur at lower levels.

Stylized fact 7 implies that the validity of the computed value for revealed comparative advantage at high levels of data aggregation cannot be taken as evidence for the validity at lower levels of data aggregation. For instance, the fact that the Balassa index for Reunion in 1997 for "machinery and transport equipment" (1-digit SITC code 7) of 2.58 relates to a true comparative advantage (as the related Hillman condition is not violated) does not mean that this holds for all Reunion sectors at lower levels of aggregation that fall in this 1-digit industry. Indeed, according to Table 4 the revealed comparative advantage recorded for Reunion at the 3-digit SITC industry "ships, boats and floating structures" does not constitute a true comparative advantage.

A further sector classification is obtained when taking into account the related factor intensity. This leads UNCTAD/WTO to distinguish between six sector categories, which are described in detail in [START_REF] Marrewijk | International trade & the world economy[END_REF]. Appendix 3 lists this classification for all 3-digit SITC sectors:

A. Primary products (83 sectors); e.g. meat, dairy, cereals, fruit, coffee, sand, minerals, oil, natural gas, iron ore, and copper ore.

B. Natural-resource intensive products (21 sectors); e.g. leather, cork, wood, lime, precious stones, pig iron, copper, aluminum, and lead.

C. Unskilled-labor intensive products (26 sectors); e.g. pipes, various textiles, clothing, glass, pottery, ships, furniture, footwear, and office supplies. D. Technology intensive products (62 sectors); e.g. various chemicals, medicaments, plastics, engines, generators, machines, tools, pumps, telecommunications and photo equipment, optical equipment, and aircraft. E. Human-capital intensive products (43 sectors); synthetic colors, pigments, perfumes, cosmetics, rubber and tires, tubes, pipes, various types of steel and iron, cutlery, televisions, radios, cars, watches, and jewellery.

F. Not classified (5 sectors).

Violations of the Hillman condition are predominantly in primary products and to some extent in natural-resource intensive products. 8 Considering Hillman condition (2) this comes not as a surprise. It is precisely in these two categories more likely for countries to enjoy a (natural) large market share of world trade and/or to specialize exclusively in the export of these commodities.

Alternatively, to the extent that these are agricultural goods, it could be that violations are caused by tighter trade restrictions.

8 At the 3-digit level, for example, 62 violations are in primary products, nine are in natural-resource intensive products, and one is in unskilled-labour intensive product (and 16 are in the non-informative 'not classified' category). Do note that studies that did not include primary product sectors and/or natural-resource intensive sectors are not exempt from possible inclusion of erroneous observations on revealed comparative advantage. This would be the case only if these industries are included when calculating total trade for all sample countries. Observe furthermore that sectors in which violations of the Hillman condition occur, typically are inter-industry trade sectors, as opposed to intra-industry trade sectors (such as human-capital intensive and technology-intensive sectors). As such this provides an additional reason for examing the Hillman condition: it points to sectors that are foremost characterized by interindustry trade. One explanation for this finding is that intra-industry trade is more important among high-income countries and that it therefore comes with smaller market shares and lower degrees of export specialisation.

Empirical violations of the Hillman condition across countries

Further empirical regularities can be distinguished if the sample of violations is examined along the country dimension. All countries hosting observations that violate the Hillman condition at the 2-digit level of sector aggregation are present in the group of violators at the 3-digit sector aggregation level, while 9 of the 13 countries with violations at the 1-digit sector aggregation level are home to violators at the 2-digit level of sector aggregation as well. The consequences of the reduction in trade flow coverage when considering the 4-digit level of sector aggregation is quite apparent in this context: only 7 out of 20 countries remain listed as the home country of sectors violating the Hillman condition at the 3-digit level of sector aggregation. This drop in trade flow coverage should not blur the following:

Stylized fact 9

The correlation between countries hosting sectors that violate the Hillman condition across levels of sector aggregation is asymmetric; violations at lower levels of sector aggregation are likely to occur at higher levels as well, while violations at higher levels of sector aggregation need not occur at lower levels.

Finally, for identifying stylized facts across groups of countries, the set of sample countries needs to be ordered. For that the classification of the World Bank of all countries into 7 distinct Europe and Central Asia (ECA, 29 countries), North America (NAM, 3 countries), Latin America and the Caribbean (LAC, 35 countries), Middle East and North Africa (MNA, 21 countries), South Asia (SAS, 8 countries), and Sub-Sahara Africa (SSA, 44 countries). As there is a good, but not perfect, correspondence between the country labeling of the World bank and the set of sample countries used in this study, a congruence is constructed (see Appendix 1 for details).

Examining then all observations violating the Hillman condition yields:

Stylized fact 10 At all levels of sector aggregation, violations of the Hillman condition occur foremost for observations involving countries in Africa (including the Middle East), and, to a lesser extend, involving countries in Latin America, the Caribbean, and Eastern Europe.

The explanation for Stylized Fact 10 has been alluded to earlier (see footnote 5); for countries that specialize in their exports it is likely that a revealed comparative advantage is recorded that does not meet the Hillman condition. And it is precisley those countries identified in Stylized fact 10 that have (highly) specialized export flows. Observe again that studies into revealed comparative advantage that did not include countries in Africa, the Middle East, Latin America, the Caribbean, and Eastern Europe are not flawless a priori as sectors from these countries contribute to total world trade and hence affect the calculated value of the Balassa index (1) and the concomitant Hillman condition (2). At the same time, studies where countries from the regions identified in Stylized fact 10 are over-represented are likely to find high shares of total trade to be represented by all observations violating the Hillman condition (as in [START_REF] Marchese | Monotonicity of indices of 'revealed' comparative advantage: empirical evidence on Hillman's condition[END_REF] who focus exclusively on a set of developing countries; see also footnote 5).

Finally, observe that countries hosting sectors that violate the Hillman condition are more active in inter-industry trade than in intra-industry trade. The same explanation as that provided in Section 5.2 applies; intra-industry trade is more prevalent among high-income countries which make the realization of a large market share and/or a high degree of export specialisation less likely. Relatedly, the Hillman condition identifies countries which are mainly involved in interindustry trade, that is, developing countries. Violations of the Hillman condition are small as a share of the number of observations (Stylized Facts 1 and 2), but often represent a disproportionally large value of trade (Stylized Fact 3). From 1970 through 1984 violations happen relatively frequently and represent a significant fraction of the value of total trade, while from 1985 onwards violations rarely occur and represent a smaller fraction of total trade value (Stylized Fact 6). Moreover, if violations are identified at low levels of sector aggregation, they are most likely to be identified at higher aggregation levels as well, while the opposite does not hold (Stylized Facts 7 and 9).

Summary and conclusions

Examining then in detail those observations that relate to violations of the Hillman condition shows that these occur in sectors that are producing primary products or, to a lesser extent, that are natural-resource intensive. Also, violations are recorded foremost for countries located in Africa, the Middle East, and Latin America. Both characteristics point to the same type of trade flow underlying the violation: inter-industry trade. Indeed, as intra-industry trade occurs foremost between high-income countries, it is expected that in these cases neither large market shares nor high degrees of export specialisation are obtained. Accordingly, the Hillman condition is an identification device for sectors that involve inter-industry trade.

The Hillman condition is further revealed to be an effective screening device in that it detects observations that suffer from erronously classified data (Stylized Fact 4). At the same time, after eliminating incorrectly classified data, the Hillman condition still identifies problemetic sectors which would otherwise have gone unnoticed (Stylized Fact 5). This leads to a natural screening phase to be followed in applied trade analysis: given any dataset compute first for all observations the Balassa index and the related Hillman condition, examine next the thus identified observations not passing the Hillman test, and dismiss those observations that are suspect of pertaining to erroneous data classifications. Indeed, this procedure is not restricted to analyses into comparative advantage, it should be used in any empirical study to identify data irregularities. This holds a fortiori if developing countries are involved, the trade flows considered are of primary products, or both (as in, e.g., [START_REF] Devadoss | Welfare impacts of Indian apple trade policies[END_REF], Gómez-Plana and Devadoss (2004), and[START_REF] Endoh | The effects of the GSTP on trade flow: mission accomplished?[END_REF]. Two separate data sets provided by the Center for International Data, University of California, Davis (CID/UCD), were merged, the first covering the years 1970 through 1993 (see [START_REF] Feenstra | World trade flows, 1970 -1992, with production and tariff data[END_REF] and the second covering the years 1980 through 1997 (see [START_REF] Feenstra | World trade flows; 1980 -1997[END_REF]. For the overlapping years, the data from the latter source are used. The data set contains bilateral trade flows between 183 trading partners, including n.e.s. (not elsewhere specified) regions for trade flows that could not be classified further than within a broad geographical region (such as "Middle East", or "North Africa"), an "Areas n.e.s." region for trade flows that cannot be attributed to any country or to any of the used broad geographical regions but that do come from a well-defined geographical region, and an "Unknown Partner" category for trade flows that could not be attributed at all due to various reasons (see [START_REF] Feenstra | World trade flows; 1980 -1997[END_REF]. This leaves a sample of 165 genuine countries that are grouped in Table A1 according to the World Bank classification of world regions (see World Bank, 2003). In some cases, the latter is more detailed than the sample of countries used here. For instance, The World Bank distinguishes between Bosnia, Croatia and Slovenia. Here all of these three countries fall under the heading "(former) Yugoslavia". As long as the countries that are grouped together belong to the same geographical region as identified by the World Bank the classification of the latter still applies. This turns out always to be the case. On the other hand, countries that are distinguished here but not as such in the World Bank classification are grouped according to their geographical location. This was done for the Falkland Islands, Guadeloupe, Reunion, St. Helena, and St. Pierre Miqu.

Finally, the constructed database contains three entries for Yemen: Former Democratic Republic of Yemen, Former Yemen, and Yemen. The World Bank classification includes Yemen only.

Needless to say that all three identified countries belong to the same geographical area (in the The bilateral trade flows are decomposed into 1,249 sectors, comprising 747 genuine 4-digit sectors, based on SITC (Standard International Trade Classification), revision 2. The remaining 502 sectors refer to aggregates at the 1-, 2-, or 3-digit level, and a "Non-identified products" category. The 4-digit subset contains 60.39 % of all trade, the 3-digit subset covers 99.46 % of all trade, and the 2-digit subset comprises 99.67 % of all trade.

The data were first compiled by Statistics Canada and made available through the CID/UCD (see [START_REF] Feenstra | World trade flows; 1980 -1997[END_REF]. The former makes use of various sources (according to Statistics Canada 87% of all trade flows is based on independent sources of both imports and exports, while 98% is based on reports of at least one side of trade), yielding a rather complete coverage of world trade flows.

The CID/UCD transforms the data such that trade flows for all years, all countries, and all industry groups are consistent and presented in a unified manner. Each observation in the raw data consists of four entries: importing country, exporting country, sector, and size of the trade flow (in 1,000 US $). The data are thus classified according to the importing country. This is not to say that the data are based on import sources only, as explained above. After merging the two separate datasets a second dataset is created by "inverting" the data, in that all trade is classified according to the exporting country.

  -product from restricting the analysis to those observations meeting the Hillman condition is that observations based on erroneously classified trade flows are identified (by the Hillman condition) and consequently can be dismissed. Indeed, the larger is a country's market share in world exports for a particular commodity, the more likely the Hillman condition is violated. As erroneously aggregated trade flows yield artificially large market shares they are identified by the Hillman condition. If only for this screening property of applying the Hillman condition it is recommended that it is checked always in empirical studies into revealed comparative advantage. The next section briefly introduces the Balassa index of revealed comparative advantage and the concomitant Hillman condition. Section 3 discusses the relation between violations of the Hillman condition and the extent of data aggregation. The ability of the Hillman condition to identify erronously classified trade flow is illustrated in Section 4. All cases violating the Hillman condition are subsequently presented and discussed in Section 5. Section 6 summarizes and concludes.

  5

Figure 1

 1 Figure 1 Violations of the Hillman condition in market share -export specialization space*

  Violations of the Hillman condition occur in 0 -0.2 percent of all cases; these violations represent 0 -3.4 percent of total trade.

  Figure 2 Development over time of violations of the Hillman condition, 1970 -1997 Panel a

Figure 2

 2 Figure 2 illustrates this development for the four different levels of aggregation, both as a share of the number of observations (panel a) and as a share of total trade (panel b). For all years the number of observations violating the Hillman condition is small (as a fraction of all annual observations never to exceed 0.4 percent in any given year), and decreasing over time. This reduction is even more pronounced in panel b; violations of the Hillman condition are very valuable in the period 1970-84, with a peak of 10.14 percent at the 1-digit level in 1974, to become much less important and to virtually disappear in the period 1988 -1997. Hence:

  At all levels of aggregation, violations of the Hillman condition occur almost exclusively in primary product sectors and to some extent in natural-resource intensive sectors.

  used (see World Bank, 2003): East Asia and Pacific (EAP, 25 countries),

  Using a comprehensive data set of annual bilateral trade flows for 1,056 4-digit SITC sectors between 183 countries for the years 1970 -1997, the empirical relevance is examined of the condition for the correspondence between revealed comparative advantage, as measured by the Balassa index, and pre-trade relative prices, the so-called Hillman condition. The findings on the empirical relevance of this Hillman condition are presented as stylized facts because of the exhaustive representation of the dataset.

Figure A1

 A1 Figure A1 Area of violations of the Hillman condition*

Table 1 Aggregation and share of exports not satisfying Hillman's condition, 1970 -1997

 1

	1-digit	2-digit	3-digit	4-digit

1 As a percentage of total trade avaliable at the respective levels of data aggregation.

2

Violations are attributed to market share if market share exceeds 50 per cent, see Table

4

for details.

Table 2 Violations of the Hillman condition and erroneous sector aggregation, 1970 -1997

 2 For 85 out of these 108 cases (or 79 percent) the violation of the Hillman condition is the result of the respective country having a reported 'monopoly'. For all cases the market share is at least 92.6 percent. In the 1980s and 1990s, for example, Germany is frequently the only country classifying products at the 'miscellaneous' 1-digit level, the categories '600', '700', '800', and '900' in Table2, resulting in an artificial monopoly. Similarly, while most other countries take the trouble to identify if the exported 'dairy products and birdseggs' are either 'milk and cream', 'butter', 'cheese and curd', or 'eggs and yolks, fresh, dried, or otherwise preserved', Hungary Hungary's classification of sectors '010', '040', and '050'. Clearly, the Hillman condition is most useful in identifying observations based on erroneous trade flow classifications:

	code description	Country	Years
	010	Meat and meat preparations	Hungary	88, 89, 91, 94
	020	Dairy products and birds eggs	Hungary	78-83
	040	Cereals and cereal preparations	Hungary	73, 76, 81, 92
	050	Vegetables and fruit	Hungary	71
	100	Beverages and tobacco	Sri Lanka	74
	110	Beverages	Hungary	93, 94
	200	Crude materials, inedible, except fuels	China	70-72, 74-78, 80, 81
			Austria	93
	300	Mineral fuels, lubricants and related	Czechoslovakia 76, 78
		materials	Guinea-Bissau 80
			Austria	93
	320	Coal, coke and briquettes	Former USSR	80
			Hungary	95

simply lists them as 'dairy products and birdseggs'. Although not leading to a monopoly for Hungary in the years 78-83, the Hillman condition does pick up this classification problem, as it Page 11 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 3 Violations of the Hillman condition masked by erroneous trade classification

 3 At the same time, because of erroneous data classifications, the number of true violations of the Hillman condition dropped from 88 to 80. This is due to the effect of artificially enlarged trade flows on all computed Balassa index values (1) and the concomitant Hillman condition (2). For eight cases this means that they are not identified as violating the Hillman condition when aggregate trade flows are erroneously classified at the 3-digit level, while they are identified as such when restricting the analysis to true 3-digit level trade flows only. These observations are listed in Table3 andgive rise to the following: Stylized Facts 4 and 5 jointly imply a natural research sequence. Given any dataset compute for all observations the Balassa index and the related Hillman condition. Examine the thus identified observations not passing the Hillman test and dismiss those observations that are suspect of pertaining to erroneous data classifications. Re-calculate the Balassa index and the concomitant

	SITC	Country	Year	BI value Market share	Export	Country size
	Code					specialization
	333	Iraq	71	16.52	0.0633	0.9413	0.0038
	333	Iraq	81	6.08	0.0335	0.9743	0.0055
	999	Former USSR	71	11.74	0.3921	0.6685	0.0334
	999	Former USSR	72	12.35	0.4193	0.6114	0.0340
	999	Former USSR	76	12.98	0.4666	0.5588	0.0359
	999	Former USSR	79	12.29	0.4554	0.5701	0.0370
	999	East Germany	70	12.59	0.1689	0.8508	0.0134
	999	East Germany	71	14.76	0.1777	0.8403	0.0120
	Stylized fact 5 The Hillman condition suffers from a masking effect in that mild violations remain
	undetected if grotesque violations are present.
	Since for most countries about 90% of all (2-digit) sectors have a Balassa index below 4 (see

Hinloopen and

[START_REF] Hinloopen | On the empirical distribution of the Balassa index[END_REF]

, all observations in Table 3 would stand out in a study into revealed comparative advantage. Meanwhile these observations do not refer to revealed comparative advantage proper and should thus be dismissed. Page 12 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table A2 in

 A2 Appendix 2 lists for each sample year and all four levels of sector aggregation the observations that violate the Hillman condition as a fraction of the total (annual) number of observations and of total (annual) trade. The annual average violations correspond reasonably well to the sample totals in Table1, both in terms of the number of violations and in terms of the value of trade represented by these observations.

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Table 4 Observations not satisfying the Hillman condition, 1970 -1997

 4

	Page 15 of 29	Submitted Manuscript
	SITC	Description	Country	Years
	code
		1-digit
	0	Food and live animals chiefly for food	St Pierre Miqu	79
	3	Mineral fuels, lubricants and related materials	Algeria	79-87, 91, 92, 94, 97
			Libya	70-83, 85, 86
			Venezuela	70, 74
			Kuwait	70-72, 74
			Qatar	70, 71
			Saudi Arabia	70-84, 90
			Iran	74-78, 83
			Oman	75
			Iraq	77, 78, 80, 85-87
			Un Arab Em	78
			Nigeria	81, 82, 84, 91
			Paraguay	91
		2-digit
	06	Sugar, sugar preparations and honey	Cuba	75-78

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Page 16 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  Factors responsible for the pattern described in Stylized Fact 6 emerge from Table4, which lists all observations violating the Hillman condition for the four different levels of sector aggregation.

	Submitted Manuscript
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Table A .

 A 1 below these are not further distinguished).

	Page

24 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
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Table A .1 Sample country classification according to World Bank regions East Asia & Pacific (EAP); 25 countries

 A

	Burkina Faso	Guinea-Bissau (incl. Cape	Seychelles
		Verde)
	Burundi	Kenya	Sierra Leone
	Cameroon	Liberia	Somalia
	Central African Republic	Madagascar	South Africa
	Chad	Malawi	St. Helena
	Comoros	Mali	Sudan
	Congo	Mauritania	Tanzania
	Cote dÍvoire	Mauritius	Togo
	Democratic Republic Congo	Mozambique	Uganda
	(Zaire)
	Equatorial Guinea	Niger	Western Sahara
	Ethiopia	Nigeria	Zambia
	Gabon	Reunion	Zimbabwe
	Gambia	Republic Congo
	F o
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		26

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

In the quote, j i refers to country j's Balassa index for good i.[START_REF] Hillman | Observations on the relation between 'revealed comparative advantage' and comparative advantage as indicated by pre-trade relative prices[END_REF] also shows that a similar condition regarding cross-sector comparisons cannot be derived.

Indeed, as[START_REF] Marchese | Monotonicity of indices of 'revealed' comparative advantage: empirical evidence on Hillman's condition[END_REF] consider developing countries only, countries that typically export a small number of commodities (i.e. raw materials) for which they hold relative large

This lack of information regarding the exact classification of trade flows at lower levels of data aggregation is of course not unique to the dataset employed here. Most if not all empirical studies into revealed comparative advantage encounter this problem.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript


Teresa Serra
email: teresa.serra-devesa@upc.edu

David Zilberman

AND José M Gil

Allen Featherstone

THE EFFECTS OF DECOUPLING ON LAND ALLOCATION

Keywords: risk, risk preferences, land allocation risk, risk preferences, land allocation

We are very grateful for your careful review of the paper and your helpful comments and suggestions.

3 lowest quality and productively use the more fertile plots. We have added this discussion in our paper, both in footnote number 4 in page 6, and on the concluding remarks section.

We also agree that crop rotation issues might be relevant and represent another factor affecting land use decisions. Crop rotation is a reason for diversification and affects the relative profitability of a crop at a given field because of soil dynamics. Farmers being aware of this can establish constraints on land use patterns. Crop rotation can occur between program crops or between program and nonprogram commodities. Since program crops are grouped under a single output category, only intergroup rotation would affect our results. Unfortunately our database does not contain information on agronomic issues. As a result, crop rotation cannot be explicitly modelled, though it is implicitly accounted for. Were data available, agronomic restrictions could easily be introduced in the model by solving a constrained optimization problem. It is also true however, that rotation constraints did not change with policy reforms and, from this perspective, the effects of not explicitly modelling crop rotation should not be very relevant for our policy analysis.

The value of crop rotation might have changed with policy reforms. On the one hand, pre-reform coupled payments to program crops not allowing to put land to other agricultural uses, are very likely to have reduced the value of rotating non-program with program commodities. With the decoupling of payments and the allowance of planting flexibility, farmers are likely to have been more willing to rotate program with non-program crops. On the other hand, however, the reform-induced reduction in price supports to program crops is likely to have cut down the value of planting non-program crops for rotation purposes. This is because any extra yields in program crops obtained as a result of rotation will now have a lower market value. As a result, the overall impact of crop rotation is not very likely to have been relevant. We add this discussion in the conceptual framework section in our model (see pages 10 and 11). A discussion of the consequences of crop rotation for land use in Kansas is offered in the empirical application section (see pages 17 and 18).

(8) (page 13) It is not clear here if you are discarding a lot of data in order to balance the panel.

If so, are you not worried about sample selection bias?

Our dataset does not offer information on PFC payments separate from other government payments, which constitute a central issue in our analysis. As a result, a method to estimate such payments was devised. Since data on PFC payment rates are available from the USDA, an estimation of the farmlevel payments can be derived by approximating the base acreage and yield for each crop and farm.

This requires to concentrate on those farms that have remained in the dataset long enough to allow a good estimation of the bases (we use the 1986-88 data for such purpose). The selection of these farms involves being left with 560 observations per year, while the incomplete panel would have had, on average, 1950 farms per year. Discarding observations, however, does not substantially alter the data means (see the table below). Thanks for emphasizing the need to provide further detail of the behavioral approach which may not be well known by readers. We have done so on page 16, where we clarify that this approach is based upon the assumption that farmers behave as if production is characterized by constant returns to scale with fixed input/land ratios. These fixed proportions are assumed to be based on regional averages, though allowing for modifications for seasonal and farm-specific conditions. We also note that the implementation of the behavioral approach requires data which are generally available (land allocation by crop, purchases by input and sales by output). Finally, we emphasize that Just et al. (1990) show the validity of the behavioral approach and its superiority relative to other alternative approaches such as the profit maximization method.

(10) (page 15) Again, the role of crop rotations should be considered here.

As we explain in the response to your comment number 7, in the empirical application section, pages 17 and 18, we discuss the likely impacts of crop rotation issues on Kansas land use. We fully agree with this referee that the implications of agronomic restrictions for land use had to be considered. Following your suggestion, table 1 now incorporates a brief definition of our variables, so that it is easier to follow the empirical specification. Details on the units of measure of the variables are also given.

(12) (page 16) You should also provide an explicit presentation of the exact empirical specification that you are estimating. This should be shown in terms of the EU function.

On page 19, we offer the exact empirical specification that is estimated in our empirical application as requested.

(13) (page 17) You refer to "market prices" here when I think you are referring to deficiency payment supports.

Thank you for your careful review, we have substituted "market prices" by "deficiency payments."

(14) (page 18) You should mention the role of expectations about future policy benefits as a factor influencing production.

The role of expectations about future policy benefits has been mentioned as a factor that may influence production. Specifically, in the concluding remarks section, we recognize the limitations of our research and consider the analysis of the effects of expectations on land use as a possible avenue for future research.

(15) (page 18) I do not fully understand your characterization of set-asides as "self-insurance."

This referee is right in pointing out that characterizing set-asides as a form of "self-insurance" was, at least, confusing and we have removed the sentence from the text. Your suggestion of including a simulation of policy changes is certainly useful. We have done so in the last paragraph of the results section, where we simulate the impacts of the policy changes occurred during the period studied on land use.

Again, we thank you for your useful review.

References:

Just, R.E., Zilberman, D., Hochman, E., and Bar-Shira, Z. (1990) (Gardner, 1992).

The unfavourable consequences of agricultural protectionism became widely recognized by the 1980s. It became clear that agricultural intervention based on price guarantees and other market insulating policies led to overproduction, which in turn brought about market distortions and disagreements in multilateral trade policy negotiations. Recognition of these problems motivated multilateral and/or bilateral trade agreements that advocated for agricultural protectionism dismantling processes. In the framework of these agreements, different countries have reformed their domestic agricultural policies.

Economic theory views lump sum transfers as the most efficient method to redistribute income among individuals (Williamson, 1996). The trade-off between political pressures for continued support to farmers and the policymakers' will to reduce efficiency losses resulted in an increased use of decoupled agricultural policies. Decoupling is a term used to designate the break of the link between subsidies and production. Price supports are usually replaced by lump sum income transfers that do not depend on current production or prices. Phimister, 1995; Hennessy, 1998; or Rude, 2001). A number of studies that have assessed economic agents' risk preferences using different methods have found evidence in favour of risk aversion (see, for example, Hansen and Singleton, 1983; Chavas and Pope, 1985; Pope and Just, 1991; Abdulkadri, Langemeier and Featherstone, 2003 and 2006; or Wik et at., 2004). In light of these findings, it has been common for policy analyses to assume aversion to risk. 1 If uncertainty and risk preferences are introduced in the analysis of the impacts of decoupling, results suggest that apparently decoupled policies can influence production decisions (Hennessy, 1998; Sandmo, 1971). It is thus very important to account for risk and risk preferences when assessing the effects of decoupling.

F

When coupled or partially coupled, income supports often involve restrictive supply management rules that limit farmers' capacity to respond to market conditions. For example, eligibility for public subsidies is usually made 1 The role of risk has also been considered when assessing farmer decisions other than strict profit maximization decisions. Key, Roberts and O'Donoghue (2006) decoupling involves increased planting flexibility in that direct payments are not tied to the production of certain commodities. Farmers being allowed more planting flexibility are likely to be more responsive to market conditions and alter their crop mix accordingly. To the extent that planting flexibility includes the possibility of agricultural land idling, farmers will also consider setting land aside when making their decisions on land allocation.

There are other mechanisms through which the decoupling of agricultural policies can influence land allocation decisions. These mechanisms are the changes in relative market prices and farmers' risk attitudes. The reduction in price supports is likely to make program crops less attractive relative to nonprogram commodities and land idling. Also, to the extent that farmers' risk preferences are influenced by wealth (Sandmo, 1971; Just and Pope, 1978; Hennessy, 1998; Just and Zilberman, 1986) and to the extent that decoupled

II. CONCEPTUAL FRAMEWORK

The objective of our model is to assess the effects of decoupling on farm land allocation. We adopt the Just and Zilberman (1986) model of production under uncertainty. Because agricultural producers are not likely to be neutral to risk, farmers' risk preferences are explicitly considered. Our model defines risk preferences as a function of wealth (Just and Zilberman, 1986; Pope and Just, 1991; Hennessy, 1998). If economic agents are risk averse and their risk aversion decreases with wealth (Pope and Just, 1991; Bar-Shira, Just and Zilberman, 1997), an increase in decoupled payments is expected to alter the crop mix towards more risky crops that offer higher expected margins. The reduction in price supports for program crops that characterizes a decoupling process will reduce the attractiveness of these crops in favour of non-program commodities and/or idle land. Apart from the substitution effects, a change in output prices will also have an income effect that, under the assumption of decreasing absolute risk averse (DARA) preferences, is likely to increase risk aversion.

The 1996 FAIR Act involved the introduction of decoupled payments that allowed, with some restrictions, full planting flexibility. We extend the Just and Zilberman (1986) .

Total crop land ( )

A5 is allocated to the production of the two crops considered or left idle6 yielding the following vector of land allocation:

( )

1 2 3 , , A A A = A
, where

1 2 3 A A A A = + + , 3
A represents idle land and 1 A and 2 A symbolize land allocated to program and non-program crops respectively. The problem of land allocation can alternatively be expressed in proportions as ( )

1 2 3 , , L L L = L
, where

i i A L A = and 1 2 3 1 + + = L L L .
It is assumed that farmers make their decisions with the aim of maximizing the expected utility of their wealth [ ]

1 2 3 1 2
, , , , max ( )

L L L x x E u W = ( ) 1 3 1 2 0 1 1 2 1 3 , , , max (1 ) + + + L L x x E u W G AL A L L
, where W represents farms' total wealth, 0 W stands for farms' initial wealth, and G are decoupled income-support payments. The quasi rent associated to idle land is assumed to be equal to zero. which leads to independence of land allocation from variable input decisions (Just and Zilberman, 1986). Under this assumption the first order conditions of the land allocation problem can be expressed as:

[ ] ( )

1 2 1 0 = E u u E L W (1.1)
[ ] ( )

2 3 0 = E u u E L W (1.2)
By approximating the marginal utility around the expected wealth ( )

0 1 1 2 1 3 (1 ) = + + + W W G AL A L L
through a second-order Taylor series expansion, the first order conditions can be alternatively expressed as:

( ) { } 1 2 1 1 3 2 (1 ) 0 + R L L A (2.1) { } 2 1 2 3 3 ( ) (1 ) 0 + R L L A (2.2) where 1 2 2 ( ) = = u u R R W W W
represents the Arrow-Pratt coefficient of absolute risk aversion. Following Bar-Shira, Just and Zilberman (1997) we 7 As Just and Zilberman note, the assumption of risk neutrality is very common in models with stochastic production and is necessary for the dual cost and production functions to be independent of risk preferences. This assumption allows to derive a theoretical framework that is more tractable at the empirical level. 1997; Isik and Khanna, 2003; Eisenhauer and Ventura, 2003) we assume here that farmers have DARA preferences ( < 0 ). The expression Let's consider a land allocation problem that only includes program and non-program commodities. In such a scenario, the system of first-order conditions is reduced to:

1 = v 2 2 1 1 2 2 2 + 1 var 0 T L = >
( ) { } 1 2 1 1 2 0 + = R L A (3) where 1 1 var = T L , 2 1 var 1 2 = T L
, and

1 1 1 2 (1 ) = + T L L .
< L .
Proposition 1 can be economically interpreted as follows. An increase in decoupled payments improves farmers' wealth which in turn increases their willingness to assume more risk. This could reduce the attractiveness of crop mix diversification as a strategy to manage farm income risk. This will only occur if yield correlation is negative or takes low positive values, and if an increase in program crop production substantially reduces the profit ( T ) variance.

Otherwise diversification will not be pursued.

PROPOSITION 2. For a negative value of the mean effect of production, land allocated to the program crop decreases with an increase in 1 p if 0 < and L requires an important reduction in the marginal variance of profit.

1 2 1 1 1 > L p p , if 1 2 0 < < ,
In order to assess the effects of decoupling on idle land, we now consider a model that examines the allocation of land among program crop production and set aside. In such a model, the first order condition in (3) changes to (4) below: This is due to the fact that an increase in decoupled payments reduces farmers' degree of risk aversion increasing their willingness to assume more risk. Given that idle land involves no risk, this alternative becomes less attractive in favour of producing agricultural commodities.

PROPOSITION 5. For a negative value of the mean effect of production, idle land increases with an increase in 1 p to the detriment of 1 L . However, if the mean effect of production is positive, idle land only increases if the risk effect outweighs the mean effect.

In a situation where the mean effect of production is positive, farmers have the incentive to increase the amount of land allocated to program crops to the detriment of idle land, as long as the increase in production risk measured as a certainty equivalent does not outweigh the mean effect. However, if the mean effect is negative, an increase in 1 p reduces program crop land in favour of idle land.

In summary, our comparative statics analysis shows that decoupled payments have the effect of reducing idle land. In contrast, the reduction in This shift requires yield correlation to be negative or take low positive values. A decrease in program crop price supports can also boost non-program crops acreage under certain conditions. It is relevant to note that, with the exception of the influence of decoupled payments on idle land, the net effects of decoupling depend on issues such as yield correlation, changes in the variance of profit, or the magnitude of the mean and risk production effects. This causes the response to a decoupled program to be inconclusive making it necessary to determine it empirically.

III. EMPIRICAL APPLICATION

As explained above, our empirical application is focused on the analysis of the Retrospective data for these farms are also used to define some lagged variables used in the application. 10 The Kansas Farm Management Association database collects information from individual farms on an annual basis through a 10 To be able to do so, a complete panel of data is built out of our sample. Table 1 contains summary statistics for the variables used in the analysis.

Following our model specification, we consider a variable input x that includes the per acre application of herbicides and fertilizer, representing the main variable costs for the farms in the sample. Because input prices are not available from the Kansas database, we define w as a country-level input price index.

Variable x is then defined as an implicit quantity index and derived through the ratio of input use in currency units to the corresponding price index. The Kansas dataset does not provide information on the consumption of variable inputs by crop. We use Just et al. (1990) behavioural proposal to allocate variable input use among different crops. The behavioral approach is based upon the assumption that farmers behave as if their production functions are characterized by constant returns to scale with fixed input/land ratios. Allowing for modifications for seasonal and farm-specific conditions, these fixed proportions are assumed to be based on regional averages. Crop rotation, which we do not observe, is a relevant practice in Kansas with much benefit from using program crops in rotation with non-program crops.

As explained above, apart from economic and policy issues, land use can also be affected by crop rotation. According to Dumler and Duncan (2005) 12 the passage of the 1996 FAIR Act may have favored rotation of program with non-program crops such as soybeans, without losing program payments. From this perspective, rotation issues would be an added reason to switch from program crops to soybeans or idle land. However, as noted above, the value of rotating nonprogram with program crops may have been reduced with the decline in program crop prices. In other words, any increase in soybeans production is more likely to 11 We should note here that another allocation mechanism based on profit maximization was also used, but yielded inconsistent results. This is not surprising in light of Just et al. (1990) findings that the behavioural method is superior.

12 Halloran (2006), on the other hand, finds that for potato cropping systems, rotating program with non-program crops can improve economic viability and reduce risk. reasons. As a result, the overall impacts are not likely to have been very relevant.

i A represents land allocated to alternative 1, 2 i = ,3, with A representing total crop acres, 3 A the acres left idle, and 1 A and 2 A the crop acres planted to program and non-program crops respectively. By using i y , i x , i p , w , the value for i can be determined. Computing quasi rents at the farm-level involves some problems. First, not every farm produces crop i 13 every year and when this happens i cannot be determined at the farm-level. Second, the composition of 1 y can vary annually within a farm as land planted to wheat, corn and sorghum changes, which complicates the definition of a reasonable value for 1 at the farm-level. In light of these problems, we define quasi rents using annual samplemeans for the production and input consumption variables. 14 Kansas database does not register PFC government payments. Instead, a single measure including all government payments received by each farm is available. To derive an estimate of farm-level PFC payments, the acreage of program crops (base acreage) and the base yield for each crop are approximated using farm-level data. The approximation uses the 1986-88 average acreage and yield for each program crop and farm. PFC payments per crop are derived by 13 The problem applies to crop 2 i = .

14 It is important to note here that other alternatives were also considered, including the use of farm-level i values whenever possible (and averages otherwise), or the use of the Kansas Farm Management Association crop budgets (http://www.agmanager.info/crops/). However, these alternatives yielded results in contrast to widely accepted previous research results and thus were discarded. In order to achieve the aforementioned objectives, the following system of first-order conditions is estimated using two-stage nonlinear least squares:

( )

( ) { } ( ) 1 2 1 1 2 1 2 3 1 2 2 var( ) var( ) 2 cov( , ) (1 ) cov( , ) var( ) 0 W L L A + + = (5.1) ( ) ( ) { } 2 1 1 2 2 3 2 cov( , ) var( ) (1 ) var( ) 0 W L L A + =
(5.2)

IV. RESULTS

Table 1 shows that, during the period studied, more than 62% of crop land was planted to program crops, 26% was devoted to non-program commodities, and 12% was left idle. Sample means also show that estimated PFC payments represent around 1.8% of farmers' initial wealth. Of interest is the fact that, for the period of analysis, the expected market profit per acre derived from nonprogram commodities outweighs the one obtained from program crops. Also, during the period of study, 16 Two-stage nonlinear least squares parameter estimates for the system of first-order conditions (see table 2) provide evidence that farmers in our sample are risk averse, and that the degree of risk aversion decreases with farmers' wealth, i.e., farmers exhibit DARA preferences.

Price, cross-price and payment elasticities of the proportion of land planted to program and non-program crops or left idle are presented in table 3.

As expected, results suggest that an increase in its own price increases the quantity of land planted to program crops. Quite the opposite, the price elasticity of non-program crops is negative. This result is not surprising given the high income risk associated with 2 y during the period of analysis. An increase in 2 p does not only involve an increase in mean income, but also a substantial increase in income variance. This lays out the necessary conditions for a failure in the 'law of supply', that contends that the quantity supplied by price-taking producers will rise in response to an increase in output prices. An increase in profit risk above the increase in its mean will originate this failure. This result is in accord with the findings of Just and Zilberman (1986) , and 3 0.16 L = .

V. CONCLUDING REMARKS

This paper investigates the effects of decoupling on farmers' land allocation decisions and, specifically, on the crop mix and idle land. Coupled policies usually restrict farmers' capacity to respond to market conditions by imposing restrictive supply management rules. In this regard, decoupling involves increased planting flexibility and thus may motivate changes in land allocation.

Other aspects of decoupling can also influence land allocation decisions. These aspects are the reduction in price supports for program crops and their replacement by lump sum transfers, which are likely to involve changes in relative market prices and in farmers' risk attitudes.

In order to show how these policy reforms could affect land use, we use an extended version of the Just and Zilberman (1986) [ ]

1 1 1 2 1 = + L R L G D W (6)
where 0 D > is the negative value of the second order condition of the optimization problem. If crop yields are negatively correlated (i.e.

0 < ), 2 0 < , which involves that 1 0 > L G if 1 1 2 > L . If the correlation coefficient is positive (i.e. 0 > ), 2 ( )0 > < if 2 1 ( ) > <
. We can thus conclude that if

2 1 0 < < and 1 1 2 ( ) > < L , then 1 ( )0 L G > < . Otherwise, if 2 1 > , land
allocated to program crops will increase with an increase in decoupled payments

1 0 L G > .
Proof of proposition 2. By totally differentiating equation ( 3), the following expression can be derived:

( ) 4), the following expression can be derived:

1 1 2 1 1 1 2 1 _ 1 11 1 = + R W L L y R L p D A W D p p ( 7
2 1 1 1 0 = > L L R G D W (8)
Proof of proposition 5. By totally differentiating equation ( 4), the following expression can be derived:

2 1 1 1 1 1 1 1 1 1 2 R dL y L R L p dp D A W D = (9)

  payments and price changes have the potential to affect the wealth of participant farmers, their willingness to assume risk may be altered. Because risk is a fundamental component of agricultural production and because yield variability can differ by crop type, government transfers might affect farms' land use by means of altering farmers' risk attitudes. To the extent that farmers are wealthy and decoupled payments only represent a small proportion of their wealth, 2 one should expect small wealth effects from decoupled payments, even if farmers display strongly decreasing absolute risk aversion. 3 2 In the sample of Kansas farms utilized in the empirical application, decoupled government payments represent less than 2% of farmers' wealth (see the results section for more detail).3 An anonymous Journal reviewer raised this issue. were introduced in the United States (US) with the 1996 Federal Agricultural Improvement and Reform (FAIR) Act, which involved a substantial change in the way income support was provided to farmers. With the FAIR Act, market price supports and deficiency payments were being partially replaced by Production Flexibility Contract (PFC) Payments whose amount and entitlement would not depend on current production or prices, and a deficiency payment program that guaranteed a minimum support price for program crops including soybeans. Under the 1990 Act, with the exception of the flex acres, producers were required to plant the base acreage to the base crop in order to be eligible for deficiency payments. Entitlement to receive PFC was based on qualified acres historically enrolled in commodity programs, allowing land to be put to any agricultural use, including the production of any crop with the exception of fruits and vegetables (unless it was used in this way in the past), or idled.The purpose of this article is to study the impacts of decoupling on land allocation decisions. Our analysis contributes to the literature by formally assessing the effects of decoupling on farms' crop mix and on the decision to set land aside. The analysis is undertaken within the framework of a model of production under uncertainty developed byJust and Zilberman (1986). We extend this model to study supply responses to decoupled payments and to include set aside among land use alternatives. Though various analyses have addressed the effects of decoupling on producers' decisions, no existing research has studied the impacts of decoupled payments on farms' land allocation using the extendedJust and Zilberman (1986) model. Our empirical application focuses on a sample of Kansas farms observed from 1998 to 2001. Results agricultural policy decoupling may result in a shift in land use away from program crops towards non-program commodities offering higher expected profits and idle land.

  literature, we assume risk neutrality in the input decision 7

  R to be a function of farms' expected wealth that can be represented by R W = , where and are parameters that represent a farmer's risk preferences. This is a flexible specification in that it does not restrict the specific type of farmers' risk preferences. Risk averse (neutral) [seeking] attitudes are represented by ( )[ ]0 > = < . We assume farmers to be risk-averse ( > 0 ). The wealth elasticity of absolute risk aversion corresponds to . If farmers have decreasing (constant) [increasing] absolute risk aversion preferences, ( )[ ]0 > = < . In accord with previous studies (Bar-Shira, Just and Zilberman,

  one-half the marginal variance of profit when 1 0 L = , i.e. at zero capacity allocation. Finally, of the variance of non-program crop quasi rents. Note that expressions (2.1) and (2.2) above involve the equalization of the marginal mean income effect derived from an increase in land allocated to crop i and the marginal risk effect discounted to a certainty equivalent using the Arrow-Pratt coefficient of absolute risk aversion.In order to determine the effects of decoupling on land allocation decisions, we use comparative statics. The consideration of a multi-product land allocation problem involves substantial complexity relative to a more simplified model and yields comparative statics formulae that cannot be signed. In order to make comparative statics more simple, but also more clear, we simplify the model to a consideration of only two alternatives in the is important to note that model simplification is only limited to the comparative statics analysis in this section, and that the empirical implementation will be based upon the generalized threeproduct model. Crop rotation issues might be relevant and represent a factor affecting land use decisions other than economic and political reasons. 9 Crop rotation is a reason for diversification and affects the relative profitability of a crop at a given field because of soil dynamics. Farmers being aware of this, can establish constraints on land use patterns. Crop rotation can occur between program crops or between program and non-program crops. Since program crops are grouped under a single output category, only the inter-group rotation would affect our results. Unfortunately, our database does not contain information on agronomic issues. As a result, crop rotation cannot be explicitly modelled, though it is implicitly accounted for. Were data available, agronomic restrictions could easily be introduced in the model by solving a constrained optimization problem. It is also true however, that rotation constraints did not change with policy reforms and, from this perspective, the effects of not explicitly modelling crop rotation should not be very relevant for our policy analysis. crop rotation might have changed with policy reforms. On the one hand, pre-reform coupled payments to program crops not allowing to put land to other agricultural uses, are very likely to have reduced the value of rotating non-program with program commodities. With the decoupling of payments and the allowance of planting flexibility, farmers are likely to have been more willing to rotate program with non-program commodities. On the other hand, however, the reform-induced reduction in price supports to program crops is likely to have cut down the value of planting non-program crops for rotation purposes. This is because any extra yields in program crops obtained as a result of rotation will now have a lower market value. As a result, the overall impact of crop rotation is not very likely to have been relevant. A discussion of the consequences of crop rotation for land use in Kansas is offered in the empirical application section.

  to formulate the following two propositions: PROPOSITION 4. Idle land is reduced with an increase in decoupled payments.

  supports can motivate land set aside. Decoupled payments can also stimulate a change in crop mix in favour of non-program commodities.

  effects of the US agricultural policy reforms in 1996 on land allocation decisions made by a sample of Kansas farms. Specifically, we are interested in observing how the planting flexibility provisions and the decoupling of farm income support influenced Kansas farms' land use. Farm-level data are taken from farm account records from the Kansas Farm Management Association database for the period 1998 to 2001.

  sharing, farm management, and tax preparation arrangement.Around 2,500 full-time commercial holdings with gross sales exceeding $100,000 provide data to this database. Various farm types and areas in Kansas are represented in the dataset(Albright, 2001). The variables in the database include, among other information, farm financial and production data, balance sheet, cash flow and income statements. Our analysis is based on farm-level data, but aggregates are also used to define important variables that are unavailable in the farm-level dataset. These aggregates are taken from the United States Department of Agriculture (USDA) and the National Agricultural Statistics Service (NASS). USDA provided state-level PFC payment rates and NASS facilitated country-level price indices and state-level output prices and quantities.

  by a change in relative market prices than by agronomic

  85 by the base acreage, yield, and the PFC payment rate. PFC payments per crop are then added to get total direct payments per farm. 15 A farm's initial wealth is defined as the farm's net worth.

  higher income risk15 This estimate is compared to actual government payments received by each farm. If estimated -program crops.

  e., the variance of the marginal profit increases, but the marginal variance of profit decreases. In such a situation, the sign of the marginal risk effect Proof of proposition 3. See proof of proposition 2.

  4. By totally differentiating equation (

  monetary values are expressed in constant 1998 currency units asterisks (**) denote statistical significance at the T = 0**) denotes statistical significance at the T = 0.05 level

Table 1 .

 1 Means for the variables of interest

	Variable	Balanced panel	Unbalanced
		(n= 2,241)	panel (n = 7824)
	1 y (USD/acre). Program crop yields	106.54	106.40
	2 y (USD/acre). Non-program crop yields	118.74	116.25
	1 x (USD/acre). Variable input allocated to 1 y	39.32	38.03
	2 x (USD/acre). Variable input allocated to 2 y	28.17	29.39
	1 p (1998=1.00). Program crop price index	1.01	1.01
	2 p (1998=1.00). Non-program crop price index	0.91	0.91
	w (1998=100). Variable input price index	1.02	1.02
	1 (USD/acre). Program crop quasi rents	67.55	68.39
	2 (USD/acre). Non-program crop quasi rents	79.61	75.76
	1 var( ) Variance of program crop quasi rents	180.81	172.16
	2 var( ) Variance of non-program crop quasi
		861.61	654.73
	rents
	Note: all monetary values are expressed in constant 1998 currency units

Table 1 .

 1 Means for the variables of interest (continued)

			Variable	Balanced panel	Unbalanced
				(n= 2,241)	panel (n = 7824)
	cov(	1 2	) Quasi rents' covariance	268.39	307.28
	0 W (USD). Farm's initial wealth	669,663.10	555,070.64
	1 L Proportion of land allocated to 1 y	0.62	0.65
	2 L Proportion of land allocated to 2 y	0.26	0.24
	3 L Proportion of land left idle	0.12	0.12
	A (acres). Total crop land	1075.90	1092.76

Note: all monetary values are expressed in constant 1998 currency units (9) (page 14) You should briefly discuss the implications of the "behavioral method."

(page 16) You need to provide a better definition of your variables (in Table 1). It is almost impossible to understand the empirical specification.

	Responses to referee1
	APE 06-0188
	(11)
	F o
	r
	P
	e e r
	R e v i e w
	6

  ' behaviour by re-optimizing land allocation in response to policy. We model PFC payments as simple lump sum transfers, thus recognizing that under the new scenario farmers manage their crop mix in accordance with

	i p represents crop i price and w is the variable input price, being the first two moments of the joint distribution of quasi rents 1 1 2 2 E = and 2 picture of farmersmarket conditions. 2 1 2 2 Consider a farm that produces two outputs, crop 1 and crop 2. Crop 1 1 1 1 2 2 cov = , where i i i p =
	represents a program crop where eligibility for government payments under the
	old policy regime required crop acres be planted to this crop. Crop 2 is a non-
	F o r program crop. Yields per acre are defined as uncertain variables and expressed as 1 2 ( , ) y y = Y . For simplicity, it is assumed that producer uncertainty derives only from production, but not from market conditions. If additive production risk is F o r
	P assumed, the production function 4 of crop i can be expressed as P	( ) i y y x i i =	i + ,
	e e r e where i E e r	= and variance
	R e v i e w = . The first two moments of the joint distribution of yields are [ ] 2 var i i denoted by 1 1 2 2 y y E y y = and 2 1 1 1 2 2 2 1 2 2 cov y = , where R e v y i e represents the correlation coefficient among the two crop yields. The quasi rents derived from crop i are expressed on a per acre basis as i i i i p y wx = , where w
	4 Our empirical application is necessarily constrained by data availability. The collection of
	information on how land quality varies across an agent's land holdings would allow to assess the
	influence of land quality on land allocation decisions. Such information could be easily
	incorporated in our model by respecifying the production function:	ij y	=	( , ) ij ij y x ij	ij + , where
						6 7

model to allow for these payments and the possibility to receive them even if agricultural land is left idle. Our model offers an improved i x is the per acre quantity of a variable input x allocated to the production of crop i , and i is a stochastic error term with mean [ ] 0 ij would represent land quality in plot j of firm i . Allowing for changes in land quality across an agent's plots would probably confirm the well known practice that farmers follow to set aside the land with the lowest quality and productively use the more fertile plots.

  The only necessary data for implementing this

	procedure are records on land allocation by crop, purchases by input and sales by
	output. Just et al. (1990) show the validity of the behavioral approach and its
	superiority to other alternative approaches. 11
	Two output categories are distinguished as quantity indices per acre ( 1 y
	and 2 y ). Variable 1 y represents program crops and includes the production of
	wheat, corn, and grain sorghum per acre. Variable 2 y is the production of
	soybeans representing a non-program commodity. Together, wheat, corn,
	sorghum and soybeans represent the main crops in Kansas. Paasche indices for F both crops are computed using state-level output prices and production to define o r P 1 p and 2 p .
	e
	e r
	R e v
	i e
	w

  High idle land elasticities are partly due to the low initial values of this variable.

	increase in program crop prices creates a strong incentive to reduce idle land to increase their area by 13%, and idle land, that is augmented by 35%. The low
	plant program commodities. 17 This shift in land use takes place because the elasticity values of decoupled payments involve small changes in land allocation
	increase in mean income originated by the increase in 1 p outweighs the increase as a result of a change in PFC payments. Both program and non-program crop
	in income risk. However, an increase in 2 p does not reduce idle land. Instead acres increase by less than 0.2%, while idle land is reduced by 1.3%. As a result
	idle acreage is increased. As noted before, the high risk associated to the of these changes, the new land allocation vector at the data means is 1 0.55 L = ,
	production of 2 y for the period studied is increased with an increase in the output 2 0.29 L =
	price. The relevance of the risk effect relative to the mean effect motivates
	F o r farmers to set some land aside. Land use is also sensitive to government subsidies. An increase in decoupled payments reduces farmers' degree of risk aversion and stimulates undertaking risky activities. This involves a reduction in F o r
	P idle land in favour of crop land planted to both program and non-program P
	e e r e Hence, our results show that agricultural policy decoupling is likely to commodities. e r
	. Results indicate that have motivated a change in farmers' crop mix. The extremely low values of R e v subsidy elasticities relative to price elasticities allow to predict a reduction in the acreage planted to program crops in favour of non-program commodities and idle R e v
	cross-price effects are negative for program crop and positive for non-program i e land. In order to better show the utility of our model, we carry out a simulation i e crop prices. Hence, a decline in program crop deficiency payments motivates a change in land use away from program crops in favour of non-program w exercise that assesses the effects of shocking the model in accordance with the policy changes occurred during the period studied. During this period, marketing w
	commodities. In contrast, farmers will respond to an increase in non-program assistance loan rates declined approximately by 6.4%, while deficiency payments
	crop prices by increasing land devoted to other uses such as program crops. The were cut by almost 29%. We assume the reduction in marketing assistance loan
	response of idle land to changes to market prices is quite different depending on rates to be fully incorporated into the output prices received by farmers. As a
	whether it is the program or the non-program crop price that is changed. An result of the decline in program crop prices, our simulations suggest a reduction
	16 Differences in the variance of profits might partly reflect the fact that 1 y is a composite output, in program crop land on the order of 12% in favour of non-program crops, that
	and 2 y is a single crop.
	21 22

17

  increase farmers' willingness to assume more risk. This could reduce the attractiveness of crop mix diversification away from program crops and in favour of non-program commodities as a strategy to manage farm income risk. This involves that this diversification will only be pursued if yield correlation between program and non-program crops is negative or takes low positive values, and if an increase in land allocated to program crops involves a substantial reduction in the profit variance. Under certain conditions of yield correlation, profit variance and mean income, a decrease in program crop price supports will motivate diversification away from these crops. Idle land will decrease as a result of a reduction in program crop prices, only if the mean effect of production is negative or if it is positive and the risk effect outweighs the mean effect. An increase in decoupled subsidies will motivate farmers to assume riskier enterprises and reduce uncultivated land.

	Submitted Manuscript
	would allow an evaluation of the effects of policy expectations on land use and APPENDIX
	constitutes another possible extension of our analysis.
	Proof of proposition 1. By totally differentiating equation (3), the following
	expression can be derived:
	F o r F o r F o r
	P P P
	e e e
	e r R e v i e w e r e r We use farm-level data collected in Kansas to illustrate our model and determine the effects of the FAIR Act on crop mix diversification. Our results show that decoupling may induce a change in farmers' crop mix by stimulating R e v R e v to reduce program crop acres in favour of non-program commodities and land i e i e idling. Our work represents a first step in the analysis of the impacts of w w
	decoupling on land allocation. Our empirical analysis is however constrained by
	model of production under data availability. Due to data restrictions, we are not able to assess the role of
	uncertainty. Our model offers an improved picture of farmers' behaviour by agronomic restrictions such as crop rotation issues on land use, which constitutes
	allowing to optimize land allocation in response to policy and by considering a promising extension of our work. Another future line of inquiry would involve
	land idling among land use alternatives. Theoretical results show that, under the the consideration of the influence of land quality on land allocation decisions.
	assumption of DARA preferences, an increase in lump sum transfers will The collection of data on farmers' expectations about future policy benefits
	24

Page 33 of 43 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Page 36 of 43 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	F o r F o r F o r F o r
	P P P P
	e e e e
	e r e r e r e r
	R e v R e v R e v R e v
	i e i e i e i e
	w w w w
	31

Table 1 .

 1 Summary statistics for the variables of interest

	Variable	Mean
		(Standard deviation)
		n= 2,241
	1 y (USD/acre)	106.54
	Program crop yields	(11.51)
	2 y (USD/acre)	118.74
	Non-program crop yields	(27.85)
	1 x (USD/acre)	39.32
	Variable input allocated to program crops	(1.48)
	2 x (USD/acre)	28.17
	Variable input allocated to non-program crops	(1.49)
	1 p (1998=1.00)	1.01
	Program crop price index	(0.06)
	2 p (1998=1.00)	0.91
	Non-program crop price index	(0.06)
	w (1998=100)	1.02
	Variable input price index	(0.03)
	1 (USD/acre)	67.55
	Program crop quasi rents	(7.07)
	2 (USD/acre)	79.61
	Non-program crop quasi rents	(6.58)

Note: all monetary values are expressed in constant 1998 currency units

Page 40 of 43 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	F o r
	P
	e
	e r
	R e v
	i e
	w
	32

Table 1 .

 1 Summary statistics for the variables of interest

			Variable	Mean
				(Standard deviation)
				n= 2,241
	1 var( )		180.81
	Variance of program crop quasi rents	(22.43)
	2 var( )		861.61
	Variance of non-program crop quasi rents	(111.13)
	cov(	1 2	)	268.39
	Quasi rents' covariance	(18.76)
	0 W (USD)	669,663.10
	Farm's initial wealth	(587,319.18)

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Because, for our sample of farms, crop land remained almost constant during the period of analysis, A is assumed to be fixed.

The Conservation Reserve Program (CRP) does not factor into the land idling consideration of this paper. Since it consists of long-term contracts that promote the establishment of conserving covers on environmentally sensitive cropland, it precludes adapting land use to changing market conditions or policy regulations.

D21 -Firm Behavior < D2 -Production and Organizations < D -Microeconomics, Q18 -Agricultural Policy|Food Policy < Q1 -Agriculture < Q -Agricultural and Natural Resource Economics, Q12 -Micro Analysis of Farm Firms, Farm Households, and Farm Input Markets < Q1 -Agriculture < Q -Agricultural and Natural Resource Economics, D80 -General < D8 -Information and Uncertainty < D -Microeconomics