Organic agriculture can be defined as a production system based on locally or farm- produced renewable inputs in preference to external ones, and aims to promote and enhance ecosystem health (FAO). The importance of the organic farming sector in the European Union is reflected in the recent reforms of the European Union’s (EU) Common Agricultural Policy (CAP), and in respective Regulations. Since the 1992 CAP Reform, organic farming has been assigned an important role in the enhancement of environmental protection throughout the EU, while EU Regulations 2078/92 and 2092/91 provided specific incentives for conversion to and maintenance of organic farming and established organic products as distinctively different from their conventional counterparts (provision of standards and certification). However, higher prices received, is the most important incentive for farmers to convert to organic agriculture (Burton, Rigby, and Young, 1999, 2003; O’Riordan and Cobb). Farmers receive higher prices for organic products when consumers believe that there is a quality premium available in organic product’s attributes (Loureiro, McCluskey, and Mittelhammer; Boland and Schroeder). On the consumer’s side, the demand for organic products in Europe exceeds supply, despite that, on average, the price of organic products is twice that of conventionally grown food (Sylvander and Le Floch Wadel).

Although consumers’ acceptance of organic products is vital for the growth of the organic farming sector, most studies on consumer demand examine consumer attitudes, identify their motivation for purchasing organic products, and elicit willingness to pay for organic products relative to their conventional counterparts. On the other hand, there is only one empirical study for organic products that employs traditional demand analysis in order to provide estimates of consumers’ responsiveness to price changes. Specifically, Thompson and Kidwell collected data on prices and cosmetic effects for five organic and conventional produce items, as well on consumers’ socio-economic and demographic characteristics, in order to estimate the choice between organic and conventional produce, and the choice between two stores for shopping. Using a two-equation probit model, Thompson and Kidwell provided estimates of the elasticities (or conditional effects) of the goods’ defects, difference in prices, type of store, and socio-economic and demographic characteristics. However, due to the lack of data on expenditures on organic and conventional produce, their resulting econometric model did not allow the derivation of measures of the interrelationships between organic and conventional produce (i.e., cross-price elasticities).

The limited number of empirical studies on consumer demand for organic products is due to the fact that organic products are relatively new compared to their conventional counterparts, and therefore to the paucity of sufficient historical data on retail prices and consumption. In this context, the aim of the present paper is to provide empirical evidence of the consumption of both organic and integrated- agriculture fresh vegetables using a cross-section of data. Specifically, the Inverse Almost Ideal Demand System (IAIDS) of Eales and Unnevehr, and Moschini and Vissa is employed for the empirical analysis of household demand for organic, integrated-agriculture and conventional fresh vegetables in Crete, Greece. The choice of an inverse instead of a direct demand system, apart of the lack of sufficient time- series data on organic consumption, is based on the nature of the goods in question. Inverse demand systems are often employed in the case of quickly perishable foods, agricultural, and fishery products for which quantities cannot adjust in the short-run. The underlying assumption is that since supply of such commodities may be fixed during short-intervals, price must adjust so that the available quantity is consumed. Fresh vegetables are produced subject to biological lags, they are quickly perishable commodities and cannot be stored. As a result the supply of fresh vegetables is highly inelastic during short-intervals. It is, therefore, more reasonable to employ an inverse demand system; that is, a demand system for which quantities are taken as predetermined (i.e., exogenous) while it is prices that adjust so that the available quantity is consumed.

The use of cross-section data in our analysis, however, is not without complications. It is common in micro-level analyses of consumer demand for many households to report zero purchases of certain commodities. The presence of these zero observations gives rise to two problems. Firstly, in the case of an inverse demand system, such as the IAIDS, where expenditure shares are functions of the logarithm of the quantities purchased, the logarithm of zero purchases, when reported, cannot be defined. One way to deal with this problem would be to estimate the IAIDS system only for the households that report positive purchases, but this may result in sample selection bias. Another way is full-sample estimation by assigning some small positive number or unity to the zero purchases. However, this approach has also serious drawbacks: it is not independent of the units of measurement of the respective explanatory variable(s), and if there is a large number of households in the sample that report zero purchases then the resulting parameter estimates may be biased. In order to overcome this problem, we employ an approach which allows full-sample estimation and results in efficient and unbiased estimates.

The second problem related to the presence of zero purchases is that standard systems estimation methods, e.g., seemingly unrelated regression or maximum likelihood, lead to biased parameter estimates. Two main approaches have emerged in the literature for the estimation of micro-level demand systems. The first approach is the Kuhn-Tucker model of Wales and Woodland, and its dual model proposed by Lee and Pitt. The Kuhn-Tucker model of Wales and Woodland assumes that preferences are random over the population. It starts with the maximisation of a random direct utility function, subject to budget and non-negativity constraints, and then, the standard Kuhn-Tucker conditions are used for the derivation of the demand equations. Lee and Pitt extended the Kuhn-Tucker approach to a dual form, taking the maximisation of the indirect utility function as a starting point and using Roy’s identity for the derivation of the demand equations. Their approach is based on the use of virtual (reservation) price relationships – which are shown to be dual to the Kuhn-Tucker conditions – in order to identify corner solutions and define demand regime switching.

The second approach for the estimation of censored demand systems was proposed also by Wales and Woodland and is a non-trivial modification of Amemiya’s extension of the tobit model (Tobin) for a system of equations. This model assumes that preferences are non-random and the non-negativity restriction for the observed shares is incorporated by assuming that the observed expenditure shares are the sum of the utility maximizing shares (the latent shares) and a random disturbance term which follows a truncated normal distribution. In the Amemiya- Tobin model, the adding-up constraints hold for the latent expenditure shares but not for the observed (i.e., censored) expenditure shares. In order to impose adding-up for the observed shares, Wales and Woodland proposed a mapping of the latent to the observed shares which specifies each positive observed expenditure share as the ratio of the respective latent share to the sum of the positive latent shares. The model then generates a density for expenditure shares which has the form of a partially-integrated mixed discrete-continuous multivariate distribution, i.e., it is a continuous pdf with respect to the positive observed shares and a discrete probability mass with respect to the zero observed shares.

The Amemiya-Tobin model by Wales and Woodland is the approach adopted in the present paper to account for the presence of zero purchases in our sample. This approach has also been employed by Dong, Gould, and Keiser, for the estimation of Mexican household demand for 12 food categories.2 The advantage of this model over the Kuhn-Tucker model and its dual lies in that it can be applied in any demand system specification. On the contrary, the applicability of the latter models is quite limited as it is difficult to solve the Kuhn-Tucker conditions or the virtual price relationships for direct or indirect utility functions underlying many demand systems, such as the IAIDS. A difficulty in the application of the Amemiya-Tobin model of Wales and Woodland (but also of the Kuhn-Tucker model and its dual) lies in the requirement for evaluation of multiple probability integrals in the likelihood function, a task that is difficult when there are many goods in the demand system. The use of two-step estimators instead, which offer simplified procedures for the estimation of censored demand systems (e.g., Heien and Wessells; Shonkwiler and Yen; Perali and Chavas), results in parameter estimates that, although consistent, lack in efficiency relative to the maximum likelihood estimators of Wales and Woodland, and Lee and Pitt. Moreover, the problem of adding-up of the observed shares is not adequately addressed