Our major concerns with the application of these “gravity” theories to analyse food trade and to compute priceelasticities stem from the four widely adopted assumptions of identical (symmetric), homothetic, monotone, CES preferences. 3 Most of these concerns are shared with other trade economists (see the section by AvW (2004) on the limits of the gravity approach). Let’s consider each successively. The assumption of identical preferences across countries is often adopted, not only for computation facilities; some researchers are clearly convinced by its relevance or, more precisely, the lack of econometric evidence for asymmetric preferences. For instance, Helpman (1999, p. 130) finds the use of a home bias in demand unappealing because there is no clear evidence that demand patterns differ across countries, except for biases that are related to income levels. There are indeed econometric evidences that the food consumption responses to income changes differ by countries (Cranfield et al. 2002; Seale, Regmi and Bernstein 2003). These studies however impose identical structural parameters (and preferences) over all countries and thus are unable to reveal asymmetric preferences. In fact there is a growing debate on this assumption and recent results suggest that its acceptability depends on the countries and/or goods considered. For example, Movshuk (2005), using a revealed preference approach, finds significant differences in tastes between developed and developing countries but much lower differences inside the group of developed countries. Blum and Goldfarb (2006), developing a gravity model extended to account for home bias, find asymmetric preferences for some free Internet activities. The first objective of this article is to test whether this assumption biases the estimation of priceelasticities of food trade functions.
This method is based on the assumption that the structure of price-elasticities for sub- categories calculated under strong separability indicates the true structure of these elasticities. In order to test this assumption, a similar study has been performed for French data. We use a French dataset from INSEE which combines at the individual level the monetary and time expenditures into a common, unique goods and services consumption structure by a statistical match of the information contained in two surveys: the Family Expenditure Survey (FES, INSEE BDF 2001) and the Family Time Budget (FTB, INSEE BDT 1999). We define 8 types of activities or time use types compatible with the available data both from FES and BDT such as Eating and cooking time (FTB) and food consumption (FES). Time uses are defined for each household in the FES by means of the time uses of a similar household in the BDT. The estimations of the full priceelasticities are presented in Gardes (2017).
by the proportion of households working on the labour market (an empirical proxy of the
household’s expected wage). The full-income is the sum of the household’s monetary
disposable income and leisure time income. The specification is double logarithmic and two equations relate the theatre attendance per capita to the ticket price and the price of leisure and, either the household’s monetary disposable income, or its full income. The elasticity over the ticket price is estimated at -0.28, while the full price elasticity culminates at -4.16 and the monetary and full income elasticities are respectively 1.16 and 5.65. The full income and full priceelasticities thus appear extremely high. In the second specification, with full income and full price, the effect of a change in the opportunity cost of time is twice as big: through the full price elasticity and the time component of the full income. Multiplying the full income elasticity by the ratio of the time component over full income 2 (0.64 as measured on our French statistics, see Table A1 in Appendix A), the sum of the income and price effect of a change in the opportunity cost of time is -0.53, which is close to the ticket price elasticity. Therefore, it seems that the direct specification used in this article is highly disputable, since it mixes the effects of changes in the monetary and time components of the full price with the effect of the opportunity cost of time through the full income.
Most trade equations, especially in operational macroeconometric models, do not take into account the so-called new theory of trade and stick to the traditional Armington  framework. Such trade equations, however, often suffer from serious estimation difficulties, excessively low trade priceelasticities or unstable ones for example 1 , notably suggesting underlying problems of missing variables. Some trade models with imperfect competition might solve such problems, especially those which shed light on new sources of trade and comparative advantages by underlining the role played by product differentiation, especially vertical 2 . More recent empirical studies confirm the increasing part played by trade in vertically differentiated products, especially within the European Union (EU). Fontagné, Freudenberg and Péridy  show that, in the mid-nineties, intra-industry trade in vertically differentiated products within EU countries was twice as substantial as intra-industry trade in horizontally differentiated goods. Erkel-Rousse and Le Gallo  highlight the part played by quality in the trade performances of several EU countries, more especially Germany and, to a lesser extent, France. These studies suggest that trade equations should take product quality into account.
TABLE 2 GOES HERE
3.3 Unit Consumption
Table 3 presents the results for a model of unit consumption, based on Equation (2). The Adjusted R 2 and F-test statistical values obtained are high. The short-term priceelasticities of demand ranged from -0.06 for France to -0.21 for the UK. These elasticities are low but are not dissimilar to the results obtained in other studies [5,13,37]. The variability of these results, with lower elasticities observed for France, Italy, and Sweden compared with the UK, may be due to the former three countries having larger home rental sectors in which tenants have fixed costs for heating. Furthermore, Figure 1 shows that prices have fallen in France between the mid-1980s and 2004, which would also result in a very low price elasticity. The large share of electricity use in this country for space and water heating may also have had an impact. Coefficients for the time trend were found to be of the same order of magnitude for each country, although they ranged from -0.001 (-0.1%) in Italy to -0.007 (-0.7%) in the UK, suggesting that the effects of technical change and regulations have not been as pronounced in Italy. An brief examination of the new IEA BEEB (Building Energy Efficiency Policies) database  suggests that this can be the case. According to the information in the database the first building energy regulations were introduced in Italy in 2006 as compared to 1955, 1946 and 1976 for France, Italy and the UK respectively. The coefficients of HDD are of similar order of magnitude and are highest for the UK and surprisingly lowest for Sweden, which has the coldest climate, i.e., the impact on unit consumption of the colder winters between 1970 and 2005 has been least potent in Sweden. This may be due to the higher levels of insulation in houses in Sweden 4 . The coefficients of the lag are similar for France, Italy, and Sweden, while they are negligible for the UK. The long-term priceelasticities, which range from -0.17 for France to -0.35 for Italy, show that in the long run Italy and Sweden “catch up with and overtake” the UK in terms of response to price changes, whereas in France
4 A meta-analysis of the price and income elasticities of food demand
Simulation models, such as general or partial equilibrium models, are often used to analyse long-term projections to assess the effects of political reforms or to shed light on a variety of issues, notably in agricultural sectors. These models use a large number of behavioural parameters, among which food demand elasticities play a crucial role (see, e.g., Rude and Meilke (2004) and Carpentier et al. (2015)). Indeed, these parameters provide information on how consumers react to income and price changes and are likely to have considerable impacts on the simulation outcomes of projection and political reform scenarios for two main reasons. First, the current global economic situation will undoubtedly evolve dramatically in the forthcoming years even if economic policies remain unchanged. This is particularly true for some developing countries in which incomes are expected to keep growing for several years. Since the level of food consumption is a key element to be analysed for one who is interested in economic projections, the impacts of income growth on household demand for food products, which strongly depend on income elasticities, must be accounted for as accurately as possible in simulation models. Second, even if agricultural policy reforms do not have strong impacts on national income levels because agriculture generally represents a small proportion of Gross Domestic Product (GDP), these reforms can have considerable impacts on agricultural prices. Demand responses to price changes are thus of crucial importance when one wishes to simulate the effects of agricultural policy reforms, and this depends on the value of food priceelasticities. Numerous price and income elasticity estimates are available in the economic literature and can be used to calibrate large-scale simulation models. However, the studies from which these estimates can be drawn use different types of data, rely on various assumptions regarding the modelling of household food demand and use different econometric estimation methods. All these sources of heterogeneity among studies may lead to significant variations in the empirical estimates reported in the literature even if these estimates are supposed to measure the same phenomenon, the responses of food demand to income or prices.
Methods to estimate priceelasticitiesPriceelasticities can be estimated: first, by the estimation of demand systems under Slut- sky constraints, which is generally applied to macro time-series (because price variability is uncommon in micro datasets). Second, by arc-elasticity computed between two peri- ods characterized by large changes in prices, see Gardes and Merrigan (2011). Third, by a method initiated in remarks by Hicks and Stone and fully discussed by Lewbel, based on a computation of price indexes weighting individual prices by current budget shares. Finally, Deaton (1988) proposed a method to compute priceelasticities on cross-sectional micro-data using unit values, for surveys containing information on the quantities con- sumed and the value of expenditures. In this paper, we use a method which consists of computing full prices for individual agents, defined as the sum of the monetary price and a shadow price corresponding to non-monetary resources such as time.
demand of its residents adequately. Indeed, residents may buy gasoline elsewhere and non- residents may inflate city sales.
To our knowledge, our study is amongst the first studies to use gasoline data at city level. Recently however, Levin, Lewis and Wolak (2013) have used daily expenditure data and prices to analyse the demand for gasoline in 243 U.S. metropolitan areas from 2006 to 2009. While, the main focus of their analysis is on the impact of using high frequency data, they do however also report some results on variations in priceelasticities across cities. They find that almost all cities have gasoline priceelasticities ranging from -0.35 to -0.45. They also find that more densely populated cities, those with more low income households or a higher share of commuters using subways or rails have somewhat more elastic demand. Besides using data from a different country, our study is different as it compares cities of very different size ranging from large metropolitan areas to small cities with a few thousands residents.
With very few exceptions, most countries in the industrialized world have implemented ER at some point of time. Indeed, the policy has been in place in all European countries except Bulgaria, Cyprus, Germany, Malta and the UK. Puig- Junoy (2004) states that ―the conditions on the EU market are in effect weakening the use of [cost-based price regulation] and giving more importance to the observed price in other European countries (external reference pricing).‖ (p. 163.) Heuer et al. (2007) reach a similar conclusion from their formal empirical analysis. They explore whether countries engaging in ER suffer from delays in the launch of pharmaceutical products, a good proxy for the importance of ER. Despite the fact that they explore several cost- containment policies as explanatory variables (therapeutic value, cost-effectiveness, and so on), it is suggestive that the dummy variable for the presence of ER is the only explanatory variable that is significant at the 5% level. Windmeijer et al. (2006) measure the effects of the implementation of ER in the Netherlands. They show that this policy resulted in considerably lower prices in general. Merkur and Mossialos (2007) simulate the effect of ER on drug prices in Cyprus and show that this effect is beneficial after identifying Cyprus as a high price country for pharmaceuticals. Both Anke (2008) and Stargardt & Schreyogg (2006) analyze the international drug price interdependencies resulting from the adoption of varying forms of ER. They also discuss implications in terms of strategic decisions by firms to sequentially launch drugs in different countries.
2. Recent developments in food commodity markets
2.1. The commodities under review
The price of most food commodities almost doubled between 2006 and July 2008. Indeed, all the synthetic indicators (see Figure 1B) show a sharp increase in the food price index over this period. For example, the CRB foodstuff spot index rose by around 50% in 2007-2008. A similar pattern can be seen between mid-2010 and December 2011. Thus, from 2007 to August 2011, almost all food commodity prices doubled (see Table 1). On an individual level, however, (i.e. when we scrutinize the different components of the synthetic indicators), some discrepancies appear between the two periods. For instance, rice was the most expensive grain during the phases of huge expansion from 2006 to 2008, but exhibited a lower price than most grains in 2011. Symmetrically, the price of sugar was significantly lower than its historical average during the first episode, but reached an all-time high in 2011. In addition, since September 2011, prices have remained high, but some (cocoa, coffee, and sugar prices) have decreased while others have continued to increase. The trends in food commodity prices obtained by the application of the Hodrick Prescott filter confirm these results (see Figure 1A).
Anton, Vander Weide, and Vettas (2002) establish a comparable result under quantity competition.
The argument is best summarized as follows. Think of a reference industry consisting of a collection of segmented submarkets (typically, the industry for postal services, with submarkets corresponding to delivery routes in different geographical areas). Suppose then that the historical operator is challenged by an entrant on a limited number of submarkets. Assume further that universal service obligations constraint the incumbent’s behavior: it must offer its services in all submarkets at a uniform price. At the price competition stage, the incumbent’s behavior is affected by the extent of the entrant’s market coverage. If the entrant is a low scale competitor, the incumbent firm is better off setting a price close to the monopoly price. In this case, it enjoys near monopoly profits on the (relatively numerous) protected markets but possibly sells very little, or nothing, on the contested markets. If the entrant covers a larger set of submarkets, the incumbent is better off being more aggressive over the whole set of submarkets. In which case the profits lost on the protected markets are compensated by larger sales on the (relatively numerous) contested ones. Hence, by choosing the number of submarkets it challenges, the entrant controls the aggressiveness of the incumbent. Prices therefore decrease with the entrant’s coverage (Valletti, Hoernig, and Barros 2002, lemma 1). For that reason, the entrant will strategically limit its entry scale.
1.5 Our Contributions
Though there have been studies on generalized Nash equi- libria and the existence of equilibrium in polytope games is known, it is not clear if it is unique and what the price of stability and the price of anarchy are. Most studies on uniqueness leverage the strict concavity (or convexity) of the underlying game. Since our game is neither strictly convex nor strictly concave, it requires a different treatment to de- termine the conditions under which the game would have a unique equilibrium. Also, though price of stability and price of anarchy have been studied with respect to congestion and other resource allocation games, such studies assume the cost functions to be continuous and do not consider common coupled constraints. Hence, this is the first game theoretic study on resource allocation polytope games, with respect to determining the conditions for uniqueness of equilibrium and deriving the price of stability and the price of anarchy.
In this article, the satisfactory consumption and labor supply elasticities of demand are measured through a model of time allocation that includes eight time assignment equations by using the full time use (the temporal values of the monetary expenditure plus time spent) concept obtained by matching the Classic Family Budget survey with the Time Use survey for Turkey. The cross-sectional data covers the period of 2003–2006 in Turkey. The elasticity results show a clear picture of the relationship between satisfactory consumption and working with commodity demands for Turkey. As a contribution to the literature, we explore the reasons behind the demand for satisfactory consumption through working decisions by measuring well-being inequality for each consumption group. In order to increase the robustness of our result, overall well-being inequality is measured by introducing the axiom of superposed utility of preferences. As expected, overall well-being inequality declines to 0.26, which is 119 percentage points lower than the average rate of well-being inequality (0.57) in Turkey.
(Gouel 2011). Deaton and Laroque (1992) demonstrated that the introduction of competitive storage also affects the distribution of prices, increasing its kurtosis and allowing for positive skewness, two of the major characteristics of commodity prices. Despite the difficulties in estimating with this model due to its non-linear components, including structural breaks and the lack of data on inventories, many developments around the competitive storage model have been proposed in the past 20 years (Gouel 2011). A common feature of the models based on competitive storage and rational expectations is that natural disasters are the only source of uncertainty and the only cause of errors in price expectations, assuming no endogenous explanations of price dynamics. Boussard and Mitra (2011) attempted to fill this gap by introducing adaptive expectations in a competitive storage model. However, their simulation results are not more accurate than the standard framework of Deaton and Laroque (1992) since price autocorrelation in simulated series remains rather low when compared to actual data.
8 Var[M t ],
where the (ex ante) variability of the posterior mean, Var[M t ], measures the precision of the
Because demand is linear, the average price and quantity levels (both equal to µ/2) are independent of the information structure. The welfare consequences of using scores to price discriminate are thus fully determined by the firms’ ability to learn from such signals. On the one hand, better information increases firms’ profits by allowing them to better tailor the price to the consumer’s type. On the other hand, with a constant average quantity, total surplus must fall with greater price discrimination because the correlation between the type and the price reduces the degree of correlation between the type and the quantity purchased. Therefore, the consumer must be unambiguously worse off.
most important factor to understand the cross sectional heterogeneity in sectoral in‡ation responses, but that the most relevant characteristic to explain sectoral output responses is whether the sector produces a durable good.
Regarding the aggregate implications of sectoral price rigidity, we show that heterogeneity in the (implied) frequency of price changes ampli…es the degree of aggregate money nonneutrality, multiplying the e¤ects of a monetary policy shock on aggregate output by a factor of 6. This am- pli…cation e¤ect has also been discussed by Carvalho (2006) and Nakamura and Steinsson (2008b), who, however, calibrate price rigidity using micro data and abstract from capital accumulation. Carvalho abstracts from materials inputs as well, while Nakamura and Steinsson model materials inputs in a symmetric manner meaning that …rms in a given sector use equal proportions of all
• Adjustment and reference case: β > 0 and ∂D/∂r > 0. If the reference price 1) adjusts and 2) affects the demand, then the firm looses some mar- ket power and change the price over time. Indeed, the demand is elastic ( ∂D/∂ p/p/D > 1 from Proposition 1) and price evolves over time (the dy- namics of price plays a role following Proposition 2). Interestingly, both reference adjustment and reference effect are conditions for weaker market power and price dynamics of a monopolist. So the monopolist may have an incentive to lower the level of the reference effect and its adjustment speed. Also, when the firm takes into account the impact on the future reference price of its current selling price (which is obvious), it also has to take into account that the trade-off between current selling price and future reference price is actually more tricky that it appears at first glance: indeed, the firm has to recognize that the presence of reference effects undermines its ability to charge at the monopolist level.
confidence band. Second, we drop marginal products and destinations, defined here as those involving less than 1% of the overall exports of each firm (column 3). Removing such transactions might make the identification cleaner, as indeed studies on multi-products firms find that products closer to the core firm competencies sell for higher prices than non-core products (Manova and Zhang, 2012b; Eckel et al., 2011). The positive price premium for FC firms is preserved, but the point estimate on the FC dummy coefficient is now statistically larger (0.897) than in full-sample baseline regression. This suggests that constrained firms tend to act even more strongly on the unit values of core products and destinations. Third, in order to account for the potentially particular behavior of multinational companies, which are usually found to set higher prices than domestic firms (cfr. Ge et al., 2013), we drop MNCs from our regression (column 4). Our baseline findings are not affected: the estimated γ is higher, but within a 1 standard error confidence band as compared to the full sample results. Finally, in order to eliminate possible confounding factors related to exchange rate dynamics, we re-estimate the model considering only the export transactions to partner countries that use the EURO currency over the entire sample period (column 5). 28 The point estimate of the FC coefficient (0.631) is larger than
allocation be disclosed in form 8-K. As a result, information disclosed in merger prospectuses (form 8-K) does not contain the purchase price allocation and may only provide very limited and factual information (e.g., form 8-K of LSI Logic filed on April 2, 2007). 7
From 2002 to 2008, 455 business combinations met the above criteria. Acquirers’ 10-Q or 10- K reports (depending on the date of acquisition), available from the SEC EDGAR database, were examined to obtain the purchase price allocations of these business combinations. The purchase price is allocated between current, tangible, and identifiable intangible assets, with the level of detail varying from one firm to another. Due to insufficient and missing disclosures in 10-Q and 10-K reports, the final sample comprises approximately 241 acquisitions with exploitable PPA data.
In turn, all of these estimates are generally smaller than those obtained using aggregate data alone. See, for example, Gali and Gertler (1999), Smets and Wouters (2003), Christiano, Eichen- baum and Evans, (2005), and Bouakez, Cardia and Ruge-Murcia (2005), who respectively report “aggregate” price durations of 5.9, 10.5, 2.5 and 6.5 quarters. Large price rigidity estimates sub- stantially contribute to the empirical success of (one-sector) sticky-price DSGE models but they are now considered implausible in light of the recent evidence on price rigidity at the micro level. As we will see below, our heterogenous, multi-sector DSGE model can reconcile fully-speci…ed macro models with the micro data.