Laurent Gobillon
email: laurent.gobillon@ined.fr

François-Charles Wolff

Patrice Guillotreau
email: patrice.guillotreau@univ-nantes.fr

The effect of buyers and sellers on fish market prices

Keywords: fish, commodity price, unobserved heterogeneity, variance analysis, panel data JEL Classification: L11, Q22

The effect of buyers and sellers on fish market prices

Introduction

Hedonic price regressions introduced by the seminal paper of Rosen (1974) have become a widely used approach to study how prices of commodity goods are affected by quality attributes. Each good is characterized by a set of attributes and the unit price of a good is fixed on the market according to supply and demand. The marginal price of every attribute at equilibrium is evaluated from the regression of the unit price on the whole set of attributes. Estimations are usually conducted on cross-section data using Ordinary Least Squares.

A limit of the traditional hedonic approach is that it does not take into account the unobserved heterogeneity of agents. Goods with specific attributes may be sold by sellers with specific marginal costs or bought only by buyers with specific tastes. Seller-buyer pairs may also matter since the information on the unobserved quality of goods sold by some sellers may be known only by some buyers. The measured effect of observable quality attributes on the price of goods can change when unobserved heterogeneity is taken into account.

The main contribution of our paper is to study the role of the unobserved heterogeneity of sellers, buyers, and seller-buyer matches in price setting using hedonic price regressions. Our application is on a unique exhaustive dataset of around 15 million transactions on the French wholesale fish auction market over the 2002-2007 period. However, it can be used to study the prices of any product whether it is raw food, transformed food or even a manufactured good as long as panel data are available, sellers and buyers' identity can be tracked across time, and there are repeated transactions involving the same economic agents.

Our approach borrows tools from labor economics. Since the seminal paper by Abowd, Kramarz and Margolis (1999), a literature has developed incorporating the unobserved heterogeneity of firms and workers in wage regressions through the use of two series of fixed effects. This approach has been expanded to take into account specific effects for pairs of firms and workers (Woodcock, 2008, 2011; Sørensen and Vejlin, 2013). In our paper, we use a similar approach for fish prices per kilo with a specification incorporating fish characteristics, time fixed effects, seller fixed effects, buyer fixed effects and seller-buyer match effects. Identification is guaranteed by the tracking across time of sellers and buyers.

Our work complements the literature on hedonic price regressions that takes into account, at best, unobserved seller heterogeneity using store fixed effects when retail prices are studied (Lach, 2002).

The most significant applications on specific food products mostly concern wine (Nerlove, 1995; Combris, Lecocq and Visser, 1997; Ashenfelter, 2008), cereals (Stanley and Tschirhart, 1991) and fish.

For applications on fish, hedonic price regressions have been used to study prices of fish sold at wholesale auction (McConnell and Strand, 2000; Kristofersson and Rickertsen, 2004, 2007; Asche and Guillen, 2012), to analyze retail prices in shops to assess the importance of packaging, brand or eco-labelling (Roheim, Gardiner and Asche, 2007; Roheim, Asche and Insignares, 2011), and to assess the validity of the law of one price (Gobillon and Wolff, 2015). 1 Contrary to previous studies on fish prices which usually focus on one single species or one single fish market, we provide results for most fish species based on estimations on transactions occurring on all French fish markets.

More precisely, we report regression results without and with unobserved heterogeneity for most fish and crustacean species with a significant market share. We also propose a way to classify species by the extent to which fish characteristics and unobserved heterogeneity among sellers, buyers and seller-buyer matches, contribute to explaining fish price variations. Our results show that, for most species, while fish characteristics remain the main determinant of fish prices, heterogeneity among sellers, buyers and matches also contributes to explaining prices. The role of matches remains nonetheless modest. Interestingly, the inclusion of unobserved heterogeneity in the analysis affects the marginal effect of fish characteristics on prices for several species. This suggests that unobserved heterogeneity terms should be included in regressions as controls to avoid biased estimates of the effect of observable fish attributes.

Data analysis techniques are used to classify fish and crustacean species into four groups. One group comprises high-quality species for which quality attributes play an important role because fish are highly differentiated with respect to their characteristics. A second group includes low-quality species for which there is a sizable explanatory power of buyer effects because wholesalers differ in their willingness to pay since they do not serve the same downstream markets. The third group is characterized by an important role of time effects because fish supply and consumers' willingness to pay vary seasonally. Finally, the fourth group consists in species for which the unobserved heterogeneity of agents and matches matters due to variability in production costs, willingness to pay and specific pairing for serving downstream markets.

The rest of the paper is organized as follows. Section 2 describes the empirical strategy used to quantify the importance of fish characteristics, time, seller, buyer and match effects in explaining variations in fish prices. Section 3 presents our dataset of fish transactions along with descriptive statistics. Section 4 comments our results and Section 5 concludes.

Empirical strategy

In this section, we explain how unobserved heterogeneity can be incorporated in hedonic price regressions when panel data on fish transactions are available, and sellers as well as buyers can be 1 Controlled experiments have also been used to assess consumers' willingness to pay for specific fish attributes such as color (Alfnes, Guttormsen, Steine and Kolstad, 2006). tracked across time. We also explain how the role of factors in explaining fish price variations can be quantified.

For a given fish species, we denote by the log price of a transaction . We suppose that it depends on the characteristics of the fish lot composed of dummies related to size, presentation and quality. The standard hedonic specification is given by:

= + + (1)
where is a vector of parameters, is a time fixed effect, and is a random error term. This specification is usually estimated with Ordinary Least Squares.

It is possible to add seller unobserved effects and buyer unobserved effects to this specification. In our setting where fish is sold at auctions, seller effects capture all the differences in fish quality across vessels that are not captured by variables in our dataset. An advantage of seller unobserved effects is that they capture the effect of all the vessel characteristics without the risk of being non-exhaustive. Similarly, buyer effects capture all the differences in willingness to pay that can affect prices, as buyers needing fish with specific characteristics are expected to make higher bids for it at auctions. As we will see below when describing the data, buyers cannot be tracked across fish markets.2 Hence, unspecified buyer effects cannot be identified separately from market effects. The specification becomes:

= + ( ) + ( ) + ( ) + (2)
where ( ) is the seller involved in transaction , ( ) is the buyer and ( ) is the month at which the transaction occurs. We treat the buyer-and seller-specific components as fixed effects because they may be correlated with the covariates . For instance, vessels fishing very close to coasts and landing their catches daily are expected to sell small quantities of high-quality fresh fish, whereas large vessels operating away from coasts sell frozen fish in large quantities after several weeks at sea.

In the same way, fish traders supplying restaurants will seek to buy high-quality fish, while traders supplying hypermarkets will purchase a broader range of fish species at lower prices.

Specification ( 2) is a panel data model with two large series of non-nested fixed effects, one for sellers and one for buyers. This type of model has been studied in the labor literature since the seminal paper by Abowd, Kramarz and Margolis (1999) who estimate a wage equation with both worker and firm fixed effects. In our context, identification of fixed effects is possible only within groups of well-interconnected sellers and buyers (see Abowd, Creecy and Kramarz, 2002, for more details). Interconnection within a group is ensured because vessels sell fish to several buyers within the group and buyers purchase from several sellers during the period covered by the data. Groups are mutually exclusive as no buyer in a group purchases fish from a vessel in another group. We only study the main group of well-interconnected vessels and buyers which includes nearly all transactions for most species in our data. As there are large numbers of seller and buyer fixed effects in the model, estimations are performed in two steps, as explained in Appendix A.

Next, we introduce in equation ( 2) the effect of a match between seller and buyer , denoted , as specific matches can influence fish prices. Indeed, specific vessels sell fish lots of higher quality and this quality is known only by a few customers through bilateral relationships. These customers agree to pay a higher price for the fish lots at auctions. More generally, match effects capture the price premium that some buyers agree to pay to some specific sellers. The resulting model can be decomposed into the two following equations:

= + ( ) + ( ) ( ) + (3a) = + + (3b)
In equation (3a), is a seller-buyer fixed effect capturing all the unobserved heterogeneity terms. 3 This fixed effect is decomposed in equation (3b) into the seller fixed effect, the buyer fixed effect and the match effect. The identification of the model is extensively discussed in Woodcock (2008, 2011).

The accuracy with which a term is estimated increases with the number of transactions between seller and buyer . For , and to be separately identified, match effects must be considered as orthogonal to seller and buyer fixed effects. As before, sellers and buyers must be interconnected, so we restrict the estimations to the main group of well-interconnected sellers and buyers. The estimation procedure is again detailed in Appendix A.

Our most general specification given by (3a) and (3b) is used to perform a variance decomposition of fish prices. The role of fish characteristics, time, sellers, buyers and matches in explaining variations in fish prices is measured by the ratio between the variance of their effect and the variance of prices.

For instance, denote by the estimated coefficients of fish characteristics and by (•) the operator giving the variance. The importance of fish characteristics is measured by the ratio / .

As a final step, we use these variance ratios to construct groups of species which are similar with respect to their price determinants. We first conduct a Principal Component Analysis (PCA) based on the five variance ratios of fish characteristics, time, seller, buyer and match effects, to assess the dimensions in which species can be distinguished. 4 The idea of the approach is to decrease the number of dimensions in which species are represented from five to a lower number by projecting species on a space of dimension lower than five such that distances between species are only slightly altered by projection. The selected subspace is such that the mean squared distance between projections is as high as possible or, put differently, such that the inertia of the projected cloud of species is maximized.

In fact, it is possible to show that the entire space can be decomposed into axes such that the first one maximizes the inertia of the projection among subspaces of dimension one, the second one maximizes the remaining inertia, and so on (see Jolliffe, 2010). As a result, axes explain a decreasing proportion of the total inertia of the cloud of species. In our application, we will focus on the two first axes as they explain most of the inertia of the cloud of species and thus contain most of the information contained in variance ratios which serves to differentiate species.

We then use an Ascendant Classical Hierarchy (ACH) based on these two first axes to construct groups of similar species. The groups are constructed by consecutive aggregation of subgroups containing one or more species using the Ward distance. The aggregation procedure involves aggregating the two subgroups at each step such that the loss of between-group inertia is minimized, and then repeating the operation until there are only a few subgroups left, and these are our selected groups. In practice, we stop the iterative procedure when four groups are left, as any further reduction in the number of groups leads to a significant loss of between-group inertia.

Description of the data

We now give some information on the French fish markets and our dataset on fish transactions. Over the 2002-2007 period, 230,000 tons of fish were landed and sold every year in France, for an average value of 658 million euros and at an average price of 2.85 euros per kilogram (France Agrimer, 2012).

The tonnage represents about 30% of total domestically produced seafood when frozen fish and aquaculture products are taken into account, but it represents less than 10% of domestic demand which mostly depends on imports. Fish is traded in markets between vessels and buyers, mostly at auctions in trading rooms, using a mobile electronic auction clock or by internet (see Guillotreau and Jiménez-Toribio, 2011, for more details).

In France, information on every transaction is collected by the national bureau of seafood products (France Agrimer). This information is then processed into a data system called RIC (Réseau Inter-Criées) and added to a unique dataset that we use in our empirical analysis. This dataset is exhaustive for all transactions on the domestic fresh fish market in France between January 2002 and December 2007.

The data contain a small number of variables providing an accurate description of transactions. We know the quantity purchased and the total value paid by the buyer, from which we deduce the price paid per kilo. We have the usual detailed characteristics of fish involved in the transaction: species, size, presentation (whole, gutted, in pieces, etc.) and quality measured by freshness (given in descending order from extra to low). The month and year of transactions are recorded but the exact day is not available. We also know whether fish is traded in auction or directly sold to the buyer.

Finally, the dataset includes two identifiers, for vessels and buyers respectively. The buyer identifier is a license code corresponding to an account specific to a fish market. A limitation of our data is that it is not possible to identify whether several accounts are owned by the same agent.5

Overall, the dataset includes 18,197,738 observations over the 2002-2007 period. We restrict the sample to transactions sold at auctions for species involving over 60,000 transactions. In line with our empirical strategy, we keep for each species the largest group of well inter-connected sellers and buyers and restrict our attention to species for which this group involves most transactions. More details on the selection of transactions are available in Appendix B. Our selection procedure leaves us with a sample of 14,564,758 transactions of fish and crustaceans belonging to 46 species. The main group of well inter-connected sellers and buyers includes more than 99.6% of transactions for 42 species and the minimum is as high as 95.1%. Contributions of species to total market value are reported in Figure A1 of the Online Appendix. It shows that trade is concentrated on a limited number of species. The two main species, sole and monkfish, represent 26.9% of total market value.

The first five species represent 44.2% of this value and the first ten species 66.7%.

Table 1 shows that there is considerable heterogeneity in the average price per kilo. The most expensive species is lobster, with a price per kilo around 21 euros. There are several very cheap species, such as whiting or mackerel, with a price per kilo ranging between 1.5 and 2.5 euros.

[ Insert Table 1 here ] Table 2 sheds some light on the market structure. The numbers of buyers and sellers vary considerably across species. Among species with a significant market share, there are around 3,200 vessels selling to 3,000 buyers for sole, but only 400 vessels selling to 1,000 buyers for Norway lobster (live). The correlation between numbers of buyers and sellers is 0.88. What matters in our empirical application is the degree of interconnection between them. It can be crudely assessed from the number of buyers per seller and the number of sellers per buyer. For all species in our sample, there is a very good inter-connection between sellers and buyers. For instance, for sole, each vessel sells fish to 43 buyers on average and each buyer purchases fish from 40 sellers on average. The two numbers exceed 12 for all species. The average number of buyers per seller is 23 and the average number of sellers per buyer is 25.

[ Insert Table 2 here ] A match is defined as a seller-buyer pair involved in at least one transaction. The number of matches varies a great deal across species. Among species with a significant market share, there are 129,482 matches for sole, but only 25,437 for Norway lobster (live). The minimum for all species is 10,328 and the average is 44,231. The correlations between number of matches and numbers of sellers and buyers are 0.82 and 0.88, respectively. The estimation accuracy of match effects depends on the number of transactions per match. Figure 1 gives statistics on the number of transactions per match for every species. The first decile is 2 or above for all species except two (grey mullet and lobster).

The median is quite high as it takes a value of 8 or above for all species. Finally, the ninth decile is above 30 for all species and reaches a maximum for sole at 144.

[ Insert Figure 1 here ]

Empirical results

Hedonic prices regressions

Coefficient estimates

In Table 3, we report results of hedonic price regressions for the two species which have by far the highest market shares, sole and monkfish. Estimation results are given for three specifications: one without unobserved heterogeneity (equation 1), one including additive seller and buyer fixed effects (equation 2), and one including seller-buyer fixed effects (equation 3a).

[ Insert Table 3 ]

In Panel A for sole, column 1 corresponds to the Ordinary Least Squares estimates when fish characteristics and month dummies are introduced. [START_REF]Average shares of price variances for each of the four groups determined by the ascendant classical hierarchy Variables Group 1 Group 2 Group 3 Group 4 All species Fish characteristics 44.6% 36[END_REF] The R² is 0.481, meaning that observable fish characteristics and time explain as much as 48.1% of price variations. The coefficients of fish characteristics have the expected sign. While small fish (sizes 4 and 5, and to a lesser extent size 3) is cheaper than large fish (size 1), medium-sized fish (size 2) is the most expensive. Medium-sized fish is 6.1% more expensive than large fish, but the smallest fish is 40% less expensive. 7 Results are consistent with medium-sized fish being the most valued. Presentation significantly influences price per kilo. Low-quality fish (grade B) is 45.6% cheaper than extra-quality fish (grade E). Gutted fish is 7.9% more expensive than whole fish because non-edible parts have been eliminated. Month-year effects are represented in Figure B1 of the Online Appendix. Overall, there is an upward trend over time. Prices also exhibit seasonality effects, fish being more expensive during summer holidays (July and August) and in December when demand is higher during the Christmas and New Year period. [START_REF]Average shares of price variances for each of the four groups determined by the ascendant classical hierarchy Variables Group 1 Group 2 Group 3 Group 4 All species Fish characteristics 44.6% 36[END_REF] The quantity of fish purchased is excluded from the specification. Indeed, it is potentially endogenous since fish lot sizes may be influenced by the expected selling price. Still, we conducted a robustness check to assess whether adding the logarithm of fish quantity to our specification affects the results. Whereas this variable is found to have a significant negative effect, its inclusion has absolutely no effect on the magnitude of the coefficients of fish characteristics and does not improve the fit of the model. For sole, for instance, the R² increases only at the margin from 0.4814 to 0.4818 when adding fish quantity to the set of explanatory variables. 7 These percentages are given by (exp(0.059)-1)*100 and (exp(-0.515)-1)*100, respectively. Other percentages in the text are computed in the same way.

We then estimate a specification where both seller and buyer fixed effects have been added. Results

reported in column (2) of panel A show a significant improvement of the fit, with an increase of the R² from 0.481 to 0.614. This suggests some heterogeneity among vessels and buyers. Some coefficients of fish characteristics change when seller and buyer fixed effects are included in the model, but the results remain qualitatively similar. In particular, the price of gutted fish is now only 1.2% higher than that of whole fish.

Finally, we consider a hedonic price specification with seller-buyer fixed effects. Results reported in column 3 show that the fit improves again, with the R² increasing from 0.614 to 0.659. This increase may seem rather modest, but the contribution of match effects to explaining variations in fish prices is significant, accounting for 25.3% of the overall contribution of unobserved heterogeneity terms.8

The introduction of seller-buyer fixed effects instead of seller and buyer fixed effects does not have much effect on the coefficients of fish characteristics.9

Results obtained for monkfish are reported in Panel B and lead to quite similar overall conclusions.

Ordinary Least Squares estimates show that prices are higher for fish which is larger, of better quality, or sold in pieces (column 1). As shown in Figure B2 of the Online Appendix, there is both an upward time trend and a seasonal effect, with fish being more expensive in December. Introducing seller and buyer fixed effects in a standard hedonic price regression increases the R² from 0.582 to 0.693 (column 2). Introducing seller-buyer fixed effects instead of seller and buyer fixed effects increases the R² to 0.734 (column 3). Hence, all sources of unobserved heterogeneity contribute to explaining price variations. Estimated coefficients of fish characteristics are influenced by the presence of unobserved heterogeneity. In particular, whereas gutted fish is 4.7% cheaper than whole fish when the specification does not contain any heterogeneity term, it is found to be 16% more expensive when seller and buyer fixed effects are added.

We estimate hedonic price regressions for every species to obtain systematic conclusions about the importance of unobserved heterogeneity in explaining variations in fish prices. 10 Interestingly, the introduction of unobserved heterogeneity changes the effect of some fish characteristics in a sizable way for several species. For cuttlefish in particular, whereas low quality fish (grade B) is 30.0% less expensive than extra quality fish (grade E) when unobserved heterogeneity terms are omitted, it is only 10.8% less expensive when seller and buyer fixed effects are introduced. There is a similar pattern for hake, the respective figures being 50.5% and 38.6%. For cod, whereas fillets are 63.7% more expensive than whole fish when unobserved heterogeneity terms are omitted, they are only 18.3% more expensive when seller and buyer fixed effects are introduced. For Norway lobster (frozen), it is the opposite with pieces being 53.2% less expensive than whole lobster when unobserved heterogeneity is omitted, but only 37.6% less expensive when seller and buyer fixed effects are introduced into the regression.

Differences can be explained by some unobserved heterogeneity among sellers correlated both with the presentation category and unobserved fish quality, as vessels use different types of fishing gear.

They can also be explained by some unobserved heterogeneity among buyers in the willingness to pay correlated with presentation category, as there are different types of buyers such as wholesalers, multiple grocers or mongers, and different downstream markets where buyers resell fish.

Price variations explained by fish characteristics and unobserved heterogeneity terms

We also evaluate the explanatory power of unobserved heterogeneity terms for every species. Figure 2 reports, for each species, the R² obtained when unobserved heterogeneity is not taken into account, the R² increase when seller and buyer fixed effects are added to the specification, and the R² increase when seller-buyer fixed effects are considered instead of seller and buyer fixed effects.

The R² obtained when unobserved heterogeneity is not taken into account is quite high, with an average of 0.47, but it varies across species. Among species with a significant market share, it is only 0.27 for the mackerel, but it reaches 0.70 for Norway lobster (frozen).

[ Insert Figure 2 ]

The explanatory power of seller and buyer fixed effects is relatively high as well, since the R² increases on average by 0.20 when they are introduced in the regression. The R² increase varies across species, from as little as 0.06 for seabass (line-caught), up to 0.37 for cuttlefish. Finally, the explanatory power of match effects is significant, but not large. When introducing seller-buyer fixed effects instead of seller and buyer fixed effects in the regression, the R² increases on average by 0.06.

The R² increase is only 0.02 for Norway lobster (live or frozen), but reaches 0.11 for ling.

Variance analysis of fish prices for all species Explanatory power of fish, seller, buyer and match effects

Another way to assess the importance of the different terms in explaining fish price variations is to conduct a variance analysis of the most general specification including fish characteristics, time fixed effects, seller fixed effects, buyer fixed effects and match effects.11 Table 4 reports, for each term, the ratio between the variance of its effect and the variance of fish price. 12 The higher the variance ratio of an effect, the higher the explanatory power of the related term.

[ Insert Table 4 ]

As expected, the explanatory power of fish characteristics is high, as the average variance ratio for fish characteristics is 31.9%. There are large variations across species: this ratio is only 7.9% for squid, but 61.1% for Norway lobster (frozen). Time fixed effects have a lower explanatory power, but it is still significant as the related average variance ratio is 10.4%. This ratio is very large for some specific species with seasonal demand. For instance, the ratio is 33.2% for lobster, which is consumed in large quantities in summer and in December, but less during the rest of the year.

Overall, unobserved heterogeneity has a high explanatory power for many species, the average variance ratio for the sum of all the unobserved heterogeneity terms being 29.2%. Buyer heterogeneity is the main unobserved term affecting prices. In particular, the variance ratio of buyer effects is larger than that of seller effects for all species, and it is larger than that of match effects for all species except one. The average variance ratio of buyer effects is 20.7%. The ratio is low for cuckoo ray and seabass (line-caught), at 4.2% and 5.2%, respectively, but very high for cuttlefish, at 43.6%. By contrast, the average variance ratio of seller effects is only 5.2%. It is very low for some species such as Norway lobster (live) for which it is only 1.5%, but it is quite high for other species such as crab and octopus, at 14.6% and 15.2%, respectively. Finally, the average variance ratio of match effects is 6.2%, with some variations across species. It is quite low for Norway lobster (frozen) at 2.1%, but reaches 10.6% for ling.

Robustness check

In our approach, a match effect is estimated as the average of price residuals at the match level once fish, seller and buyer effects have been netted out (see Appendix A for more details). When there is only one transaction for a match, the estimated match effect is the single price residual. It becomes clear that there is an identification issue as the estimated match effect captures both the true match effect and the noise specific to the price of the transaction. As a robustness check, we replicated our analysis considering only transactions for matches with at least 2, 5 or 10 transactions, as this should alleviate identification problems at the expense of making a non-random selection on transactions. 13 We find that the explanatory power of matches is smaller, but otherwise conclusions remain qualitatively similar.

A classification of fish and crustacean species

As a last step in our analysis, we attempt to construct groups of fish and crustacean species which are similar with respect to their price determinants. We first conduct a principal component analysis to 13 Detailed results are reported in part C of the Online Appendix.

identify the dimensions in which fish and crustaceans differ. We use five variables, which are the variance ratios of fish characteristics, time effects, seller effects, buyer effects and match effects, and whose values are reported in Table 4. 14 Results are summarized in Table 5 and the two main axes of the principal component analysis are represented in Figure 3. 15 The first axis is by far the main dimension in which species differ, as it explains 46% of the inertia of the cloud of species. It opposes fish characteristics to the unobservables related to sellers, buyers and matches. This opposition is driven by the large negative correlations between the effects of fish characteristics and match effects (-0.68), seller effects (-0.43) and buyer effects (-0.43). The second axis has less importance, explaining less than 23% of the inertia of the cloud of species. It mostly opposes time effects and buyer effects, the correlation between these two types of effects being equal to -0.17.

[ Insert Table 5 here ]

[ Insert Figure 3 here ]

We then use the positions of species on the first two axes in an ascendant classical hierarchy to construct groups of species with similar price determinants. We consider a classification with four groups which are represented in Figure 4. 16 Most species in the first group have negative values on the first axis and fish characteristics usually have a large explanatory power. The variance ratio of fish characteristics is 44.6% on average in this group, compared to 32.4% for the whole sample of species.

Unobserved heterogeneity does not play much of a role for most species in this group. The average variance ratios of seller, buyer and match effects are all below the averages computed for the whole sample of species. In particular, the group contains sole, monkfish, Norway lobster (live or frozen), seabass (line-caught), turbot and haddock. Most species are expensive (around 10€/kg) and highly differentiated across presentation categories, consistent with an important role of fish characteristics in price setting. For instance, Norway lobsters are less valued when frozen rather than alive, except the largest ones, monkfish is more valued whole rather than beheaded, and portion-size soles (size 2) are the most appreciated.

[ Insert Figure 4 here ] Most species in the second group have negative values on the second axis. Time effects usually have a low explanatory power and buyer effects have an explanatory power slightly above average. As shown in Table 6, the average variance ratios of time and buyer effects are respectively 5.6% and 22.2%, compared to 10.5% and 19.3% for the whole sample of species. This group includes hake, cuttlefish, John Dory, cod, ray, plaice and conger eels. These species have a low price (around 4€ per kilo) which is not subject to seasonal variability as fish is caught the whole year and is purchased mostly by wholesalers. Willingness to pay differs among buyers depending on their downstream markets. Indeed, marketing efforts (such as discounted prices and advertising) are sometimes considerable as these species are of low value and the profits buyers can derive from sales vary across downstream customers.

[ Insert Table 6 here ] Nearly all species in the third group have positive values on both the first and second axis, and are characterized by a large explanatory power of time effects and a slightly below average explanatory power of seller and match effects. In particular, time effects have an average variance ratio of 18.3% compared to 10.5% for the whole sample of species. This group includes lobster, squid, red mullet, seabass (non-line caught), pollack and ling. With the noticeable exception of lobster which is caught in traps, all these species sell at around 7€ per kilo and are caught seasonally by pelagic trawlers. For lobster, consumers' willingness to pay varies seasonally and is highest during summer and the Christmas holidays.

Finally, the fourth group is characterized by a high explanatory power of buyer, seller and match effects. The variance ratios of these three types of effects are respectively 30.0%, 9.1% and 8.3%, compared to 19.3%, 5.0% and 6.2% for the whole sample of species (see Table 6). The only species in that group with a significant market share is mackerel. This low-value species is mainly harvested in the English Channel by trawlers and sold to wholesalers who export it frozen or canned to foreign markets where it is sold at rather cheap prices. It is also caught by small-scale vessels (such as purseseiners, gill-netters or liners) and sold to wholesalers who resell it on retail markets for higher prices.

This may explain the high variance ratios of the three unobserved heterogeneity terms, as large trawlers and small-scale vessels differ in their production costs, sellers differ in their willingness to pay depending on how products are presented on the downstream markets, and there can be specific matches depending on the segment of the downstream market involved.

Conclusion

In this paper, we have shown how the unobserved heterogeneity of sellers, buyers as well as matches between sellers and buyers can be simultaneously taken into account in hedonic price regressions. Estimations were conducted separately for most fish and crustacean species with a significant market share using a unique exhaustive dataset containing some information on all transactions occurring in French fish markets over the 2002-2007 period. Our work contrasts with the literature, as the typical study usually focuses on one single species or one single fish market, and regresses fish prices on a set of observable characteristics related to fish quality without taking the unobserved heterogeneity into account.

When unobserved heterogeneity terms are included in hedonic price regressions, the effects of quality-related fish characteristics change significantly for some species. For almost all species, observable fish characteristics are found to have the largest explanatory power, but the explanatory power of seller, buyer and match effects is also significant. We finally propose a classification of fish and crustacean species depending on the explanatory power of observables and unobservables using a principal component analysis followed by an ascendant classical hierarchy. This classification tends to differentiate species by their value, seasonality and downstream markets.

Future research could study how buyers sort across sellers, and how prices evolve over time for matches between sellers and buyers as buyers acquire information on the unobserved quality provided by sellers through repeated transactions. Note: NLC = not line-caught, LC = line-caught. "OLS R²" gives the R-square of a specification without any unobserved heterogeneity terms related to sellers and buyers, which is estimated with OLS. "seller and buyer fixed effects R²" gives the R-square of a specification additionally including seller and buyer fixed effects. "seller-buyer fixed effects R²" gives the Rsquare of a specification including seller-buyer fixed effects, but not seller and buyer fixed effects. Note: the first five columns give the coordinates of variance ratios on the five axes determined by the principal component analysis. Column labeled "Axis" gives the rank of the axis and "Proportion" gives the proportion of inertia of the cloud of species explained by the axis.

Figure 1 .

 1 Figure 1. Number of transactions per match

Figure 2 .

 2 Figure 2. Differences in model goodness of fit

Figure 3 .

 3 Figure 3. Principal component analysis of variance decomposition of fish prices

Figure 4 .

 4 Figure 4. Classification of fish and crustacean species obtained from the Ascendant Classical Hierarchy

Table 1 . Descriptive statistics on transactions by species

 1

	Fish species	Price per kilo (in euros)		Number of
		Average	St. dev.	transactions
	Sole	12.65	4.61	1,457,282
	Hake	5.19	2.37	1,206,817
	Monkfish	5.79	2.44	863,500
	Seabass (NLC)	10.55	4.92	705,547
	Red mullet	7.08	3.89	690,916
	Squid	7.37	3.75	549,083
	Whiting	2.38	1.48	526,094
	Mackerel	1.52	1.12	466,378
	Pollack	4.36	2.08	466,037
	Cuttlefish	2.99	2.41	423,015
	Plaice	1.47	0.78	352,040
	Conger eel	2.20	1.39	349,239
	Norway lobster (live)	11.03	4.74	348,816
	Ray	2.89	1.42	347,955
	Turbot	14.67	5.78	338,921
	Pouting	0.86	0.67	335,741
	Brill	9.86	3.91	319,475
	Red gurnard	1.76	1.88	310,892
	Megrim	4.60	2.49	290,904
	Black seabream	3.36	2.30	280,202
	John Dory	9.34	3.91	278,069
	Cod	4.13	1.66	260,137
	Dogfish	0.62	0.45	248,799
	Seabass (LC)	14.55	3.98	239,293
	Norway lobster (frozen)	9.43	4.79	215,206
	Gilthead seabream (NLC)	9.78	5.84	185,221
	Horse mackerel	0.95	0.73	181,585
	Capelin	1.56	0.87	180,664
	Octopus	3.15	2.01	177,485
	Tub gurnard	2.85	3.24	176,692
	Ling	2.69	0.91	175,774
	Lemon sole	4.44	2.22	161,666
	Smouth-hound	1.39	0.80	158,639
	Haddock	1.80	0.86	154,963
	Thornback ray	3.17	1.52	138,070
	Grey mullet	1.51	1.12	133,904
	Cuckoo ray	1.80	0.85	111,493
	Meagre	4.71	3.16	109,290
	Spider crab	2.00	1.15	102,430
	Crab	2.59	1.31	101,098
	Spotted ray	3.03	1.20	92,074
	Lobster	20.89	6.75	86,372
	Common seabream	7.38	5.96	73,041
	Common dab	1.18	0.87	67,961
	Sand sole	6.06	2.65	65,692
	Wedge sole	5.58	2.22	60,286
	Source: RIC 2002-2007, authors' calculations.
	Note: NLC = not line-caught, LC = line-caught.

Table 2 . Descriptive statistics of the market

 2

	Fish species	Number of	Average	Number of	Average	Number of
		vessels	number of	accounts	number of	matches
			vessels per		accounts
			account		per seller
	Sole	3216	40.26	3023	42.83	129,482
	Hake	2254	44.08	2745	36.19	99,348
	Monkfish	2339	34.72	2786	29.15	81,208
	Seabass (NLC)	3543	29.63	2986	35.15	104,971
	Red mullet	2768	34.11	2884	32.73	94,403
	Squid	2195	29.88	2787	23.53	65,587
	Whiting	2444	30.55	2237	33.38	74,671
	Mackerel	2553	27.96	2895	24.66	71,383
	Pollack	2695	28.61	2153	35.81	77,092
	Cuttlefish	3108	22.33	2672	25.97	69,389
	Plaice	3334	17.16	2433	23.51	57,205
	Conger eel	2432	23.72	2042	28.25	57,681
	Norway lobster (live)	390	65.22	959	26.52	25,437
	Ray	2576	19.96	1996	25.76	51,423
	Turbot	2898	20.62	2476	24.13	59,753
	Pouting	2477	23.26	2013	28.62	57,621
	Brill	2742	22.74	2553	24.42	62,352
	Red gurnard	2340	21.84	2606	19.61	51,107
	Megrim	1007	30.48	1948	15.76	30,694
	Black seabream	2462	21.77	2135	25.11	53,610
	John Dory	2178	22.69	2418	20.44	49,413
	Cod	1780	21.00	1642	22.76	37,376
	Dogfish	2753	17.80	2119	23.13	49,012
	Seabass (LC)	1186	22.23	1464	18.01	26,361
	Norway lobster (frozen)	489	40.03	962	20.35	19,577
	Gilthead seabream (NLC)	1902	19.29	1916	19.15	36,699
	Horse mackerel	1845	15.33	1999	14.15	28,278
	Capelin	210	61.25	705	18.24	12,862
	Octopus	1726	15.36	1638	16.19	26,513
	Tub gurnard	1894	17.29	1854	17.66	32,747
	Ling	1723	19.45	1668	20.09	33,517
	Lemon sole	1361	20.21	1599	17.20	27,510
	Smouth-hound	2114	12.10	1149	22.27	25,587
	Haddock	810	24.01	1163	16.72	19,449
	Thornback ray	1692	17.47	1153	25.64	29,563
	Grey mullet	2419	14.78	2134	16.75	35,749
	Cuckoo ray	847	18.87	762	20.97	15,981
	Meagre	1039	22.37	667	34.84	23,238
	Spider crab	1304	18.17	1294	18.31	23,699
	Crab	1116	17.08	1418	13.44	19,061
	Spotted ray	1069	17.81	827	23.02	19,037
	Lobster	1453	14.04	1684	12.11	20,394
	Common seabream	343	37.09	659	19.30	12,721
	Common dab	768	13.45	511	20.21	10,328
	Sand sole	1213	12.48	858	17.64	15,138
	Wedge sole	446	23.30	461	22.54	10,392
	Source: RIC 2002-2007, authors' calculations.
	Note: NLC = not line-caught, LC = line-caught.

Table 3 . Results of hedonic price regressions for sole and monkfish A. Sole

 3 RIC 2002-2007, authors' calculations. Note: standard errors are in parentheses; ***: significant at 1%, **: significant at 5%, *: significant at 10%.

	Explanatory variables	OLS	Seller and buyer	Seller-buyer
				fixed effects	fixed effects
	Size	2	0.059***	0.028***	0.028***
	(ref: 1 Large)		(0.001)	(0.001)	(0.001)
		3	-0.075***	-0.067***	-0.065***
			(0.001)	(0.001)	(0.001)
		4	-0.193***	-0.197***	-0.195***
			(0.001)	(0.001)	(0.001)
		5 (small)	-0.515***	-0.537***	-0.536***
			(0.001)	(0.001)	(0.001)
	Presentation	Gutted	0.076***	0.012***	0.009***
	(ref: Whole)		(0.000)	(0.002)	(0.002)
	Quality	A	-0.135***	-0.062***	-0.058***
	(ref: Extra)		(0.001)	(0.001)	(0.001)
		B (low)	-0.680***	-0.579***	-0.582***
			(0.002)	(0.002)	(0.002)
	Time fixed effects		YES	YES	YES
	Seller fixed effects		NO	YES	NO
	Buyer fixed effects		NO	YES	NO
	Seller-buyer fixed effects	NO	NO	YES
	Number of observations	1,457,282	1,457,282	1,457,282
	R²		0.481	0.614	0.659
	B. Monkfish
	Explanatory variables	OLS	Seller and buyer	Seller-buyer
				fixed effects	fixed effects
	Size	2	0.014***	0.018***	0.018***
	(ref: 1 Large)		(0.001)	(0.001)	(0.001)
		3	-0.045***	-0.072***	-0.073***
			(0.001)	(0.001)	(0.001)
		4	-0.112***	-0.134***	-0.133***
			(0.001)	(0.001)	(0.001)
		5 (small)	-0.365***	-0.365***	-0.360***
			(0.001)	(0.001)	(0.001)
	Presentation	Gutted	-0.048***	0.150***	0.155***
	(ref: Whole)		(0.001)	(0.002)	(0.002)
		Gutted head-off	0.546***	0.711***	0.691***
			(0.003)	(0.004)	(0.004)
		Gutted head-off, peeled	0.726***	1.003***	0.985***
			(0.003)	(0.016)	(0.020)
		Pieces	0.743***	0.834***	0.824***
			(0.002)	(0.003)	(0.003)
	Quality	A	-0.090***	-0.018***	-0.020***
	(ref: Extra)		(0.001)	(0.001)	(0.002)
		B (low)	-0.608***	-0.517***	-0.508***
			(0.002)	(0.002)	(0.002)
	Time fixed effects		YES	YES	YES
	Seller fixed effects		NO	YES	NO
	Buyer fixed effects		NO	YES	NO
	Seller-buyer fixed effects	NO	NO	YES
	Number of observations	863,500	863,500	863,500
	R²		0.582	0.693	0.734
	Source:

Table 4 . Variance decomposition of fish prices, by species

 4

	Fish species	Variance	Fish	Time	Unobserved heterogeneity		Residual
		of price	characte-
			ristics		All	Sellers	Buyers	Match
	Sole	0.163	36.1%	10.5%	19.3%	2.2%	11.6%	4.5%	34.1%
	Hake	0.220	41.0%	5.9%	28.5%	6.9%	21.0%	4.6%	36.2%
	Monkfish	0.154	40.0%	9.9%	18.3%	2.4%	10.4%	4.1%	26.6%
	Seabass (NLC)	0.202	22.4%	15.6%	26.6%	5.1%	24.7%	5.1%	25.4%
	Red mullet	0.490	25.0%	18.2%	20.8%	6.0%	11.0%	5.7%	31.9%
	Squid	0.213	7.9%	24.0%	35.5%	5.0%	20.3%	4.8%	28.6%
	Whiting	0.506	32.2%	4.9%	27.4%	5.8%	15.2%	6.5%	27.3%
	Mackerel	0.654	14.7%	7.8%	33.0%	7.4%	22.9%	9.3%	42.6%
	Pollack	0.252	18.1%	14.7%	30.5%	8.0%	12.7%	8.4%	32.9%
	Cuttlefish	0.467	35.7%	6.4%	50.7%	2.0%	43.6%	3.9%	16.9%
	Plaice	0.426	42.4%	2.2%	26.6%	3.3%	17.8%	6.5%	30.4%
	Conger eel	0.429	29.9%	5.5%	28.5%	3.4%	19.2%	7.0%	26.7%
	Norway lobster (live)	0.178	48.0%	20.8%	12.9%	1.5%	11.0%	2.2%	23.8%
	Ray	0.359	48.7%	3.0%	26.1%	2.9%	18.8%	5.0%	23.1%
	Turbot	0.175	40.9%	7.7%	23.2%	2.1%	14.1%	5.3%	20.6%
	Pouting	0.573	26.8%	3.7%	36.4%	3.9%	23.0%	7.9%	29.5%
	Brill	0.194	24.2%	3.4%	38.6%	3.7%	29.7%	7.0%	24.7%
	Red gurnard	0.830	45.3%	1.4%	27.9%	11.5%	34.4%	5.1%	20.5%
	Megrim	0.405	32.0%	6.3%	30.5%	2.2%	22.8%	4.7%	31.0%
	Black seabream	0.711	43.9%	5.7%	19.2%	3.5%	10.3%	5.9%	19.4%
	John Dory	0.261	37.0%	8.1%	22.5%	2.7%	13.3%	7.6%	25.5%
	Cod	0.184	32.3%	10.5%	25.6%	4.1%	13.8%	5.9%	30.1%
	Dogfish	0.354	23.8%	15.7%	31.9%	3.2%	20.7%	10.2%	35.0%
	Seabass (LC)	0.089	41.7%	21.0%	10.9%	1.9%	5.2%	3.8%	26.2%
	Norway lobster (frozen)	0.275	61.1%	7.8%	15.0%	2.8%	10.6%	2.1%	18.5%
	Gilthead seabream (NLC)	0.602	41.0%	17.1%	15.9%	10.5%	16.8%	5.0%	20.5%
	Horse mackerel	0.574	10.5%	4.5%	53.0%	17.2%	83.7%	6.4%	32.1%
	Capelin	0.388	36.0%	21.8%	30.5%	0.7%	27.3%	3.1%	32.7%
	Octopus	0.470	26.9%	15.8%	41.8%	15.2%	24.5%	7.1%	32.8%
	Tub gurnard	1.167	11.4%	2.0%	66.6%	5.3%	46.6%	5.9%	22.8%
	Ling	0.134	11.3%	16.4%	32.6%	4.7%	16.3%	10.6%	34.9%
	Lemon sole	0.363	34.5%	7.1%	21.7%	2.4%	13.4%	5.4%	25.1%
	Smouth-hound	0.460	35.3%	12.1%	31.4%	3.5%	18.8%	6.8%	31.2%
	Haddock	0.305	46.6%	11.1%	12.7%	2.3%	8.5%	4.4%	24.2%
	Thornback ray	0.361	36.4%	3.9%	34.6%	4.0%	21.2%	7.8%	28.4%
	Grey mullet	0.561	14.4%	5.2%	43.7%	7.5%	33.4%	10.3%	27.8%
	Cuckoo ray	0.321	60.1%	5.1%	9.7%	1.7%	4.2%	4.5%	24.2%
	Meagre	0.674	21.0%	14.2%	23.4%	6.8%	9.6%	8.9%	29.6%
	Spider crab	0.405	21.1%	12.2%	45.7%	7.9%	27.5%	9.4%	28.8%
	Crab	0.338	26.8%	11.7%	29.4%	14.6%	23.7%	7.1%	29.4%
	Spotted ray	0.280	46.2%	4.5%	16.2%	2.6%	6.2%	5.8%	20.3%
	Lobster	0.105	15.7%	33.2%	28.1%	8.5%	23.2%	7.5%	22.2%
	Common seabream	0.921	48.4%	9.2%	32.5%	2.6%	28.0%	5.2%	23.7%
	Common dab	0.512	40.4%	3.6%	21.5%	3.0%	14.5%	5.0%	24.7%
	Sand sole	0.286	11.1%	9.3%	54.6%	11.7%	25.7%	7.8%	24.6%
	Wedge sole	0.190	20.7%	16.2%	31.5%	5.0%	21.3%	7.3%	32.3%
	Source: RIC 2002-2007, authors' calculations.
	Note: NLC = not line-caught, LC = line-caught.

Table 5 . Results of the principal component analysis

 5

	Variables	Component

Indeed, in our data, we only have the license codes of accounts used by buyers to purchase fish. These license codes are market-specific and can thus be tracked only within markets.

It would be tempting to simply introduce the match effect in equation (2) as a random effect and take it into account using standard panel estimation techniques. However, this approach is less general than ours since it does not allow for a correlation between fish characteristics and match effects. Our approach is robust to that issue.

As the five variance ratios do not have the same dispersion, we follow the common practice of dividing them by their standard deviation so that they have a comparable influence in the determination of axes when conducting the principal component analysis.

To ease the exposition, we will refer to an account as a buyer, but it should be kept in mind that several accounts on one or several markets may correspond to a single buyer.

This percentage is computed as (0.659-0.614)/(0.659-0.481)*100.

The profile of time effects when all sources of unobserved heterogeneity are taken into account is nearly confounded with the one obtained without any source of unobserved heterogeneity.

Results for all other species are reported in part B of the Online Appendix.

Match effects are obtained by further estimating equation (3b), as explained in Appendix A.

Note that ratios in Table4do not sum to 1. This is because the covariances between the different types of effects are not equal to zero. The values of covariances are available upon request.

Horse mackerel is excluded from the analysis because it looks like an outlier (its variance ratio of buyer effects is very high, at 83.7%) and the market share of this species is very low.

Appendix C reports the coordinates of species on the two first axes, as well as their contributions and some projection information.

This is the number of classes below ten where the Calinski/Harabasz Pseudo-R² has a local maximum.

For the sake of robustness, we also computed the weighted least square estimator proposed by[START_REF] Card | School quality and black-white relative earnings: a direct assessment[END_REF] where the weights are the inverse of the first-stage variances. This approach is much more time-consuming because it involves computing the standard errors of estimated fixed effects. This approach leads to very similar results (available upon request).

Appendix A. Estimation procedure

Estimating the model without match effects

When estimating equation (2), time effects can easily be taken into account with month-year dummies as there are only 72 months of data. The main difficulty is that there are many seller and buyer fixed effects, so that a direct estimation of the model with dummies for the two sets of fixed effects is unfeasible in practice. However, since the number of sellers is not that high, we can include seller dummies to take into account the set of seller fixed effects.

We use the Frisch-Waugh theorem to deal with buyer fixed effects. We first sweep out buyer fixed effects using a within transformation in the buyer dimension. Ordinary Least Squares allow to recover the coefficients of fish characteristics as well as the month-year and seller fixed effects denoted respectively by , and . Estimators of buyer fixed effects denoted can then be recovered from the second step of Frisch-Waugh theorem using the formula

, where is the number of transactions in which buyer is involved.

Estimation of the model with match effects

The parameters in equation (3a) are estimated using the Frisch-Waugh theorem. In a first step, variables are centered with respect to their mean computed at the level of the match between a seller and a buyer. This makes the terms disappear and the resulting equation can be estimated using Ordinary Least Squares. This allows to recover some estimators of the coefficients of fish characteristics and month-year fixed effects denoted and . An estimator of denoted ̂ is given by the second step of Frisch-Waugh theorem using the formula

, where is the number of transactions between seller and buyer . We can then rewrite equation (3b) as:

where # = + ̂is the sum of the match effect and a sampling error arising from the fact that the dependent variable is an estimated parameter. Seller and buyer fixed effects can be taken into account with two sets of dummies. The resulting equation can then be estimated using Ordinary Least Squares, but this procedure is not efficient as it does not take properly into account the sampling error on the dependent variable. Therefore, we prefer to use Weighted Least Squares where the weights are the number of transactions per match . 17

As in the case of the model without match effects, parameters are estimated in two steps using the Frisch-Waugh theorem. Estimators of the seller and buyer fixed effects are denoted by and , respectively. Finally, the estimator of the match effect is given by the formula $ = ̂ --.

Note that replacing ̂ by its expression yields $ = ∑ ̂ ∈( , )

/ , where ̂ = ---( ) -( ) . Hence, estimated match effects are simply averages of estimated residuals computed at the match level.

Appendix B. Sample restrictions

First, we exclude transactions with a missing buyer identifier (149,709 observations deleted). 18 Second, we delete observations corresponding to direct sales and restrict our attention to transactions at auctions (909,307 observations deleted). 19 Third, we keep only the 49 species for which there are more than 60,000 transactions over the period (2,197,513 observations deleted).

Fourth, for each species, we exclude the few incoherent transactions with a negative total value or a negative quantity (30,382 observations deleted) as well as transactions with a price per kilo in the bottom 0.1% or the top 0.1% to avoid potential outliers (63,971 observations deleted). Finally, in line with our empirical strategy, we keep for each species the largest group of well inter-connected sellers and buyers and exclude three species for which this group does not contain most of the observations (282,098 observations deleted). 20

18 There are missing identifiers only for buyers. The identifier is always given for vessels involved in transactions. 19 We eliminated direct sales because the fish price for such transactions is fixed in a very different way. 20 The three fish species excluded from the sample are sardine (114,784 transactions), white seabream (75,279 transactions) and anchovy (72,884 transactions). For each of these three species, the share of transactions in the main group is 53.8%, 61.1% and 76.3%, respectively. For the remaining 46 species, only 19,151 transactions are excluded because they are not in the main group.


Heath Heatley

Trung N Tran

Arnaud Bourdin

Andrew Menzies-Gow

Joshua David

Ekaterina Jackson

Jatin Maslova

Derek Chapaneri

Victoria Skinner

Jeffrey Carter

Kai Shi

Chan

David Joshua Jackson

Ekaterina Maslova

Jatin Chapaneri

Derek Skinner

Victoria Carter

Jeffrey Shi

Kai Chan

Con Ariti

John Haughney

Professor David B Price
email: dprice@opri.sg

Observational UK cohort study to describe intermittent oral corticosteroid prescribing patterns and their association with adverse outcomes in asthma

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Oral corticosteroids (OCS) for asthma are associated with increased risks of developing adverse outcomes (adverse outcomes); no previous study has focused exclusively on intermittent OCS use.

Methods

This historical (2008-2019) UK cohort study using primary care medical records from two anonymised, real-life databases (OPCRD and CPRD) included patients aged≥4 years with asthma receiving only intermittent OCS. Patients were indexed on their first recorded intermittent OCS prescription for asthma and categorised by OCS prescribing patterns: oneoff (single), less frequent (≥90 day gap) and frequent (<90 day gap). Non-OCS patients matched 1:1 on gender, age and index date served as controls. The association of OCS prescribing patterns with OCS-related AO risk was studied, stratified by age, Global Initiative for Asthma (GINA) 2020 treatment step, and pre index inhaled corticosteroid (ICS) and shortacting β2 -agonist (SABA) prescriptions using a multivariable Cox-proportional hazard model.

Findings

Of 476 167 eligible patients, 41.7%, 26.8% and 31.6% had one-off, less frequent and frequent intermittent OCS prescribing patterns, respectively. Risk of any AO increased with increasingly frequent patterns of intermittent OCS versus non-OCS (HR; 95% CI: one-off 1.19 (1.18 to 1.20), less frequent 1.35 (1.34 to 1.36), frequent 1.42 (1.42 to 1.43)), and was consistent across age, GINA treatment step and ICS and SABA subgroups. The highest risks

INTRODUCTION

Despite the availability of novel and innovative treatments for asthma, oral corticosteroids (OCS) are still widely used.1 2 Both the British Thoracic Society/ Scottish Intercollegiate Guidelines Network3 and the Global Initiative for Asthma (GINA) report1 recommend an intermittent OCS dose of 40-50 mg prednisolone daily for at least 5 days for the management of severe exacerbations, and in 2021, a Delphi study found consensus on a dose of 0.5 mg/kg/day for a short course of OCS.4 In a real-world study of OCS prescription patterns that included both intermittent and longterm OCS prescriptions in France, Germany, Italy and the UK from 2012 to 2017, 14%-44% of patients with asthma aged≥12 years were prescribed OCS and 6%-9% had high OCS use (defined as ≥450 mg within 90 days, ie, corresponding to an average of ≥5 mg per day) at some point during follow-up (median range 33-55 months).5 In a systematic review of studies from Europe, North America and Asia in patients with asthma aged>5 years, annual systemic corticosteroid (SCS) or OCS prescription was reported in ~50% of patients, with short-term use reported in up to 36% of patients; well above what might be expected for treatment according to guideline recommendations. [START_REF] Bleecker | Systematic literature review of systemic corticosteroid use for asthma management[END_REF] Recent studies have shown a high prevalence of exacerbations treated with OCS across all severities of asthma,7 8 and exacerbations are increasingly being recognised as a major problem or as a risk factor for asthma death outside of severe asthma.

The use of SCS, even in the short-term, is associated with an increased risk of developing acute and chronic adverse outcomes (adverse outcomes).9 10 A study of both intermittent and long-term SCS prescriptions (parenteral or oral; median follow-up 7.4 years) showed that this risk increased with higher cumulative and mean daily SCS exposure.11 This is supported by another study of intermittent and long-term SCS prescriptions (parenteral or oral; median follow-up 7.1 years) in which increases in cumulative incidences of steroid-related adverse outcomes were dose dependent.12 Such OCS-related adverse outcomes can have a major impact on health-related quality of life13-16 and are associated with increased healthcare resource use.17

Prior research on OCS-related adverse outcomes has focused mostly on overall OCS exposure, on cumulative or average daily OCS exposure from both intermittent and long-term prescriptions. There have been no longitudinal studies that have focused exclusively on examining the association between patterns of intermittent-only OCS prescriptions and risk of adverse outcomes. Previous attempts to classify OCS use as intermittent or long-term use were varied and based on aggregate measures over a specific time period, such as continuous OCS prescription,18 continuous OCS use without a gap,19 average number of days on OCS,20 titration patterns and cumulative daily dosage,17 21 none of which are perfect. As a result, it is challenging to separate out the adverse outcomes associated with intermittent use and long-term use given this absence of a clear definition of long-term use in secondary data. There is also a risk that, instead of identifying adverse outcomes related to intermittent OCS use, hidden historical cumulative OCS adverse outcomes are identified instead. Therefore, in this study, we specifically aimed to assess for the first time the association between longitudinal patterns of intermittent OCS prescriptions, cumulative OCS dosages and OCSrelated adverse outcomes in a large cohort of UK primary care patients with asthma identified as treated with intermittent-only OCS.

METHODS

Study design and data sources

This was a historical UK cohort study of patients≥4 years with asthma using primary care medical records from 2008 to 2019, where adverse outcomes in a cohort of patients with intermittent-only OCS use were compared with a matched patient cohort of never users of OCS. Data were sourced from the Optimum Patient Care Research Database (OPCRD)22 and Clinical Practice Research Datalink (CPRD) GOLD,23 two anonymised, real-life UK databases containing patient electronic medical records extracted from primary care and linked, in the case of CPRD, to a range of other health-related data to provide a longitudinal, representative UK population health dataset. CPRD contains data from primary care using Vision (Surgical Information Systems, Georgia, USA) software only; OPCRD contains data from a range of software providers, including EMIS (EMIS Health, Leeds, UK), iSoft (DXD Technology, Sydney, Australia) and Vision. The OPCRD comprises data extracted through the optimum patient care (OPC) clinical service evaluation and contains research-quality data for ~17 million patients across the UK. [START_REF]Optimum patient care UK[END_REF] At the time of study, the CPRD GOLD database had coverage of over 11 million current patients from 674 practices in the UK, with data linked to Hospital Episode Statistics up to March 2019, allowing for identification of any hospital admission, including admissions with asthma as the primary diagnosis, as well as outpatient visits and emergency department attendances. To avoid overlap of the same primary care data between CPRD and OPCRD, Vision data were dropped from the OPCRD database prior to commencing the study.

Patients

Patients aged≥4 years with at least 12 months' clinical data prior to index date receiving only intermittent OCS (OCS cohort) were matched 1:1 on gender, age and index date with patients with or without asthma who had received no exposure to OCS ('never users' or 'non-OCS' cohort). Patients who were receiving or suspected of receiving long-term OCS prescriptions were excluded, as per a previously defined algorithm. [START_REF] Heatley | The burden of intermittent oral corticosteroid use in asthma[END_REF] The index date for patients in the OCS cohort was the first intermittent OCS prescription within 3 months of an asthma event, which included asthma medication, consultation and/or diagnosis. Patients in the non-OCS cohort were indexed on the nearest general practitioner visit to the index date of the matched OCS patient.

OCS and non-OCS patients were also excluded if they had a diagnosis, ever, of one of the following chronic conditions commonly treated with OCS: ankylosing spondylitis, Sjögren's syndrome, systemic lupus erythematosus, ulcerative colitis, rheumatoid and psoriatic arthritis, multiple sclerosis, and Crohn's diseases. In order to ensure that the post index adverse outcomes were incident events, patients with chronic adverse outcomes pre index were excluded, which led to different match sets for different individual adverse outcomes Non-OCS patients were matched with all patients receiving OCS prescriptions according to a 1:1 ratio. **Patients with less frequent OCS use received all OCS prescriptions with a gap of ≥90 days. # Patients with frequent OCS use received at least some OCS prescriptions with a gap of <90 days, allowing for other prescription gaps to be ≥90 day. ‡ HRs were calculated using Cox regression analysis, adjusted for age, gender, body mass index, smoking and time-varying OCS prescriptions. *Behavioural disorders include diagnoses for distress, agitation, nervousness, emotional problems, irritable and abnormal behaviour among patients <18 years.

Study variables and outcomes

OCS exposures were converted into prednisolone equivalents using the defined daily dose (DDD) obtained from the Anatomical Therapeutic Chemical/DDD classification system. 25 A patient's cumulative dose was calculated as the sum of all prednisolone, or equivalent, doses (g) prescribed from index date up until the outcome event.

The methodology for classification of intermittent OCS prescribing patterns has been described separately.24 Briefly, OCS prescription patterns were evaluated across the entire follow-up period and classified as one-off, for patients with a single OCS prescription (as a proxy for OCS use), less frequent pattern, for patients with >1 prescription with any gaps>90 days but no gap<90 days, or frequent pattern, for patients with >1 prescription with <90 day gap(s).

Each patient was followed until first OCS-related AO and censored for that specific AO, or death or end of follow-up, but remained in the dataset for other conditions. The following adverse outcomes were recorded, defined according to International Classification of Diseases codes for diagnosis, and-for some adverse outcomes-other criteria, such as disease-specific medication prescription and/or physiological biomarkers: dyslipidaemia, behavioural disorders (diagnoses of distress, agitation, nervousness, emotional problems and irritable and abnormal behaviour for patients<18 years), renal impairment, osteoporosis/osteoporotic fractures, hypertension, peptic ulcer, cardiovascular disease, depression/anxiety, sleep disorders, cataracts, glaucoma, type 2 diabetes mellitus, pneumonia and sleep apnoea (online supplemental table S1).

Statistical analysis

Descriptive statistics were reported for the absolute and relative number of patients, mean, median, SD and IQR for continuous and categorical variables.

Patient demographic and clinical characteristics for the 12 months prior to index date (referred to as baseline) included age (4-<12, 12-<18, 18-<65 and ≥65 years), sex, body mass index (BMI; underweight, normal, overweight, obese and unknown), smoking status (never, current, former and unknown), short-acting β2-agonist (SABA) prescriptions (0, 1-2, 3-11 and ≥12 fills) and inhaled corticosteroid (ICS) prescriptions (0, 1-3, 4-6, 7-9, 10-12 and ≥13 fills). The SABA and ICS prescription categories were based on the distribution of the study data in the OCS cohort (online supplemental figure S1).

The risk of developing an AO was analysed using survival analysis methods. Patients with prior diagnosis of an AO, and which was classed as chronic, were excluded from the corresponding analysis in order to specifically assess incident-only adverse outcomes, meaning that the sample size for analysis of individual adverse outcomes or a set of any adverse outcomes differed from one to another. Kaplan-Meier curves were used to describe the overall risk profile of each AO. To assess the association between intermittent OCS (vs non-OCS) prescription and risk of adverse outcomes, a multivariable Cox proportional hazard model was used to calculate HR and 95% CI for each AO. The Cox models were adjusted for age, sex, BMI, smoking status and time-varying OCS prescriptions, defined a priori. The multivariable analysis was further stratified by age, GINA 2020 treatment step and prescriptions for ICS and SABA in the 12 months pre index To assess the relation between cumulative OCS dose and each AO, adjusted incidence rate ratios and 95% CI were calculated for each AO, comparing the OCS categories (>0 to <0.5 g, 0.5 to <1.0 g, 1.0 to <2.5 g, 2.5 to <5.0 g, 5.0 to <10.0 g and ≥10.0 g) to the non-OCS group.

Analyses were conducted using Stata SE V.14.2 (StataCorp, College Station, Texas, USA) and statistical significance was defined at two-sided p<0.05.

RESULTS

Patient characteristics

Of 2 130 881 patients receiving an OCS prescription for any condition (CPRD and OPCRD) between 1985 and 2019, 476 167 met the eligibility criteria (figure 1); records from 476 167 matched non-OCS patients were included, 16 716 (3.5%) of whom had an asthma diagnosis or asthma treatment ever (0.8% and 1.1% of non-OCS patients had ≥1 ICS and ≥1 SABA prescription, respectively, in the 12 months before the index date). The median follow-up (IQR) duration was 8.3 (4.2-13.7) years for the OCS cohort and 9.0 (4.7-14.7) years for the non-OCS cohort; length of time in database preindex was 17.0 (7.5-31.1) and 16.8 (7.8-30.4) years, respectively. The mean (SD) age and sex distribution at index date for patients receiving OCS prescriptions and matched non-OCS was 38.1 (22.4) years and 55.7% were female in both cohorts. There were more obese patients in the OCS cohort than in the non-OCS cohort (table 1).

Of the study patients, 198 422 (41.7%), 127 419 (26.8%) and 150 326 (31.6%) had one-off, less frequent and frequent patterns of intermittent OCS prescription during the follow-up, respectively. The mean (median (IQR)) cumulative OCS dose was 176 (150 (150-200)) mg for one-off, 510 (420 (300-600)) mg for less frequent and 2357 (940 (540-1800)) mg for frequent patterns. Patients who had more frequent patterns of intermittent OCS prescriptions were older and more likely to be female. Those who had a frequent pattern of intermittent OCS prescriptions were more likely to be obese and to be current or ex-smokers compared with the one-off and less frequent OCS groups (table 1). Across all patterns of intermittent OCS prescriptions, in the 12 months prior to initial OCS prescriptions, patients were most commonly receiving 1-2 SABA fills and ≤3 ICS fills. The proportion of patients receiving≥3 SABA and≥4 ICS fills at baseline increased with increasingly frequent patterns of OCS prescription (table 1).

Intermittent OCS prescribing patterns and risk of OCS-related adverse outcomes

The overall analysis of the association between patterns of intermittent OCS prescriptions and any OCS-related adverse outcomes included 231 196 patients, due to the exclusion of those with prevalent conditions. Compared with non-OCS patients, the risk of experiencing any adverse outcomes was elevated for one-off OCS and increased with increasing frequent pattern of intermittent OCS prescribing. The HR (95% CI) of experiencing any adverse outcomes versus non-OCS patients was 1.19 (1.18 to 1.20) for one-off OCS, 1.35 (1.34 to 1.36) for less frequent OCS and 1.42 (1.42 to 1.43) for frequent pattern of OCS prescriptions.

Similar to the risk of any OCS-related adverse outcomes, the risk of all individual OCSrelated adverse outcomes except behavioural disorders, renal impairment and peptic ulcer was already detectable in one-off OCS, and increased with increasingly frequent patterns of intermittent OCS prescriptions (figure 2). The highest risk (HR>2) of OCS-related individual adverse outcomes with increasingly frequent OCS prescribing were for pneumonia and sleep apnoea (figure 2). Kaplan-Meier curves for the relation between patterns of intermittent OCS prescriptions and individual adverse outcomes are shown in online supplemental figure S2.

The association between patterns of intermittent OCS prescription and risk of OCS-related adverse outcomes remained consistent when stratified by age, GINA treatment step and ICS or SABA prescriptions (table 2).

When examining the dose-response relation between annual cumulative OCS exposure and risk of adverse outcomes, the risk increased in a dose-response fashion with greater annual cumulative OCS dose. Importantly, compared with the non-OCS group, risks started to increase at 0.5-1.0 g for all adverse outcomes except dyslipidaemia, with modest increases for hypertension and renal impairment (figure 3).

DISCUSSION

In this historical UK cohort study of patients with asthma, we found that almost a third of the patients with intermit-tent OCS use had a frequent pattern of use (ie, more than one prescription with less than 90-day gaps) at some point during the follow-up period. In those patients with intermittent-only OCS use, compared with matched individuals who were nonusers of OCS, the risk of experiencing any OCS-related adverse outcomes increased with increasing frequent pattern of intermittent OCS prescriptions for most adverse outcomes studied, particularly pneumonia and sleep apnoea. The elevated risk of adverse outcomes was observed even for patients with one-off OCS prescriptions. The association between patterns of intermittent OCS prescriptions and risk of OCS-related adverse outcomes was relatively consistent across age categories, GINA treatment steps and prior asthma medication use.

To our knowledge, this study is the largest (with almost half a million patients), has the longest patient follow-up (34 years, with a median study period of over 25 years (pre-first and post-first OCS exposure)) and is the most definitive study yet to identify intermittent OCS use and assess the association of patterns of intermittent OCS use with risk of developing OCSrelated adverse outcomes. Our study overcame the issues associated with mixed reporting of long-term and intermittent OCS prescriptions and related adverse outcomes by focusing exclusively on intermittent-only OCS prescriptions 24 ; it also fills a need for a longitudinal study using objective methods to collect data on intermittent OCS-related adverse outcomes, increasing the specificity of the findings by minimising the risk of bias.5

Despite the extensive research on adverse outcomes associated with OCS, the use of OCS remains widespread5 and recommended in certain instances. 1 3 Our finding that increasingly frequent patterns of intermittent OCS prescription were associated with an increased risk for adverse outcomes is consistent with previous studies reporting a high risk of corticosteroidrelated adverse outcomes with OCS prescriptions,1 12 26 and with studies in adult patients with severe asthma, showing that long-term high-dose use of OCS (defined as >10 mg/day) resulted in a higher risk of developing OCS-related complications than medium OCS use (defined as 5-10 mg/day), when both were compared with low OCS use (defined as <5 mg/day) and non-OCS patients. 13 27 The fact that the risk of an OCS-related AO was highest for pneumonia in our study is not unexpected, as this is one of the most wellrecognised adverse effects of even short-term OCS use. 6 11 28 The elevated risk of sleep apnoea was more surprising, as this is not as commonly associated with OCS use. However, a link with sleep apnoea has previously been shown in patients with severe asthma receiving SCS29 and in patients with difficult-to-control asthma receiving long-term or frequent bursts of OCS, 30 as well as in a broader population of patients with active asthma of all severities receiving SCS.11 Furthermore, as our analysis was adjusted for BMI, our findings suggest that the association with OCS use may be independent of obesi-ty-one of the best-known risk factors for sleep apnoea 31 and also a common adverse effect of OCS use2 -and is instead likely mediated by other mechanisms. Possible explanations include fat deposition in the upper airway or airway dilator muscle myopathy, as has been suggested for ICS, 32 33 or an increase in airway collapsibility.

Our results demonstrating increased risks with even a one-off OCS prescription are also supported by previous research showing that short bursts of OCS can be associated with certain adverse outcomes and that each OCS prescription contributes to a cumulative burden, regardless of the dose and duration. 9 Given that the median cumulative OCS dose is higher in this study in patients with a frequent pattern of prescription than the less frequent and one-off patterns, there may be correlation between frequent patterns of intermittent prescriptions and total exposure. This observation gives physicians another tool to gauge the risk of adverse outcomes in their patients, that is, future risk is higher if patients have received OCS with smaller gaps between prescriptions. Our finding that risks started to increase at dose levels of 0.5-1.0 g also confirms the importance of minimising total exposure, and the reasons behind persistent prescribing of OCS should be further investigated. Therefore, all patients, including those with mild disease and/or receiving regular ICS and SABA treatment, could potentially benefit from being monitored for frequent patterns of OCS prescription.

Our results also showed that over 30% of patients with intermittent-only OCS prescriptions had ≥3 SABA fills in the 12-month baseline period, and those with a more frequent pattern of intermittent OCS prescriptions had more prescriptions for SABA. It has been previously shown that increased SABA exposure is associated with severe exacerbation risk, 34 which is reflected in this study with more frequent pattern of intermittent OCS use among patients with a higher number of SABA prescriptions. This supports the move away from SABA-only treatment at GINA step 1. Similarly to the findings for SABA prescriptions, more ICS prescriptions were also observed in those with a more frequent pattern of OCS prescription, although the number of ICS prescriptions was low. On that note, the fact that 40% of the OCS cohort had no ICS prescriptions during the 12-month baseline period suggests that some patients might have received their first OCS prescriptions at the same time as their first attendance in primary care with asthma, and there might also be a population of patients with asthma who are underusing ICS. It is worth noting the population in this study generally had milder disease as a result of the exclusion of long-term OCS use.

This study had several strengths including the use of an algorithm that exclusively included patients on intermittent OCS and took a longitudinal view on the patterns of intermittent OCS use, resulting in a highly specific representation of patients receiving intermittent OCS only. Furthermore, the real-world design of this study allows for generalisation of the results to patients managed in all healthcare settings. Using two well-established databases (OPCRD and CPRD) with large size and high data quality and granularity allowed us to study the association between intermittent OCS prescriptions and associated risk of multiple different adverse outcomes.

Limitations of the study included the fact that, despite using a sophisticated algorithm that was reviewed by experts familiar with the clinical implications of our study, some of the intermittent and long-term OCS prescriptions might have been misclassified, thereby underestimating the strengths of the effect estimates. The validity and completeness of individual patient records could not be assessed because the datasets represent information collected for clinical and routine use rather than specifically for research purposes. As a result, there were some missing data, especially for BMI and smoking status, which could potentially affect how confounding by these factors is adjusted for. Further-more, since the multivariable Cox proportional hazard model was not adjusted for obesity but for BMI, with some missing values, there could have been some residual confounding. Although our study included patients of all ages, the only children-specific and adolescent-specific adverse outcomes to be analysed were behavioural disorders (including diagnoses of distress, agitation, nervousness, emotional problems, irritability and abnormal behaviour). Such diagnoses are difficult to capture and of varying origin, hence a possible reason for not detecting associations with this outcome. However, analysis of all adverse outcomes stratified by the different age categories also showed an increased risk with higher frequency of prescribing patterns of intermittent OCS for the youngest patients. In patients with one-off OCS use, there could be additional bursts that were not captured, which might explain the association detected between one-off OCS prescription and developing adverse outcomes. In the context of a chest infection, prescription of prednisolone alongside antibiotics in a patient with asthma, coupled with the potential for mislabelling of a chest infection as pneumonia, may have contributed to an association between the two. Lastly, OCS prescriptions may not be directly linked to OCS use, as there is no guarantee that patients used the prescriptions that they received.

CONCLUSIONS

In conclusion, our study found that a considerable proportion of patients with asthma who are prescribed OCS intermittently have a frequent pattern of use at some point. Increasingly frequent prescribing patterns of intermittent OCS were associated with a higher risk of individual OCS-related adverse outcomes, and this association remained consistent across levels of age, GINA treatment step and ICS maintenance and SABA reliever use. The increase in risk occurred early, even with one-off prescriptions and with doses as low as 0.5-1.0 g. Our results suggest that the use of OCS, even intermittently, in the management of asthma should be minimised whenever possible.

Figure 1

 1 Figure 1 Flow chart of UK patients with asthma receiving intermittent OCS prescriptions in this study. 1 Asthma events include asthma medication, asthma review or asthma

Figure 2

 2 Figure 2HRs ‡ of adverse outcomes in UK patients with asthma receiving intermittent OCS prescriptions versus non-OCS patients. OCS, oral corticosteroid. Non-OCS patients were matched with all patients receiving OCS prescriptions according to a 1:1 ratio. **Patients with less frequent OCS use received all OCS prescriptions with a gap of ≥90 days. # Patients with frequent OCS use received at least some OCS prescriptions with a gap of <90 days, allowing for other prescription gaps to be ≥90 day. ‡ HRs were calculated using Cox regression analysis, adjusted for age, gender, body mass index, smoking and time-varying OCS prescriptions. *Behavioural disorders include diagnoses for distress, agitation, nervousness, emotional problems, irritable and abnormal behaviour among patients <18 years.

Figure 3

 3 Figure 3 HR (95% CI) for each adverse outcome by overall, cumulative OCS exposures, compared with the reference category of non-OCS patients in UK patients with asthma. OCS, oral corticosteroid

Acknowledgements

We would like to thank Sam Hijazi and Stefan Courtney of in Science Communications, Springer Healthcare, UK, for providing medical writing support, which was funded by AstraZeneca in accordance with Good Publication Practice guidelines (http://www.ismpp.org/gpp3http://www.ismpp. org/gpp3).

Funding AstraZeneca funded the study (grant/award number: not applicable).

AstraZeneca and OPRI had a role in study design, data collection, data analysis, data interpretation and writing of the report.

Twitter Jeffrey Shi Kai Chan @JeffreyChansky and David B Price @OPRI_SG Contributors All authors contributed to the writing of the manuscript. In addition, the following authors participated in research design and performed data analysis: HH, TNT, EM, DS, VC, CA, JH and DBP. DBP had full access to the data, had final responsibility to submit for publication, and accepts full responsibility for the work

Ethics approval

The study adhered to standards recommended for observational research. [START_REF] Heatley | The burden of intermittent oral corticosteroid use in asthma[END_REF] The OPCRD is maintained by Optimum Patient Care and has ethical approval from the National Health Service Research Authority (Research Ethics Committee reference: 15/EM/0150). This study was approved by the Anonymised Data Ethics & Protocol Transparency (ADEPT) Committee25 (OPCRD; ADEPT1120), and the Independent Scientific Advisory Committee (CPRD; ISAC 20_000071). The study is registered with the European Network of Centres for Pharmacoepidemiology and Pharmacovigilance (registration number: EUPAS37065). No patient-identifying information was accessible during the study.

Provenance and peer review Not commissioned; externally peer reviewed. Data availability statement Data are available upon reasonable request. Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.