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To assess the robustness of the methodologies and data used for analysing price transmission and its determinants we use the following criteria: Effort, Applicability, Reliability, Validity, Flexibility, and Largest advantages and disadvantages. Of course there is substantial heterogeneity in methods used, but this will be considered in the assessment. In assessing the robustness of the various methodologies used for analysing price transmission and its determinants it should be noted that most studies only focus on quantifying and testing (asymmetric) price transmission without investigating its determinants explicitly. Often the asymmetries found are ascribed to market power or other factors without formal tests backing up these claims.

Effort

The effort in implementing most of the applied empirical methodologies can be rated as low. Econometric techniques used for analysing price transmission such as asymmetric ADL, ECMs or VECMs are readily available in software packages as Stata or R, e.g. the APT R package. Also the more advanced methods such as threshold ECM or regime-switching techniques are often available. For meta-analysis the methodological effort is also low as this often uses standard regression techniques. Of course one needs to have knowledge about the methodologies but these are also well- documented.

Relating the found asymmetries to possible determinants would require more effort, since this often requires non-standard techniques (Abbassi et al., 2012) and additional data for possible determinants.

The effort in collecting price data for transmission studies can in general be qualified as low. Many studies use monthly farm, wholesale, or retail prices and these are often available from national statistical agencies. Weekly data may be more difficult to obtain for various stages of the food supply chain and therefore these are used less often. To illustrate, of the 71 studies reviewed 63 use data, of which 48 use monthly data, 10 use weekly data, and the remaining studies use yearly, half-yearly or four-

weekly data. No study uses daily data. So, doing the analysis at higher frequencies requires substantially more effort in obtaining such data.

If one also wants to investigate the factors affecting price transmission, additional efforts have to be made in order to have good proxies for possible factors responsible for price transmission at the same frequency (e.g. monthly). These may not always be available, e.g. data on processing or menu costs, or data on inventory.

Applicability

Most of the methods can easily be applied to other sectors, countries or time periods, provided of course that complete weekly or monthly data are available. So, applicability is rated as high. This is reflected in the large number of similar studies that were reviewed, which often use similar methods. Another illustration is the study by Kim & Ward (2013) who compare price transmission for 100 different food products in one study. The high applicability also implies that most studies are easily replicable. This also holds for simulation studies and meta-analyses, provided of course that all steps taken in existing studies are well described.

The applicability of the data can be classified as moderate. Data for a specific food supply chain can only be used for that chain. However, it is easy to extend the data to a longer period, split it up in multiple periods for robustness checks or to make comparisons over multiple periods. Of course results from an existing dataset can also be compared to results from other data, either a different food chain or a different frequency.

Reliability

Most methods allow for a highly reliable assessment of size, speed, nature and direction of price asymmetries since not only the asymmetry parameters are estimated, but also the standard errors, allowing for statistical tests on the parameters. Some studies apply and compare different methods to test for asymmetries, which enlarges the reliability of the outcomes even further. However, the factors affecting price transmission are not always considered, so on this aspect reliability has to be evaluated as moderate. There are studies that explicitly test the relation between price transmission parameters and market power (e.g. using a concentration index), inventories, temporary sales, or consumer inertia. Moreover, regime-switching studies explicitly link certain periods of market turmoil to the price asymmetry parameters. However, even the studies that do investigate underlying factors of price transmission do so in isolation. The only exception to this is the meta- analysis performed by Bakucs et al. (2014).

The reliability of the data is judged as moderate. Most data used are official price statistics. Despite the stamp 'official' it is not always clear how these are obtained or processed. E.g. are monthly data equal to values from the first or last day of the month, or are they simply averages? How are missing values and outliers dealt with? Or more fundamental question is what average farm or retail prices actually represent. Farmers receive different prices for their products based on many factors, e.g. product quality, competition among processors etc.. T. Lloyd (2017) showed that the price of a loaf of bread varies dramatically in the major UK supermarket chain due to different average prices, different timing of temporary sales, leading him to conclude that economic concepts like 'law of one price' and 'representative firm' don't seem to make sense in food retail. In their empirical study on this issue von Cramon-Taubadel, Loy, & Meyer (2006) conclude that results based on aggregated data can lead to wrong conclusions about price transmission behaviour at the level of the individual retail stores. Therefore analyses at the individual retail level would require supermarket scanner data, as e.g. used by Tifaoui & von Cramon-Taubadel (2017). A problem in

such analyses is however that individual data at wholesale or processing level are often not available. Tifaoui & von Cramon-Taubadel (2017) in the end also aggregated their scanner data in order to match them with average wholesale prices.

Another issue is whether a monthly time-frame is sufficient to capture price asymmetries. If these happen within a month, an average monthly price may only partly capture the asymmetries. In such cases it is advisable to do the analysis with both monthly and weekly data (if available) in order to assess the robustness of the results.

Validity

In terms of size, speed, nature and direction of price asymmetries most methodologies applied provide valid measurement of price transmission, so this validity can be classified as high. However, again when it comes to the factors affecting price transmission, most studies simply attribute price asymmetries found to market power or other factors, so that in this respect validity has to be qualified as low.

Since the price series used are often time-series, validity depends on careful checking of the data properties, in particular whether the data are stationary, or in case of non- stationarity whether series are cointegrated. Failure to assess this correctly may lead to invalid (spurious) inference. Recent studies also have accounted for the possibility of structural breaks in the data series. Market conditions may have changed due to policies, a food crisis or other major events. Methods such as regime-switching models can deal with such changes in data properties. So, validity largely depends on the care taken by the researcher in the analysis.

As mentioned before, price series can only provide a valid assessment of the nature of price transmission, not for its causes. In order to assess these additional data are necessary to represent factors such as market power, menu costs, inventories, etc. Since often proxy variables are used for these, validity in this case has to be judged as moderate.

Flexibility

Most approaches used are highly flexible in their application. The methods can be used with different data frequencies, different lengths of data (although for time-series applications one would argue that a certain minimum number of observations (>40?) is required, different sets of prices (farm, processing, wholesale, retail, etc.) for different products. On the other hand, one can argue that the used methods are only able to investigate certain aspects of price transmission that can be quantified, such as speed or direction of transmission, but less flexible in integrating the factors that cause price transmission.

Flexibility of monthly price data is judged as high, but for other data frequencies moderate or even low. Many countries regularly update their monthly price series and the large variety of series used in the reviewed studies from different countries and for various food supply chains illustrates the wide availability. Price series are also flexible in their application as they allow for including lagged values, first-differences etc. Largest advantages

1. Econometric methods for assessing price transmission can quantify a wide range of aspects of price transmission, such as speed of adjustment in both short-run and long-run, the direction of adjustment, the size of asymmetries etc. Also thresholds for price adjustment can be quantified as well as different regimes for price

transmission. This provides a very good quantitative overview of how prices in food supply changes adjust to one another.

2. The methods are rather well developed and described in the literature and are often available in standard econometric software packages such as Stata and R, making it possible for many researchers to apply them.

3. Various econometric methods exist for assessing price transmission, allowing for a comparison of results based on different methods, thereby enlarging the reliability of the results.

4. Price data are often relatively easy to obtain. This enables replication or follow-up of analyses in order to check robustness of findings on price asymmetries. It also makes it possible to compare price transmission of many different products in various regions.

5. Price data are flexible to use. It is easy to include lagged values or first- differences. Analyses can be performed with subsets of data to check the robustness of the analyses.

6. Price data allows for quantifying various aspects of price transmission, e.g. speed, magnitude, nature and direction of price transmission, providing a clear picture of price transmission.

Largest disadvantages

1. Most methods do not allow for testing which factors affect price transmission. Many researchers simple ascribe the asymmetries found to plausible factors, without formally testing what is causing the asymmetries.

2. Most methods assume and estimate a constant adjustment parameters in time. However, structure of the supply chain may change and therefore also the price asymmetry parameters. There are some studies that test for structural breaks and allow for different regimes, but then it also matters how these regime switches are modelled. Some studies allow for gradual regime shifts (Hahn et al., 2016;

Hassouneh et al., 2012)

3. Although the methods are available and well-documented in the academic

literature, their specification and the various aspects of price transmission that can be estimated (distributed lag parameters, speed of adjustment parameters,

threshold parameters, etc.) can be quite overwhelming for non-academics or policy makers. In other words presenting the models and their outcomes requires quite some effort by researchers.

4. Most studies only use price data, which only allows for assessing the quantitative nature of price transmission, not the factors that cause it. However, such data are often difficult to obtain, particularly at the same time interval (monthly) as price data.

5. Data are often only available at aggregate level, so that price transmission at individual retail, wholesale or farm level cannot be investigated. This also holds for product level. E.g. it may not be clear what a general meat price or dairy price represents.

6. Not always clear how the data series are constructed. E.g. how are missing values and outliers dealt with, or what is the date of measurement?

3.2 Gaps in the current literature