Separating Vertical from Horizontal Differentiation

Empirical work in demand estimation seldom states clearly what type of product differentiation firms face in the market. This happens due to the generality of demand models–such as Berry (1994) and Berry et al. (1995), among many—that in most cases can encompass both types of differentiation. However, counter-factual simulations that use the demand estimates may vary depending on what kind of differentiation one assumes. According to Sutton (1998), not accounting for vertical differentiation, for example, may lead to a too large predicted number of product entries.

Based on Khandelwal (2010), a “quality ladder” is a measure of within-industry quality dispersion. “Quality” is here understood as a demand shifter: A certain product (which is exported by a certain country or supplied by a certain firm) is identified as higher quality when, conditional on price, it has a larger demanded quantity.

Our interest in using this database is solely in product market characteristics, and not in international trade patterns or comparative advantages. For example, we are interested in cross-industry differences in quality ladder lengths, and not in explaining what makes an exporting country occupy the top or the bottom of the quality ladder in a certain industry.

The product-country fixed-effect is important not only for directly explaining the exported quantity, but also to account for endogeneity in the number of varieties. For example, there may be fixed costs to developing or producing a different variety, which gives bigger countries an advantage. Or, as Khandelwal (2010) suggests, there may be “hidden varieties” that depend positively on country size. Finally, there may be “hysteresis” in countries’ industrial development that makes them large exporters of certain products. All of those effects are captured by β_ij.

Khandelwal (2010) assumes Berry’s (1994) nested logit system and infers quality directly from the sum \(\left({\beta }_{t}+{\beta }_{ij}+{\varepsilon }_{ijt}\right)\). Provided that we assume Eq. (5), we need to divide it by \({\sigma }_{P}\).

For those not familiar with Khandelwal’s (2010) method, an example may be in order: Suppose that a demand system is estimated for the sedan-type automobile industry. The Toyota Corolla would sell a zero quantity at the price $500,000. Indeed, this is how much a Rolls-Royce Phantom costs, and yet it sells some positive quantity. We must therefore conclude that the Rolls-Royce is higher quality, being located on a higher demand curve than is the Toyota Corolla. That is why quality, the way it is estimated here, is called a “demand shifter”. We thank the editor for this example.

In our sample, the cross-industry correlation between price dispersion and the quality ladder is only 0.18.

The definition in Eq. (10) makes this measure dependent on the 10-digit HS classification system. In Sect. 4 we will address this issue more carefully and show that our results for the number of varieties are robust to alternative measures.

To be realistic, the price elasticity tends to be higher when the level of disaggregation is greater, which reflects the fact that varieties of the same product are generally closer substitutes than are different products. But the spirit of the analysis here is: Given the level of disaggregation (in our case, the industry level), when industry A is less price elastic than is industry B, this is consistent with A’s being more horizontally differentiated than is B.

Lahmandi-Ayed (2007) challenges this view. According to him, finiteness may also arise in horizontally differentiated markets – as long as consumers agree on the ranking of products when these are sold at marginal costs.

The idea of moving up technology levels is straightforward: there is an increase in R&D intensity. On the other hand, moving up Rauch categories is more involved: According to Rauch (1999), when a product has a reference price (and is thus classified as “homogeneous”) it means that it is traded on an organized exchange. Conversely, when a product does not have a reference price (and is thus classified as “differentiated”), matching buying and sellers is something that depends on “relational aspects” and is favored by proximity and common language/colonial ties.

This database is described in detail in Feenstra et al. (2002).

See Eq. (1) above. Our quality estimation is based on Khandelwal (2010), who also uses U.S. imports in his empirical implementation.

So that, if country j exports four HS goods and country l exports two HS goods that are all classified under the 5-digit SITC product ZZZZZ tag, then we will say that j exports twice as many ZZZZZ varieties as l. If only countries j and l produce and export ZZZZZ – and j exports the varieties ZZZZZ1, ZZZZZ2, ZZZZZ3, and ZZZZZ4, and l exports ZZZZZ4 and ZZZZZ5 – then we will say that there exist five ZZZZZ varieties. This way of interpreting a “variety” is consonant with the approach of Hummels and Klenow (2005), but is not unique. For example, Broda and Weinstein (2006) define a “variety” as a disaggregated-product/exporting-country pair. In Appendix D, we give examples of 4-digit industries and all of their component 5-digit products and all of their component 10-digit HS varieties.

Because the most recent year that is available in the U.S. import database is 2006, we cannot estimate product market characteristics for a period around 2011, which is the base year for Galindo-Rueda and Verger’s revision. Since our sample period is 2002-2006, we have alternatively tried the older revision in http://​www.​oecd.​org/​sti/​ind/​48350231.​pdf, based on the OECD Science, Technology and Industry Scoreboard 2003. The results (available on request) are practically identical to the results that are presented in the following sections.

Throughout the paper, we take the identification highly R&D intensive = high tech as given. As Galindo-Rueda and Verger (2016) warn, R&D intensity is an indicative but insufficient measure of high technology, which could also be detected by patenting, skill intensity, etc. However, until their working paper appeared, all OECD-STI publications made the above-mentioned identification, which is still prevalent nowadays.

According to Rauch (1999), the difference between the “conservative” and the “liberal” versions arises because of a few products that cannot be unambiguously classified. The conservative version is simply the version that is less lenient in classifying products as homogeneous. Indeed, of the 502 4-digit industries that are in our final sample, 374 industries are classified as “differentiated” by the Rauch “conservative” version, and 364 industries are so classified by the Rauch “liberal” version.

As Rauch (1999) defines, “organized” products are those that are traded on an organized exchange, such as a commodity exchange. He gives as an example Lead and Lead Alloys, Unwrought (SITC 6851), which is globally traded on the London Metal Exchange. Although “reference priced” products are not traded on an organized exchange, their prices are listed in trade publications without mentioning the name of the manufacturer. Rauch gives as an example Polymerization and Copolymerization Products (SITC 583), the price of which is quoted weekly in Chemical Marketing Reporter. In contrast, Rauch Differentiated products (defined by default as those that are neither Organized nor Reference Priced)–such as “shoes”–would require a very high level of disaggregation to be properly characterized. In the limit, this process of disaggregation would lead to products that have only one manufacturer: “branded products”.

In our webpage (https://​sites.​google.​com/​view/​eduardocorreiade​souza?​usp=​sharing), under this paper’s title, we provide the list of 4-digit industries in our sample, classified by technology level and by Rauch category, and with the number of SITC 5-digit products, the number of exporting countries, and the total value of U.S. imports (2002–2006) by industry.

Factor endowments data are also from Cadot et al. (2010). Physical capital is in U.S. dollars per worker, and human capital is in average years of schooling for the working age population. Because some SITC products appear in the U.S. import database but not in Comtrade’s, we were able to estimate factor intensities for 411 4-digit industries only.

The real exchange rates relative to the U.S. are from http://​bruegel.​org/​2012/​03/​real-effective-exchange-rates-for-178-countries-a-new-database/​.

In Table 10 of Appendix B, we re-estimate Eq. (6) in a panel that pools all industries belonging to a certain technology level or Rauch category together, instead of first estimating (6) for each industry, and then taking cross-industry averages. Because the different price-elasticities are estimated jointly in this panel, the correlations across industries are accounted for, providing a sense of their importance. The implied t-statistics of equal price-coefficients in Table 10B (the square root of the F-test statistics of equal coefficients) are higher than the respective coefficients in Table 7, which indicates the conservativeness of our inferences.

Not shown in Table 4, we note that the t-statistic of the difference in means between -1.32 (Top-tech mean) and -1.61 (Bottom-tech mean) is 6.70.

Khandelwal (2010) also finds that quality ladders are increasing with the industry R&D intensity.

Not shown in Table 4, we note that the t-statistic of the difference in means between 1.94 (Medium-high mean) and 1.56 (Medium-low mean) is 6.01. And the t-statistic of the difference in means between 1.97 (Top-tech mean) and 1.49 (Bottom-tech mean) is 8.68.

The quality ladder and price dispersion patterns across technology levels and Rauch categories are the same if these characteristics are measured by the standard deviation instead of by the interquartile range, for example. Results can be provided upon request.

Notice that our results concerning variety proliferation corroborate Kugler and Verhoogen’s (2012) choice of the Rauch classification as a proxy for horizontal differentiation, and of R&D and advertising intensity as a proxy for vertical differentiation. Drawing on Shaked and Sutton (1987), Beath and Katsoulacos (1991) further associate finiteness (a limited number of varieties) and vertical differentiation with R&D intensive goods.

Khandelwal (2010) also finds a positive correlation between the industry’s quality ladder length and its physical capital intensity.

Our conclusions here depend on the assumption that quality ladders are the main indicator of vertical differentiation. But we must admit that some of the increase in price dispersion as we move from low-techs to high-techs within the Rauch-homogeneous category may reflect an increase in vertical differentiation that is not captured by the quality ladders. Also, one may find the fact that price dispersion exists within Rauch-homogeneous industries to be at odds with the Law of One Price (LOP). However, as is known, many empirical exceptions to LOP arise because of things such as preferential trade agreements that cause the importer to buy not from the cheapest exporting country.

Because Rauch-differentiated industries represent 75% of the industries in our dataset, this type of R&D is the prevalent one, which justifies our conclusions with regard to the OECD-STI classification at the end of Sect. 4: That real-world R&D efforts are directed mainly at improving quality.

In Appendix D, the reader will find how some of the 4-digit industry examples given here subdivide into 5-digit products, and how these subdivide into 10-digit HS varieties.

Another example–based only on its long (4.69) quality ladder and very high (26) number of varieties–is SITC 7812 (Motor vehicles for transport of persons): This is a Medium high-tech, Rauch-Differentiated industry.

One might conjecture whether the means in Table 7 are not hiding heterogeneity within groups, and if these patterns hold for important sectors and industries as well. In Appendix C, we group the 4-digit SITC industries into 20 ISIC sectors, and report average product market characteristics for them. Broadly, the patterns that are detected for the four-group grid analysis also hold for the ISIC sectors classified by technology level and Rauch category.

The Spearman correlation ranks each 4-digit SITC industry by the product market characteristic in question and by the R&D intensity. Given that the OECD-STI taxonomy is an ordinal variable, this is the natural correlation to use for a comparison with alternative R&D intensity measures.

Here, the number of countries that are product i’s exporters, M_it, coincides with the number of countries for which we have factor endowments data, from Cadot et al. (2010).