Estimating Import Quality: Do Countries Agree on Rankings? * Kan Yue. Purdue University. Abstract

Transcription

1 Estimating Import Quality: Do Countries Agree on Rankings? * Kan Yue Purdue University Abstract In the trade literature, there are a number of approaches that rely on price and quantity to measure quality. This paper examines three most applied approaches (unit values, demand residuals derived from a CES model, and demand residuals from an augmented nested logit framework) to answer: do these approaches yield estimates of quality that are consistent across importers? Results from Spearman s rank correlation tests show that unit values are the most consistent quality measure. As we use import quantity in addition to unit value to infer quality and estimate import demand with more controls, quality estimates become less consistent in the sense that importers disagree on the quality rankings of goods from different exporters in more product categories. Further analyses demonstrate that differences in the estimated price elasticity of demand in the CES model give rise to inconsistent quality rankings. Meanwhile, distortions in the quality rankings obtained from nested logit framework are caused by explicitly controlling for hidden variety. Keywords: Import quality, Unit value, CES, Nest logit framework JEL Classification: F1 F14 * I m grateful to David Hummels and Anson Soderbery for their invaluable guidance, discussions and support. I also thank Zhiying Gu, Robert Johnson, John Lopresti and Alexandre Skiba for helpful comments and suggestions. All errors are my own. Department of Economics, Purdue University, West Lafayette, IN kyue@purdue.edu.

2 1. Introduction Product quality matters in international trade. It has been well established that both supply of and demand for quality are positively related to trade partners income per capita, suggesting that quality differentiation plays an important role in determining international trade patterns. These systematic relationships give rise to unequal effects of trade on consumers welfare across income groups within a country. While quality upgrading is often viewed essential to a country s export success, it also results in rising wage inequality in developing countries. To better understand the welfare effects of quality specialization and how it is affected by economic development and trade liberalization, it requires us to accurately extract quality from trade data. In the trade literature, there are a number of approaches that rely on price and quantity to measure quality. The first approach is to use price or unit value as a proxy for quality under the assumption that higher quality goods are sold at higher prices. 3 The second relies on demand residuals. Higher quality products are those that sell higher quantities or higher market shares, after conditioning on price. Some of the literature (Hummels and Klenow 2005 and Hallak and Schott 2011) estimates quality as a residual of demand curves derived from models that assume a constant elasticity of substitution (CES) utility function. Other papers in the literature, following Khandelwal (2010) construct quality as a residual of demand curves derived from an augmented version of the nested logit framework in Berry (1994) (e.g. Amiti and Khandelwal 2013 and Colantone and Crino 2014). As these approaches proliferate in the literature, a question remains unanswered. Do these approaches yield estimates of quality that are consistent across importers? International trade data allows us to make use of observations on the same exporter from the perspective of multiple importers. That is, if a methodology estimates that Italian cotton shirt is of superior quality to Chinese cotton shirt when using US imports data, does it conclude the same when using Canadian or German imports? Suppose that all importers agree on which exporter produces high/low quality, then if the methodology in question accurately extract quality from the data, quality rankings of the products from different exporters should be the same for all importer. If quality rankings differ across importers, it reveals one or more of the following. First, the methodology is problematic. Second, exporters choose to sell products at different quality levels to different destinations. For instance, Japan exports their higher quality cars to the US but lower quality ones to China, therefore, Japanese 3 One line of the literature examines the relationship between quality and importer (exporter) characteristics (e.g. Baldwin and Harrigan 2011, Choi et al 2009, Hallak 2006 and Schott 2004). Another line of the literature explains different outcomes of export with firms heterogeneity in quality and uses firm-level unit price as a proxy for quality (e.g. Bastos and Silva 2010, Fasil and Borota 2013, Hallak and Sivadasan 2013, Johnson 2012 and Manova and Zhang 2012). 2

3 cars rank higher in the US but lower in China. Finally, importers valuation over the same set of import varieties within a particular product differ from each other significantly. 4 This paper proposes that consistency of quality estimates across importers is an important metric for gauging the validity of a particular methodology. In this paper, I estimate the quality of imported varieties at HS 6-digit level from 1991 to 2010 for 20 countries and the US, using the aforementioned three mostly applied approaches. The main goal of this study is to test the consistency of quality estimates across importers, approach by approach. To do so, I compare the estimated import qualities between each country and the US. Specifically, I keep the varieties that are commonly imported by each country and the US in each year and examine the similarity of their quality rankings of common varieties, product by product. To measure the similarities of quality rankings, I obtain the rank correlation of quality estimates using Spearman s rank correlation test. A rank correlation of one implies that two importers are in perfect agreement about the quality orderings of products from different exporters. A rank correlation of negative one suggests that rank orders are totally inverted and the two importers completely disagree on which exporter produces high/low quality. A rank correlation smaller than one indicates that two importers disagree on the quality rankings to some extent. If a given approach provides more consistent quality estimates than the others, we would expect to find fewer negative rank correlations and a higher mean of rank correlations. Results on the rank correlations of unit values show that the mean rank correlation is positive and relatively few products exhibit negative rank correlations. Cleaning the c.i.f. (cost, insurance and freight) unit values by conditioning on trade costs provides tighter distribution of positive rank correlations. This suggests that under the assumption that price equals to quality, countries more or less agree on the relative qualities of their imports, which is in line with the literature using micro level data. For example, Faber and Fally (2015) uses detailed matched US home and store scanner microdata and show that households strongly agree on their relative evaluation of product quality across producers. 5 Note that unit values can vary across exporters for reasons other than quality, such as the cost of production. While higher product quality shifts demand curve out, an increase in the production costs causes an upward movement along the demand curve. The response of quantity demanded to a production cost 4 Here, I define a variety as an import of a particular product from a particular exporter. For example, men s cotton shirts imported from Italy and China are considered as two different varieties. 5 Faber and Fally (2015) compare the rank order of budget shares across producers. Relative product quality is preserved across rich and poor household. 3

4 change depends on the price elasticity of demand. In principle, using import quantity in addition to unit value to infer quality should separate the two reasons that prices vary. Using the CES demand model, I show that quality can be represented as a weighted average of unit value and import quantity. The weight that is placed on import quantity is negatively related to the inverse of the price elasticity of demand, which is governed by the substitutability among varieties in the same industry. Therefore, if an importer and the US agree on which exporter produces high/low quality, quality estimates obtained from CES models should generate more consistent rankings. However, I find a substantial increase in the mass of negative rank correlations for all importers. On average, 30% of the total products exhibit negative rank correlations. In addition, the distributions of rank correlations are more disperse with lower means. These results are robust to including different sets of instruments for unit price or using the subsample where F-statistics of the first stage regressions are greater than 10. The nested logit framework in Khandelwal (2010) uses a similar intuition to extract information from both price and quantity. However, compared to the CES model it provides a richer structure for price elasticities. It allows varieties within the same product to be closer substitutes instead of assuming a constant substitutability among all varieties in the same industry. In addition, trade data groups a number of varieties into a single product category, so that varieties are hidden by their product headings. Unlike CES models, Khandelwal (2010) controls for hidden variety in the estimation of import demand so as to disentangle quality from within-product variety. Therefore, it would yield higher rank correlations of quality estimates between each importer and the US, if they truly agree on quality rankings. Surprisingly, I find a substantially large number of significantly negative rank correlations in almost 50% of the total products for all importers. 6 Mean rank correlations are close to zero. Recall that quality estimates are constructed residuals of a demand equation conditional on price and other control variables. This means that differences in the price elasticity of demand and the coefficients of other control variables could give rise to differences in quality estimates. Based on nested logit framework in Khandelwal (2010), I recalculate each country s import quality by restricting one common parameter at a time to be equal to the US estimates. Results show that negative rank correlations of quality rankings are caused by the differences in the estimated coefficients (γ) of the proxy for hidden variety, exporter s population. While γ is meant to capture consumers love of variety, it does not correlate with the country characteristics that explain the variations of 6 A rank correlation is significant when its p-value is smaller than

5 consumers valuation of variety across importers. In addition, within-product variations of quality estimates are explained by exporters population. Put another way, the ranking of quality estimates is determined by the relative size of exporters population instead of the relative level of their true quality. Excluding hidden variety from the estimation of import demand curve substantially reduces the number of negative rank correlations, while the distributions of rank correlations are centered to zero. This suggests that there still exists a relatively strong disagreement on which exporters produce high/low quality goods in many products. 7 Future studies on why importers valuation of products from different exporters are not uniform and how it contributes to importers disagreement on quality rankings would be very useful. This paper proceeds as follows. Section 2 derives quality estimates in CES demand system and nested logit framework. Section 3 describes the data and identification strategy. Section 4 examines the consistency of unit values and the quality estimates obtained from CES model and nested logit framework in Khandelwal (2010) across importers, separately. Section 5 explores three possible explanations for the large set of inconsistent quality estimates across importers. Section 6 concludes. 2. Demand System and Empirical Implementation 2.1. CES Demand and Unit Value Consumption I model consumer s preference for a single importer and industry, so importer and industry subscripts are suppressed. Consumers buy from up to C countries in each of the H products within the same industry. In a CES demand system, consumers utility takes the following form: σ 1 σ U = [ λ cht N cht q cht h H c C ] σ σ 1, σ 1 (1) U is defined over all the products (h) from all the exporters (c) within the industry. I define a variety ch as an import of product h from exporter c. q cht is the total quantity of variety ch within the industry imported at time t. Here, I assume that exporter c produces N cht symmetric varieties within product h at time t. These varieties share the same quality and they are sold at the same price. λ cht is the quality of variety ch at time t. Quality is a demand shifter that raises the quantity of a variety imported at a given price. σ is the elasticity of substitution. 7 Same results are found when I restrict price elasticities in the CES model to be equal to the US estimates. 5

6 Under the assumption of Independence of Irrelevant Alternatives (IIA), all the varieties within a particular industry are equally substitutable with one another. There are two implications for any given industry. First, the substitutability between two varieties within the same product category equals to that between two varieties from different product categories. Second, the elasticity of substitution of varieties is a constant across products, i.e. σ h = σ h = σ. For example, in the automobile industry, this means that the substitutability between Japanese passenger cars and German passenger cars and the substitutability between Japanese trucks and German trucks are the same. Consumers maximize their utility subject to N cht p cht q cht h H c C < E t (2) Here, p cht is the price of variety ch imported at time t, and E t is the importer s expenditure in the industry at time t. Demand for variety ch at time t is q cht = (N chtλ cht ) σ σ P p t E t (3) cht where P t = ( [( p cht h H c C ) σ 1. λ cht )1 σ ] Taking logarithms on both sides of Eq. (3), we obtain the following prediction for the quantity of variety ch imported at time t : ln q cht = σ(ln N cht + ln λ cht ) σ ln p cht + ln P t + ln E t (4) where ln P t + ln E t is a constant in a given year t at the industry level. They are independent of who exporter c is. In the econometric specification, they will be captured in the year fixed effect. In Eq. (4), we cannot disentangle quality (λ cht ) from within-product variety (ln N cht ), unless we have detailed data on the number of varieties per product from each exporter (Hummels and Klenow 2005 and Blonigen and Soderbery 2010). Due to the same issue, the observed quantity in the import data is an aggregated quantity, Q cht = N cht q cht. Therefore, within each industry, import demand is estimated as follows: ln Q cht = θ t σ ln p cht + σλ cht (5) 6

7 where θ t is year fixed effect. Therefore, the quality of variety ch from CES model is calculated as: 8 λ cht CES = ln p cht + 1 σ ln Q cht (6) Conceptually, we can think of λ cht CES as a weighted average of price and quantity. The demand system incorporates both quality differentiation and horizontal differentiation. The importance of horizontal differentiation is revealed by the parameter, σ. That is, how much weight we place on quantity demanded when inferring quality is negatively related to the substitutability among varieties in the industry or the price elasticity of demand. The IIA assumption restricts the substitutability among varieties to be a constant across products within an industry. In the automobile industry, this means that consumers put same weight on horizontal differentiations when they choose a passenger car and a truck. To show how consumers spending pattern reveals their perceptions on the quality ranking of different varieties, consider this example. Suppose that US imports passenger cars (h) from Japan (exporter c) and Germany (exporter c ). Based on Eq. (3), the ratio of US imports of Japanese passenger cars relative to German passenger cars in the automobile industry is Q cht Q c ht = ( N cht N c ht λ cht λ c ht σ ) ( p σ cht ) p c ht (7) From Eq. (7), we obtain the ratio of quality of Japanese passenger cars to German passenger cars in the US market: 9 λ cht λ c ht = ( Q 1/σ cht ) ( p cht ) (8) Q c ht p c ht Eq. (8) demonstrates that the quality ratio, i.e. how US consumers rank passenger cars from Japan and Germany, depends on a weighted average of price ratio and quantity ratio of the two varieties. The weight is negatively related to the substitutability among cars from different exporters or the price elasticity of demand in US automobile market. 8 Note that the year fixed effect may also capture quality upgrading in the industry over time, so it is included in the quality estimates. Because ln P t + ln E t is the same value for all the varieties within a given industry in a given year, the quality estimate of each variety will be raised by a constant, while relative qualities remain unchanged. Therefore, quality rank orders are unaffected. 9 For simplicity, let us assume that the numbers of symmetric varieties within passenger cars from Japan and Germany are equal, because we cannot separate quality from within-product variety. 7

8 There are two special cases in Eq. (8). First, if σ = 1, then the shares of consumption allocated to Japanese cars and German cars are constants regardless of changes in the prices. Relative quality of Japanese cars to German cars is then inferred from their relative import value shares. 10 Second, if cars from different exporters are considered perfect horizontal substitutes (σ ), the relative quality of Japanese cars to German cars is implied by their relative prices. For intermediate cases of sigma, the intuition is as follows. Suppose that German cars are more expensive than Japanese cars. If σ is small, Japanese cars and German cars are less substitutable with each other and consumers put more weight on horizontal differentiations. In this case, German cars can survive in the market with higher prices and the same quality because consumers enjoy their distinct features. In contrast, a big σ suggests that Japanese cars and German cars are considered close substitutes in a horizontal sense and the market demand becomes elastic. In an extreme case where consumers do not care about horizontal differentiations at all (σ ), the demand curve is flat. Consumers choices depend only on quality adjusted prices. The only way that more expensive German cars can survive in the market is if higher prices are the result of higher quality (on a higher demand curve). In this case, we can infer quality rankings directly by comparing unit values of imports. This is an approach that has been commonly applied in the trade literature. I will discuss this in the following section Production and Pricing Firms that produce the same product h differ in two dimensions of heterogeneity across countries. The first source of heterogeneity is productivity, a ch, which measures the labor cost used in producing one physical unit of product h. A decrease in a ch lowers the marginal cost of production. The second source is the quality of variety ch, λ ch. A higher quality implies a higher marginal cost of production. 11 Each firm sets the factory gate price as a constant markup over marginal cost: f p cht = a cht λ β cht σ, 1 σ 0 < β < 1 (9) Each firm sets price in destination i as the factory gate price p f cht, multiplied by ad-valorem trade costs (τ icht ): p cht = a cht λ β cht σ 1 σ τ icht (10) 10 Import value share of variety ch is defined as the share of the value of variety ch in the total import value of the industry. 11 Previous literature assumes a positive relationship between quality and marginal cost, e.g. Baldwin and Harrigan (2011), Khandelwal (2010) and Verhoogen (2008). Kugler and Verhoogen (2012) provide with empirical supports and show that high quality production requires high quality inputs. 8

9 Here, β is the elasticity of marginal cost with respect to quality. I assume that trade costs take the following form: ln τ cht = δ 1 ln(1 + t iht ) + δ 2 ln d ic ln p oil,t + δ 3 (ln d ic ) 2 ln p oil,t + δ 4 ln ER ct + δ 5 I ct + ε cht (11) where t ht is an MFN tariff of product h facing all exporters in importer i. d ic is the distance between exporter c and importer i. p oil,t is the oil price at time t. ER ct is the exchange rate of exporter c at time t. I ct include dummies that indicate whether the country pair shares a common border, a common language, a preferential trade agreement, a colonial relationship, and a common colonizer. 12 For a given importer, taking logarithms on both sides of Eq. (10), we obtain the following prediction for the unit value of variety ch imported at time t: 13 ln p cht = ln a cht + β ln λ cht + ln ( σ 1 σ ) + ln τ cht (12) Based on Eq. (12), if we measure quality using only unit value, we cannot disentangle quality (λ cht ) from productivity (a cht ). ln ( σ ) is a constant. Therefore, the c.i.f. price of variety ch at time t is estimated as 1 σ follows: ln p cht = δ 1 ln(1 + t ht ) + δ 2 ln d c ln p oil,t + δ 3 (ln d ic ) 2 ln p oil,t + δ 4 ln ER ct + δ 5 I ct + ε cht (13) Given that trade data reports the c.i.f. (cost, insurance and freight) import value and higher unit value of a variety ch may simply arise from a higher trade cost of shipping product h from exporter c, removing trade cost would give us a pure measure of quality. Therefore, to control for trade cost, the quality of variety ch at time t is then calculated as 14 λ cht UNITVAL = ln p cht δ 1 ln(1 + t ht ) δ 2 ln d c ln p oil,t δ 3(ln d ic ) 2 ln p oil,t δ 4 ln ER ct δ 5I ct (14) 12 Dropping ln ER ct and I ct does not affect the results in section Note that in log terms, the technology of producing variety ch of quality λ cht has a country-specific intercept, ln a c, while the slope, β (the elasticity of marginal costs with respect to quality) is the same across countries. 14 UNITVAL λ cht cannot separate the technology or the productivity in producing variety ch from consumers valuation for quality. Given UNITVAL that a c does not vary across importers, any inconsistency of the ranking of λ cht between two importers would stem from the difference in the product quality. 9

10 2.2. Nested Logit Framework In Khandelwal (2010), consumer n makes discrete choices across varieties within an industry and chooses variety j that provides the highest indirect utility given by: V nj = θλ j αp j + ε nj (15) where λ j is quality, representing any attribute that enhances consumers willingness to pay for variety j. θ reflects consumers valuation for quality. ε nj is assumed to be distributed i.i.d. Type-I extreme value, which captures the horizontal product differentiation among varieties. To apply the nested logit framework in Berry (1994), Khandelwal (2010) defines industries at the SITC 5-digit level and products at the HS 10-digit level. 15 In addition, a product is referred to as a nest, and an import from country c within product h is called variety ch. Therefore, for a single industry, consumer n s indirect utility of choosing variety ch is: V ncht = λ 1.ch + λ 2.t + λ 3.cht αp cht + μ nht d ch + (1 σ)ε ncht (16) H h=1 Quality consists of three components: 1) λ 1.ch is the time-invariant valuation that consumers attach to variety ch; 2) λ 2.t is the year fixed effect; and 3) λ 3.cht is the variety-time deviation from the fixed effect, which is not H observed by econometricians. h=1 μ nht d ch + (1 σ)ε ncht captures horizontal product differentiation and allows consumer n s preferences to be more correlated for varieties within product h. 16 σ (0, 1] controls for the substitutability of varieties within a nest. As σ approaches 1, the correlation in consumers tastes for varieties within a nest is close to 1. Thus, the varieties are highly substitutable. According to Berry (1994), the demand curve of variety ch implied by Eq. (16) is ln s cht ln(s 0t ) = x cht β + αp cht + σ ln(ns cht ) + λ 3.cht (17) where s cht = q cht ch 0 q cht + q 0t 15 For example, HS is a women s or girls silk sweater containing 70% silk, while SITC is a jersey, pullover, slipover, cardigan, etc. 16 μ nht is the common valuation that consumer n places on all varieties within product h, and d ch is a dummy variable that takes the value of 1 if country c s exports lies in product h. 10

11 s 0t = q 0t + q 0t ch 0 q cht = 1 import penetration t s cht is variety ch s total market share within the industry, while s 0t is the market share of outside (domestic) variety. q cht is the quantity of variety ch, and q 0t is the quantity of domestic output. x cht includes variety characteristics. Import penetration is defined as the share of all foreign varieties in an industry s total consumption. ns cht = q cht q ht is variety ch s share within imported product h (nest share), where q ht = c C q cht. Given that variety characteristics are unobservable in the trade data, Khandelwal (2010) utilizes the year fixed effect and the variety fixed effect to capture the deviation from the average quality of variety ch, λ 3.cht. Eq. (17) then becomes: ln s cht ln(s 0t ) = λ 1.ch + λ 2.t + αp cht + σ ln(ns cht ) + λ 3.cht (18) Khandelwal (2010) argues that a country s large markets share in the industry may simply be the result of exporting more unobserved or hidden varieties. Therefore, he includes the population (pop ct ) of exporting country c at time t to the regression as a proxy for hidden varieties. The demand curve of variety ch is estimated by ln s cht ln(s 0t ) = λ 1.ch + λ 2.t + αp cht + σ ln(ns cht ) + ln pop ct + λ 3.cht (19) The quality of variety ch at time t is calculated using estimated parameters: λ cht = λ 1,ch + λ 2,t + λ 3,cht = ln s cht ln(s 0t ) α p cht σ ln(ns cht ) γ ln pop ct (20) Eq. (19) has two advantages over Eq. (5) derived from CES demand system in estimating import demand curve. First, nested logit model partially relaxes the IIA property in the CES model by introducing nest share ( q cht q ht ) and allowing varieties within the same product category to be closer substitutes. Second, Eq. (19) explicitly controls for hidden variety so as to disentangle quality from within-product variety. Based on Eqs. (17) and (19), λ cht is the relative quality of variety ch to outside variety, domestic variety. Khandelwal s (2010) approach has been applied to estimating import quality for countries in the European Union and the United States, where domestic production data is available at the combined nomenclature (CN) 8-digit level and standard industrial classification (SIC) 4-digit level, respectively. 11

12 However, its application to other countries, particularly developing countries, is handicapped by the lack of disaggregated data on domestic production or s 0t. Note that q cht ch 0 q cht s cht = q cht ch 0 q cht ch 0 q cht ch 0 q cht is the share of variety ch in the total imports of an industry. + q 0t ch 0 q cht ch 0 q cht total imports in an industry s total consumption. Thus, we can rewrite Eq. (19) as: +q 0t = 1 s 0t is the share of ln q cht q t + ln(1 s 0t ) ln(s 0t ) = λ 1.ch + λ 2.t + αp cht + σ ln q cht q ht + γ ln pop ct + λ 3.cht where q t = ch 0 q cht. Since ln(1 s 0t ) ln(s 0t ) only varies over time, it can be absorbed in λ 2.t. Therefore, identical α, σ, and γ are obtained by running 17 ln q cht q t = λ 1.ch + λ 2.t + αp cht + σ ln q cht q ht + γ ln pop ct + λ 3.cht (21) The advantage here is that Eq. (21) can be estimated using only import data. Then, the quality estimates is calculated as λ cht = ln q cht q t 2.3. Consistency of Quality Estimates α p cht σ ln q cht q ht γ ln pop ct (22) Based on Eq. (21), quality estimates of all varieties are scaled up by a constant compared to those obtained from running Eq. (19). This leaves their relative qualities unaffected and allows us to test the consistency of quality estimates across importers by exploring the quality rankings of common varieties. I compare each country s import quality estimates with the US estimates, approach by approach. For example, suppose that Canada and the US import cotton shirts from five common exporters, I compare the rankings of the estimated quality of these five shirt varieties in the two countries to examine whether Canada and the US agree on the relatively quality of their commonly imported shirt varieties. 17 To verify the feasibility of estimating quality without domestic production data, I run Eq. (19) and (21) separately using US import data at HS 10-digit level from the same source as in Khandelwal (2010). Appendix B describes data and results. 12

13 To measure the similarities among quality rankings, Spearman s rank correlation test is performed on two sets of quality estimates within each product and each year. The correlations are between -1 and 1. A rank correlation of one implies that two importers are in perfect agreement about the quality orderings of products from different exporters. A rank correlation of negative one suggests that rank orders are totally inverted and the two importers completely disagree on which exporter produces high/low quality. A rank correlation smaller than one indicates that two importers disagree on the quality rankings to some extent. If a given approach provides more consistent quality estimates than the others, we would expect to find fewer negative rank correlations and a higher mean of the distribution of rank correlations. 3. Data and Identification I estimate the qualities of imported varieties at the HS 6-digit level from 1991 to 2010 for 21 countries, running Eqs. (5), (13), and (21). 18 Import data are collected from the UN ComTrade Database, where c.i.f. (cost, insurance, and freight) values are recorded. Products at HS 6-digit level serve as nests and an import from country c within a HS6 product is defined as variety. 19 All of the varieties that report a quantity of one unit or a total value of less than $7500 in 2010 US dollars are excluded. The sample is also restricted to manufacturing industries at the SIC 4-digit level. Identifying price effect in Eqs. (5) and (21) can be problematic because some of the price variation is correlated with quality which is partially captured in the error term. To address the endogeneity issue, I instrument unit value with exporter c s exchange rate (ER c ) and the interaction of distance between country c and the US with oil price (dist c oilprice t ). 20 Any change in ER c, dist c or oilprice t will cause a movement along the demand curve. However, they are uncorrelated with quality. These instruments only vary across exporter*time. 21 The other independent variable in Eq. (21), ns cht, is also endogenous in that, within product h, a country imports more from exporter c due to higher quality. Following Khandelwal (2010), ns cht is instrumented with the number of varieties imported within product h (prodnv ht ) and the number of varieties 18 HS6 is the most disaggregated classification that is common to all countries in the sample. 19 Appendix Table A1 lists the countries along with their total imports, total number of SIC industries and total number of HS products. 20 Appendix Table A2 lists the source of data. 21 Khandelwal (2010) instruments unit value by variety-specific unit transportation cost (Trans cht ), because the proxy for delivered price is the c.i.f. unit value, which is defined as the sum of the values, total duties and total transportation cost divided by import quantity. However, variety-specific unit transportation cost is not available at HS 6-digit level for the other countries in the sample. 13

14 exported by country c (ctrynv ct ). 22 The first instrument is positively correlated with the total imports within product h. As the country imports more varieties, the share of certain variety ch becomes smaller. The second instrument is positively correlated with the quantity of each variety exported by country c. If an exporter produces more varieties, then its share in the total imports of the product becomes larger. These two instruments vary across product*time and exporter*time, respectively. 4. Results on Consistency of Quality Estimates across Importers 4.1. Unit Value Unit value has been widely used as a proxy for quality in the trade literature. In this section, I focus on the rankings of unit values rather than the absolute level of unit values. That is, do importer i and the US agree on which varieties are high priced (and under the restrictive assumptions of Eq. (8), high quality) and which are low? In each year, I keep the varieties that are commonly imported by country i and the US and conduct the Spearman s rank correlation test on the two sets of unit values of commonly imported varieties, product by product. The number of rank correlations obtained for each importer i is equal to the total number of products that country i and the US both import from 1991 to Rank correlations are positive (negative) if importer i and the US relatively agree (disagree) on the quality rankings. Here, I take Canada and product HS (ice cream) as an example. In 2007, both Canada and the US import ice cream from ten exporters that are listed in the Column (2) of Table 1. Columns (3) and (5) report the unit values of these ice cream varieties. Columns (4) and (6) list the rank orders of those unit values. The rank correlation of the two sets of unit values is In total, there are over 50,000 common HS 6-digit product * year categories imported by Canada and the US, so that we obtain over 50,000 rank correlations. Instead of looking into every single rank correlation, I examine the distribution of all the rank correlations for Canada as in Figure 1. Similarly, Figure 2 presents the distributions of the rank correlations of unit values for developed and developing importers, separately. Two findings are worth noting. First, the share of negative correlations is small with very few of them being statistically significant. Second, the mean rank correlations are positive for all importers. Meanwhile, they are slightly higher in developed countries. As mentioned, trade data reports the c.i.f. (cost, insurance and freight) import value and higher unit value of a variety ch may simply arise from a higher trade cost of shipping product h from exporter c, removing 22 According to Khandelwal (2010), it is standard in the literature to assume that variety entry and exit occur prior to exporting firms quality choice, therefore, these instruments are correlated with the nest share and uncorrelated with λ 3.cht. 14

15 the trade cost would give us a pure measure of quality. I run Eq. (13) and calculate the unit value residuals as in Eq. (14). Then, I perform Spearman s rank correlation test on unit value residuals for each product*year. Figure 3 plots the distributions of rank correlations of unit value residuals. They share similar patterns with those in Figure 2. To investigate the distributional differences of rank correlations of unit values and unit value residuals, I look into two developed countries, Australia and Canada, and two developing countries, China and Mexico. Figure 4 compares the distributions of rank correlations of unit values and unit value residuals between each selected importer and the US. I find that the mass of negative rank correlations decreases and the density of the rank correlations at the mean increases in the two developed countries. In addition, removing trade cost leads to a tighter distribution of rank correlations with more than 75% of them being positive for all four selected importers Quality Estimates under the CES Demand System I run Eq. (5) industry by industry separately for each of the 21 countries and calculate the quality of each variety ch imported by each country i at time t. Then, I compare the quality estimates, λ cht s, as revealed in country i s imports to estimates of the same set of λ cht s from the perspective of the US. Similar to the procedure described in Section 4.1, I keep the varieties that are commonly imported by country i and the US. A rank correlation of the two sets of quality estimates are obtained for each product in each year. Table 2 shows the summary statistics of first stage regressions of unit value run separately for each SIC 4-digit industry. In this case, five countries are included: Australia, Canada, China, Mexico and the United States. The first two rows list the median coefficient of each instrument. 23 The results show that delivered prices decrease with exchange rate. This means that, as the currency in exporting country depreciates, the price of its products become lower, which is in line with the theory. The effect of distance or oil price change on the unit value is positive in the case of Australia, China and the US, which is reasonable because a longer distant between trade partners and a higher oil price will result in higher trade cost and an increase in unit value. 24 Among all the industries, 50% 70% of the estimated coefficients are significant in the selected 23 Mean coefficients are close to the medians. 24 It also applies to fifteen of the other countries in the sample. 15

16 countries. Row 5 reports the first stage F-statistics. 25 They are small in Australia, Canada, China and the United States. In fact, 80% of the countries in the sample have F-statistics less than Figure 5 presents the distributions of rank correlations for developed countries and developing countries, separately. I find a larger mass of rank correlations that are significantly negative. On average, more than 30% of the total products exhibit negative rank correlations. As a result, the share of products with positive rank correlations decreases. Compared to the distributions of rank correlations of unit value residuals, the distributions in Figure 5 are more disperse with lower mean. 27 Therefore, based on CES models that infer quality using both unit value and import quality, we find that importers disagree on the quality ranking of different exporters in more products. In particular, rank orders are reversed. For instance, whenever an exporter is at the top of the quality ladder in Canada, it is at the bottom in the US. That is to say, the best way to predict what Canadian consumers love is to look at what American consumers hate Quality Estimates under the Nested Logit Demand System In this section, Eq. (21) is estimated industry by industry separately for each of the 21 countries. I then calculate the quality of each variety ch imported by each country i at time t and perform the Spearman s rank correlation test on the qualities of common varieties imported by country i and the US for each product in each year. Table 3 provides the summary statistics of the first-stage regressions of nest share. 28 Similarly, only five countries are included: Australia, Canada, China, Mexico and the United States. 29 The first two rows list the median coefficient of each instrument. Our results reveal that the share of a particular variety decreases as the total number of imported varieties increases. Moreover, a variety s share in the total imports of the product becomes larger when the exporter produces more varieties. Rows 3 and Row 4 calculates the share of significant coefficients in the total estimations for each instrument. The coefficients of both the number of 25 The median is reported instead of the mean of each coefficient and F-statistic, since the mean is driven by extremely large (small) estimates or statistics. 26 Alternatively, I include all the independent variables in Eq. (13) in the first stage regressions. Appendix Table A5 lists median first stage F-statistics for all the importers. F-statistics are smaller than 10 in most cases. 27 To show that it is not the weak instruments of unit value that cause the lower rank correlations of CES quality estimates, I keep the industries where first stage F-statistics are greater than 10, and plot the distribution of quality rank correlations within the products in those industries in Appendix Figure A1. Compared to the distributions in Figure 4, mean correlations do not get larger and the fraction of negative correlations are unchanged or similar. 28 Results from the first stage regressions of unit value confirm the conclusion in section Weak instruments may result in biased estimates of α in Eq. (21) and lead to inconsistent quality estimates across countries. However, the next two subsections show that α has no impact on quality rankings. 29 Results of other counties also verify the validity of instruments. 16

17 varieties imported within product h (prodnv ht ) and the number of varieties exported by country c (ctrynv ct ) are significant in more than 50% (and as high as 80%) of the total industries in all cases. Row 5 reports the first stage F-statistics. They are well above 10. Figure 6 presents the distributions of quality rank correlations from the nested logit methodology. All the importers exhibit negative correlations in almost 50% of the total products. Roughly 60% of the negative correlations are significantly different from zero. I find significantly positive correlations in the rank orderings only 30% of the time on average. Therefore, this methodology yields quality estimates that are wildly inconsistent between each importer and the US. Put it another way, each importer and the US strongly disagree on which exporters sell high/low quality goods in 50% the total products. In addition, the bimodal pattern of the rank correlation distribution is a common phenomenon in both developed and developing countries. To better illustrate the bimodal rank correlations, let s focus on a single country, Canada, which is similar to the US in terms of country size, geographic location, GDP per capita, economic integration, and consumers preferences. Table 4 provides an example of two products: HS Vitamin C and Its Derivatives and HS HS : Vitamin C and Its Derivatives; HS : Air Conditioning Machines, Window or Wall Types, Self-contained. Column 3 lists the common exporters (varieties). Columns 4 and 6 report the quality estimates of each variety in Canada and the US, respectively. Columns 5 and 7 report their rankings. The rank orders in the two countries are almost identical for HS with a rank correlation of 0.94 (Column 8), suggesting that Canada and the US strong agree on the quality ranking of those Vitamin C varieties. In contrast, Canada and the US disagree on the quality rankings of common varieties within HS For instance, China s air conditioning machines are ranked highest in Canada but they are of low quality in the US, and there are similar discrepancies throughout the rank order. These inconsistent quality estimates generate a rank correlation of 0.95 in HS Panel A of Figure 7 plots a bimodal distribution of rank correlations in the case of Canada. In summary, as we use import demand in addition to unit value to infer quality (CES model) and estimate import demand with more controls (Khandelwal 2010), we are supposed to extract import quality from trade data more accurately by separating shifts of the demand curve from moves along the demand curve. However, these estimates show that bringing in additional controls actually worsens disagreement in rankings. If we were to take these estimates at face value we would conclude that quality estimates become 17

18 less consistent across importers in the sense that each importer disagrees with the US on the quality rankings of their commonly imported varieties in more and more product categories. 30 As mentioned, these quality estimates have often been applied to study quality specialization in international trades. For example, how is quality upgrading affected by trade liberalization? What are the differential impacts of international trade on consumers and workers welfare among industries with heterogeneous scopes of quality differentiation? A consistent measure of quality upgrading and industrial scope of quality differentiation is essential to comparing and generalizing results obtained using different import data. However, in Appendix D, I show that importers also do not agree on which exporters are producing higher quality over time and which industries are more differentiated than the others. Therefore, it would be useful to explore some possible explanations for the inconsistency of these quality estimates. 5. Possible Explanations Suppose that all importers agree on which exporter produces high/low quality, then if a methodology accurately extracts quality from the data, quality rankings of the products from different exporters should be the same for all importer. If quality rankings differ across importers, it reveals one or more of the following. First, the methodology is problematic. Recall that quality estimates are constructed residuals of a demand equation conditional on price (and other control variables). This means that differences in the price elasticity of demand and the coefficients of other control variables could give rise to differences in quality estimates. Second, exporters choose to sell products at different quality levels to different destinations in some industries. Finally, importers valuation over the same set of products from difference exporters significantly differ from each other. In this section, I examine the first two explanations for negative quality rank correlations of quality estimates derived from nested logit framework in Khandelwal (2010). First, products with negative correlations may be concentrated in some particular industries. Second, negative correlations are likely caused by the differences in parameter estimates (α, σ and γ ) across importers. The following subsections will discuss these points in more detail Here, I compare the CDF of the distributions of quality rank correlations across products from different estimation approaches for each importer. As shown in Appendix Figure A2-A4, the distribution of rank correlations of unit value residuals (Eq. 14) stochastically dominates the one obtained using quality estimates from CES model (Eq. 6) in the range of [-1,0) for all importers. Similarly, the latter dominates the distribution obtained using quality estimates from Khandelwal s (2010) nested logit framework (Eq. 21). 31 Results on the test of the first hypothesis conclude the same when using quality estimates derived from CES model. I explore the second explanation using CES model in Appendix E. 18

19 5.1. Are negative correlations results of differences in the delivered quality across importers? Suppose that exporters choose to sell products at different quality levels to different destinations in some particular industries, we would expect to see the following two consequences. First, unit price of the same products sold by the same exporter are different across importers. If the rank correlations of the quality estimates are significantly negative in 50% of the total products, the distribution of the rank correlations of their unit values are supposed to follow similar patterns. However, we find very small share of negative rank correlations in Figure 2 and Figure 4. Second, negative correlations are concentrated in some particular industries. To understand how negative correlations are distributed among industries within each importer, I calculate the share of significantly negative rank correlations within each SIC 2-digit industry. Table 5 provides the summary statistics. Columns (1) and (3) list the SIC industries in which the largest and the smallest shares are observed, respectively. Columns (2) and (4) report the corresponding shares. Our findings are twofold. First, significantly negative rank correlations are not concentrated in any specific industries. Second, within each importer, 30%- 40% of the products in each industry exhibit significantly negative rank correlations. 32 Therefore, it is not some particular products in a particular industry that generate the large mass of negative correlations Are negative correlations caused by differences in parameter estimates? To determine whether it is the differences in parameter estimates that cause the quality rankings to differ across importers, I recalculate each country s import quality using US parameter estimates as follows: λ cht = ln q cht α US p q cht σ US ln(ns cht ) γ US ln pop ct (23) t Then, I run the Spearman s rank correlation test over the common varieties that are imported by each country and the US within each product, using the recalculated quality estimates. Again, let us first consider the case of Canada to study how quality rankings are affected. Table 6 reports the new quality estimates calculated from Eq. (23) and their rankings for HS and HS In HS , quality estimates are different from those in Table 4 whereas the rankings are similar. As for HS , rank orders reverse and match US rankings. Here, the rank correlation becomes 1. This also occurs in the other products where rank correlations were significantly negative prior to the parameter 32 The above two findings hold if we examine developed and developing countries separately. 19

20 estimates change. Panel B of Figure 7 presents a distribution of rank correlations with an average of 0.79 and a median of Figure 8 plots the distribution of new rank correlations and shows that the majority is close to one for all importers, suggesting that quality rankings are sensitive to the changes in parameter estimates. The question then becomes: which parameter matters? First, are the negative rank correlations results of the differences in price coefficients (α )? 33 Second, is it attributed to the variations in the coefficient of nest share (σ )? 34 Finally, is it caused by controlling for hidden variety in the original nested logit framework in Berry (1994)? To assess the importance of α, σ and γ in affecting quality rankings, I recalculate each country s import quality by restricting one common parameter at a time to be equal to the US estimates in the following ways: λ cht = ln q cht α US p q cht σ ln(ns cht ) γ ln pop ct (24) t λ cht = ln q cht α p q cht σ US ln(ns cht ) γ ln pop ct (25) t λ cht = ln q cht α p q cht σ ln(ns cht ) γ US ln pop ct (26) t Figure 9 presents three sets of rank correlations distributions. The first two panels present the distributions of rank correlations using quality estimates calculated from Eqs. (24) and (25), respectively. While the share of products that exhibit significantly negative rank correlations decreases slightly, the bimodal pattern of the distributions remains. This is true for both developed and developing countries. Therefore, 33 On average, the difference in the estimated price coefficient between each country and the US is in the range of ( 0.484, 0.03) cross industries, while its median is close to zero for all importers (see Appendix Table A6). Our median absolute deviations are also very small, suggesting an interquartile range of ( 0.03, 0.03). However, since the change in price coefficient affect quality estimates and the difference in price coefficient across importers can potentially lead to inconsistent quality rankings, the following paragraphs will investigate it separately. In addition, it would be helpful to show the distribution of rank correlations separately in two subsamples that consist of industries where F-statistics of the first stage regression of price (unit value) are smaller and greater than 10, respectively. However, the mean share of the industries where F-statistics are smaller than 10 in the total industries is 95%. Therefore, comparison between the two subsamples is unconvincing. 34 Columns 4 to 6 of Appendix Table A6 shows the mean and the median of the differences in the estimated coefficient of nest share between each country and the US (σ σ US ) across industries. The mean difference is as large as The medians are very close to the means. In addition, I find large cross-importer variations of the mean of σ σ US. These differences and variations are sensible. In the nested logit framework, σ captures the substitutability among varieties. How substitutable the varieties are depends on the composition of the import basket within each product. If a country and the US import the same set of varieties within each product, then their σ will be identical. Differences in σ imply different compositions of imported varieties by the two countries. The latter is reflected in the share of commonly imported varieties in the total varieties within each product (S var ). Appendix Table A7 lists the mean of S var over all the products. 20

21 differences in the coefficients of price and nest share are quantitatively unimportant for explaining inconsistent quality estimates. However, if we restrict γ = γ US to allow α and σ to differ from US estimates and calculate quality using Eq. (26), we lose the left peak of the distributions in Figure 6. The distribution is similar to the Panel B of Figure 7 where most of the rank correlations are positive and close to one. Therefore, negative correlations of quality rankings are mainly caused by the differences in the estimated coefficients of hidden variety (γ ), magnified by larger differences across exporter s population. 35 Note that for all importers, variations of quality estimates across varieties (ch) within the same product (h) are mostly driven by the variation of γ ln pop ct across exporters (c). 36 Given that exporter s population, ln pop ct, does not vary across importers, forcing γ to be the same for all importers makes the rankings of quality estimates look very similar. In other words, the rankings of quality estimates using this method are mostly explained by relative size of exporters population, not by the fundamental variation in price and quantity that these methods employ to identify quality Hidden variety Recall that γ ln pop ct is a proxy that is not present in the original nested framework in Berry (1994). Here, I will analyze the role of this deviation. Inherently, trade data provides aggregated flows even at the finest level of classification, as it groups a number of varieties into a single product category. For example, Honda Accord and Toyota Camry are two distinct varieties of cars. However, in the trade data, these varieties would be aggregated with all the other makes and models of passenger vehicles from Japan as one unique variety. In this way, varieties are hidden by their product heading (e.g., Passenger Vehicles from Japan). Feenstra (1994) raises the issue of hidden variety by showing that variety changes affect the exact price index, and the import demand elasticity. Blonigen and Soderbery (2010) confirm this with evidence from US 35 To illustrate, let us consider two varieties in the same industry: ch and c h. We use the same set of coefficient to calculate the quality of ch and c h. as we substitute coefficient with US estimates, Then, the change in quality for each variety becomes: λ cht = (α α US )p cht + (σ σ US ) ln(ns cht ) + (γ γ US ) ln pop ct λ c ht = (α α US )p c ht + (σ σ US ) ln(ns c ht ) + ( γ γ US ) ln pop c t Suppose that variety ch is of higher quality than c h and γ < γ US. If the difference between populations in exporter c and exporter c is large enough, then it will result in a larger decrease in the quality estimates of variety ch and reverse the rank order of ch and c h. 36 For each variety, I calculate the ratio of -γ ln pop ct to λ cht in Eq. (21) and the ratio of γ US ln pop ct to λ cht in Eq. (26) as the explanatory power of these factors, γ ln pop ct and γ US ln pop ct, in the variation of quality estimates, respectively. Appendix Table A8 lists the share of the ratios that are greater than 0.5 in the total varieties for each importer. On average, 80% of the variation in quality estimates across varieties are driven by the variation in γ ln pop ct. 21

22 automobile market. They find that the impacts of new variety on prices and welfare are greatly underestimated using import data instead of market data. 37 Khandelwal (2010) argues that this issue could cause an upward bias in the quality estimates. Therefore, he augments Berry (1994) with ln pop ct as a proxy for hidden variety. As in Eq. (21), γ is meant to capture elasticity of the imports of variety ch with respect to the number of unobserved varieties that country c exports within product h, which is consumers love of variety. It is well documented in the trade literature that the extensive margin of a country s imports increases with its income per capita (Hummels and Klenow, 2002), as richer countries consume relatively more high income-elastic good that are more differentiated (Fieler, 2010). 38 Therefore, we would expect to obtain larger γ in richer (and larger) importers. In Appendix C, I show that there is no discernible relationship between importers income per capita or population and the estimate of γ, which contradicts the well-established facts in the literature. So far, I have demonstrated that the variations in quality estimates is mostly explained by the differences in exporters population, ln pop ct. Controlling for ln pop ct causes distortions in quality estimate and leaves us a large set of inconsistent quality estimates across importers. In addition, γ does not correlate with the country characteristics that explain the variations of consumers valuation of variety across importers Therefore, it is preferable to estimate import demand as follows: ln q cht q t = λ 1.ch + λ 2.t + αp cht + σ ln q cht q ht + λ 3.cht (27) Figure 10 plots the distribution of rank correlations of new quality estimates based on Eq. (27) between each importer and the US. Most importers do not exhibit bimodal distributions, however, the shares of negative rank correlation are still high. Compared to Figure 3 and 5, distributions of rank correlations in Figure 37 The market data used in Blonigen and Soderbery (2010) includes information on distinct varieties (i.e. specific make and model) of Japanese cars (e.g. Honda Accord and Toyota Camry). They show that market data reveals greater net variety change over time than import data. 38 Hummels and Klenow (2002) find that the extensive margin of imports also increases with importer s size. 39 One may argue that the issue of hidden variety is not explicitly addressed in Eq. (19). However, it is worth noticing that the impact of hidden variety on market shares ( q cht ) is reflected in the nest share, q cht. To illustrate, if Japan produces more hidden varieties q t q ht within the category of passenger vehicles, Japanese passenger vehicles will absorb a larger share of a country s total imports of passenger vehicles, and thus a larger share of a country s total imports of automobiles. Therefore, not controlling for hidden variety directly as in Khandelwal (2010), implies that σ captures both the elasticity of substitution across varieties within any product and the elasticity of import demand with respect to hidden variety. Without a direct control for hidden variety, these two elasticities are not separately identifiable in the estimation. Given the focus of this methodology is to uncover quality differences across imported varieties, we are willing to sacrifice our interpretation of σ in favor of reliable estimates of quality. 40 One could still estimate import demand using Eq.(21), but include γ ln pop ct in the calculation of quality. In fact, when we compare the quality rankings between each importer and the US, this gives us almost identical distributions of rank correlations to the ones obtained using quality estimates from running Eq. (27). 22

23 10 are more disperse with a lower mean close to zero. Therefore, even if we modify the methodology to more accurately measure import quality, we still find a huge disagreement on quality rankings across importers. 41 This leads to the third explanation that preferences over products from different exporters are heterogeneous across importers. I will discuss it in the following subsection Heterogeneous Preference across Importers For a particular product h, the quality attached by importer i is as follows: ln λ ih = ln λ h + ln ε ih where λ ih = ( λ ic1 h.... λ icn h ). c and c denote exporters. λ h = ( attached to the product by all importers. ε ih = ( ε ic1 h.... ε icn h λ c1 h.... λ cn h ) is the part of quality that is commonly ) is the idiosyncratic valuation of the product by importer i. Here, let us consider three conditions when comparing quality rankings of n varieties within product h between importer i and importer j. First, the importer-specific valuation of all varieties are the same in importer i and importer j, so ε ih = ε jh. Therefore, λ ih = λ jh and the ranking of λ ic1 h λ icn h will be the same in importer i and importer j. In consequence, we will obtain a perfect rank correlation of one. Second, the importer-specific valuation of all varieties in importer i and importer j are different. However, the commonly attached quality λ h dominates within each importer, so that the rankings of λ ic1 h λ icn h is the same as the rankings of λ c1 h λ cn h in both importers. Therefore, importer i and j still perfectly agree on the quality rankings of varieties within product h. In a third case, ε ih vary across importers and the ranking of the elements in ε ih deviates far enough from that in λ h to change the rank orders of elements in λ h in one or both importer(s). 42 This can happen in 41 In Appendix E, I restrict the price elasticity in the CES model to be equal to the US estimates and recalculate import quality for each importer. I find fewer negative rank correlations and tighter distributions of rank correlations for all importers. However, mean rank correlation is still relatively small (<0.5) in all cases, suggesting that each importer still disagrees with the US on which exporters produce high (low) quality in many products. 42 For example, the composite of final demand varies across importers. Several industries contain intermediate goods. If country i s imports of product h are mainly driven by industry demand for intermediate goods instead of household demand, then ε ih may greatly deviate from λ h and reverse the ranking of the elements in λ h. 23

24 the following two scenarios. First, ε ih dominates in importer i but it doesn t in importer j, so the ranking of λ ic1 h λ icn h and λ jc1 h λ jcn h do not agree, which leads to a rank correlation smaller than one. Alternatively, ε ih dominates in both importers, but it changes the ranking of elements in λ h differently in importer i and importer j. In short, how dissimilar the quality rankings of varieties within product h look between two importers depends on 1) how much the idiosyncratic valuations of varieties in the two importers (ε ih and ε jh ) differ from each other and 2) how far the ranking of elements in ε ih deviates from that in λ h in each importer. 6. Conclusion This paper examines three most applied quality measures: unit value, demand residuals derived from a CES model (Hummels and Klenow, 2005), and demand residuals from an augmented nested logit framework and an augmented nested logit framework (Khandelwal, 2010). I answer the following question: Do these approaches yield estimates of quality that are consistent across importers? Results from Spearman s rank correlation tests show that conditional on trade cost, unit value is the most consistent quality measure across importers. As we use import demand in addition to unit value to infer quality and estimate import demand with more controls, quality estimates become less consistent across importers in the sense that each importer disagrees with the US on the quality rankings of their commonly imported varieties in more product categories. Further analyses demonstrate that the distortion of the quality rankings obtained using nested logit framework in Khandelwal (2010) is caused by explicitly controlling for hidden variety and using exporter s population as a proxy. Modifying the methodology still leaves us a huge disagreement on which exporters produce high/low quality. Future studies on understanding why importers valuation of products from different exporters are not uniform and evaluating its contribution to importers disagreement on quality rankings would be very useful. 24

25 Table 1 Unit Values of HS (Ice Cream) and Their between Canada and the US HS/Year Exporter Canada US Quality Rank Quality Rank (1) (2) (3) (4) (5) (6) (7) / Hong Kong Indonesia Israel Japan Lithuania Philippines Russia South Africa South Korea Thailand Correlation Notes: This table provides unit values and their rankings of commonly imported varieties within HS (Ice Cream) in Canada and the US. Column (2) reports the common exporters of Canada and the US (common varieties). Columns (3) and (5) list unit values. Columns (4) and (6) list the rank orders of unit values. Rank correlation of the unit values of common imported ice cream varieties between Canada and the US is reported in the last column. 25

26 Table 2 Summary Statistics of First Stage Results (CES Model) Dependent Variable: Unit Value Australia Canada China Mexico USA ln(exchange rate) ln(distance) ln(oil price) Share of stat. sig. ln(exchange rate) Share of stat. sig. ln(distance) ln(oil price) F-statistics (median) Total Industries (estimations) Notes: This table presents the summary statistics of the first-stage results from regressions of unit value for Australia, Canada, China, Mexico and the US. The first two rows list the median coefficients of exchange rate and the interaction of distance and oil price. Rows 3 and 4 report the shares of statistically significant coefficient of exchange rate and the interaction of distance and oil price in the total estimations, respectively. Row 5 presents the median F-statistics over all the industries. The last row lists the total number of industries (estimations). 26

27 Table 3 Summary Statistics of First Stage Results (Nested Logit Framework) ln(number of within-product Dependent Variable: Nest Share Australia Canada China Mexico USA varieties) ln(number of within-country varieties) Share of stat. sig. ln(number of within-product varieties) Share of stat. sig. ln(number of within-country varieties) F-statistics (median) Total Industries Notes: This table presents the summary statistics of the first-stage results from regressions of nest share for Australia, Canada, China, Mexico and the US. The first two rows list the median coefficients of the number of varieties within each product (ln prodnv) and the number of varieties exported by each country (ln ctrynv). Rows 3 and 4 report the shares of statistically significant coefficient of ln prodnv and ln ctrynv in the total estimations, respectively. Row 5 presents the median F-statistics over all the industries. The last row lists the total number of industries (estimations). 27

28 Table 4 Quality Estimates from Nested Logit Framework in Kahndelwal (2010) and Their Rank Correlation between Canada and the US HS/Year Exporter Canada US Quality Rank Quality Rank (1) (2) (3) (4) (5) (6) (7) / China Japan Great Britain South Korea Colombia Hong Kong / China Brazil Japan Mexico South Korea Thailand Italy Malaysia Israel Singapore Correlation Notes: This table provides quality estimates and quality rankings of commonly imported varieties within two products obtained from running Eq. (21) in Canada and the US. Column (2) reports the common exporters of Canada and the US (common varieties). Columns (3) and (5) list quality estimates. Columns (4) and (6) list quality rank orders. Rank correlation of common varieties qualities for each product between Canada and the US is reported in the last column. HS : Vitamin C and Its Derivatives; HS : Air Conditioning Machines, Window or Wall Types, Self-contained. 28

29 Table 5 Summary Statistics of the Share of Significantly Negative s within SIC 2- digit Industries (Nested Logit Framework in Kahndelwal (2010)) Country Maximum Minimum Mean Median SIC Share SIC Share (1) (2) (3) (4) (5) (6) Developed Country Australia Canada France Germany Great Britain Ireland Japan New Zealand Singapore Spain Developing Country Argentina Brazil China India Mexico Russia Saudi Arabia Turkey Ukraine South Africa Note: This table presents the summary statistics regarding the share of significantly negatively rank correlations within SIC 2-digit industries for 20 countries. Columns (1) and (3) list the SIC 2-digit industries that have largest and smallest share of significantly negative rank correlations, respectively. Columns (2) and (4) report the largest and smallest share, respectively. Column (5) reports the average share of significantly negative rank correlation across all SIC 2-digit manufacturing industries. Column (6) reports the median. 29

30 Table 6 Quality Estimates from Nested Logit Framework in Kahndelwal (2010) and Their Rank Correlation between Canada and the US (Calculated using US Coefficient) HS/Year Exporter Canada US Quality Rank Quality Rank (1) (2) (3) (4) (5) (6) (7) / China Great Britain Japan Colombia Hong Kong South Korea / Singapore Israel Malaysia South Korea Thailand Italy Maxico Japan Brazil China Correlation Notes: This table provides quality estimates (re-calculated as in Eq. 23 using US coefficient estimates from running Eq. 21) of commonly imported varieties within two products and their rankings in Canada and the US. Column (2) reports the common exporters where Canada and the US import (common varieties). Column (3) and (5) list quality estimates. Columns (4) and (6) list quality rankings. Rank correlations of common varieties qualities between Canada and the US are reported in the last column. HS : Vitamin C and Its Derivatives; HS : Air Conditioning Machines, Window or Wall Types, Self-contained. 30

31 Figure 1 Distribution of s of Unit Value (Canada vs. US) Figure 2 Distribution of s of Unit Value 1.5 Developed Country Density 1 Developing Country Density Australia Germany France Ireland New Zealand Canada Spain Great Britain Japan Singapore Argentina China Mexico Saudi Arabia Ukraine Brazil India Russian Turkey South Africa 31

32 Figure 3 Distribution of s of Unit Value Residuals Developed Country Developing Country Density Density Australia Germany France Ireland New Zealand Canada Spain Great Britain Japan Singapore Argentina China Mexico Saudi Arabia Ukraine Brazil India Russia Turkey South Africa Figure 4 Comparing Distributions of s of Unit Value and Unit Value Residual for Selected Importers Australia Canada mean (UV)=0.35 std (UV)=0.33 Density mean (UVR)=0.35 std (UVR)= mean (UV)=0.37 std (UV)= Density 1 mean (UVR)=0.40 std (UVR)= Unit Value (UV) Unit Value Residual (UVR) Unit Value (UV) Unit Value Residual (UVR) China Mexico mean (UV)=0.23 std (UV)=0.32 Density mean (UVR)=0.16 std (UVR)= mean (UV)=0.24 std (UV)= Density 1 mean (UVR)=0.19 std (UVR)= Unit Value (UV) Unit Value Residual (UVR) Unit Value (UV) Unit Value Residual (UVR) 32

33 Figure 5 Distribution of s of Quality Estimates derived from CES Model Developed Country 1.5 Developing Country Density.5 Density 1 1 Australia Germany France Ireland New Zealand Canada Spain Great Britain Japan Singapore Argentina China Mexico Saudi Arabia Ukraine Brazil India Russia Turkey South Africa Figure 6 Distribution of s of Quality Estimates derived from Nested Logit Framework based on Khandelwal (2010) Developed Country Developing Country Density Density Australia Germany France Ireland New Zealand Canada Spain Great Britain Japan Singapore Argentina China Mexico Saudi Arabia Ukraine Brazil India Russia Turkey South Africa 33

34 Figure 7 Distribution of s of Quality Estimates derived from Nested Logit Framework based on Khandelwal (2010) between Canada and the US Panel A. Original quality estimates Panel B. Quality estimates using US coefficients Figure 8 Distribution of s of Quality Estimates derived from Nested Logit Framework based on Khandelwal (2010) (US coefficients) Developed Country Developing Country Density Density Australia Germany France Ireland New Zealand Canada Spain Great Britain Japan Singapore Argentina China Mexico Saudi Arabia Ukraine Brazil India Russian Turkey South Africa 34