Non-price competitiveness of exports from emerging countries

Abstract

We construct a relative export price index that adjusts for changes in non-price factors (e.g. quality or taste) and changes in the set of competitors for nine emerging economies (Argentina, Brazil, Chile, China, India, Indonesia, Mexico, Russia and Turkey). The index is calculated using highly disaggregated (6-digit Harmonized System, HS) trade data from UN Comtrade for the period between 1996 and 2012. Our method highlights the crucial importance of non-price competitiveness in assessing emerging countries’ performance on external markets, as well as notable differences in non-price competitiveness dynamics across exporters. China shows a huge gain in international competitiveness due to non-price factors, while the role of the exchange rate in explaining China’s competitive position may have been overstressed. Similarly, Brazil, India and Turkey show discernible improvements in their competitive position when accounting for non-price factors. Oil exports account for strong improvement in Russia’s non-price competitiveness, as well as losses of competitiveness for Indonesia. Mexico’s competitiveness deteriorates prior to 2006 and improves afterwards.

Appendix

1.1 Import price index

1.1.1 Household utility function

We closely follow Broda and Weinstein (2006) and define a constant elasticity of substitution (CES) utility function for a representative household consisting of three nests. At the topmost level, a composite import good and domestic good are consumed:

$$\begin{aligned} U_{t}=\left( {D_{t}^{\frac{\kappa -1}{\kappa }}+M_{t}^{\frac{\kappa -1}{\kappa }}} \right) ^{\frac{\kappa }{\kappa -1}};\quad \kappa >1, \end{aligned}$$

(3)

where $D_{t}$ is the domestic good, $M_{t}$ is composite imports and $\kappa$ is the elasticity of substitution between domestic and foreign good. At the middle level of the utility function, the composite imported good consists of individual imported products:

$$\begin{aligned} M_{t}=\left( \sum \limits _{g\in G} {M_{g,t}^{\frac{\gamma -1}{\gamma }}} \right) ^{\frac{\gamma }{\gamma -1}}; \quad \gamma >1, \end{aligned}$$

(4)

where $M_{g,t}$ is the subutility from consumption of imported good $g, \gamma$ is elasticity of substitution among import goods and G denotes the set of imported goods.

The bottom-level utility function introduces variety and quality into the model. Each imported good consists of varieties (i.e. goods have different countries of origins, so product variety indicates the set of competitors in a particular market). A taste or quality parameter denotes the subjective or objective quality consumers attach to a given product. $M_{g,t}$ is defined by a non-symmetric CES function:

$$\begin{aligned} M_{g,t}=\left( \sum \limits _{c\in C_{g,t}}{d_{gc,t}^{\frac{1}{\sigma _g}} m_{gc,t}^{\frac{\sigma _g-1}{\sigma _g}}} \right) ^{\frac{\sigma _g}{\sigma _g -1}}; \quad \sigma _{g}>1\quad \forall \quad g\in G, \end{aligned}$$

(5)

where $m_{gc,t}$ denotes quantity of imports g from country $c, C_{g,t}$ is a set of all partner countries, $d_{gc,t}$ is the taste or quality parameter and $\sigma _{g}$ is elasticity of substitution among varieties of good g.

1.1.2 Conventional import price index

After solving the utility maximization problem subject to the budget constraint, the minimum unit-cost function of import good g is defined as

$$\begin{aligned} \phi (p_{g,t}, C_{g,t}, d_{g,t})=\left( \sum \limits _{c\in C_{g,t}}{d_{gc,t} p_{gc,t}^{1-\sigma _{g}}} \right) ^{\frac{1}{1-\sigma _g}}, \end{aligned}$$

(6)

where $\phi$ denotes minimum unit-cost function of import good $g, p_{gc,t}$ is the price of good g imported from country $c, p_{g,t}$ and $d_{g,t}$ are the corresponding vectors of prices and taste/quality parameters of good g in period t. The price index for good g is defined as a ratio of minimum unit costs in the current period to minimum unit costs in the previous period:

$$\begin{aligned} P_{g}\equiv \frac{\phi \left( p_{g,t}, C_{g,t}, d_{g,t}\right) }{\phi \left( {p_{g,t-1}, C_{g,t-1}, d_{g,t-1} } \right) }. \end{aligned}$$

(7)

The conventional assumption is that taste or quality parameters are constant over time $(d_{g}=d_{g,t}=d_{g,t-1})$, and the set of varieties is unchanged. The price index is calculated over the set of product varieties $C_{g}=C_{g,t}\cap C_{g,t-1}$ available both in periods t and $t-1$, where $C_{gt}\subset C$ is the subset of all varieties of goods consumed in period t. Sato (1976) and Vartia (1976) show that, for a CES function, the exact price index will be given by the log-change price index

$$\begin{aligned} P_{g}^{\mathrm{conv}} \equiv \frac{\phi \left( p_{g,t}, C_g, d_{g}\right) }{\phi (p_{g,t-1} ,C_g, d_g)}=\prod _{c\in C_g} \left( \frac{p_{gc,t}}{p_{gc,t-1}}\right) ^{w_{gc,t}(C_{g})}, \end{aligned}$$

(8)

whereby weights $w_{gc,t}(C_{g})$ are computed using cost shares $s_{gc,t}(C_{g})$ for the set of product varieties available in periods t and $t-1$ as follows:

$$\begin{aligned} w_{gc,t}(C_{g})=\frac{\frac{s_{gc,t}(C_{g})-s_{gc,t-1}(C_{g})}{\ln s_{gc,t}(C_{g})-\ln s_{gc,t-1}(C_{g})}}{\sum \limits _{c\in C_g}{\frac{s_{gc,t}(C_{g})-s_{gc,t-1}(C_{g})}{\ln s_{gc,t}(C_{g}) -\ln s_{gc,t-1}(C_{g})}}}; \quad s_{gc,r}(C_{g})\equiv \frac{p_{gc,r} x_{gc,r}}{\sum \limits _{c\in C_g}{p_{gc,r}x_{gc,r}}};\quad r=t-1, \;\, t, \end{aligned}$$

where $x_{gc,t}$ is the cost-minimizing quantity of good g imported from country c.

1.1.3 Adjusting for changes in varieties

The import price index in (8) ignores possible changes in variety (set of partner countries) and taste or quality. Feenstra (1994a, b) relaxes the underlying assumption that variety is constant. The cost share of imports from country c in total imports of good g in period t is given by:

$$\begin{aligned} s_{gc,t}(C_{g,t})\equiv \frac{p_{gc,t} x_{gc,t} }{\sum \limits _{c\in C_{g,t}}{p_{gc,t} x_{gc,t}}}=\frac{p_{gc,t}^{1-\sigma _g } d_{gc,t}}{\phi (p_{g,t}, C_{g,t}, d_{g,t})^{1-\sigma _{g}}}, \end{aligned}$$

(9)

from which it follows that

$$\begin{aligned} s_{gc,t}(C_{g,r})=s_{gc,t}(C_{g})\lambda _{g,r}, \end{aligned}$$

(10)

where

$$\begin{aligned} \lambda _{g,r}\equiv \frac{\sum \limits _{c\in C_g}{p_{gc,r} x_{gc,r}}}{\sum \limits _{c\in C_{g,r}}{p_{gc,r} x_{gc,r}}};\quad r=t-1,\;\quad t. \end{aligned}$$

After taking the summation of (10) over $c\in C_{g}$ and raising to the power $1/(\sigma _{g}-1)$:

$$\begin{aligned} \left( \lambda _{g,r}\sum \limits _{c\in C_g}{s_{gc,r}(C_{g})}\right) ^{\frac{1}{\sigma _g -1}}= & {} \lambda _{g,r}^{\frac{1}{\sigma _g-1}} =\phi \left( p_{g,r}, C_{g,r}, d_{g,r}\right) \left( \sum \limits _{c\in C_g}{d_{gc,t} p_{gc,t}^{1-\sigma _g }}\right) ^{\frac{1}{\sigma _g -1}}\\= & {} \frac{\phi \left( p_{g,r}, C_{g,r}, d_{g,r}\right) }{\phi \left( p_{g,r}, C_g, d_{g,r}\right) }, \end{aligned}$$

from which one could obtain

$$\begin{aligned} \frac{\phi \left( p_{g,t}, C_{g,t}, d_{g,t}\right) }{\phi \left( p_{g,t-1}, C_{g,t-1}, d_{g,t-1}\right) }=\frac{\phi \left( p_{g,t}, C_g, d_{g,t}\right) }{\phi \left( p_{g,t-1}, C_g, d_{g,t-1}\right) }\left( \frac{\lambda _{g,t}}{\lambda _{g,t-1}}\right) ^{\frac{1}{\sigma _g-1}}. \end{aligned}$$

This is the brief proof of the Proposition 1 in Feenstra (1994a, b) and Broda and Weinstein (2006), which posit that if $d_{g}=d_{g,t}=d_{g,t-1}$ for $c\in C_{g}=(C_{g,t}\cap C_{g,t-1})$, $C_{g}\ne$Ø, then the exact price index for good g is given by

$$\begin{aligned} P_g^f \equiv \frac{\phi \left( p_{g,t}, C_{g,t}, d_g\right) }{\phi \left( p_{g,t-1}, C_{g,t-1}, d_{g}\right) }= & {} \prod _{c\in C_g }{\left( \frac{p_{gc,t}}{p_{gc,t-1}}\right) ^{w_{gc,t}(C_{g})}} \left( {\frac{\lambda _{g,t} }{\lambda _{g,t-1}}}\right) ^{\frac{1}{\sigma _g-1}}\nonumber \\= & {} P_g^{conv} \left( {\frac{\lambda _{g,t}}{\lambda _{g,t-1} }} \right) ^{\frac{1}{\sigma _g-1}}. \end{aligned}$$

(11)

Therefore, the price index derived in (8) is multiplied by an additional term to capture the role of new and disappearing varieties.

1.1.4 Adjusting for changes in taste or quality parameter

The price index in (11) assumes that taste or quality parameters are unchanged for all varieties existing in both periods $(d_{g}=~d_{g,t}=d_{g,t-1})$. Benkovskis and Wörz (2014) further introduce an import price index that allows for changes in taste or quality. The derivation is straightforward and directly follows from Feenstra (1994a, b) and Broda and Weinstein (2006). From (9) we obtain that

$$\begin{aligned} \frac{\phi \left( p_{g,t}, C_g, d_{g,t}\right) }{\phi \left( p_{g,t-1}, C_g, d_{g,t-1}\right) }=\frac{s_{gc,t}(C_{g})^{\frac{1}{\sigma _g -1}}p_{gc,t} d_{gc,t}^{\frac{1}{1-\sigma _g }} }{s_{gc,t-1}({C_g})^{\frac{1}{\sigma _g -1}}p_{gc,t-1} d_{gc,t-1}^{\frac{1}{1-\sigma _g}}}. \end{aligned}$$

(12)

After taking the geometric mean of (12) using weights $w_{gc,t}(C_{g})$ we arrive to

$$\begin{aligned} \frac{\phi (p_{g,t}, C_g, d_{g,t})}{\phi (p_{g,t-1}, C_g, d_{g,t-1})}= & {} \prod _{c\in C_g } {\left( \frac{p_{gc,t} d_{gc,t}^{\frac{1}{1-\sigma _g}}}{p_{gc,t-1} d_{gc,t}^{\frac{1}{1-\sigma _g}}}\right) ^{w_{gct}\left( {C_g} \right) }}\nonumber \\&\prod _{c\in C_g}{\left( {\frac{s_{gc,t}\left( {C_g} \right) ^{\frac{1}{\sigma _g-1}}}{s_{gc,t-1} \left( {C_g} \right) ^{\frac{1}{\sigma _g-1}}}}\right) ^{w_{gct} \left( {C_g} \right) }}. \end{aligned}$$

(13)

To prove that the last term of (13) equals unity, we take its natural log:

$$\begin{aligned}&\sum \limits _{c\in C_g} {\frac{w_{gct}(C_{g})}{\sigma _g -1}\left( {\ln s_{gc,t}(C_{g})-\ln s_{gc,t-1}(C_{g})}\right) } \\&\quad \quad =\frac{\frac{1}{\sigma _g -1}\sum \limits _{c\in C_g }\left( s_{gc,t}(C_{g})-s_{gc,t-1}(C_{g})\right) }{\sum \limits _{c\in C_g} {\left( \frac{s_{gc,t}(C_{g})-s_{gc,t-1}(C_{g})}{\ln s_{gc,t}(C_{g})-\ln s_{gc,t-1}(C_{g})}\right) }}=0, \end{aligned}$$

since the sum of cost shares equals unity in both t and $t-1$. Thus,

$$\begin{aligned} \frac{\phi (p_{g,t}, C_g, d_{g,t})}{\phi (p_{g,t-1}, C_g, d_{g,t-1})}= & {} \prod _{c\in C_g}{\left( \frac{p_{gc,t} }{p_{gc,t-1}}\right) ^{w_{gct}(C_{g})}}\prod _{c\in C_g}{\left( \frac{d_{gc,t} }{d_{gc,t-1}}\right) ^{\frac{w_{gct} (C_{g})}{1-\sigma _g}}} ;\nonumber \\&P_{g}^{q} \equiv \frac{\phi \left( p_{g,t}, C_{g,t}, d_{g,t}\right) }{\phi (p_{g,t-1}, C_{g,t-1}, d_{g,t-1})}\nonumber \\= & {} \prod _{c\in C_g} {\left( \frac{p_{gc,t}}{p_{gc,t-1}}\right) ^{w_{gct}(C_{g})}} \left( \frac{\lambda _{g,t}}{\lambda _{g,t-1}} \right) ^{\frac{1}{\sigma _g -1}}\prod _{c\in C_g}{\left( \frac{d_{gc,t} }{d_{gc,t-1}}\right) ^{\frac{w_{gct}(C_{g})}{1-\sigma _g}}}\nonumber \\= & {} P_{g}^{f}\prod _{c\in C_g}{\left( \frac{d_{gc,t}}{d_{gc,t-1}}\right) ^{\frac{w_{gct} \left( {C_g } \right) }{1-\sigma _g }}}. \end{aligned}$$

(14)

Equation (14) can therefore be seen as a more general version of Eq. (11) with an additional term that captures changes in the quality or taste parameter.¹⁴

Note that (14) does not contradict the Proposition 2 from Feenstra (1994b), which states that even when $d_{g,t}$ changes over time, a price index in (11) can be interpreted as a ratio of minimum unit costs with constant taste or quality parameters lying between a normalized version of $d_{g,t-1}$ and $d_{g,t}$. According to the Proposition 2, one can always find the vector of constant taste or quality parameters for which the exact price index will coincide with price index in (11). Thus, the Proposition 2 does not state that one can evaluate the exact price index by using (11) in the case of $d_{g,t-1} \ne d_{g,t}$. Rather it provides useful interpretation of obtained price index that still ignores the developments of taste or quality.

1.2 Relative export price index

Equation (14) gives us a formula for a variety- and quality-adjusted import price index. We can easily interpret $x_{gc,t}$ (imports of product g originating from country c) as country’s c exports of a product g to the importing market (assuming for the moment that there exists only one destination of exports for all exporting countries—the importing country where the representative household resides). From Eq. (9), it follows that the market share of an emerging country k equals to

$$\begin{aligned} s_{gk,t}(C_{g,t})=\frac{p_{gk,t} x_{gk,t} }{\sum \limits _{c\in C_{g,t}}{p_{gc,t} x_{gc,t}}}=\frac{p_{gk,t}^{1-\sigma _g} d_{gk,t}}{\phi (p_{g,t}, C_{g,t}, d_{g,t})^{1-\sigma _g}}, \end{aligned}$$

and we further derive changes in adjusted relative export price as inverse growth of country k’s export market share:

$$\begin{aligned} \mathrm{RXP}_{gk,t}= & {} \frac{s_{gk,t-1}(C_{g,t})}{s_{gk,t} (C_{g,t})}\nonumber \\ {}= & {} \frac{\left( {p_{gk,t} }/{p_{gk,t-1}}\right) ^{\sigma _g -1}}{\left( {\phi \left( p_{g,t}, C_{g,t}, d_{g,t}\right) }/{\phi \left( p_{g,t-1}, C_{g,t-1}, d_{g,t-1}\right) }\right) ^{\sigma _g -1}\left( {{d_{gk,t} }/{d_{gk,t-1} }}\right) },\nonumber \\ \end{aligned}$$

(15)

where $\mathrm{RXP}_{gk,t}$ represents changes in the adjusted relative export price index for an emerging country k, when defined for a single market (exports of good g to a single destination country). We use the inverse growth of the market share in order to keep the usual interpretation of the relative price indicator—an increasing index denotes losses in competitiveness. Combining (14) and (15), we obtain

$$\begin{aligned} \mathrm{RXP}_{gk,t}= & {} \prod _{c\in C_g }{\left( {\frac{p_{gk,t} }{p_{gc,t} }\frac{p_{gct-1} }{p_{gk,t-1}}} \right) ^{\left( {\sigma _g -1} \right) w_{gc,t} \left( {C_g }\right) }} \left( {\frac{\lambda _{g,t-1} }{\lambda _{g,t}}}\right) \nonumber \\&\prod _{c\in C_g } {\left( {\frac{d_{gk,t} }{d_{gc,t}}\frac{d_{gc,t-1} }{d_{gk,t-1} }} \right) ^{-w_{gc,t}(C_{g})}} . \end{aligned}$$

(1)

Finally, we need to design an aggregate relative export price; the index in (1) only describes relative export prices for a specific product exported to a particular market. The assumption of a single destination for exports is relaxed to allow for multiple importing countries. In all these countries, consumers are assumed to be maximizing their utility. All parameters and variables entering the three-layered utility function can differ across countries. If we denote the export price, export volume and relative export price index of a product g exported by emerging country k to country i as $p(i)_{gk,t}$, $x(i)_{gk,t}$ and $\mathrm{RXP}(i)_{gk,t}$ accordingly, the aggregate-adjusted relative export price index can be defined as

$$\begin{aligned} \mathrm{RXP}_{k,t}=\prod _{i\in I}{\prod _{g\in G}{\mathrm{RXP}(i)_{gk,t}^{W(i)_{g,t}}}}, \end{aligned}$$

(2)

where

$$\begin{aligned} W(i)_{g,t} =\frac{S(i)_{g,t} +S(i)_{g,t-1}}{2};\quad S(i)_{g,t} =\frac{p(i)_{gk,t} x(i)_{gk,t} }{\sum \limits _{i\in I} {\sum \limits _{g\in G} {p(i)_{gk,t} x(i)_{gk,t}}}}. \end{aligned}$$

The aggregate index $(\mathrm{RXP}_{k,t})$ in Eq. (2) is just the Tornqvist index. Its weights are computed using the share of product g exports to country i out of total exports by country k.

1.3 Evaluation of relative quality

The calculation of the adjusted relative export price index in (1) is challenging as relative taste or quality is unobservable. Following Hummels and Klenow (2005), we evaluate unobserved taste or quality from the utility optimization problem, i.e. after taking first-order conditions and transformation into log-ratios, we express relative taste or quality in terms of relative prices, volumes and the elasticity of substitution between varieties as

$$\begin{aligned} \ln \left( \frac{d_{gc,t}}{d_{gk,t}}\right) =\sigma _{g}\ln \left( \frac{p_{gc,t} }{p_{gk,t}}\right) +\ln \left( {\frac{x_{gc,t}}{x_{gk,t}}}\right) , \end{aligned}$$

(16)

where k denotes a particular emerging country.

Relative taste or quality, as any relative measure, is highly sensitive to the choice of a benchmark country. The emerging country of interest serves as a benchmark in our analysis. This choice is driven by the design of the RXP index, which compares export prices and quality of an emerging country to weighted world export prices and quality.

1.4 Elasticities of substitution between varieties

We estimate elasticities of substitution between varieties according to the methodology proposed by Feenstra (1994a, b) and later applied by Broda and Weinstein (2006). To derive the elasticity of substitution, one needs to specify both demand and supply equations. The demand equation is defined by re-arranging the minimum unit-cost function from (6) in terms of market share, taking first differences and ratios to a reference country l:¹⁵

$$\begin{aligned} \Delta \ln \frac{s_{gc,t}(C_{g,t})}{s_{gl,t} (C_{g,t})}=-\left( \sigma _{g}-1\right) \Delta \ln \frac{p_{gc,t} }{p_{gl,t} }+\varepsilon _{gc,t}, \end{aligned}$$

(17)

where $\varepsilon _{gc,t}=\Delta \hbox {ln}d_{gc,t}+\xi _{gc,t}$, and $\xi _{gc,t}$ is an error term (e.g. a measurement error) in the demand equation. Following Feenstra (1994a, b) and Broda and Weinstein (2006), we treat $\varepsilon _{gc,t}$ as an unobserved random variable, reflecting changes in the taste or quality of product variables. Note that $d_{gc,t}$ reflects fundamental characteristics of a particular variety and should be treated as exogenous.¹⁶

The export supply equation relative to country l is given by:

$$\begin{aligned} \Delta \ln \frac{p_{gc,t}}{p_{gl,t}}=\frac{\omega _g }{1+\omega _g}\Delta \ln \frac{s_{gc,t}(C_{g,t})}{s_{gl,t}(C_{g,t})}+\delta _{gc,t}, \end{aligned}$$

(18)

where $\omega _{g}\ge 0$ is the inverse supply elasticity assumed to be the same across partner countries, and $\delta _{gc,t}$ is an error term of supply equation which is assumed to be independent of $\varepsilon _{gc,t}$.

A nasty feature of the system of (17) and (18) is the absence of exogenous variables to identify and estimate elasticities. By rearranging (17) and (18), one can get the following system that cannot be estimated:

$$\begin{aligned}&\Delta \ln \frac{p_{gc,t} }{p_{gl,t}}=\frac{\omega _g }{1+\omega _g \sigma _g }\left( \Delta \ln d_{gc,t} +\xi _{gc,t}\right) +\frac{1+\omega _g }{1+\omega _g\sigma _g}\delta _{gc,t},\\&\quad \Delta \ln \frac{s_{gc,t}(C_{g,t})}{s_{gl,t}(C_{g,t})}=-\frac{\left( {1-\omega _g}\right) (\sigma _{g}-1)}{1+\omega _{g} \sigma _g }\delta _{gc,t} +\frac{1+\omega _g }{1+\omega _g \sigma _g }\left( \Delta \ln d_{gc,t} +\xi _{gc,t}\right) . \end{aligned}$$

To get the estimates, the system of two equations is transformed into a single equation by exploiting the insight of Leamer (1981) and the independence of errors $\varepsilon _{gc,t}$ and $\delta _{gc,t}$.¹⁷ This is done by multiplying both sides of the equations. After transformation, the following equation is obtained:

$$\begin{aligned} \left( \Delta \ln \frac{p_{gc,t} }{p_{gl,t}}\right) ^{2}= & {} \theta _1\left( \Delta \ln \frac{s_{gc,t}(C_{g,t})}{s_{gl,t}(C_{g,t})}\right) ^{2}\nonumber \\&+\,\theta _2 \left( \Delta \ln \frac{p_{gc,t}}{p_{gl,t}}\right) \left( \Delta \ln \frac{s_{gc,t}(C_{g,t})}{s_{gl,t} (C_{g,t})}\right) \,+\,u_{gc,t}, \end{aligned}$$

(19)

where

$$\begin{aligned} \theta _1 =\frac{\omega _g }{(1+\omega _{g})(\sigma _{g}-1)};\quad \theta _2 =\frac{1-\omega _{g}(\sigma _{g}-2)}{(1+\omega _{g})(\sigma _{g}-1)};\quad u_{gc,t} =\varepsilon _{gc,t}\delta _{gc,t}. \end{aligned}$$

Note that the evaluation of $\theta _{1}$ and $\theta _{2}$ leads to inconsistent estimates as relative price and relative market share are correlated with error $u_{gc,t}$. Broda and Weinstein (2006) argue that it is possible to obtain consistent estimates by exploiting the panel nature of data and define a set of moment conditions for each good g. If estimates of elasticities are imaginary or of the wrong sign, the grid search procedure is implemented. Broda and Weinstein (2006) also address the problem of measurement error and heteroskedasticity by adding a term inversely related to the quantity and weighting the data according to the amount of trading flows. Recent papers by Soderbery (2010, 2013), however, report that this methodology generates severely biased elasticity estimates (median elasticity of substitution is overestimated by more than 35 %). Soderbery (2010, 2013) proposes the use of a limited information maximum likelihood (LIML) estimator instead. Where estimates of elasticities are not feasible $({\hat{\theta }}_{1}<0)$, nonlinear constrained LIML is implemented. Monte Carlo analysis performed by Soderbery (2010, 2013) demonstrates that this hybrid estimator corrects small sample biases and constrained search inefficiencies. It further shows that Feenstra’s (1994a) original method of controlling a measurement error with a constant and correcting for heteroskedasticity by the inverse of the estimated residuals performs well. We thus follow Soderbery (2010, 2013) and use a hybrid estimator, combining LIML with a constrained nonlinear LIML to estimate elasticities of substitution between varieties using the Feenstra’s (1994a, b) method.