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\section*{Tariff Pass-through, Firm Heterogeneity and Product Quality$^{\S}$
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\singlespacing{
Rodney Ludema$^{\dag}$\\
Georgetown University
}
\singlespacing{
Zhi Yu$^{\ddag}$}\\
Shanghai University of Finance and Economics
}
\singlespacing{
July 2011
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\textbf{Abstract:} Previous studies on tariff pass-through have been conducted at the industry level. This paper is the first attempt to explore tariff pass-through at the firm level, and to investigate how it depends on firm heterogeneity in productivity and product differentiation in quality. Using an extended version of the Melitz and Ottaviano (2008) model, we show that exporting firms absorb tariff changes by adjusting both their markups and product quality, which leads to an incomplete tariff pass-through. Moreover, the absolute value of tariff absorption elasticity (the percentage change in the tariff-exclusive export price in response to a one percent change in the gross tariff rate) negatively depends on firm productivity for products with high scope for quality differentiation, but positively depends on firm productivity for products with low scope for quality differentiation. Using the U.S. transaction-level export data and plant-level manufacturing data, we find evidence for these predictions. The firm-level tariff absorption elasticity is $-0.87$ on average. Pooled regressions reveal that the tariff absorption elasticity is higher (in terms of absolute value) for low productivity firms ($-1.27$) and lower for high productivity firms ($-0.44$). Estimation done separately on quality differentiated goods and quality homogeneous goods finds that the inverse relationship between tariff absorption elasticity and firm productivity is more pronounced for quality differentiated goods and non-existent for quality homogeneous goods, which is consistent with the model.
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\textbf{Key Words}: Tariff Pass-through, Firm Heterogeneity, Product Quality, Markups
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\textbf{JEL Numbers}: F1, D2, L1
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\footnotesize{$^{\S}$ The authors thank J. Bradford Jensen, Anna Maria Mayda, Antoine Gervais, Tom Holmes, William Kerr, Kala Krishna, Ben Mandel, Tom Prusa, Andres Rodriguez-clare, Daniel Reyes, French Scott, Justin Pierce, Cheryl Grim, and participants at Georgetown International Economics Seminar, the Midwest Trade Meetings, the Southern Economic Association Conference, the Census Bureau RDC Research Conference, and the Eastern Economic Association Conference for helpful comments and discussions. Zhi Yu also thanks Lynn Riggs of the Census Bureau for technical support and Jim Davis of the NBER for timely disclosure of the data analysis. Support for this research at the Census Bureau RDC from NSF (ITR-0427889) is also gratefully acknowledged. The research in this paper was conducted while Zhi Yu was a Special Sworn Status researcher at the U.S. Census Bureau, Center for Economic Studies. Any opinions and conclusions expressed herein are those of the authors and do not necessarily represent the views of the U.S. Census Bureau. All results have been reviewed to ensure that no confidential information is disclosed.}
\footnotesize{$^{\dag}$ Georgetown University, Department of Economics, 37th and O Streets, Washington, DC 20057, U.S.A. E-mail: ludemar@georgetown.edu.}
\footnotesize{$^{\ddag}$ Shanghai University of Finance and Economics, School of International Business Administration, Shanghai 200433, China. E-mail: yu.zhi@mail.shufe.edu.cn}
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\section*{1. Introduction}
This paper is the first attempt to explore tariff pass-through at the firm level, and to investigate how it depends on firm heterogeneity in productivity and product differentiation in quality. Using an extended version of the Melitz and Ottaviano (2008) model, we show that exporting firms absorb tariff changes by adjusting both their markups and product quality, which leads to an incomplete tariff pass-through. Moreover, tariff absorption elasticity (the percentage change in the tariff-exclusive export price in response to a one percent change in the gross tariff rate) negatively depends on firm productivity for products with high scope for quality differentiation, but positively depends on firm productivity for products with low scope for quality differentiation. Using the U.S. transaction-level export data and plant-level manufacturing data, we find evidence for these predictions: The firm-level tariff pass-through is indeed incomplete, and tariff absorption does depend on firm productivity and product quality as the model predicts, especially for quality differentiated goods.
This paper derives its motivation from the literature in two areas: the incompleteness of tariff pass-through, and the heterogeneous firm models of international trade. The incompleteness of tariff pass-through is the source of terms-of-trade effect of trade policies. It says that when a large country raises its tariff rate on a product, foreign countries that sell in its market may absorb part of the tariff increase by lowering their tariff-exclusive exporting prices\footnote{For this reason we also refer to incomplete tariff pass-through as ``tariff absorption" hereafter. Graphically, tariff-absorption is represented by the downward movement along the upward-slopping foreign export supply curve of the home country.}. Thus the tariff-inclusive consumer prices increase by a magnitude less than the tariff increase, and the impact of tariff change on market demand is mitigated. Tariff increase improves terms of trade for the home country and worsens the terms of trade of its trading partners\footnote{Similarly, tariff reduction of a large country leads to increases of the tariff-exclusive prices of foreign countries that sell in its market, and thus has an opposite terms-of-trade effect.}. This terms-of-trade effect is the basis for the optimal tariff argument and a driving force for international trade agreements, as shown in Edgeworth (1894), Broda, Lim$\tilde{a}$o and Weinstein (2008), Bagwell and Staiger (2009), and Ludema and Mayda (2010).\footnote{The optimal argument says that, the lower is the export supply elasticity that a country faces, the higher is the optimal tariff that the country could and would set to exploit the terms-of-trade gain. Broda, Lim$\tilde{a}$o and Weinstein (2008) examine this with the tariff schedules of non-WTO countries; Bagwell and Staiger (2009) consider this with changes in the tariff schedules of recent WTO accession countries; Ludema and Mayda (2010) explore this with MFN tariffs set by existing WTO members.}
There have been several empirical studies on the incompleteness of tariff pass-through. Feenstra (1989) finds that around 40 percent of the U.S. tariff increase in 1980s against the imports of Japanese automobiles was passed on as lower prices to Japanese automobile exports to the U.S. Kreinin (1961) finds that more than two-thirds of U.S. tariff reductions in Geneva Round were passed on as higher prices to countries exporting to the US. Mallick and Marques (2007) find similar qualitatively results for India's trade liberalization in 1990s.
However, all the existing studies on tariff pass-through have been done at the industry level. That is, they study how the average price of all firms in an industry responds to a tariff change\footnote{This is partly due to the data availability constraints faced by the researchers.}. In these studies, it was not clear whether the industry-level price response to tariff change is caused by the intra-industry reallocation between firms with different prices, or the firm-level price change due to cost change or markup adjustment. Feenstra (1989) controls for the marginal cost of production in his estimation of the tariff pass-through elasticity. However, it is still not clear whether the industry-level price change is caused by firm-level markup adjustment or intra-industry reallocation.\footnote{In another paper, Feenstra and Weinstein (2010) estimate the magnitude of markup reduction and welfare gain in the liberalizing country, instead of the markup adjustment of foreign firms exporting to the liberalizing country, and hence it is not directly related to tariff pass-through.} Thus firm-level studies are needed to investigate this.
For this purpose, we turn to the second literature relevant to this paper --- heterogeneous firm models of international trade, since these models focus on the intra-industry reallocation between firms. Heterogeneous firm models were spurred by empirical studies, beginning with Bernard and Jensen (1995)\footnote{Others include Roberts and Tybout (1997), Bernard and Jensen (1999), Bernard, Jensen, Redding, and Schott (2007), etc.}, which use plant or firm-level data to document that exporting firms are on average larger and more productive than non-exporting firms. These models are characterized by firm heterogeneity in productivity, and focus on the intra-industry reallocation between firms caused by changes in trade environment. The representative models include Melitz (2003) and Bernard, Eaton, Jensen, and Kortum (2003). Melitz (2003) shows the exposure to trade induces the more productive firms to enter the export market, some less productive firms produce only for domestic market, and the least productive firms to exit the market. Thus the exposure to trade leads to inter-firm reallocations towards more productive firms.
None of the heterogeneous firm models focuses directly on how firm heterogeneity impacts tariff pass-through, though most of them have some implications for this. The first-generation heterogeneous firm models assume constant marginal cost as well as CES utility, with the latter implying constant markups. With constant marginal cost and markups, firms do not have any room for price adjustment. Thus the firm-level tariff pass-through is complete, and the observed incomplete tariff pass-through at the industry level must be completely due to the intra-industry reallocation between firms with different prices. For intra-industry reallocation to explain incomplete tariff pass-through, it must be that, after tariff increase, the surviving exporting firms, which are more productive than the exiting firms, should have lower-than-average prices, so that the average industry price after the tariff increase is lower than before. However, this contradicts the prediction of a large body of heterogeneous firm models that incorporate product quality into CES utility, such as Baldwin and Harrigan (2007), Kugler and Verhoogen (2008), Mandel (2008), and Gervais (2009), among others. These models predict that more productive firms could have higher-than-average prices since they produce high quality differentiated goods. The researchers also provide empirical evidence supporting this prediction. Therefore the first-generation heterogeneous firm models based on CES utility and constant markups are not very convincing in explaining the incompleteness of tariff pass-through.
Given this consideration, we switch to the second-generation heterogeneous firm models, beginning with Melitz and Ottaviano (2008). These models feature linear demand and variable markups. With variable markups, the firm-level tariff pass-through could be incomplete, since firms could adjust their markups and hence their exporting prices in response to a tariff change, even if they have constant marginal cost. Antoniades (2008) incorporates product quality into the Melitz and Ottaviano (2008) model. Given the empirical evidence supporting heterogeneous firm models with quality dimension, this model is a good starting point for analyzing firm-level tariff pass-through.
Our model is similar to Antoniades (2008). The difference is that the quality-upgrading cost in his model only contains a quantity-invariant R\&D cost, but in our model we add another type of quality-upgrading cost, the quantity-dependent component-upgrading cost. This extension makes it easier to justify that a firm chooses different quality levels for different markets, which is crucial to guarantee a closed form solution to the model. In our model, exporting firms absorb the tariff change not only by adjusting their markups due to the linear demand structure, but also by adjusting the quality of their products. Both these two adjustments lead to an incomplete tariff pass-through. Moreover, high productivity firms have high absolute magnitude of quality adjustment and tariff absorption. For products with high scope for quality differentiation, the relative tariff absorption, i.e., tariff absorption elasticity, is lower for high productivity firms, since their initial prices are higher. In contrast, for products with low scope for quality differentiation, the tariff absorption elasticity is higher for high productivity firms, since their initial prices are low. In sum, the model predicts that tariff pass-through depends on both firm heterogeneity in productivity and product differentiation in quality.
In order to empirically test these predictions, we need to use firm-level data on trade and productivity, as well as product level data on quality scope. From the U.S. Linked/Longitudinal Firm Trade Transaction Database (LFTTD) we construct the U.S. firm-level export price changes over time for each exported product to each destination country. From the World Integrated Trade Solution (WITS) we get the changes of tariff rates of other countries against U.S. exports of different products. We also use the U.S. Census of Manufacturing (CMF) data to construct the firm-level productivity, and use the R\&D/sales ratio data from the National Science Foundation or Rauch classification to derive the quality scope of different industries/products. Then we link the tariff data, the firm productivity data, and the product quality scope data to the export price data. We use the combined data in 1997-1998 (part of the applied period of Uruguay Round), during which there are a wide range of large tariff changes and relatively accurate data for firm productivity and product quality scope, to test model predictions. We conduct the empirical analysis for the full sample, quality homogeneous goods, and quality differentiated goods, respectively. For each sample, we test the price-productivity schedule, and check whether the firm-level tariff pass-through is incomplete as well as how the absolute and relative tariff absorption depends on firm productivity.
We find evidence supporting the predictions of the model. First, we find that firm-level tariff pass-through is indeed incomplete: The firm-level tariff absorption elasticity is $-0.87$ on average. Second, pooled regressions reveal that products in the sample on average fit the definition of quality differentiated goods, and the tariff absorption elasticity is higher (in terms of its absolute value) for low productivity firms ($-1.27$) and lower for high productivity firms ($-0.44$), as the model predicts for products with high scope for quality differentiation. The overall tariff absorption elasticity and that for low productivity firms are very high (in terms of the absolute value), since firms change not only their markups but also their product quality in response to tariff changes. Third, estimation done separately on quality differentiated goods and quality homogeneous goods finds that the inverse relationship between tariff absorption elasticity and productivity is more pronounced for quality differentiated goods and non-existent for quality homogeneous goods, which is consistent with the model.
To our knowledge, this is the first paper that (1) finds empirical evidence for incomplete tariff pass-through at the firm level, and (2) investigates, both theoretically and empirically, how tariff pass-through depends on firm productivity and product quality. Both of these two are contributions of the paper to the tariff pass-through literature. The second one is also a contribution of the paper to the literature on heterogeneous firm models in international trade.
The paper is organized as follows. Section 2 presents the theoretical model. Section 3 describes the data used. Section 4 contains the empirical strategies and results. Conclusions are included in section 5.
\section*{2. The Model}
\textbf{2.1. Consumers and Demand}
As mentioned in section 1, our model is based on Melitz and Ottaviano (2008) and Antoniades (2008). Consider a world consisting of a Home country ($h$) and a Foreign country ($f$), with consumers $L^{h}$ and $L^{f}$ in each country. Preferences are defined over a homogeneous good chosen as numeraire, and a continuum of horizontally-differentiated varieties indexed by $i \in \Omega$. Consumers in both countries share the same quasi-linear utility function as in Antoniades (2008):
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\begin{equation}\label{utility}
U=q_{0}^{c}+\alpha \int_{i \in \Omega}(q_{i}^{c}+z_{i})di -\frac{1}{2}\gamma \int_{i \in \Omega}(q_{i}^{c}-z_{i})^{2}di-\frac{1}{2}\eta \left(\int_{i \in \Omega}(q_{i}^{c}-\frac{1}{2}z_{i})di\right)^{2},
\end{equation}
where $q_{0}^{c}$ and $q_{i}^{c}$ represent, respectively, the individual consumption levels of the numeraire good and variety $i$; $z_{i}$ stands for the quality level of variety $i$, and thus indexes the vertical differentiation of the variety. If the quality level for all varieties is 0 ($z_{i}=0$ for all $i$), then the utility function boils down to that in Melitz and Ottaviano (2008). The demand parameters $\alpha$ and $\eta$ index the substitution pattern between the numeraire and the horizontally-differentiated varieties, while the parameter $\gamma$ indexes the degree of horizontal differentiation between the varieties. They are all positive.
The utility function implies the following linear market demand for variety $i$ in country $l \in \{h,f\}$:
\begin{equation}\label{demand}
q_{i}^{l} \equiv L^{l} q_{i}^{c} =\frac{\alpha L^{l}}{\eta N^{l}+\gamma} -\frac{L^{l}}{\gamma}p_{i}^{l} +\frac{\eta N^{l}L^{l}}{(\eta N^{l}+\gamma)\gamma}\bar{p^{l}}+L^{l}z_{i}^{l}-\frac{1}{2}\frac{\eta N^{l}L^{l}}{\eta N^{l}+\gamma}\bar{z^{l}},
\end{equation}
where $p_{i}^{l}$ and $z_{i}^{l}$ are, respectively, the price and quality of variety $i$ in country $l$; $N^{l}$ is the measure of varieties actually consumed in country $l$ (with $q_{i}^{l}>0$); $\bar{p^{l}} =\frac{1}{N}\int_{i \in \Omega^{l}}p_{i}^{l}di$ and $\bar{z^{l}} =\frac{1}{N}\int_{i \in \Omega^{l}}z_{i}^{l}di$ are the average price and quality (across both local and foreign firms selling in country $l$) of these consumed varieties, where $\Omega^{l} \subset \Omega$ is the subset of varieties that are consumed. The demand function implies: (1) The demand for variety $i$ is negatively related to its own price but positively related to its own quality; (2) It is positively related to the average price of all varieties and negatively related to the average quality of all varieties, and (3) All these relationships are linear.
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\textbf{2.2. Firms, Production and Export}
Each firm in each country produces a differentiated variety and faces a fixed entry cost $f_{E}$, which is common across firms. Subsequent production of firm $i$ incurs the following total cost function:
\begin{equation}\label{total cost}
TC_{i}=c_{i}q_{i}+bq_{i}z_{i}+\theta (z_{i})^2.
\end{equation}
where $q_{i}$ and $z_{i}$ are the quantity and quality of the variety that the firm produces. The first term on the right hand side, $c_{i}q_{i}$, depends on the quantity but not the quality of output, and could be interpreted as ``processing cost" of a firm. The third term, $\theta (z_{i})^2$, depends on the quality level of the output but fixed with respect to the quantity of output, which captures the definition of ``R$\&$D cost" for quality upgrading. The second term, $bq_{i}z_{i}$, depends on both the quantity and the quality of the output, which captures the definition of ``component-upgrading cost" associated with quality upgrading. A firm could choose a component with one quality level for the home market but another component with another quality level for the foreign market.
There are three things worth pointing out. First, both the ``processing cost" and the ``R\&D cost" exist in Antoniades (2008), but the ``component-upgrading cost" is what we add to his model. The purpose of this extension is to justify that a firm can choose different product quality levels for different markets, which is crucial to ensure a closed form solution to the model, as will be shown below. Second, $c_{i}$ is a firm-specific constant which indexes the marginal processing cost; parameters $b$ and $\theta$ are product-specific constants which index the ``toughness" of quality upgrading for a product, but they are common across all firms producing different varieties of the same product. Third, $c_{i}$ is the marginal ``processing" cost of the firm, and the overall marginal cost of the firm is $MC_{i}=c_{i}+bz_{i}$, where $z_{i}$ is a function of $c_{i}$ (as will be shown shortly). $1/c_{i}$ indexes the processing productivity of the firm, and $1/MC_{i}$ indexes the overall productivity of the firm.
The timing of firms' decisions is as follows. First, firms learn about product-specific, quality-upgrading costs $b$ and $\theta$, the distribution of firm processing cost $G(c)$, and the fixed entry cost $f_{E}$, all of which are common knowledge, and they decide whether to enter the industry or not. Second, after they enter the industry by making the irreversible investment $f_{E}$, they learn about their individual processing cost $c_{i}$, and decide on the quality and price for the product that they will produce.
Consider a firm in the Home country $h$ with parameter $c$. The firm faces both domestic and foreign markets. Assume (1) the two markets are segmented, and (2) the firm chooses separate levels of product quality for the two markets. As mentioned above, the validity of the second assumption is based on the ``component-upgrading cost" that we add to Antoniades (2008). These two assumptions, together with the assumption of constant marginal ``processing cost" $c$, imply that the firm independently maximizes the profits earned from domestic and export sales:
\\
\begin{equation}\label{profit}
\begin{split}
\pi^{hh}=&p^{hh}q^{hh}-cq^{hh}-bq^{hh}z^{hh}-\theta (z^{hh})^2,
\\ \pi^{hf}=&\frac{p^{hf}}{\tau^{f}}q^{hf}-cq^{hf}-bq^{hf}z^{hf}-\theta (z^{hf})^2,
\end{split}
\end{equation}
where $p^{hh}$ and $p^{hf}$ denote its prices in the domestic and foreign markets; $q^{hh}$ and $q^{hf}$ stand for the corresponding quantities sold in the two markets; $\tau^{f}>1$ is the ad valorem gross tariff rate imposed by the foreign country. Note that the tariff-exclusive export price of the firm is $p^{*}=p^{hf}/\tau^{f}$.
Solutions to the profit maximization problems are:
\begin{equation}\label{price and quality}
\begin{split}
p^{hh}=&\frac{1}{2}(c^{hh}+c)+\frac{\gamma+b}{2}z^{hh},
\\p^{hf}=&\frac{\tau^{f}}{2}(c^{hf}+c)+\frac{\gamma+\tau^{f}b}{2}z^{hf},
\\z^{hh}=&\lambda^{hh}(c^{hh}-c),
\\z^{hf}=&\tau^{f}\lambda^{hf}(c^{hf}-c),
\end{split}
\end{equation}
where $c^{hh}=sup\{c:\pi^{hh}>0 \}$ and $c^{hf}=sup\{c:\pi^{hf}>0\}$ are cost upper bounds for firms to earn positive profits from domestic and export sales; $\lambda^{hh}=\frac{(\gamma-b)L^{h}}{4\gamma\theta-(\gamma-b){^2}L^{h}}$ and $\lambda^{hf}=\frac{(\gamma-\tau^{f}b)L^{f}}{4\gamma\theta\tau^{f}-(\gamma-\tau^{f}b){^2}L^{f}}$. We can show that $c^{hf}=c^{ff}/\tau^{f}$. Assume that $\gamma-b>0$, $\gamma-\tau^{f}b>0$, $4\gamma\theta-(\gamma-b){^2}L^{h}>0$ and $4\gamma\theta\tau^{f}-(\gamma-\tau^{f}b){^2}L^{f}>0$ to ensure $z^{hh}$ and $z^{hf}$ to be positive.
We can also show that the level of quality upgrading that the firm chooses ($z^{hh}$ or $z^{hf}$) is increasing in (i) the processing productivity of the firm ($1/c$), (ii) the market size ($L^{h}$ or $L^{f}$), and (iii) the degree of product horizontal differentiation ($\gamma$), but it is decreasing in (i) the toughness for quality upgrading ($\theta$ and $b$), and (ii) the foreign tariff rate ($\tau^{f}$). The intuition for these conclusions is straightforward and thus is omitted here.
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\textbf{2.3. Equilibrium and Price Structure}
The free entry condition implies that the expected profits from domestic and export sales should be equal to the fixed entry cost, $f_{E}$, that is,
\begin{equation}\label{free entry}
\int_{0}^{c^{hh}}\pi^{hh}dG(c)+\int_{0}^{c^{hf}}\pi^{hf}dG(c)=f_{E}
\end{equation}
where $G(c)$ is the distribution of the ``processing cost" $c$. Assume that this cost has a Pareto distribution with parameter $k$ and upper bound $c_{M}$: $G(c)=(c/c_{M})^k$, where $ c\in [0,c_{M}]$. Substituting this and $\eqref{profit}$-$\eqref{price and quality}$ into $\eqref{free entry}$, doing the same thing for the free-entry condition in the foreign country, and using $c^{hf}=c^{ff}/\tau^{f}$, we get the two cost bounds:
\begin{equation}\label{cost bound}
\begin{split}
c^{hh}=&\left[\frac{\gamma\phi}{L^{h}[1+(\gamma-b)\lambda^{hh}]}\cdot\frac{1-\rho^{f}\sigma^{f}}{1-(\rho^{f}\sigma^{f})(\rho^{h}\sigma^{h})}\right]^{\frac{1}{k+2}},
\\c^{hf}=&\left[\frac{\gamma\phi}{L^{f}[1+(\gamma-b)\lambda^{ff}]}\cdot\frac{1-\rho^{h}\sigma^{h}}{1-(\rho^{h}\sigma^{h})(\rho^{f}\sigma^{f})}\right]^{\frac{1}{k+2}}/\tau^{f},
\end{split}
\end{equation}
where $\phi=2(k+1)(k+2)c_{M}^{k}f_{E}$, $\rho^{l}=(\tau^{l})^{-k-1}$, $\sigma^{l}=\frac{1+(\gamma-\tau^{l}b)\lambda^{jl}}{1+(\gamma-b)\lambda^{ll}}$, and $l,j\in\{h,f\},l\neq j$. Equations $\eqref{price and quality}$ and $\eqref{cost bound}$ determine the closed form solutions to the model.
It is very helpful to have a careful examination for the structure of the equilibrium export price. As mentioned before, the incompleteness of tariff pass-through is equivalent to ``tariff absorption" of exporting firms, i.e., an adjustment of their tariff-exclusive prices. Here we focus on the tariff-exclusive price:
\begin{equation}\label{price structure}
\begin{split}
p^{*}=&\frac{p^{hf}}{\tau^{f}}
\\=&\frac{1}{2}\left(c^{hf}+c\right)+\frac{(\gamma+\tau^{f}b)}{2}\frac{z^{hf}}{\tau^{f}}
\\\equiv&p_{q}^{*}+p_{z}^{*}
\\=&\frac{1}{2}\left(c^{hf}+c\right)+\frac{(\gamma+\tau^{f}b)\lambda^{hf}}{2}\left(c^{hf}-c\right)
\\=&(1-B)c^{hf} +Bc.
\end{split}
\end{equation}
where $B=\frac{2\gamma\theta\tau^{f}-\gamma(\gamma-\tau^{f}b) L^{f}}{4\gamma\theta\tau^{f}-(\gamma-\tau^{f}b)^{2} L^{f}}$, and $1-B=\frac{2\gamma\theta\tau^{f}+\tau^{f}b(\gamma-\tau^{f}b)L^{f}}{4\gamma\theta\tau^{f}-(\gamma-\tau^{f}b)^{2}L^{f}}>0$.
The first equality is the definition of the tariff-exclusive export price. The second equality shows that the price consists of two components: the first term, $\frac{1}{2}\left(c^{hf}+c\right)$, is derived from the quantity processing; the second term, $\frac{(\gamma+\tau^{f}b)}{2}\frac{z^{hf}}{\tau^{f}}$, is derived from the quality upgrading. We refer to these two terms as the quantity component $p_{q}^{*}$ and the quality component $p_{z}^{*}$, respectively --- as indicated by the third equality (equivalence).
The forth equality shows the relationship between these two components and firm processing productivity. The quantity component, $p_{q}^{*}=\frac{1}{2}\left(c^{hf}+c\right)$, is negatively related to firm processing productivity ($1/c$), i.e.,
\begin{equation}\label{processing effect}
\frac{\partial p_{q}^{*}}{\partial (\frac{1}{c})}<0.
\end{equation}
We refer to this as the ``processing effect": the higher is firm processing productivity, the lower is the marginal processing cost, and hence the lower is the unit price. The quality component, $p_{z}^{*}=\frac{(\gamma+\tau^{f}b)\lambda^{hf}}{2}\left(c^{hf}-c\right)$, is positively related to firm productivity ($1/c$), i.e.,
\begin{equation}\label{quality effect}
\frac{\partial p_{z}^{*}}{\partial (\frac{1}{c})}>0.
\end{equation}
We refer to this as the ``quality effect": the higher is firm processing productivity, the higher is the product quality level that the firm will choose (as mentioned in section 2.2), and thus the higher is the quality-upgrading cost and the unit price.
The fifth (the last) equality describes the relationship between the overall price and firm processing productivity. From this equality we can get
\begin{equation}\label{homogeneous goods}
\frac{\partial p^{*}}{\partial (\frac{1}{c})}<0 \quad\quad \text{if}\quad\quad B>0, i.e., \left(\frac{2\theta}{L^{f}}+b\right)\tau^{f}>\gamma,
\end{equation}
\begin{equation}\label{differentiated goods}
\frac{\partial p^{*}}{\partial (\frac{1}{c})}>0 \quad\quad \text{if}\quad\quad B<0, i.e., \left(\frac{2\theta}{L^{f}}+b\right)\tau^{f}<\gamma.
\end{equation}
The intuition is as follows. The condition $\left(\frac{2\theta}{L^{f}}+b\right)\tau^{f}>\gamma$ implies that (1) the quality-upgrading toughness for the product, $\theta$ and $b$, are relatively high, (2) the foreign tariff rate, $\tau^{f}$, is relatively high, (3) the market size, $L^{f}$, is relatively small, and (4) the product horizontal differentiation $\gamma$ is relatively low. All these imply that the quality level chosen by all firms (producing different varieties of the same product) is relatively low (as mentioned in section 2.2), and the product has low scope for quality differentiation. As the result, the ``processing effect" dominates the ``quality effect", and hence the overall price is negatively related to firm processing productivity --- We refer to this type of products as ``quality homogeneous goods". In contrast, the condition $\left(\frac{2\theta}{L^{f}}+b\right)\tau^{f}<\gamma$ implies that the opposite is true: the product has high scope for quality differentiation, and the overall price is positively related to firm processing productivity --- We refer to this type of products as ``quality differentiated goods".
An interesting observation here is that the horizontal differentiation of a product $\gamma$ is related to the vertical differentiation or quality scope of the product. A product with low horizontal differentiation $\gamma$ is also likely to have low vertical differentiation or quality scope, and thus is likely to be a quality homogeneous good. A product with high horizontal differentiation $\gamma$ is also likely to have high vertical differentiation or quality scope, and thus is likely to be a quality differentiated good.
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\textbf{2.4. Tariff Absorption, Firm Productivity and Product Quality}
Now we shall turn to explore how a tariff change impacts the tariff-exclusive price $p^{*}$. From $\eqref{price structure}$ we can derive that the absolute magnitude of this impact is
\begin{equation}\label{absolute tariff absorption}
\begin{split}
\frac{\partial p^{*}}{\partial \tau^{f}}
=&-\frac{\partial B}{\partial \tau^{f}}(c^{hf}-c)+(1-B)\frac{\partial c^{hf}}{\partial \tau^{f}}
\\<&0.
\end{split}
\end{equation}
The last inequality holds since we can show that $\frac{\partial B}{\partial \tau^{f}}>0$, $1-B>0$, and $\frac{\partial c^{hf}}{\partial \tau^{f}}<0$, and $c^{hf}-c>0$ by definition of cost bound.
The relative magnitude of the impact is
\begin{equation}\label{tariff absorption elasticity}
\begin{split}
\Theta^{*}\equiv&\frac{\partial p^{*}}{\partial \tau^{f}}\frac{\tau^{f}}{p^{*}}
\\=&\left[-\frac{\partial B}{\partial \tau^{f}}(c^{hf}-c)+(1-B)\frac{\partial c^{hf}}{\partial \tau^{f}}\right]\frac{\tau^{f}}{(1-B)c^{hf}+Bc}
\\<&0.
\end{split}
\end{equation}
The negative signs of the absolute and relative price changes in response to a tariff change imply the incompleteness of tariff pass-through, i.e., ``tariff absorption": the tariff-exclusive export price increases in response to a tariff reduction\footnote{Note that here, and hereafter, we interpret ``tariff absorption" in terms of the increase of the tariff-exclusive price in response to a tariff reduction, instead of the decrease of the tariff-exclusive price in response to a tariff increase (as in section 1). This is mainly because that most tariff changes in the real world are tariff reductions instead of tariff increases, as will be indicated in section 4.}. $\Theta^{*}$ is the tariff absorption elasticity: the percentage increase in the tariff-exclusive export price in response to a one percent decrease in the gross tariff rate.
There are three things worth pointing out. First, we can verify that both the quantity component and the quality component of the tariff-exclusive export price increase in response to a tariff reduction, that is, $\frac{\partial p_{q}^{*}}{\partial \tau^{f}}<0$ and $\frac{\partial p_{z}^{*}}{\partial \tau^{f}}<0$. The increase of the quantity component of the price is essentially an increase in its markup, i.e., $\frac{\partial u_{q}}{\partial \tau^{f}}<0$, where $u_{q}=p_{q}^{*}-c=\frac{1}{2}(c^{hf}-c)$, since the processing cost $c$ is fixed. This markup adjustment is possible because of the linearity of the demand structure. The increase of the quality component of the price is caused by the quality upgrading of the product in response to the tariff reduction, that is,
$\frac{\partial z^{hf}}{\partial \tau^{f}}<0$.\footnote{We can also show the following. (1) The increase of the quality component of the price caused by the quality upgrading is due to the increase of quality-upgrading cost, i.e., $\frac{\partial c_{z}}{\partial \tau^{f}}<0$, where $c_{z}=[bq^{hf}z^{hf}+\theta (z^{hf})^{2}]/q^{hf}$ is the unit quality-upgrading cost. (2) However, the sign of the markup change associated with quality-upgrading, $\frac{\partial u_{z}}{\partial \tau^{f}}$, is ambiguous, where $u_{z}=p_{z}^{*}-c_{z}$.} In sum, when exporting firms face a tariff reduction, they will not only increase their markups due to the linear demand structure, but also upgrade the quality level of their products. That is, they will transfer the cost advantage due to tariff reduction to higher markups and quality advantage. Thus the model shows that both markup adjustment and quality adjustment are sources of firm-level tariff absorption.
Second, we can show that the absolute magnitude of tariff absorption, in terms of its absolute value, positively depends on firm processing productivity, i.e.,
\begin{equation}\label{absolute tariff absorption and productivity}
\frac{\partial|\partial p^{*}/\partial \tau^{f}|}{\partial(\frac{1}{c})}>0.
\end{equation}
We can also verify that, the absolute increase of the quantity component of the tariff-exclusive price in response to a tariff reduction is independent of firm processing productivity, that is, $\frac{\partial|\partial p_{q}^{*}/\partial \tau^{f}|}{\partial(\frac{1}{c})}=0$.\footnote{This is due to the following reason. From equation $\eqref{price structure}$ we can see that $p_{q}^{*}$ consists of two additive components (which is determined by the linear demand function): the first component ($c^{hf}$) depends on foreign tariff rate but not firm processing productivity, and the second component ($c$) depends on firm processing productivity but not foreign tariff rate. When foreign tariff rate changes, only the first component changes, which does not depend on firm processing productivity.} However, the absolute increase of the quality component of the tariff-exclusive price in response to a tariff reduction is positively related to firm processing productivity, that is, $\frac{\partial|\partial p_{z}^{*}/\partial \tau^{f}|}{\partial(\frac{1}{c})}>0$; this is because that firms with high processing productivity will upgrade their product quality more than firms with low processing productivity, i.e., $\frac{\partial|\partial z^{hf}/\partial \tau^{f}|}{\partial(\frac{1}{c})}>0$, since their ability for quality upgrading is high.
Third, the relative magnitude of tariff absorption, i.e., the tariff absorption elasticity, depends on firm processing productivity in the following way:
\begin{equation}\label{tariff absorption elasticity and productivity: low scope}
\frac{\partial |\Theta^{*}|}{\partial(\frac{1}{c})}>0\quad\quad \text{if}\quad\quad B>0, i.e., \left(\frac{2\theta}{L^{f}}+b\right)\tau^{f}>\gamma,
\end{equation}
\begin{equation}\label{tariff absorption elasticity and productivity: med scope}
\frac{\partial |\Theta^{*}|}{\partial(\frac{1}{c})}\sim 0\quad\quad \text{if}\quad\quad B<0, i.e., \left(\frac{2\theta}{L^{f}}+b\right)\tau^{f}<\gamma,
\end{equation}
\begin{equation}\label{tariff absorption elasticity and productivity: high scope}
\frac{\partial |\Theta^{*}|}{\partial(\frac{1}{c})}<0\quad\quad \text{if}\quad\quad B \ll 0, i.e., \left(\frac{2\theta}{L^{f}}+b\right)\tau^{f} \ll \gamma,
\end{equation}
where the notation ``$\sim$" in $\eqref{tariff absorption elasticity and productivity: med scope}$ denotes ``greater than, equal to, or less than", and ``$\ll$" in $\eqref{tariff absorption elasticity and productivity: high scope}$ denotes ``far less than". Notice that the condition $\frac{2\theta}{L^{f}}+b>\gamma$ implies that the product is a quality homogeneous good, $\frac{2\theta}{L^{f}}+b<\gamma$ implies that the product is a quality differentiated good, and $\frac{2\theta}{L^{f}}+b \ll \gamma$ implies that the product is a quality differentiated good and the scope for quality differentiation is very high.
These results could be explained by the impacts of firm processing productivity ($1/c$) on both the numeraire and the denominator of the tariff absorption elasticity ($\Theta^{*}\equiv\frac{\partial p^{*}}{\partial \tau^{f}}\frac{\tau^{f}}{p^{*}}$). As for the numeraire ($\partial p^{*}/\partial\tau^{f}$), we have seen that the absolute magnitude of tariff absorption, in terms of its absolute value, positively depends on firm processing productivity, as indicated in $\eqref{absolute tariff absorption and productivity}$. As for the denominator ($p^{*}$, the initial export price), its relationship with firm processing productivity is determined by product quality scope. For quality homogenous goods, the initial export price is negatively related to firm processing productivity, as indicated in $\eqref{homogeneous goods}$. Thus the tariff absorption elasticity, in terms of its absolute value, is positively related to firm processing productivity ($1/c$), as indicated in $\eqref{tariff absorption elasticity and productivity: low scope}$. In contrast, for a quality differentiated good, the initial export price is positively related to firm processing productivity, as indicated in $\eqref{differentiated goods}$. Thus the relationship between the tariff absorption elasticity, in terms of its absolute value, and firm processing productivity is ambiguous (as indicated in $\eqref{tariff absorption elasticity and productivity: med scope}$), depending on whether the numeraire or the denominator effect is dominant. If the product quality scope is sufficiently high, then the denominator effect dominates the numeraire effect, and thus the tariff absorption elasticity (in terms of its absolute value) is negatively related to firm processing productivity, as indicated in $\eqref{tariff absorption elasticity and productivity: high scope}$.\footnote{We can also show with numerical examples that there indeed exist model parameters that make this case possible.}
These results could also be explained in another way. We can verify that, the relative increase of the quantity component of the tariff-exclusive price in response to a tariff reduction is positively related to firm processing productivity, that is, $\frac{\partial|\Theta_{p_{q}^{*}}|}{\partial(\frac{1}{c})}>0$, where $\Theta_{p_{q}^{*}}\equiv \frac{\partial p_{q}^{*}}{\partial \tau^{f}}\frac{\tau^{f}}{p_{q}^{*}}<0$. \footnote{This is due to two facts: $\frac{\partial|\partial p_{q}^{*}/\partial \tau^{f}|}{\partial(\frac{1}{c})}=0$ and $\frac{\partial p_{q}^{*}}{\partial(\frac{1}{c})}<0$.} We can also refer to this as ``processing effect", as our interpretation for $\eqref{processing effect}$. However, the relative increase of the quality component of the tariff-exclusive price in response to a tariff reduction is negatively related to firm processing productivity, that is, $\frac{\partial|\Theta_{p_{z}^{*}}|}{\partial(\frac{1}{c})}<0$, where $\Theta_{p_{z}^{*}}\equiv \frac{\partial p_{z}^{*}}{\partial \tau^{f}}\frac{\tau^{f}}{p_{z}^{*}}<0$; this is because that firms with high processing productivity will upgrade their product quality by a less percentage, i.e., $\frac{\partial|\Theta_{{z}^{hf}}|}{\partial(\frac{1}{c})}<0$, where $\Theta_{{z}^{hf}}\equiv \frac{\partial {z}^{hf}}{\partial \tau^{f}}\frac{\tau^{f}}{{z}^{hf}}<0$, since their initial quality level is already high and thus the quality-upgrading cost is also high. We can also refer to this as ``quality effect", as our interpretation for $\eqref{quality effect}$. For quality homogenous goods, the ``processing effect" dominates the ``quality effect", and thus we see a positive relationship between the overall tariff absorption elasticity ($|\Theta^{*}|$) and firm processing productivity ($1/c$), as indicated in $\eqref{tariff absorption elasticity and productivity: low scope}$. For quality differentiated goods with high scope for quality differentiation, the ``processing effect" is dominated by the ``quality effect", and thus we see a negative relationship between the overall tariff absorption elasticity ($|\Theta^{*}|$) and firm processing productivity ($1/c$), as indicated in $\eqref{tariff absorption elasticity and productivity: high scope}$. For quality differentiated goods with medium scope for quality differentiation, it is not quite clear which effect is dominant, and thus we end up with an ambiguous relationship between the overall tariff absorption elasticity ($|\Theta^{*}|$) and firm processing productivity ($1/c$), as indicated in $\eqref{tariff absorption elasticity and productivity: med scope}$.
Table 1 summarizes the model predictions for comparative statics regarding (i) price and productivity, (ii) tariff absorption, (iii) absolute tariff absorption and productivity, as well as (iv) relative tariff absorption and productivity.
Notice that in $\eqref{homogeneous goods}$-$\eqref{differentiated goods}$ and $\eqref{absolute tariff absorption and productivity}$-$\eqref{tariff absorption elasticity and productivity: high scope}$, we focus on the relationship between export price or tariff absorption and firm ``processing" productivity ($1/c$). We can show that, for exported goods, the overall marginal cost is $MC=\partial TC^{hf}/\partial q^{hf}=c+bz^{hf}=c+b\lambda(c^{hf}-c)=b\lambda c^{hf}+(1-b\lambda)c$. Under the condition $1-b\lambda>0$ (which we assume is true), the overall marginal cost $MC$ and the marginal ``processing" cost ($c$) are positively correlated. Then all the relationships mentioned above ($\eqref{homogeneous goods}$-$\eqref{differentiated goods}$ and $\eqref{absolute tariff absorption and productivity}$-$\eqref{tariff absorption elasticity and productivity: high scope}$) could be re-written and re-interpreted in terms of firm overall productivity ($1/MC$).
\section*{3. Data}
Now we turn to the empirical side. We use the U.S. export data to test the model predictions on how tariff absorption depends on firm heterogeneity in productivity and product differentiation in quality. Four types of data are needed for empirical analysis: trade data, tariff data, firm productivity data, and product quality scope data.
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\textbf{3.1. Trade Data}
The trade data are used to compute firm-level export prices. The data that we use is the U.S. Linked/Longitudinal Firm Trade Transaction Database (LFTTD), which was assembled by Bernard, Jensen and Schott (2008). The data link all individual U.S. import and export transactions to the respective U.S. importing and exporting firms. The dataset comes from two sources: the first one is the foreign trade data (FTD) assembled by the U.S. Census Bureau and U.S. customs, which contains all U.S. international trade transactions between 1992 and 2005 inclusive; the second is the Longitudinal Business Database (LBD) of the U.S. Census Bureau, which records annual employment and survival information for most U.S. establishments. We use the export data in the LFTTD database. For each export transaction, the database records its product category (at HS10 level), quantity, (tariff-exclusive) value, exporting firm, destination country, year and month in which the transaction occurs, etc.
Before constructing export prices we clean the data in the following way. (1) We drop transactions with missing values in value, quantity, product category, export firm, destination country, or time. (2) Since measurement error in values or quantities causes measurement error for the constructed prices and leads to biased estimation, we remove the transactions (around 5 percent of the total) with extraordinary computed prices which are 20 times higher or lower than the average price of all transactions in the same product-firm-country-year cell. (3) We also remove related party transactions\footnote{Related-party transactions refer to trade between U.S. companies and their foreign subsidiaries and trade between U.S. subsidiaries of foreign companies and their affiliates abroad.} (around 30 percent of the total), since the price behavior for related party transactions is quite different from normal arm's length transactions. For the rest of transactions, we construct firm-level prices (unit values) as $P_{ifct}^{*}=V_{ifct}/Q_{ifct}$, where $V_{ifct}$ and $Q_{ifct}$ are the total value and quantity of product $i$ (HS10) exported by firm $f$ to country $c$ in year $t$. The constructed export prices are tariff-exclusive since export values are tariff-exclusive. Among all product-firm-country-year cells for which we constructed export prices, we keep those surviving in two consecutive years, and computer changes of absolute prices $\Delta P_{ifct}^{*}= P_{ifct}^{*}-P_{ifc(t-1)}^{*}$ and changes of log prices $\Delta lnP_{ifct}^{*}= lnP_{ifct}^{*}-lnP_{ifc(t-1)}^{*}$.
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\textbf{3.2. Tariff Data}
The tariff data contain the tariff rates of other countries against U.S. exports of different products. The data were collected by the World Integrated Trade Solution (WITS) at the World Bank. They are annual data at the HS6 level, and thus are more aggregate than the trade data in both time and product dimensions. Since tariff rates are annual, the time dimension $t$ of all variables in all regressions is also year. The actual tariff rate may vary across HS8 or HS10 products within a same HS6 category. For each HS6 category, the data include the maximum, minimum, and mean tariff rates of all HS8 or HS10 products within the category. We only include HS6 categories within which there is no tariff variation (that is, the maximum, minimum and mean tariff rates are all identical), since it is only for these HS6 categories that we can calculate accurate tariff change over time for products at HS10 level\footnote{For a HS6 industry within which there is tariff variation across HS8 or HS10 products, we can only calculate the change of average tariff rate for the HS6 industry, but not the accurate tariff change for each HS8 or HS10 product.}, $\Delta\tau_{ict}$. These tariff changes are then merged to U.S. export price changes of corresponding products to corresponding destination countries.
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\textbf{3.3. Firm Productivity Data}
Firm productivity is constructed from the U.S. Census of Manufactures (CMF) collected and maintained by the U.S. Census Bureau. For years ending with 2 or 7 (1987, 1992, 1997, etc.), the dataset records the production information (output, capital stocks, labor hours, energy and materials inputs, etc.) for all U.S. manufacturing establishments (plants). From this data we construct plant-level TFP from the typical constant returns to scale index form:
\[ln TFP_{pt}=ln Q_{pt}-\phi _{K}ln K_{pt}-\phi _{L}ln L_{pt}-\phi _{E}ln E_{pt}-\phi _{M}ln M_{pt}\]
where $TFP_{pt}$ is the TFP of plant $p$ in period $t$; $Q$, $K$, $L$, $E$ and $M$ represent plant-level output (value of shipment), capital stocks, labor hours, and energy and materials inputs; and the $\phi$'s are the factor elasticities for the corresponding inputs. The firm-level productivity, $TFP_{ft}$, is computed as the average of the productivity of the plants within the same firm weighted by their output shares\footnote{Total factor productivity corresponds to the ``overall" firm productivity $1/MC$ instead of the ``processing" productivity $1/c$ in section 2.}, and is then merged to the U.S. export price changes of corresponding firms.
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\textbf{3.4. Product Quality Scope Data}
The model predicts that the relationship between tariff absorption and firm productivity depends on product scope for quality differentiation. Thus we also need data to identify product quality scope. Since product quality is not directly observed, it is hard to find a very good criterion to identify the quality scope of a product. A potential criterion is the price-productivity schedule for each individual product. According to the model, if a product has a negative price-productivity schedule, then it could be classified as a quality homogeneous good; if it has a positive price-productivity schedule, then it could be classified as a quality differentiated good. We can even possibly use the slope of price-productivity schedule to measure the magnitude of the quality scope of a product. However, this method may cause an endogeneity problem: if we use the price-productivity schedule to classify the products in the first stage, and then explore the relationship between price changes (in response to tariff changes) and firm productivity for each group of products in the second stage, the dependent variable and the independent variables in the first stage are related to those in the second stage, and thus there may exist an endogeneity problem between these two stages.
Given this consideration, we turn to exogenous criteria for product quality scope. The first one that we are going to use is the Rauch classification. Rauch (1999) classifies products into commodities and differentiated goods: goods traded on organized exchanges or with reference prices are classified as commodities, and others are classified as differentiated goods. Intuitively speaking, products traded on organized exchanges or with reference prices should have relatively low scope for quality differentiation, and other products should have relatively high scope for quality differentiation. Thus we treat commodities in Rauch classification as quality homogeneous goods, and differentiated goods in Rauch classification as quality differentiated goods.
The second criterion that we use to identify the product quality scope is the R\&D investment for different industries/products. The model implies that quality upgrading is associated with both R\&D cost and component-upgrading cost. The higher are those costs in an industry, the higher should be the scope for quality differentiation. Data for component upgrading cost are hard to find, while R\&D investment data are available for a wide range of industries at the U.S National Science Foundation (NSF). The data contain U.S R\&D investment at the 2-digit or 3-digit SIC (Standard Industry Classification) industry level for the period 1995-1997. The R\&D investment comes from three different sources: federal funds, company funds and other funds. The data on federal funds in many industries are not publicly available for confidential consideration, but the data on company and other funds are available for almost all industries. The data contain the company and other R\&D investment for each industry as a percent of the net sales of the same industry, the R\&D/sales ratio. We merge the data to the trade and tariff data by using a concordance between SIC classification and HS classification, which was created by Pierce and Schott (2009). Then we use the R\&D investment for different industries to classify products: If a product is in an industry with a low R\&D/sales ratio, then it is classified as a quality homogeneous good; otherwise, it is classified as a quality differentiated good\footnote{We can also further classify quality differentiated goods into two subcategories in terms R\&D/sales ratio, those with medium-level scope for quality differentiation and those with high scope for quality differentiation, and then test the model predictions separately with three categories of products.}.
People may question that the Rauch classification may reflect horizontal differentiation instead of quality (vertical) differentiation, and the R\&D investment may also be used to make horizontal differentiation instead of quality (vertical) differentiation for a product. This is indeed true. However, as shown in section 2.3, the level of quality (vertical) differentiation of a product is positively related to the level of horizontal differentiation of the product: products with low level of horizontal differentiation (low $\gamma$) are more likely to be quality homogeneous goods, and products with high level of horizontal differentiation are more likely to be quality differentiated goods. Thus even though using the Rauch classification or the R\&D investment to identify product quality scope may not be accurate, they are not too bad approximation, especially when there are no other better alternatives. As will be seen in section 4, using these two criteria to classify products does result in estimates consistent with model predictions.
We also use GDP data to measure the market size, and use GDP change and exchange rate change as control variables. Both the GDP data and exchange rate data come from the Penn World Table.
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\textbf{3.5. Sample Selection}
The benchmark sample that we use for the empirical analysis contains the above-mentioned data for the period 1997-1998. The choice of this period is based on the joint consideration of the following facts: (1) The firm productivity data is only available for 1992, 1997 and 2002, (2) the R\&D data is only available for 1995-1997, and (3) there are a wide range of large tariff changes occurred around 1997 in the tariff data. In the benchmark 1997-1998 sample, export price changes and tariff changes are from 1997 to 1998, and firm productivity is for the base year 1997.\footnote{We have found that there is a huge change in firms' productivity from 1997 to 2002, both in the absolute magnitude and in the relative ranking. Thus we restrict our analysis to the price changes from 1997 to 1998, without extending to the years beyond (1998 to 1999, etc.); otherwise, the firm productivity data (in 1997) will not be an accurate measure for the actual firm productivity in the base year.} For R\&D data, since the R\&D investment may have a lag effect, we average the R\&D/Sales ratios for each industry for 1995, 1996 and 1997, and use this average ratio as the indicator for R\&D cost of the industry in 1997, the base year in the benchmark sample.
Panel a in table 2 lists the summary statistics for the full benchmark 1997-1998 sample, including number of industries (HS2 and HS6), products (HS10), exporting firms, and destination countries, as well as the total export value in the base year ($TV_{t-1}$) and summary statistics for the main variables in the data.\footnote{Note that the sample size is constrained by the following operations: (i) As mentioned in the beginning of this subsection, many export transactions were dropped when we constructed the export price and their changes. (ii) When we combined the export price changes with tariff changes, firm productivity, and R\&D/sales ratios, we also dropped HS6 products within which there is tariff variation, transactions conducted by firms for which we do not have the TFP data, as well as products (industries) for which we do not have the R\&D data.}
An observation from the table is the structure of tariff change. The table shows that, observations with tariff reduction account for 43 percent of all observations, those without any tariff change account for 53 percent, and those with tariff increase only account for 4 percent. Thus most of the tariff changes are tariff reductions, and the regression results about tariff absorption in next section could be interpreted as the increases of the tariff-exclusive prices in response to tariff reductions.
\section*{4. Empirical Strategies and Results}
We now turn to test the model predictions on tariff pass-through. Since the export prices we will get from the trade data are tariff-exclusive, we will focus on exploring how tariff changes impact the tariff-exclusive prices, i.e., tariff absorption, and how this impact depends on firm productivity and product quality. The main predictions of the model are: (i) The firm-level tariff pass-through is incomplete, that is, firms do absorb tariff change (see $\eqref{absolute tariff absorption}$ and $\eqref{tariff absorption elasticity}$). (ii) The absolute tariff absorption (in terms of its absolute value) positively depend on firm productivity, for both quality homogeneous goods and quality differentiated goods (see $\eqref{absolute tariff absorption and productivity}$). (iii) The relationship between the relative tariff absorption (tariff absorption elasticity) and firm productivity depends on the scope for quality differentiation of the product (see $\eqref{tariff absorption elasticity and productivity: low scope}$-$\eqref{tariff absorption elasticity and productivity: high scope}$). We test these predictions in two different ways: by pooling all products in the sample, and by dividing them into ``quality homogeneous goods" and ``quality differentiated goods".
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\textbf{4.1. All Products Pooled}
In this subsection, we pool all products in the sample, without dividing them into quality homogeneous goods and quality differentiated goods, to test the model predictions. We conduct the test for two samples: the first one is the full benchmark sample for 1997-1998, and the second one is a sub-sample which only contains the U.S. exports to certain countries with large tariff changes during this period.
\textbf{\textit{4.1.1. Full Sample}} \hspace{5pt} We start with the full benchmark sample. Table 3 contains the empirical specifications and results for this full sample.
In column 1, we use the following specification to check whether the products, on average, are quality homogeneous goods or quality differentiated goods:
\begin{equation}\label{test price-productivity schedule}
\begin{split}
ln P_{ifc(t-1)}^{*}=&\beta lnTFP_{f(t-1)}+\delta_{ic}+\mu_{ifc(t-1)}.
\\&(-: \text{homogeneous})
\\&(+: \text{differentiated})
\end{split}
\end{equation}
where $ln P_{ifc(t-1)}^{*}$ denotes the log tariff-exclusive price of product $i$ exported by firm $f$ to country $c$ in the base period $t-1$ (1997), $ln TFP_{f(t-1)}$ represents the log total factor productivity of firm $f$ in period $t-1$, $\delta_{ic}$ stands for a product-country fixed effect, and $u_{ifc(t-1)}$ is the error term. Here we use a product-country fixed effect to control any product-country specific determinants for export prices, so that the only variation in export prices unexplained by this fixed effect is the firm level variation. In this specification, coefficient $\beta$ measures the price-productivity schedule, i.e., how export prices are related to firm productivity: if $\beta$ is negative, then the products, on average, are quality homogeneous goods (see $\eqref{homogeneous goods}$); if $\beta$ is positive, then the products, on average, are quality differentiated goods (see $\eqref{differentiated goods}$). The estimated $\beta$ is positive (0.06) and significant: a 10 percent increase of firm TFP leads to a 0.6 percent increase of the export price. According to the model, this positive price-productivity schedule indicates that all products on average fit the definition of quality differentiated goods.
In column 2, we use the following specification to check whether the absolute tariff absorption depends on firm productivity or not:
\begin{equation}\label{test absolute tariff absorption and productivity}
\begin{split}
\Delta P_{ifct}^{*}=&\beta_{1}\Delta \tau_{ict}+\beta_{2}lnTFP_{f(t-1)}+\beta_{12}[\Delta\tau_{ict}\times lnTFP_{f(t-1)}]+\delta_{i}+\delta_{c}+\mu_{ifct},
\\&(-)\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad(-)
\end{split}
\end{equation}
where $\Delta P_{ifct}^{*}$ denotes the absolute change of the tariff-exclusive price of product $i$ exported by firm $f$ to country $c$ from period $t-1$ to period $t$, $\Delta\tau_{ict}$ is tariff change of country $c$ on product $i$ from period $t-1$ to period $t$\footnote{Tariff changes are typically announced by governments before the actual changes occur, and export contracts are typically set before the actual transactions occur. When exporting firms learn the information of future tariff changes, they can adjust their contracts beforehand accordingly by (i) changing their export prices for transactions that will occur when the tariffs change (contemporaneous effect), and/or (ii) change their export prices for transactions that will occur before the tariffs change (lead effect), if they want to smooth their price changes. Here the coefficient for the tariff change term, $\Delta\tau_{ict}$, only captures the contemporaneous effect but not the lead effect, and thus should be lower than the total effect of tariff changes on price changes. We could add another term, $\Delta\tau_{ic(t+1)}$, to capture the lead effect.}, $TFP_{f(t-1)}$ is the TFP of firm $f$ in the base year $t-1$, and $\delta_{i}$ and $\delta_{c}$ stand for the product fixed effect and the country fixed effect. We use the product fixed effect and the country fixed effect to control for any product-specific shocks and country-specific shocks (such as exchange rate changes and demand changes) on export price changes\footnote{Note that since the specification that we use is first order difference, we have already removed all time-invariant fixed effects (including product, firm, country, product-firm, product-country, firm-country, and product-firm-country fixed effect) on price levels. The fixed effects here and those in the regressions hereafter refer to fixed effects on price changes.}. The reason for using these two fixed effects instead of using a product-country fixed effect is that the latter will absorb the effect of tariff change, which is product-country specific (since the tariff change is just for one period, from 1997 to 1998). In this specification, the coefficient of the tariff change term, $\beta_{1}$, measures the absolute change of the tariff-exclusive price of a benchmark firm (with $lnTFP_{f(t-1)}=0$) in response to the tariff change. This coefficient should be negative according to $\eqref{absolute tariff absorption}$, and the estimated one is indeed negative (though insignificant) in column 2; however, since the absolute magnitudes of export price changes for different products are not comparable, the magnitude of $\beta_{1}$ is meaningless. The coefficient of the interaction term between tariff change and firm TFP, $\beta_{12}$, measures how firm productivity impacts the absolute change of the export price in response to the tariff change. According to $\eqref{absolute tariff absorption and productivity}$, this coefficient should be negative\footnote{Notice that a negative coefficient $\beta_{12}$ means that, for firms with high productivity, the impact of tariff change on tariff-exclusive price is even more negative, i.e., higher in terms of absolute value (indicated by $\eqref{absolute tariff absorption and productivity}$). This is due to the fact $\partial p^{*}/\partial\tau^{f}<0$. }, and the estimated one is indeed negative (though insignificant) in column 2. The separate TFP term is added in this specification in case firm productivity (or cost) has a direct effect on price change, but the model does not have an unambiguous prediction about the sign of this direct effect, captured by coefficient $\beta_{2}$.
In cloumn 3, we use the following regression to estimate tariff absorption elasticity:
\begin{equation}\label{estimate tariff absorption elasticity}
\begin{split}
\Delta ln P_{ifct}^{*}=&\beta\Delta ln(1+\tau_{ict})+\delta_{i}+\delta_{c}+\mu_{ifct},
\\&(-)
\end{split}
\end{equation}
Notice that we now have logs for both the price change and the tariff change. Thus coefficient $\beta$ measures the percent change of tariff-exclusive prices in response to percent change of tariff rates, that is, it measures tariff absorption elasticity.\footnote{ Also notice that we have gross tariff rate ($1+\tau_{ict}$) on the right hand side since that is the tariff rate in the theoretical model. In specification $\eqref{test absolute tariff absorption and productivity}$ we have the absolute change of net tariff rate since that is equivalent to absolute change of gross tariff rate, i.e., $\Delta\tau_{ict}=\Delta(1+\tau_{ict})$.} Again here we use both product and country fixed effects. According to $\eqref{tariff absorption elasticity}$, the tariff absorption elasticity $\beta$ should be negative. The estimated overall tariff absorption elasticity is indeed negative ($-0.87$) and significant. This indicates that the firm-level tariff absorption does exist: on average exporting firms absorb 87 percent of the tariff reduction by increasing their tariff-exclusive prices. In other words, the firm-level tariff pass-through is indeed incomplete: only 13 percent of the tariff reduction is passed on to consumers as lower consumer prices.
You may wonder why the tariff absorption elasticity (in terms of absolute value) is so high comparing to the estimates in previous studies at the industry level\footnote{Recall that in Feenstra (1989), the tariff absorption in the automobile industry is only 40 percent. In Kreinin (1961), the average tariff absorption in all industries is higher at around 67 percent, but still much lower than the estimate in this paper.}. There are two possible reasons for this. First, the tariff absorption we get here is at the firm-level and is for incumbent firms after tariff reductions. As shown in the model, these firms not only increase their markups but also upgrade their product quality in response to tariff reductions, and hence their price increase is high. Second, according to the model, the new entrants caused by tariff reductions (which are less productive than incumbents) may have lower-than-average prices since they produce lower quality goods, and thus the average industry-level prices after tariff reductions only increase by a smaller magnitude, which is consistent with the previous smaller estimates at the industry level.
In column 4, we add firm productivity and its interaction with the relative tariff change to estimate its direct effect on price change and its impact on tariff absorption:
\begin{equation}\label{test tariff absorption elasticity and productivity}
\begin{split}
\Delta lnP_{ifct}^{*}=&\beta_{1}\Delta ln(1+\tau_{ict})+\beta_{2}TFPH_{f(t-1)}+\beta_{12}[\Delta ln(1+\tau_{ict})\times TFPH_{f(t-1)}]
\\&(-)\hspace{160pt}(-: \text{homogeneous})
\\&\hspace{178pt}(\pm: \text{modestly differentiated})
\\&\hspace{178pt}(+: \text{highly differentiated})
\\&+\delta_{i}+\delta_{c}+\mu_{ifct}
\end{split}
\end{equation}
This specification is a counterpart of $\eqref{test absolute tariff absorption and productivity}$, but with two differences: (1) Here we have logs for both the price change and the tariff change; (2) Here we use a high TFP dummy $TFPH_{f(t-1)}$ to replace the level of firm TFP --- This dummy is set to 1 if the TFP of the exporting firm $f$ in the base year $t-1$, $TFP_{f(t-1)}$, is higher than the average TFP of all firms exporting the same product $i$ to the same destination country $c$, and 0 otherwise.
Now the coefficient for the tariff change, $\beta_{1}$, measures the tariff absorption elasticity for low productivity firms. According to the model, it should be negative (by $\eqref{tariff absorption elasticity}$). The estimation is indeed negative ($-1.27$) and significant. A tariff absorption elasticity less than $-1$ implies that, when low productivity firms face a tariff reduction, they increase their tariff-exclusive prices so much that the tariff-inclusive consumer prices actually increase instead of decreasing. This is known as the ``Metzler Paradox". The possible reason again lies in quality upgrading: the initial product quality for low productivity firms is low; when they face a tariff reduction, they upgrade their product quality by a significant relative magnitude, which leads to a high increase in their tariff-exclusive prices. Thus, quality upgrading provides a reasonable explanation for the ``Metzler Paradox".
The coefficient for the interaction term between tariff change and the high TFP dummy, $\beta_{12}$, measures the difference between the tariff absorption elasticity for high productivity firms and the elasticity for low productivity firms. A negative $\beta_{12}$ implies that high productivity firms have a higher tariff absorption elasticity (in terms of its absolute value) than low productivity firms, since the elasticity itself is negative, while a positive $\beta_{12}$ implies that the opposite is true. According to the model, $\beta_{12}$ should be negative for quality homogeneous goods (by $\eqref{tariff absorption elasticity and productivity: low scope}$), ambiguous for quality differentiated good with medium-level scope for quality differentiation (by $\eqref{tariff absorption elasticity and productivity: med scope}$), but positive for quality differentiated goods with high scope for quality differentiation (by $\eqref{tariff absorption elasticity and productivity: high scope}$).\footnote{Again, notice that the signs of these coefficients are seemingly opposite to, but actually consistent with, the expressions and word interpretations in terms of absolute values ($\eqref{tariff absorption elasticity and productivity: low scope}$-$\eqref{tariff absorption elasticity and productivity: high scope}$). This is again caused by the fact $\partial p^{*}/\partial\tau^{f}<0$.} The estimated $\beta_{12}$ is positive (0.83) and significant, indicating that high productivity firms actually have lower (in terms of its absolute value) tariff absorption elasticity, which is $-0.44$ ($-1.27+0.83=-0.44$). This is consistent with the model prediction for quality differentiated goods with high scope for quality differentiation. Thus, on average the products in the full sample have a relatively high scope for quality differentiation.
In column 5, we add two other control variables, exchange rate changes and GDP changes of the destination countries:
\begin{equation}\label{test tariff absorption elasticity and productivity}
\begin{split}
\Delta lnP_{ifct}^{*}=&\beta_{1}\Delta ln(1+\tau_{ict})+\beta_{2}TFPH_{f(t-1)}+\beta_{12}[\Delta ln(1+\tau_{ict})\times TFPH_{f(t-1)}]
\\&(-)\hspace{160pt}(-: \text{homogeneous})
\\&\hspace{178pt}(\pm: \text{modestly differentiated})
\\&\hspace{178pt}(+: \text{highly differentiated})
\\&+\beta_{3}\Delta lnXR_{c(t-1)}+\beta_{4}\Delta lnGDP_{ct}+\delta_{i}+\mu_{ifct},
\\&\quad(-)\hspace{70pt}(+)
\end{split}
\end{equation}
Notice that here the change of log exchange rate (measured as units of foreign currency per U.S. dollar), $\Delta lnXR_{c(t-1)}$, is one period ahead of the tariff change\footnote{We use the exchange rate changes one-period ahead, because exchange rate changes are not announced beforehand, and thus it will take exporting firms some time to adjust their contracts, which are typically set before the actual transactions occur. Hence exchange rate changes typically have a lag effect on price changes, as shown in the exchange rate pass-through literature. This is quite different from the impacts of tariff changes on price changes, where there are a contemporaneous effect and a lead effect, as discussed in footnote 17.}. A dollar appreciation should cause U.S. exporting firms to lower their export prices denominated in U.S. dollars\footnote{As shown in the exchange rate pass-through literature.}, and thus $\beta_{3}$ should be negative. The change of log GDP of the destination country, $\Delta lnGDP_{ct}$, is used to control for the change of market demand. An increase of the market demand should push up export prices, and thus $\beta_{4}$ should be positive. Since these two variables are country specific, we drop the country fixed effect and only keep the product fixed effect in the regression. The estimates for these two controls are not significant\footnote{As you will see, even though we get significant tariff pass-through elasticities in almost all regressions throughout the paper, we do not get significant exchange rate pass-through elasticity in any regression. Two possible explanations are: (1) As we indicated earlier, exchange rate pass-through has a lag effect, but the length of the lag effect depends on the nature of contracts of trade transactions, which is very complicated in reality, and thus our specification of one-period lag effect may be inaccurate. (2) In many cases firms regard exchange rate changes as temporary changes, but tariff changes as permanent changes. Thus firms' response to exchange rate changes is less prominent than their response to tariff changes.}, but including them in the regression changes the tariff absorption elasticities to $-0.89$ for low productivity firms and $-0.05$ ($-0.89+0.84=-0.05$) for high productivity firms. The lower (in terms of its absolute value) elasticity for higher productivity firms is still consistent with the model prediction for products with high scope for quality differentiation.
In cloumn 6, we add the market size and the initial tariff of the destination country, as well as their interaction with the relative tariff change, to estimate their impacts on price change and tariff absorption:
\begin{equation}\label{test tariff absorption elasticity, initial tariff and market size}
\begin{split}
\Delta lnP_{ifct}^{*}=&\beta_{1}\Delta ln(1+\tau_{ict})+\beta_{2}TFPH_{f(t-1)}+\beta_{12}[\Delta ln(1+\tau_{ict})\times TFPH_{f(t-1)}]
\\&(-)\hspace{160pt}(-: \text{homogeneous})
\\&\hspace{178pt}(\pm: \text{modestly differentiated})
\\&\hspace{178pt}(+: \text{highly differentiated})
\\&+\beta_{3}\Delta lnXR_{c(t-1)}+\beta_{4}\Delta lnGDP_{ct}
\\&\quad(-)\hspace{70pt}(+)
\\&+\beta_{5}ln(1+\tau_{ic(t-1)})+\beta_{15}[\Delta ln(1+\tau_{ict})\times \ln(1+\tau_{ic(t-1)})]
\\&+\beta_{6}lnGDP_{c(t-1)}+\beta_{16}[\Delta ln(1+\tau_{ict})\times lnGDP_{c(t-1)}]+\delta_{i}+\mu_{ifct},
\end{split}
\end{equation}
where $\tau_{ic(t-1)}$ is the initial tariff rate in the base year, and $GDP_{c(t-1)}$ is GDP of country $c$ in the base year, which measures its market size in the base year. The model shows that these two factors do affect price changes and tariff absorption, as indicated by $\eqref{price structure}$ and $\eqref{tariff absorption elasticity}$. However, the model does not have an unambiguous prediction about the signs of their impacts on price changes (captured by coefficients $\beta_{5}$ and $\beta_{6}$), or the signs of their impacts on tariff absorption (captured by coefficients $\beta_{15}$ and $\beta_{16}$). Here we add these terms as we wanted to empirically check the nature and significance of their impacts. The estimates show that none of these impacts is significant. Notice that in this specification the estimate for the coefficient of the tariff change term ($-4.96$) measures the tariff absorption elasticity for low productivity firms ($TFPH=0$) exporting to a country with a hypothetical tariff rate for the product ($ln(1+\tau)=0$) and a hypothetical GDP ($lnGDP=0$), and thus its magnitude is meaningless. However, the positive coefficient for the interaction term between the relative tariff change and the high TFP dummy (0.83) still shows that firms with high productivity have lower (in terms of its absolute value) tariff absorption elasticity, which is consistent with the model prediction for products with high scope for quality differentiation.
\textbf{\textit{4.1.2. Sub-sample with Large Tariff Changes}} \hspace{5pt} Next, we conduct the same analysis as above for a sub-sample that only includes countries with large tariff changes for certain products during the period 1997-1998. More specifically, we only include 38 countries for which there is at least one HS6 industry with tariff change higher than 5 percentage points; but for each of these countries, we keep all industries no matter whether they have large tariff change or not. The purpose of choosing this sample is to ensure that there are enough observations with large tariff changes to induce price changes and, at the same time, there are also enough observations with small tariff changes for the purpose of comparison. The countries contained in the sub-sample are listed in table 4.
People may wonder whether the construction of the sub-sample containing only countries with large tariff changes will lead to selection bias. To address this concern, we compare the full benchmark sample and the sub-sample by including the summary statistics for the sub-sample in panel b of table 2. The comparison between these two samples shows that even though the sub-sample only contains two thirds of the countries (38 vs. 61) in the full sample, all the other indicators in the two samples are pretty close to each other, which indicates that the sub-sample is quite representative for the full sample. This is because that the countries contained in the sub-sample not only include all the large trade partners of the U.S. (such as Canada, Mexico, European Union countries, Japan, China, etc.), but also include middle-size countries (such as Egypt, Turkey, Argentina, etc.) and small countries (such as Dominica, Salvador, Honduras, Ecuador, etc.).
Table 5 contains the regression results for this sub-sample. This table shows the qualitatively same results as those in table 3. First, there is a positive and significant price-productivity schedule (with estimate 0.05), which shows that all products on average fit the definition of quality differentiated goods. Second, the firm-level tariff pass-through is indeed incomplete, and the overall tariff absorption elasticity is $-0.65$, as shown in column 3. Third, the absolute magnitude of tariff absorption (in terms of absolute value) is positively related to firm productivity, as shown by the negative (though insignificant) estimate for the interaction term between the absolute tariff change and firm TFP in column 2. Next, tariff absorption elasticity (in terms of absolute value) is higher for low productivity firms, and lower for high productivity firms, as shown by the positive and significant estimates (0.90) for the interaction term between the relative tariff change and the high TFP dummy in columns 4-6. This is consistent with the model predictions for products with high scope for quality differentiation. Finally, the impacts of initial tariff rate and market size on tariff absorption are insignificant, as shown by the estimates for the interaction terms between tariff change and GDP as well as initial tariff rate.
In short, the results presented in this subsection show that (1) firm-level tariff absorption does exist, i.e., firm-level tariff pass-through is indeed incomplete; (2) all products on average fit the definition of quality differentiated goods, as they have a positive price-productivity schedule; and (3) tariff absorption elasticity (in terms of absolute value) is higher for low productivity firms and lower for high productivity firms, which is consistent with the model prediction for products with high scope for quality differentiation.
\\
\\
\textbf{4.2. Quality Homogeneous Goods vs. Quality Differentiated Goods}
In this subsection we divide all products in the benchmark full sample into two groups, ``quality homogeneous goods" and ``quality differentiated goods", and run the regressions specified above separately for the two groups. As mentioned in section 3, we classify the products by two criteria: Rauch classification and R\&D/sales ratio.
\textbf{\textit{4.2.1. In terms of Rauch Classification}} \hspace{5pt} The first criterion that we use to classify products is the Rauch classification: We treat commodities in terms of the Rauch classification as quality homogeneous goods, and treat differentiated goods in terms of Rauch classification as quality differentiated goods. Among the 84,902 observations (product-firm-country-year cells) in the benchmark full sample, only 6,171 belong to quality homogeneous goods, and the other 65,277 belong to quality differentiated goods. Table 6 and table 7 present the regression results for these two groups, respectively.
In table 6 (for commodities), the slope for the price-productivity schedule is not significant and even not negative, as shown in column 1. This indicates that it may not be accurate to treat all commodities in terms of the Rauch classification as quality homogeneous goods. The relationship between absolute magnitude of tariff absorption and firm productivity is not significant, as shown in column 2. Column 3 shows that the overall tariff absorption elasticity is indeed negative and significant ($-1.21$), indicating that firm-level tariff pass-through is indeed incomplete\footnote{A surprising finding here is that the tariff absorption elasticity is higher than 1 in terms of its absolute value, that is, ``Metzler Paradox" also exists for commodities, for which there should be no large quality adjustment in response to tariff change.}. The estimates in columns 4-6 for the interaction term between the relative tariff change and the high TFP dummy are all negative (though insignificant), which shows that high productivity firms have a higher (but not significant) tariff absorption elasticity (in terms of its absolute value) than low productivity firms. This is qualitatively consistent with the model prediction for quality homogeneous goods. The impacts of initial tariff rate and market size on tariff absorption are again insignificant.
In table 7 (for differentiated products), we do find a positive and significant price-productivity schedule, as shown in column 1, which shows that differentiated products in terms of the Rauch classification fit the definition of quality differentiated goods. Column 2 shows that the absolute magnitude of tariff absorption (in terms of its absolute value) is positively (though not significantly) related to firm productivity, which is consistent with model predictions. Column 3 shows that the overall tariff absorption elasticity for this group is indeed negative and significant ($-0.80$), which implies that firm level tariff pass-through is indeed incomplete. Column 4 shows that the tariff absorption elasticity is higher (in terms of its absolute value) for low productivity firms ($-1.30$), and lower (in terms of its absolute value) for high productivity firms ($-1.30+1.04=-0.26$), which is consistent with the model prediction for products with high scope for quality differentiation. The positive estimates for the interaction term between tariff change and the high TFP dummy in columns 5-6 show the same conclusion. Again the impacts of initial tariff rate and market size on tariff absorption are insignificant.
\textbf{\textit{4.2.2. In terms of R\&D/Sales Ratio}} The second criterion that we use to classify products is the R\&D/sales ratio for different industries/products. We treat goods with R\&D/sales ratios lower than the 25th percentile of R\&D/sales ratios for all products in the full benchmark sample as quality homogeneous goods, and other goods as quality differentiated goods. The reason for using the 25th percentile as the cutoff is that, comparing to the mean or median, this cutoff leads to 15,408 observations in the group of quality homogeneous goods and 69,494 observations in the group of quality differentiated goods, which are close to sample sizes of the two groups under the Rauch classification\footnote{The correlation between these two classifications is 0.30.}. Table 8 and table 9 present the regression results for these two groups, respectively.
In table 8 (for products with low R\&D/sales ratios), we did not find a negative and significant price-productivity schedule, as shown in column 1, which indicates that it may not be accurate to treat all products with low R\&D/sales ratios as quality homogeneous goods. Again the absolute magnitude of tariff absorption (in terms of its absolute value) is positively (though not significantly) related to firm productivity, as shown by the negative estimate for the interaction term between tariff change and TFP in column 2. Column 3 shows that the overall tariff absorption elasticity is not significant for this group of goods. The estimates in columns 4-6 for the interaction term between the relative tariff change and the high TFP dummy are all insignificant, which shows that the impact of firm productivity on tariff absorption is insignificant for this group of goods. The last column shows that the impacts of initial tariff rate and market size on tariff absorption are also insignificant.
In table 9 (for products with high R\&D/sales ratios), we do have a positive and significant price-productivity schedule, as shown in column 1, which shows that products with high R\&D/sales ratios do fit the definition of quality differentiated goods. Again column 2 shows that the absolute magnitude of tariff absorption (in terms of its absolute value) is positively (though not significantly) related to firm productivity, which is consistent with the model prediction. Column 3 shows that the overall tariff absorption elasticity is $-1.01$ and significant for this group, which again confirms the incompleteness of firm-level tariff pass-through and the ``Metzler Paradox". Column 4 shows that the tariff absorption elasticity is higher (in terms of its absolute value) for low productivity firms ($-1.60$), and lower (in terms of its absolute value) for high productivity firms ($-1.60+1.23=-0.37$), which is consistent with the model prediction for products with high scope for quality differentiation. The positive estimates for the interaction term between the relative tariff change and the high TFP dummy in columns 5-6 show the same conclusion. Again the last column shows that the impacts of initial tariff rate and market size on tariff absorption are insignificant.
In short, the regression results presented in this subsection show that the inverse relationship between tariff absorption elasticity and productivity is more pronounced for quality differentiated goods and non-existent for quality homogeneous goods, which is consistent with the model. Note that the group of quality homogeneous goods that we got in terms of the two criteria (the Rauch classification and the R\&D/Sales ratios) does not fully fit the definition of quality homogeneous goods, since they do not have a significant negative price-productivity schedule. Thus, even though we did not find a significant positive relationship between tariff absorption elasticity and productivity for this group of products (as the model predicts), we attribute this to the empirical measurement error instead of the failure of the model.
\section*{5. Conclusions}
This paper explores the incompleteness of tariff pass-through at the firm level, as well as its dependence on firm heterogeneity in productivity and product differentiation in quality. On the theoretical side, we use an extended version of the Melitz and Ottaviano (2008) model and show that, when exporting firms face a foreign tariff change, they will absorb part of the tariff change by adjusting both their markups and their product quality, which leads to an incomplete tariff pass-through. Moreover, tariff absorption elasticity (in terms of its absolute value) and firm productivity are negatively correlated for products with high scope for quality differentiation, but positively correlated for quality homogeneous goods.
On the empirical side, we use the U.S. transaction-level export data and plant-level manufacturing data, and find evidence for the predictions of the model. The firm-level tariff absorption elasticity is $-0.87$ on average. Pooled regressions reveal that the tariff absorption elasticity is higher (in terms of its absolute value) for lower productivity firms ($-1.27$) and lower for high productivity firms ($-0.44$). Estimation done separately on quality differentiated goods and quality homogeneous goods finds that the inverse relationship between tariff absorption elasticity and productivity is more pronounced for quality differentiated goods and non-existent for quality homogeneous goods, which is consistent with the model.
\section*{References}
\begin{description}
\onehalfspacing
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\end{description}
\footnotesize
\onehalfspacing
\newpage
\section*{Tables}
\vspace{25pt}
\begin{center}
\textbf{Table 1. Summary of Model Predictions for Comparative Statics:
\\ Products with Different Scopes for Quality Differentiation}
\vspace{10pt}
\\
\doublespacing
\begin{tabular}{lllccccccc}
\hline\hline
Item &\vline &Comparative &\vline &Low Scope &\vline &Medium Scope &\vline &High Scope \\
&\vline &Statics &\vline &$\left(\frac{2\theta}{L^{f}}+b\right)\tau^{f}>\gamma$ &\vline
&$\left(\frac{2\theta}{L^{f}}+b\right)\tau^{f}<\gamma$ &\vline
&$\left(\frac{2\theta}{L^{f}}+b\right)\tau^{f}\ll\gamma$ \\
\hline
&\vline &
&\vline & &\vline & &\vline &\\
Price and &\vline &$\partial p^{*}/\partial(\frac{1}{c})$
&\vline &$-$ &\vline &$+$ &\vline &$+$\\
&\vline &\hspace{15pt} $\partial p_{q}^{*}/\partial(\frac{1}{c})$
&\vline &$-$ &\vline &$-$ &\vline &$-$\\
Productivity &\vline &\hspace{15pt} $\partial p_{z}^{*}/\partial(\frac{1}{c})$
&\vline &$+$ &\vline &$+$ &\vline &$+$\\
&\vline &
&\vline & &\vline & &\vline &\\
\hline
&\vline &
&\vline & & & & &\\
Absolute Tariff &\vline &$\partial p^{*}/\partial\tau^{f} $
&\vline & & &$-$ & &\\
Absorption &\vline &\hspace{15pt} $\partial p_{q}^{*}/\partial\tau^{f}$
&\vline & & &$-$ & &\\
&\vline &\hspace{15pt} $\partial p_{z}^{*}/\partial\tau^{f}$
&\vline & & &$-$ & &\\
Relative Tariff &\vline &$\Theta^{*}\equiv\frac{\partial p^{*}}{\partial \tau^{f}}\frac{\tau^{f}}{p^{*}}$
&\vline & & &$-$ & &\\
Absorption &\vline &\hspace{15pt} $\Theta_{p_{q}^{*}}\equiv\frac{\partial p_{q}^{*}}{\partial
\tau^{f}}\frac{\tau^{f}}{p_{q}^{*}}$
&\vline & & &$-$ & &\\
&\vline &\hspace{15pt} $\Theta_{p_{z}^{*}}\equiv\frac{\partial p_{}^{*}}{\partial
\tau^{f}}\frac{\tau^{f}}{p_{z}^{*}}$
&\vline & & &$-$ & &\\
&\vline &
&\vline & & & & &\\
\hline
&\vline &
&\vline & & & & &\\
Absolute Tariff &\vline &$\frac{\partial|\partial p^{*}/\partial\tau^{f}|}{\partial(\frac{1}{c})}$
&\vline & & &$+$ & &\\
&\vline &
&\vline & & & & &\\
Absorption and &\vline &\hspace{15pt} $\frac{\partial|\partial p_{q}^{*}/\partial\tau^{f}|}{\partial(\frac{1}{c})}$
&\vline & & &$0$ & &\\
&\vline &
&\vline & & & & &\\
Productivity &\vline &\hspace{15pt} $\frac{\partial|\partial p_{z}^{*}/\partial\tau^{f}|}{\partial(\frac{1}{c})}$
&\vline & & &$+$ & &\\
&\vline &
&\vline & & & & &\\
\hline
&\vline &
&\vline & &\vline & &\vline &\\
Relative Tariff &\vline &$\frac{\partial|\Theta^{*}|}{\partial(\frac{1}{c})}$
&\vline &$+$ &\vline &$\pm$ &\vline &$-$\\
&\vline &
&\vline & &\vline & &\vline &\\
Absorption and &\vline &\hspace{15pt} $\frac{\partial|\Theta_{p_{q}^{*}}|}{\partial(\frac{1}{c})}$
&\vline &$+$ &\vline &$+$ &\vline &$+$\\
&\vline &
&\vline & &\vline & &\vline &\\
Productivity &\vline &\hspace{15pt} $\frac{\partial|\Theta_{p_{z}^{*}}|}{\partial(\frac{1}{c})}$
&\vline &$-$ &\vline &$-$ &\vline &$-$\\
&\vline &
&\vline & &\vline & &\vline &\\
\hline\hline
\end{tabular}
\end{center}
\onehalfspacing
\newpage
\begin{center}
\textbf{Table 2. Summary Statistics for Two Samples}
\vspace{10pt}
\\
\begin{tabular}{lrrrrrrrrrr}
\hline\hline
&\vline & a. & Full Sample & &\vline & b. &Sub-sample &\\
\hline
$\text{No. of HS2}$ &\vline &85 & & &\vline &85 & &\\
$\text{No. of HS6}$ &\vline &2,005 & & &\vline &1,979 & &\\
$\text{No. of HS10}$ &\vline &2,735 & & &\vline &2,679 & &\\
$\text{No. of Firms}$ &\vline &14,404 & & &\vline &13,275 & &\\
$\text{No. of Countries}$ &\vline &61 & & &\vline &38 & & \\
$TV_{t-1}$ &\vline &$5.28\times10^{10}$& & &\vline &$4.26\times10^{10}$ & & \\
\hline
Variables &\vline &No. of Obs. & Mean & Std.Dev. &\vline &No. of Obs. & Mean & Std.Dev.\\
\hline
$\Delta lnP_{ifct}$ &\vline &84,902 &-0.010 &1.474 &\vline &65,227 &-0.009 &1.431\\
$\Delta\tau_{ict}: \text{all}$ &\vline &84,902 &-0.006 &0.023 &\vline &65,227 &-0.008 &0.026\\
$\Delta\tau_{ict}<0$ &\vline &36,175(43\%) &-0.019 &0.028 &\vline &34,612(53\%) &-0.019 &0.028\\
$\Delta\tau_{ict}=0$ &\vline &45,125(53\%) &0 &0 &\vline &27,047(41\%) &0 &0\\
$\Delta\tau_{ict}>0$ &\vline &3,602(4\%) &0.035 &0.034 &\vline &3,568(6\%) &0.035 &0.035\\
$lnTFP_{f(t-1)}$ &\vline &84,902 &1.888 &0.577 &\vline &65,227 &1.889 &0.581\\
\hline\hline
\end{tabular}
\end{center}
Notes:
\\ \quad\quad\quad\quad\quad\quad\quad\quad(1) Full Sample: 1997-1998. (Benchmark Sample)
\\ \quad\quad\quad\quad\quad\quad\quad\quad(2) Sub-sample: 1997-1998, countries with large tariff change (higher than 5 percentage points) in at least one HS6 industry.
\singlespacing
\newpage
\begin{center}
\textbf{Table 3. Tariff Absorption: Full Sample, All Products}
\vspace{10pt}
\\
\begin{tabular}{llllllllllll}
\hline\hline
Dependent Variable &$lnP_{ifc(t-1)}^{*}$ &$\Delta P_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ \\
Regressors &(1) &(2) &(3) &(4) &(5) &(6)\\
\hline
$\Delta\tau_{ict}$ & &-516 & & & & \\
& &(33000) & & & & \vspace{6pt}\\
$lnTFP_{f(t-1)}$ &0.06*** &1,500*** & & & & \\
&(0.01) &(548) & & & & \vspace{6pt}\\
$\Delta\tau_{ict} \times lnTFP_{f(t-1)}$ & &-1700 & & & & \\
& &(16000) & & & & \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})$ & & &-0.87** &-1.27*** &-0.89** &-4.96 \\
& & &(0.35) &(0.42) &(0.38) &(5.1) \vspace{6pt}\\
$TFPH_{f(t-1)}$ & & & &0.02** &0.02** &0.02** \\
& & & &(0.01) &(0.01) &(0.01) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict}) \times TFPH_{f(t-1)}$ & & & &0.83* &0.84* &0.83* \\
& & & &(0.50) &(0.50) &(0.50) \vspace{6pt}\\
$\Delta lnXR_{c(t-1)}$ & & & & &0.03 &0.03 \\
& & & & &(0.07) &(0.07) \vspace{6pt}\\
$\Delta lnGDP_{ct}$ & & & & &-0.0002 &-0.01 \\
& & & & &(0.05) &(0.05) \vspace{6pt}\\
$ln(1+\tau_{ic(t-1)})$ & & & & & &0.12 \\
& & & & & &(0.12) \vspace{6pt}\\
$lnGDP_{c(t-1)}$ & & & & & &0.0005 \\
& & & & & &(0.004) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})\times ln(1+\tau_{ic(t-1)})$ & & & & & &4.12 \\
& & & & & &(3.42) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})\times lnGDP_{c(t-1)}$ & & & & & &0.14 \\
& & & & & &(0.19) \vspace{6pt}\\
\hline
Fixed Effects &product &product &product &product &product &product \\
&$\times$country &+country &+country &+country& & \\
\hline
No. of Obs. &84,902 &84,902 &84,902 &84,902 &84,902 &84,902 \\
$R^{2}$ &0.81 &0.14 &0.03 &0.03 &0.03 &0.03 \\
\hline\hline
\end{tabular}
\end{center}
Notes: Standard errors are reported in parentheses. *, **, and *** denote the 10, 5, and 1 percent of significance levels.
\onehalfspacing
\newpage
\begin{center}
\textbf{Table 4. Countries in the Sub-sample: with Large Tariff Change ($|\Delta\tau_{ict}|>0.05$) \\in at Least One HS6 Industry}
\vspace{10pt}
\\
\begin{tabular}{lllllllll }
\hline\hline
Country &\vline &No. of product-firm &Ranking &\vline &Country &\vline &No. of product-firm &Ranking \\
&\vline &-country-year cells & &\vline & &\vline &-country-year cells & \\
&\vline &with $|\Delta\tau_{ict}|>0.05$ & &\vline & &\vline & with $|\Delta\tau_{ict}|>0.05$ &\\
\hline
Dominica &\vline &457 &1 &\vline &Guatemala &\vline &36 &21 \\
U.K. &\vline &402 &2 &\vline &Sri Lanka &\vline &32 &22 \\
Canada &\vline &279 &3 &\vline &Denmark &\vline &29 &23 \\
Germany &\vline &271 &4 &\vline &Poland &\vline &28 &24 \\
France &\vline &225 &5 &\vline &Brazil &\vline &25 &25 \\
Nethelands &\vline &154 &6 &\vline &China &\vline &23 &26 \\
Phillipines &\vline &154 &7 &\vline &Austria &\vline &22 &27 \\
Italy &\vline &128 &8 &\vline &Venezuela &\vline &19 &28 \\
El Salvador &\vline &111 &9 &\vline &Turkey &\vline &10 &29 \\
Sweden &\vline &111 &10 &\vline &Greece &\vline &7 &30 \\
Ireland &\vline &93 &11 &\vline &Argentina &\vline &6 &31 \\
Egypt &\vline &87 &12 &\vline &Colombia &\vline &6 &32 \\
Mexico &\vline &76 &13 &\vline &Norway &\vline &4 &33 \\
Belgium &\vline &68 &14 &\vline &Hungary &\vline &3 &34 \\
Costa Rica &\vline &62 &15 &\vline &Mauritius &\vline &2 &35 \\
Panama &\vline &61 &16 &\vline &Uruguay &\vline &2 &36 \\
Honduras &\vline &53 &17 &\vline &Ecuador &\vline &2 &37 \\
Finland &\vline &46 &18 &\vline &Madagascar &\vline &2 &38 \\
Japan &\vline &45 &19 &\vline & &\vline & & \\
Spain &\vline &43 &20 &\vline & &\vline & & \\
\hline\hline
\end{tabular}
\end{center}
\singlespacing
\newpage
\begin{center}
\textbf{Table 5. Tariff Absorption: Sub-sample (with Large Tariff Change), All Products}
\vspace{10pt}
\\
\begin{tabular}{llllllllllll}
\hline\hline
Dependent Variable &$lnP_{ifc(t-1)}^{*}$ &$\Delta P_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ \\
Regressors &(1) &(2) &(3) &(4) &(5) &(6) \\
\hline
$\Delta\tau_{ict}$ & &-2,200 & & & & \\
& &(38000) & & & & \vspace{6pt}\\
$lnTFP_{f(t-1)}$ &0.05*** &1,800** & & & & \\
&(0.01) &(695) & & & & \vspace{6pt}\\
$\Delta\tau_{ict} \times lnTFP_{f(t-1)}$ & &-620 & & & & \\
& &(973) & & & & \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})$ & & &-0.65* &-1.08** &-0.75** &-6.96 \\
& & &(0.35) &(0.43) &(0.38) &(5.3) \vspace{6pt}\\
$TFPH_{f(t-1)}$ & & & &0.03*** &0.03** &0.03** \\
& & & &(0.01) &(0.01) &(0.01) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict}) \times TFPH_{f(t-1)}$ & & & &0.90* &0.90* &0.90* \\
& & & &(0.50) &(0.50) &(0.50) \vspace{6pt}\\
$\Delta lnXR_{c(t-1)}$ & & & & &0.04 &0.04 \\
& & & & &(0.08) &(0.08) \vspace{6pt}\\
$\Delta lnGDP_{ct}$ & & & & &-0.07 &-0.07 \\
& & & & &(0.10) &(0.10) \vspace{6pt}\\
$ln(1+\tau_{ic(t-1)})$ & & & & & &0.03 \\
& & & & & &(0.15) \vspace{6pt}\\
$lnGDP_{c(t-1)}$ & & & & & &0.001 \\
& & & & & &(0.006) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})\times ln(1+\tau_{ic(t-1)})$ & & & & & &3.23 \\
& & & & & &(3.62) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})\times lnGDP_{c(t-1)}$ & & & & & &0.22 \\
& & & & & &(0.19) \vspace{6pt}\\
\hline
Fixed Effects &product &product &product &product &product &product \\
&$\times$country &+country &+country &+country& \\
\hline
No. of Obs. &65,227 &65,227 &65,227 &65,227 &865,227 &65,227 \\
$R^{2}$ &0.82 &0.14 &0.04 &0.04 &0.04 &0.04 \\
\hline\hline
\end{tabular}
\end{center}
Notes: Standard errors are reported in parentheses. *, **, and *** denote the 10, 5, and 1 percent of significance levels.
\newpage
\begin{center}
\textbf{Table 6. Tariff Absorption: Benchmark Sample, Commodities}
\\
\textbf{--- In terms of the Rauch Classification}
\vspace{10pt}
\\
\begin{tabular}{llllllllllll}
\hline\hline
Dependent Variable &$lnP_{ifc(t-1)}^{*}$ &$\Delta P_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ \\
Regressors &(1) &(2) &(3) &(4) &(5) &(6) \\
\hline
$\Delta\tau_{ict}$ & &231 & & & & \\
& &(7,700) & & & & \vspace{6pt}\\
$lnTFP_{f(t-1)}$ &0.23 &-37.4 & & & & \\
&(0.15) &(207) & & & & \vspace{6pt}\\
$\Delta\tau_{ict} \times lnTFP_{f(t-1)}$ & &47.5 & & & & \\
& &(6,100) & & & & \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})$ & & &-1.21** &-0.73 &-0.67 &22.4* \\
& & &(0.60) &(0.72) &(0.65) &(13.6) \vspace{6pt}\\
$TFPH_{f(t-1)}$ & & & &0.007 &0.008 &0.008 \\
& & & &(0.02) &(0.02) &(0.02) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict}) \times TFPH_{f(t-1)}$ & & & &-1.14 &-1.10 &-1.18 \\
& & & &(0.92) &(0.91) &(0.92) \vspace{6pt}\\
$\Delta lnXR_{c(t-1)}$ & & & & &0.19 &0.17 \\
& & & & &(0.17) &(0.18) \vspace{6pt}\\
$\Delta lnGDP_{ct}$ & & & & &0.16 &0.15 \\
& & & & &(0.10) &(0.10) \vspace{6pt}\\
$ln(1+\tau_{ic(t-1)})$ & & & & & &0.11 \\
& & & & & &(0.18) \vspace{6pt}\\
$lnGDP_{c(t-1)}$ & & & & & &-0.01 \\
& & & & & &(0.01) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})\times ln(1+\tau_{ic(t-1)})$ & & & & & &-3.41 \\
& & & & & &(8.16) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})\times lnGDP_{c(t-1)}$ & & & & & &-0.86* \\
& & & & & &(0.49) \vspace{6pt}\\
\hline
Fixed Effects &product &product &product &product &product &product \\
&$\times$country &+country &+country &+country& \\
\hline
No. of Obs. &6,171 &6,171 &6,171 &6,171 &6,171 &6,171 \\
$R^{2}$ &0.86 &0.07 &0.08 &0.08 &0.07 &0.07 \\
\hline\hline
\end{tabular}
\end{center}
Notes: Standard errors are reported in parentheses. *, **, and *** denote the 10, 5, and 1 percent of significance levels.
\newpage
\begin{center}
\textbf{Table 7. Tariff Absorption: Benchmark Sample, Differentiated Products}
\\
\textbf{--- In terms of the Rauch Classification}
\vspace{10pt}
\\
\begin{tabular}{llllllllllll}
\hline\hline
Dependent Variable &$lnP_{ifc(t-1)}^{*}$ &$\Delta P_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ \\
Regressors &(1) &(2) &(3) &(4) &(5) &(6) \\
\hline
$\Delta\tau_{ict}$ & &-1,300 & & & & \\
& &(40,000) & & & & \vspace{6pt}\\
$lnTFP_{f(t-1)}$ &0.05*** &-1,600 & & & & \\
&(0.01) &(592) & & & & \vspace{6pt}\\
$\Delta\tau_{ict} \times lnTFP_{f(t-1)}$ & &-1,300 & & & & \\
& &(18,000) & & & & \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})$ & & &-0.80** &-1.30***&-0.93** &-6.73 \\
& & &(0.38) &(0.46) &(0.41) &(5.37) \vspace{6pt}\\
$TFPH_{f(t-1)}$ & & & &0.02** &0.2** &0.02** \\
& & & &(0.01) &(0.01) &(0.01) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict}) \times TFPH_{f(t-1)}$ & & & &1.04* &1.05* &1.04* \\
& & & &(0.54) &(0.54) &(0.54*) \vspace{6pt}\\
$\Delta lnXR_{c(t-1)}$ & & & & &0.03 &0.02 \\
& & & & &(0.07) &(0.08) \vspace{6pt}\\
$\Delta lnGDP_{ct}$ & & & & &-0.02 &-0.03 \\
& & & & &(0.06) &(0.06) \vspace{6pt}\\
$ln(1+\tau_{ic(t-1)})$ & & & & & &0.13 \\
& & & & & &(0.13) \vspace{6pt}\\
$lnGDP_{c(t-1)}$ & & & & & &0.001 \\
& & & & & &(0.005) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})\times ln(1+\tau_{ic(t-1)})$ & & & & & &4.37 \\
& & & & & &(3.62) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})\times lnGDP_{c(t-1)}$ & & & & & &0.20 \\
& & & & & &(0.20) \vspace{6pt}\\
\hline
Fixed Effects &product &product &product &product &product &product \\
&$\times$country &+country &+country &+country& \\
\hline
No. of Obs. &78,731 &78,731 &78,731 &78,731 &78,731 &78,731 \\
$R^{2}$ &0.80 &0.14 &0.03 &0.03 &0.03 &0.03 \\
\hline\hline
\end{tabular}
\end{center}
Notes: Standard errors are reported in parentheses. *, **, and *** denote the 10, 5, and 1 percent of significance levels.
\newpage
\begin{center}
\textbf{Table 8. Tariff Absorption: Benchmark Sample, Quality Homogeneous Goods}
\\
\textbf{--- With Low R\&D/Sales Ratios}
\vspace{10pt}
\\
\begin{tabular}{llllllllllll}
\hline\hline
Dependent Variable &$lnP_{ifc(t-1)}^{*}$ &$\Delta P_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ \\
Regressors &(1) &(2) &(3) &(4) &(5) &(6) \\
\hline
$\Delta\tau_{ict}$ & &-38 & & & & \\
& &(528) & & & & \vspace{6pt}\\
$lnTFP_{f(t-1)}$ &0.24 &-0.86 & & & & \\
&(0.25) &(19) & & & & \vspace{6pt}\\
$\Delta\tau_{ict} \times lnTFP_{f(t-1)}$ & &-47 & & & & \\
& &(550) & & & & \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})$ & & &-0.60 &-0.64 &-0.43 &3.30 \\
& & &(0.49) &(0.56) &(0.43) &(7.26) \vspace{6pt}\\
$TFPH_{f(t-1)}$ & & & &0.006 &0.006 &0.006 \\
& & & &(0.017) &(0.017) &(0.017) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict}) \times TFPH_{f(t-1)}$ & & & &0.08 &0.10 &0.11 \\
& & & &(0.59) &(0.59) &(0.59) \vspace{6pt}\\
$\Delta lnXR_{c(t-1)}$ & & & & &0.32** &0.33 **\\
& & & & &(0.15) &(0.15) \vspace{6pt}\\
$\Delta lnGDP_{ct}$ & & & & &0.05 &0.05 \\
& & & & &(0.10) &(0.10) \vspace{6pt}\\
$ln(1+\tau_{ic(t-1)})$ & & & & & &0.02 \\
& & & & & &(0.16) \vspace{6pt}\\
$lnGDP_{c(t-1)}$ & & & & & &-0.002 \\
& & & & & &(0.008) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})\times ln(1+\tau_{ic(t-1)})$ & & & & & &3.97 \\
& & & & & &(4.49) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})\times lnGDP_{c(t-1)}$ & & & & & &-0.19 \\
& & & & & &(0.28) \vspace{6pt}\\
\hline
Fixed Effects &product &product &product &product &product &product \\
&$\times$country &+country &+country &+country& \\
\hline
No. of Obs. &15,408 &15,408 &15,408 &15,408 &15,408 &44,167 \\
$R^{2}$ &0.82 &0.01 &0.04 &0.04 &0.04 &0.04 \\
\hline\hline
\end{tabular}
\end{center}
Notes: Standard errors are reported in parentheses. *, **, and *** denote the 10, 5, and 1 percent of significance levels.
\newpage
\begin{center}
\textbf{Table 9. Tariff Absorption: Benchmark Sample, Quality Differentiated Goods}
\\
\textbf{--- With High R\&D/Sales Ratios}
\vspace{10pt}
\\
\begin{tabular}{llllllllllll}
\hline\hline
Dependent Variable &$lnP_{ifc(t-1)}^{*}$ &$\Delta P_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ &$\Delta lnP_{ifct}^{*}$ \\
Regressors &(1) &(2) &(3) &(4) &(5) &(6) \\
\hline
$\Delta\tau_{ict}$ & &-3,900 & & & & \\
& &(24,000) & & & & \vspace{6pt}\\
$lnTFP_{f(t-1)}$ &0.03** &1,500** & & & & \\
&(0.01) &(609) & & & & \vspace{6pt}\\
$\Delta\tau_{ict} \times lnTFP_{f(t-1)}$ & &-3,400 & & & & \\
& &(29,000) & & & & \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})$ & & &-1.01** &-1.60*** &-1.15** &-8.90 \\
& & &(0.46) &(0.56) &(0.50) &(7.10) \vspace{6pt}\\
$TFPH_{f(t-1)}$ & & & &0.03** &0.03** &0.03** \\
& & & &(0.01) &(0.01) &(0.01) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict}) \times TFPH_{f(t-1)}$ & & & &1.22* &1.23* &1.23* \\
& & & &(0.66) &(0.66) &(0.66) \vspace{6pt}\\
$\Delta lnXR_{c(t-1)}$ & & & & &-0.003 &-0.013 \\
& & & & &(0.081) &(0.082) \vspace{6pt}\\
$\Delta lnGDP_{ct}$ & & & & &-0.008 &-0.018 \\
& & & & &(0.06) &(0.06) \vspace{6pt}\\
$ln(1+\tau_{ic(t-1)})$ & & & & & &0.13 \\
& & & & & &(0.15) \vspace{6pt}\\
$lnGDP_{c(t-1)}$ & & & & & &0.002 \\
& & & & & &(0.005) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})\times ln(1+\tau_{ic(t-1)})$ & & & & & &3.52 \\
& & & & & &(4.38) \vspace{6pt}\\
$\Delta ln(1+\tau_{ict})\times lnGDP_{c(t-1)}$ & & & & & &0.28 \\
& & & & & &(0.26) \vspace{6pt}\\
\hline
Fixed Effects &product &product &product &product &product &product \\
&$\times$country &+country &+country &+country& \\
\hline
No. of Obs. &69,494 &69,494 &69,494 &69,494 &69,494 &69,494 \\
$R^{2}$ &0.79 &0.14 &0.03 &0.03 &0.03 &0.03 \\
\hline\hline
\end{tabular}
\end{center}
Notes: Standard errors are reported in parentheses. *, **, and *** denote the 10, 5, and 1 percent of significance levels.
\end{document}