\section{Introduction} \label{sec:introduction}

\noindent
Emerging Market economies rely heavily in imported intermediate inputs and capital goods (see \cite{eaton2001trade} for example). In these countries, exporting firms show a particularly dependence of imports as they represents a significant share of their total production inputs (see \cite{kugler2009plants,brambilla2012exports}). The purchase of imported inputs implies establishing and maintaining firm-to-firm linkages with foreign firms. The inherent frictions pervasive to the market for input suppliers in domestic markets (see \cite{giulietti2014estimation} for energy suppliers and \cite{mortensen1999new} for labor supply) are exacerbated in international markets (see \cite{startz2016value}). Not only the quality of firm-to-firm matches is slowly revealed, but repeated interactions with suppliers usually involve significant informational frictions (see \cite{macleod2007reputations} and \cite{antras2015poultry}). The presence of these frictions imply that linkages with foreign suppliers are costly to adjust and not quickly substitutable (see \cite{huneeus2018production}). This paper seeks to quantify the adjustment costs of firms' foreign linkages' and the degree of complementarities between foreign inputs and export performance.

The impact of an increase in the cost of imported inputs on export performance is a classic question in the international trade literature. \cite{kasahara2013productivity} showed that more productive firms tend to import and export more, and argued that due to import and export complementarities, increases in the cost of foreign intermediate inputs can have a large adverse effect on the exports of final goods. The literature on international trade has also emphasized the importance of imported inputs for the production of high-quality goods (see \cite{fan2015trade} and \cite{bas2015input}). \cite{bastos2018export} show that firms which source higher-quality imported inputs tend to export higher quality products to richer and more selective countries.

Studying the complementarity between imported inputs and exports is of particular importance for Emerging Market economies, like Argentina. These economies generally lack sophisticated domestic network of high-quality intermediate inputs (see \cite{kugler2009plants}) and usually have export bundles which rely heavily in low-value-added commodity goods (see \cite{statecommodityUNCTAD}). Thus, to achieve high levels of income, it is crucial for firms in these countries to access imported inputs to produce and export high-quality and high-value-added goods (see \cite{de1997export}) and \cite{gonzalez2012insertion}).

To quantify the complementarities between imported inputs and export performance and the adjustment costs of firms' linkages with foreign suppliers I use a unique data set of Argentinean firms which identifies both the domestic importing firm and the foreign exporting supplier.\footnote{Appendix \ref{subsec:appendix_additional_evidence} presents evidence on the aggregate relevance of imports of inputs and capital. In that Appendix, Figure \ref{fig:impo_bec} shows that imports of intermediate and capital goods explain between 80\% and 90\% of Argentina's total imported value for the period 1994-2019. Figure \ref{fig:impo_investment} shows that imported capital goods explain between 55\% and 65\% of the total investment in machinery and/or equipment for the same period.} This dataset allows me to observe domestic firms' network of foreign suppliers and their imported-input sourcing strategy. In particular, I can observe trade flows at the ``domestic firm''-``foreign supplier''-``product''-''source country'' level. This allows me to observe finely defined changes in firms' cost of imported inputs.

To organize my empirical work, I construct a heterogeneous firm model subject to quality choice which can sell to foreign markets with different preferences for quality. Domestic firms are heterogeneous both in their ability to produce using lower amounts of inputs and in their ability to produce high-quality products at low costs (see \cite{hallak2013product}). Crucially, domestic firms face search and matching frictions in the market for foreign suppliers which differ in their efficiency to supply inputs at a low cost. Although firms have incentives to match with the most efficient supplier, searching involves the payment of a fixed cost and matching is random. The model's features produce a framework in which firms' export scope and performance is appreciably heterogeneous but still delivers two sharp predictions. First, the impact of an imported cost shock is increasing in the severity of search and matching frictions in the market for foreign suppliers. Second, the impact of an imported cost shock on exports is increasing in the role of imported in production and in the destination market's preference for quality.

While the prediction that an increase in imported inputs negatively affects export performance is straightforward, taking it to the data presents a challenge. First, firms endogenously choose their network of foreign suppliers (see instance \cite{dhyne2021trade}). This implies that firms observe market prices and endogenously choose from whom to buy and how much. To properly deal with this empirical challenge I use a shift-share analysis as presented by \cite{ad2019shift}. I measure a firm's exposure to import cost shocks using its lagged shares of imported value at the ``foreign-supplier''-``product''-``source-country'' level. I measure price shifts as the change in the average price a foreign-supplier charges for a product coming from a specific source country to all Argentinean firms. I find that a one standard deviation import cost shock leads to a $7.44\%$ drop in imported quantities and a persistent $2.44\%$ drop in exported quantities up to 2 years after the initial shock. These results suggest that the presence of costly to adjust frictions between Argentinean firms and their foreign suppliers, and strong complementarity between imported inputs and exported quantities.

Finally, while \textit{a priori} one would expect high-quality products to be impacted harder by a rise in imported input costs, this is also a challenging prediction to test in the data. Direct measures of product quality are not available in the Argentinean customs data. To test the differential impact of an import cost shock across products I estimate my empirical model across different sample partitions. I proxy product quality exploiting destination market's level of income and by exploiting export's degree of product differentiation. Through these sample partition exercises I find that the complementarities between imported inputs and export performance is twice as big for high-quality goods compared to the full sample results.

\section{Theoretical Framework} \label{sec:theoretical_framework}

This section of the paper builds a model of heterogeneous firms subject to quality choice and search and matching frictions in the market for foreign suppliers. The model is developed in partial equilibrium and time is discrete, indexed by $t = 0,1,2,\ldots$ . I assume that every period firm can only be matched with one foreign supplier.\footnote{While this may seem as a far-fetched assumption, recent evidence suggests that domestic firms' network of foreign suppliers is granular or limited, see \cite{bernard2018firm}.} Firms' decision problem can be divided into two sub-periods: a search and matching stage and a production and sale stage.

Firm $i$ maximizes the discounted present value of profits
\begin{align*}
    \Pi = \sum^{\infty}_{t=0} \beta \pi \left(z_i,\xi_i,c_{j,t}\right)
\end{align*}
where $\{x_i,\xi_i \}$ are firms attributes described below and $c_{j,t}$ represents the efficiency of supplier $j$ with which firm $i$ is matched with in period $t$. The timing of the model is the following: (i) period $t$ starts with firm $i$ observing the efficiency of supplier $j$ she is currently matched with, (ii) firm decides whether to search or not, and if the firm searches, whether to remain with the current supplier or change to the newly matched supplier, (iii) finally, firm $i$ decides which markets to serve, produces and sells.

\noindent
\textbf{Production \& sale stage.} I build on \cite{hallak2013product} and \cite{bastos2018export} and assume that firms differ across two dimensions: (i) "process productivity" $z_i$ which denotes firm $i$'s ability to produce with a lower amount of inputs; (ii) “product productivity” $\xi_i$ as the ability to produce quality incurring lower fixed outlays. Both $z_i$ and $\xi_i$ are exogenously distributed across domestic firms.

In each country, there is a representative consumer which demands goods according to the following utility function
\begin{equation*} \label{eq:utility_function_quality_one}
    U_d = \left[\sum_{i \in I_d} \left(\lambda^{\zeta \left(y_d\right)}_{i,d}  x_{i,d} \right)^{\frac{\rho-1}{\rho}} \right]^{\frac{\rho}{\rho-1}}
\end{equation*}
where $I_d$ is the set of firms selling in country $d$; $\lambda_{i,d}$ is product quality; $x_{i,d}$ is the quantity consumed and; $\zeta_{d} \left(y_d\right)$ captures the representative consumer's valuation of quality. To simplify notation, I write $\zeta_d = \zeta \left(y_d\right)$. This preferences give way to the following demand function for firm $i$'s output coming from country $d$ as
\begin{equation} \label{eq:consumer_demand_quality_one}
    x_{i,d} = \frac{\left(p_{i,d}\right)^{-\rho} \left(\lambda_{i,d}\right)^{\left(\rho-1\right) \zeta_d} y_d }{P^{-\rho}_d}
\end{equation}
where $p_{i,d}$ is the price charged by firm $i$ in country $d$, and $P_d$ is the country-wide quality-adjusted price index:
\begin{equation*} \label{eq:price_index_quality_one}
    P_d = \left[\sum_{i\in I_d} \left(\frac{p_{i,d}}{\lambda^{\zeta_d}_{i,d}}\right)^{1-\rho} \right]^{\frac{1}{1-\rho}}
\end{equation*}
Note that demand is increasing in product's quality, governed by parameter $\zeta_d$.

I assume that firms use a constant return to scale technology on separate production lines for each of the $d$ markets served.\footnote{This assumption is common in the literature of international trade (see for instance \cite{bastos2018export}).} In particular, the production technology is a Cobb Douglas production function.
\begin{align}
    x_{i,d} &= z_i L^{\alpha}_{i,d} M^{1-\alpha}_{i,d}  \label{eq:production_function_tier1_one}

\end{align}
where $L_{i,d}$ and $M_{i,d}$ represent firm $i$'s labor and imported input quantities. Firm $i$'s marginal cost on production line $d$ can be expressed as a function of wages, $w$, and the matched supplier's efficiency levels $c_j$.
\begin{align}
    C_{i} \left(z_i, c_{j} \right) &= \frac{1}{z_{i}} \frac{1}{\alpha^{\alpha}(1-\alpha)^{1-\alpha}} w^{\alpha} \left( c_j\right)^{1-\alpha} \label{eq:marginal_cost}

\end{align}

I assume that product quality also involves incurring costs. I introduce a quality cost specification similar to that presented by \cite{hallak2013product}. Quality costs are represented by the following function
\begin{equation}
    F^{q}\left(\xi_i \right) =  \frac{f}{\xi_i} \lambda_{i,d}
\end{equation}
where $f$ is a constant and $\lambda_{i,d}$ represents firm $i$'s quality choice. Note that firms with higher $\xi_i$ are able to produce high-quality products at lower costs. These costs can be thought of as product design and development costs. Lastly, in order to export to destination market $d$, a firm must pay a market specific fixed cost $F^{d}$.

\noindent
\textbf{Profit Maximization.} Firm $i$'s production line $d$'s profit maximization problem can be stated as
\begin{equation} \label{eq:profit_maximization_text}
\begin{aligned}
\max_{\lambda_{i,d},x_{i,d},p_{i,d}} \pi_{i,d} \left(z_i, \xi_i, c_{j} \right) = \quad & \left(p_{i,d} - C_{i} \right) x_{i,d} - \frac{f}{\xi_i}\lambda_{i,d} - \mathbbm{1}\left[x_{i,d}>0\right] \times F^d \\
\textrm{s.t.} \quad & x_{i,d} = \frac{\left(p_{i,d}\right)^{-\rho} \left(\lambda_{i,d}\right)^{\left(\rho-1\right) \zeta_d} y_d }{P^{-\rho}_d} \\

  & C_{i} \left(z_i, c_{j} \right) = \frac{1}{z_{i}} \frac{1}{\alpha^{\alpha}(1-\alpha)^{1-\alpha}} w^{\alpha} \left( c_j\right)^{1-\alpha}
\end{aligned}
\end{equation}
This framework allows for rich a heterogeneity in firms' export performance and scope. Firms' differences in attributes $\{x_i,\xi_i\}$ imply that differences in both quantities sold in each market, but also differences in export scope. For instance, firms with high $x_i$ but low $\xi_i$ might be able to serve low-income countries but may not be able to serve high-income countries due to the high costs they face in order to produce quality goods.\footnote{Appendix \ref{subsubsec:appendix_model_features} provides additional details and characterizes firms' export scope through a calibrated numerical exercise}.

Firm $i$'s optimal quality and quantities sold in destination market $d$ can be expressed as
\begin{align}
    \lambda^{*}_{i,d} &= \Lambda_1 \times C^{\frac{\rho-1}{\left(\rho-1\right)\zeta_d-1}}_{i,d} \label{eq:optimal_quality_short} \\
    x^{*}_{i,d} &= \Lambda_2 \times  C^{\frac{\rho-1}{\left(\rho-1\right)\zeta_d-1}-1}_{i,d} \label{eq:optimal_quantity_short}
\end{align}
where $\Lambda_1$ and $\Lambda_2$ are constant which depend on model parameters and exogenous variables.\footnote{See Appendix for more model details \ref{subsec:appendix_model_details}.} Note that as long as condition
\begin{align} \label{eq:condition_profit_KEY}
    \zeta_d < \frac{\rho}{\rho-1}
\end{align}
is satisfied, the optimal quality and optimal quantities sold are decreasing in $C_i$. This condition implies that consumers' love for quality, represented by $\zeta_d$, can not outweigh the demand's price elasticity of substitution. If the condition is not met, the problem boils down to a rather uninteresting case in which firms' optimal behavior is to rise quality and prices to infinity.\footnote{This condition is also necessary for the second order conditions to be met, see Appendix \ref{subsubsec:appendix_profit_maximization_SOC}.}

Next, I characterize how an increase in the cost of imported input $c_j$ impacts quantities sold in market $d$. By taking logarithms on both sides of Equation \ref{eq:optimal_quantity_short} and using the expression from $C_i$ in Equation \ref{eq:marginal_cost}, the impact of an increase in $c_j$ on $x^{*}_{i,d}$ is given by
\begin{align}
    \frac{\partial \ln x^{*}_{i,d}}{\partial \ln c_{j}} = \left( \frac{\rho-1}{\left(\rho-1\right)\zeta_d-1}-1 \right) \left(1-\alpha\right)
\end{align}
Note that this impact is increasing in the importance of imported inputs in production, $1-\alpha$, and in destination country consumer's love for quality, $\zeta_d$. To understand the intuition behind love for quality amplifying the impact of changes in marginal costs on quantities sold it is useful to study firms' first order conditions. Re-writing firm $i$'s profit maximization in Equation \ref{eq:profit_maximization_text} in terms of optimal quantities and quality leads to the following two first order conditions
\begin{align}
    \frac{\partial \pi }{\partial x_{i,d}}: & \quad \psi x^{-\frac{1}{\rho}}_{i,d} \left(\lambda_{i.d}\right)^{\frac{\left(\rho-1\right)\zeta_d}{\rho}} = C_{i} \left(z_i, c_j\right)  \label{eq:FOC_quantities_text} \\
    \frac{\partial \pi }{\partial \lambda_{i,d}}: & \quad \psi x^{1-\frac{1}{\rho}}_{i,d} \left(\lambda_d\right)^{\frac{\left(\rho-1\right)\zeta_d}{\rho}-1}  \zeta_d = \frac{f}{\xi_i} \label{eq:FOC_quality_text}
\end{align}
where $\psi = (\rho-1)/\rho \times y^{\frac{1}{\rho}}_d P_d$. Equation \ref{eq:FOC_quantities_text} shows that an increase in $C_{i} \left(z_i, c_j\right)$ leads to a reduction in quantities sold. Simultaneously, the left hand side of Equation \ref{eq:FOC_quality_text} shows that the marginal benefit of quality is increasing in quantities sold $x_{i,d}$ and $\zeta_d$. Consequently, an increase in $C_{i}$ which reduces optimal quantities $x_{i,d}$ leads to a larger drop in the marginal benefit of quality the greater $\zeta_d$ is. In turn, this leads to a drop in firms' optimal quality choice which reinforces the drop in optimal quantities sold due to lower consumer demand. Thus, an increase in the marginal cost $C_i$ triggers a reduction in optimal quantities and qualities which reinforce each other, leading to an amplification of the initial shock, which is increasing in consumer's love for quality.

\noindent
\textbf{Search \& matching stage.} I build on \cite{defever2017supplier} and assume that there are many foreign suppliers that can potentially match with domestic firms and produce the imported input. Foreign suppliers differ in their efficiency or marginal cost $c$ of producing the input. Marginal costs are distributed across potential suppliers following a probability density function $g(c)$ with support $\left[\underline{c},\bar{c} \right]$, where $\underline{c}>0$.

Under this framework, a domestic firm has an incentive to match with a supplier with the lowest possible marginal cost $c$. In order to search for a new supplier, domestic firms must pay a fixed cost $F$.\footnote{Note that I abstract from any potential strategic behavior and assume that foreign suppliers have a passive role} Firms' search is not direct, i.e., can not choose with which foreign supplier to match. Finally, I assume that after searching and observing the foreign supplier's efficiency, domestic firms have the option to remain matched with her old supplier.

I turn to characterizing the conditions under which a domestic firm searches for a new supplier. Firm $i$ searches for a new foreign supplier if the expected discounted gains of matching with a more efficient supplier outweigh the fixed cost of searching. Denoting firms' current supplier's efficiency by $\tilde{c}$, and given that the search problem is the same every period, the search condition boils down to
\begin{equation} \label{eq:IC_search_prop1}
    \frac{ \{ \mathbb{E} \left[ \pi \left(z_i,\xi_i,\tilde{c}\right) | c<\tilde{c} \right] - \pi \left(z_i,\xi_i,\tilde{c}\right) \} G\left(\tilde{c}\right) }{1-\beta}  \geq F
\end{equation}
The term $\{ \mathbb{E} \left[ \pi \left(z_i,\xi_i,\tilde{c}\right) | c<\tilde{c} \right] - \pi \left(z_i,\xi_i,\tilde{c}\right)$ on the left hand side's numerator reflects the expected profit differential if the searching firm matches with a supplier with higher efficiency, i.e. $c < \tilde{c}$. In this case, the firm changes foreign suppliers and experiences an increase in profits. The second term on the numerator, $G\left(\tilde{c}\right)$ represents the probability of matching with a foreign supplier more efficient than $\tilde{c}$. Given that if the firm matches with a more efficient supplier, this becomes her default benchmark for period $t$ onward, the firm discounts the gains of searching by $1-\beta$.

The condition in Equation \ref{eq:IC_search_prop1} implies that the higher the fixed costs $F$, the less likely it is for a firm to search for new suppliers. Also, the less efficient firm $i$'s current supplier is, the greater the expected profit differential of matching with a new supplier. Furthermore, the less efficient firm $i$'s current supplier is, the higher the probability of matching with a more successful supplier, i.e. higher $G\left(\tilde{c}\right)$, increasing firm $i$'s incentive to search.

\noindent
\textbf{Model predictions.} The model constructed above yields sharp predictions over the impact of an increase in $c_j$ on firms' export performance. First, it is straightforward to see that the magnitude and persistence of the impact depend positively on the adjustment cost of domestic firms' supplier linkages. This is represented by the model's fixed cost of searching $F$ and the random match with heterogeneous suppliers, represented by $G(c)$. If fixed cost $F$ is zero and firms can substitute toward more efficient suppliers immediately, an increase in $c_j$ should lead to no impact on firms' export performance. Consequently, the higher the fixed cost $F$ and the lower the probability of matching with a more efficient supplier, the greater and more persistent the impact of the shock will be.

Second, given the search and matching frictions in the market for foreign suppliers which determine firms' supplier efficiency, the model provides sharp predictions on export performance. A rise in $c_j$ increases firms' overall marginal cost $C_i$ and thus negatively impacting sales. The impact magnitude depends positively on the relative importance of imported inputs in production, $1-\alpha$, and on the destination market's love for quality $\zeta_d$. While my dataset does not allow me to estimate firm's production functions and import intensity, it does provide with proxy variables for product quality. This allows me to test the prediction that exports of higher-quality goods are more sensitive to import cost shocks.

\section{Data \& Identification Strategy} \label{sec:data_empirical_methodology}

In this section of the paper I describe the datasets used in this paper and the identification strategy proposed to identify import cost shocks.

\noindent
\textbf{Data description.} I use data from administrative customs records, based on customs declarations forms collected by Argentina's customs office, which comprises the entire universe of Argentinian trade flows for the period 2000-2008. Information is dis-aggregated by firm, date of shipment, product at 6-digit HS, exports by destination and imports by source country. For import flows, I am able to identify the foreign supplier firm. Since foreign suppliers do not have a unique ID that identifies them (I only observe the firms' name declared in customs' form), their registration is not harmonized and is subject to errors. Therefore, I carry out a cleaning procedure that allows me to join the information of suppliers that were registered in two or more different ways. Details of this cleaning procedure and secondary datasets used can be found in Appendix \ref{subsec:Appendix_cleaning} and Appendix \ref{subsec:appendix_additional_data}, respectively.

\noindent
\textbf{Identification strategy.} Based on firms' search and matching frictions described in Section \ref{sec:theoretical_framework}, I follow \cite{hummels2014wage}, \cite{huneeus2018production} and \cite{bernard2020heterogeneous} and use a shift share design to construct firm-level shocks. I define an import cost shock for firm $i$ in year $t$, as
\begin{equation} \label{eq:shift_share}
    \Delta \log p^{I}_{i,t} = \sum_{k \in \Omega^{I}_{i,0}} s^I_{ik,0} \Delta \log p_{k,t}
\end{equation}
where $\Omega^{I}_{i,0}$ is the set of foreign suppliers $k$ that firm $i$ sources from in period $t=0$, $s^I_{ik,0}$ is the share of imports of firm $i$ from supplier $k$ in $t=0$ and $\Delta \log p_{k,t}$ is the percentage growth of the import price from supplier $k$. Before defining in detail what a foreign supplier $k$ means in my setting, I address two issues: (i) discuss the usefulness and appropriateness of the shift-share analysis,  (ii) which measure of price change to use for $\Delta \log p_{k,t}$.

To begin with, I momentarily assume that the measure of changes in import prices is exogenous and discuss how a shift-share analysis is appropriate for the current analysis. Even if import prices are exogenous to Argentinean firms, firms choose their network of suppliers, composition of their input bundle and source countries endogenously. I use \cite{ad2019shift}'s shift-share design which assumes the exogeneity of the shifts rather than from the shares. The reasoning behind this choice is that firms choose which suppliers $k$ to trade with and are subject to the shocks generated through these established linkages. When firms make the decision about which foreign supplier $k$ to trade with, future shocks might be already in firms' informational set. In order to address any bias arising from anticipation behavior I used lagged shares of exposure (in particular, I construct the shocks using period $t-1$, i.e., year $t-1$ weights). Note that this is in line with the search and matching stage of firms described in Section \ref{sec:theoretical_framework}, where firms at the start of period $t$ observe their current supplier's efficiency and can search in international markets before producing.

The shift-share analysis provides a source of significant heterogeneity in the cost shock across firms. This significant heterogeneity comes from the high dimensional space of foreign suppliers the Argentinean firms can choose from. For instance, Argentinean firms imported from 220 different countries, 4,961 different products and from 512,915 different suppliers during the period 2000-2008. This high degree of heterogeneity in sourcing strategies makes it unlikely that any two Argentinean firms are exposed exactly the same to the same set of foreign suppliers. A second source of heterogeneity across firms is each firms' link intensity or amount traded in said trade flow.

Next, I turn to discussing the appropriate price change to be considered as shifts in Equation \ref{eq:shift_share}. An initial candidate as a shift would be to use log import price changes at the domestic firm $i$, foreign supplier $s$, product $p$ and destination country $d$
\begin{align*}
    \Delta \log p_{i,s,p,d,t} =  \log p_{i,s,p,d,t} - \log p_{i,s,p,d,t-1}
\end{align*}
which implies defining $k$ as $k = \{i,s,p,d\}$. For this specification to be a valid representation of the framework presented in Section \ref{sec:theoretical_framework} two assumptions must be met. First, firm $i$ has no bargaining power on the determination of its import prices, i.e. take foreign supplier $s$ price as exogenous. Second, for this shift to represent a true exogenous increase on its import prices firm $i$ must have no firm-specific shock which increases the cost of its inputs across every possible combination of foreign-supplier, product and source country.\footnote{For instance, a shock that increases firm $i$'s cost of international trade, such as distribution costs.} Additionally, this specification of price shift is highly susceptible to a attrition. This is, if firm $i$ does not buy in period $t$ from the same supplier, the same product from the same source country my dataset will not report price $p_{i,s,p,d,t}$, and I will impute a price-shift $\Delta \log p_{i,s,p,d,t} = 0$.

Given the concerns described above I define the price shift in Equation \ref{eq:shift_share} at the foreign supplier $s$, product $p$ and destination country $d$. This is, I define supplier $k$ as $k=\{s,p,d\}$
\begin{align*}
    \Delta \log p_{s,p,d,t} =  \log p_{s,p,d,t} - \log p_{s,p,d,t-1}
\end{align*}
Under this empirical specification, I assume that firm $i$ takes the average price supplier $s$ charges for product $p$ from destination country $d$ to all Argentinean firms. This is a less extreme assumption as it does not rely on assumptions on firm $i$'s direct behavior and is less prone to attrition.\footnote{The latter is due to it being more likely that a specific link between domestic $i$ and foreign supplier $s$ breaks than foreign supplier $s$ breaking all of her linkages with Argentinean firms.} Appendix \ref{subsec:appendix_additional_shocks} presents basic descriptive statistics of this shock specification.\footnote{Appendix \ref{subsec:appendix_additional_shocks} also presents three other shock specifications in which prices are defined at the: (i) ``firm $i$''-``supplier''-``product''-``source'' level as defined above, (ii) at the ``all firms except firm $i$''-``supplier''-``product''-``source'' level; and at the ``product''-``source'' level. This last specification is a standard specification in the literature, used for instance by \cite{huneeus2018production}. Results are robust across specifications which exploit the supplier dimension of the data set, but not the specification which computes price shifts at the ``product''-``source'' level.}

\section{Results} \label{sec:results}

This section presents the main results of the paper. I start by estimating the impact of an import cost shock on firms' imported quantities, which allows me to quantify adjustment costs on domestic firms' linkages with foreign suppliers. Then, I estimate the impact of an import cost shock on firms' exported quantities in order to quantify the complementarities between imported inputs and exports. Finally, I test whether high-quality exports are more sensitive to changes in the price of imported inputs.

\noindent
\textbf{Costly to adjust input linkages.} I start by estimating the impact of an import cost shock on firms' imported quantities. To do so, I estimate the following  regression
\begin{align} \label{eq:intensive_imports}
    \ln QI_{i,p,d,t} &= \alpha_0 + \gamma_{i,p,d} +\gamma_t+ \beta^{M} \text{Shock}_{i,t} + \Gamma_{i,p,d,t} + \epsilon_{i,p,d,t}
\end{align}
where $\ln QI_{i,p,d,t+j}$ represent the log total quantities imported by firm $i$ of product $p$, from source country $d$ in year $t+j$ for $j\in\{0,1\}$, $\gamma_{i,p,d}$ is a firm - product- source country fixed effect, $\gamma_t$ is a time fixed effect, $\text{Shock}_{i,t}$ is the shock constructed in Section \ref{sec:data_empirical_methodology}, and $\Gamma_{i,p,d,t}$ is a set of controls which include lagged values of $\text{Shock}_{i,t}$ and $\ln QI_{i,t}$. Parameter $\beta^{M}$ represents imported quantities semi-elasticity to an import cost shock. The standard errors of the estimated parameters are computed using two-way clustering, at the firm $i$ and source country $d$ level.\footnote{The reasoning behind this clustering strategy is twofold. First, the constructed exogenous shocks are defined at the firm level, thus it implies clustering at the treatment level unit. Second, I want to incorporate source country level information.}

Table \ref{tab:import_cluster} presents estimated values of $\beta^M$ on impact at time $t$, and for the year after the shock, time period $t+1$.
\begin{table}[ht]
    \centering
    \caption{Cost Shocks and Imported Quantities 2001 - 2008}
    \label{tab:import_cluster}
    \small
\begin{tabular}{lcc}
  & \multicolumn{2}{c}{Log - Quantities Imported - $\ln Q_{i,p,d,t+j}$} \\
  & (1) & (2) \\
  & Period $t$ & Period $t+1$ \\ \hline \hline
$\beta^M-\text{Shock}_{i,t}$ & -0.305*** & -0.0465 \\
 & (0.0498) & (0.0579) \\
 &  &   \\
 Observations & 354,538 & 234,709 \\ \hline \hline
\multicolumn{3}{c}{\footnotesize Two Way Clustered (Firm - Source Country) Standard Errors in Parentheses} \\
\multicolumn{3}{c}{\footnotesize *** p$<$0.01, ** p$<$0.05, * p$<$0.1} \\
\end{tabular}
\floatfoot{\footnotesize \textbf{Note:} The regressions are computed controlling for the first and second lagged values of the dependent variable $\ln QI_{i,p,d,t}$, import-instance fixed effects and year fixed effects.}
\end{table}
Column (1) shows that the estimated coefficient for year $t$ is negative and statistically significant different from zero. In terms of magnitude, a positive one standard deviation import-cost-shock ($24.4\%$ firm level price increase) leads to a reduction in firms' imported quantities of 7.44\% at the product-source country level. However, the impact of an import-cost-shock on imported quantities is short lived. Column (2) shows that an import cost shock in period $t$ does not predict lower imported quantities in period $t+1$. Thus, an import cost shock leads to a transitory one year reduction in firm's imported quantities. This result is in line with the presence of costly to adjust linkages and imperfect substitution across firms' foreign suppliers.

\noindent
\textbf{Benchmark exports results.} Following the analysis on imported quantities, I turn to analyzing the impact of a import cost shocks on firms export performance. To do so, I estimate the following regression
\begin{align} \label{eq:intensive_exports}
    \ln QX_{i,p,d,t} &= \alpha_0 + \gamma_{i,p,d} +\gamma_t+ \beta^{X} \text{Shock}_{i,t} + \Gamma_{i,p,d,t} + \epsilon_{i,p,d,t}
\end{align}
where $\ln QX_{i,p,d,t}$ represents the log quantities exported at the firm $i$, product $p$, destination country $d$ level at year $t+j$ for $j=\{0,1,2\}$; $\gamma_{i,p,d}$ represents firm-product-destination fixed effects, $\gamma_t$ is a time fixed effect, and $\Gamma_{i,p,d,t}$ control variables which include lagged values of the outcome variable and the $\text{Shock}_{i,t}$. Parameter $\beta^{X}$ represents exported quantities semi-elasticity to an import cost shock.

Table \ref{tab:export_cluster_all} presents estimated values of $\beta^{X}$ for periods $t,t+1$ and $t+2$ in Columns (1) to (3), respectively. A positive import cost shock leads to persistent and significantly lower exported quantities.
\begin{table}[ht]
    \centering
    \caption{Import Cost Shocks \& Export Performance}
    \label{tab:export_cluster_all}
    \small
\begin{tabular}{lccc}
  & \multicolumn{3}{c}{Log - Quantities Exported - $\ln Q_{i,p,d}$} \\
  & (1) & (2) & (3) \\
  & Period $t$ & Period $t+1$ & Period $t+2$ \\ \hline \hline
$\beta^{X}-\text{Shock}_{i,t}$  & -0.0711** & -0.146*** & -0.118* \\
 & (0.0320) & (0.0410) & (0.0668) \\
 &  &  &  \\
Observations & 168,615 & 107,149 & 69,391 \\ \hline \hline
\multicolumn{4}{c}{\footnotesize Two Way Clustered (Firm - Destination Country) Standard Errors in Parentheses} \\
\multicolumn{4}{c}{\footnotesize *** p$<$0.01, ** p$<$0.05, * p$<$0.1} \\
\end{tabular}
\floatfoot{\footnotesize \textbf{Note:} The regressions are computed controlling for the first and second lagged values of the dependent variable $\ln QX_{i,p,d,t}$, export-instance fixed effects and year fixed effects.}
\end{table}
Import cost shocks cause a negative hump-shaped response of exported quantities. In terms of magnitude, a positive one standard deviation shock ($24.4\%$) leads to a drop in exported quantities of 1.90\% period $t$, 2.44\% in $t+1$ and 2.1\% in $t+2$. These results imply a strong imported-input to export complementarity, as the estimated coefficients in Table \ref{tab:import_cluster} and \ref{tab:export_cluster_all} imply that a reduction in imported quantities of 10\% lead to a reduction in exported quantities between 2.3\% and 4.8\%. This result validates the theoretical prediction that a rise in marginal costs caused by a higher cost of imported inputs leads to a reduction of exported quantities.

The persistence of the impact of an imported cost shock is noteworthy. The fact that the estimated coefficient for period $t+1$ is greater than the one for period $t$  may be driven by lags or temporal considerations in the process of production and exporting. Imported inputs which arrive at customs in year $t$ may be used in the production of goods exported through customs in year $t+1$. Nevertheless, the fact that the initial shock leads to lower exported quantities two years into the future suggest that frictions in the market for suppliers also play a significant role. In other words, the slow and costly to adjust foreign supplier linkages not only cause a drop on impact, but also leads to persistently lower export performance across time. This result provides further evidence on domestic firms' costly to adjust linkages with foreign suppliers.

\noindent
\textbf{Results for high-quality exports.} Lastly, I test the theoretical prediction that exports to consumers with higher love for quality are more sensitive to import cost shocks. However, customs data does not provide direct evidence of either product's quality or consumers love for quality. Thus, to test this theoretical prediction I estimate Equation \ref{eq:intensive_exports} partitioning the sample across two dimensions: (i) product differentiation and (ii) destination countries' income per capita levels.

Argentina's export bundle is primarily composed of commodity-based goods.\footnote{According to UNCTAD commodity dependence report, Argentina is a country which depends heavily on agricultural commodity goods. See, \url{https://unctad.org/webflyer/state-commodity-dependence-2019}} For instance, \cite{bernini2018micro} show that under different good classifications and across time, around 60\% of Argentina's exports are undifferentiated or commodity based goods. A priori, it is expected that products which involve a higher degree of differentiation and customization are of a higher quality and more exposed to imported input cost shocks. To test the model prediction that exports to consumers with higher love for quality are more sensitive to import cost shocks, I partition the sample using two different product classifications: (i) \cite{bernini2018micro} classification between differentiated and undifferentiated goods, (ii) \cite{rauch1999networks} classification between undifferentiated or world priced goods and differentiated goods.\footnote{The good classification introduced by \cite{rauch1999networks} is composed of two classifications, conservative and liberal, into three different type of goods, world-priced goods, reference priced goods and differentiated goods. The results presented in this section follow the liberal good classification although results are robust to using the conservative classification.} The former classification was specifically constructed for the Argentinean case, while the latter classification has been widely used by the literature in international trade.

Table \ref{tab:export_cluster_all_diff} presents estimated values of $\beta^{X}$ for differentiated and undifferentiated goods.
\begin{table}[ht]
    \centering
    \caption{Import Cost Shock \& Export Performance \\ Differentiated Goods}
    \label{tab:export_cluster_all_diff}
    \footnotesize
\begin{tabular}{lcccccc}
  & \multicolumn{6}{c}{\cite{bernini2018micro} - Log - Quantities Exported - $\ln Q_{i,p,d}$} \\
 & \multicolumn{2}{c}{Period $t$} & \multicolumn{2}{c}{Period $t+1$} & \multicolumn{2}{c}{Period $t+2$} \\
\small & $D$ & $U$ & $D$ & $U$ & $D$ & $U$   \\
 & (1) & (2) & (3) & (4) & (5) & (6) \\ \hline \hline
 $\beta^{X}-\text{Shock}_{i,t}$  & -0.0856** & -0.0518 & -0.168*** & -0.0772 & -0.162** & -0.128 \\
 & (0.0425) & (0.0434) & (0.0581) & (0.158) & (0.0764) & (0.0931) \\
  &  &  &  &  &  &  \\
Observations & 116,743 & 34,324 & 73,359 & 22,340 & 47,013 & 14,866 \\ \hline \hline
\multicolumn{7}{c}{ Two Way Clustered (Firm - Destination Country) Standard Errors in Parentheses} \\
\multicolumn{7}{c}{ *** p$<$0.01, ** p$<$0.05, * p$<$0.1} \\
\multicolumn{7}{c}{} \\
\end{tabular}
\begin{tabular}{lcccccc}
  & \multicolumn{6}{c}{\cite{rauch1999networks} -Log - Quantities Exported - $\ln Q_{i,p,d}$} \\
 & \multicolumn{2}{c}{Period $t$} & \multicolumn{2}{c}{Period $t+1$} & \multicolumn{2}{c}{Period $t+2$} \\
\small & $D$ & $U$ & $D$ & $U$ & $D$ & $U$   \\
 & (1) & (2) & (3) & (4) & (5) & (6) \\ \hline \hline
 $\beta^{X}-\text{Shock}_{i,t}$ & -0.0714** & 0.0136 & -0.159*** & 0.0873 & -0.140* & -0.000858 \\
 & (0.0338) & (0.0687) & (0.0438) & (0.180) & (0.0744) & (0.158) \\
  &  &  &  &  &  &  \\
Observations & 151,035 & 8,953 & 95,795 & 5,733 & 62,024  & 3,686 \\ \hline \hline
\multicolumn{7}{c}{ Two Way Clustered (Firm - Destination Country) Standard Errors in Parentheses} \\
\multicolumn{7}{c}{ *** p$<$0.01, ** p$<$0.05, * p$<$0.1} \\
\end{tabular}
\floatfoot{\footnotesize \textbf{Note:} The regressions are computed controlling for the first and second lagged values of the dependent variable $\ln QX_{i,p,d,t}$, export-instance fixed effects and year fixed effects.}
\end{table}
The top panel shows the results using the \cite{bernini2018micro} classification, while the bottom panel shows the results using the \cite{rauch1999networks} classification. Across product classifications, a positive import cost shock leads to a persistent drop in exported quantities of differentiated goods but not for undifferentiated goods. On the one hand, the top panel shows that the estimated coefficient for exported quantities of differentiated goods is between 15\% and 37\% greater than those found for the full sample in Table \ref{tab:export_cluster_all}, across time horizons.\footnote{Under the \cite{rauch1999networks} classification, the estimated coefficients are between 0.5\% and 26\% across time periods.} On the other hand, the estimated coefficients for undifferentiated products are not significantly different from zero across any of the time periods. The fact that exported quantities of differentiated goods are more sensitive to import cost shocks than those of undifferentiated goods is in line with the theoretical framework's predictions in Section \ref{sec:theoretical_framework}. This is because there is a higher probability that differentiated goods involve a greater amount of imported inputs and are sold to consumers with higher love for quality than undifferentiated or commodity based goods.

To provide additional evidence that exports to consumers with higher love for quality are more sensitive to import cost shocks I carry out a sample partition exercise across destination countries. In particular, I partition countries across their income levels based on evidence that ``\textit{High-Income}'' countries demanding higher quality products.\footnote{See for \cite{hallak2011estimating,bastos2018export} for example.} The partition is carried out using the IMF's World Economic Outlook partition between Advanced Economies (Adv.) and Emerging Markets (EM).

The top panel of Table \ref{tab:expo_cluster_all_HI} presents the estimated coefficients for $\beta^X$ of this second sample partition exercise for all exports. For all time periods the estimated semi-elasticity for exported quantities to ``\textit{Advanced-Economies}'' is higher than that estimated for exported quantities to ``\textit{Emerging-Economies}''.
\begin{table}[ht]
    \centering
    \caption{Import Cost Shocks \& Export Performance \\ By Destination Country's Income}
    \label{tab:expo_cluster_all_HI}
    \footnotesize
\begin{tabular}{lcccccc}
  & \multicolumn{6}{c}{Log - Quantities Exported - Full Sample - $\ln Q_{i,p,d}$} \\
 & \multicolumn{2}{c}{Period $t$} & \multicolumn{2}{c}{Period $t+1$} & \multicolumn{2}{c}{Period $t+2$} \\
\small & Adv. & EM & Adv. & EM & Adv. & EM \normalsize \\
 & (1) & (2) & (3) & (4) & (5) & (6) \\ \hline \hline
$\beta^{X}-\text{Shock}_{i,t}$ & -0.173*** & -0.0487 & -0.194** & -0.147*** & -0.171* & -0.119 \\
 & (0.0582) & (0.0326) & (0.0717) & (0.0502) & (0.101) & (0.0787) \\
 &  &  &  &  &  &  \\
Observations & 29,154 & 139,448 & 17,920 & 89,227 & 11,514 & 57,875 \\ \hline \hline
\multicolumn{7}{c}{ Two Way Clustered (Firm - Destination Country) Standard Errors in Parentheses} \\
\multicolumn{7}{c}{ *** p$<$0.01, ** p$<$0.05, * p$<$0.1} \\
\multicolumn{7}{c}{} \\
\end{tabular}
\begin{tabular}{lcccccc}
  & \multicolumn{6}{c}{Log - Quantities Exported - Differentiated Goods - $\ln Q_{i,p,d}$} \\
   & \multicolumn{2}{c}{Period $t$} & \multicolumn{2}{c}{Period $t+1$} & \multicolumn{2}{c}{Period $t+2$} \\
\small & Adv. & EM & Adv. & EM & Adv. & EM \normalsize \\
 & (1) & (2) & (3) & (4) & (5) & (6) \\ \hline \hline
$\beta^{X}-\text{Shock}_{i,t}$ & -0.212*** & -0.0719 & -0.299** & -0.157** & -0.239* & -0.161* \\
 & (0.0619) & (0.0496) & (0.125) & (0.0683) & (0.141) & (0.0862) \\
 &  &  &  &  &  &  \\
Observations & 18,569 & 98,166 & 11,091 & 62,268 & 6,952 & 40,061 \\ \hline \hline
\multicolumn{7}{c}{ Two Way Clustered (Firm - Destination Country) Standard Errors in Parentheses} \\
\multicolumn{7}{c}{ *** p$<$0.01, ** p$<$0.05, * p$<$0.1} \\
\end{tabular}
\floatfoot{\footnotesize \textbf{Note:} The regressions are computed controlling for the first and second lagged values of the dependent variable $\ln QX_{i,p,d,t}$, export-instance fixed effects and year fixed effects. The bottom panel partitions the sample between differentiated and undifferentiated goods using the \cite{bernini2018micro} classification.}
\end{table}
On the one hand, the estimated coefficients for exported quantities to Advanced Economies are negative and statistically significant from zero for all time periods. The estimated semi-elasticities are between $32\%$ and $243\%$ greater than those estimated for the full benchmark sample. These estimated coefficients imply that an import cost shock which decreases imported quantities by 10\%, decreases exported quantities by roughly 6.4\%. On the other hand, the impact of an import cost shock on exported quantities to Emerging Economies is only significantly different from zero for period $t+1$ and with a relatively lower magnitude to that estimated for exports to Advanced Economies.

The bottom panel of Table \ref{tab:expo_cluster_all_HI} presents the estimates of $\beta^{X}$ partitioning the sample between Advanced Economies and Emerging Markets but only for exports of differentiated goods. Within exports of differentiated, those to Advanced Economies exhibit estimated coefficients larger in magnitude compared to those estimated for Emerging Markets across all the time periods considered. This result provides evidence in favor of the model's prediction of exports to consumers with higher love for quality being more sensitive to import cost shocks.

\section{Conclusion} \label{sec:conclusion}

This paper exploits information on firms' foreign supplier network to analyze how increases in the cost of imported inputs affects their export performance. The constructed theoretical framework predicts that the impact of an increase in the cost of imported inputs is increasing in the adjustment costs of firms' linkages and in the love for quality of destination countries.

Motivated by these predictions and based on the theoretical framework' search frictions in the market for foreign input suppliers, I construct firm-specific shocks using a shift share methodology. These shocks exploit firms' lagged exposure to foreign suppliers and finely defined import price shifts. I find that a positive import cost shock leads to lower imported quantities, providing evidence that firms face costly to adjust linkages. Furthermore, an import cost shocks leads to significant and persistent drop in exported quantities up to two years after the initial shock. Exports of differentiated products and exports to high-income countries exhibit an estimated semi-elasticity twice as big as the benchmark results in line with the model's predictions.

This paper shed light on the inherent frictions in the market for imported inputs. Results suggest the presence of significant adjustment costs in domestic firms' foreign supplier linkages, and provide evidence of strong complementarities between imported inputs and exports. These results are of particular importance for Emerging Market economies which seek to diversify export bundles whilst lacking developed networks of domestic suppliers.

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