Trade Liberalization & Firm Dynamics

The study begins by acknowledging the diverse responses of firms within the same industry and country to globalization. Initial empirical research, using micro-level data, revealed that export decisions are strongly correlated with firm size and productivity, with only larger, more productive firms engaging in exporting. Further research expanded this to encompass various responses to globalization, all showing significant variation across firms and correlation with performance indicators. This empirical evidence prompted the development of models featuring heterogeneous firms in open economies, focusing on how changes in the degree of globalization (trade and investment frictions, global market size) influence diverse firm-level responses. The majority of these models, however, simplified the analysis by assuming stable aggregate environments with no firm dynamics—ignoring changes over time in firms' responses to globalization. The paper aims to address this limitation by introducing firm dynamics into the analysis of the aggregate effects of trade liberalization.

The core of the paper lies in its development of a model that incorporates firm dynamics, export-market selection, firm-level innovation, sunk export costs, and firms' expectations about the future path of trade liberalization to generate aggregate transition dynamics. The model considers various scenarios to isolate the individual and interactive effects of these factors. The authors emphasize that the interaction between firm dynamics and endogenous export market selection is crucial for generating long-lasting aggregate transition dynamics in response to a sudden, unanticipated drop in trade costs. The analysis highlights how modeling these elements differently affects the time path of trade volumes, innovation, and aggregate output following a trade liberalization. This is a significant departure from static models that only examine steady-state comparisons. The incorporation of firms' expectations regarding future trade costs adds another layer of complexity and realistically reflects decision-making under uncertainty. The study also contrasts the implications of permanent versus temporary trade liberalization on innovation dynamics.

The research employs both analytical and computational methods to analyze the model. Simpler model variants are analyzed analytically to understand fundamental mechanisms, while computational methods are used to derive the transition dynamics for more complex versions. The analysis shows how the response of innovative activities magnifies productivity differences between exporters and non-exporters and how the responses of average productivity and trade flows can differ substantially from those predicted by static trade models, varying across short and long-term horizons. The study develops analytical models with either firm productivity dynamics or endogenous export market selection to demonstrate that both are necessary to generate endogenous transition dynamics. The authors detail how differences in current and future export market profitability, relative to domestic sales profitability, drive transition dynamics. Furthermore, they show how endogenous innovation further amplifies these dynamics and illustrate how expectations about future trade costs shape the overall response.

The analysis uses several scenarios to examine specific aspects of the model. The paper investigates a scenario where there's no export market selection (all firms export), demonstrating that this condition alone does not produce endogenous transition dynamics. Conversely, a scenario with no firm productivity dynamics, where firm productivity remains constant, also fails to generate endogenous transition dynamics, highlighting the interaction between these two features. Subsequently, the authors introduce endogenous innovation, comparing it to the exogenous innovation case. This reveals how endogenous innovation amplifies the impact of trade liberalization, leading to significant differences in transition dynamics. The model also incorporates the concept of temporary trade liberalization, exploring how firms' expectations about the persistence of policy changes affect their innovation decisions. Anticipated trade liberalization is also analyzed, showing how anticipation further amplifies the response of endogenous innovation ahead of the policy's actual implementation. The inclusion of sunk export costs adds another dimension by impacting the option value of becoming an exporter.

The literature review begins by noting the extension of workhorse general equilibrium models of heterogeneous firm dynamics from closed to open economy settings. Models such as those by Hopenhayn (1992), Atkeson and Kehoe (2005), and Luttmer (2007), initially focused on closed economies, have been adapted to incorporate international trade. The review highlights the work of Arkolakis (2008) and Irarrazabal and Opromolla (2008), which extended Melitz's (2003) model by incorporating exogenous random productivity shocks to better capture firm-level dynamics in both domestic and exporting firms. While these studies focused on stable aggregate environments, others like Alessandria and Choi (2007) and Ruhl (2008) examined the transition dynamics associated with trade liberalizations, emphasizing the role of entry into domestic and export markets. Alessandria and Choi (2007) importantly demonstrated that welfare calculations based solely on steady-state consumption comparisons can differ substantially from those incorporating transition dynamics. This underscores the importance of dynamic modeling in evaluating trade liberalization’s welfare effects.

A significant portion of the literature review explores studies examining the joint decisions of firms regarding export status and technology adoption. Bustos (2007) and Yeaple (2005) analyzed static models with a binary technology choice, showing how firms' decisions to enter export markets are linked to technology adoption. Costantini and Melitz (2008) extended this to a dynamic framework, incorporating idiosyncratic uncertainty and sunk costs for both exporting and technology adoption. This dynamic model generates option values for export and exit decisions, a crucial aspect the current paper explores. The authors' model of innovation closely follows Atkeson and Burstein (2010), which builds upon Griliches' (1979) model of knowledge capital. This approach, similar to Ericson and Pakes (1995) and Doraszelski and Jaumandreu (2008), allows for stochastic outcomes of innovation, accommodating firm growth, decline, entry, and exit in steady state. While Atkeson and Burstein (2010) focused on offsetting responses of various firm decisions to permanent trade liberalizations, the current paper concentrates on the transition dynamics of productivity, trade flows, and output, also incorporating sunk export costs and considering temporary and anticipated liberalizations.

The review also considers a strand of literature focusing on demand dynamics. These models explore how firms accumulate customers in foreign markets, a crucial aspect of export performance not always captured in models emphasizing only productivity shocks. Ruhl and Willis (2008) introduced demand shifters to explain the slow growth of exporters entering new markets, emphasizing the time-dependent nature of customer acquisition. Eaton et al. (2008) modeled firms' investments in increasing foreign demand, such as searching for buyers and maintaining relationships, highlighting these investments as a dynamic process linked to market entry. Chaney (2011) offers another perspective, modeling exporter growth through interactions within international social networks. These demand-related investments, the review notes, have effects similar to innovation but with returns affecting only export profits. The review concludes by acknowledging the existence of models incorporating hysteresis effects in export dynamics, where past export experience significantly influences current and future performance even after controlling for observable firm characteristics. This hysteresis is explained by a combination of sunk export costs and firm-level uncertainty.

The literature review cites significant empirical evidence supporting the links between export market entry and firm-level outcomes. Das, Roberts, and Tybout (2007) provided econometric evidence of substantial sunk export costs for Colombian exporters, impacting firms' expectations about future market conditions. Multiple studies, including Lileeva and Trefler (2009) for Canada, Verhoogen (2009) for Mexico, Bustos (2011) for Argentina, and Aw, Roberts, and Xu (forthcoming) for Taiwan, documented a positive association between export market entry (driven by trade cost reductions) and increased firm innovation. Bloom, Draca, and Van Reenen (2008) also found a link between changes in the trading environment (import competition from China) and increased innovation and skill upgrading in European industries. Bernard, Jensen, and Schott (2006) documented a similar effect of import competition on the capital and skill intensity of affected U.S. firms. The review also mentions research showing a relationship between export market entry and subsequent firm productivity growth, often termed “learning by exporting.” The existing empirical work provides a strong foundation for the current paper's theoretical model, which aims to integrate several of these dynamic factors.

The model economy is set up with two symmetric countries (home and foreign), using a discrete-time framework. The focus is on the home country, with foreign variables denoted by an asterisk. Aggregate uncertainty is not modeled. Households supply labor inelastically and derive utility solely from consumption. Production involves a final non-traded consumption good, produced using a continuum of differentiated intermediate goods. The production function for the final good employs a constant elasticity of substitution (CES) technology with an elasticity of substitution greater than 1. These intermediate goods can be domestically produced or imported. Exports incur fixed costs (fX, measured in units of domestic labor) and per-unit iceberg costs (1 + τ, where τ represents the trade cost, with τ > 0). The model assumes a constant returns to scale production technology for the intermediate goods. This structure establishes a foundation for analyzing the impact of trade liberalization, particularly on the production and allocation of these intermediate goods. The core of the model focuses on the dynamic behavior of firms, which are heterogeneous in their productivity and export decisions.

The model incorporates firm-level productivity dynamics and explicitly models firm entry and exit. At the beginning of each period, existing firms face an exogenous probability of a ‘death shock,’ leading to exit, irrespective of their productivity. Surviving firms can choose to exit endogenously, conditional on their productivity levels, or continue operating, incurring fixed overhead costs (f). Firm productivity evolves stochastically based on innovation investment. The productivity evolution is modeled as a Markov process where a firm with productivity index z has a probability q of increasing productivity and a probability (1-q) of decreasing productivity. The expected productivity growth is given by (2q - 1)z. A special case with no productivity dynamics (z=0) is also considered. For larger firms, the innovation intensity (qt) is modeled as a limit, and the innovation cost function is assumed to be c(q) = h exp(bq), reflecting elasticity based on parameter b. This allows for scenarios with both exogenous (b is very high) and endogenous innovation. The model considers steady states with and without entry, requiring specific parameter restrictions for steady states with positive entry.

A steady state in the model represents an equilibrium where all aggregate variables remain constant. The model has two types of steady states: one with entry and one without. The study focuses on the steady state with positive firm entry. The parameter values are calibrated using data from the U.S. economy to enhance the model's empirical relevance. Specifically, the elasticity of substitution (σ) is set to 5, consistent with estimates by Broda and Weinstein (2005). The distribution of productivity draws for entering firms (G) is chosen such that all entering firms begin with a common productivity index (z=0). Other parameters (z, exogenous exit rate, fixed costs of operation (f), fixed export costs (fX), per-unit trade costs (τ), and innovation cost parameters (h, b)) are chosen to match three key observations in the U.S. data: (1) the fraction of exports in gross output; (2) the fraction of total production employment accounted for by exporting firms; and (3) the shape of the right tail of the firm size distribution. The specific parameter choices for these three data points aim to make the model's predictions for aggregate variables consistent with observed patterns in the U.S. economy.

This scenario removes endogenous export market selection by setting fixed export costs to zero (fX = 0), forcing all firms to export regardless of productivity. A permanent, unanticipated reduction in the per-unit trade cost is introduced. The results show that this trade liberalization does not induce any transition dynamics; final output and the share of exports in total revenue immediately jump to their new steady-state levels. There are no further reallocations of resources; innovation intensity, entry, and production labor remain unchanged. This lack of response is attributed to offsetting effects of lower trade costs on export opportunities and domestic sales—firms face similar trade-offs, eliminating incentives for reallocation or changes in innovation decisions. This outcome mirrors the response in Krugman's (1980) model with representative firms. The absence of transition dynamics in this scenario highlights the importance of endogenous export market selection in driving dynamic responses to trade liberalization.

Here, firm productivity dynamics are eliminated by keeping firm productivity constant after entry. A permanent trade liberalization is again introduced. While the liberalization does not induce transition dynamics (output jumps to its new steady state), there is inter-firm reallocation. High-productivity firms become exporters, while low-productivity firms, disproportionately affected by reduced domestic sales, exit. Labor reallocates from exiting and non-exporting firms to exporting firms, increasing average firm productivity. The share of exporters in domestic and total revenues increases due to both intensive and extensive margin effects. This scenario demonstrates the immediate reallocation effects of trade liberalization in the absence of productivity dynamics. The lack of transition dynamics highlights that changes in firm productivity over time are another important driver of the aggregate transition process observed in the full model.

This section develops intuition on how adding firm productivity dynamics alters the impact of trade liberalization on entry. A simplified model is used to derive a simple analytic rule governing this trade-off, which isn't tied to a specific parametrization. This rule predicts the response of entry under more general conditions. The analysis focuses on how the relative size of entering firms influences the change in entry and the aggregate transition dynamics. The key insight is that if entering firms are smaller than incumbents (as in the exogenous innovation case), incumbent exporting firms benefit proportionally more from lower trade costs than entering non-exporting firms, making entry less profitable and leading to a decline in entry following trade liberalization. This leads to an overshooting of the entry response and a subsequent adjustment of the mass of producing firms towards a new lower steady state. This finding is not limited to specific parameterizations and provides insight into the more complex scenarios.

Scenario 3 introduces a full model with exogenous innovation, confirming the earlier analytic results—a permanent trade liberalization leads to a decline in entry and subsequent transition dynamics. Scenario 4 adds endogenous innovation, using a more elastic parametrization. This scenario shows the innovation intensity response to trade liberalization and its influence on transition dynamics. With endogenous innovation, exporters innovate more, increasing their relative value. This reallocation of innovation, also affecting non-exporters anticipating future export opportunities, generates longer-lasting transition dynamics. The response of entry is similar to the exogenous innovation case, leading to overshooting and a subsequent decline to the new steady state. Importantly, non-exporters near the export threshold also increase innovation, anticipating future exporting. The analysis contrasts the resulting dynamics of average productivity, trade flows, and output to scenarios with exogenous innovation, emphasizing the significant role of endogenous innovation in shaping the aggregate response to trade liberalization.

Scenario 5 examines the impact of a temporary trade liberalization, where the initial trade cost reduction is later reversed. This scenario focuses on firms’ expectations about the permanence of the liberalization, revealing that the benefits of innovation are muted when liberalization is perceived as temporary. This contrasts with the permanent liberalization scenario. The response of innovation is significantly weaker in the temporary liberalization scenario, highlighting the importance of firms' beliefs about policy persistence. Scenario 6 explores anticipated trade liberalization, where the cost reduction is announced ahead of implementation. Exporters respond by increasing innovation intensity before the actual policy change, illustrating that anticipation of liberalization also significantly impacts firms' behavior and the resulting aggregate dynamics. This preemptive response shows a clear contrast between the effects of anticipated versus unanticipated liberalization.

The final scenarios introduce sunk export costs, demonstrating how they affect the option value of becoming an exporter and influencing entry decisions. The analysis initially contrasts the effects of a temporary versus permanent reduction in trade costs, focusing on the export entry decisions of firms under different expectations about the policy’s permanence. The introduction of sunk costs creates an option value of waiting before entering the export market, which is affected by expectations about future trade costs. When trade liberalization is anticipated, the option value of waiting decreases, and more firms enter the export market ahead of the reduction in trade costs, particularly when liberalization is expected to be permanent. This demonstrates how sunk costs, in combination with expectations, generate additional anticipation effects ahead of changes in trade costs. The presence of sunk export costs is highlighted in comparison to a benchmark scenario with only fixed costs.

The computational results demonstrate significant variation in the responses of trade volumes, innovation, and aggregate output over time, depending on the specifics of firm dynamics, endogenous innovation, and the anticipated time path of trade liberalization. These findings highlight the limitations of static models, which often fail to capture the richness of the adjustment process. For example, the response to a permanent, unanticipated reduction in trade costs differs considerably across scenarios. In some cases, the economy jumps immediately to a new steady state, showing no transition dynamics, while in others, substantial transition dynamics are observed, with variables like entry, average productivity, and output exhibiting significant time-dependent adjustments. The analysis shows that long-run trade elasticities (with respect to changes in trade costs) are substantially larger than short-run elasticities. The dynamic nature of the response underscores the need for models that incorporate time explicitly.

The paper emphasizes the significant impact of transition dynamics on welfare calculations. Comparisons of consumption across steady states can either over- or underestimate the true welfare gains from trade liberalization, depending on the specific model assumptions. The reason is that the transition period involves reallocations of resources, changes in innovation, and adjustments in the firm size distribution—factors not captured by a simple steady-state comparison. For instance, when endogenous innovation is incorporated, the speed at which average productivity increases affects welfare during the transition. If average productivity rises slowly, steady-state consumption will overstate welfare gains, and vice-versa. The analysis concludes that incorporating transition dynamics is crucial for accurately assessing the welfare implications of trade liberalization.

The study concludes by highlighting the importance of considering dynamic effects when analyzing the consequences of globalization. Empirical work focusing on a single point in time captures only a snapshot of the response, which can evolve significantly over time without changes in underlying economic fundamentals. The response is also sensitive to many unobservable factors, including firms' expectations and anticipations. The model is presented as a starting point for understanding the complexity of the adjustment process; the authors acknowledge limitations related to modeling international market participation (only exports considered) and innovation (labor as the only input). Future research could extend the model by incorporating additional forms of market participation, more detailed innovation processes (including alternative inputs and spillover effects), and destination-specific dynamics, improving the model’s ability to realistically represent firm-level decision-making within a dynamic global environment.