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International shock transmission through heterogeneous firms

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International shock transmission through heterogeneous firms

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After decades of globalisation, the structure of production is increasingly international, with supply chains crossing country borders. An important feature of this internationalisation of production is that the bulk of international trade linkages in a typical economy are held by only a few large firms (Freund and Pierola 2015). As a result, while only a minority of firms have direct trade linkages with foreign countries, those firms tend to account for a large share of aggregate economic activity (di Giovanni et al. 2017, 2018). How resilient is such an economy then to foreign business cycle shocks? 

Our recent paper (di Giovanni et al. 2020) quantifies the consequences of a foreign shock to such an economy to study international shock transmission. Our point of departure is that even purely aggregate foreign shocks affect firms differentially depending on the extent and nature of their international linkages. In that sense, an aggregate shock to a country’s trading partners manifests itself as a set of heterogeneous shocks to individual firms. Our analysis combines a dataset covering the universe of French firm sales and country-specific imports and exports over the period 1993-2007 and a quantitative multi-country multi-sector model with heterogeneous firms. Below, we present one micro finding and one macro finding. 

Micro heterogeneity

We begin by documenting the novel stylised fact that larger French firms are significantly more sensitive to foreign GDP growth than smaller firms. This pattern is not driven by differences in overall procyclicality, as larger firms are not differentially more sensitive to domestic GDP growth. This empirical regularity is prima facie evidence that larger firms are more susceptible to foreign fluctuations.

Next, we employ a quantitative framework to simulate the effects of foreign shocks on the French economy. The model is calibrated to the observed firm-level information for France, and to the sector-level information for France’s trading partners from the World Input-Output Database (WIOD). A distinctive feature of our framework is that it is implemented directly on firm-level data. In other words, objects inside the model are actual firms in France. Hence, we are able to capture the full extent of joint heterogeneity across French firms in size and international linkages. Importantly, our model is solved in general equilibrium with discrete firms, implying that shocks experienced by individual firms can move equilibrium objects such as wages, prices, and GDP. It is hence an appropriate environment to quantify the impact of micro heterogeneity on aggregate outcomes. 

When we subject our model French economy to foreign shocks, we find that even an aggregate foreign shock has substantial distributional consequences across firms. Figure 1(a) plots the histogram of firm-level value added changes following a 10% rest-of-the-world productivity increase. While most firm value-added changes are positive, there is substantial density below zero as well — some firms shrink in response to a positive shock in the rest of the world. At the same time, there is an upper tail as well, as the density of firm value-added changes above 10 percentage points is visible. 

The distributional consequences across firms take a particular form: a positive foreign shock favours larger firms at the expense of smaller ones (the opposite is true for a negative shock).  Figure 1(b) displays the average value-added change for firms of different sizes following a 10% foreign productivity shock. We break firm shares in aggregate value added into size bins, and plot the mean value-added change in each size bin. We find that indeed larger firms do better. Notably, the aggregate GDP change (the horizontal red line) also happens towards the top of the plot, coinciding with the value-added change of the largest firms. 

Figure 1 Micro responses to a 10% world productivity shock

(a) Firm-level value added changes      

International shock transmission through heterogeneous firms 2   

(b) Average firm-level value added changes by firm size

International shock transmission through heterogeneous firms 3

To summarise this micro heterogeneity in a single summary metric, we decompose the GDP change following a foreign shock into an average response of all firms in the economy, and a granular residual (Gabaix 2011, Gabaix and Koijen 2019), which is essentially a cross-sectional covariance between firm size and firm response to the shock. Figure 1(b) shows that this covariance is positive. Quantitatively, the granular residual accounts for 40-85% of the fluctuations in French GDP induced by foreign shocks as foreign shocks affect predominantly the largest firms in France which leads to granular fluctuations.

Macro impact

Our macro finding shows that the observed heterogeneity across firms described above dampens the impact of foreign shocks. Following the same foreign shock, the GDP change in an economy with identical amounts of trade and output, but without within-sector firm heterogeneity is 10-20% larger than the GDP change in the baseline economy. Thus, the micro structure indeed affects aggregate outcomes.

To understand this finding, we note that our baseline model differs from the homogeneous firm model in two respects: (i) heterogeneous firm sales, and (ii) heterogeneous imported intermediate input shares. We investigate the consequences of these two sources of heterogeneity in turn. First, we prove analytically that if production functions are identical among firms within a sector, the real GDP change due to a foreign shock is invariant to the distribution of market shares across firms. This theoretical result allows us to  characterise the source of the dampening effect: a necessary condition for dampening is heterogeneity in the use of foreign inputs. 

The intuition for how this dimension of heterogeneity generates dampening hinges on the observation that raising a firm’s imported input share lowers its impact on domestic GDP. This is because mechanically, a higher imported input share means lower demand for domestic value added by the firm. At the same time, raising a firm’s imported input share increases its exposure to foreign shocks. Thus, relative to a representative firm world, introducing heterogeneity in imported input shares induces a negative covariance in the cross section of firms between impact on domestic GDP and exposure to foreign shocks. This negative covariance is the source of the dampening effect of firm heterogeneity in importing. 

Summary

Superstar firms have received much attention in recent years. Phenomena as varied as aggregate fluctuations (Gabaix 2011), executive compensation (Gabaix and Landier 2008), top income inequality (Ma and Ruzic 2020), comparative advantage in trade (Gaubert and Itskhoki 2020), and the fall in the labour share (Autor et al. 2019) have been linked to superstar firms. Yet another important difference between superstar firms and the rest of the economy is the extent of international linkages. Our research explores the consequences of this aspect of superstar firms for international business cycle transmission.

Heterogeneity across firms in the responsiveness to foreign shocks is indeed pervasive at the micro level.  This aspect of the micro structure is relevant for macro adjustments. Heterogeneity dampens the response of the economy to foreign shocks, because the firms most susceptible to foreign shocks are also the least engaged with the domestic economy (conditional on size).

References

Autor, D, D Dorn, L F Katz, C Patterson and J Van Reenen (2020), “The Fall of the Labor Share and the Rise of Superstar Firms”, Quarterly Journal of Economics, forthcoming.

di Giovanni, J and A A Levchenko (2010), “Putting the Parts Together: Trade, Vertical Linkages, and Business Cycle Comovement”, American Economic Journal: Macroeconomics  2(2): 95–124. 

di Giovanni, J,  A A Levchenko and I Mejean (2017), “Large Firms and International Business Cycle Comovement”, American Economic Review: Papers & Proceedings 107(5): 598–602. 

di Giovanni, J, A A Levchenko and I Mejean (2018), “The Micro Origins of International Business Cycle Comovement”, American Economic Review 108(1): 82–108. 

di Giovanni, J, A A Levchenko and I Mejean (2020), “Foreign Shocks as Granular Fluctuations”, CEPR Discussion Paper 15458.

Freund, C and M D Pierola (2015), “Export Superstars”, Review of Economics and Statistics 97(5): 1023–1032. 

Gabaix, X (2011), “The Granular Origins of Aggregate Fluctuations”, Econometrica 79(3): 733–772. 

Gabaix, X and R S J Koijen (2019), “Granular Instrumental Variables”, mimeo, Harvard and Chicago Booth. 

Gabaix, X and A Landier (2008), “Why has CEO Pay Increased So Much?”, Quarterly Journal of Economics 123(1): 49-100.

Gaubert, C and O Itskhoki,“Granular Comparative Advantage”, Journal of Political Economy, forthcoming.

Ma, L and D Ruzic (2020), “Globalisation and top income shares”, Journal of International Economics 125: 103312.

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