OLS estimate of the Zipf’s coefficient in linear and quadratic formulation in much greater detail, we simply use the Hill estimator to check for the robustness of our results.

# **_Measuring participation and the knowledge content of GVCs_**

Besides domestic content, the value added in gross exports of a country can be decomposed into the following three categories (Koopman et al., 2010):

- (i) Value added exported in intermediates directly to the importers

- (ii) Value added exported in intermediates re-exported to third countries, and,

- (iii) Valued added exported in intermediates that are re-imported home.

Each of these categories represents a measure for capturing a country’s participation in GVCs. The OECD TiVA database offers several indices for measuring participation in GVCs. Some examples include the following measures (as a percent of gross exports): (i) DVA in exports of intermediate products, (ii) DVA embodied in foreign exports, and (iii) re-imported DVA. These indices are defined in Annex table A.1.

Participation in GVCs is, however, not an indicator of the knowledge content of participation. We rely on sectoral measures to measure knowledge content. Within manufacturing, we follow Banga (2013) in defining the high-tech manufacturing to include the following sectors: Electrical and optical equipment; Machinery and equipment, nec; Transport equipment; and Chemicals and non-metallic mineral products. Low-tech manufacturing includes the following sectors: Textiles, textile products, leather and footwear; Food products, beverages and tobacco; Agriculture, hunting, forestry and fishing; Mining and quarrying; and Manufacturing nec; recycling. For services, we use the extent of forward participation in GVCs in the services sector, in general, and in highly knowledge intensive R&D and business services, in particular, to draw comparison within and across the sectors.

# **_Endogeneity of GVCs with city size distribution_**

We are interested in capturing the _causal_ effect of GVCs on city size distribution -- however, it is possible that changes to the urban system come from some other unobserved sources and countries respond to this by integrating their economies in global supply chains. For instance, analysis of firms in the Italian automotive industry (Bacchiocchi and Florio 2012) shows that being located in a high-density industrial district and producing more research-intensive automotive-specific goods increases the probability of internationalization of supplier firms. Thus, we expect that some exogenous factors can drive spatial dynamics of cities within a country which in turn affect the participation in GVCs, making the latter an endogenous determinant.

Similarly, location of firms in urban clusters improves their probability of participating in GVCs and perhaps also impacts the knowledge content of their participation. If this is so, our regression of city size distribution on variables measuring the participation and knowledge content of GVCs will capture the association between GVCs and urban system that includes not only the direct causal effect (from GVCs to urban system) but also any indirect feedback effect (from urban system to GVCs). In the worst case where participation in GVCs does not impact the urban system at all, our estimations could pick the reverse feedback effect from the urban system.

To address endogeneity of GVCs with urban structure, we adopt an instrumental variables approach. Certain factors affect the general environment for trade but are less likely to be spatially consequential. For instance, the real effective exchange rate (REER), defined as the nominal exchange rate deflated by an index of price or index of costs, takes account of price level differences between trading partners and 7