11 Other explanatory variables relate to initial conditions and are observed in the first year of any 10-year nonoverlapping period. _Initial_Quality_ denotes the initial product quality level. _Determinants_ denotes the vector of potential determinants, which includes in our baseline specification initial GDP per capita, initial FDI inflows, initial institutional quality, initial human capital, and indexes measuring the levels of initial trade and agricultural liberalization (see Table 2 for all summary statistics).

GDP per capita is drawn from the World Bank’s _World Development Indicators_ . FDI inflows are measured as a percentage of GDP, and the data are drawn from the IMF’s _International Financial Statistics_ . Institutional quality is measured using the “Constraints on the Executive” variable from the Polity IV data set.<sup>31</sup> Human capital is measured using the secondary-school completion rate from the World Bank’s _World Development Indicators_ . The indexes measuring initial trade and agricultural liberalization are de jure indicators drawn from Prati et al. (2013).<sup>32</sup> To contain any omitted variable bias, we include sets of fixed effects to control for any other observables or unobservables that may drive quality growth. The basic specification includes fixed effects for country, product, and time. Country fixed effects control for quality growth being faster in some countries, for instance owing to unobserved institutional circumstances, such as the quality of business organizations or other mechanisms to exploit knowledge spillovers. Product fixed effects allow for quality improvements being easier to attain in some products. Time fixed effects detect changes over time in the global average speed of quality growth, for instance reflecting advances in information and communications technology or reductions in transportation costs.

The extended specification instead includes country-product and product-time fixed effects.<sup>33</sup> Countryproduct effects account, for instance, for unobserved institutional circumstances in a specific country favoring quality upgrading, but only in some types of products. Similarly, product-time fixed effects allow global developments to have different impacts on average quality growth in different products.

# **B.   Results**

The first key finding is that the quality of individual products converges unconditionally across countries over time. Specifically, in a bivariate regression, the growth rate of product quality depends negatively on the initial quality level (Table 3 and Figure 19). This implies that new, low-quality entrants into a sector see their quality rise over time relative to other countries. The speed of unconditional convergence toward the world quality frontier equals 3.5 percent per year when fixed effects are not included. The convergence speed tends to increase as more detailed fixed effects are introduced. This highlights the significant heterogeneity in the data, and in particular the presence of considerable obstacles to quality upgrading in specific sectors within specific countries. Evidence of within-product quality convergence also suggests that managing to enter ‘long quality-ladder’ sectors today could increase a country’s future potential to climb up the value chain, supporting growth.

> 31 Similar results are obtained if the Kaufmann-Kraay-Mastruzzi indicators are used.

> 32 Both indexes vary between zero and unity. The trade liberalization measure is based on average tariff rates: zero means the tariff rates are 60 percent or higher, while unity means the tariff rates are zero. The agricultural liberalization index measures the extent of public intervention in the market of each country’s main agricultural export commodity; it includes the presence of export marketing boards and the incidence of administered prices. Both indexes are available from 1960 onwards.

> 33 We do not include country-time fixed effects, because the determinants we are primarily interested in only vary along the country-time dimension.

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