parametric methods in Ackerberg et al. (2015) but will also present results based on other methods (Wooldridge, 2008), and with fixed effects to check for robustness. These measures are proxies for revenue productivity, which depends both on physical productivity and markups.<sup>7</sup> The dependent variables in our regressions are 3‐year changes in these productivity measures, employment, sales, average wage and return on assets (ROA). We winsorize these long differences at the 5<sup>th</sup> and 95<sup>th</sup> percentiles of their distribution, calculated separately for each 2‐digit industry‐year combination.

As for the construction of our main explanatory variable, multiple definitions for HGFs exist in the literature. A key difference between these methods is whether they rely (i) exclusively on relative growth rates or (ii) on absolute growth. The former approach tends to identify HGFs as mostly small firms, while the latter provides a less skewed identification. As all theoretical spillover channels – either via vertical linkages or the labor market – are likely to be stronger when they originate from larger firms, the latter measure is more likely to capture these externalities. Hence, that is our preferred approach. Specifically, we choose to identify HGFs based on the Birch index (Birch, 1981), computed for all firms with at least 5 employees in year t : We rank firms according to their Birch�� values for each year and classify a firm as HGF if the Birch index is above the 95<sup>th</sup> percentile in that year. The constant and absolute threshold generates variation across industries, regions and years.

As a robustness check, we will estimate the regressions with the OECD definition of HGFs whereby a firm is high‐growth if it employs at least 5 employees at the beginning of the period and has an annualized growth rate of employment of at least 20 percent for a period of 3 years (OECD, 2010).

By definition, the share of Birch‐firms is 5 percent for the full sample in each year. There are some differences across industries, with the most HGFs in high‐tech manufacturing industries.<sup>8</sup> The OECD definition shows similar patterns across industries, but by construction it also varies across years, following the macro cycle (see Table 1).

Importantly, the data set allows us to exploit the detailed geographical information of each firm. The data on the municipality of the firms’ headquarters are used to construct our spillover measures. Municipalities are the smallest geographical unit of measurement in Hungary: they can be aggregated up to 174 microregions, where each microregion tends to include one city and the neighboring smaller

> 7 In spite of the conceptual differences between TFPR and TFPQ, Foster et al. (2017) use US data to show that these measures are highly correlated, have similar relationships with growth and survival, and show similar dispersion. These results cast doubt on the interpretation of TFPR as a proxy for distortions as in the Hsieh and Klenow (2009) framework.

> 8 We rely on Eurostat’s indicators on high‐tech industry and knowledge‐intensive services. Manufacturing industries are grouped in four categories: high‐tech, medium‐high‐tech, medium‐low‐tech and low tech. Services are organized in knowledge‐intensive services and other services.

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