High-Growth Firms: Rising Tide Lifts All Boats

How do high-growth firms affect the rest of the economy? This paper explores this question using Hungarian administrative microdata. It finds evidence of stronger productivity growth for firms supplying and operating in industries with more high-growth firms. The surge of high-growth firms' demand for intermediate inputs could explain this positive vertical spillover. Firms with intermediate productivity levels seem most likely to benefit from this effect. The results hold irrespective of the level of spatial aggregation.


1 Introduction
Promoting job creation is a policy priority for many governments seeking to create gainful employment for their growing youth population and create pathways to economic transformation. For their potential contribution to this goal, high-growth firms (HGF) -firms with significant ability to rapidly grow employment -have increasingly attracted the attention of policy makers. Programs catering to these entities tend to rely on broad policy instruments, similar to those used to support SMEs. See Autio et al. (2007) and World Bank (2018) for a review of the evidence on these measures from advanced and developing countries, respectively. Governments in developing countries have scarce resources and administrative capacity to support entrepreneurship and may be concerned about how much of them to devote to HGF promotion in the hope of creating jobs. This is, however, is a simplistic way to frame the issue for policy makers, as HGFs can generate employment but they can also generate spillover benefits for other firms in the economy.
Much attention in the literature and among policy makers has focused on the benefits generated by HGFs and how to implement policies to encourage more HGFs. But HGFs also generate externalities and the net effect on the overall economy is ambiguous. On the one hand, HGFs may exert competitive pressures on input and output prices, crowding out other firms. They may poach workers from competitors, put upward pressure on labor and other input costs, or drive output prices down by exploiting economies of scale. On the other hand, HGFs may generate positive spillovers. HGFs may develop or possess knowledge of technology, organization or markets that may transfer to other firms through movement of employees or demonstration. The knowledge transfer is likely to occur over relatively short distances through face-to-face contact with their clients or suppliers or within the labor market. In addition, HGFs' high demand for inputs may generate opportunities for suppliers to exploit economies of scale (Javorcik, 2004), and/or facilitate technology upgrading. Because of their advanced technology, HGFs may sell high-quality or innovative inputs, benefitting downstream firms using that input. Assessing whether positive or negative spillovers prevail is the empirical question we explore in this paper.
We rely on detailed firm-level administrative data from Hungary and exploit regional and time variation in the share of HGFs to infer their connection with the performance of other related firms. We focus on vertical spillovers and use the 2-digit industry input-output matrix to determine the share of HGFs in upstream and downstream industries. This focus is motivated by the fact that the related literature on MNE spillovers documents stronger evidence for vertical or intra-industry spillovers rather than horizontal ones. We also consider a more refined measure of horizontal spillovers, or intra-industry spillovers, where we measure the share of HGFs in the firm's 2-digit industry and county, omitting the firms' own 4-digit industry.
In our empirical strategy, we carefully adapt the methods in the FDI spillover literature to the HGF environment. From a technical point of view, a crucial difference is that the HGF phase is more transient than the FDI one, which, in turn, limits the application of fixed effects methodologies employed in the latter literature. We handle this issue by regressing log differences on the level of spillover measures and firm controls. Relatedly, in contrast with the FDI case, the share of HGFs is mechanistically linked to the growth distribution, generating challenges discussed in the peer effect literature (see, for example, Angrist 2014). We handle this problem by excluding firms in the same narrowly defined (4-digit) industry from the calculation of spillover measures. A third issue is that unobserved demand shocks can confound the relationship between high growth and productivity increase in related industries. While we employ a large set of fixed effects to control for these shocks, our results can be interpreted as correlation between high share of HGFs and productivity growth rather than a causal relationship.
We find evidence consistent with positive spillovers. Rather than attracting workers from or reducing profits of non-HGFs, HGFs' presence seems to be linked to improvements in productivity, income and employment of other local firms. Among them, suppliers of HGFs appear to benefit most from their presence. Effects are heterogeneous: firms with medium productivity levels appear to gain most from HGFs' presence in downstream sectors. This may be explained by the low absorptive capacity of low productivity firms, and the looser relations between local markets and the most productive firms.
We contribute to different strands of the literature. First, we build on and add to the literature on the role of entrepreneurship in development. This literature emphasizes that while entrepreneurship in general is a key determinant of economic growth and employment (Carree and Thurik, 2010), a subset of entrepreneurs, often called high-impact entrepreneurs, contributes disproportionately to employment and economic growth (Autio et al., 2007). The literature also emphasizes key functions of high-impact entrepreneurs: they apply existing knowledge in innovative ways (Audretch, 2005) and operate where demand or supply characteristics were unknown (Ács, 2010). Both activities yield new knowledge, at least locally, thus having the potential to create externalities. Our paper contributes to better understanding the externalities generated by such entrepreneurs.
The entrepreneurship literature is partly motivated by the literature on the role of industrial policy in development. Hausman and Rodrik (2003) interpret development as a process of discovering a country's cost structure when producing different goods. In general, this type of self-discovery is under-provided because of public good problems (Rodrik, 2005). High impact entrepreneurs can play a key part in providing such self-discovery, as they are likely to investigate production functions and generate externalities via learning by doing for firms in similar activities. Furthermore, our analysis of interindustry spillover effects resulting from HGFs may also inform industrial policy (Harrison and Rodríguez-Clare, 2010).
Second, we expand the growing literature on HGFs. So far, the debate has focused on the identification of these fast-growing firms and their characteristics. HGFs tend to be more productive, younger, engaged in scientific R&D and computer programming, but are not concentrated in any given sector (Coad et at, 2014 andOECD, 2016). However, to the best of our knowledge, the literature has not yet investigated the impact of HGFs on other firms. This paper aims to fill this gap.
Third, we extend the productivity spillover literature. This literature has often found positive backward spillovers (see for example, Görg and Greenaway (2004) for a summary of the literature on spillover effects from foreign firms). Other studies show that positive spillovers may result from intentional or non-intentional technology transfer to suppliers from higher quality or productivity requirements (Blalock and Gertler, 2008), or from access to a higher quality, larger variety or lower priced pool of inputs (Javorcik, 2004). We contribute to this literature by investigating a different source of spillovers. We also discuss and propose solutions for new methodological challenges which emanate from the 4 more transient nature of the HGF phase relative to FDI. This contributes to the generalizability of the FDI spillover methodology to other problems.
The paper is organized as follows. Section 2 describes the data used, the construction of the main variables of interest and the empirical strategy. Section 3 presents our results. Finally, Section 4 summarizes the evidence presented.

Data
The primary data set is firm level corporate income tax statements during the period 1998-2014 from the Hungarian National Tax Authority (NAV). The data set has almost universal coverage as it covers all firms that require double-entry bookkeeping. 2 The sample includes more than 95 percent of employment and value added of the business sector and about 55 percent of the full economy in terms of GDP. The data set includes information on a wide range of matters such as ownership, financial information, employment, and industry at the NACE 4-digit code level and the location of their headquarters. The Centre for Economic and Regional Studies, Hungarian Academy of Science (CERS-HAS) extensively cleaned and harmonized the data.
Given the scope of our analysis, we restrict the data in several ways. First, we exclude non-profit organizations. Second, we drop firms that operate either in agriculture or in the non-market service sectors of the economy. 3 Third, we drop all firm-year observations with fewer than 5 employees. 4 Finally, we drop all firm-year observations with missing, negative or zero employment, turnover, material cost, capital or value added. As we will discuss in detail in section 2.3, our regression will be run for 3-year intervals, which further reduces the number of observations. We also restrict the sample to surviving firms, given our primary interest in TFP change. Finally, we exclude firms which operate in the capital, Budapest. 5 Our final regression sample consists of more than 140,000 firm-year observations. 6 The data include the most important balance sheet items. Nominal variables were deflated by the appropriate deflators from Eurostat. We rely on two proxies of productivity. First, labor productivity is value added over employment. Second, we estimate total factor productivity (TFP) using the semi-5 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. 7 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 th and 95 th 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 : ℎ We rank firms according to their ℎ values for each year and classify a firm as HGF if the Birch index is above the 95 th 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. 8 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.
settlements. The microregions can be grouped into 20 counties, including Budapest, which can be further aggregated into 7 regions, which represent the NUTS-2 geographic aggregation. 9 The choice of the geographical unit to create the spillover variables is essential to reduce spurious results. A highly aggregated geographical unit may result in spurious correlations between the spillover and firm performance variables. 10 Counties are likely to involve many supplier-buyer relationships as firms within a value-chain tend to co-locate near each other. 11 Microregions are the relevant unit of observation of local labor markets, and thus may be the appropriate unit for the analysis of knowledge spillovers via labor mobility. We show that spillovers from HGFs are the strongest when counties are the geographical unit of consideration, underlining the importance of buyer-supplier relationships in HGF spillover effects.

Spillover measures
HGFs may affect the rest of the economy through direct and indirect channels. They may affect firms that buy from and sell to them, but they may also impact firms that are not directly linked to them but operate in the same sector.
Let be the share of HGFs in (2-digit) industry , region (county or microregion) , and year , it accounts for the firms with at least 5 employees and an HGF phase starting in year , 1 or 2 : 12 where is the number of firms in industry in region (county or microregion) and year , and is an indicator variable that equals 1 if firm i is a HGF.
The upstream (forward) and downstream (backward) measures are based on the average share of HGFs in supplier and buyer industries in the region, weighted by the volume of intermediate-good flows across other industries. Importantly, when calculating these measures for a given firm, we omit said firm's 2-digit industry from the computation to capture only genuine inter-industry spillovers. Buyerseller connections are identified using information from the 2-digit (symmetric harmonized) inputoutput matrices for Hungary provided by the OECD: 13 and where are the normalized coefficients from the symmetric input-output matrix representing (domestic) intermediate good flows from industry to .
We also control for intra-industry spillovers by calculating the share of HGFs in the firms' 2-digit industry; using data on all entities with the same 2-digit code, save for the ones that belong to the firm's own 4-digit industry 14 (denoted by ). Thus, this measure is calculated as: All these spillover variables contain extreme values, mainly because of some firms' small size. To prevent such outliers driving the results, we censor values at 15% for all spillover measures. 15 Note that is very close to the `traditional' horizontal HGF measure, as defined in, for example, Javorcik (2004). The difference is that we omit the firm's 4-digit industry, to avoid generating spurious correlation. If all firms -including HGFs -are in the sample, then the high growth of the HGF will show up both in the HGF measure and on the left-hand side. Omitting HGFs from the regressions would introduce endogenous selection based on the dependent variable. 16 Nevertheless, re-running the regressions with the traditional horizontal measure yields similar results. 17 Table 2 shows the mean and standard deviation of our key spillover measures (with the 3-year Birch definition). Less than 10% of the firms in the sample are HGF in upstream or downstream industries, and this measure has a relatively small variation.  Ackerberg et al. (2015) approach, at the 2-digit industry level, using the sample of firms with at least 5 employees.
Let us illustrate the main correlations in our data at the industry-level. Figure 1 shows the relationship between the share of HGFs upstream in year and the subsequent growth, both computed at the (county-year-) industry level. Clearly, the share of HGF upstream is positively related to both productivity and sales growth. Next, we regress these aggregate variables and find that the correlations are robust to including county and year fixed effects into a regression (Table 3). A one standard 9 deviation increase in the share of HGFs in downstream industries is associated with an extra 10 percentage points improvement in productivity. 18 Higher downstream HGF share is also associated with stronger sales growth and higher wages, but not with increased employment. These descriptive results suggest that HGF presence in vertically related industries, and especially, in downstream ones, is positively associated with firms' size and productivity growth.

Figure 1 The univariate relationship between upstream HGF share and average 3-year productivity and sales growth, at county-year-industry level
Note: This figure is a binscatter, creating 30 quantiles based on upstream HGF share and shows the average 3-year labor productivity and employment growth rates for these quantiles.

Table 3 Correlation between spillover measures and average productivity and size growth at the county-industry-year level
(1)

Empirical strategy
Our specification for our baseline regression model is: where indexes firms, years, industries and regions. Δ is three-year growth rate (between and 3 of the main firm performance variables: labor productivity, TFP, employment (in logs), sales (in logs), average wages (in logs), and ROA. 19 are the variables of interest, described in the previous subsection.
captures three firm level characteristics, all related to productivity growth: (log) employment, labor productivity and capital intensity (or log(assets/employee)). Note that these variables are included as levels in year , an initial value before the growth measured by the dependent variable. Together with the differentiation of the dependent variable, they are likely to capture a rich set of heterogeneous firm-level characteristics.
We also include two types of fixed effects to capture industry-level and regional shocks. First, we include the (1-digit industry) sector-year dummies to control for macro sectoral shocks ( ). Second, we include region-year fixed effects to control for regional macro-shocks ( . 20 Both types of fixed effects are measured at a somewhat more aggregated level than the spillover variables themselves, to allow for some variation across the industries within sectors, and across counties within regions. The results are robust to including other types of fixed effects. Given that both the dependent variable and the spillover variables are calculated for 3-year periods, running the regression at the annual level would inflate the number of observations artificially. Therefore, we run the regressions at 3-year periods (and for 2-year periods at the end of the sample). 21 The periods included are 1998-2001, 2001-2004, 2004-2007, 2007-2010, 2009-2012, 2011-2014. The different temporal nature of the variables is a feature of our identification strategy. The spillover variables measure the stock of HGFs -the share of firms in their HGF phase -in year . The dependent variable measures how subsequent medium-term performance growth -between year and 3 -is correlated with this stock. We think that this specification captures medium-term effects of HGFs. We control for firm characteristics which may affect firm-level growth at time . Modifying these timing assumptions does not affect the results significantly.

11
Our identification strategy relies on variation from three main sources: geographic variation within regions, industry variation within sectors and time variation (and the interactions of these variables). We show that the results are robust to alternative specification. Across-industry cross-sectional variation is necessary for our results. Our results are mainly driven by the stronger productivity growth in industries vertically related to industries with more HGFs. This is a consequence of several factors. First, there is limited variation of links in input-output tables and HGF shares in 2-digit industries. Second, many periods are involved when measuring the dependent and the spillover variables. The dependent variable captures firm growth between periods and 3, which depends on changes during this period, including firms starting their high growth period in any of these years. 22 The explanatory variables consider firms which start their high growth period between 2 and . Consequently, in the empirical specification one 'year' observation consists of changes across 5-6 years, even not considering delayed effects of high growth phases. Useful time variation is quite limited.
Clarifying our identification strategy, we compare it to the usual method employed in the FDI spillovers literature. From a technical point of view, an important difference between the two empirical exercises is that HGF status is much more transient than foreign ownership: most firms which become foreign owned remain in that state. As a result, in typical FDI-spillover equations (e.g. Javorcik, 2004), the dependent variable is the level of productivity and the equation is estimated with firm fixed effects. This method is less appropriate when the variable of interest is less persistent, as in the case of HGF status. It is more intuitive in our setting to check whether productivity growth is higher when more firms are experiencing an HGF phase in vertically related industries. Note that, similarly to the level-fixed effects specification, differencing the dependent variable also filters out time-invariant firm characteristics.
A second issue with applying the methodology of the FDI spillover literature to measuring HGF spillovers is that any kind of horizontal measure of HGFs will include the firm itself: if our firm is an HGF, the share of HGFs in its industry will be automatically higher. The more disaggregated the data, the larger is this problem. This issue is easily handled in the FDI spillover literature by running the regression only on the subsample of always domestic firms. This, however, is less of an option in the HGF case, because restricting the sample to non-HGFs would lead to the endogenous exclusion of firms with the strongest growth performance. We will handle this issue in two ways. First, we exclude horizontal spillovers from our regressions and include different industry fixed effects. Second, we exclude the firm's 4-digit industry from the intra-industry measure, as indicated above. 23 In summary, our identification strategy attempts to use sensible timing assumptions together with a set of fixed effects. Still, our results are best interpreted as correlations: productivity growth in industries which supply industries with more HGFs. It is possible that there are unobserved industry characteristics, which may partly drive this correlation. Also, reverse causality is possible: stronger productivity growth of suppliers may help their buyers to grow rapidly. Given that regressions aimed at predicting HGF status usually have a low explanatory power, it is unlikely that one can find credible instruments for regional HGF presence. Consequently, we find our strategy a relatively transparent and credible way to document the correlation between HGFs and productivity growth in related industries.

Main firm-level regression results
Our main results are reported in Table 4. First, the top panel reports the positive relation between productivity growth and HGF share in vertically related industries. A one-standard-deviation increase in HGF share in downstream (buyer) industries is associated with about 4-5 percent of a standard deviation increase in labor productivity and TFP growth. These relationships are significant also from an economic perspective, representing about a 2.5 percentage points additional productivity growth in three years. The impact from HGFs in upstream (seller) industries is also positive but significant only for labor productivity. Additionally, we find evidence consistent with the existence of vertical spillovers. The coefficient on the share of HGFs in same industry is again positive and significant, albeit smaller in economic terms. The results are robust to two alternative methodologies to measure aggregate productivity (fixed effects and Wooldridge (2008) estimator) (Table A1).
Second, the middle panel examines whether productivity growth is related with firm growth. The presence of HGFs in downstream industries is associated with higher sales growth, but no extra growth in employment. This is consistent with HGFs generating additional demand, which may drive the premium in productivity growth. We do not find similar effects for HGFs in upstream industries. Also, there is weak evidence for a positive relationship between HGF share in the industry and firm growth.
Third, the bottom panel reports how potential productivity gains are related to income of the two key shareholders of firms: employees (through higher wages) and owners (through higher ROA). A comparable increase in wages and ROA is observed when the share of HGF in buyer industries grows. This similar magnitude reflects different impacts, due to differences in levels of the dependent variables. The wage effect is small, corresponding to about 0.25 percentage point additional wage growth in 3 years. The ROA effect is more significant, representing nearly an additional 0.4 percentage point increase in ROA. Taken together, the results suggest that the HGF presence in buyer industries is associated with higher productivity and stronger sales growth, which seem to benefit workers and, to a larger extent, owners. This is consistent with backward productivity spillovers from the higher demand of HGFs.
We also find positive association between HGFs in the same 2-digit industry, probably due to the presence of demand effects. We only find weak association between HGF in upstream industries and productivity growth. The results are robust to using alternative definitions for HGFs (

Which firms benefit?
Examining the heterogeneity of the spillover effects can provide us with some additional insights into the mechanisms behind our previous results and some related policy considerations. We explore this avenue in three ways. First, we study the difference between these relationships for manufacturing and services firms (Table 5). We find evidence of a positive relationship between productivity growth and intra-industry HGF presence for both groups of firms. Vertical linkages, however, are more important in manufacturing, where all three spillover variables are positively associated with subsequent productivity, employment and sales growth. In services, it is still mainly intra-industry linkages that matter, with a higher share of HGFs being associated with stronger subsequent productivity growth and higher profitability. These distinctions, however, may capture the different breadths of industries in manufacturing and services, rather than substantive differences between the two groups. Second, we investigate whether the strength of the association depends on the absorptive capacity of the non-HGFs. We measure the absorptive capacity by the productivity of the firm. More productive firms are more likely to attract the business of rapidly growing buyers or may benefit more from knowledge spillovers because of their better absorptive capacity.
To test these hypotheses, we split the sample into four productivity quartiles within each industry-year combination and run the main specifications in these subsamples (Table 6). 25 We find some evidence of heterogeneity, as productivity and wage effects are the strongest for firms with a medium level productivity, with significant differences between the middle quartiles on the one hand and the lower and upper quartile on the other. Firms with very low productivity levels may lack the capabilities to serve HGFs effectively, while very productive firms may already have easy access to domestic and international markets and therefore their performance is less dependent on the local HGFs. This difference is robust to taking deciles instead of quartiles and to using the other two TFP measurements, and to employing the OECD definition of HGF instead of the one developed in the first section.  Table 7 presents two sets of regressions. In the first and third columns, we include only the microregionlevel measures. This exercise is the same as our main regression, but the explanatory variables are calculated at a more detailed level of geographic aggregation. In the second and fourth columns we include the microregion-level measures together with the county-level measures.
Microregion-level variables have very similar coefficients to county-level ones, suggesting that the channels at small distances are not systematically different. Importantly, the positive association between HGF share in buyer industries is positively associated with productivity growth both at the microregion and the county levels. The smaller point estimates and weaker statistical significance may reflect the noisier nature of the microregion-level measures, which can result from strong granularity at this fine level of aggregation.
This exercise also serves as a robustness check. Our results are robust to different geographic aggregation levels, and the forces we quantify act both at very short and somewhat longer distances. Note: The reported coefficients are beta coefficients, t-values in parentheses. The explanatory variables are measured at time t, while the dependent variables are 3-year changes between t and t+3. The explanatory variables show the share of HGFs in different industries at the same microregion and county, by using the 2-digit input-out matrix from OECD STAN. Firm controls are log employment, labor productivity and log capital per labor ratio. Standard errors are clustered at the county-industry (2-digit NACE)-year level. The definition of HGF is the 3-year Birch employment definition.

Robustness checks
To test the robustness of our results, we first investigate whether the measured relationships changed after the Great Recession in 2007 (Table 8). We find that HGF share among buyer industries matters in both periods, though somewhat more after the Great Recession. The results also indicate that HGF in supplier industries had been significant before the recession and has become less important afterwards.
The results are largely robust when controlling for autocorrelation (Table A3). The larger coefficient following the crisis comes from the 2009-2012 period, a period of sluggish recovery. Firms with potential buyers who have been high growth even during the crisis, have increased their productivity rapidly. Note: The reported coefficients are beta coefficients, t-values in parentheses. The explanatory variables are measured at time t, while the dependent variables are 3-year changes between t and t+3. The explanatory variables show the share of HGFs in different industries at the same microregion and county, by using the 2-digit input-out matrix from OECD STAN. Firm controls are log employment, labor productivity and log capital per labor ratio. Standard errors are clustered at the county-industry (2-digit NACE)-year level. The definition of HGF is the 3-year Birch employment definition. Small firms are firms with less than 5 employees We conduct further robustness checks to investigate whether the results are robust to including different sets of fixed effects to the regressions. Recall that our baseline regression includes region-year and sector-year fixed effects and identify from variation across counties in regions and across industries within sectors.
We control for finer geographic heterogeneity with microregion-year fixed effects (Table 9). This set of fixed effects can capture very fine local demand or supply shocks. This change does not affect the results substantially. Still, it is possible that the results are identified from industry-specific demand shocks. To capture this, we include county-sector-year level fixed effects to find that our results are robust to different ways of controlling for local demand shocks.
An additional concern is that unobserved firm-level heterogeneity may bias the results. Recall, however, that firm-level heterogeneity is already handled in the original specification by differentiating the dependent variable and controlling for key firm characteristics. Also, the explanatory variables only vary at a more aggregated level. Still, we report specifications with firm fixed effects to control fully for unobserved firm-level heterogeneity (representing "fixed trends"). Results are somewhat sensitive to this, but we still find a significant positive relationship between the share of HGFs in buyer industries and productivity growth. A relevant concern about our empirical specification is that the share of HGFs can also be correlated with other industry characteristics. For example, the share of HGFs in an industry may be strongly correlated with the share of foreign firms. If foreign firms generate productivity spillovers, it is possible that our regressions capture that. We thus construct downstream/upstream/same industry measures from several relevant industry characteristics and control for them (   Table 10).
HGF may simply be more prevalent in industries with higher sales growth, and this sales growth, rather than the high growth firms themselves, drives the increased productivity. To investigate this, we calculate aggregate sales for each industry-county combination between and 3, and create the downstream, upstream, and same industry measures from these. In column (1) of Table 10, we find that controlling for change in sales at the industry level does not change our results significantly -HGF activity itself, rather than sales growth seems to be associated with productivity change.
In columns (2) and (3), we check whether our results are driven by a correlation between the share of globally integrated firms and HGFs. We control for the share of foreign firms in column (2). Note that this is indeed an FDI spillover equation in Javorcik (2004), which was the basis for our HGF measures. Similar to the FDI spillover literature, we find correlations which are consistent with positive backward spillovers -both the downstream measure and the within industry measure are significantly positive. These variables are correlated with HGF share and reduce our point estimate for the downstream HGF measure by two-thirds, yet the effect remains significant. Interestingly, controlling for FDI share yields a significantly positive estimate for the upstream HGF measure. The positive intra-industry effect becomes much weaker than in the previous specification. As an additional proxy for internationalization, column (3) controls for the share of exporters. This is, naturally, strongly correlated with FDI share at the industry level, and its inclusion yields very similar results to column (2).
It is also possible that HGFs are simply more prevalent in more innovative or more high-tech sectors. In column (4) we control for this by the share of innovative firms at the industry-level, calculated from the Community Innovation Survey (only available for the whole country, rather than at a geographically disaggregated way). We find stronger productivity growth in industries with more innovative firms and in industries supplying more innovative industries. The regressions yield positive and mostly significant coefficients for the HGF measures, but they are substantially smaller than in the baseline model. Finally, in column (5), we control for the industry's technology by including the average productivity of the vertically related sectors. This is calculated from our data, hence available at the same level of aggregation as the HGF measures. We find that firms supplied by and supplying industries with more productive firms experience higher productivity growth. The downstream HGF measure again becomes smaller but remains significant.
We find that HGF share in industries is indeed correlated with technology level and international integration. These industry-level variables explain a significant part of the association between HGF share in vertically related industries and productivity growth, but even conditional on these factors more HGF share seems to be associated with a premium in productivity growth. The reported coefficients are beta coefficients, t-values in parentheses. The explanatory variables are measured at time t, while the dependent variables are 3-year changes between t and t+3. The explanatory variables show the share of HGFs in different industries at the same microregion and county, by using the 2-digit input-out matrix from OECD STAN. Firm controls are log employment, labor productivity and log capital per labor ratio. We always include a similarly calculated upstream, downstream and same industry measure of the different control variables mentioned in the column headings. Standard errors are clustered at the countyindustry (2-digit NACE)-year level. The definition of HGF is the 3-year Birch employment definition. Small firms are firms with less than 5 employees.

Conclusions
High-growth firms have a disproportionate ability to create jobs and generate output. But there is less evidence and understanding about whether the benefits to economic growth outweigh the costs they impose on other firms. To understand the impact of HGFs on the economy as a whole, we rely on detailed administrative microdata from Hungary. We find that productivity growth of firms in Hungary is stronger if they serve industries with more HGFs. The fact that the premium in productivity growth is associated with growth in sales and that spillovers exceed local labor markets suggests that the surge in demand generated by HGFs may allow their suppliers to exploit economies of scale. Not only do HGFs have positive spillovers, but they benefit more firms in the middle of the productivity distribution. Firms in the bottom quartile of the distribution are not productive enough to take fuller advantage of HGFs demand. Firms in the top quartile of the distribution have access to wider markets and do not depend on HGFs as much. We also find that manufacturing firms are better able to benefit from the presence of HGFs than services firms. Lastly, we ascertain that the spillover effects are still present at a finer geographical level.
The results are robust to alternative definitions of HGFs, sample and estimation method. As discussed in the paper, establishing causality presents significant econometric challenges. The fact that they continue to hold when controlling for a plethora of factors and are not sensitive to several robustness checks gives us confidence in them.