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01-02-2015

Are high-growth firms one-hit wonders? Evidence from Sweden

Authors: Sven-Olov Daunfeldt, Daniel Halvarsson

Published in: Small Business Economics | Issue 2/2015

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Abstract

Most firms do not grow, and a small number of high-growth firms seem to create most new jobs. These firms have therefore received increasing attention among policymakers. The question is whether high-growth tends to persist? We investigate this question using firm-level data from Sweden during 1997–2008. We find that high-growth firms had declining growth rates in the previous 3-year period, and their probability of repeating high growth rates was very low. Thus, these are essentially “one-hit wonders,” and it is doubtful whether policymakers can improve economic outcomes by targeting them.

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Previous studies using quantile regression have not incorporated firm-specific fixed effects.

Note that HGFs are identified over 3-year periods, which means that our analysis mainly is focused toward the 1999–2008 period.

Daunfeldt et al. (2014) discuss implications of using different growth indicators to identify HGFs. Their results indicated that the results were not sensitive to whether employment or sales were used as growth indicator, but they found a clear trade-off between employment growth and productivity growth. Policies that are targeted toward promoting firms that grow fast in terms of number of employees might thus come at the cost of reduced productivity growth.

We can formalize the definition by relating the set of HGFs to the probability distribution of growth rates. We define HGFs as the subset of all firms with growth rates higher than some \(x\), which correspond to growth rates with a probability of at most \(1-\tau\). The lower bound \(x\) to high growth is thus given by \(\inf \{x:F(x)\ge \tau \}=F^{-1}(\tau ) \quad {\mathrm{for}} \quad \tau \in (0,1),\) where \(F(x)=P(g\le x)\) is the cumulative distribution of growth rates \(g\). To identify the 1 % fastest growing firms we set \(\tau =0.99\), then HGFs are all firms with growth rates higher than \(F^{-1}\left( 0.99\right)\), which coincides with the 99th percentile.

The expression (3) derives from the relationship between arithmetic and geometric means: \({\displaystyle {\mathrm{ln}}\left( \prod\nolimits_{i=1}^{n}E_{i}\right) ^{\frac{1}{n}}=\frac{1}{n}\sum\nolimits_{i=1}^{n}{\mathrm{ln}}\left( E_{i}\right) }\)

In Sect. 7, for comparison and robustness, we also present results when growth rates have been calculated annually.

All results remain qualitatively similar if we instead adopt a forward-looking or backward-looking approach when defining firm subsamples based on size. The results are available from the authors upon request.

Logarithmic growth rates are good approximation of percentage growth rates in this range.

Note that Hölzl (2014) only calculates the probability that a employment-HGF will remain a HGF in the next period, whereas we estimate transition probabilities for eight different growth categories and use both number of employees and sales as growth indicators.

The expression \(\gamma _{k}\) follows from the two moment conditions \({\mathbb {E}}{{\left( \upsilon _{i,t}^{2}\right) }} =\upsigma _{\varepsilon }^{2}/\left( 1-\beta ^{2}\right)\) and \(\mathbb {E}{\left( \upsilon _{i,t}\upsilon _{i,t-k}\right) }= \beta ^{k}\sigma _{\varepsilon }^{2}/\left( 1-\beta ^{2}\right)\) (see Han and Phillips 2010 for further details).

Because of a tent-shaped distribution in the error term, quantile regressions are often advocated over OLS (see e.g., Reichstein et al. 2010). While OLS traditionally do not account for heavier than Gaussian tails of \(\varepsilon _{i,t}\) in (7), the Han and Phillips (2010) estimator does not presuppose a Gaussian distribution, but only that the fourth moment of \(\varepsilon _{i,t}\) is finite. Even if a higher forth moment does affect the variance \((\sigma _{FDLS}^{2})\), the FDLS estimator is still consistent.

For the standard OLS estimator of (7), it can be shown that the bias is inversely related to \(\beta\) and vanishes as \(\beta \rightarrow 1\). Madsen (2010) even argues that OLS can yield superior estimates even when \(\beta <1\), provided that the variation in \(\alpha _{i}\) is relatively low and that \(\sigma (\alpha _{i})<\sigma (\varepsilon _{i,t})\), which Hall and Mairesse (2005) argue are likely for short panels of firm data.

We have also analyzed alternative consecutive 3-year periods during 1998–2007 and 1997–2006, and only firms that belong to a business group. All results remain qualitatively similar.

In contrast to the results presented from the FDLS estimator, we cannot control for firm-specific fixed effects here. In this regard, the results from estimating the quantile autocorrelation function should be considered with more caution.

Results are similar if we use annual growth rates, although confidence intervals are narrower due to more observations.

The first number correspond to the estimated autocorrelation coefficient when number of employees is used as growth indicator (Table 12), while sales is used as growth indicator in the latter case (Table 13).

We also examined whether growth persistence differed by business group member or not, since we know that much firm growth is non-organic (i.e., through acquisitions). However, all results are very similar to the ones reported in the paper and are available upon request.

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Title: Are high-growth firms one-hit wonders? Evidence from Sweden
Authors: Sven-Olov Daunfeldt
Daniel Halvarsson
Publication date: 01-02-2015
Publisher: Springer US
Published in: Small Business Economics / Issue 2/2015
Print ISSN: 0921-898X
Electronic ISSN: 1573-0913
DOI: https://doi.org/10.1007/s11187-014-9599-8

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