Catching Gazelles with a Lasso: Big data techniques for the prediction of high-growth firms

The working papers by Miyakawa et al. (2017) and McKenzie and Sansone (2017), who apply LASSO to firm performance data. Miyakawa et al. (2017) seek to predict high growth performance in a sample of Japanese firms, although they use a non-standard definition of high-growth firms. McKenzie and Sansone (2017) investigate top 10% growth among business plan competition winners and non-winners in Nigeria. These working papers came to our attention at an advanced stage of this research.

See also the exchange between Derbyshire and Garnsey (2014) and Coad et al. (2015) on the randomness of growth. We are grateful to a reviewer for this suggestion.

Relatedly, Bernerth et al. (2018) recommend that the control variables be mentioned specifically in the formulation of the hypotheses. Of course, we cannot do this in our context, because we have several hundred explanatory variables, and we apply data-driven procedures to decide which of these explanatory variables to keep. Nevertheless, in step 7 of Algorithm 1, we add in a minimalist set of control variables that are included for theoretical reasons, i.e., sector dummies, year dummies, a dummy for the Zagreb capital region, and firm age.

At the Eurostat web site, under the National accounts aggregates by industry (up to NACE A*64), we obtain current prices, million units of national currency and previous year prices, million units of national currency. To obtain the share of current in previous year prices, the two are divided and were set at constant prices in 2010. When two-digit NACE deflators were not possible to obtain, the one-digit deflators were used (e.g., mining and quarrying, the NACE one-digit deflators were used for the four separate NACE 2-digit sectors).

Previous research has shown that employment growth and sales growth are the two most common indicators of firm growth, and we include them both because they are alternative and complementary indicators that capture different aspects of the firm growth process (Delmar 1997; Shepherd and Wiklund 2009).

Including firms with 1 or 2 employees was not possible, because the LASSO computations could not converge to a solution. However, this does not seem to be a problem because, despite the large number of firms with one or two employees, nevertheless these firms make a small aggregate contribution to the national economy, and moreover these micro firms are relatively unlikely to become HGFs (Neumark et al. 2011). Note also that the Eurostat-OECD HGF definition excludes all firms with fewer than 10 employees.

Note that the share of HGFs jumps up from 1.53 to 10.75% when we exclude firms with fewer than 10 employees. This could explain why some countries have higher HGF shares than others—it could be because the databases being used have different coverage of micro firms (e.g., Coad and Scott 2018).

The number 7.8 comes from the minimum possible growth increment to become an HGF according to the OECD definition. A firm with 10 employees in the first year, with average annual growth of 20% over 3 years, will need to grow by 10 × [1.20³ − 1] = 7.28 employees.

By applying the natural log transformation on all variables, we are in line with the recommendations of Makridakis et al. (2018, p. 21) to automate the preprocessing of data before the application of data-intensive forecasting methods, to avoid the role of potentially ad hoc decisions being made by the researcher.

Croatia has twice larger population (4.15 million) in comparison to Slovenia (2.07 million).

These data-driven penalty loadings for LASSO are different from the canonical penalty loadings proposed in Tibshirani (1996).

Logit LASSO has the same intuition as in the linear LASSO case because logit regression can be reduced to the linear case by employing reweighted regression.

These results are available from the authors upon request.

Nevertheless, note that the studies in Table 1 display heterogeneity regarding their HGF indicators (Birch index, top 10% of firms, etc.) as well as size of firms in the samples, which limits the comparability of the pseudo-R² statistics across studies.

It is possible that the usage and significance of inventories differs between manufacturing and services sectors. We therefore repeated the analysis on subsamples of manufacturing and services sectors, and the results for inventories remained.

Note that growth of profits is only selected by LASSO in model 2, for Croatian employment HGFs.

The level of intangible assets is positive in the subsample of all firms with 3 or more employees (i.e., model 2), while growth of intangible assets is positive in the subsample of all firms with 10 or more employees (i.e., model 1).

One possible explanation for the varying results could be that the regression specifications for Slovenia do not include an age variable, because this variable is not present in the Slovenian data.

Table 2 shows that “cash in bank” is positive and significant in model 1 (i.e., for firms with 10+ employees) for Croatia.

Ries (2011, p. 184) gives the example of folding newsletters, sealing them into envelopes, and attaching a stamp. The standard approach might be to begin by folding all newsletters, then afterward putting them all into envelopes. However, this approach has drawbacks relating to time taken to sort, stack, and move around large piles of half-complete envelopes. Also it is possible that the letters do not fit in the envelopes, a problem which would only be discovered late into the production process. Instead, “single-piece flow” (see also “continuous flow manufacturing”), which corresponds to completing each envelope one at a time, is a surprisingly efficient production method, and the superiority of “single-piece flow” has been confirmed by studies (Ries, 2011, p. 184).

One possibility could be that the effects of previous growth rate on subsequent HGF status are nonlinear across the distribution of previous growth rates.