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where, y: dependent variable vector. X: design matrix, independent variables corresponding
to fixed effects. β: fixed effects vector. Z and W: Design matrices for random effects corresponding
to individual company id and time, respectively. . u and v: random effects vectors for id and time,
respectively. ϵ: error term.
Empirical analysis.
From 2007 to 2021, financial statements of 25,849
SME and large
enterprises registered as software companies with the Korea Software Industry Association (KOSA,
https://www.sw.or.kr) were used. If there are missing values for some variables in the financial
statements, they are corrected with a 3-year moving average and scaling. Employment statistics were
compiled using the National Insurance Statistics. The variables and sources used in the model can be
summarized in Table 1.
Table 1
Variable
definition and data sources
Variables
Descriptions and unit
Sources
firmcode
Firm code: business registration code
SPRi
fiscalyear
Fiscal year
SPRi
employee
Number of employees
NIS
Establishdate
Establishment date
SPRi
venture
Firm that holds venture certification: 1: yes, 0: no
Inno biz
Firm that holds inno-biz certification: 1: yes, 0: no
firmage
Firm age aggregated from the date of establishment to the date of
economic event (or 2021.12.31), days
class
Firm's scale: 1: large, 2: medium, 3:
small
revenue
Total revenue (sales), Korean won in millions
SPRi
oprprofit
Operating income, Korean won in millions
SPRi
netprofit
Net income, Korean won in millions
SPRi
totasset
Total assets, Korean won in millions
SPRi
totcapital
Total equity, Korean won in millions
SPRi
totliability
Total liabilities, Korean won in millions
SPRi
exportsales
Export sales, Korean won in millions
SPRi
curasset
Current assets, Korean won in millions
SPRi
cashequv
Cash equivalents, Korean won in millions
SPRi
accountrecvable
Account receivable, Korean won in millions
SPRi
noncurasset
Non-current assets, Korean won in millions
SPRi
curliability
Current liabilities, Korean won in millions
SPRi
acctpayable
Account payable, Korean won in millions
SPRi
noncurliability
Non-current liabilities, Korean won in millions
SPRi
equcapital
Equity capital, Korean won in millions
SPRi
capitalsurplus
Capital surplus, Korean won in millions
SPRi
retainedearnings
Retained earnings, Korean won in millions
SPRi
expresearch
Research
expenses, Korean won in millions
SPRi
expdevelop
Development expenses, Korean won in millions
SPRi
rnd
R&D expenses, Korean won in millions
SPRi
profitratio
Net profit margin ratio (%): net income/revenue*100
roe
Return on equity (%): net income/total equity*100
debtratio
Debt ratio (%): total liabilities/total equity*100
currentratio
Current ratio (%): current assets/current liabilities*100
laborprod
Labor productivity in Korea, employment/gross domestic product,
constant prices, Korean won in millions
WEO, October 2021,
IMF
rndintensity
R&D intensity (%): R&D expense/revenue*100
revgrowth
Annual revenue growth (%)
Source
: financial statement of company and SPRi, NTS, NIS , 2022
For estimation
, Markov chain Monte Carlo generalized linear mixed models
(MCMCGlmm) was
used.
In this model, we attempted to make more elaborate estimates by reflecting the volatility and time
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between and within software companies as random effects. Monte Carlo simulation was performed 10000
times per Markov Chain, of which the initial 2000 times were removed due to autocorrelation. Valid samples
are 800 for each chain. Markov
Chain was given three times
The estimation model was set up as in equation (4).
mcmc_01 <- MCMCglmm(revenue ~ rnd + sgr + rnd*sgr ,
random = ~id + year,
data = dat06,
family = "gaussian",
# prior = prior,
nitt = 10000,
thin=10,
burnin=2000) (4)
