I think your second definition is more appropriate than the first one.

To set a definition on startup company, you need to know the main characteristic of startup company. In other words, what makes a startup company different from other types of company.

The common feature of all startup companies is they grow fast. Therefore, when we we talk about startup company, we are talk about growth. That is the reason of why investors to startup companies are willing to accept an extremely high P/E ratio.

I believe the most suitable definition of a startup-company is any (new) enterprise that is aimed to grow fast. For quantitative analysis, you may want to focus on their growth rate (in terms of equity, revenue, etc...).

The term Start up has come under recent cache to describe budding Entrepreneurs who have and idea,solicit an Angel investor,prove the concept,then enter a second or elevator round of funding,and follow a fairly well defined path.This is common in the .com space.Outside that world any company going from a twinkle in the eye,to boots on the ground would be considered a start up and as such starts as a zero.

That is my impression and I hope it helps,

Zac

A startup is a company which operates on a limited set of resources at a disequilibrium with high-growth demand market(s).

Source: I've built one (Simbound)

Since you intend to conduct a quantitative study it will be difficult to use the second definition. Though the second definition is more representative of a typical startup, there are too many subjective factors in it. The first definition of yours is more suitable for quantification.

When is a startup to be counted as a startup? While it remains a subjective question, I believe that once resources are committed (of any size) and a venture is established (of any shape), it is ready to be counted. This may require you to create a definition for your research. But creating one with some similar aspects will allow you to count a much wider group (non technology) of startups.

Hope this helps.

This is one of the difficult questions in entrepreneurship research!! The confusion is due to factors like 1. The entrepreneur/s (Individuals) 2. Organization (Legal Status)

1. From the employment perspective: Yes the system (may or may not be an organization as yet) should be at least having one PAID (?) employee. I think it should be a paid one, otherwise commercial (as opposed to voluntary) nature of the organization is not known. This aspect is quantified.

2. From the organization perspective: It should be separate entity. But it may not be registered always. There are many start ups which may be registered or unregistered. The legal independence of the organization may be established or not. However, there could be a 'Name/Brand Name etc' separated from the individual. Thus it can be separated from self employments with some help as identified in the first point. 

3. Time Dimension: If one organization is working for last couple of years then it ideally should not be called a start up. But what should be that cut-off duration. There is no clarity. However the duration depends on the industry characteristics and scale. (Supply chain start up duration would be different from Mom-and-pop shop duration, if the small retail store is more than 6 months old it may not be considered start up, whereas a manufacturing company would be known as a new start up for quite many years).  The distinction is possibly in the customers mind rather than actual number of years it is in operation. Time has to be decided for the research and for the sector.

4. Growth: Start ups SHOULD have higher growth, but the question is how much, how to know it independently, and within what time frame the growth should be achieved. There are no agreed standards for such parameters. This is also a subjective assessment. The organization can run with growth or no growth as long as entrepreneurs is able to support or the organization is running in low sustainable mode. The rate of growth can be indicative but can not distinguish between start up or not. Another point is that, if the base is very low then any growth will APPEAR to be very high (example: adding one employee to existing one is 100 % growth, but not so if you add one to existing 20 employees).

Thank you very much 

Another difficulty with the second one is the growth-orientation.Depending on which age you would like to sample the firms, the growth might not have materialized yet. And every founder can easily say in his pitch that he aims for the scaleable business.

You could also look at GEM (Global Entrepreneurship Monitor, http://www.gemconsortium.org/) or the National Systems of Entrepreneurship project by Erkko Autio and Zoltan Acs (http://www.sciencedirect.com/science/article/pii/S0048733313001613).  

Two papers might help you---

i) Sarkar et al. (2006; p. 526) define an "entrant" into an industry "as firms who are less than 5 years old in the focal industry. The 5-year time span has been used in earlier studies of entrant survival (e.g., Baldwin, 1995; Robinson and Min, 2002), and is consistent with our focus on early year survival patterns."

So, I guess, after five years of entry, an "entrant" becomes an "incumbent." Sarkar et al. (2006) use Thomas Register of American Manufacturers to find the entry date for a firm. 

Further, they (p.526) distinguish between a "diversifying entrant" from startups by "consulting the annual firm index volumes of the Thomas Register for the year preceding a given firm's industry entry to see if the firm had produced in any other manufacturing category prior to its entry in the focal industry."

ii) That distinction of startup from 'diversifying entrant" is consistent with prior research. For example, Bayus & Agarwal 2007; pp.1893-1894 ) distinguish among "Startup Entering With Intel x86, Diversifying Entrant Entering With Intel x86, Startup Not Entering With Intel x86" and they use the Thomas Register as well. They also note, "As is typically the case in new industries (Carroll et al. 1996, Helfat and Lieberman 2002), the majority of entrants in the personal computer industry are entrepreneurial startups with no prior industry experience (almost 75% of the firms in our sample are startups). We define the binary variable Diversifying Entrant to be one if the firm is classified as having pre-entry experience, and zero if the firm is a startup."

I have listed the two major references below. Hope that helps. Good luck!

Raja

References:

Bayus, B. L., & Agarwal, R. (2007). The role of pre-entry experience, entry timing, and product technology strategies in explaining firm survival. Management Science, 53(12), 1887-1902.

Sarkar, M. B., Echambadi, R., Agarwal, R., & Sen, B. (2006). The effect of the innovative environment on exit of entrepreneurial firms. Strategic Management Journal, 27(6), 519.

If  i may be frank and perhaps very objective, the answer to your question is: THERE IS NO SUCH  DEFINITION. This is one of the many issues in social science that is yet to be resolves in literature (if at all it will be resolve). My worry has always been that certain definitions do not defined clearly, on measurable term, the concept or phenomenon in question. The obvious is that, every definition tend to be contextual because most concepts and terms in humanities are polemical, in which case their meaning lies within the context used. To be academic, by having our definition backed by empirical or previous work, we adopt inferential approach. For example, if Start-up is defined by Dee at al. (2015) according to the first respondent as growth-oriented or higher growth firms as opined by the 7th respondent, your interest should now be what is "growth" and what "type of growth"?. As we may all know, growth can occur daily (as in daily profit from sales/revenue as can be found in petty cash trading records), or weekly, monthly depending on the firm's accounting and reporting system. therefore, your definition will depend on your knowledge of growth as well as the time within which growth takes place. This can be known from the etymology of growth and empirically from what other writers have said about growth, being aware of the context used.

Therefore time plays a major role in your definition of start-up from growth perspective. Based on the above vignette, I will agree to some extent with all scholars who mentioned time frame within which a business is qualified to be called Start-up. This is very important because knowing this time frame will allow the choice of variables. Growth as a measure is a generic variable. what type of growth? Profit? or Asset? or Revenue? or Returns? all of which are time-bound? meaning the business must have commenced and been in existence for some time.

So if you are interested in growth variables, you defined Startup within your context as a business that must have existed within say one -eleven months (if you are interested in revenue/sales, operational profit, working capital growth) one year and beyond (if you consider growth in returns like ROA, ROE, P/E, or other investment related measures) . Your definition should be based on others who defined Start-up from growth perspective. For certain, the number of employees should also make the list of variables and is also moderated by how you define Start-up.

WHAT YOU NEED TO DO:

Defined Start-up the way you want to use it in your study and support your definition inferentially with past definitions.

Then choose and define your variables to use and be sure they are either directly or indirectly supported by a theory you intend to use in your investigation

i hope this guide you.

Good luck

I consider startups as a young, innovative, growth–oriented business in search of a sustainable and scalable business model.

It may be tweaked to suit the context geography.

Maybe we have to "define" the definition before. An Innovative start-up is probably what you need ?

1 - A start-up is a young firm under 7 years (in France, by now). We have to work on this base. Easy to use because it is registered.

2 - Among these start-ups, you need to select some indicators that means "innovation".  For example :

- independent + patent holder + under seven 7 years = innovative company.

- independent + significant research budget + under seven 7 years = innovative company.

- independent + a local label "innovative company + under seven 7 years = innovative company.

Maybe, the work of the Rome University could help you.

see : http://politiques-innovation.org/innovation-allocation-knowledge-composition-and-long-run-growth/ 

or : http://www.dis.uniroma1.it/~bibdis/RePEc/aeg/report/2015-10.pdf

A startup should have following elements : - 

a. product or service being experimented

b. identification of market potential based on market research and surveys

c. business definitions, purpose, vision, goals and objectives are being defined. 

d. the promotors are preparing the basic framework and foundation of the business 

e. the business is yet to be launch on full scale but pilot level projects are being undertaken. 

Better an index normalized by employees (potential founders) rather than the conventional normalization by stock of existing firms.

You can be interested into the attached article.

Regards,

MV

https://www.masterclass.com/articles/quantitative-analysis