Early research on business failure traces back to Marshall (1980) and Schumpeter (1934). Their ideas were later applied to the study of industrial organization by scholars such as Gibrat (1931) and Bain (1956). The initial focus of the literature was on developing theoretical models capable of explaining the process of corporate bankruptcy, such as the single-period model (Scott, 1981) and the gambler’s ruin model (Wilcox, 1973).

Single-period models assume that firms exist for only two accounting periods—created in the first and liquidated in the second. A firm is considered bankrupt if its liquidation value falls below the amount owed to creditors (Scott, 1981). Although this represents the simplest form of bankruptcy modeling, its predictions diverge considerably from empirical evidence, as single-period models account only for equity and exclude cash flows (Black & Scholes, 1973; Merton, 1974; Schwartz, 1977).

The gambler’s ruin model, by contrast, assumes that changes in a firm’s capital result from operating cash flows. A firm fails when its working capital becomes negative. This model further assumes that firms are isolated from financial markets and must finance losses by selling assets (Wilcox, 1973). Despite its simplicity, the gambler’s ruin model represents an important step forward by incorporating book values instead of liquidation values, thereby improving the empirical applicability of bankruptcy models (Borch, 1967; Santomero & Vinso, 1977; Tinsley, 1970).

Both approaches assume that companies can access external capital to cover losses by issuing debt or equity, thus remaining in business indefinitely. Under this assumption, firms remain solvent as long as their market value is positive, even if operating results are ignored (Scott, 1976, 1981). To address these limitations, empirical methods have since been developed to more accurately discriminate between firms that fail and those that remain solvent, making bankruptcy modeling increasingly consistent with real-world data.

According to Kliestik et al. (2017), academic research on business survival began in the 1930s with Paul Joseph FitzPatrick, who conducted a comparative analysis of financial ratios between solvent and failing companies (FitzPatrick, 1932). The earliest predictive models of corporate bankruptcy employed univariate regression analysis (Beaver, 1966). Although these methods were useful as an initial approximation, they proved insufficient, as multiple factors influence business failure. This limitation led to the development of a wide range of multivariate techniques.

These early analyses provided the foundation for later survival models. One of the most influential was Altman’s (1968) model, which identified a linear combination of variables to discriminate between failing and surviving firms. The model gained broad acceptance among financial institutions during the 1980s. Other statistical regression approaches followed, such as Ohlson’s (1980) logistic regression model. Overall, the most widely used statistical techniques for predicting business failure include multiple discriminant analysis, logistic regression, and survival analysis.

A variety of factors have been explored in relation to the probability of business survival. The most commonly examined internal variables include firm size, financial structure, performance, and liquidity metrics (Ohlson, 1980). Human capital–related aspects have also received attention (Amankwah-Amoah, 2015). Regarding external factors, researchers have studied the effects of crisis contexts (Udenio et al., 2015), market conditions (Chiu et al., 2013), and business networks (Tobback et al., 2017).

Early literature also focused on the entry of new firms into markets, framing entry and exit as normal and simultaneous processes within the economic cycle (Evans & Siegfried, 1992; Love, 1996). Firm size—often measured by investment in assets—can delay market exit but may also increase insolvency risk (Renski, 2011). Although the relationship between firm age, size, and survival has been well established, empirical validation has largely been confined to the manufacturing sector (Dunne & Hughes, 1994; Geroski, 1995; Sutton, 1997).

Some studies suggest that failure can occur not only among firms facing financial distress but also among profitable companies (Wennberg et al., 2010). While profitability is generally assumed to promote growth and reduce insolvency risk, rapid expansion may, under certain conditions, undermine survival prospects (Delmar et al., 2013).

The above literature review identifies several factors relevant to the survival or failure of firms. Based on prior empirical research, a set of variables has been selected that may influence business continuity and can be managed strategically to mitigate insolvency risk.

The Kaplan–Meier estimator is one of the most widely used survival analysis techniques because it is nonparametric and imposes very few restrictions. Its only assumption is that censored observations continue to behave similarly to uncensored ones until the event of interest occurs. This condition, known as noninformative or random censoring, applies when each observation has a censoring time that is independent of the event being studied. The observed survival time is therefore the minimum between the censoring time and the event (Efron, 1988).

To implement the model, all survival times are arranged from the shortest to the longest, with the goal of determining the number of exits and censored observations over time. For each period, the survival function provides an estimate of the individual probability of survival (Jenkins, 2005). It is assumed that the time axis can be divided into a sequence of contiguous, nonoverlapping intervals whose limits are a₀ = 0, a₁, a₂, a₃, …, a_k. These intervals are represented as follows:

Time was discretized into yearly intervals, with calculations for year j based on (a_j-1, a_j). Survival analysis seeks to obtain a time-dependent function whose value represents the probability that the event of interest will occur. This failure function, F(t), before the start of year j, is expressed as:

The survival function, derived from the hazard function, gives the probability that a failure will not occur. The probability of survival up to time t is therefore:

The survival function at the end of year j is:

Finally, the probability of exiting the market within a given interval is calculated as:

The complementary log–log (cloglog) model estimates the parameters that describe risk over a continuous period, taking into account the discrete-time nature of the survival data (Jenkins, 2005). The discrete-time interval hazard function, h(a_j,X)—also written as h_j(X)—is defined as:

This expression can be transformed into:

or equivalently:

Here, γ_j represents the logarithm of the difference between the integrated baseline hazard θ(t) evaluated at the beginning and end of the interval (a_j−1, a_j). The transformation log(–log(.)) corresponds to the complementary log-log conversion.

The sample consists of 249 enterprises classified as SMEs in the province of Málaga, observed over a ten-year period from 1996 to 2005. Among these, 128 firms went bankrupt, whereas 121 remained in operation or were dissolved for reasons unrelated to bankruptcy. Based on the censored data, no firm failures occurred before 1999, which ensures that firms surviving fewer than four years were excluded from the analysis.

Because of incomplete regional data for bankrupt companies, national-level information for Spain was used. The source of the economic and financial data is the SABI (Sistema de Análisis de Balances Ibéricos) database. The dataset includes 18 variables—nine derived from firms’ financial statements and nine binary variables representing qualitative characteristics—yielding a total of 2,047 panel observations.

The dataset is unbalanced, meaning that not all firms are observed for every year. Some companies were dissolved before the end of the study period, whereas others were incorporated after 1996, the initial year of observation.

Table 1 presents the descriptive statistics, including the number of observations, mean, median, standard deviation, range, and coefficient of variation.

None of the variables follow a normal distribution. The coefficients of variation are relatively high, indicating the presence of outliers. Consequently, the median provides a more accurate measure of central tendency than the mean, as the latter is susceptible to distortion by extreme values.

Table 2 presents the results of the median test comparing two groups of observations: bankrupt firms and active firms. Because the assumption of normality is not satisfied, the nonparametric Mann–Whitney Z statistic is used (Peña, 2008).

For all indicators except debt and personnel costs over revenues, the median is higher for firms that remain active than for those in their final year before bankruptcy. This pattern holds for equity, fixed assets, working capital, financial result, EBITDA, ROA, and the solvency ratio. The opposite relationship is observed for debt and personnel costs over revenues, whose medians are lower for firms that remain active than for those facing bankruptcy.

The test confirms that significant differences exist in the central values of all variables between the operating and insolvency years, except for working capital. The most pronounced differences appear in ROA and EBITDA. Working capital is the only variable that does not exhibit statistically significant median differences.

Table 3 and Figure 1 present the results of the survival analysis, showing the number of firms remaining over time and the estimated Kaplan–Meier survival function.

The probability of survival is highest during the fourth and fifth years and decreases steadily thereafter, reaching 48.6% by the ninth and tenth years. The sharpest decline in survival occurs between the sixth and seventh years. From the eighth year onward, the survival curve levels off, indicating that firms that reach this stage tend to develop the financial capacity and industry experience needed to maintain, or only slightly reduce, their probability of survival over time.

Figure 2 presents the smoothed estimate of the hazard coefficient. From the sixth year onward, the risk of failure increases substantially, reaching its peak during the sixth and seventh years. Shortly after the eighth year, the risk begins to stabilize, indicating that from this point onward, firms maintain a relatively constant probability of failure over time.

Table 4 presents the results of the complementary log–log (cloglog) logistic regression, showing the ratios and relative weights of the independent variables associated with business failure. The model is statistically significant overall, and all examined factors display a substantial relationship with bankruptcy outcomes.

An inverse relationship is observed for equity, ROA, debt, fixed assets, financial result, and EBITDA, indicating that increases in these variables reduce the probability of bankruptcy (i.e., increase the likelihood of survival). Conversely, a direct relationship is found for working capital, personnel expenses over revenue, and the solvency ratio, meaning that higher values in these variables increase the probability of bankruptcy (or decrease the likelihood of survival).

The hazard ratio indicates the change in the probability of failure associated with a one-unit increase in an independent variable. For the inversely related factors, a one-unit increase in ROA is associated with a 0.00057% reduction in the hazard function, multiplying the probability of survival by 2.65. For equity, fixed assets, and EBITDA, the probability of not failing increases by a factor of 2.72, while for debt and financial result it increases by 2.71.

Among the directly related factors, a one-unit increase in the solvency ratio corresponds to a 0.00745% increase in the hazard function, multiplying the probability of failure by 2.74. Similarly, for working capital and personnel expenses over revenue, the probability of bankruptcy increases by a factor of 2.72.

This study identifies key financial and managerial factors influencing the survival of small and medium-sized enterprises (SMEs). Using survival analysis based on the nonparametric Kaplan–Meier estimator and complementary log–log logistic regression, the findings confirm that firm survival depends on both structural and managerial elements beyond traditional financial ratios. Financial structure, return on assets, EBITDA, and human capital productivity emerge as positive predictors of business longevity, whereas excessive working capital is negatively associated with survival. These results extend the literature on firm survival by incorporating underexplored variables—such as extraordinary financial results and employee cost productivity—and by linking quantitative modeling with theories of strategic management and organizational performance (Jackson et al., 2013; Verwijmeren & Derwall, 2010).

The study provides managers and policymakers with evidence-based insights to enhance financial and strategic decision-making. The results highlight measurable performance indicators that can serve as early warning systems to identify vulnerability and prevent insolvency. They also underscore the importance of aligning financial structure and human capital productivity to strengthen organizational resilience and optimize resource efficiency. These implications are particularly relevant for SMEs operating across diverse institutional and economic contexts (Gemar et al., 2019; Serer et al., 2009).

Although the dataset originates from a specific regional context, the methodological framework and variables analyzed are generalizable to a broad range of business environments. Future research could expand this approach by integrating qualitative dimensions such as innovation, digital transformation, and environmental, social, and governance (ESG) factors to deepen understanding of firm resilience in dynamic markets. Cross-country comparative analyses would further strengthen the external validity of these findings and illuminate institutional differences that shape SME survival.