Firm-Specific, Macroeconomic and Institutional Determinants of Stochastic Uncertain Firm Growth

Abstract

This study distinguishes between observed, uncertain, and stochastic uncertain firm growth. Observed firm growth is measured via historical growth of fixed assets scaled by growth of sales revenue. Uncertain firm growth is the volatility of unobserved (estimated error terms) firm growth. The latter is simulated using nonuniform Monte Carlo to generate stochastic uncertain firm growth. The objective of this study is to examine the relationships among the firm specific, economic, and institutional factors that affect the uncertain and stochastic uncertain growth of a firm. The sample includes the nonfinancial firms listed in the DJIA30 and NASDAQ100, covering quarterly data from 1996Q1 to 2022Q4 for 121 companies. The results reveal that (a) sales growth, profitability, cash flow, and long-term financing help reduce a firm’s uncertain growth, (b) high involvement in exporting exposes firms to higher geopolitical uncertainty, (c) institutional quality (especially political stability and regulatory quality) paradoxically contribute to uncertain firm growth. This study contributes to related studies via offering perspectives to firm managers and policy makers about the factors that help manage the uncertainties of firm growth.

1. Introduction

The determinants of firm growth must consider the distinction between planning for growth and the actual occurrence of growth. Empirically, the latter is plausibly accompanied by uncertainty. Previous studies on the determinants of firm growth have focused on the first aspect of growth, which is related to the determinants (usually resources) of firm growth. Intrinsically, this is historical growth that is affected by market forces such as changes in labor and invested capital as well as barriers such as internal inefficiencies (Ponikvar et al. 2022).

As actual firm growth is intrinsically composed of two components: observed and unobserved, the latter usually matters when planning for subsequent growth. Related studies on the determinants of firm growth have reached well-established determinants. Nevertheless, unobserved firm growth remains of significant research interest, reflecting the difference between firm’s observed and predicted growth. The latter is due to variety of factors that can be classified into firm-specific, macroeconomic factors and institutional factors. This study takes a step forward by examining the volatility of the unobserved firm growth, which is referred to as uncertain firm growth. The latter offers empirical benefits to a firm’s management in terms of redesigning plans and/or resources to manage uncertain firm growth. These benefits can be further illustrated considering the stochastic specification of uncertain firm growth being not under a firm’s control, such as macroeconomic and institutional factors.

1.1. Objectives

This study aims to examine how firm specific, economic, and institutional factors affect the uncertainty and stochastic uncertainty of firm growth.

1.2. Contribution

Although many studies have examined the impact of several determinants of observed firm growth, the relationship between these determinants and uncertain firm growth remains extensively underexplored. Therefore, this study contributes to previous studies in two ways. First, this study examines the determinants of the uncertain, rather than observed firm growth, as uncertain growth is a critical component for business planning. Second, this study further examines the behavior of uncertain firm growth via stochastic nonuniform normal Monte Carlo simulation, which adds value to the modeling of the uncertainty of firm growth.

1.3. Measuring the Uncertainty of Firm Growth

This study extends the benefits of measuring firm growth as the weighted growth of fixed assets (Eldomiaty et al. 2023) as follows:

$${\mathrm{Weighted} \mathrm{Growth} \mathrm{of} \mathrm{Fixed} \mathrm{Assets}}_{\mathrm{t}} = \ln \left({\displaystyle \frac{{\mathrm{FA}}_{\mathrm{t}}}{{\mathrm{FA}}_{\mathrm{t}-1}}}\right){\displaystyle \frac{{\mathrm{sales} \mathrm{revenue}}_{\mathrm{t}}}{{\mathrm{Max} \mathrm{sales} \mathrm{revenue}}_{\mathrm{n}}}}$$

(1)

${\mathrm{Max} \mathrm{sales} \mathrm{revenue}}_{\mathrm{n}}$ is the maximum sales revenue at a certain period of time. This variable is computed as rolling quarterly from 1996Q1 to 2022Q4. ${\mathrm{FA}}_{\mathrm{t}}$ and ${\mathrm{FA}}_{\mathrm{t}-1}$ refer to fixed assets in quarters t and t−1, respectively. The measurement of the uncertainty of firm growth follows previous studies (Aizenman and Marion 1999; Bo 2002; Fiori and Scoccianti 2023; Kim et al. 2022; Ghosal and Loungani 1996, 2000) as follows:

$$G_{ft}={\alpha }_0+{\beta }_1{G}_{ft-1}+{\beta }_2{\epsilon }_t$$

(2)

$${\epsilon }_{t+1}={\beta }_3{\epsilon }_t+{\nu }_{t+1}$$

(3)

where $G_{ft}$ = weighed growth of the firm, ${\epsilon }_t$ = unobservable determinants of growth of the firm, ${\epsilon }_{t+1}$ = the future value of growth of the firm, and ${\nu }_{t+1}$ = the idiosyncratic firm growth, which is equivalent to the unexpected growth of the firm. Uncertain growth is calculated for each firm as the rolling variance of ${\nu }_{t+1}$.

Statistically, the error term in Equation (2) represents the unobserved components of firm growth, which are usually affected by exogeneous factors that are related to macroeconomic and/or institutional factors. As these factors are not under a firm’s control, they reflect uncertainty about firm growth, which is usually measured by the rolling standard deviation of error terms demonstrated in Equation (3). Figure 1 conceptualizes the estimation process and distinguishes uncertain and stochastic uncertain firm growth.

1.4. How Does Observed Firm Growth Differ from Uncertain Firm Growth?

The observed firm growth (weighted fixed assets) is computed via Equation (1). Uncertain firm growth is estimated via Equation (3). The comparison between observed and uncertain firm growth can be carried out via skewness. The latter is a convenient metric (Doane and Seward 2011; Ijiri and Simon 1997) for measuring the trend of observed and uncertain firm growth. The authors computed the skewness for each firm during the period 1996Q1–2022Q4. Figure 2 depicts the trend of each estimated growth. Note that the estimates of observed firm growth are arranged in an ascending order to facilitate the comparison between the trends of observed and uncertain firm growth.

Figure 2 is generated as follows. For every respective firm, the skewness of both observed and uncertain firm growth (using Equation (3)) are computed over the period 1996Q1–2022Q4. Therefore, for a single firm, the skewness at 2022Q4 indicates the trend of observed and uncertain firm growth. The next step is to arrange the skewness of only observed firm growth in an ascending order. Therefore, firms at the far left (right) are those associated with the smallest (largest) skewness of observed firm growth. The figure shows that uncertain firm growth (weighted fixed assets growth) is much more volatile for every firm during the period 1996Q1–2022Q4. This can be considered a convenient call for examining the determinants of uncertain growth of the firm.

1.5. Empiricism of Stochastic Firm Growth

The foundation of the behavior of firm growth as stochastic has been treated by Romer (1990), who assumed that expected market conditions determine expected firm growth. As market conditions are uncertain, stochastic treatment of firm growth is plausible, leading to empirical conclusions. Therefore, heterogeneity is an integral part of firm growth (Holly et al. 2013; Davis et al. 2025). Firm growth has been stochastically examined, assuming that firm size is iid (independently and identically distributed). This conclusion is empirically weak, as firm growth deviates from the assumption of normality (Jensen and Reichstein 2003). Therefore, realized firm growth cannot be predicted symmetrically. Arata (2019) and Alfarano et al. (2012) reported that the Laplace distribution is convenient for modeling firm growth characterized by large jumps. This is an extended argument that firm growth must be examined stochastically. Consequently, uncertain firm growth remains a significant concern for firm managers. In addition, stochastic firm growth has its own intrinsic significance, as growth is usually associated with a probability of occurrence (Bottazzi and Secchi 2003a; Reginster 2021). As classic studies of the distributions of firm size have treated size and firm growth interchangeably, stochastic treatment has been found to be convenient for the mechanics of firm growth in major European industrial economies (Barbosa and Eiriz 2011; Bottazzi et al. 2002, 2011; Bottazzi and Secchi 2003b, 2006; Luttmer 2011; Duschl 2014; Fu et al. 2005; Duschl 2014; Riccaboni et al. 2008).

1.6. How Does Uncertainty Differ from Stochastic Uncertain Firm Growth?

As the uncertainty of firm growth implies estimated error terms, the effectiveness of the management of firm growth requires a simulation of uncertain firm growth to examine the stochastic characteristics of uncertainty. The authors carried out nonuniform normal distribution Monte Carlo simulations for the estimates of uncertain firm growth (Kadry 2015). The simulation is carried out for every firm independently, taking into consideration the firm’s mean and standard deviation (volatility) of the uncertain components of firm growth. The simulated uncertain firm growth takes the form that follows:

$${\widehat{S}}_t=\epsilon$$

(4)

where ${\widehat{S}}_t$ is the stochastic uncertain firm growth. $\epsilon$ is the Weiner process that follows random normal distribution with $\mu$ and $\sigma$ = average and standard deviation of uncertain firm growth respectively. The number of runs for every firm equals the number of quarters (108). The benefit of firm-level nonuniform simulation is to develop an empirical probability distribution that fits each respective firm’s uncertain growth.

The stochastic characteristic of uncertain firm growth has significant empirical implications. That is, the statistical estimation of uncertain firm growth is actually the unobserved components of firm growth which have been recognized and examined in related literature as probabilistic. Therefore, a stochastic treatment of uncertain firm growth reflects probabilistic uncertainty of firm growth. The trends (skewness) of uncertain and stochastic uncertain firm growth from 1996Q1 onward until 2022Q4 are depicted in Figure 3.

Figure 3 is generated as follows. The skewness of both uncertain (using Equation (3)) and nonuniform stochastic uncertain firm growth are computed for every respective firm over the period 1996Q1-2022Q4. Therefore, for a single firm, the skewness at 2022Q4 indicates the trend of both the uncertain and stochastic uncertain firm growth. The next step is to arrange the skewness of only uncertain firm growth in an ascending order. Therefore, firms at the far left (right) are those associated with the smallest (largest) uncertain firm growth. Figure 3 shows disparities among firms between uncertain and stochastic uncertain growth. As uncertain growth increases, stochastic uncertain growth is greater than uncertain growth for a number of companies and vice versa for other companies. The relative magnitude of the skewness of uncertain growth versus stochastic uncertain growth can be further illustrated via simple statistics of the sample firms. That is, 76.85% (93/121) of the sample firms are associated with positive skewness of stochastic uncertain firm growth greater than the skewness of uncertain firm growth. Therefore, scholars as well as firm managers need to further examine the determinants of stochastic uncertain firm growth.

The rest of the study is organized as follows. Section 2 reviews the related literature that discusses the findings of related studies on the effects of firm specific, economic, and institutional determinants on firm growth. Section 3 describes the data, variables, and statistical estimation methods. Section 4 discusses the results. Section 5 presents the conclusions.

2. Literature Review

Previous studies have discussed a variety of factors that affect firm growth, including short-term liquidity, internal funds, product innovation, and the age of the firm (Lee 2023; Erdogan 2023). Furthermore, external factors such as external financing are determinantal to expansion plans and thus the growth of the firm. Recent studies have shown that economic and institutional factors, such as infrastructure quality, foreign direct investment, and stable economic conditions, are positively correlated with firm growth (Burger et al. 2024). In addition, institutional factors (i.e., political uncertainty and business cycle fluctuations) contribute to the unpredictability of firm growth (Gulen and Ion 2016). Accordingly, the abovementioned interplay between firm-wide, economic-wide, and institution-wide factors has complex effects reshaping the uncertainty surrounding the growth of the firm.

The authors of this study argue that two reasons warrant further examination of firm growth. The first reason is related to the theory of firm growth, which combines internal (firm-wide) and external (economic and institutional) influences (Penrose 2009). The second reason is related to viewing a firm as a nexus of contracts between the firm and its stakeholders in a variety of markets (Oaki et al. 1990; Jankovic 2010). As uncertainty is an intrinsic component of business decisions (Geroski et al. 1997), the growth of a firm requires an examination of the uncertain component of growth. Larger firms can maintain stability through better management of uncertainty (Demirhan and Yüncüler 2017). Nevertheless, along the path of growth, further limitations have also been examined. For example, excessive debt can introduce financial risks that hinder innovation and limit growth (Yadav et al. 2021; Hermelo and Vassolo 2007; Mowery 1983).

As firms age, they often face challenges related to a lack of knowledge and operational inefficiencies, but can benefit from established market positions, better resource utilization, capital access, and a strong brand reputation, which can foster growth (Shanmugam and Bhaduri 2002). Furthermore, as firm size increases, uncertainty decreases, leading to a more stable environment. In competitive markets, risk-neutral firms may increase investment in uncertain environments, but state-owned enterprises (SOEs) are less affected by government backing (Khan et al. 2019, 2020). The impacts of uncertainty are also associated with the nexus of firm specific, industry-specific, and institutional factors. That is, older firms, exporters, foreign-owned companies, and those in manufacturing are less affected by both demand and financial shocks than their younger, nonexporting, domestically owned, and service-sector counterparts are (Lourenço and Cerdeira 2024).

The following review of related studies offers a synthesis that is derived from the measure of firm growth as weighted growth of fixed assets (Equation (1)). This synthesis includes the role of firm’s assets (as a common measure of firm size), firm liquidity, and firm stock liquidity. The latter are used empirically as sources of financing firm growth.

2.1. The Impact of Size on Firm Growth

Studies of the impact of firm size (Evans 1987; Bachmann et al. 2021; Coad and Hölzl 2009; Calvino et al. 2018) illustrate that larger firms tend to have more stable growth and lower uncertainty due to their available resources and stable operations, which help them manage uncertainty and navigate unpredictable environments. Adelman (1958) supports the negative relationship between firm size and stochastic uncertainty, as when firms grow larger, their operational stability increases, especially in the iron, steel, and manufacturing industries. The opposite conclusions have been reached for smaller firms because they are exposed to market volatility (Ballantine et al. 1993). Additionally, smaller firms tend to decrease investments during uncertain times, as seen after the global financial crisis, further worsening their vulnerability (Lensink et al. 2005). Accordingly, the abovementioned literature helps develop the following hypothesis.

H1: 

There is a negative relationship between size and the uncertainty of firm growth.

2.2. The Impact of Firm Liquidity on Firm Growth

Studies that examined the impact of firm liquidity on firm growth have revealed the significance of cash management in sustaining growth, particularly under financial constraints (Alshehadeh et al. 2023; Bottazzi et al. 2012; Gill and Mathur 2011; Mateev and Anastasov 2010; Mukherjee and Sen 2018). However, linking these factors to the concept of uncertain firm growth is relatively rare, except for Fagiolo and Luzzi (2006), who suggest that higher liquidity challenges increase uncertainty in a firm’s growth trajectories. Accordingly, the abovementioned literature helps develop the following hypothesis.

H2: 

There is a negative relationship between firm liquidity and the uncertainty of firm growth.

2.3. The Impact of Stock Market Liquidity on Firm Growth

Roll (1984) argues that larger firms with higher stock trading volumes benefit from efficient capital allocation because lower transaction costs (such as bid–ask spreads) help firm growth by fostering stable market equilibrium. Amihud (2002) explored how stock illiquidity, dividend yields, and volatility affect expected returns, concluding that illiquidity increases stock returns over time. However, larger firms experience less illiquidity risk and lower expected returns, which help stabilize their growth during periods of uncertainty. Næs et al. (2011) conclude that stock market liquidity provides better predictions of economic conditions during economic downturns. That is, reduced liquidity hinders GDP growth, increases unemployment, and decreases firm investment while triggering a “flight to quality”, where investors shift to safer assets. Accordingly, the abovementioned literature helps develop the following hypothesis.

H3: 

There is a positive relationship between firm stock liquidity and the uncertainty of firm growth.

2.4. The Impact of Macroeconomic Conditions on Firm Growth

Poudel (2017) concludes that GDP growth and money supply positively influence sales growth, thereby promoting firm growth. In contrast, the real interest rate has a negative effect on sales growth due to the high cost of borrowing, leading to a decrease in firm growth. Realized and expected inflation rates are found to have a negative impact on firm growth due to the unpredictability of changing costs that affect a firm’s revenue (Borraz and Gianelli 2010; Brida et al. 2024). Malinić et al. (2020) conclude that in less developed countries such as in Poland, Hungary, the Czech Republic, and Slovakia, capital market liquidity has a greater impact on growth, leading firms to rely more on internal cash flow. Inflation had a neutral effect in Bosnia and Herzegovina, Croatia, North Macedonia, Montenegro, Slovenia, and Serbia, leading to uncertainty and risk. Gulen and Ion (2016) reported that demand uncertainty negatively impacts the growth and investment of a firm because of costly irreversibility, particularly in industries with high capital intensity and sunk costs. Moreover, Khan et al. (2020) conclude that economic policy uncertainty has a significant and negative effect on investment, although firms with redeployable assets are less affected. Zhang et al. (2021) examined the role of interest rates (treasury bills) and concluded that increases in long-term interest rates lead to greater stock market volatility by increasing borrowing costs. Accordingly, the abovementioned literature helps develop the hypotheses that follow.

H4: 

There is a negative relationship between inflation and the uncertainty of firm growth.

H5: 

There is a positive relationship between GDP growth, the business cycle, and the uncertainty of firm growth.

H6: 

There is a positive relationship between interest rates and the uncertainty of firm growth.

2.5. The Impact of Institutional Factors on the Growth of Firms

Shehu et al. (2024) conclude that strong institutional quality, including accountability and rule of law, positively impacts private sector investment, whereas corruption increases uncertainty and negatively affects investment, which ultimately influences the growth of the firm. Lourenço and Cerdeira (2024) and Dubey and Das (2021) show that corruption may negatively affect market performance, although it may also have positive effects on operational activities. Gulen and Ion (2016) conclude that institutional and policy uncertainty affect growth trajectories negatively. In addition, Kang et al. (2014); Firth et al. (2013), and Wang et al. (2014) conclude that policy shifts have resulted in challenges for firms in developing and transition economies in terms of firm share price, financing choices, and firm value. Bhattacharya et al. (2017) also stated that, because of uncertainty of government regulations, firms choose the option to wait to invest, leading to the irreversibility of investment in intangible assets. Accordingly, the abovementioned literature helps develop the following hypothesis.

H7: 

There is a negative relationship between institutional quality and the uncertainty of growth of a firm.

3. Data, Variables, and Estimation Methods

The data includes the nonfinancial firms listed in the Dow Jones Industrial Average index (DJIA30) and the National Association of Securities Dealers Automated Quotations (NASDAQ100). The data are obtained from the Reuters Finance database© (https://www.reuters.com/markets/) for the period 1996Q1–2022Q4 (accessed on 21 July 2023).

The conceptual framework of the methodology is based on classifying the potential influences of uncertain firm growth into three groups, namely, firm-specific, macroeconomic, and institutional. The three groups represent the internal and external environment of a business firm.

3.1. Dependent Variables

Two dependent variables are examined: (a) the uncertainty of weighted firm growth and (b) the stochastic simulated uncertain growth via Monte Carlo nonuniform simulation carried out for each firm individually.

3.2. Independent Variables

The independent variables are classified into firm-specific determinants, economic determinants and institutional determinants of firm growth. In addition, this study examines the effect of industry classification on the uncertainty of firm growth (Aggarwal 2015). These studies have reached relatively, and to a large extent, common factors that are currently recognized in the related literature as determinants of firm growth, as shown in

Table 1. The variables examined in this study.

	Variables	Measurement
Firm-specific variables	Size of the firm	Natural log of total Assets (Evans 1987; Calvino et al. 2018; Gill and Mathur 2011)
	Growth in Earnings before tax	${\displaystyle \frac{{\mathrm{EBT}}_{\mathrm{t}}{\text{-}\mathrm{EBT}}_{\mathrm{t}-1}}{{\mathrm{EBT}}_{\mathrm{t}-1}}}$ (Kaur 2024; Liu and Hsu 2006)
	Liquidity Ratio	Current Asset/Current Liability (Kaur 2024; Gill and Mathur 2011)
	Fixed Asset Turnover	Net sales revenue/average Fixed assets (Kaur 2024; Rabinovich 2023)
	Current Asset Turnover	Net sales revenue/average Current assets (Kaur 2024)
	Age of the firm	Number of years since establishment (Age (Glancey 1998; Coad et al. 2013)
	EBIT Margin	EBIT/Total Revenue (Feeny and Rogers 1999)
	Debt to Equity Ratio	Total Liabilities/Shareholder’s Equity (Feeny and Rogers 1999)
	Tobin Q ratio	Market Value of Firm/Replacement Cost of Assets (Feeny and Rogers 1999; Danbolt et al. 2010)
	Capital intensity	Majudmar (1997)
Macroeconomic Variables	Inflation Rate	Quarterly % change in CPI (Poudel 2017; Malinić et al. 2020)
	Capital Market Illiquidity	Relative spread being measured as the ratio of ask–bid stock price to the average of ask–bid price. (Næs et al. 2011)
	Natural Rate of Unemployment	Natural unemployment/Total employment (Næs et al. 2011)
	Real GDP Growth Rate	$\begin{array}{l}{\displaystyle \frac{{\mathrm{Real} \mathrm{GDP}}_{\mathrm{t}}{\text{-}\mathrm{Real} \mathrm{GDP}}_{\mathrm{t}-1}}{{\mathrm{Real} \mathrm{GDP}}_{\mathrm{t}-1}}}\\ {\mathrm{Real} \mathrm{GDP}}_{\mathrm{t}}={\displaystyle \frac{{\mathrm{Nominal} \mathrm{GDP}}_{\mathrm{t}}}{{\mathrm{GDP} \mathrm{deflator}}_{\mathrm{t}}}}\end{array}$ (Poudel 2017)
	Interest Rate	Effective Federal Fund Rate (Zhang et al. 2021)
	Business Cycle	Skewness of quarterly GDP growth (Gulen and Ion 2016; Næs et al. 2011)
Institutional variables	World Governance indicators	Control of Corruption; Government Effectiveness; Political Stability & Absence of Violence; Regulatory Quality; Rule of Law; Voice & Accountability (Shehu et al. 2024) https://www.worldbank.org/en/publication/worldwide-governance-indicators (accessed on 21 August 2023)

The descriptive statistics of the independent variables are reported in Appendix A and Appendix B.

.

4. Discussion

This section includes statistical estimations regarding the impacts of firm specific, macroeconomic, and institutional variables on the uncertainty and stochastic uncertainty of firm growth. The results are reported in

Table 2. Firm-Specific and Institutional Determinants of Uncertain Firm Growth.

Variable	Model 1: Base Model Including Firm-Specific	Model 2: Base Model and Macroeconomic Factors	Model 3: Basic Model and Institutional Factors (WGI)	Model 4: Stochastic Uncertain Firm Growth
Constant	1.105173 (60.516) ***	1.166892 (30.804) ***	−6.247053 (−4.424) ***	1.2556 (1.7453) *
Realized Firm Growth Rates	0.015948 (4.8942) ***	0.014361 (4.9824) ***	0.012793 (4.492) ***	2.07 × 105 (0.0088)
Growth Rate of Wages	3.62 × 1011 (23.5365) ***	3.65 × 1011 (19.45613) ***	3.51 × 1011 (19.836) ***	4.01 × 1013 (0.2776)
13Firm Size (Ln Total Assets)	−3.99 × 106 (−2.3313) **	4.8 × 105 (6.1788) ***	0.000111 (14.040) ***	4.73 × 108 (0.01171)
Growth of Earnings before Taxes	−1.58 × 1045 (−8.571) ***	−1.65 × 1045 (−9.0181) ***	−1.72 × 1045 (−9.0170) ***	−4.55 × 1046 (−2.9253) ***
EBDIT Margin	−9.5 × 109 (−4.4513) ***	−8.83 × 109 (−3.4952) ***	−8.31 × 109 (−3.3192) ***	−1.88 × 108 (−2.4112) ***
Cash Flow to Total Assets	−6.88 × 1041 (−10.124) ***	−2.16 × 1041 (−2.5520) **	−8.07 × 1041 (−8.6167) ***	1.11 × 1041 (1.0626)
Sales Revenue Growth Rate	1.68 × 107 (1.25412)	3.71 × 107 (0.98822)	3.85 × 107 (0.8435)	−2.41 × 107 (−2.2252) **
Retention Ratio	1.16 × 1011 (2.2696) **	2.03 × 1011 (1.2031)	1.84 × 1011 (1.0468)	4.96 × 1012 (1.2745)
Liquidity Ratio	7.58 × 1010 (5.2272) ***	8.84 × 1010 (4.05145) ***	8.69 × 1010 (4.1257) ***	−1.58 × 1010 (−1.5674)
Long Term Finance	−0.004423 (−60.0246) ***	−0.004623 (−53.883) ***	−0.00482 (−46.917) ***	−0.000105 (−0.2607)
Debt-to-Equity Ratio	1.09 × 1013 (3.3616) ***	1.01 × 1013 (3.6748) ***	1.17 × 1013 (5.022) ****	−2.32 × 1014 (−2.4475) **
Fixed Assets Turnover	−6.79 × 109 (−0.72146)	5.33 × 108 (2.25907) **	9.48 × 108 (2.7037) ***	−5.29 × 1010 (−0.0241)
Current Assets Turnover	4.71 × 1011 (0.341161)	−2.08 × 1010 (−0.44518)	6.85 × 1011 (0.08924)	1.07 × 109 (0.6629)
Capital Intensity	0.003024 (0.85454)	0.0013 (0.43476)	0.000284 (0.1163)	0.001091 (1.0701)
Tobin Q Ratio	−6.11 × 1010 (−3.0902) ***	−6.11 × 1010 (−3.0852) ***	−6.07 × 1010 (−3.0859) ***	−6.97 × 1011 (−0.4447)
Inflation Rate		−515.0312 (−1.1103)		168.071 (0.70204)
Relative Spread		1.36177 (5.0158) ***		0.2433 (2.0662) **
Stock Illiquidity Ratio		2.63 × 101 (0.10649)		−1.84 × 108 (−1.0047)
Implicit Spread Estimator		−0.000692 (−0.9913)		−0.000728 (−2.0152) **
Natural Rate of Unemployment		188.110 (3.9203) ***		19.1018 (0.3381)
GDP Growth Real		879.96 (0.7694)		59.146 (0.122151)
Effective FFR		71.6917 (2.6002) **		−13.1177 (−0.78491)
Net Exports of Goods and Services		0.02582 (0.11179)		0.216525 (2.9089) ***
Stock Market Skewness		0.00434 (0.4146)		0.003452 (0.7056)
Business Cycle		0.00241 (0.7949)		0.0003 (0.2191)
Economic Policy Uncertainty		−0.0287 (−3.286) ***		0.004871 (1.1376)
Control of Corruption: Percentile Rank			0.134889 (1.52922)	0.06081 (0.6648)
Government Effectiveness: Percentile Rank			0.103155 (0.66352)	−0.13990 (−1.2309)
Political Stability: Percentile Rank			0.034671 (4.4406) ***	−0.00896 (−1.3317)
Regulatory Quality: Percentile Rank			0.341999 (3.1215) ***	0.0308 (0.5993)
Rule of Law: Percentile Rank			0.04184 (0.11503)	0.10641 (0.718984)
Voice and Accountability: Percentile Rank			0.956762 (12.232) ***	−0.052993 (−0.6849)
Industry Dummy	Yes	Yes	Yes	Yes
Adjusted R-squared	0.827122	0.800431	0.796214	0.790206
S.E. of Regression	1.775302	1.454672	1.396973	1.551689
Durbin–Watson Stat	0.184303	0.132753	0.119743	2.033521
Mean Dependent Var	3.733241	2.48034	2.26366	2.886373
S.D. Dependent Var	3.511758	2.923884	2.847541	2.751794
Sum Squared Resid	39,610.54	26,571.5	24,515.18	30,219.52
J-Statistic	2.11 × 10−16	2.30 × 10−16	4.07 × 10−6	4.96 × 10−6

* Significant at 10%; ** Significant at 5%; *** Significant at 1%.

.

4.1. The Impact of Firm Specific, Macroeconomic, and Institutional Determinants on the Uncertain Growth of the Firm

The dependent variable is a firm’s uncertain growth. The independent variables are determinants of firm growth classified into three groups, namely, firm-specific determinants, economic determinants, and institutional determinants. Model 1: The firm-specific and economic determinants of uncertain growth of the firm. Model 2: The institutional determinants of uncertain growth of the firm; Model 3: The firm specific, economic and institutional determinants of uncertain growth of the firm. The results of the RESET test (Ramsey 1969) show that a nonlinear model fits the data (F statistic = 5.469859 df = 1, 12,708; p value = 0.0194). Therefore, quadratic estimation is carried out. The Hausman test results show that all the models fit fixed effects as the p-value associated with the test is less than 5%. Accordingly, industry dummies are included. The results for the Breusch–Pagan/Cook–Weisberg test for heteroskedasticity (Breusch and Pagan 1979) show that the variances of residuals are not constant, requiring a robust estimation of the model’s parameters [${\chi }^2$(34) = 79.10001; p value = 0.0000]. The results of the endogeneity tests (Appendix C) show that all the variables except three (firm size, capital intensity, and the Tobin’s Q ratio) are not endogenous, indicating that the cited determinants of firm growth uncertainty are good predictors. Accordingly, GMM is a convenient estimation method. The results of structural break Chow test (Appendix D) show that the 2008 financial crisis did not have significant effect on either uncertain or stochastic uncertain firm growth.

4.1.1. The Impact of Firm-Specific Factors on Uncertain Firm Growth

The results in Table 2 show that the positive and significant estimate of realized growth rates extends the abovementioned results that firm uncertain growth is derived, intrinsically, from realized growth. Nevertheless, the insignificance of the expected (stochastic) effect of realized growth offers an indication that growth uncertainty may arise due to exogenous factors that are present and examined in this study as macroeconomic and institutional factors.

The results in Table 2 also have insightful implications for the size–uncertainty relationship. The negative size–uncertainty firm growth relationship in the base model extends the implications in previous studies. That is, as larger firms are able to influence demand and prices, uncertain growth can be reduced (Siddharthan et al. 1994; Narayanan 1998). Nevertheless, macroeconomic and institutional factors may not help a firm sustain that negative relationship. This is evident in models 2 and 3 when the size–uncertain growth relationship turns positive. The consistency of the positive impacts of size shows extended evidence that growth uncertainty is associated with large firms (Coad et al. 2013). Furthermore, Burger et al. (2017) and Lourenço and Cerdeira (2024) conclude that the size–uncertainty relationship remains consistent across industries, countries, and firm ages, highlighting the role of firm size in managing uncertainty effectively. This finding suggests that larger firms continue to grow despite uncertainty (Kim et al. 2022). Notably, the stochastic insignificant size–uncertainty growth relationship may not be persistent. The same stochastic insignificance is extended to the effects of wages (as a proxy for human contribution) on uncertain firm growth, although wages were a contributing factor to the growth of the US manufacturing sector from the 1920s to the 1940s (Mowery 1983). The abovementioned discussion leads to a rejection of hypothesis 1.

Firm profitability and cash flow offer persistent safeguards against uncertain growth even if uncertainty stems from macroeconomic and institutional surroundings. The results show negative effects of EBT, EBIT, and cash flow on uncertain firm growth. Furthermore, the stochastic negative effects of EB and EBIT are expected to prevail. The negative relationship between cash flow and firm growth is well established in both theory and empirical research, with higher cash flow—particularly when measured relative to total assets—consistently associated with reduced uncertainty in growth outcomes. Pecking order theory posits that firms prefer internal to external financing, making cash flow a critical enabler of growth by alleviating financial constraints (Gill and Mathur 2011; Mateev and Anastasov 2010). This conclusion is extended to other countries, such as Canada, across both the manufacturing and service sectors, where cash flow serves as a key predictor of firm expansion. Furthermore, Alshehadeh et al. (2023) and Mukherjee and Sen (2018) conclude that higher cash flow ratios not only support immediate investment but also strengthen liquidity, profitability, and leverage management, which are essential for sustaining growth and reducing its volatility. In uncertain environments, higher cash flows enable firms to maintain or even increase investment levels, reducing the impact of external uncertainty on growth trajectories (Khan et al. 2020). As such, an increased cash flow-to-total assets ratio emerges as a key financial metric in explaining and mitigating uncertainty in firm growth. The abovementioned discussion leads to a rejection of hypothesis 2. Nevertheless, the insignificant stochastic effects of cash flow extend the argument of Yadav et al. (2021) that as firms grow larger, the benefits diminish due to organizational inefficiencies and reduced innovation, particularly in firms with high leverage and asset tangibility. The stochastic negative effects of sales revenue growth offer extended support to this argument. These structural conditions, coupled with high debt levels and fewer growth opportunities, can lead profit-focused firms to transition into a low-growth, low-profit, poor position in the short term (Jang 2011). Furthermore, the positive effects of liquidity on uncertain firm growth indicate that excessive liquidity deprives firms from further growth.

In terms of debt financing, the negative effects of debt financing on uncertain firm growth indicate that greater reliance on long-term financing significantly reduces the uncertainty surrounding firm growth by providing stable capital for sustained investment and operational resilience (Liu and Hsu 2006; Ballantine et al. 1993). Further empirical findings across multiple economies confirm that higher levels of long-term debt—when strategically managed—lower the risk associated with future growth outcomes (Malinić et al. 2020; Anton 2016). Furthermore, Vuković et al. (2022) conclude that in capital-intensive sectors, long-term external financing is essential for overcoming structural challenges and reducing volatility (Mukherjee and Sen 2018). Cardao-Pito (2022) further observed that in uncertain markets, lower debt levels are perceived more favorably, often raising Tobin’s Q, while cautioning that capital structure may distort true growth signals. Nevertheless, the positive effects of debt-to-equity financing on uncertain firm growth indicate that large firms are not able to manage capital structure effectively enough. Interestingly, the negative stochastic effect of debt-to-equity financing (model 4), shows that an efficient management of capital structure may reduce firm uncertain growth. Taken together, these insights confirm that the more firms rely on stable, long-term financing, the lower the uncertainty associated with their growth trajectories.

The results offer a distinct difference between fixed and current assets turnover. That is, the general understanding is that high fixed asset turnover reflects high operational efficiency that impacts firm growth stability. The positive impacts of fixed asset turnover extend the conclusion reported in Rama (1999) and Gharaibeh and Sarea (2015) that when firms optimize asset utilization, the associated consequences include increased efficiency; increased net sales; and reduced operational, maintenance, and financing burdens, which ultimately promote sustainable growth. This positive impact implies that size helps reduce the unpredictability of firm growth. Notably, an extended advantage of using the weighted average growth of fixed assets in this study is to examine the uncertainty–investment relationship. Uncertain environments have been proven to be good environments for large firms to grow due to their ability to manage risks and maintain demand resources. The results of stochastic simulation (Model 4) show that a firm’s fixed asset turnover is a viable measure of investment policy to address uncertain firm growth. The insignificant effects of current assets turnover indicate that fixed assets are more influential than current assets in managing uncertain firm growth.

The significant and negative relationship between Tobin’s Q and uncertain firm growth extends the implications of previous related studies. That is, a high Tobin’s Q indicates that the market places a premium on a firm’s assets relative to their replacement cost, reflecting strong investor confidence in the firm’s future growth potential (Feeny and Rogers 1999; Jang 2011. In such cases, even firms with high internal cash flow face a greater likelihood of deteriorating performance, as limited viable investment opportunities result in inefficient capital allocation. This dynamic illustrates how uncertain growth prospects, especially under low Tobin’s Q conditions, can negatively affect a firm’s ability to achieve sustainable growth (Listiani and Supramono 2020). These findings show that while a high Tobin’s Q reflects strong growth potential, a low Tobin’s Q serves as a warning signal for declining investor confidence and uncertain growth, with potentially adverse implications for firm performance and investment outcomes (Kraft et al. 2017).

Notably, the majority of the coefficients of the industry dummy variables are positive and significant. Feeny and Rogers (1999) conclude that industry-specific and structural factors further shape the profit–growth relationship. Manufacturing firms, which constitute the majority of the firms examined in this study, tend to be more profitable but exhibit lower average growth. Overall, profit margins can be considered key drivers of growth, particularly under uncertain conditions.

4.1.2. The Impact of Macroeconomic Factors on Uncertain Firm Growth

The results in Table 2 show that the positive effects of the relative spread signal higher trading costs and lower liquidity, which reduces market efficiency and increases uncertainty in firm valuation and investment decisions (Roll 1984). Market illiquidity is closely tied to broader economic conditions. The abovementioned discussion leads to an acceptance of hypothesis 3, although the estimate of the implicit spread shows the opposite effect.

Næs et al. (2011) demonstrated that stock liquidity indicators such as implicit spread estimators act as forward-looking signals of economic downturn, with large firms being less responsive to shifts in stock liquidity. As Amihud (2002) argues that higher stock illiquidity (being associated with slower GDP growth, higher unemployment, and a weak economy) leads firms to pursue more expensive funding sources, such as traditional banking (Malinić et al. 2020), a last resort is to raise debt to finance expected growth opportunities. The authors verify this argument by depicting the skewness of uncertain growth and the DE ratio, as shown in Figure 4.

The positive impacts of unemployment rates on uncertain firm growth extend the effects of unstable economic environments on firm growth (Radha et al. 2024; Basovskaya and Basovskiy 2024). High unemployment levels are usually associated with decreased consumption and slower GDP growth, all of which constrain firms’ operational stability and discourage investment, therefore increasing firms’ uncertain growth (Zhorzholiani 2024). Moreover, the inability to fully utilize labor resources represents a missed opportunity for productivity gains, amplifying the uncertainty surrounding firm performance and growth trajectories. The abovementioned discussion leads to inconclusive decision about hypothesis 5.

The positive effects of the federal fund rate extend the conclusion of Poudel (2017) and Zhang et al. (2021) that rising interest rates contribute to increased uncertainty surrounding firm growth by increasing borrowing costs, which directly constrains investment and operational expansion leading to an acceptance of hypothesis 6.

The positive stochastic effects of net exports on uncertain firm growth indicate that export growth exposes firms to higher geopolitical uncertainty, which emphasizes the significant role of stable international trade policy on firm growth (Yazdani et al. 2023; Wu and Niu 2025). Overall, the negative impact of economic policy uncertainty (EPU) on firms’ uncertain growth confirms the significant role of macroeconomic perceptions in firms’ uncertain growth.

4.1.3. The Impact of Institutional Factors on Uncertain Firm Growth

Notably, several studies conclude that while regulatory quality and political stability are intended to increase institutional efficiency and ensure market integrity, they can paradoxically introduce uncertainty for firms, especially in sectors highly sensitive to compliance demands (Mwombeki 2023). The abovementioned discussion leads to a rejection of hypothesis 7, concluding that rigid and complex government regulations increase firm uncertain growth.

Figure 4 is generated by sorting the average skewness of uncertain firm growth in an ascending order. Therefore, firms at the far left (right) are those associated with the smallest (largest) skewness of uncertain firm growth.

4.1.4. Causality Between Realized, Uncertain, and Stochastic Firm Growth

The estimation of uncertain firm growth (Equation (3)) assumes that uncertain firm growth is an observable part of realized growth. In this sense, the results in Table 2 examine this assumption, concluding that realized firm growth significantly affects uncertain growth. The same argument holds for the relationship between uncertain and stochastic uncertain firm growth. Further validation requires causality analysis.

Table 3. Causality of realized, uncertain and stochastic uncertain firm growth.

Null Hypothesis:	F-Statistic
Stochastic Uncertain Firm Growth does not Granger Cause Uncertain Firm Growth	87.2163 ***
Uncertain Firm Growth does not Granger Cause Stochastic Uncertain Firm Growth	691.333 ***
Realized Firm Growth does not Granger Cause Uncertain Firm Growth	0.00655
Uncertain Firm Growth does not Granger Cause Realized Firm Growth	27.993 ***
Realized Firm Growth does not Granger Cause Stochastic Uncertain Firm Growth	0.01152
Stochastic Uncertain Firm Growth does not Granger Cause Realized Firm Growth	0.3852

*** Significant at the 1% level; N = 12,740.

shows two fundamental relationships. First, uncertain firm growth Granger causes realized firm growth. Firms take unexpected growth (reflecting expectations of unobserved macroeconomic and institutional factors) into consideration when planning for weighted growth of fixed assets. Second, uncertain and stochastic uncertain growth Granger cause each other. This is true as long as uncertain firm growth reflects unobserved factors and therefore remains subject to stochastic movements.

5. Conclusions

This study examines the determinants of the uncertain component of firm growth being unobserved (statistically) and requires significant attention from firm managers and policymakers. Therefore, this study examines comprehensive factors being classified into three groups, namely firm-specific (reflecting the role of firms’ managers), and both macroeconomic and institutional factors (reflecting the role of policy makers). In addition, complexities in the business environment call for treating the uncertain component of firm growth stochastically, as expected firm growth cannot be known in advance. In this sense, the stochastic treatment offers an advantage to firm managers and policy makers of preparing financial (on the firm’s side) and institutional (on the public policy side) resources that help firms grow. Therefore, an integration between a firm’s resource view and firm growth can be fulfilled. At the firm’s level, uncertain firm growth can be managed effectively via sales growth, profitability, cash flow, efficient use of capital structure, focusing relatively more on long-term financing, and exporting to regions that do not expose firms to geopolitical risks. At public policy level, institutional quality plays a significant role, although firms may benefit from political favoritism (which is associated with instability). In addition, excessive regulations contribute to a firm’s uncertain growth significantly.

It is worth addressing an extended limitation, which is to do with the estimation of firm growth in the case of large U.S. firms. That is, the examination of uncertain growth is a common statistical property of firm growth estimation apart from firm size. Therefore, the same estimation technique can be extended to SME uncertain firm growth.