Mean Reverting Financial Leverage and Firm Life Cycle: Theory versus Evidence (Pakistan)

Abstract

The purpose of the study³

This article is a part of a PhD thesis submitted at School of Accounting, Dongbei University of Finance and Economics, Dalian, P. R. China.

is to decide between two competing theories of capital structure (trade-off theory and pecking order theory) along a firms’ life cycle and to find out whether there exists a target capital structure or not. To carry out the purpose, we develop a database of 13,375 firm-year observations of non-financial firms listed on Pakistan Stock Exchange spread over 39 years (1972–2010). A multivariate approach has been followed to classify 13,375 firm-year observations into different life cycle stages, and Fisher type panel unit root test has been applied to check the mean reversion of financial leverage ratios. The results of unit root analysis for growing and mature firms clearly support trade-off financing behavior while for declining firms results do not support trade-off financing behavior.

Keywords

Target capital structure firm life cycle unit root analysis panel data Pakistan

Introduction

There are two competing theories of capital structure: trade-off theory (TOT) and pecking order theory (POT). Most of the research studies in the field of capital structure use these theories to explain determinants of capital structure. The trade-off theory was given by Modigliani and Miller, (1963). They argue that there exists a trade-off between costs and benefits associated with leverage and define breakeven point of these leverage-related costs and benefits as optimal (target) capital structure. On the other hand, pecking order theory states a specific order of financing where internal funds are considered as first choice; external debt second choice; and equity as a last choice (Donaldson, 1961; Myers & Majluf, 1984). Accordingly, pecking order theory states that the firms follow a specific order of financing while trade-off theory explains that the firms follow a target capital structure.

The empirical studies carried out internationally as well as in Pakistan provide evidence both in favor of pecking order theory and trade-off theory (Ahsan, Wang, & Qureshi, 2016a; Booth, Aivazian, Kunt, & Maksimovic, 2001; Sheikh & Qureshi, 2014; Titman & Wessels, 1988). All of these studies have applied time series or panel data regression analysis to find out determinants of capital structure and to decide between pecking order and trade-off theory. The purpose of this study is to decide between pecking order and trade-off theory while using a different approach. We use mean reversion property of target (optimal) capital structure to find out the existence of target (optimal) capital structure during different life cycle stages of the firms operating in Pakistan. Further, we follow a multivariate approach to classify firms into different life cycle stages and apply panel data unit root test to a large dataset of Pakistani listed non-financial firms to check if their capital structure is mean-reverting along their life cycle or not.

The study classifies firms into growth, maturity and decline stage and contributes to the literature by discovering that growing as well as mature firms do follow target capital structure but declining firms do not have target capital structure.

Apart from the Introduction section, the rest of the paper is organized in the following manner: next section describes theoretical framework, data and methodology; the empirical results and their discussion is presented in another section; and last section is about the conclusions drawn and suggested directions for future research. References have been provided at the end.

Theoretical Framework, Data, and Methodology

A firm progresses through different stages during its life cycle. These life cycle stages starts from birth and ends at death. However, theorists explain various number of life cycle stages of a firm. Such as, some theorist explain that structure and strategies of firms vary in growth, maturity, and decline stage (Anthony & Ramesh, 1992; Chandler, 1962). Some others explain four life cycle stages including birth, growth, maturity, and revival (Miller & Friesen, 1980), and some explains birth, growth, maturity, revival, and decline (Dickinson, 2011). But most of these theorists agreed upon growth, maturity, and decline stages. Accordingly, in this study we also classify firm-year observations into growth, maturity and decline stages.

Further, empirical studies use the mean leverage ratio as a proxy of target leverage (Frank & Goyal, 2009; Jõeveer, 2013) for firms and attribute of stationarity of the data necessitates reversion towards its mean value. This attribute can be used to find out the existence of target leverage, and consequently to decide between trade-off theory and pecking order theory of capital structure (Ahsan, Wang, & Qureshi, 2016b). Furthermore, unit root analysis can be used to find out the stationarity of the data (Bontempi, 2002).

To examine mean reversion of capital structure in Pakistan, we develop a unique dataset of all Pakistani non-financial firms listed at PSE (Pakistan Stock Exchange) taken from the State Bank of Pakistan (SBP) publications for the period 1972–2010 (SBP 1972–2010). The time (years) and space (firms) dimensions make it an unbalanced panel dataset comprising 13 sectors and 13,375 firm-year observations.

To classify firms into different life cycle stages, we choose multivariate methodology (Anthony & Ramesh, 1992) instead of univariate because it is more reliable, and analysis proves that their methodology is not driven by firm size effect, risk differences, and measurement errors. Moreover, this methodology is used by similar studies (Jenkins, Kane, & Velury, 2004; Rocha, 2005). We use following three classification variables: Dividend payout ratio (Dividend paid/Net profit before tax); Sales growth (% Change in annual sales); and Age (Natural logarithm of number of years since a firm is listed). We calculate the dividend payout ratio and sales growth for each year and firm included in our data and then we measure median values of these variables based on prior five years’ data. Further, we group three classification variables (median of dividend payout ratio, median of sales growth and age) into three life cycle stages according to the criteria presented in Table 1.

Table 1.

Life Cycle Variables and Classification Method

Life cycle stages	Dividend payout	Sales growth	Age
Growth	Low	High	Young
Mature	Medium	Medium	Adult
Decline	High	Low	Old

Source: Anthony and Ramesh (1992). Association between accounting performance measures and stock prices. Journal of Accounting and Economics, 15(2–3), 203–227.

Note: Dividend payout is annual dividend paid over net profit before tax; sales growth is percentage change in annual sales and age is natural logarithm of number of years since a firm is listed.

Due to the use of five years’ prior data to calculate median values for the dividend payout ratio and sales growth, our total number of firm-year observations is reduced from 13,375 to 8,419. The summary in Table 2 indicates that we have 1,713 firm-year observations for growth stage, 6,255 firm-year observations for the mature stage, and 451 firm-year observations for the decline stage.

The textile sector has largest number of firm-year observations in total (3,297) and in individual life cycle stages also while tobacco sector has the smallest number of firm-year observations (111) in total.

Table 2.

Sector and Life Cycle Stage-wise Number of Firms-year Observations

Sr. No.	Sector	Growth	Mature	Decline	Total	Percentage of total no. of observations
1	Cement	81	188	25	294	3.49
2	Chemical	101	467	14	582	6.91
3	Engineering	173	610	48	831	9.87
4	Fuel and energy	29	268	47	344	4.09
5	Jute	26	134	5	165	1.96
6	Miscellaneous	183	790	73	1046	12.42
7	Paper and board	28	199	8	235	2.79
8	Sugar	126	564	44	734	8.72
9	Textile	842	2337	118	3297	39.16
10	Textile ancillary products	51	325	32	408	4.85
11	Tobacco	05	76	30	111	1.32
12	Transport and communications	20	92	01	113	1.34
13	Vanaspati	48	205	06	259	3.08
	Total	1,713	6,255	451	8,419

Source: Authors’ own.

The growing use of panel data in empirical studies has forced econometrics to extend time series unit root tests to panel data. Consequently, there are a number of unit root tests available for panel data such as: LLC (Levin, Lin, & Chu, 2002), IPS (Im, Pesaran, & Shin, 2003), and Fisher type (Choi, 2001; Maddala & Wu 1999;) tests. These panel data unit root tests are different from each other in their technique and assumptions. We compare these tests and finally choose Fisher test for our study due to following reasons;

LLC requires independence of each cross section and is not applicable if there is cross-sectional correlation.

LLC is also restrictive to the assumption that all cross sections have or do not have a unit root while IPS and Fisher type tests relax this restrictive assumption and allow some of the groups to be non-stationary while others may not, under the alternative hypothesis (Baltagi, 2005; Maddala & Wu, 1999).

Both, Fisher test and IPS test relax the restrictive assumption of LLC that is why they are comparable. The Fisher test is non-parametric while the IPS test is parametric. Being a parametric test IPS requires t-bar distribution, which is based on mean and variance of t-statistics. IPS computes t-distribution tables for different values, sample sizes, and number of lags based on ADF test statistics. The validity of these tables is conditional to the ADF test being used for unit root tests. Moreover, the IPS prepared tables also faces problems while dealing with different lengths of time series for different samples. While Fisher test, being non-parametric, do not have such limitations. It can be used with ADF test as well as with any other unit root test and lag lengths can also be determined separately for each sample.

Furthermore, the Fisher test also allows T (time dimension) to be different for each i. It follows that the Fisher test does not require a balanced panel (Choi, 2001) and considered as a preferred choice for our study because, we are using unbalanced panel of 13,375 firm-year observations. In the following equation, we present our panel data unit root (Fisher test) model:

P = - 2 \sum_{i = 1}^{N} \ln ρ_{i}

where N is cross-sectional (firm-year) dimension and ρ_i is the combination of p-values of unit root tests carried out for each cross section i. Furthermore, –2ln ρ_i follows χ² distribution with two degrees of freedom.

This model contains the following hypothesis:

$H_{O} : | ρ_{i} | = 1$ for all i’s (All panels are non-stationary)

$H_{A} : | ρ_{i} | < 1$ for some i’s (Some panels are non-stationary while others not).

Leverage is our variable of interest in this study. Different methods can be used to measure leverage. We measure leverage using three proxies: short-term leverage as the ratio of short-term liabilities to total assets; long-term leverage as the ratio of long-term liabilities to total assets; and total leverage as the ratio of total liabilities to total assets.

Empirical Results and Their Discussion

In this section, we present and discuss descriptive statistics of life cycle as well as leverage ratios and empirical results of unit root analysis for three different measurements of leverage ratios during growth, maturity, and decline stages.

Descriptive Statistics

Table 3 presents the descriptive statistics of life cycle classification variables. The median dividend payout has a mean value of 0.0107 during the growth stage which increases to 0.1495 during the mature stage and further increases to 0.3734 during the decline stage. This explains that growing firms use a bigger part of retained earnings to finance their projects and pay very less dividends while declining firms having less investment opportunities pay more dividends. On the other hand, the median sales growth has a mean value of 0.2580 during the growth stage that decreases to 0.0808 during the mature stage and further decreases to 0.0340 during the decline stage. This explains that sales growth decreases as a firm matures and then declines. Further, firm age increases through growth to decline stage.

Table 3.

Descriptive Statistics for Life Cycle Variables Used to Classify Firms

Variable	Obs.	Mean	Std. Dev.
Growth Stage
Median dividend payout	1,713	0.0107	0.0439
Median sales growth	1,713	0.2580	0.3216
Age	1,713	2.5070	0.3564
Mature Stage
Median dividend payout	6,255	0.1495	0.2242
Median sales growth	6,255	0.0808	0.1662
Age	6,255	2.9674	0.5086
Decline Stage
Median dividend payout	451	0.3734	0.1856
Median sales growth	451	0.0340	0.0895
Age	451	3.3558	0.3339

Source: Authors’ own.

Note: The table presents the descriptive statistics of the three variables used to classify firms into growth, mature and decline stage. Median dividend payout is the median value of annual dividend paid over net profit before tax based on prior five years data; Median sales growth is the median value of percentage change in annual sales based on prior five years data; age is natural logarithm of number of years since a firm is listed.

Descriptive statistics (Table 4) explain that short-term leverage (mean of 0.5656 during the growth stage; 0.6459 during the mature stage and 0.5265 during the decline stage) is a dominant mode of financing throughout the life cycle of Pakistani firms conforming earlier studies in Pakistan (Qureshi 2009; Sheikh & Qureshi 2014). While long-term leverage is a small portion (mean of 0.2320 during growth stage; 0.1727 during mature stage and 0.1188 during decline stage) of total financing and decreases as the firms mature and decline. The highest mean value of short-term leverage (mean=0.6459) during the mature stage and long-term leverage (mean=0.2320) during the growth stage suggests that mature firms consider short-term debt while growing firms consider long-term debt as capital structure policy tool. The mean of total leverage (mean of 0.7989 during growth stage; 0.8278 during mature stage and 0.6432 during decline stage) represents a low-high-low leverage pattern during growth, maturity and decline stage.

Table 4.

Descriptive Statistics for Leverage Ratios during Different Life Cycle Stages

Variable	Obs.	Mean	Std. Dev.
Growth Stage
Short-term leverage	1,713	0.5656	0.3264
Long-term leverage	1,713	0.2320	0.2315
Total leverage	1,713	0.7989	0.3659
Mature Stage
Short-term leverage	6,255	0.6459	0.5001
Long-term leverage	6,255	0.1727	0.2217
Total leverage	6,255	0.8278	0.5755
Decline Stage
Short-term leverage	451	0.5265	0.2575
Long-term leverage	451	0.1188	0.1401
Total leverage	451	0.6432	0.2675

Source: Authors’ own.

Notes: The table presents the descriptive statistics for three leverage ratios during growth, mature and decline stage separately. Short-term leverage is the ratio of short term liabilities over total assets; long-term leverage is the ratio of long term liabilities over total assets; total leverage is the ratio of total liabilities over total assets.

Empirical Analysis

In Table 5, we present the results of unit root analysis for short-term, long-term, and total leverage ratio during growth stage. For growth stage, we have 380 firms and 1,713 firm-year observations available for the analysis. The results of unit root analysis finds no unit root in short-term, long-term as well as total leverage ratio during growth stage and rejects the null hypothesis. It explains mean reverting short-term, long-term as well as total leverage ratio and depicts trade-off financing behavior of Pakistani listed non-financial firms during their growth stage.

Table 5.

Panel Data Unit Root Results during Growth Stage

	Number of Firms			Number of Observations			Lag Length based on AIC	ADF-FisherChi-Square
	Available	Included	Dropped	Available	Included	Dropped	Statistic	Probability
Short Term Leverage	380	214	166	1,713	1,167	546	0–2	609.47	0.0000
Long Term Leverage	380	211	169	1,713	1,154	559	0–1	714.17	0.0000
Total Leverage	380	214	166	1,713	1,168	545	0-–1	595.14	0.0000

Source: Authors’ own.

In Table 6, we present the results of unit root analysis for short-term, long-term, and total leverage ratios during the mature stage. For the mature stage, we have 551 firms and 6,255 firm-year observations available for the analysis. The results of unit root analysis finds no unit root in the short-term, long-term, as well as total leverage ratios during the mature stage also and rejects the null hypothesis. It explains mean reverting short-term, long-term, as well as total leverage ratios and depicts trade-off financing behavior of Pakistani listed non-financial firms during their mature stage.

Table 7 presents the results of unit root analysis for the short-term, long-term and total leverage ratios during the decline stage. For the decline stage, we have 133 firms and 451 firm-year observations available for the analysis. The results of unit root analysis finds unit root in short-term, long-term, as well as total leverage ratios during the decline stage and accepts the null hypothesis. It explains that declining Pakistani firms do not have mean reverting short-term, long-term as well as total leverage ratio and do not follow trade-off financing behavior

Table 6.

Panel Data Unit Root Results during Mature Stage

	Number of Firms			Number of Observations			Lag Length based on AIC	ADF-FisherChi-Square
	Available	Included	Dropped	Available	Included	Dropped	Statistic	Probability
Short Term Leverage	551	461	90	6,255	5,428	827	0-6	1466.88	0.0000
Long Term Leverage	551	446	105	6,255	5,301	954	0-6	1693.63	0.0000
Total Leverage	551	462	89	6,255	5,429	826	0-6	1223.85	0.0000

Source: Authors’ own.

Table 7.

Panel Data Unit Root Results during Decline Stage

	Number of Firms			Number of Observations			Lag Length based on AIC	ADF-FisherChi-Square
	Available	Included	Dropped	Available	Included	Dropped	Statistic	Probability
Short Term Leverage	133	49	84	451	258	193	0–2	114.54	0.1214
Long Term Leverage	133	47	86	451	251	200	0–1	112.78	0.0908
Total Leverage	133	49	84	451	259	192	0–2	96.84	0.5141

Source: Authors’ own.

Conclusions

We apply panel unit root test developed by Fisher on a unique and large dataset comprising of 13,375 firm-year observations of Pakistani non-financial firms listed on Pakistan Stock Exchange spread over 39 years period (1972–2010) to provide some evidence on their leverage behavior. If the leverage ratios do not have unit root they are stationary and mean-reverting, then the firms are expected to have target leverage ratios as explained by trade-off model. Otherwise, they are non-stationary and not mean-reverting, and as such the firms may not have target leverage ratios and may not depict trade-off leverage behavior. Further, we follow multivariate approach to classify firms into growth, maturity and decline stages.

The results of the study suggest that short-term leverage is a main source of financing of Pakistani listed non-financial firms throughout their life cycle. Further, the results explains that during growth and maturity stage Pakistani non-financial listed firms do have a target capital structure in line with TOT but declining firms do not have any target leverage ratio and they may follow pecking order theory. If this is the case, growing and mature Pakistani firms definitely strive to achieve their target leverage ratios. Further research can be carried out to find out the speed of adjustment of these firms towards their target leverage ratios.

Footnotes

Authors’ Biography

Tanveer Ahsan is a PhD Candidate at School of Accounting, Dongbei University of Finance and Economics, Dalian, Liaoning, P. R. China. He has published numerous articles. His research focuses on different aspects of corporate financing policy such as determinants of corporate financing policy, financing behavior over a firm’s life cycle, and adjustment towards target financial leverage.

Dr. Man Wang is a professor at School of Accounting, Dongbei University of Finance and Economics, Dalian, Liaoning, P. R. China. She started academia almost 31 years ago. During these years, she has published many books on corporate finance, managerial accounting, and numerous research papers in well reputed journals including Accounting Research, Research on Financial and Economic Issues, and Contemporary Accounting Review. She has supervised a number of bachelors and masters theses. She is currently supervising many PhD candidates from different countries.

Dr. Muhammad Azeem Qureshi is an Associate Professor at Oslo Business School, Oslo and Akershus University College of Applied Sciences, Oslo, Norway. Dr. Qureshi holds MBA, DAIBP, M.Phil and PhD. He started his career as investment banker in 1990 and joined academia in 1996. Dr. Qureshi has 22 publications in different international academic journals and 16 refereed conference papers to his credit. He is acting as reviewer for 10 academic journals, member of editorial board of one journal, and examiner for masters and PhD theses of four universities. Dr. Qureshi has supervised a number of bachelors and masters theses. He is currently supervising four bachelors, four masters and two PhD candidates.

References

Ahsan

Wang

Qureshi

M. A.

(2016a). Mean reverting financial leverage: theory and evidence from Pakistan. Applied Economics , 48(5), 379–388.

Ahsan

Wang

Qureshi

M. A.

. (2016b). Firm, industry and country level determinants of capital structure: evidence from Pakistan. South Asian Journal of Global Business Research, Forthcoming.

Anthony

J. H.

Ramesh

(1992). Association between accounting performance measures and stock prices. Journal of Accounting and Economics , 15(2-3), 203–227.

Baltagi

B. H.

(2005). Econometric Analysis of Panel Data. (3rd ed.).

Bontempi

M. E.

(2002). The dynamic specification of the modified pecking order theory: Its relevance to Italy. Empirical Economics , 27(01), 1–22.

Booth

Aivazian

Kunt

A. D.

Maksimovic

(2001). Capital structure in developng countries. The journal of Finance , 56(1), 87–130.

Chandler

A. D.

(1962). Strategy and structure . Cambridge, MA: MIT Press.

Choi

(2001). Unit root tests for panel data. Journal of International Money and Finance , 20(02), 249–272.

Dickinson

(2011). Cash Flow Patterns as a Proxy for Firm Life Cycle. The Accounting Review , 86(06), 1969–1994.

10.

Donaldson

(1961). Corporate debt capacity: A study of corporate debt policy and the determination of corporate debt capacity. Boston: Harvard, Graduate School of Business Administration.

11.

Frank

M. Z.

Goyal

V. K.

(2009). Capital structure decisions: Which factors are reliability important. Financial Management , 39(1), 1–37.

12.

Pesaran

M. H.

Shin

(2003). Testingfor unit roots in heterogeneous panels. Journal of Econometrics , 115, 53–74.

13.

Jõeveer

(2013). Firm, country and macroeconomic determinants of capital structure: Evidence from transition economies. Journal of Comparative Economics , 41(01), 294–308.

14.

Jenkins

D. S.

Kane

G. D.

Velury

(2004). The impact of the corporate life-cycle on the value-relevance of disaggregated. Review of Accounting and Finance , 3(4), 5–20.

15.

Levin

Lin

C. F.

Chu

C. S. J.

(2002). Unit root tests in panel data:Asymptotic and “finite-sample properties”. Journal of Econometrics , 108(01), 1–24.

16.

Maddala

G. S.

(1999). A comparative study of unit root tests with panel data and a new simple test. Oxford Bulletin of Economics and Statistics , 61(S1), 631–652.

17.

Miller

Friesen

P. H.

(1980). Momentum and revolution in organizational adaptation. Academy of Management , 23(4), 591–614.

18.

Modigliani

Miller

M. H.

(1963). Corporate income taxes and the cost of capital: A correction. American Economic Review , 53(03), 433–443.

19.

Myers

S. C.

Majluf

N. S.

(1984). Corporate financing and investment decisions when firms have information that investors do not have. Journal of finacial economics , 13(2), 187–221.

20.

Sheikh

N. A.

Qureshi

M. A.

(2014). Crowding-out or shying-away: impact of corporate income tax on capital structure choice of firms in Pakistan. Applied Financial Economics , 24(19), 1249–1260.

21.

Teixeira

G. R.

Coutinho

dos Santos M.

(2014). Do Firms have Financing Preferences along their Life Cycles? Theory, and Evidence from Iberia. Retrieved from SSRN: http://ssrn.com/abstract=676869 or https://dx-doi-org.web.bisu.edu.cn/10.2139/ssrn.676869.

22.

Titman

Wessels

(1988). The determinants of capital structure choice. The journal of Finance , 43(1), 1–19.