Age Effects, Leverage and Firm Growth∗
Kim P. Huynh†

Robert J. Petrunia‡

July 1, 2009

Abstract
Recent theories of firm dynamics emphasize the role of financial variables as determinants of firm growth. Empirically examining these relationships has been difficult,since there is a lack of financial data on the small, young, and private firms. Using aunique administrative data set, this paper considers the growth of new firms in Canadian manufacturing from a financial perspective. We find that financial factors, suchas leverage and initial financial size, impact growth rates for new firms. Further, theinclusion of leverage has little impact on the economic significance of the conditional
age and size relationships with firm growth.
Key Words: Firm Size Dynamics, Leverage, Age Effects, Dynamic Panel Data.
JEL Classification: D21, G3, L3, C23.

∗

The assistance and hospitality of Statistics Canada Business and Labour Market Analysis department is
gratefully acknowledged. We are especially indebted to Leonard Landry and Steve Romer for their gracious
efforts on data management and requests for hardware/software upgrades. Comments and suggestions fromMichael Baye, Gerhard Glomm, Boyan Jovanovic, Peter Thompson, and participants of Carleton University,
Kelley Business Economics Public Policy workshop, Statistics-Canada, 12th Society of Computational Economics, 14th Panel Data Conference, and 2006 Latin American Meetings of the Econometric Society, 2008
International Industrial Organization conference are greatly appreciated. The second author acknowledges
financial support from the Statistics Canada Research Fellowship. The usual disclaimer on liability applies.
†
Department of Economics, Indiana University, 105 Wylie Hall, 100 South Woodlawn Avenue, Bloomington, IN 47405–7104, USA. Phone: +1 (812) 855 2288.
Fax: +1 (812) 855 3736.
E-mail:kphuynh@indiana.edu.
‡
Department of Economics, Lakehead University, 955 Oliver Road, Thunder Bay, ON P7B 5E1,
CANADA. Phone: +1 (807) 343 8384. Fax: +1 (807) 346-7936. Email: rpetruni@lakeheadu.ca

Electronic copy available at: http://ssrn.com/abstract=879284

1

Introduction

Recent theories highlight the impact of financial considerations in firm dynamics, especiallyfor young firms. These theories suggest financial variables contain relevant information regarding firm growth. Very little is known about the financial state of new firms. Empiricallyexamining these relationship has been difficult because of the lack of financial data on thesmall, young, and private firms. This paper considers the role of financial variables in thegrowth process of new firms in manufacturing using administrative corporate tax files. Once
controlling for firm age and size, we find that financial factors, such as leverage and initialfinancial size, have significant, positive effects on growth of new firms.
Previous empirical firm growth studies by Evans (1987a, 1987b) and Dunne, Roberts,
and Samuelson (1989) find a negative correlation between firm growth with size and age.
Further, conditional on age, firm growth remains negatively related to size, while conditionalon size, firm growth continues to have a negative relationship with age. In response to theseempirical findings, theoretical models use alternative mechanisms to try to explain the size
and age effects on firm growth. In these models, there is typically one source of heterogeneity across firms. Learning and productivity shocks provide devices which generate different
dynamics across firms. Given the simultaneous age and size dependence, a second heterogeneity is needed to better understand growth dynamics.
As a result, newer models, such as Cooley and Quadrini (2001), were built to explain theconditional size and age correlations with growth. This model extends Hopenhayn (1992)
by making financial considerations relevant for firm dynamics. In Hopenhayn (1992), size
captures productivity differences across firms, which makes growth independent of age. The
addition of financial heterogeneity means a conditional relationship between firm growth andage occurs, as age captures the omission of a firm’s financial state measured in terms of thedebt-to-asset ratio.

1

Electronic copy available at: http://ssrn.com/abstract=879284

There are alternative reasons for age effects to remain even after controlling for financial variables. Theoretical work by Jovanovic (1982) proposes a learning model of industry
dynamics. Firms enter an industry with incomplete information regarding their own productivity but gain information through production.1 Although the model deals with selection(exit) and not explicitly with growth, the learning effect generates a negative conditionalfirm growth-age dependence under certain general conditions, see Evans (1987b). Whereas,
Klepper and Thompson (2006) suggest conditional age effects in firm growth are due to thecreation and destruction of submarkets combined with selection effects.
This paper’s main avenue of assessment is the hypothesis that age effects occur becauseof financial factors; financial measures, such as the debt-to-asset ratio and initial financial
size (assets), augment the conditional firm growth relationship. Firm growth relationships
with financial aspects are investigated using a new unique universal database compiled by
Statistics-Canada called T2LEAP. Financial and balance sheet information is collected from
corporate tax files. This information allows us to establish firm growth patterns for young
firms related, not only to size and age, but also to financial variables. If age effects occur
mainly because of financial frictions, as suggested by Cooley and Quadrini (2001), then the
inclusion of financial variables in the firm growth regression should reduce the economic
significant of age.2
The correlation between growth and leverage (debt-to-asset ratio) is positive as suggested by Figure 1. This figure shows median firm growth across leverage classes and four
age groups. For entrant firms at age one, there is a positive correlation between leverageand growth. Further, figure 2 compares growth across size and leverage classes for age: one,
four, seven, and ten firms. For age one, firms in the top leverage decile have higher growth1

Ericson and Pakes (1995) also allow for learning to affect firm growth through productivity. Unlike
Jovanovic (1982), they endogenize the learning process by making it “active”. With active learning, a firmknows its own productivity and can invest to improve its relative position within an industry.
2
Cabral and Mata (2003) have investigated the effect of financial constraints on within-industry size
dynamics.

2

than firms in the lowest leverage decile. Across the age and leverage deciles, firms in thelowest size classes have the highest growth rates. At age four, little difference occurs for firm
growth rates across leverage classes. For ages seven and ten, firms in the smaller size classes(one to four) with low leverage still have the lowest growth, while no clear pattern emerges
in the upper leverage classes.
Controlling simultaneously for size, age, and leverage, the findings are as follows:• A positive and nonlinear relationship occurs between firm growth and leverage.
• Negative conditional relationship occurs between firm growth and firm size.
• Youngest firms are the fastest growers (age effects level off at age seven).
• A firm’s future growth exhihits a positive relationship with its initial asset size.
The last result indicates that a firm’s ability to obtain financial resources provides some
information about its future growth. Zingales (1998) shows deep pockets or fatness have apositive effect on the future success of a firm. Higher initial level of assets may provide a
proxy for deeper pockets and these deep pockets allows a firm to easily expand in the future.
As an alternative view, high levels of initial assets may indicate a firm has higher growthpotential. Firm size is measured by sales. A firm with high expected sales growth shouldbe able to obtain more funds initially. A high amount initial financial assets provides thefirm with the necessary financial capital to fund future expansionary investment projects.
This alternative explanation suggests that firms have deep pockets for a reason. Investors
are willing to provide funds to a firm if there is a belief that the firm is high quality withsignificant growth potential. Further, a firm with strong sales growth potential may choose
to initially have a large amount of physical capital in order to meet future sales demands.
The rest of paper is organized as follows. The next section discusses the T2LEAP
database. The third section presents our empirical methodology for estimating the firm size
3

dynamics relationships. Section four discusses the results, while the last section concludes.

2

The T2LEAP Database

The database used in this study, known as T2LEAP, was constructed by Statistics-Canada
through the linkage of two administrative databases to provide information on the universeof all incorporated enterprises in Canada employing workers. The first database, the Corporate Tax Statistical Universal File (T2SUF), contains balance sheet information collected off
a firm’s T2 tax record. The second database, Longitudinal Employment Analysis Program(LEAP), contains yearly employment information for all firms hiring employees. LEAP uses
a firm’s payroll deduction record, filed with Revenue Canada, to track any firm hiring employees.
T2LEAP uses a business registry number (BSNUM) to track all incorporated firms operating in a given year. Entry and exit is identified when firms enter and leave the database.
A firm’s unique BSNUM identifier ensures exit and re-entry does not occur. Further, a namechange by a firm is not recorded as a simultaneous exit and entry because the BSNUM does
not change for this firm. The database accounts for mergers, acquisitions and spin-offs in a
retrospective manner, so these activities do not create false entrants or exits, or false growth
due to acquisition.3
The database contains information on firms from 1984 until 1998. One problem is there
is no observable birth year for those firms operating at the first year of the database (1984).
A second problem is the potential for partial reporting by firms in their birth year or exit
year. Given truncation due to partial reporting and non-measurable birth year, firms musthave a birth year between 1985 and 1996, inclusive, to be part the analyzed sample. This3

For example, if firm A merged with firm B in year t, then a new firm, C, is created in year t with a pasthistory synthesized by aggregating the histories of firms A and B. The individual histories of firms A and B
do not appear in the database, while firm C emerges in the database to represent the joint operations before,
and after, year t. However, we are focusing on small, young and private firms so the number of mergers andspinoffs is trivial.

4

truncation reduces the usable sample period from 1985 to 1997.
Firm variables include annual employment, sales, assets, equity, debt and other balance
sheet information. Firm assets are the sum of current financial assets, capital, both tangible and intangible, and long-term financial assets. Firm sales equals firm revenue plus
other revenues. Firm equity is the sum of common shares, preferred shares and retained
earning/losses. The data appendix contains a detailed breakdown of the financial variables.
Sales is measured as the flow of revenues to the firm within a year. Equity, debt and assets
are stock variables measured at the fiscal year end. Accounting rules justify that a firms assets must equal its liabilities (debt plus equity). Assets, equity, debt and sales are measured
in nominal terms within the database. We use price index data available through CANSIM
to deflate values of these variables. Sales are deflated using Industry Price Indexes (CANSIM
table number 329-0001) available at the three digit SIC level. Similarly, assets, equity anddebt are deflated using the CPI (CANSIM table number 326-0001). Finally, the database
contains information on the industry of the firm. Each firm has a three-digit Standard Industrial Classification (SIC) number. This study limits attention to manufacturing firms.
Table 1 presents summary statistics for variables used in this paper.

3

Model Specification

In Cooley and Quadrini (2001), the combination of productivity movements and financial
considerations reconciles firm growth’s simultaneous size and age dependence. Age controls
for the equity (financial) differences across firms, while size captures productivity differences.
This model suggests financial variables are relevant when studying firm size dynamics. For
example, leverage (debt-to-asset ratio) can provide a direct measure for productivity differences. Higher productivity means a firm wants to be larger to take advantage of its goodstate. Thus, more productive firms have higher debt levels and higher leverage ratios conditional on their size (equity).
5

For all specifications, we remove industry specific-time means from all variables. Thisdemeaning provides controls for industry specific-time effects equivalent to including dummy
variables in the regressions.4 The canonical specification for the firm growth is augmented
by the first lag of the leverage (dai,t−1 ):5∆ log(Sizeit ) = αi + β log(Sizei,t−1 ) + φ1 log Ageit + φ2 [log Ageit ]2 + γdai,t−1 + ²it . (1)where ∆ log(Sizeit ) or the growth in the size of the firm is the difference of the logarithmof firm sales and log Age is the log of firm age since birth. A quadratic function is used tocapture the age dependence.6 Finally, αi is the unobserved firm fixed-effect.
To account for the notion of deep pockets or large initial financial size, the following
equation is estimated:∆ log(Sizeit ) = αi + β log(Sizei,t−1 ) + φ1 log Ageit + φ2 [log Ageit ]2(2)+γdai,t−1 + δ log(Assetsi0 ) + λP ublici,t−1 + ²it .
where log(Assetsi0 ) is the initial assets measures financial size and P ublici,t−1 is an indicatorvariable of whether a firm is publicly-traded or not. Less than one percent of these entrants
go public during this time period. The firms in our sample are young and generally do notuse external equity. Access to public equity markets may indicate a firm has better financial
4

There is a voluminous literature testing for Gibrat’s Law. The implication of Gibrat’s Law holding is
the growth of firms is a random process or logarithm of firm size follows a unit root or in the parlance oftime-series a difference stationary process (DSP). However, most studies reject Gibrat’s Law in favour ofhighly persistent autoregressive with serial correlation. (Hall and Mairesse 2005) conduct a comprehensive
study and apply a battery of panel unit root tests on real firm data. They overwhelming reject a unit root.
Further, they conduct a large scale Monte Carlo simulation study and find it is quite hard to distinguishbetween a unit root and highly persistent trend-stationary process (TSP). In an earlier paper, (Petrunia2008) rejects Gibrat’s Law in favour of stationarity with the same dataset. We go further and compute somepanel unit root test by (Maddala and Wu 1999) for the 1985-1988 cohorts (cohorts with T ≥ 9). This test
is apropos since our data is largely unbalanced. The results are overwhelming in favour of the rejection of aunit root in our data. Given our findings and the previous findings, we treat firm size as a TSP and demean
the data with time, industry, and industry-time interacted dummies to remove any inherent trends in thedata.
5
The leverage is treated as a predetermined variable. For robustness, it has been treated as endogenous
variable and instrumented with its second and third order lags. The results remain quantitatively the sameand are available upon request.
6
An alternative specification uses age dummies with little difference in the fundamental findings.

6

resources. A firm may choose to go public at an early age in order to have financial resources
to grow in the future. This public/private variable captures any differences in the growth
patterns of public and private firms in our sample.

3.1

Estimation Methods

T2LEAP is a longitudinal database, which enables the use of dynamic panel data methods
to estimate the firm growth relationships. The advantage of using dynamic panel data
methods is that they provide consistent estimates and avoid any biases created by spurious
correlations due to unobserved heterogeneity. To account for industry and year effects, thedata is demeaned before estimating the firm growth relationships.
3.1.1

System-GMM

We use the System-GMM dynamic panel data estimator proposed by Blundell and Bond(1998). This estimator has finite-sample properties superior to alternative dynamic panel
estimators such as the Difference-GMM estimator espoused by Arellano and Bond (1991).
Dynamic panel data methods allow for robust inference of lagged dependent variables in thepresence of unobserved heterogeneity (αi ).
3.1.2

Serial Correlation

The Lagrange multiplier (LM) test is an important diagnostic which investigates whether
differencing the lagged dependent variable results in second-order serial correlation. The
instrument set must be adjusted with second order serial correlation, as the second lag levelvalue of the dependent variable is no longer exogenous in the difference equation and theresulting estimates are inconsistent. If the hypothesis of no second-order serial correlation isrejected, then, similar to Chesher (1979), an additional lag is added in the firm size dynamics
relationship to soak up this serial correlation. With the extra lag of firm size, the firm growth7relationship (1) becomes:∆ log(Sizeit ) = αi +2Xβk log(Sizei,t−k ) + φ1 log Ageit + φ2 [log Ageit ]2

(3)

k=1

+γdai,t−1 + δ log(Assetsi0 ) + λP ublici,t−1 + ²it .
We find that serial correlation exists when including only the first lag of the dependence
variable. LM tests of lag order three are also implemented to ensure that the estimates fromthis two lag firm size dynamics relationship (4) are consistent. We only report consistentestimates, which allow for the presence of serial correlation.
3.1.3

Financial Nonlinearities

In the corporate finance literature, as exemplified by Fazzari, Hubbard, and Petersen (1988),
the method of financing occurs in discrete stages - retained earnings, private debt, public
debt, and then equity markets. The nonlinear nature of the leverage may lead to insignificant
results. The following procedure is used to account for any nonlinearities in the relationshipbetween a firm’s growth and its leverage. First, firms are binned into one of five classes
based on their leverage quintile value for a given year. Next, a firm’s leverage is interactedwith leverage quintile dummy variables. This flexible specification allows for nonlinearities
by having differential slopes in each leverage class. The nonlinear specification is:∆ log(Sizeit ) = αi +2Xβk log(Sizei,t−k ) + φ1 log Ageit + φ2 [log Ageit ]2

(4)

k=1

+

5
X

γk dak,i,t−1 + δ log(Assetsi0 ) + λP ublici,t−1 + ²it ,k=1

where k indicates a firm’s leverage class going from the lowest to the highest quintile.

4

Results

We start by comparing the movements of leverage across age classes before examining thefirm growth relationships. Cooley and Quadrini (2001) assume young firms have a limited
8

amount of equity and play off the mechanism that external debt financing involves higher
costs. Production allows a firm to accumulate equity through retained earnings. A firm’s
equity grows as it ages. The accumulation of internal equity reduces a firm’s reliance on debt.
The portion of debt used for financing falls even through a firm may continue to increase
its debt with expansion. Within Cooley and Quadrini (2001)’s framework, leverage ratios
should fall with age as a firm’s need for debt falls.
Table 2 examines this prediction by presenting median leverage across ages. The tablealso presents initial versus current median leverage of firms surviving until age t.7 In thetable, leverage gradually drops from a median value of 0.908 at age one to 0.608 at age 12.
A substantial portion of the fall in the leverage ratio results from survivors using a lower
portion of debt in financing. For surviving firms, the current leverage is always lower thaninitial leverage on average. Cooley and Quadrini (2001)’s prediction of a negative correlation
between age and leverage is consistent with the current data.
Tables 3 and 4 present estimates of firm growth relationships. The empirical investigation
focuses on new entrants and controls for firm age, firm size and firm leverage.8 In Table 3,
the value on the coefficient for the lagged dependent variable is approximately -0.1 for all
specifications. The estimate implies a one percent increase in the previous period’s size leads
to a 0.9 percent increase in the current period’s size. These elasticities are in line with results
found in previous studies such as Evans (1987a, 1987b) and Dunne, Roberts, and Samuelson(1989). The coefficient on the second lag of log size is positive, approximately 0.07, andstatistically significant. The interpretation of the positive coefficient on the second order
lagged term is that there is negative growth persistence (i.e. transitory shocks). Higher
7

The sample number of firms drop with age for two reasons. First, firms exit. Second, there is a restriction
on the maximum observable age for each cohort, since the database ends in 1997. Only the 1985 entry cohort
has observations at age 12, only the 1985 and 1986 entry cohorts have age 11, and so on.
8
A selection model (i.e. probit) was used to account for firm exit. There are no natural exclusion
restrictions, so identification is achieved through parametric and semiparametric specifications (inverse mills
ratio and its squared term). The results are quantitatively similar and available on request.

9

growth today leads to lower growth next period, which suggests mean reversion occurs in
the firm growth process.
In all specifications, the impact of age on firm growth is non-monotonic since estimateson the linear and quadratic terms have the opposite sign. The coefficient on the linear termis always negative indicating that firm growth rates should fall with age in the early yearsof a firm’s life, while the positive coefficient on the quadratic term suggests firm growth
eventually levels off and increases with age. The switch from a negative to a positive firm
growth-age relationship occurs between ages 7 and 8 for all specifications. The length of the
T2LEAP panel allows us to capture the nonlinear effects of age. The oldest age of firms inthe sample is 12 years; in comparison, the oldest age of firms is six in Evans (1987b).
Next, the discussion turns to the empirical relationship between leverage and firm-growth.
The first column (M1) of Table 3 does not include leverage and serves as a benchmark
estimate. Subsequent columns of Table 3 include the leverage. The estimate of the leveragecoefficient is positive and statistically significant. The positive relationship between growth
and the leverage may proxy for a firm’s access to financial markets. To account for therole of financial fatness or deep pockets in firm growth, initial assets and/or an indicator of
publicly-traded firms are included in the last three specifications of Table 3. Initial assets
has a positive effect on firm growth and marginally alters the coefficient on size and leveragevariables in the firm growth regression. The estimated coefficient is statistically significant
and implies that a one percent increase in initial assets increases current period size (sales)by about 0.02 percent while holding all other variables constant. However, the long run
elasticity implies a one percent increase in initial assets causes a 0.64 percent increase insize.9 In column M5, the estimated coefficient on the indicator of publicly-traded firms is-0.0177 and statistically insignificant. Initial assets appears to encapsulate the financial sizeof a firm.
9

Estimates based on specification M5 in Table 3.

10Table 4 presents the results when allowing for a nonlinear relationship between firm
growth and leverage. The coefficient estimates on the other variables, such as size, age,
public dummy, and initial assets, do not materially change. Focusing on the results ofcolumn M9, the estimated slope coefficients suggest a nonlinear response, since the slopes
are different across the quintiles. All slope coefficients are positive. The slope coefficientsfor the first and second quintiles are the largest and statistically significant. The slopes forthe third and fourth quintiles are insignificant. The fifth quintile is the smallest coefficientin magnitude, but is statistically significant. Finally, the LM(3) test does not reject thenull hypothesis of no third-order serial correlation at the five percent significance level for
specifications M1 to M9.
Elasticities of current period firm sales with respect to last period’s leverage are presented
in Table 5. Elasticities are calculated using the specifications M5 and M9 from Table 4. The
five rows in Table 5 contain an estimated elasticity for each of the five leverage classes. The
elasticities are evaluated at the mean leverage value within each class. Focusing on column
M9, the absolute value of the elasticities vary between 0.012 and 0.068 with the exceptionof the fifth leverage class, which sees very little response between a firm’s current size andlast period’s leverage. Although always positive, the response peaks at the fourth leveragequintile group with current size increasing approximately 0.068 percent for a one percent
increase in leverage while holding the other variables constant. These estimates suggest thatfirm size movements have a positive but nonlinear relationship with leverage.
For concreteness, Table 6 shows the elasticities between current size and age of a firm
across the different specifications. For most specifications, the age elasticity is statisticallysignificant except at ages 7 and 8. Although the ranges differ, age elasticity monotonicallyincreases for all specifications. For example, the age elasticity increases from -0.285 at age
one to 0.072 at age twelve for specification M9. Figure 3 presents the two standard deviations
confidence interval bands for age elasticities for each specification. As a comparison, each11panel contains the confidence interval band from the specification M1 which contains only
firm age and size as controls. The confidence interval bands for specifications containing
additional financial variables lie close to the confidence interval band for specification M1.
Table 6 and figure 3 suggest that including financial variables has little impact on the firm
growth-firm age profile.

5

Implications for Models of Firms Dynamics

Since the work by Evans (1987a, 1987b) and Dunne, Roberts, and Samuelson (1989), empirical literature studying firm size dynamics has documented negative age effects on firm growth
while simultaneous observing negative size effects. Learning, productivity movements, selection and financial frictions have all been used in theoretical models to explain the empiricalfindings. However, most of the theoretical models offer to explain only one of the effects
at a time. In Jovanovic (1982), learning and selection effects lead to age being the relevant
factor determining a firm’s dynamic path. Size effects are possible but potentially rendered
neutral with age controls. Further, age negatively affects the variance of growth, but isindeterminant for the mean of growth. Hopenhayn (1992) suggests productivity movements
drive a firm’s size evolution, which implies age effects on growth disappear when controllingfor a firm’s size.
As a first attempt explain the joint size and age effects in firm growth, Cooley andQuadrini (2001) combine two sources of heterogeneity across firms: productivity differences,a la Hopenhayn (1992), with financing differences. If Cooley and Quadrini (2001)’s model
provides a complete description of firm size dynamics then we should observe the following:
1. A negative relationship between age and leverage ratio with firms accumulating more
equity than debt as they age;
2. Significant and jointly negative age and size effects on firm growth when only age and12size are included as control variables;
3. The inclusion of a firm’s leverage ratio in regressions should result in negative size
effects on firm growth, while firm leverage should have a positive coefficient. Size
captures the accumulation of equity; larger firms, controlling for productivity, shouldhave more equity with less need to expand. Leverage captures productivity differences
as higher leveraged firms, controlling for equity, should be more productive with moredesire to expand;
4. If other age effects can be excluded, the firm age-growth profile should be almost flator at least greatly reduced with the inclusion of leverage in the regressions.
Empirically, predictions 1 and 2 hold, while prediction 3 appears to hold with a caveat.
The relationship between growth and leverage is positive and nonlinear, but not necessarily
economic or statistically significant across leverage quintiles. Finally, prediction 4 fails tohold in our data as very little change ensues to the age-growth profile when adding leverageto the regressions. The empirical findings show that financial variables provide information
regarding size dynamics in addition to a firm’s size and age.
The empirical implications of our results are clear; current models of firm dynamics
provide only partial explanations of observed relationships for firm size dynamics. The
significance of the financial variables clearly show that financial frictions matter as in Cooley
and Quadrini (2001). However, age effects still remain after controlling for a firm’s debt-toasset ratio, so that financial frictions alone cannot explain age effects. Thus, it seems that
other sources of age effects are likely also to matter empirically. Klepper and Thompson(2006) and Jovanovic (1982) provide two alternatives for age effect, but there are likely tobe other reasons as well for age effects to matter empirically.

13

6Conclusions

This paper empirically investigates the role of financial variables in firm growth. The study
finds the following empirical results. First, the relationship between firm growth and firm
leverage is positive, robust to alternative specifications and also nonlinear. The sensitivity ofgrowth to leverage is highest for firms in the lowest to intermediate leverage quintiles. Second,a non-monotonic U-shaped relationship exists between firm growth and firm age. Young
firm grow faster but the firm age-growth relationship reaches a minimum at approximately
age seven. Further, the inclusion of leverage has little impact on the firm growth-firm age
relationship.
Third, current firm growth increases with a firm’s initial asset level. These results suggestthat deep pockets matter for firm growth. Entrants who start off their life with higher levelsof assets have been able to raise substantial amounts of capital indicating significant accessto financial resources. These financially fat entrants may face less constraints, and thus, areable to grow faster in the future. An alternative plausible explanation is that new firms
with growth opportunities obtain a high level of financial capital as a method to fund future
investment projects. Access to financial resources is a function of firm quality; thus, firms
with a high level of initial assets likely obtain substantial financing since they are good quality
and have good potential investment opportunities. As is the case with leverage, accounting
for a firm’s financial resources does not greatly change the age-growth relationship.
Fourth, firm growth is found to have a negative relationship with firm size. The finding
matches the empirical result of previous studies such as Evans (1987a, 1987b), Hall (1987)
and Dunne, Roberts, and Samuelson (1989). Finally, firm growth displays negative growth
persistence.
These findings point to the need to account for firm growth’s simultaneous dependenceon size, age, and financial conditions. Theoretical models of industry dynamics are starting14

to incorporate financial considerations into determinants of firm size dynamics. Cooley andQuadrini (2001) provide a model where financial and productivity heterogeneity across firms
generate a simultaneous size and age dependence for firm growth. However, these results
suggest that conditional age effects generated from combining persistent productivity shocks
with financial frictions, as done in Cooley and Quadrini (2001), does not provide a complete
picture of firm size dynamics. Alternative explanations for the presence age effects include
the passive-learning model by Jovanovic (1982) and the model of industry submarkets ofKlepper and Thompson (2006).
It is now an open question to determine which of these mechanisms plays the biggest rolein firm dynamics. Financial variables are required to separate firm dynamics attributable tofinancial factors versus other age related aspects. None of the theories should be discounted
if their implications do not completely match the empirical findings. Rather we provide
empirical evidence to motivate richer models of firm dynamics.

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Windmeijer, F. (2005): “A finite sample correction for the variance of linear efficient
two-step GMM estimators,” Journal of Econometrics, 126(1), 25–51.
Zingales, Z. (1998): “Survival of the Fittest or the Fattest? Exit and Financing in the
Trucking Industry,” Journal of Finance, 53(3), 905–938.

16

A

Data Appendix

The data appendix provides details on the assets, equity, debt and sales variables, and deflation of these variables. The following information lists the components of assets, equity andsales variables. The information is taken from the General Index of Financial Information(GIFI) on the T2 corporate tax return.
1. Assets =• Current (Cash and deposits + Accounts receivable + Allowance for doubtful accounts + Inventories + Short term investments + Loans and notes receivable +Other currents assets)• Capital (Land +Depletable assets +Accumulated amortization of depletable assets +Buildings +Accumulated amortization of buildings +Machinery and Equipment +Accumulated amortization of machinery and equipment +Furniture and
Fixtures +Accumulated amortization of furniture and fixtures +Other tangible
assets +Accumulated amortization of other tangible assets)• Intangible capital assets (Intangible assets (i.e. goodwill, quota, licenses, incorporation costs, trademarks/patents, customer lists, rights, and research and development). + Accumulated amortization of intangible assets + Resource rights+ Accumulated amortization of resource rights)• Long term (Due from shareholder(s) and/or director(s) + Investment in joint
venture(s) and/or partnership(s) + investment in related parties + Long term
investments + Long term loans + Other long term assets)
2. Equity = Common shares + Preferred shared + Retained earnings/deficit
3. Debt = Assets - Equity
4. Sales =• Revenue (Trade sales of goods and services + Sales from resource properties• Other revenue (Investment revenue + Divided income + Commission income +Rental income + Fishing revenue + Realized gains/losses on disposal of assets+ Income/loss on subsidiaries/affiliates + Income/loss on joint ventures + Income/loss on partnerships + Alberta royalty tax credits

17

Table 1: Descriptive Statistics
Variable
Sales
Growth Rate Sales
Age
Leverage ratio
Growth Leverage
PublicInitial Assets

Average
MedianStd Dev.
2585.045 496.7565167 23939.49
0.0676
0.05680.487
4.9552 4.000022556
2.60850.86650.76642.9801
0.0614-0.0168
3.63040.008900.094
1625.7 175.7038663 22789.56

25th Quartile
210.3136525-0.0932.999963134
0.5262-0.1143078.84626943

75th Quartile
1311.596006
0.22426.999928957
0.99070.08050436.8107347

Note: Summary statistics are calculated using observations from the estimation sample with the
exception of the logarithm of initial assets. The summary statistics for the logarithm of initialassets are calculated using the firm sample from the estimations to avoid double counting on firmsthat appear multiple times.

Table 2: Age versus Leverage
Age
1
2
3
4
5
6
7
8
9
10
11
12

Leveraget
0.908
0.857
0.813
0.782
0.759
0.735
0.714
0.693
0.675
0.650
0.630
0.608

Survivors
Number Leverage1
28742
0.908
23569
0.892
19253
0.878
15966
0.868
13365
0.858
11215
0.849
9208
0.836
7421
0.822
5732
0.804
4123
0.789
2708
0.779
1281
0.787

Exitors
Number Leverage1
0
.
5173
0.990
9489
0.974
12776
0.962
15377
0.952
17527
0.947
19534
0.942
21321
0.939
23010
0.933
24619
0.928
26034
0.922
27461
0.914

Note: The columns contain the median leverage and number of firms within each category. Column
two presents median leverage of survivors at age t, while column four presents median leverage atage one for those firms surviving until age t.

18

Table 3: Firm Growth Relationship∆ log(Sizeit ) = αi + β1 log(Sizei,t−1 ) + β2 log(Sizei,t−2 ) + φ1 log Ageit + φ2 [log Ageit ]2+γdai,t−1 + δ log(assetsi0 ) + λpublici,t−1 + ²it .
Sizei,t−1
Sizei,t−2
Leveragei,t−1
Age
Age2

M1
-.1046

M2-.1044M3-.0986M4-.1029M5-.0969(.0100)∗∗∗(.0100)∗∗∗(.0096)∗∗∗(.0101)∗∗∗(.0097)∗∗∗

.0688

.0688

.0693

.0682

.0687

(.0100)∗∗∗(.0097)∗∗∗(.0096)∗∗∗(.0098)∗∗∗(.0097)∗∗∗

.

.0016

.0017

.0016

.0017

(.0003)∗∗∗(.0005)∗∗∗(.0003)∗∗∗(.0005)∗∗∗-.3112-.3115-.3087-.3071-.3047(.0347)∗∗∗(.0347)∗∗∗(.0350)∗∗∗(.03471)∗∗∗(.03499)∗∗∗

.0773

.0775

.0750

.0763

.0739

(.0100)∗∗∗(.0100)∗∗∗(.0100)∗∗∗(.0100)∗∗∗(.0100)∗∗∗Assetsi,0

.

.

.0190

.

Publici,t−1.

Constant
Observations
Number of Firms
Hansen-Sargan χ2
LaGrange Multiplier(1) χ2
LaGrange Multiplier(2) χ2
LaGrange Multiplier(3) χ2(.0064)∗∗∗

.

.

.0180
(.0063)∗∗∗.0175-.0177(.0298)(.0267)

.3181

.3183

.3219

.3137

.3180

(.0290)∗∗∗(.0290)∗∗∗(.0287)∗∗∗(.0291)∗∗∗(.0290)∗∗∗

89283
19233
0
0
.1350
.1070

89283
19233
0
0
.1365
.1061

88856
19125
0
0
.1078
.1010

88740
19149
0
0
.1634
.1000

88319
19042
0
0
.1304
.0958

Note: All results are estimated using the System-GMM estimator due to Blundell and Bond (1998). The
measure of firm size in the paper is sales. All variable have been demeaned of two-digit SIC and year variation.
Standard errors, in parentheses, are estimated using a two-step robust correction due to Windmeijer (2005).
*, **, *** indicate significance at the 10%, 5% and 1% level, respectively. The Hansen-Sargan and LaGrange
Multipliers χ2 test statistics are reported as p-values.

19Table 4: Firm Growth Relationship: Leverage Nonlinearities∆ log(Sizeit ) = αi + β1 log(Sizei,t−1 ) + β2 log(Sizei,t−2 ) + φ1 log Ageit + φ2 [log Ageit ]25X+
γk dak,i,t−1 + δ log(assetsi0 ) + λpublici,t−1 + ²it .
k=1

Sizei,t−1
Sizei,t−2
Leveragei,t−1
Quintile 1
Leveragei,t−1
Quintile 2
Leveragei,t−1
Quintile 3
Leveragei,t−1
Quintile 4
Leveragei,t−1
Quintile 5
Age
Age2

M6
-.1249

M7
-.135

M8
-.1283M9-.1219(.0107)∗∗∗(.0106)∗∗∗(.0111)∗∗∗(.0107)∗∗∗

.0794

.0713

.0696

.0712

(.0113)∗∗∗(.0110)∗∗∗(.0111)∗∗∗(.0110)∗∗∗

.0670

.0886

.0784

.0878

(.0082)∗∗∗(.0089)∗∗∗(.0090)∗∗∗(.0089)∗∗∗

.0287

.0756

.0446

.0758

(.0209)(.0182)∗∗∗(.0209)∗∗(.0183)∗∗∗-.0437.0133-.0535.0144(.0506)(.0447)(.0508)(.0449)

.0337

.0643

.0754

.0699

(.0513)(.0532)(.0539)(.0535)

.0015

.0013

.0013

.0013

(.0003)∗∗∗(.0002)∗∗∗(.0002)∗∗∗(.0002)∗∗∗-.3039-.2927-.2944-.2850(.0357)∗∗∗(.0364)∗∗∗(.0357)∗∗∗(.0363)∗∗∗

.0776

.0741

.0768

.0719

(.0102)∗∗∗(.0103)∗∗∗(.0102)∗∗∗(.0103)∗∗∗

.0364

.

Assetsi,0.

Publici,t−1.

Constant
Observations
Number of Firms
Hansen-Sargan χ2
LaGrange Multiplier(1) χ2
LaGrange Multiplier(2) χ2
LaGrange Multiplier(3) χ2(.0082)∗∗∗

.

.0352
(.0082)∗∗∗.0575-.0138(.0322)∗(.0282)

.3171

.3200

.3054

.3129

(.0305)∗∗∗(.0304)∗∗∗(.0306)∗∗∗(.0303)∗∗∗

89283
19233
0
0
.0204
.0875

88856
19125
0
0
.0496
.0916

88740
19149
0
0
.0858
.0891

88319
19042
0
0
.0598
.0863

Note: All results are estimated using the System-GMM estimator due to Blundell and Bond (1998). The
measure of firm size in the paper is sales. All variable have been demeaned of two-digit SIC and year variation.
Standard errors, in parentheses, are estimated using a two-step robust correction due to Windmeijer (2005).
*, **, *** indicate significance at the 10%, 5% and 1% level, respectively. The Hansen-Sargan and LaGrange
Multipliers χ2 test statistics are reported as p-values.

20Table 5: Firm Size/Leverage Elasticities
Leverage
Quintile 1
Quintile 2
Quintile 3
Quintile 4
Quintile 5

M60.02080.0175-0.0350
0.03270.0027M90.02720.04620.01150.06780.0024

Note: The table provides the elasticity of end of period size with respect to beginning of period debt-to-asset
ratio. Mean debt-to-asset ratio values within each quintile group are used to calculate elasticity values. The
columns represent two estimated specifications. Column one includes only the first two lags of firm sales
and firm age controls as additional regressor (column one of table 4), while column two contains two lags offirm sales, firm age controls, initial firm assets and public/private dummy variable as additional regressors(column four of table 4).

Table 6: Age Effects on Firm Size
Age
1
2
3
4
5
6
7
8
9
10
11
12

M1
-0.311∗∗∗-0.204∗∗∗-0.141∗∗∗-0.096∗∗∗-0.062∗∗∗-0.034∗∗∗-0.0100.011
0.029∗∗∗
0.045∗∗∗
0.060∗∗∗
0.073∗∗∗

M2-0.312∗∗∗-0.204∗∗∗-0.141∗∗∗-0.097∗∗∗-0.062∗∗∗-0.034∗∗∗-0.0100.011
0.029∗∗∗
0.045∗∗∗
0.060∗∗∗
0.074∗∗∗

M5-0.305∗∗∗-0.202∗∗∗-0.142∗∗∗-0.100∗∗∗-0.067∗∗∗-0.040∗∗∗-0.017∗∗∗0.003
0.020∗
0.036∗∗∗
0.050∗∗∗
0.063∗∗∗

M9-0.285∗∗∗-0.185∗∗∗-0.127∗∗∗-0.086∗∗∗-0.054∗∗∗-0.027∗∗∗-0.0050.014
0.031∗∗∗
0.046∗∗∗
0.060∗∗∗
0.072∗∗∗

Note: The table provides the elasticity of end of period size with respect to beginning of period age. The
figure provides the 95% confidence interval bands of the elasticity of end of period size with respect tobeginning of period age. Specification M1 and M2 calculate elasticities using coefficient estimates from
Table 3, respectively. Specification M6 and M9 calculates elasticities using coefficient estimates from Table
4. *, **, *** indicate significance at the 10%, 5% and 1% level, respectively. For a graphical representation,
see figure 3.

21

Figure 1: Growth and Leverage0

Growth rate of sales
.05
.1
.15

.2

Measured in terms of sales

1

2

3

4

5
6
7
Debt−to−asset deciles
Age=1
Age=7

8

9

10

Age=4
Age=10Note: The figure shows the median firm growth rate across the three age groups and ten leverage(debt-to-asset ratio) classes. Age one leverage decile points are used as cutoff values. Firms are thenplaced into leverage classes at a particular age given these cutoff values. Firm growth is calculated
as ∆ log(sizei,t ), where sales is used to measure size.

4

7

10

−.2 0 .2 .4 .6

1−.2 0 .2 .4 .6

Growth rate of Sales

Figure 2: Growth, Age, Size and Leverage

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

Size deciles
Debt−to−asset ratio: decile 1
Debt−to−asset ratio: decile 5
Debt−to−asset ratio: decile 10
Graphs by age

Note: The figure shows the median firm growth rate across age, size, and leverage (debt-to-asset
ratio). There are four different ages (one, four, seven, and ten), ten size deciles, and three leverage
deciles. Firms growth is calculated as ∆ log(sizei,t ), where sales is used to measure size.

22

Figure 3: Age Effects
M2

M5

M9

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

−.2
−.4
.2
0
−.4

−.2

Confidence Interval Range

0

.2

M1

age
M1 − No Financial Variables

Comparison

Note: The figure provides the 95% confidence interval bands of the elasticity of end of period size withrespect to beginning of period age. Specification M1 and M2 calculate elasticities using coefficient estimatesfrom Table 3, respectively. Specification M6 and M9 calculates elasticities using coefficient estimates from
Table 4.
M1 : ∆ log(sizeit )= αi +

2X

βk log(sizei,t−k ) + φ1 log Ageit + φ2 [log Ageit ]2 + ²it .

k=1

M2 : ∆ log(sizeit )= αi +

2X

βk log(sizei,t−k ) + φ1 log Ageit + φ2 [log Ageit ]2 + γdai,t−1 + ²it .

k=1

M5 : ∆ log(sizeit )= αi +

2X

βk log(sizei,t−k ) + φ1 log Ageit + φ2 [log Ageit ]2

k=1+γdai,t−1 + δ log(assetsi0 ) + λpublici,t−1 + ²it .
M9 : ∆ log(sizeit )= αi +

2X

βk log(sizei,t−k ) + φ1 log Ageit + φ2 [log Ageit ]2

k=1

+

5
X

γk dak,i,t−1 + δ log(assetsi0 ) + λpublici,t−1 + ²it ,k=123