ESSAYS IN FIRM DYNAMICS by ROBERT JOHN PETRUNIA B.A. (Honours), The University of Alberta, AB, 1996 M.A, The University of British Columbia, BC, 1997 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Economics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 2004 © Robert Petrunia, 2004 Abstract This thesis comprises three essays that analyze financial and non-financial aspects of firm and industry dynamics. The first essay investigates the evolution of a cohort of entrants during their first ten years of life. The study looks at the distributions of sales, assets, employment and debt-asset ratio for these firms over time and compares how these distributions change relative to distributions for incumbent firms. Entrants are smaller in terms of employees, assets and sales, but have a higher debt-asset ratio when compared with incumbents. These differences lessen over time because entrants have higher growth rates and smaller entrant firms have higher failure rates than compared to larger entrants. The second essay investigates whether long-term growth of a firm is independent of initial financial structure. I look at a panel of Canadian retail and manufacturing firms born in 1985. The analysis involves a two-part testing process. The first part tests whether firm growth exhibits initial size dependence. The growth process for retail firms exhibits initial size dependence, while the growth process for manufacturing firms does not. The second part looks at whether growth of ten-year old manufacturing firms is independent of initial debt-asset ratio. The result rejects independence with the finding that age ten conditional size of a manufacturing firm has a non-monotonic relationship with initial debt-asset ratio. The final essay examines whether Gibrat's law holds for groups of Canadian firms operating in manufacturing and retail sectors. Gibrat's law holds when firm growth and variability of growth are independent of firm size and firm growth is independent across time. Firm growth and variability of growth depend on size for each set of firms, which leads to violations of Gibrat's law. The source of these two violations is not survival bias, since the violations occur with the inclusion or exclusion of failing firms. A further violation is that negative growth persistence exists. Finally, 1 look at possible failure because of age effects. I examine a group of new firms with a common age and find the violations continue to occur for this group. 111 Contents Abstract ii Contents iv List of Tables vi Acknowledgements viii Introduction 1 Post-Entry Performance of Incorporated Entrants 11 1. Introduction 11 2. The Data 15 3. The Dynamics of the Cohort of Entrants 21 4. A Comparison of Entrants and Incumbents 27 5. Conclusion 32 6. Appendix: Variable Definitions 44 Impact of Initial Debt on the Long-Term Employment Growth of New Firms 46 1. Introduction 46 2. Models of Firm Dynamics 50 2.1. Passive Learning Model 51 2.2. Active Learning Model 54 2.3. Introducing the Debt-Asset Ratio 56 3. Data 57 4. Evolution of Size Distribution 60 5. Econometric Method 64 5.1. A Non-Parametric Test for Independence 64 iv 5.2. A Non-Parametric Test for Monotonicity 67 6. Results 69 7. Conclusions 72 8. Appendix: Maximum Likelihood Estimates 81 Does Gibrat's Law Hold? Evidence From Canadian Retail and Manufacturing Firms. 84 1. Introduction 84 2. Previous Studies 86 3. Testing Gibrat's Law 88 4. Data and Measurement Issues 90 4.1. Data 90 4.2. Measurement 91 5. Empirical Results 92 5.1. Are Firm Growth and the Variance of Firm Growth Related to Firm Size? 92 5.2. Growth Persistence 97 6. Conclusions 99 Conclusion 107 Bibliography 110 v List of Tables 1 Total General Corporate Income Tax Rates by Province, 1987 and 1997 3 2 Firm Breakdowns by Sector 35 3 Summary Statistics on 1985 Cohort For Selected Years 36 4 Cohort Distribution for Selected Years 37 5 Survival Patterns of Cohort 38 6 Summary Statistics on Cohort Survivors For Selected Years 38 7 Cohort Survivor Distribution For Selected Years 39 8 1986-1995 Quartile Transition Matrices: Cohort Survivors 40 9 Cohort: Mean Change in Variable Values by Asset Change Class 41 10 Summary Statistics on 1985 Incumbents For Selected Years 42 11 Incumbent: Mean Change in Variable Values by Asset Change Class 42 12 Exit Rates, Shares, and Mean Size of Cohort Firms Relative to Incumbents For Selected Years 43 13 Ratio of Cohort to Incumbent Percentiles in 1986 and 1995 43 14 Evolution of Employment Size Distribution over Age Manufacturing: 1985 Cohort 74 15 Evolution of Size Distribution over Age Retail: 1985 Cohort 74 16 Kolmogorov-Smirnov test, Manufacturing 75 17 Kolmogorov-Smirnov test, Retail 75 18 Kolmogorov-Smirnov test, Manufacturing 76 19 Kolmogorov-Smirnov test, Retail 76 20 Manufacturing: Mean, Standard Deviation and Number of cohort survivors for 1995 Employment Size (age 10) by Age 9 and Age 1 Size Class Categories 77 vi 21 Retail: Mean, Standard Deviation and Number of cohort survivors for 1995 Employment Size (age 10) by Age 9 and Age 1 Size Class Categories 77 22 Manufacturing: Mean, Standard Deviation and Number of cohort survivors for 1995 Employment Size (age 10) by Age 9 and Age 0 Leverage Class Categories 78 23 Test for mean independence of E[S]Q \ S9,...,S9_k,S] ,0]O =l] on S], Manufacturing 79 24 Test for mean independence of E[S]0 \ Sg,...,Sg_k ,S,,01O =l] on S], Retail 79 25 Test independence of E[S]0 \ Sg,...,S9_k,lev0,<f>}0 - l] from levo, Manufacturing 80 26 Maximum Likelihood regression results, Manufacturing 83 27 Maximum Likelihood regression results, Retail 83 28 1986-1995 Growth and Variance of Growth by 1986 Size Class, Survivors. 101 29 1986-1989 Growth and Variance of Growth by 1986 Size Class, Survivors. 101 30 1989-1992 Growth and Variance of Growth by 1989 Size Class, Survivors. 102 31 1992-1995 Growth and Variance of Growth by 1992 Size Class, Survivors. 102 32 1986-1995 Growth and Variance of Growth by 1986 Size Class, All Firms. 103 33 1986-1989 Growth and Variance of Growth by 1986 Size Class, All Firms. 103 34 1989-1992 Growth and Variance of Growth by 1989 Size Class, All Firms. 104 35 1992-1995 Growth and Variance of Growth by 1992 Size Class, All Firms. 104 36 Test of size-growth independence, 1986-1995 Growth 105 37 Test of size-growth variance independence, 1986-1995 Growth 105 38 Empirical results for persistence of growth (1989, 1992, 1995) 106 vii Acknowledgements I would like to thank my co-supervisors, Ken Hendricks and David Green, for all the help, suggestions and guidance provided along the way. My work benefited from helpful discussions with John Cragg. I have also benefited from discussions with Matthew Aharonian, Kim Huynh, Francisco Gonzales, Guofu Tan, and Okan Yilankaya. Thanks to all the participants of the empirical microeconomic lunch workshop at UBC for their questions and comments. 1 am hugely indebted to Andrew Heisz, Richard Dupuy, Leonard Landry, and Garnett Picot of Statistics Canada for assistance accessing the data and to Statistics Canada in general. They have made my life easier on my visits to Ottawa. 1 gratefully acknowledge the financial support of SSHRC (MCR1 grant 412-98-0025), through the Entrepreneurship Research Alliance, and the Bank of Montreal Fellowship. This would not have been possible without the love and support of my parents over the years. Finally, 1 owe the greatest amount of thanks to my wife, Mary-Lou, who was there for every step of the process with unconditional love and support. 1 can only hope to help you in your journey as much as you helped me in mine. viii Chapter 1 Introduct ion This thesis comprises three essays that analyze financial and non-financial aspects of firm and industry dynamics. I examine three issues: how does the size and financial state of firms change with age, how random is firm growth and what impact does a firm's initial debt structure have on its future growth. I argue they are worth investigating since there has long been a concern in industrial economics about firm and industry dynamics. Each chapter of the thesis looks at incorporated firms operating in Canada between 1985 and 1995.1 The period between 1985 and 1995 represented one of turbulence in Canada, where the peak and trough of one business cycle occurred. The mid to late 1980s were a time of economic boom in Canada. The cycle reached its peak in 1989. This peak was followed by a period, in the early and mid 1990s, which Pierre Fortin (1996) has called the Great Canadian Slump. The Great Canadian Slump, occurring between 1990-1993 and 1995-1996, was the most severe recession in Canada since the great depression. The economic environment in the early 1990s in Canada was not one, which induced success. Several other events occurred in Canada during the 1985 to 1995 period. The Bank of Canada began to pursue the goal of inflation targeting in the early 1990s. Fortin (1996) documents that real interest rates were high in Canada beginning in 1989. Real Canadian short-term interest rates were over three percent higher than real U.S. short-term interest rates in 1989. The Bank of Canada, in order to obtain price stability, maintained this ' Incorporated firms provide the focus group because of data limitations. There is no balance sheet information or financial information available for unincorporated businesses. Therefore, analysis using financial variables, which is done in this thesis, is limited to incorporated firms. 1 differential until after 1995. Exchange rates also varied over this period. The real value of the Canadian dollar appreciated against the U.S. dollar in the late 1980s. The real value of the Canadian dollar remained high until 1991, but depreciated 25 percent between 1991 and 1995 (Freedman and Macklem (1998)). The monetary environment of Canada in the early 1990s was such that Canadian firms dealt with high interest rates, but real prices of Canadian exported goods fell as the value of the Canadian dollar fell. The early 1990s was also a time of political uncertainty in Canada. Constitutional issues took centre stage. Uncertainty over the future direction of Quebec meant there was a potential political risk to investment in Quebec and even the rest of Canada. Further political events occurred with provincial and federal governments practising fiscal restraint by cutting budgets in order to reduce burgeoning debt levels. Structural changes happened in Canada over the period of concern. The 1989 Canada-U.S. Free Trade Agreement (FTA) and later the addition of Mexico with NAFTA meant trade liberalization and globalization began. There was a gradual reduction in tariffs following the agreements. Canadian firms would no longer be protected from U.S. rivals by Canadian tariffs, but Canadian firms would have easier access to U.S. markets with the elimination of U.S. tariffs.2 A second structural change was the replacement of the Manufacturers Sales Tax (MST) with the Goods and Services Tax (GST) in 1991. Also, the period between 1985 and 1995 had a large increase in the number of self-employed individuals.3 Finally, the retail sector experienced the entry of large U.S. discount 2 Baggs (2001) examines the effect of changing Canadian and U.S. tariffs on the survival of Canadian manufacturing firms. The reduction of Canadian tariffs has an adverse effect on firm survival, while the reduction of U.S. tariffs has a positive effect on firm survival. 3 Kuhn and Schuetze (2001) note that the number of self-employed in Canada between the ages of 25 and 54 grew by 119 percent between 1982 and 1998, while number of paid employed increased by 53 percent over the same period. 2 competitors, such as Walmart and Costco, in the 1990s. Canadian retailers were forced to deal with a greater competition as the result of entry by large U.S. retailers. Table 1 Total General Corporate Income Tax Rates by Province, 1987 and 1997 Corporate Tax Rate: Federal Corporate Tax Rate plus Provincial Corporate Tax Rate 1987 1997 Percent Newfoundland 52 42 Prince Edward Island 51 44 Nova Scotia 51 44 New Brunswick 51 55 Quebec 50 44.71 Ontario 51.5 43.5 Manitoba 53 45 Saskatchewan 53 45 Alberta 50 43.5 British Columbia 51 44.5 Source: Calculated from data in table 4.2 in Robin W. Boadway and Harry M . Kitchen, Canadian Tax Policy Third Edition, Canadian Tax Paper no. 103 (Toronto: Canadian Tax Foundation, 1999). Changes in corporate tax rates, payroll taxes and minimum wages in Canada also occurred in the late 1980s and 1990s. Beginning in 1987, corporate income tax rates fell. Table 1 shows the changes in the total general corporate income tax rate by province between 1987 and 1997. Total corporate income tax rate refers to the sum of federal corporate tax rate and provincial corporate tax rate.4 General refers to the tax rate paid by businesses before any allowable rate deductions.5 The table shows that in all provinces in Canada the rate of corporate income tax fell between 1987 and 1997. The corporate tax changes were the result of the major income tax reform in 1987, which, as Boadway and Kitchen (1999) point out, "broadened the corporate tax base and reduced the rates in 4 The general federal corporate income tax rate was 36 percent in 1987 and 28 percent in 1997 (source: Boadway and Kitchen (1999)). 5 For example manufacturing firms and small businesses receive preferential treatment in the tax system with corporate income tax rates lower than those reported in the table. Patterns of changes remain the same for these other groups. 3 order to make the corporate tax rate less intrusive in the business decision making and the corporate tax rate comparable to those in our major international competitors." The 1987 reform to corporate taxes sought to eliminate the favourable treatment received by firms in certain sectors of the economy relative to firms in other sectors of the economy.6 Employment costs for a firm increased in the late 1980s and early 1990s. Employer payroll taxes and provincial minimum wage rates rose over the period (Fortin (1996)). We now discuss the remainder of the thesis and the potential impacts the listed events might have on the analysis completed in each chapter. Chapter 2, which is written jointly with my supervisor Ken Hendricks, empirically examines post-entry dynamics of a cohort of entrants from both a financial and non-financial prospective. We use a unique longitudinal data set, which contains employment and balance sheet information for Canadian incorporated enterprises. The entry cohort analyzed includes those firms identified as employing workers for the first time in 1985 and as becoming incorporated in the same year. The study looks at the distribution of sales, employment, assets and debt-asset ratio for the cohort and examines how these distributions change with the age of these firms. The results show that cohort size (employment, sales and assets) increases greatly at the upper end of the distributions, but very little change occurs for the lower end of the distributions. The opposite occurs for the debt-asset ratio distribution with very little change in the values of upper quantiles and a substantial reduction in value of lower end quantiles. 6 For example, the general federal corporate tax rate in 1987 was 36 percent compared to 30 percent for manufacturing and processing firms. Further, Boadway and Kitchen (1999) note that manufacturing and processing firms received preferential treatment regarding capital depreciation deductions prior to the 1987 income tax reform. 4 Although, there appears to be a general increase in the mean size of a firm belonging to the entry cohort, the total contribution of the cohort in terms of employment, and sales reaches a peak in 1989. One likely explanation for this finding is the aforementioned occurrences in the Canadian economy over the time of analysis. Political circumstances, monetary and fiscal policy in the early 1990s, and the serious downturn in the business cycle in 1989 had serious effects on all businesses operating in the Canadian economy. We would expect that these events would have their greatest impact on young firms. Young firms are likely to be financially constrained and do not have access to sources of financing that could smooth over any impacts of the events in the Canadian economy. To isolate the effect of growth from survival on these distributions, I also calculate the distributions for the cohort firms that survive until the end of 1995. The patterns remain similar to the previous analysis for size and debt-asset distributions. 1 also look at how these firms grow. Equity is important for firm expansion. Analysis indicates that growing survivors finance a large portion of their growth out of retained earnings, which results in a lowering of their debt-asset ratios. Furthermore, the total contribution of cohort survivors increases over time. The result shows that there is likely a differentia] impact of the business cycle even among entry cohort firms. The downturn of the business cycle swept out a large number of these new firms reducing the total contribution of the entry cohort, but those entry cohort firms that do survive over the business cycle, on average, do continue to grow even with the downturn of the Canadian business cycle.7 Finally, the results show that cohort survivors are larger and have lower debt-asset ratios than compared to failing cohort firms. Exit happens to those firms that 7 Employment costs, such as payroll taxes, also play a role in a firm's employment choice. Surviving cohort firms continue to grow even through employment costs rise over the period of analysis. 5 experience losses and must accumulate debt to cover these losses. There are two forces at play, which drive the post-entry dynamics. First, there is the growth and falling debt-asset ratio of some survivors. Second, higher failure rates occur for firms with fewer employees, less assets, smaller sales and higher debt-asset ratios. The last part of Chapter 2 compares the performance of entrant firms to the performance of incumbent firms. Incumbents represent the set of firms operating before the 1985 time of birth for the entry cohort analyzed and therefore, incumbents have hired employees and are incorporated before 1985. This analysis addresses the questions: how do new firms compare to incumbent rivals at the time of entry and what differences occur between the two groups in the years after entry by the new firms? These questions have potential relevance for policy implications. Some believe that young firms face financing constraints, which hurt the survival prospects of young firms. Competitively strong firms fail because they are financially weak. Therefore, some form of help should be provided to competitively strong, financially weak in order to ensure their survival. Two comparisons are made. First, survival patterns are examined. The cohort of entrants has lower survival rates and higher hazard rates than compared to the incumbent group. The higher hazard rate for the cohort remains after ten years. The second comparison looks at the size gap between entrants and incumbents. The results show that the entrants start off smaller than incumbents, but the gap narrows substantially over time when looking at employment and sales numbers. Although narrowing, there is still a large gap in asset levels between the two groups. Finally, we note that like the entry cohort the total contribution of incumbent firm in terms of employment and sales also reaches a peak in 1989 and then drops off. Although, the drop off for incumbents is not as 6 great as occurs to the entry cohort. The comparison shows that events in the early 1990s such as the business cycle are likely to have different impacts for firms of different ages. Chapter 3 is an essay that provides a non-parametric test of the Modigliani-Miller (1958) hypothesis. The Modigliani-Miller (1958) theorem states that the value of a firm is independent of the amount of debt versus equity it uses to finance operations. The theorem has the implication that the debt structure of a firm should not affect its growth dynamics. The test examines whether the conditional employment size of a firm at age ten depends upon its debt-asset ratio at birth. The test is applied to a panel of Canadian retail and manufacturing firms that are born in 1985. The process generating size dynamics must be such that conditional size is independent of initial size in order for the test to be valid. In this case, conditional size refers to a firm's age ten-size conditional on size history of the firm. In Ericson and Pakes (1995), firms face a known productivity shock, but firms can invest each period to improve their productivity relative to competitors. The changing state of firms implies that conditional size does not exhibit initial size dependence. Alternatively, Jovanovic (1982) provides an example of a theoretical framework where conditional size does exhibit initial size dependence. I apply a non-parametric test developed in Pakes and Ericson (1998) to determine if conditional age ten-size depends on initial size for these firms. The finding is that size at age ten is independent of initial size for manufacturing firms after conditioning for firms' size history, while size at age ten for retail firms is increasing in initial size even after 8 Mata and Portugal (1994) find that the business cycle has a greater impact on younger firms. Further, Sharpe (1994) documents that employment fluctuations over the business cycle are much greater for smaller firms. 7 conditioning for size history. The models, such as Jovanovic (1982) where initial size contains information relevant to future growth dynamics, are consistent with retail data. Given these results, I test the hypothesis that age ten conditional employment size of a manufacturing firm is independent of its initial debt-asset ratio. The size of manufacturing firms does depend on initial debt-asset ratio, even after controlling for size history. A u-shaped relationship forms between age ten conditional size and initial debt-asset ratio for firms that have a history of being large. The analysis completed in Chapter 3 follows new retail and manufacturing firms from their start in 1985 until 1995. The business cycle is likely to have differential impacts on these firms. Sharpe (1994) finds that smaller firms and firms with higher debt-asset ratios have greater movements in employment levels over the cycle. Small firms or high debt-asset ratio firms tend to shed employees to reduce costs in order overcome the impact of potential reduced revenues when there is a downturn in the business cycle. Financing constraints are believed by many to affect the production activities of small firms or high debt firms. Some believe the monetary policy changes of the Bank of Canada further enhanced the borrowing constraints faced by all firms (see Fortin (1996)). Age ten for these new firms occurs in 1995 a year when the Canadian economy experienced a downturn. A negative relationship between initial debt-asset ratio and age ten conditional size might be expected because of business cycle and financial reasons. The analysis in Chapter 3 finds that a negative relationship is not necessary the case since the relationship between age ten conditional size and initial debt-asset ratio of manufacturing firms is nonlinear. 8 The result shows that debt-asset ratio of a manufacturing firm at birth does contain information about the long-term growth prospects of the firm. The result also shows that too much debt may be a hindrance to a firm's, especially a young firm's, operations. Therefore, policies aimed at reducing debt burdens are important to help young firms overcome any financial burdens. Chapter 4 looks at whether Gibrat's Law holds for Canadian firms operating in 1985. Robert Gibrat provided one of the first descriptions of firm and industry dynamics in his book Inegalites Economiques (1931). Gibrat noticed that firm size distributions for an industry were highly skewed and approximately lognormal. He proposed the Law of Proportionate Effect (LPE), or what has become known as Gibrat's Law, as an explanation for this finding. Sutton (1997) describes a large and growing literature, which examines validity of Gibrat's Law for various samples of firms. The Law of Proportionate effect, or Gibrat's Law, says that a firm's size change is proportionate to its size. If Gibrat's Law holds then three propositions hold: (i) firm growth is independent of firm size, (ii) variability of firm growth does not depend on firm size and (iii) firm growth is independent across time. I look at the validity of each proposition. Attention is limited to firms operating in manufacturing and retail industries, and a comparison is made across the two industries and between 1985 incumbents and 1985 entrants in these industries. The analysis is broken into two parts. Static analysis looks at whether proposition (i) and (ii) hold. For each group of firm analyzed, I compare mean growth rates and variability of growth rates for surviving firms across different size classes. The results are 9 quite clear in that these two propositions fail to hold. In all cases, smaller firms generally had higher growth rates and higher variability of growth. Mansfield (1962) notes that choice of sample is important for the analysis. Conclusions could differ when one looks at the sample of all firms versus the sample of only survivors. In order to address this issue, the above analysis is repeated for the sample of firms that contains both survivors and non-survivors. Results do not change with the inclusion of failing firms. Smaller firms continue to have higher expected growth rates and variability of growth. The second part of the analysis focuses dynamic growth and looks at whether proposition (iii) holds. This analysis concentrates only on survivors. There is negative growth persistence present for these firms. Negative growth persistence means that higher than expected growth in one period causes lower growth in the next period. Proposition (iii) is rejected because firm growth is negatively correlated across periods. Gibrat's Law fails to hold for each of the samples of firms. This result holds for manufacturing and retail firms. Age effects are not the likely cause of these violations, as the violations continue to occur when examining a group of new firms with a common age. Furthermore, the above analysis is completed for different years to account for any business cycle or other time effects. Accounting for the year has little impact on the results of the analysis. Gibrat's Law fails to hold for Canadian retail and manufacturing firms. 10 Chapter 2 Post-Entry Performance of Incorporated Entrants Joint with Ken Hendricks The purpose of this paper is to describe the dynamics of a cohort of entrants during its first ten years. The particular cohort studied is the set of firms in Canada that employed people for the first time in 1985 and was incorporated in that year. We compute the distributions of sales, employment, assets, and debt-to-asset ratio for the cohort and study how these distributions change as the cohort ages. We also compare the cohort distributions to incumbent distributions. Our results suggest that start-ups are on average smaller in employment, assets and sales than incumbents, and they have substantially higher debt-to-asset ratios than incumbents do. Differences in employment, sales, and debt-to-asset ratios diminish as the cohort ages. This reflects the impact of two forces: higher failure rates among smaller, younger firms and higher growth rates for cohort survivors than incumbent survivors. However, differences in asset levels persist. 1. Introduction Recent theoretical models of firm and industry dynamics highlight the role of firm specific productivity shocks. In these models, a firm grows or shrinks depending whether it experiences a "good" or a "bad" productivity shock. Exit is a consequence of a succession of "bad" draws, and entry is an equilibrium response to exit. Jovanovic (1982) introduced the first model of this kind and, in his model, the firm's shocks are drawn from a distribution with unknown, firm-specific mean and a known variance. Hopenhayn 11 (1992) considers a model in which the shocks follow a known Markov process that is independent across firms. Finally, Pakes and Ericson (1995, 1998) develop a model in which the shocks follow a known, but endogenous Markov process in which firms can invest to stochastically improve their chances of drawing a "good" productivity shock. Although the models differ in their specification of the probability law for firm-specific shocks, they generate predictions about patterns of entry and exit, and size dynamics that are broadly consistent with data. The theoretical focus on firm-specific sources of uncertainty has been motivated by empirical studies that have established its importance in accounting for firm and industry dynamics. Dunne, Roberts, and Samuelson (1988,1989a) have shown that entry and exit rates in the U.S. manufacturing sector are highly correlated across industries and that most of their variation is accounted for by industry effects. Dunne, Roberts, and Samuelson (1989b) and Davis and Haltiwanger (1992) have documented high turnover rates of jobs and firms in the U.S. manufacturing sector. The implication that hazard rates are non-increasing in firm size at a given age is consistent with the findings of virtually every empirical study (e.g., Evans (1987a,b), Dunne, Roberts, and Samuelson (1988), Wagner (1994)). Finally, the implication that the size distribution of firms that survive from an entry cohort is stochastically increasing in age9 is consistent with the evidence presented by Dunne, Roberts, and Samuelson (1988) and by Pakes and Ericson (1998). Baldwin (1995), Baldwin and Gorecki (1987, 1991), and Baldwin and Rafiquzzam (1995) obtain similar results in their studies of entry and survival in the Canadian manufacturing sector. 9 This implication can be obtained from each of the three models i f certain (plausible) restrictions are imposed on the probability law determining productivity shocks in the model. 12 The picture that emerges from these studies is of a Darwinian struggle in which the most productive firms survive and grow, and the least productive die, replaced by a new generation of firms willing to try their luck. The dynamics of individual entry cohorts is largely determined by the interplay of these two forces: growth of the strong and failure of the weak. It is a picture that gives Nature the predominant role in determining the fate of individual firms. Financial markets play no role. The implicit assumption is that firms are able to obtain the financing required to implement their optimal production plans as long as the present value of these plans are positive. Moreover, the nature of the financing, whether it is debt or equity, is irrelevant. Yet, many believe that the lower survival rates and higher turnover rates experienced by young firms can be attributed at least in part to borrowing constraints. Indeed, there is a body of empirical work (e.g., Gertler and Gilchrist (1994), Fazzari, Hubbard, and Peterson (1988)) that suggests borrowing constraints are important. This paper examines the post-entry performance of an entry cohort from a financial perspective. The goal is to provide stylized facts on which to base future theoretical and empirical work on the potential role of borrowing constraints. To accomplish this task we use a new longitudinal data set that has been constructed from two data bases maintained by Statistics Canada: the Longitudinal Employment Analysis Program (LEAP), which provides employment information on every employer in Canada, and The Corporate Tax Statistical Universe File (T2SUF), which provides selected balance sheet data on every incorporated employer in Canada. The data set covers all incorporated firms in Canada that employed workers during the period 1984 to 1995. The data allows us to identify the 13 entrants in each industry in each year, to compare them with incumbent firms, and to track their growth or exit in each subsequent year of the sample period. The particular cohort chosen for this study is the set of firms in Canada that employed people for the first time in 1985 and were incorporated in that year. The set of incumbents is all other incorporated firms that employed workers in Canada in 1985. The annual data available on each firm are the dollar value of sales, assets, and equity, and the number of full-time equivalent employees. The value of assets is drawn from the firm's balance sheet. It consists of capital assets like land, building, and machinery; short-term financial assets like cash; long-term financial assets like bonds; and intangible assets like goodwill. Liabilities, which we call debt throughout the paper, are derived from the accounting formula, which states that value of assets must equal the sum of the value of equity and liabilities.10 Also available, but not exploited in this study, is the three-digit standard industrial classification (SIC) number of each firm. The novel features of our study lie in the definition of the entry cohort {and incumbents) and the inclusion of financial variables in evaluating post-entry performance. Most of the previous studies have focused on the manufacturing sector and do not distinguish between incorporated and unincorporated firms. One exception is Pakes and Ericson (1998) who consider the retail sector as well as the manufacturing sector and define birth as the first time a firm hires at least one worker. Our definition is similar except that we have excluded unincorporated firms. Incorporation is an important financial decision since it changes the tax status of the firm11 and, perhaps more 1 0 Many previous studies define debt as a firm's liabilities net of its short-term debt. We break from this convention due to data limitations. 1 1 Private, Canadian-controlled incorporated firms are eligible for the small business deduction, which is calculated as 16 percent of the first $200,000 of taxable income. 14 importantly, the liability of the equity holders. Hendricks, Amit and Whistler (1997) have documented that attrition rates for unincorporated firms are at least twice that of incorporated firms. The paper is organized as follows. Section II presents the data and variable definitions. Section III provides an analysis of cohort dynamics. Section IV provides a comparison of the cohort to incumbents. Section V summarizes the main findings of the paper. 2. The Data The data for this study is a new longitudinal database that was prepared by Statistics Canada in collaboration with, and the support of, the W. Maurice Young Entrepreneurial and Venture Capital Research Centre at the University of British Columbia. The data set is based upon two data bases maintained by Statistics Canada: LEAP, a longitudinal data set that provides primarily employment information on all employer businesses, incorporated and unincorporated, that register a payroll deduction account with Revenue Canada; and T2SUF, which provides selected balance sheet information on all incorporated firms that file a T2 form with Revenue Canada. The latter data set consists of a series of annual cross-sections that can be linked through a number that identifies the corporation. The period of coverage is from 1984 to 1996. The analysis limits attention to incorporated firms since financial information is only available for incorporated firms. An enterprise that employs workers is required to register payroll deduction account with Revenue Canada for the purposes of unemployment insurance. Hence, an enterprise enters LEAP in the first year that it hires employees. It may have previously existed without employees as an owner-operated business or partnership. The measure of annual 15 employment provided is called "average labour units" or ALUs. These ALUs are computed by dividing the total annual payroll of the enterprise by the average annual income for workers in the relevant province, size class, and industry at the 3-digit SIC level.12 Thus, ALUs measure what might be thought of as the number of "standardized workers" employed by an enterprise over any year in which it operates the entire year. It represents an underestimate of the number of workers in the enterprise's first year in LEAP, since it is unlikely to have operated the entire year. The same issue arises with the enterprise's last year in LEAP, which is defined as the final year in which it records positive ALUs. In this case, the A L U measure, also, underestimates the enterprise's employment. An incorporated enterprise is required to file a T2 tax form on which it records important financial information. An enterprise enters T2SUF in the year that it is first incorporated. We will refer to this year as the T2 start-date of the enterprise. The date at which it ceases to be incorporated is called the fiscal end-date. Of the list of variables provided in T2SUF, we have selected three: sales, assets, and equity.13 Sales are gross revenue of the business as reported on the financial statement plus revenues from investments and joint ventures. Assets consist of current financial assets like cash, long-term financial assets like bonds, intangible assets like goodwill, patents or trademarks, and physical capital. Equity consists of common and preferred shares, and accumulated retained earnings (or losses). Debt is obtained by the following formula: Assets = Equity + Debt. A more detailed description of the variables is given in the Appendix. All financial values are measured in thousands of dollars. 1 2 Appendix 1 of Picot and Dupuy, 1996 provides details about L E A P and the employment measure. 1 ' We have not used other variables such as profit or net income because of measurement problems. \6 The presence of intangible assets does create a problem in the measurement of a firm's asset value. The value of an intangible asset is its cost; such costs include acquisition costs or development costs. However, if a valuable intangible asset is accumulated without any such costs then the actual value of the intangible asset does not appear on a firm's balance sheet. For example, goodwill is defined for accounting purposes as "the present value of future earnings in excess of the normal rate on net identifiable assets" (Meigs et al: 1991). Factors, such as extensive customer relations, reputation, and managerial quality, lead to a business earning more than the normal rate of return on net identifiable assets, which creates goodwill value for a firm's assets.14 Goodwill is recorded on the balance sheet only when identifiable assets are purchased by a firm for a price greater than dictated by their normal rate of return.1 5'1 6 Ideally, a firm's assets would include any potential goodwill or any other intangible asset values. This may lead to an undervaluing of a firm's assets. It is unclear how the degree of undervaluing varies with age. Older firms, having built up customer relations and experience, are likely to have higher levels of unvalued goodwill than compared to younger firms. Alternatively, entry may occur because new firms are developing new products or production processes. In this case, asset values for younger firms have greater biases than older firms, since the new products or processes are undervalued. One problem with merging the two data sets is the difference in time units. LEAP uses calendar time to report an enterprise's employment, whereas T2SUF uses the corporation's fiscal year in reporting its financial data. Fortunately, the fiscal year start 1 4 Meigs et al. (1991) define a normal rate of return as "the rate of return that investors demand in a particular industry to justify their buying a business at the fair market value." 1 5 A tangible assets economic value may differ from its accounting book value because of differences in rates of depreciation. This undervaluing problem is identical to valuing goodwill. 1 6 The value of a patent or trademark is similarly only known when the objects are traded. 17 and end dates were available and these were used to convert financial information into calendar years. If a firm's fiscal year-end is month z, then the values of its T2 variables for year t are calculated by taking a weighted average of the values reported for fiscal year ending in years t and t+1 with the weights being z/12 and (l-z)/12 respectively. Approximately 20% of firms have fiscal start dates of January 1 and the remaining 80% are distributed more or less uniformly across the first days of the other eleven months. The other problem is matching the corporate identifiers in the two data sets. The populations are not identical. An incorporated firm with no employees is present in T2SUF but not in LEAP. An unincorporated firm with employees is recorded in LEAP but not in T2SUF. Thus, firms could be matched only if they filed at least one tax return during the sample period 1984 to 1995 and employed someone during this period. Furthermore, the reporting units are not the same in the two data sets. In LEAP, an enterprise is defined primarily as a set of employees; in T2SUF, it is a legal entity. This difference created instances in which a single employer in LEAP was matched to multiple T2 identifiers and a single T2 identifier was matched to different LEAP identifiers over time. For more details on how these matching problems were resolved, and on the matching algorithm itself, the reader is referred to Whistler (2000). We shall adopt the LEAP definition of an enterprise. Therefore, when a firm in LEAP files multiple T2 forms17, we simply sum across the T2 accounts. The main reason for choosing the LEAP definition is that, in constructing this data set, Statistics Canada was quite careful to eliminate "false" births and deaths that can arise when an enterprise changes its name or breaks up into smaller units. It did so by tracking employees by their social security numbers and classifying an enterprise as a continuing enterprise if there is 1 7 The incidence of such cases in our data set was approximately 8%. 18 no substantive change in the set of employees. This procedure also proved useful in treating mergers and acquisitions. If enterprises A and B merge in year t, then a new enterprise called C is identified in that year and given a synthetic "history" that is constructed from the histories of A and B. The history of C is recorded in LEAP but the individual histories of A and B are lost. The retrospective reconstruction of cohorts creates some problems for studying cohort dynamics. Fortunately, the incidence of mergers and acquisitions appears to be negligible. The cohort of entrants studied in this paper is the set of firms that began life in 1985 as incorporated employers. Since a firm's employment is not accurately measured in its birth year, we will use the value of the firm's employment, assets, and equity at the end of 1986, its first complete operating year, to measure the initial state of the firm. Consequently, we dropped firms that did not survive 1985 or 1986. More precisely, the cohort consists of all firms that have • a LEAP birth date18 in 1985 • a T2 start date19 in 1985 or January 1, 1986, • employed a worker in 1986 and 1987. The number of firms satisfying the above criteria is 21,206. There were 1,854 firms that failed to meet the third criteria. Similarly, the control group against which we will evaluate the performance of the cohort of entrants consists of firms that have • a LEAP date prior to 1985 • a T2 start date prior to 1985 1 8 L E A P birth date is the year, which a firm first hires employees. 1 9 T2 start date is incorporation date. 2 0 Unfortunately, very little can be said about dropouts in 1985 and 1986 since partial reporting is a problem. 19 • employed someone in 1986 and 1987 We will refer to the latter set as the incumbents. The number of incumbents is 309,286. 36,759 incumbent firms failed to meet the third criteria. We included in our data set only those entrants and incumbents for whom we had complete data. Missing values in T2SUF and LEAP are recorded as zeros, which did not allow us to distinguish between missing values and actual zeros. We also dropped firms that stopped filing tax forms but continued to employ workers. This may reflect a switch from incorporated to unincorporated status but it is more likely to indicate a mismatch. The number of cohort firms in these categories is 8,076 and the number of incumbents is 102,667. Thus, the final sample sizes for the cohort and incumbents are 13,130 and 206,619 respectively. Table 2 provides a breakdown of cohort firms and incumbent firms by sector. The distribution of firms across sectors is similar for the two groups. Firms can exit from the data set in two ways. In LEAP, the exit year of an enterprise is defined as the final year in which the enterprise records positive ALUs. In T2SUF, the exit year is the last year for which the enterprise files a tax form. These two dates may not coincide since an incorporated firm that exits LEAP may continue to exist as an owner-operated enterprise, in which case, we can infer that the firm's employment is zero in the intervening years. In what follows, we report the results based upon the LEAP definition of an exit. They are not substantively different if the T2 exit definition is adopted. The last year of data is 1996. However, we will use 1995 rather than 1996 as the end of the sample period because many firms whose fiscal year ended in 1997 had not yet 20 filed tax returns for 1996. In addition, it is not possible to identify the firms that exited in 1996 without 1997 data. 3. The Dynamics of the Cohort of Entrants The purpose of this section is to document the behavior of the cohort in the first ten years of its existence. Table 3 provides summary statistics on the cohort at three-year 21 intervals. All dollar values are in thousands of real dollars. The producer price index was used to deflate sales values and the capital price index was used to deflate asset and equity values. Between the end of 1986 and the end of 1995, 5,302 firms exited from the cohort, with approximately half of the failures occurring in the first three-year interval. This is reflected in the hazard rate that declines sharply after the first three-year period from 20%' to 13%. The ten-year mortality rate for the cohort is 40.4%. This rate is considerably lower than the mortality rates cited in other studies. For example, Dunne, Roberts and Samuelson report an average ten-year exit rate of 79.6% in U.S. manufacturing during the period 1967 to 1982, and Pakes and Ericson report eight-year mortality rates of 52.9% and 60.7% respectively for the 1979 manufacturing and retail cohorts in Wisconsin. One factor is the exclusion of failures in 1985 and 1986 and firms with missing observations.23 However, another important factor is the exclusion of unincorporated firms in our definition of an entry cohort. A study by Hendricks, Amit, and Whistler (1997), working with the same data as this study, found that unincorporated firms 2 1 Series number D693420 in the CANS1M database of Statistics Canada. 2 2 Series number D15641 in the CANS1N database of Statistics Canada. 2 3 There were 9,930 firms dropped for these reasons. Out of the dropped firms 2,330 firms would have been classified as survivors. The failure rate for the dropped group is 76.5%. This accounts for the difference between our findings and the findings of Pakes and Erikson (1998). 21 comprise about 80% of any entry cohort and typically have ten-year mortality rates in excess of 80%. Clearly, incorporation is a significant predictor of survival.24 Despite the loss of firms, total employment for the cohort increased by 9.8% and total sales increased by 23.5%. The increase was not monotonic with time, however, since both employment and value of sales were highest in 1989. This pattern may be due to the business cycle. The year 1989 was a peak year and 1992 was a trough year. The value of cohort assets increased throughout the sample period by 27.7%. The average size of the cohort survivors, measured in employment, assets or sales, is approximately twice as large as the average entrant, which implies that the exits tend to be smaller than survivors are. Standard deviation of mean employment, sales and assets also rose by a factor close to two. The increase in the size of the median firm is much smaller than the increase in the mean. This suggests that the largest survivors are significantly larger than the largest entrants are. We have computed two measures of financial structure. The simple debt-to-asset measure is given by ( l / N ) I i = i ( D i / A i ) where Dj is value of firm i's debt, Aj is value of firm i's assets, and N is the number of firms in the set of firms to which firm i belongs. This measure is reported in Table 3 as the mean debt-to-asset ratio. Clearly, with a mean value of 1 in 1986, many members of the cohort must have suffered negative profits in 1986 and finished the year with more debt than assets. The ratio declined in subsequent years, probably due to exit of firms with excessive debt. 2 4 We wish lo look at financial and sales dynamics for entrants in addition to employment dynamics. Previous work has not looked at financial dynamics. Financial and sales data is only available for incorporated firms. Thus, we limit analysis to incorporated establishments. 22 A second measure of financial structure is the weighted average debt-to-asset ratio. For a group of firms, this measure gives the portion of total assets that can be attributed to debt for this group. Thus, this creates a measure of aggregate financial activity for a group of firms. The weighted average debt-to-asset ratio reported in Table 3 weights firm i's debt-to-asset ratio by its share of total assets. It is given by L=i((D i/A i)(A i/IN i=,A i)) = (LDO/CliAi). For entrants, the weighted average is slightly less than 80%. It declined to 70% within three years and stayed at this level for the remainder of the sample. Debt provides the main source of financing for these new firms. The negative difference between the cohort's simple and weighted averages implies that firms with more assets have lower debt-to-asset ratios. Most theoretical models that allow for idiosyncratic cost or productivity uncertainty and mortality imply (for plausible parameter values) that the size distribution of surviving firms increases with age. If a distribution is stochastically increasing with age, then its percentiles are also increasing with age. Table 4 examines this prediction, measuring size by employment, sales, or assets. Firms are ranked from smallest to largest and we report quartiles as well as the 10lh and 90 th percentiles. The last two panels provide information on the debt-to-asset ratio and how its distribution changes as the cohort ages. The percentiles of the employment and sales distributions increase over the first three-year interval. However, over the next two intervals, the lower percentiles decline while the upper percentiles, especially the 90th percentile, continue to increase. These results imply that the employment and sales are not stochastically increasing with age, at least after the first three years. The top 10% of the cohort survivors are getting larger, but 23 the bottom 10% is getting slightly smaller. One explanation for the absence of a stochastic ordering in employment and sales is that we are focusing here on a subset of the entry cohort, namely, incorporated firms, and not the entire cohort. Hendricks, Amit, and Whistler (1997) find that incorporated firms are typically have two to three times the number of employees at start up compared to unincorporated firms. This size discrepancy remains after ten years of age. An alternative explanation is that we do not explicitly account for business cycle conditions. The Canadian economy entered a recession in 1989, which lasted until 1992. A full recovery did not occur until after 1996 with residual effects of the recession felt in 1995. By contrast, the percentiles of the asset distribution are non-decreasing over each three-year period. The lower percentiles increased over the first three-year period and then remained roughly constant. The upper percentiles increased throughout the period and, by the end of the sample period, were more than double their initial values. The percentiles of the debt-to-asset ratios are strictly decreasing, which suggests that the equity-to-asset ratio of cohort survivors is stochastically increasing with age. This is not too surprising, since survivors tend to earn positive profits, which, if retained, raise the equity of surviving firms. The final panel in Table 4 decomposes the debt-to-asset ratio by asset classes. In 1986, firms in the bottom 10% of the asset distribution had on average more than twice as much debt as assets and firms in the next highest percentile set had almost as much debt as assets. Firms in the remaining percentiles averaged debt-to-asset ratios of approximately 80%. This pattern is repeated in each of the reported years. Thus, most of the negative correlation between debt-to-asset ratios and asset levels noted earlier arises 24 from the bottom quartile. As the cohort ages, debt-to-asset ratios tend to fall. In the first three years, they fall substantially across all asset classes, and in subsequent years, for firms in the top 50% of the asset distribution. The two forces that cause the percentiles on the cohort distributions to change as the cohort ages are exit and growth. Table 5 documents the effect of exits. The survival rates for firms in the bottom quartile of the cohort's employment or asset distributions in 1986 are at least 10% lower than the cohort average for each three-year period. Thus, large firms are more likely to survive than small firms are, thereby causing the percentiles of the size distribution of survivors to increase. The percentages are similar if one uses the top quartile of the debt-to-asset ratios. Note that the three-year hazard rates for the bottom quartile are substantially lower after the first three-year period. This result is consistent with many plausible specifications of the probability law for productivity shocks. To isolate the effect of growth on the cohort distributions, we considered the set of firms from the cohort that survived to the end of 1995. Table 6 provides summary statistics on this sample at three-year intervals. The values and patterns are similar to those reported for the cohort in Table 3, which is not surprising since the survivors comprise the bulk of the cohort.25 However, one striking difference between the survivor population and the exits is that the latter had much higher debt-to-asset ratios in 1986. The mean debt-to-asset ratio of survivors in 1986 was 0.83, which is substantially less than 1.0, the mean debt-to-asset ratio of the cohort in 1986. Table 7 gives the percentiles of the size and debt-to-asset distributions of survivors at three-year intervals. The percentile values are quite similar to those reported in Table 4, 2 5 The total sales, assets and employment of entrant firms that survive until 1995 grow over the years. For entrant survivors, the business cycle conditions does not appear to have as great an impact as it does on failing firms who are part of the entrant group. 25 which suggests that most of the changes in cohort percentiles are due to growth of survivors rather than exit. It is also interesting to note that most of the growth of most of the survivors occurred in the first three years. The only percentile that is strongly increasing throughout the sample period in each of the three size distributions is the 90 th percentile. Table 8 presents 1986-1995 size transition matrices. Surviving cohort firms are partitioned into groups based on size quartiles in 1986 and 1995. There is very little movement across the quartiles. With the exception of employment numbers, the majority of firms that start in a particular quartile in 1986 remain in the same quartile of the size distribution in 1995 (47.5% for employment, 53.2% for sales, and 50.1% for assets). Further, less than 20% of the firms that start in the lower 50% of the size distribution in 1986 end up in the upper 50% of the size distribution in 1995. Thus, only those firms that move to the top of the size distribution in 1995, a relatively small group of entrants, appear to have experienced continuous growth over the period. In Table 9, the population of cohort survivors is partitioned into six categories that correspond to the 10th, 25 th, 50th, 75th, and 90 th percentiles of the distribution of changes in asset values. The subsequent columns give the mean value of asset, employment, sales, equity and debt changes for survivors in each category. For example, the lowest 10% of survivors had a loss of asset value that averaged $513,200, a reduction in employees of 2.09, and a reduction of sales of $499,240. By contrast, the highest 10% of survivors had gains in asset value that averaged $4,034,730, an average increase of 26.5 employees, and an average increase of sales of $2,940,230. 26 Table 9 yields several interesting conclusions. First, surviving entrants that lose asset value also on average lose employment, sales, equity and debt. On the other hand, surviving entrants, who gain asset value, also on average, gain employment, sales, equity, and debt. Furthermore, the magnitudes of the mean changes in each of these variables are ordered across the categories in exactly the same way as the change in asset values. Second, the changes in sales are comparable to the change in asset values, which suggests that the latter changes are at least in part due to changes in physical capital.26 Third, the fall in debt for firms that lose asset value is more than three times their loss of equity. By contrast, except for the top 10%, firms that gain asset value have a larger increase in equity than debt. 4. A Comparison of Entrants and Incumbents In this section, we address the following question: how did the experiences of a cohort of entrants differ, if at all, from that of incumbents? From this question, we want to know whether the cohort of entrants are smaller than incumbents, and if yes, do entrants catch up to incumbents in the given time frame? Does growth help facilitate the improvement of cohort of entrants relative to incumbents? How do survival patterns compare across the two groups? What are the differences, if any, in financial structure between incumbents and the cohort of entrants? The comparisons between incumbents and entrants provide a look at the life-cycle patterns of firms and how growth and survival varies with age. 2 6 A firm's output increases with the accumulation of productive assets. Sales changes are bigger, in dollar terms, than compared to assets changes for the entrants. In comparison, incumbents have sales changes that are smaller, in dollar terms, than compared to asset changes. It appears that productive assets represent a greater portion of the accumulated assets for entrants than for incumbents. 27 The macro environment changes greatly between 1986 and 1995, which has implications for the comparison between the entry cohort and the incumbents. Firms in the entry cohort started operations during the booming portion of the cycle, where the incentives to enter are high. Life was somewhat easy for these firms during this period with the expanding economy. The downturn in the business cycle in Canada began in 1989 and lasted until 1992. Firms in the entry cohort now faced a not so friendly world. Older firms have established relationships and reputations, which firms in the entry cohort have not had time to develop due to their young age. We know from Table 3 that the mean employment, sales and asset size for an entry cohort firm rises with time. The size improvement occurs for the entry cohort whether the economy is booming or not. Now we look at incumbents to judge whether the experiences of the cohort of entrants are the same as the experiences of older firms over the cycle. Summary statistics on the set of incumbents at three-year intervals between 1986 and 1995 are provided in Table 10. The ten-year mortality rate for incumbents was 33.5%, substantially lower than that of the entrant cohort. The hazard rate is slightly higher in the first three-year period but is roughly constant thereafter at 11-12%. Employment and sales gains among incumbent survivors peaked in 1989 but over the ten-year period appear to approximately equal the losses from exits since total incumbent employment fell marginally from about 5 million to 4.6 million and total incumbent sales increased marginally from 578 billion to 619 billion. Once again exits were smaller than survivors since mean employment increased from 24.1 workers in 1986 to 33.5 workers in 1995, an increase of 38.9%. Similarly, mean sales increased from $2.8 million to $4.5 million, an 28 increase of 61.7%. Standard deviations of these two variables increased marginally. Median employment and sales were essentially unchanged throughout the sample period. The behavior of incumbent assets is quite different from that of employment and sales. Despite the loss of firms and the impact of the business cycle, asset values increased in each three-year period, and were 43% higher at the end of the sample period than they were at the beginning of the sample period. Mean assets increased 116% from $3.98 million to $8.62 million and median assets increased by 59.5%. The standard deviation of mean assets also doubled, indicating that the largest incumbents in 1995 had significantly more assets than the largest incumbents in 1986. The dramatic increases in total, mean, and median asset values contrasts sharply with the much lower increases for the corresponding statistics for employment and sales. We suspect that most of the growth in assets is in financial assets since investment in physical assets would have presumably caused incumbent sales to increase substantially more than they did. The mean debt-to-asset ratio for incumbents fell sharply in the first three-year period. However, the asset weighted average debt-to-asset ratio was essentially constant at 70% throughout the ten year period, which suggests that most of the decline in the mean ratio is due to exit of small firms with high debt-to-asset ratios. Table 11 decomposes the set of incumbent survivors in 1995 by their ten-year changes in asset values. As in the case of the cohort of entrants, there is a striking correlation between changes in assets and changes in employment and sales. Firms that lose assets also lose employment and sales, and firms that gain assets also gain employment and sales. The relative magnitudes of the changes are also similar. The major difference between incumbents and survivors is apparent in the lowest and highest 29 percentiles. Entrant firms that experienced the largest decline in asset values also lost a comparable amount of sales. By contrast, the loss of sales for incumbent firms in the same category is less than half the loss of assets. Similarly, entrant firms that experienced the largest increase in asset values also gained an equivalent amount of sales whereas the gain in sales for incumbents in this category was only !4 of the gain in asset values. Our conjecture is that the asset changes for the entrant cohort reflect primarily changes in physical assets, whereas a substantial component of the changes in asset values for incumbents involves changes in financial capital. Table 12 compares exit rates, shares, and the mean size of firms in the entry cohort to those of incumbents. The cohort of entrants experienced a higher mortality rate than incumbents, although the difference, especially after the first three years, is small. Although younger firms are more likely to fail than older firms are, they tend to grow faster conditional on survival than do older firms. In our sample of incorporated firms, the latter effect dominates, at least with respect to employment and sales. The cohort of entrants' share of employment and sales increased as they age, with most of the increase once again occurring in the first three-year period. In 1986, the average entrant had a little more than l/5 t h of the number of workers and sales of the average incumbent. Higher exit rates for smaller, younger firms and higher growth for entrant survivors caused these ratios to increase. Although, there is a fall in the relative mean employment size of an entry cohort firm from .297 to .295 between 1989 and 1992. By 1995, the employment and sales mean size ratios had increased to .31 and .273 respectively. Once again, the pattern for assets is quite different. The cohort of entrants' share of total assets declined throughout the sample period, from 0.6% to 0.54%. Assets of the 30 average entrant in 1986 were less than 10% of the assets of the average incumbent and this percentage was essentially constant throughout the sample period. Thus, entrant firms grew relative to incumbents in employment and sales but not in assets. One explanation for this anomaly is that incumbents over the sample period are accumulating primarily financial assets, which explains why they are not producing a whole lot more, whereas the cohort is accumulating physical assets and producing more. The comparison of mean size in Table 12 as a measure of the size "gap" between the cohort of entrants and incumbents is somewhat misleading since the set of incumbents includes some very large firms. Table 13 gives a more informative comparison by computing the ratio of selected percentiles of the entry cohort and incumbent distributions of employment, sales, and assets. The ratios for each variable, including the 90 th percentile, are considerably larger than the ratio of the means. Therefore, the percentile ratios provide a better measure of the size "gap" and the extent to which the cohort closed the gap over the sample period. The results for 1986 reveal that entrants are much smaller in sales, employment, and assets than incumbent firms at every percentile. Not surprisingly, the differential is greatest in assets, where even the smallest entrants have less than 60% of the assets of the smallest incumbents. The higher the percentile in sales, employment and assets, the larger is the differential. The 90 th percentile incumbent is always at least twice as large as the 90 th percentile entrant is, and in assets, the difference is considerably greater. The ratios for 1995 indicate that the entrants have closed the gap in sales, employment and assets at every percentile. The reduction in gaps was highest for employment. They were the smallest for assets, where percentile ratios increased 31 between 0.08 and 0.17 points. At the lower percentiles, entrant survivors were comparable to incumbent survivors in employment and sales, but their asset values were 30-40% less than the asset values of incumbent survivors. At the highest percentile, entry cohort survivors employed approximately 65% as many workers as incumbent survivors and sold a similar percentage of incumbent sales, but their asset values are still less than Vi the value of incumbent assets. One explanation of these findings is that the entrants' assets are more productive, and this may be a factor at the lower percentiles. However, a more plausible explanation is that incumbent survivors have relatively more financial assets than entrant survivors do. Unfortunately, we are not able to observe the age of incumbent firms. Therefore, it is only speculation that asset composition of firms is related to the age of the firm and not factors that are specific to the entry cohort. 5. Conclusion As the entrants age, the lower percentiles of the cohort size distributions do not change very much but the upper percentiles increase strongly, often more than doubling in size. Thus, ten years after the entrants were born, the average survivor is larger than the size typical of entrants in earlier years. These size dynamics reflect the interplay of two forces: growth of survivors and higher failure rates among firms with less assets, fewer employees and lower sales. The results suggest that most of the increases in the upper percentiles of the cohort distributions are due to growth of survivors rather than exit of small firms. On the financial side, it is the lower percentiles of the debt-to-asset ratio that decline sharply and the upper percentiles that do not change much. These dynamics represent the impact of exit and growth on the cohort's financial structure. Firms that exit have typically experienced losses and therefore have higher debt-to-asset 32 ratios. Survivors that grow finance a disproportionate amount of their growth out of retained earnings, thereby lowering debt-to-asset ratios. We explored this picture of survivor dynamics more carefully by classifying them depending upon whether or not they accumulated assets over the sample period. Firms that experienced a fall in asset values also lost employment and sales, and typically an almost equal amount of equity. The likely cause of the fall in asset value is depreciation of sunk capital. If correct, these firms appear to be dying, since their accounting profits are sufficient to meet variable costs, but not capital costs. By contrast, survivors that accumulated assets experienced strong positive growth in sales, employment, and equity. Equity accounted for most of the change in asset value. Strikingly, the growth rate in assets was typically two to three times higher than the growth rate in employment and sales. Thus, the picture that emerges is one of economically profitable firms who are 27 reinvesting their profits and expanding operations, causing debt-to-asset ratios to fall. We also compared the cohort of entrants to incumbents. Our results suggest that start-ups are stochastically smaller in employment, assets and sales than incumbents and have significantly higher debt-to-asset ratios. The cohort has higher failure rates and, conditional on survival, higher growth rates in employment and sales than incumbents. As a result, the difference between the cohort and the incumbents in employment and sales decrease as the cohort ages. The cohort also achieves convergence in debt-to-asset ratios. However, they remain substantially below incumbents in asset values. The typical incumbent survivor appears to be accumulating financial assets in addition to physical assets, whereas the average cohort survivor is accumulating primarily physical assets. 2 7 It is tempting to infer that capital-to-labour ratios rise, but the data does not distinguish between investment in financial assets and investment in physical capital. 33 This conjecture would also explain why the sales per dollar of assets are substantially lower for incumbents than the cohort when sales per dollar of employment are comparable. The major caveat to our comparative analysis of the cohort is that we have not controlled for industry effects. The composition of entrants is unlikely to be the same as the composition of the incumbents, since entry rates are likely to differ considerably across industries. We intend to address this issue in a subsequent paper. 34 Table 2 Firm Breakdowns by Sector Sector Number of Entrants Proportion of Total Entrants Number of Incumbents Proportion of Total Incumbents Primary and Agriculture 880 0.07 14,202 0.07 Manufacturing 1,189 0.09 20,943 0.10 Construction 2,094 0.16 30,612 0.15 Transportation 588 0.04 8,529 0.04 Communication and Other Utilities 70 0.01 1,121 0.01 Wholesale Trade 1,185 0.09 22,000 0.11 Retail Trade 2,433 0.19 40,728 0.20 Financial Services 2,248 0.17 37,298 0.18 Government Services 493 0.04 5,470 0.03 Other Services 1,950 0.15 25,716 0.12 35 Table 3 Summary Statistics on 1985 Cohort For Selected Years Year 1986 1989 1992 1995 Number of Firms 13,130 10,443 9,058 7,828 Survivor Rate .795 .690 .596 Hazard Rate .205 .133 .136 Employment: Total 73,177 92,549 83,515 80,326 Mean 5.57 8.86 9.22 10.26 (17.1) (23.7) (24.0) (28.1) Median 2.37 3.93 4.04 3.91 Sales: Total 7,836,355 10,025,509 9,601,225 9,680,555 Mean 597 960 1,060 1,237 (2,603) (3,504) (4,295) (5,766) Median 209 330 334 343 Assets: Total 4,990,357 5,650,886 5,576,595 6,371,010 Mean 380 541 616 814 (5,925) (5,689) (4,357) (6,138) Median 93 143 169 196 Debt-Asset Ratio: Mean 1.00 0.77 0.77 0.77 (2.66) (0.87) (0.71) (0.90) Median 0.88 0.72 0.68 0.67 Weighted Mean 0.79 0.71 0.68 0.69 *A11 dollar values in thousands of dollars. 36 Table 4 Cohort Distribution for Selected Years Employment Percentiles Year 1986 1989 1992 1995 10 th 0:55 0.95 0.91 0.77 25 t h 1.15 1.89 1.86 1.66 Median 2.37 3.93 4.04 3.91 75 , h 5.06 8.49 9.21 9.20 90 t h 11.25 18.52 19.40 22.40 Sales Percentiles Year 1986 1989 1992 1995 10 ,h 51 81 77 71 25 t h 101 155 153 144 Median 209 330 334 343 75 t h 463 772 830 872 90 t h 1066 1806 2031 2231 Asset Percentiles Year 1986 1989 1992 1995 10 , h 16 27 30 30 25 , h 40 61 67 72 Median 93 143 169 197 75 , h 221 355 435 520 9 0 ' h 535 830 1016 1248 Debt-Asset Ratio Percentiles Year 1986 1989 1992 1995 10 th 0.38 0.23 0.18 0.17 25 t h 0.64 0.46 0.40 0.39 Median 0.88 0.72 0.68 0.67 75 , h 1.02 0.96 0.95 0.93 90 t h 1.27 1.15 1.25 1.26 Debt-Asset Ratio By Asset Class Asset Class (percentile) Year 1986 1989 1992 1995 0-10% 2.30 1.25 1.35 1.55 10-25% 0.98 0.81 0.87 0.87 25-50% 0.87 0.73 0.74 0.71 50-75% 0.83 0.66 0.62 0.60 75-90% 0.79 0.65 0.60 0.60 90-100% 0.80 0.74 0.70 0.68 37 Table 5 Survival Patterns of Cohort 1989 1992 1995 Survival Rate Cohort Firms in Bottom Quartile of Employment in 1986 64.79% 53.65% 44.29% Assets in 1986 64.89% 53.74% 44.39% in Top Quartile of Debt-Asset Ratio in 1986 64.79% 53.76% 44.26% Hazard Rate Cohort Firms in Bottom Quartile of Employment in 1986 35.21% 17.20% 17.44% Assets in 1986 35.11% 17.19% 17.39% in Top Quartile of Debt-Asset Ratio in 1986 35.21% 17.02% 17.68% Table 6 Summary Statistics on Cohort Survivors For Selected Years Number of Survivors = 7,828 Year 1986 1989 1992 1995 Employment: Total 47,627 72,721 74,879 80,326 Mean 6.08 9.29 9.57 10.26 (16.8) (22.9) (23.2) (28.1) Median 2.76 4.30 4.30 3.91 Sales: Total 4,913,972 7,665,553 8,477,605 9,680,555 Mean 628 979 1,083 1,237 (1,850) (2,887) (3,799) (5,766) Median 244 361 361 343 Assets: Total 2,860,816 4,102,740 5,040,005 6,371,010 Mean 365 524 644 814 (2,330) (3,566) (4,576) (6,138) Median 110 160 184 196 Debt-Asset Ratio: Mean 0.83 0.71 0.73 0.77 (0.67) (0.50) (0.63) (0.90) Median 0.83 0.69 0.67 0.67 Weighted Mean 0.73 0.67 0.6.6 0.69 *A11 dollar values in thousands of dollars. 38 Table 7 Cohort Survivor Distribution For Selected Years Employment Percentiles Year 1986 1989 1992 1995 10 th 0:77 1.14 1.02 0.77 25 t h 1.44 2.15 2.04 1.66 Median 2.76 4.30 4.30 3.91 75 t h 5.76 9.03 9.67 9.20 90 t h 12.71 19.53 19.90 22.40 Sales Percentiles Year 1986 1989 1992 1995 10 th 70 94 85 71 25 , h 126 172 167 144 Median 244 361 361 343 75 t h 524 826 884 872 90 t h 1173 1868 2083 2231 Asset Percentiles Year 1986 1989 1992 1995 10 , h 24 32 32 30 25 t h 50 70 74 72 Median 110 160 184 197 75 , h 255 378 461 520 90 t h 585 849 1042 1248 Debt-Asset Ratio Percentiles Year 1986 1989 1992 1995 10 th 0.37 0.23 0.18 0.17 25 t h 0.60 0.43 0.39 0.39 Median 0.83 0.69 0.67 0.67 75 t h 1.00 0.92 0.92 0.93 90 t h 1.13 1.08 1.19 1.26 Debt-Asset Ratio By Asset Class Asset Class (percentile) Year 1986 1989 1992 1995 0-10% 1.14 1.04 1.23 1.55 10-25% 0.86 0.75 0.82 0.87 25-50% 0.79 0.68 0.70 0.71 50-75% 0.78 0.64 0.61 0.60 75-90% 0.78 0.63 0.59 0.60 90-100% 0.77 0.71 0.69 0.68 39 Table 8 1986-1995 Quartile Transition Matrices: Cohort Survivors Employment Transition 1995 Quartile 1 2 3 4 1986 1 1,045 528 256 124 Quartile 2 557 741 486 192 3 283 531 714 417 4 74 150 507 1,223 Sales Transition 1995 Quartile 1 2 3 4 1986 1 1,218 479 212 81 Quartile 2 531 826 427 167 3 156 539 833 410 4 77 111 471 1,290 Asset Transition 1995 Quartile 1 2 3 4 1986 1 1,191 459 257 73 Quartile 2 567 748 487 159 3 192 595 710 440 4 36 149 489 1,276 40 Table 9 Cohort: Mean Change in Variable Values by Asset Change Class Asset Change Class (percentile) Asset Change Employment Change Equity Change Sales Change Debt Change 0-10% -513.20 -2.09 -148.38 -499.24 -364.82 10-25% -39.18 -0.16 -3.62 -42.48 -35.56 25-50% 15.13 0.65 14.74 35.08 0.38 50-75% 134.19 2.47 79.10 203.94 55.09 75-90% 435.00 6.55 217.65 633.19 217.35 90-100% 4034.73 26.51 1094.50 4900.88 2940.23 A l l Firms Mean 448.42 4.18 150.07 588.02 298.35 Median 51.33 0.73 31.02 57.44 13.61 41 Table 10 Summary Statistics on 1985 Incumbents For Selected Years Year 1986 1989 1992 1995 Number of Firms 206,619 175,378 155,570 136,913 Survival Rate .849 .753 .663 Hazard Rate .151 .113 .119 Employment: Total 4,987,782 5,249,750 4,867,427 4,601,298 Mean 24.14 29.88 31.22 33.53 (980) (977) (1,085) (1,050) Median 4.38 5.49 5.43 4.96 Sales: Total 578,161,285 688,612,948 610,688,479 619,579,244 Mean 2,798 3,926 3925 4,525 (68,502) (107,773) (72,988) (80,112) Median 340 439 438 437 Assets: Total 823,415,972 949,398,280 1,102,678,604 1,180,921,175 Mean 3,985 5,413 7,088 8625 (219,072) (251,974) (343,770) (436,519) Median 210 269 303 335 Debt-Asset Ratio: Mean 0.78 0.67 0.69 0.71 (2.74) (0.93) (1.00) (1.46) Median 0.69 0.62 0.60 0.61 Weighted Mean 0.69 0.71 0.72 0.71 *A11 dollar values in thousands of dollars. Table 11 Incumbent: Mean Change in Variable Values by Asset Change Class Asset Change Class (percentile) Asset Change Employment Change Equity Change Sales Change Debt Change 0-10% -8894.74 -22.12 -2823.37 -4103.14 -6071.38 10-25% -119.48 -2.48 -42.07 -223.57 -77.41 25-50% -10.08 -1.31 -0.03 -54.58 -10.05 50-75% 118.02 0.16 71.63 66.32 46.39 75-90% 524.80 5.25 269.53 556.64 255.28 90-100% 40655.79 34.40 11079.93 10770.45 29575.86 A l l Firms Mean 3263.75 1.36 877.63 719.58 2386.12 Median 27.74 -0.24 18.28 -3.66 5.30 42 Table 12 Exit Rates, Shares, and Mean Size of Cohort Firms Relative to Incumbents For Selected Years Year 1986 1989 1992 1995 Relative Exit Rates Survivor Rates .937 .916 .900 Hazard Rates 1.353 1.124 1.141 Cohort Shares Employment .0145 .0173 .0169 .0172 Sales .0134 .0144 .0155 .0154 Assets .0060 .0059 .0050 .0054 Relative Mean Size of Cohort Survivors Employment .231 .297 .295 .310 Sales .213 .245 .270 .273 Assets .095 .100 .087 .094 Relative Mean Size of Cohort Exits Employment .163 .236 .225 Sales .154 .212 .233 Assets .067 .141 .062 Table 13 Ratio of Cohort to Incumbent Percentiles in 1986 and 1995 Year 10 th 25 t h 50 , h 75 t h 90 t h Sales 1986 0.84 0.72 0.62 0.52 0.43 1995 1.06 0.88 0.81 0.71 0.61 Employment 1986 0.64 0.61 0.55 0.49 0.42 1995 0.98 0.88 0.79 0.69 0.58 Assets 1986 0.57 0.53 0.45 0.39 0.35 1995 0.71 0.62 0.60 0.55 0.47 Debt-Asset Ratio 1986 2.02 1.58 1.29 1.13 1.14 1995 1.31 1.20 1.08 1.06 1.10 *Numbers are calculated using the simple average of ratios by industry. The results are almost identical when the industry ratio is weighted by the fraction of cohort firms in that industry. The industry classifications are primary and construction, manufacturing, distributive services, business services, consumer services, and public services 43 6. Appendix: Variable Definitions This section lists the components of assets, equity and sales variables. The information taken from the General Index of Financial Information (GIFI) and 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 assets28 - Accumulated amortization of intangible assets Resource rights Accumulated amortization of resource rights • Long term Due from shareholder(s)/director(s) Investment in j oint venture(s)/partnership(s) - Due from/investment in related parties Long term investments Long term loans Other long term assets Intangible assets include things such as goodwill, quota, licenses, incorporation costs, trademarks/patents, customer lists, rights, and research and development. 44 2. Equity • Common shares • Preferred shared • Retained earnings/deficit 3. 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 Other revenue Income/loss on subsidiaries/affiliates Income/loss on joint ventures Income/loss on partnerships Alberta royalty tax credits 45 Chapter 3 Impact of Initial Debt on the Long-Term Employment Growth of New Firms This paper provides a non-parametric test of the Modigliani-Miller (1958) hypothesis that the growth of a firm is independent of its debt structure. The test consists of determining whether the conditional size distribution of a firm that has survived its early years of life depends upon its debt-asset ratio at birth. The test is valid if the stochastic process determining firm growth does not exhibit initial size dependence, as in the Ericson and Pakes (1995) active learning model. Therefore, we first test for initial size dependence using the non-parametric test developed in Pakes and Ericson (1998). We apply this test to a ten-year panel of all Canadian retail and manufacturing firms born in 1985. Our results are similar to the findings of Pakes and Ericson: the growth process of retail firms exhibits initial size dependence and the growth process of manufacturing firms does not. We then test the hypothesis that initial debt-asset ratios are irrelevant to growth of ten-year old manufacturing firms. We reject the null of independence, and find evidence of a non-monotonic relationship between age ten conditional size and the initial debt-asset ratio. 1. Introduction New firms face the post-entry challenges of survival and growth. These firms lack financial resources and rely heavily on borrowing to finance operations. Many believe that borrowing constraints hinder the development of new firms. These individuals 46 believe that higher failure rates of new firms and size restrictions on new firms are at least partially caused by borrowing constraints. Further, the severity of the borrowing constraint on firm operations is directly related to the firm's level of debt. Highly indebted new firms face a debt burden that is not easily overcome. This paper addresses these issues by examining the relationship a firm's initial debt-to-asset ratio (leverage) has with future employment dynamics of the new firm. We ask the question, "Do financial conditions matter to firm dynamics?" Modigliani and Miller (1958) demonstrate under certain conditions that financial structure is irrelevant in determining the value of a firm. In this world, real side firm operations do not depend on financial factors. Leverage has no impact on investment. The ability of a firm to obtain financing depends on the quality of its projects. A firm with good projects is able to obtain the financing required to implement optimal production plans regardless of the state of its balance sheet. Jovanovic (1982), and Ericson and Pakes (1995) introduce models of firm and industry dynamics, which implicitly assume that the financial state of a firm is irrelevant to its production. In these models, firm dynamics depend on productivity shocks a firm faces. Idiosyncratic sources of uncertainty in these models mean that similar firms operating under the same circumstances can exhibit very different future histories. These theoretical models of firm dynamics have been motivated by trying to explain the findings in a number of empirical studies that examine the dynamics and performance of firms. Dunne, Roberts, Samuelson (1989a) and Evans (1987a,b) have documented for U.S. manufacturing firms that employment growth is negatively related to the age and size of a firm, while hazard rates are decreasing in firm age and firm size. Virtually every 47 empirical study on manufacturing firms finds that hazard rates are non-increasing with firm age.29 Troske (1996) finds that firm employment growth is negatively related to firm age and size for Wisconsin manufacturing and financial service firms. The effects of financial variables on the firm dynamics have largely been ignored in this theoretical and empirical literature on firm dynamics. In the finance literature, theoretical and empirical results show that leverage can have a restrictive role on the real side operations of firms through liquidity effects. Highly leveraged firms face cash-flow demands from debt service payments, which limits the firm's ability to take advantage of new opportunities. Myers (1977) shows that it is possible that highly leveraged firms cannot obtain financing for new projects with positive net present value, because of debt requirements. Thus, too much debt can lower the growth and value of firms. There have been a series of empirical studies that document the effect a firm's leverage has on its growth. Whited (1992) estimates Euler equations for firms and finds that the investment-cash flow relationship depends on a firm's leverage. Cash flows have a greater impact on investment for highly leveraged firms. Opler and Titman (1994) find that sales declines are much greater for highly leveraged firms in declining industries. Sharpe (1994) shows that employment fluctuations over the business cycle are greater for highly leveraged firms. Lang, Ofek and Stulz (1996) find a negative relationship between leverage and the growth of core and non-core segments of firms. These studies suggest that leverage is important to investment. This paper looks at the impact initial leverage has on future long-term employment dynamics of new firms. One problem when analysing the relationship between leverage 2 9 See for example Wagner (1994) for German firms, Mata and Portugal (1994) for Portuguese firms, and Audretch (1991) U.S. firms. 48 and employment size is that leverage and employment size might be correlated because they are determined by similar factors. A second similar problem is that leverage might be a proxy for the quality of a firm or the growth opportunities of a firm. There are two basic arguments describing why leverage might proxy for growth. First, Lang, Ofek and Stulz (1996) argue that firms with good investment opportunities choose lower levels of leverage to build up financial slack to be able to take advantage of the growth opportunities. Second, a manager could choose a high level of debt to signal that his firm has good future growth opportunities.30 Leverage can be positively or negatively related to firm growth for endogenous reasons. We address these problems two ways. First, we compare the size dynamics of firms at age ten with initial leverage, rather than current leverage. The growth opportunities for a firm are likely to be different at age ten then they are at age zero. Second, we test whether age ten size depends upon initial size. In the passive learning model of Jovanovic (1982), a firm's productivity shocks each period are taken from a distribution with a time-invariant, firm specific productivity parameter. Higher productivity leads to higher revenues, which increases a firm's size. In the Bayesian world, the dependence between current firm size and initial size always exists, because firms are endowed with a permanent factor that determines productivity and a firm's productivity determines its size. This dependence does not disappear even when we condition on the firm's size history. The use of initial leverage is still problematic in this situation, since initial leverage might also depend on the permanent factor determining size dynamics, which means that initial leverage and current firm size are correlated through the permanent productivity parameter. 3 0 Financial signaling arguments began with Ross (1977). 49 In the active learning model of Ericson and Pakes (1995), the value of the productivity parameter determining a firm's productivity shock each period is no longer time-invariant. In the active learning world, current (conditional) size becomes independent of initial size with time. Factors determining initial firm size and initial firm leverage will be different than factors determining firm size in the future. Initial leverage and current firm size will not be related through common determining factors. Therefore, we first check whether age ten conditional size depends on initial size. Pakes and Ericson (1998) develop a non-parametric test that tests for initial size dependence. We apply this test to a ten-year panel of all Canadian retail and manufacturing firms born in 1985. Next, we check for a relationship between initial leverage and current firm size only in cases where the current firm size is independent of initial firm size. The paper is organized as follows. Section 2 outlines the two models of firm dynamics and their empirical implications. Section 3 describes the data used, while section 4 examines the firm size distributions for a cohort over time. In section 5, we discuss the non-parametric procedures used to test the relevant hypotheses, while section 6 provides the results of these testing procedures. Section 7 concludes. 2. Models of Firm Dynamics We start our discussion of firm dynamics by outlining the basic decision problem a firm faces each period. Next, two alternative models of firms dynamics are considered and their differing empirical implications are highlighted. In each period, firms compete in a homogeneous product industry, take prices as given and are endowed with a payoff relevant random variable, 77,, which varies across firms and over time. A higher realization of 7] implies a firm is more productive, and thus, the firm earns higher profits. 50 2.1. Passive Learning Model Jovanovic (1982) develops a model in which each firm is endowed with a time-invariant productivity parameter, 0, which is specific to the firm.31 The firm's productivity shock, 77,, depends on the true value of the firm's 6. Larger values of the firm's permanent 6 will generate larger realizations of 77, which lead to higher output levels, and thus, higher profits.32 At entry, a firm's manager does not know the value of his firm's productivity parameter, but he knows that 6 is taken from a random draw from the prior probability distribution Go(#). Firms use this prior along with realizations of 77, say n' = («,,...,«,), to update (in a Bayesian fashion) beliefs about its 6 and the value of future cash flows. Each period, a firm's manager uses the updated posterior to form a new expected value of his firm's 6. The process generating 77,, conditional on 6, is allowed to depend on past realizations of 77. The dependence allows the productivity shocks to be correlated over time even after conditioning on c?. It is assumed that firms with good productivity shocks, conditional on 6, should continue to have good realizations of shock values in the future. The firm's problem in each period becomes a sequence of two choices. First, the firm must decide whether to produce in period t. This decision is based on current beliefs about 6, which determines beliefs about future profits. Second, given the firm decides to continue to operate; the firm must decide a level of production. A firm discovering that it has a low 6 shrinks in size and eventually exits the industry, while a firm discovering 3 1 Lippman and Rumelt (1982) develop a similar model where innate ability is unknown to the firm upon entry, but which is revealed to the firm immediately after entry. 3 2 One interpretation of the uncertainty is that it represents managerial skill. For example, the skill of a manager is not necessarily matched to the skill required to manage a firm. The mismatch of skill is only learned after time. 51 that is has a high 6 continues to operate and expand. Therefore, only firms with high values of 6 are survivors, and thus, the 0-distribution increases with time. An empirical implication of the passive learning model from this selection process is that the size distribution of surviving firms is also stochastically increasing in age, since TJ, and therefore size, is stochastically increasing in 6. Pakes and Ericson (1998) show that the passive learning model has implications concerning the process generating firm size conditional on survival. The payoff relevant productivity shock in period t has two sources of dependence on past size realizations. First, there is a dependence created because the distribution of r\t, conditional on 6, depends on past realization of 77. The first source of size dependence may die out as time passes and will, for example, if the process generating 77,, conditional on 6, is a finite Markov process. Second, the passive updating process continues to lead to this dependence on the past. The second source means that current size and survival depends on initial size since initial firm size contains information about the firm. These implications result from the fact that 6 is time invariant. Al l previous realizations of a firm's 77 contain information about a firm's 6. A firm's 6 determines the distribution of future values. The time invariance means that there exists a dependence of the joint distribution of r/t and 77,, so that a larger realized value of 77, means that a firm is likely to have a larger value 6, which leads to larger realization of 77,. This dependence does not erode as time passes. Given the relationship between 77, and 77,, and the fact that size is increasing in current realizations of 77 implies that current conditional size or E[St I 5,,_1,...,.S'(_i,5'1,^ = l] where St is the firm's size at age t, is increasing in Si. 52 The value of a firm in the passive learning model depends on the fixed permanent parameter 6. Although the firm does not know the value of its 6, production provides signals that are used by the firm to update its beliefs. Financial decisions might also depend on these signals. For example, we measure initial leverage at the end of the firm's first operating year. Initial leverage could be large because the firm has received a bad productivity shock in the first period and must build up debt. Thus, initial leverage might contain information about a firm's 6. Further, a measure of leverage at the firm's birth would not necessarily solve this problem. Firms could receive signals before operations, which then are used by the firm to make its financing choice. Again, initial leverage contains information about the firm's 8. Current conditional size could be related to initial leverage through the permanent 6 It is possible that factors other than productivity shocks affect the determination of a firm's size. One example is that leverage constrains production activity of a firm, so that highly leveraged firms have lower growth rates than lower leveraged firms. A second possibility is that leverage is correlated with a variable that determines a firm's size in a given period. In the analysis, a firm's employment is the measure of firm size. However, there are other measures of firm size, which are directly related to a firm's employment size. Capital level is also a measure of firm size. The capital requirements are different across manufacturing industries. A firm's employment in any given period is increasing in the firm's level of fixed physical capital. Leverage and physical capital could be correlated. For example, it could be the case that firms with higher levels of physical capital have lower leverage levels, because creditors are willing to provide small levels of debt to finance capital purchases, but large capital purchases must be financed with 53 equity. In this case, leverage and employment size are correlated because leverage is correlated with physical capital and physical capital determines the employment size of a firm. This world is similar to the passive learning model with a firm's level of capital providing a fixed component that determines labour productivity. Current conditional employment size depends on leverage because a firm's leverage determines an underlying factor in the choice of a firm's employment. Therefore, we do not test whether current conditional size is independent of initial leverage when size dynamics appear to be driven by a permanent factor, as is the case in the passive learning model. 2.2. Active Learning Model Ericson and Pakes (1995) provide an alternative model of firm dynamics. Firms are endowed with a 77,, which is a random variable that has a positive effect of firm profits. As with the previous model, the payoff relevant random variable is stochastically increasing in the firm's productivity parameter, 6t. However, a manager now knows the value of its firms 9, (as well as those of other firms) and can improve 6t through an investment process. A firm's managers have three decisions to make each period. First, they must decide whether to operate the firm. As in the passive learning model, if a firm is shutdown then it is shutdown forever. If management decides to operate the firm in period t then managers must decide on a level of production and a level of investment. A firm's relative value of 0, determines its profitability. Those firms with larger relative values of 0, are more profitable than firms with lower values of 6t. Successful investment will enable the firm to become more profitable, since successful investment improves the value of a firm's 6t. Unsuccessful investment or no investment causes the 54 firm to fall behind its competitors, since 6t does not change. Many periods of unsuccessful investment leads to exit since the firm has fallen too far behind its competitors to be profitable. Although not necessarily the case, it is possible that the size distribution of surviving firms in a cohort increases with age in the active learning model. The distribution of surviving cohort firms converges, as t grows large to a time invariant distribution. Further, Pakes and Ericson (1998) show that it is possible for the convergence of the distribution to be monotone after some finite age t*. This slightly contrasts the passive learning model where the size distribution should stochastically increase with age. However, we expect that only in very specialized cases do firm size distributions not increase over time for a cohort. There is one significant difference between the two models enables one to empirically differentiate between the two models. In the active learning model, the parameter, which determines the distribution of profits, 6t, evolves over time. Current values of 77, are governed by different value of 6 than those in earlier years. The dependence between 77, and 77, will eventually die out, as t grows large. This will mean that the current year size will eventually become independent of initial year size as time passes, since the determinant of current year size is independent of the determinant of initial size. The independence holds for the conditional distribution of St, so the distribution of St conditional on recent size history quickly becomes independent of initial year sizes. The independence of the condition current size distribution implies that E[St | 5,_,,...,iS'(_t,S1,0( =l] will not depend on Si . This contrasts the passive learning model, where E[s, | S',_],...,S',_t,S'1,0, =l] is increasing in Si. Industry data can be used 55 to test these implications to determine which model is consistent with the industry in question.33 2.3. Introducing the Debt-Asset Ratio In the active learning model or other similar models, the parameter that determines a firm's value and size is changing from period to period. Financial decisions could still depend upon the firm's underlying productivity parameter. However, the movement of a firm's productivity parameter means that a firm's productivity at birth becomes independent of a firm's productivity in the future. An active learning world does not mean that future size is independent of initial leverage, but we can rule out dependence of these two variables through a third underlying permanent factor, such as underlying productivity. Once we accept the independence of E[St | 5 , / _, , . . . ,5 / _ t ,5 ' 1 ,^ , =l] with Si the next step of the process determines whether E[St | S/_,,...,S,_A,Z,evo,0/ =l] is independent of Levo, or a firm's initial debt-asset ratio. The conditioning follows from the previous discussion of the active learning model. The random productivity parameter, 77,, provides the evolution of the distribution of a firm's profits over time. We must control for the movements of nt when looking at the impact of leverage on future employment size. There is a direct relationship between a firm's size at time t and the value of its 77,. 3 3 One final note regarding the active learning model is that it is similar to Hopenhyan's (1992) model. In Hopenhyan (1992), the productivity shock evolves exogenously as a known (finite) k order Markov process. Lag size dependence disappears because the productive shock follows a finite process. 56 Therefore, a firm's size history continues to condition for its productivity shocks or profit history.34 The test of independence between E[St | St_x,...,St_k,Lev0,<j)t =l] and Levo looks at whether a firm's financial situation provides information about the future of the firm. Cooley and Quadrini (2001) extend Hopenhyan's (1992) model of firm and industry dynamics. There are two sources of firm heterogeneity in this model. First, similar to Hopenhyan (1992), firms receive a known productivity parameter, which changes exogenously over time through a finite order Markov process. Again, we can control for this source of heterogeneity through size conditioning. The second source of heterogeneity is that firms have different values of equity at birth and in subsequent periods. Differences in debt-asset ratios reflect differences in equity since low equity firms must use debt to finance operations. The rejection of independence between E\St | S,_],...,Sl_k,LevQ,<pt = l] and Lev0 leads one to believe that a firm's debt-asset ratio contains information that is specific to the firm. A world similar to Cooley and Quadrini's exists, where a firm's financial state matters and a firm's initial leverage tells us something about its future employment growth. 3. Data This section provides a brief description of the data set and the variables used in the analysis. The data are taken from the T2LEAP database. This database was created by Statistics Canada through the merging of two databases. The first database, Longitudinal Employment Analysis Program (LEAP), contains employment information from all 3 4 Debt-asset ratio could also contain profit information. Firms make adjustments to equity through the accumulation of retained earnings or losses. Equity accumulation or de-accumulation changes the value of a firm's debt-asset ratio. 57 employer enterprises within Canada. An employer enterprise files a payroll deduction record with Revenue Canada if they hire employees. Firms enter the LEAP database in the first year they hire employees and exit the database in the last year they hire employees. Each firm is provided with a business registry number (BSNUM) so that exit and re-entry by the same firm does not occur. Similarly, a firm that changes its name will not be recorded as a simultaneous entry and exit since BSNUM does not change for this firm. The second database is the T2SUF database, which contains balance sheet information taken from a firm's T2 tax records. A firm enters the T2SUF database when it becomes incorporated since only incorporated firms file T2 tax returns. A firm exits when it is liquidated.35 Therefore, the T2LEAP data consists of all incorporated enterprises in Canada that employ workers. The sample period is 1984 through to 1996. However, partial reporting by some firms in 1984 and 1996 reduces the useable sample period to 1985 to 1995. The database accounts for mergers, acquisitions and spin-offs, so these activities do not create false entrants or exits. The T2LEAP database defines firms retrospectively. For example, if firm A merged with firm B in year t, then a new firm, C, is created in year t with a synthetic history aggregated from the histories of firms A and B. The individual histories of firms A and B disappear from the database, and firm C represents their joint operations before and after year t. The variables in the database are annual firm employment, sales, assets, and equity. Firm sales and employment are measured as flows over a year, while firm assets and firm equity are measured as stocks at the end of the year. Firm sales include the revenues from 3 5 A firm may also exit i f it becomes unincorporated but this occurs rarely. 58 the firm's operations plus the portion of any revenues from joint operations with other enterprises. The measure of annual employment is called "average labour units" or ALUs. ALUs for a firm are computed by dividing the total annual payroll of an enterprise by the average annual income for workers in the relevant province, size class, and industry at the 3-digit SIC level. This means that the reported ALUs for a given firm can be thought of as the number of "standardized employees" working for a firm during that year. In addition to these variables, the database contains three-digit standard industrial classification (SIC) number for each firm. A firm's assets consist of financial assets like cash, long-term financial assets like bonds, intangible assets like goodwill, and physical capital. Equity consists of common and preferred shares, and accumulated retained earnings (or losses). Debt is obtained by the usual formula: Assets = Equity + Debt. Assets and debt are measured at the end of each fiscal year, which we converted to calendar years (see Petrunia and Hendricks (2001) for details on this conversion). Debt measures the total liabilities of a firm net of shareholder equity. Leverage in period t is defined as the ratio of a firm's book value of debt to its book value of assets at the end of period t. We focus primarily on a cohort of manufacturing and retail firms born in 1985, the first year that we can identify new entrants. A firm is part of the 1985 cohort if it meets the following criteria. First, the firm must have a LEAP birth date of 1985 and, second, the firm must have an incorporation date between January 1, 1985 and December 31, 1985, inclusive. A firm's exit year is defined as the last year that it hires employees. 3 6 For a further discussion on the construction of this cohort, on the firm size measures or on the construction of the database see Chapter 2. 59 Firms with asset values equal to zero in 1985 were dropped from the sample, as were firms that had gaps in their asset and employment histories. The first restriction eliminated 35 (1.5 %) observations, while the second restriction eliminated 145 (6.1%) observations. The remaining sample consists of 885 manufacturing firms and 1317 retail firms. Of these, 444 manufacturing firms and 637 retail firms survived until 1995. 4. Evolution of Size Distribution In this section, we examine the prediction of the learning models that the size distribution of the cohort is stochastically increasing in age. Table 14 provides information on the evolution of the employment size distribution of surviving manufacturing firms from birth in 1985 (age 0) to 1995 (age 10). Table 15 provides the same information for retail firms. The numbers in the first two age columns seem to imply that firms typically double in size in their first two years of existence. This is not correct. Many firms did not operate for the entire year of 1985, which creates a bias in measuring their employment and sales. For example, a firm with 10 employees in 1985 could be a firm that operates for the full year with 10 employees, or a firm that operated for only half of 1985 with 20 employees. The two firms cannot be distinguished. For this reason, when we test for initial employment dependence, we will use employment in 1986 rather than employment in 1985 as a measure of initial employment.37 3 7 We also computed similar distributional statistics for firm sales and firm assets. The sales measure is also subject to the partial reporting problem in 1985, while asset size does not suffer from this problem. The average sales level for these firms is found to nearly double between 1985 and 1986 in both industries. In contrast to the other two variables, average asset size increases by approximately 30% in both industries between 1985 and 1986. 60 The row labelled "count" gives the number of firms active at each age. Manufacturing had 50% of the cohort firms exit before age 10, while retail had a 52% of the cohort firms exit before age 10. This contrasts with the results of Pakes and Ericson (1998), who find that the proportion of exiting firms is higher in retail than in manufacturing (60% in retail versus 50% in manufacturing). Mean employment increases more or less monotonically with age. In manufacturing, the typical firm doubles in size over ten years, from 11.89 employees to 22.39; in retail, the increase is smaller, from 6.15 employees to 9.77 employees. The mortality rate at age t is the number of firms that exited in period t divided by the number of firms in the cohort. The hazard rate in period t measures the fraction of firms that do not survive until age t+1 conditional on surviving until age t. In both industries, the mortality and hazard rates decline with age but not monotonically. If size distributions are increasing with age then the proportion of surviving firms with size greater than X, the numbers in each row in the body of the tables, should also increase with age. Violations are "squared off in the table. The size distributions are stochastically increasing with age during the early years but appear to reach steady state by age five. For example, manufacturing has only one violation before age 4, while retail has no violations until age 5. Twenty-three out of a possible 60 violations in manufacturing occur after age 4 with 16 falling by more than 1.0%. Similarly, 21 out of a possible 50 violation in retail occur after age 5 although only 4 of these violations fall by more than 1.0%. Overall, the data appears to provide support for the learning models. The statistics on cohort dynamics reflect the interplay of two forces: higher failure rates among smaller, 61 younger firms and growth by the survivors. The lack of monotonicity in the mortality statistics may reflect the impact of the business cycle, which peaked in the first quarter of 1990 (age 5 for cohort firms) and troughed in the first quarter of 1992 (age 7 for cohort firms). The business cycle may also have had an impact on the size distribution from always increasing with age.38 We formally test whether the distributions are stochastically increasing with age using a Kolmogorov-Smirnov type test. It has recently been extended by Barrett and Donald (2001). The procedure involves comparing two samples taken from two populations that have associated cumulative distribution functions given by G and F. Weak first order stochastic dominance of G over F corresponds to G(z) < F(z) for all z. This forms the null hypothesis for the test. The hypothesis for testing first order stochastic dominance can be written as, H 0 : G(z) < F(z) for all z Hi: G(z) > F(z) for some z The empirical distributions used to construct the test statistic are respectively, 1 N 1 M ^ ( z ) = - X / ( J f , . <z), and GM (z) = — , < z). where I(.) is the indicator function equal to 1 if statement is true and 0 otherwise, N is the sample size of the sample taken from F and M is the sample size of the population taken from G. The test statistic can now be written as follows: 3 8 Pakes and Ericson (1998) analyse firms in Wisconsin in the period 1978-1986. In this period, there was a contraction in manufacturing in Wisconsin, but their cohort of firms has many fewer violations and appears to be consistent with increasing size distributions. Pakes and Ericson (1998) further note that the assumption on the evolution of exogenous demand conditions and on input prices, which effectively rule out contractions, would have to be introduced to formally prove size distributions are increasing with age. 62 12 max z (G M (z) -F„(z)) . (3.1) Barrett and Donald (2001) show that the p-value for the above statistic is given by exp(-2(S)2). We apply this test for first order stochastic dominance to the employment size distributions.39 For each age, we test the hypothesis that the firm size distribution at age t weakly first order stochastic dominates the firm size distribution at age t - l . Rejection of this null is taken as evidence that the learning models are not consistent with the data. Table 16 and Table 17 report the test statistic at various ages for manufacturing and retail cohort firms, respectively. The tables show that the null hypothesis is never rejected. These results confirm the story told by Tables 14 and 15: the hypothesis that firm size distributions of surviving firms are increasing is consistent with the data, at least weakly, with age, as predicted by the learning models. The Kolmogorov-Smirnov test can also be used to test the hypothesis that the size distributions are strictly increasing with age. This is done by testing whether the size distribution at age t - l weakly dominates the size distribution at age t. Rejection of the null hypothesis is taken as evidence that the size distribution increases with age. If the null hypothesis fails to be rejected then this will be taken as evidence of equivalence between the size distribution at age t - l and the size distribution at age t. Tables 18 and 19 report the values of the test statistic and their p-values for the manufacturing and retail industries, respectively. In the early years of the cohort, the 3 9 The test requires the comparison of samples taken from two independent distributions. If we compare the firm size distribution of the cohort in year t with the firm size distribution of the cohort in year t - 1 then these samples are dependent. In order to obtain independent samples, the cohort firms are randomly divided into two samples: A and B. The size distribution of sample A firms in year t -1 is then compared with the size distribution of sample B firms in year t. 63 S = (NM) (N + M) hypothesis that the size distribution in year t - 1 weakly stochastically dominates the size distribution in year t is rejected for both industries. After age 3 in manufacturing and after age 4 in retail, the null hypothesis is never rejected with a statistical significance level of at least 10 percent. The evidence presented here indicates that the size distributions are increasing during the first five years of life for a cohort of firms. They do not change greatly after this initial shakeout period. 5. Econometric Methods We began our investigation of the determinants of size conditional on survival using linear regressions. However, like Pakes and Ericson, we found that the results of the parametric regressions were quite sensitive to the inclusion of high order terms. Consequently, we decided to use the non-parametric procedure described in Pakes and Ericson to test the hull hypothesis that the conditional distribution of size is independent of initial conditions. For comparison, we have reported the estimates of the parametric models in Appendix 1. 5.1. A Non-Parametric Test for Independence The basic idea of the Pakes and Ericson test for independence is easily described. Survivors in period t are allocated to different cells based on their size histories. Let J denote the number of possible size classes. The size classes can be represented by non-overlapping intervals on the positive real line. Firms have the same size history if their sizes belong to the same interval class at time t -1 until time t - k and time 1. Given a size history (St = st,..., S t.k = st.k,..., Si = s,), let E[St |S,_,,...,S,_J,.,S,,0, =l] denote the expected size at time t conditional on the immediate past sizes, the initial size, and 64 survival until time t {(j)t = l). The Pakes and Ericson test looks at groups of firms with the same ,...,st_k) cell, but in different st cells, and compares their average values of st. We illustrate how the test works under the assumption that t = 10, k =1 and J = 5, where the size cut-offs are 2, 5, 10, 25, and + oo. Table 20 reports the number, mean size, and standard deviation of size of manufacturing firms that survive to age ten conditional on their age nine and age one size category. Table 21 does the same for retail firms. A test that age ten size is independent of initial size conditional on age nine size is based on comparing means across categories within the same column. The differences in means are zero if the conditional size of firms at age ten is independent of initial size. There are 25 (J2) possible cell categories given the realizations of S9 and Si, and the number of intervals.40 Let ji and V denote the column vectors of population means and variances of Sio- The sample equivalents of these two vectors are obtained by stacking the mean and variance vectors in each table. Let fi and V be the sample versions of ju and V. The number of rows in the fi vector is 21 for manufacturing data and 19 for retail data because not all size history cells contain firms.41 The null hypothesis that the conditional expectation Sio is independent of Si can be written as H}:Rfi = r = 0 (3.2) where R is a CxL matrix, where L gives the number of rows in ju (21 for manufacturing and 19 for retail) and C is number different comparisons of means that can 4 0 There are J k + I possible cell categories when controlling for k lags of size history. 4 1 The cells become thinner as we increase the number of lags. Wi th two lags, tables 7 and 8 would consist o f 5 rows and 25 columns. There would be five age eight-category columns corresponding to each age nine-size category. 65 be made from ft vector. The hypothesis jointly tests whether a sequence of mean differences equals zero. The matrix R determines which elements of ji are differenced and compared. Each row of R contains one element equal to -1 , one element equal to 1, and the rest of the elements equal zero since each row of R defines one comparison of two means across cells. The rows of R must also be linearly independent. There are 20 possible comparisons to be made across cells.42 After taking into account empty cells, the number of comparisons drops to 16 for manufacturing, and 14 for retail. Let N(p) be the number of observations in the pth cell. By definition, N= ^ N(p). Finally, let Q denote a diagonal matrix whose diagonal elements are given by V(p) divided by the proportion of observations in a given cell, N(p)/N. A test of Hi compares r = Rft with r = 0. The standard test statistic for//" is which is distributed chi-square with C degrees of freedom. We use essentially the same procedure to test the null hypothesis that the conditional expectation of Sio is independent of the initial debt-asset ratio, LEVo. Table 22 illustrates how the test works for k =1 and J = 5, where the values of cut-offs for the debt-ratio cells are .5, .75, .9, 1.0, and +°°. The table reports the number, mean size, and standard deviation of size of ten-year old manufacturing firms conditional on their age nine size and initial debt-asset ratio. Under the null hypothesis, the differences in cell means within 4 2 In tables 7 and 8, there are a maximum of 4 possible comparisons to be made for each column, which means 20 possible comparisons given there are 5 columns. More generally, the maximum number of comparisons possible is J k(J-l), where J is the number of intervals and k is the number of size lags. (3.3) 66 each column are zero. Note that, in contrast to Tables 20 and 21, there are no empty cells, so the number of equality constraints being tested is 20. 5.2. A Non-Parametric Test for Monotonicity Pakes and Ericson (1998) also use a non-parametric procedure to test the hypothesis that the conditional distribution of future size of survivors is increasing in initial size. The test allows them to distinguish between the passive and active learning models. We are also interested in identifying the properties of the underlying stochastic process determining growth in the manufacturing and retail industries and test for monotonicity in initial size. There are two parts to the Pakes and Ericson's (1998) testing procedure. First, we need to test the null hypothesis that expected size in period t conditional on lagged sizes is weakly increasing in initial size. In terms of Tables 20 and 21, the null implies that the cell means should be increasing as one goes down each column. The second part of the testing procedure maintains that current conditional firm size is weakly increasing in initial size and tests the null hypothesis of independence against the alternative of a strictly increasing relationship. Again, we compare means within each column of Tables 20 and 21. In this case, a decrease in mean size is essentially "zeroed" out under the maintained hypothesis of a weakly increasing relation and, as a result, does not contribute to the test statistic. The null is rejected if the increases in means are too large to be attributed to sampling error. More formally, define the vectors /u,V, fi, V and r, and the matrices Q and R as before. The first part tests whether expected current conditional size is weakly increasing in initial size. This hypothesis is written as: 67 Hi :Rju = r>0. (3.4) The test statistic for HQM is obtained by comparing r with rm where rm minimizes the quadratic form with (RCIR') as a weighting matrix subject to the inequality constraint given in H°M , that is, fM =argmin r,0|r-r)(i?ai?')"'(r-r)}. (3.5) The test statistic for the hypothesis H°M is given by Zl = N\rM - f)(RQRf {rM -r)\ (3.6) The hypothesis is rejected if f contains relatively large negative values in sufficient number. This differs from the test of independence where both negative and positive differences contribute to the rejection of H°. The second step of the sequence tests H°z:Rp: = r = 0 (3.7) conditional on the maintained hypothesis that HQM is true. The test statistic is given by Xl = N\M\R£lR)~X fM\ (3.8) Large positive realizations in the vector rM cause the rejection of H\. The calculation of X\ is similar to the calculation of XT > D u t n o w K contains a series of elements constrained to be equal to zero.43 43 Xz a n d ZM ^° n o t n a v e standard chi-square distributions, as (fM — r) and PM both contain elements 2 • 2 equal to zero. For % z , the p-value of this statistic is calculated by the weighted average of p-values of Xz for chi-squared distributions with degrees of freedom between 0 and C (the number of constraints). The weights do not have an analytical expression. As a result, the weights are obtained using a simulation procedure described in Pakes and Ericson (1998). This procedure involves taking a series of draws from a C dimensional normal N(0,RQ.R') distribution. For each draw, we obtain a rM . The weight given to the 68 6. Results Table 23 investigates the dependence of future size on initial size for manufacturing firms. The first column reports the values of the test statistic for the null hypothesis that Sio conditional on k lags is independent of Sj and the associated p-values. . We do not reject the null for k = 1, but do reject the null for k = 2, or 3. The last two columns of the table report the values of test statistics and p-values for the other two hypotheses. Not surprisingly, the null hypothesis of weak monotonicity is not rejected by the tests for k = 1,2,3. The null hypothesis that Sio is independent of S] conditional on the maintained hypothesis of weak monotonicity is rejected for k = 1, but is not rejected for k = 2,3. The result provides strong support for the hypothesis that the sizes of ten-year-old survivors in the manufacturing industry are independent of initial size. These data are consistent with the active learning model, in which the effects of initial productivity shocks on firm size fade quickly. The results are quite different in the retail industries. Table 24 reports the values of the test statistics and associated p-values for the three hypotheses. For each value of k<3, we reject the null of independence between the size of ten-year-old survivors and their initial size. The null hypothesis of weak monotonicity is not rejected at any value of k. Finally; the null hypothesis of independence conditional on weak monotonicity is rejected at the 90% level in favour of a positive dependence. Thus, in retail industries, ten year old survivors with larger values of Si are larger, even after controlling for lagged p-value of Xz f ° r a chi-squared distribution with b degrees of freedom is determined by the number of times in the simulation procedure rM has exactly b zero elements. The p-value of XM a ' s o requires simulation and is calculated in a similar fashion. 69 values of size. These data are consistent with the passive learning model, but not the active learning model. We turn next to our test of the impact of initial debt on long-term growth. A test of whether age ten size of firms, conditional on a firm's size history, depends on initial leverage is troublesome for retail data when a firm's leverage decision directly depends on factors that determine firm size. The results for retail data show that there is a permanent component to the underlying process determining firm size. Initial leverage and future size of a firm could be related through the factors that are permanent to the firm. In manufacturing, the process determining firm growth does not exhibit initial size dependence. Here S i 0 is independent of Si after controlling for the size history of firms. The underlying factors determining firm size are changing. Initial employment size and initial leverage are likely determined by common factors specific to the firm. The factors determining firm size change, so that Sio is determined by different factors then those factors that determine initial leverage. The finding that Sio depends on Si prevents this conclusion for retail firms. Therefore, we limit our attention to manufacturing firms when testing whether the current conditional size of firms depends on initial leverage. We limit attention to survivors in this analysis, as we did when looking at size persistent. Table 25 reports the test statistic and p-values for the hypothesis that, conditional on a firm's size history, a firm's size at age 10 is independent of the firm's initial debt-asset ratio. The null hypothesis of independence is rejected when controlling for 1, 2, or 3 lags of firm size. There is little doubt about rejecting the null hypothesis, as the p-values 70 are essentially zero in all cases. The evidence shows that future growth of manufacturing firms does depend on their initial leverage. The rejection of the independence test does not indicate whether future size and initial debt-asset ratios are positively or negatively correlated. However, Table 22 provides some evidence that the relationship is not monotonic. If we look at the first two columns, which correspond to the lowest age nine size classes, the mean employment size for cohort firms at age ten does not change very much with initial debt-asset ratio. In the third column, mean employment size at age ten declines marginally with initial debt-asset ratio. More interestingly, in the larger age nine-size classes, the relationship between age ten size and initial debt-asset ratio is u-shaped. Firms that began life with very high equity-asset ratios or very high debt-asset ratios do better than firms with moderate debt-asset ratios. Given this non-monotonic relationship, there is little point repeating the two-part testing sequence with initial leverage. The results show that age ten conditional employment size of a manufacturing firm does depend on initial debt-asset ratio of the firm, but does not depend on the initial employment size of the firm. A final result is that initial debt-asset ratio has a weak correlation with initial size for manufacturing data. The correlation coefficient between the two variables is small at a value of -0.10. The small correlation shows that the lack of equity capital at birth has very little impact on the birth size of manufacturing firms. The iong-term growth of manufacturing firms does depend on initial leverage, while future growth does not exhibit initial size dependence. These results indicate a situation where factors determining a firm's size are changing. One of these factors is financial information about the firm or a firm's leverage. A firm's initial leverage contains little or 71 no information relevant for the initial size of the firm, but initial leverage is relevant for age ten size even after controlling for a size history. The result suggests that debt structure is relevant for growth dynamics of firms. 7. Conclusions This paper has established several important properties about the stochastic process determining the survival and growth of retail and manufacturing firms in Canada. The properties can be summarized as follows. First, in both manufacturing and retail industries, the size distributions of cohort survivors are weakly increasing with age and strictly increasing in the first four years. Second, the size of a retail firm at age ten is increasing in initial size even after controlling for its history. Third, the size of a manufacturing firm at age ten is independent of initial size after controlling for its history. These empirical findings match the findings of Pakes and Ericson (1998). Fourth, the size of manufacturing firms at age ten does depend on their debt-asset ratio at birth, even after controlling for size history. The relationship is u-shaped for firms that have a history of being large. The first fact shows that the forces of selection are at work in both manufacturing and retail industries: smaller firms are more likely to die and survivors grow. The second and third facts confirm the findings of Pakes and Ericson: the stochastic process determining the growth of manufacturing firms is different from that of retail firms. Retail data are consistent with models such as the passive learning model of Jovanovic (1982) where initial size contains information that is relevant to long-term growth. The manufacturing data are not consistent with these models. The new and novel result is the fourth fact, 72 which implies the debt-asset ratio for manufacturing firms at birth does contain information that is relevant to long-term growth. This is a striking, and challenging, result. I intend to examine the robustness of this result and explore explanations for it in subsequent work. 73 Table 14 Evolution of Employment Size Distribution over Age Manufacturing: 1985 Cohort (Entries are Proportion of Active Firms with Employment > X) X Age 10 1 69.5 87.4 90.9 92.8 94.0 94.9 92.1 92.5 93.2 91.1 89.9 2 47.2 71.8 76.5 81.9 84.5 84.6 81.3 83.0 81.6 78.2 77.0 3 35.1 58.2 65.0 71.6 76.0 74.3 72.1 72.8 73.1 69.7 68.9 4 27.0 49.3 55.7 62.1 66.4 64.5 64.4 64.4 65.3 64.4 65.1 5 23.2 42.2 49.0 54.2 59.4 59.0 57.2 58.7 59.9 58.3 59.2 10 11.0 24.3 30.5 34.1 39.2 39.5 39.6 42.1 41.5 42.6 40.3 15 7.7 16.0 20.9 24.7 27.3 27.1 27.9 29.1 30.5 32.2 30.2 20 5.2 11.7 14.3 19.2 20.0 20.3 20.1 21.2 22.0 23.7 23.9 25 4.4 9.0 11.2 13.9 14.6 15.4 15.5 17.2 17.4 19.1 20.9 50 2.1 4.2 4.9 5.5 5.1 4.5 5.2 5.5 7.4 10.2 11.9. Count 885 819 761 697 645 602 556 Mean 6.45 11.89 14.38 15.91 | 16.56 15.91 15.91 Mortality Rate 7.46 6.55 7.23 5.88 4.86 5.20 3.73 Hazard Rate 7.46 7.08 8.41 7.46 6.67 7.64 5.94 523 499 472 444 16.66 17.77 20.24 22.39 2.71 3.05 3.16 4.59 5.41 5.93 Table 15 Evolution of Size Distribution over Age Retail: 1985 Cohort (Entries are Proportion of Active Firms with Employment > X) X Age 10 1 66.4 85.1 89.3 90.9 91.4 93.0 92.5 92.4 92.7 92.0 92.0 2 41.8 64.0 71.2 74.7 77.4 78.9 77.8 78.3 77.7 76.1 75.8 3 28.5 48.8 56.4 60.4 62.4 65.2 61.9 62.2 62.8 63.6 62.3 4 20.5 39.2 44.3 48.8 51.7 53.7 53.3 53.5 52.1 51.5 51.6 5 15.9 29.9 34.9 39.1 42.0 45.2 45.0 44.1 44.2 42.5 44.4 10 6.2 13.7 15.7 17.0 19.1 20.4 19.8 20.8 20.4 20.7 20.9 15 3.4 8.3 9.7 11.3 11.8 13.0 12.6 13.6 13.0 13.4 14.3 20 2.4 5.5 6.8 7.8 8.8 9.4 9.5 9.4 9.6 11.4 11.6 25 1.7 3.9 4.4 4.6 6.0 6.7 7.1 7.4 6.8 7.6 9.3 50 0.5 1.3 1.4 1.8 1.9 2.4 2.1 2.3 2.4 2.9 3.3 Count 1317 1210 1119 1044 965 882 Mean 3.59 6.15 6.92 7.51 8.03 8.72 Mortality Rate 8.12 6.91 5.69 6.00 6.30 3.04 Hazard Rate 8.12 7.52 6.70 7.57 8.60 4.54 789 842 8.72 4.02 3.04 6.29 5.07 749 8.88 8.72 4.71 8.28 687 9.18 3.80 7.28 637 9.77 74 Table 16 Kolmogorov-Smirnov test, Manufacturing Null Hypothesis: Firm size distribution at age t weakly first order stochastically dominates the firm size distribution at age t - l . Age Statistic P-value 1 0.00 1.00 2 0.06 0.99 3 0.07 0.99 4 0.13 0.97 5 0.46 0.66 6 0.73 0.35 7 0.15 0.96 8 0.28 0.85 9 0.84 0.24 10 0.76 0.31 Table 17 Kolmogorov-Smirnov test, Retail Null Hypothesis: Firm size distribution at age t weakly first order stochastically dominates the firm size distribution at age t - l . Age Statistic P-value 1 0.03 1.00 2 0.12 0.97 3 0.06 0.99 4 0.06 0.99 5 0.05 0.99 6 0.69 0.39 7 0.29 0.84 8 0.36 0.78 9 0.43 0.70 10 0.52 0.58 75 Table 18 Kolmogorov-Smirnov test, Manufacturing Null Hypothesis: Firm size distribution at age t - 1 weakly first order stochastically dominates the firm size distribution at age t. Age Statistic P-value 1 5.17 0.00 2 1.58 0.01 3 1.46 0.01 4 1.05 0.11 5 0.41 0.71 6 0.29 0.85 7 0.45 0.66 8 0.62 0.46 9 0.56 0.53 10 0.44 0.67 Table 19 Kolmogorov-Smirnov test, Retail Null Hypothesis: Firm size distribution at age t - l weakly first order stochastically dominates the firm size distribution at age t. Age Statistic P-value 1 5.78 0.00 2 2.02 0.00 3 1.18 0.06 4 1.09 0.09 5 0.86 0.23 6 0.21 0.92 7 0.49 0.62 8 0.30 0.84 9 0.36 0.77 10 0.43 0.69 76 Table 20 Manufacturing: Mean, Standard Deviation and Number of cohort survivors 1995 Employment Size (age 10) by Age 9 and Age 1 Size Class Categories Age 9 Size Class 1 2 3 4 5 Age 1 1 1.1 3.8 6.9 18.8 86.7 Size 0.7 2.3 3.7 5.2 42.0 Class 53 33 15 4 3 2 1.0 3.2 6.4 16.6 51.6 0.5 1.9 2.2 8.3 19.3 28 38 29 30 7 3 1.5 3.7 7.4 15.7 78.3 0.8 1.5 2.0 9.1 55.9 7 10 18 42 17 4 - 4.0 11.3 14.0 59.1 - 3.0 5.8 5.9 38.9 - 6 9 29 29 5 - - - 19.5 121.3 - - - 2.6 119,1 - - - 3 30 Notes: Category Size Cut-offs: 2, 5, 10, 25, + «> Table 21 Retail: Mean, Standard Deviation and Number of cohort survivors for 1995 Employment Size (age 10) by Age 9 and Age 1 Size Class Categories Age 9 Size Class 1 2 3 4 5 Age 1 1 1.3 3.1 6.9 10.5 -Size 0.7 1.3 1.9 2.1 -Class 96 80 26 5 -2 1.5 3.4 7.0 12.3 -0.6 1.4 2.3 3.5 -43 106 58 16 -3 1.1 3.9 7.3 14.4 41.3 0.7 1.6 2.0 6.7 18.3 5 19 51 26 8 4 - 3.2 7.4 16.9 50.6 - 1.5 2.7 6.0 42.8 - 3 8 37 20 5 - - - 26.5 71.8 - - - 1.3 37.7 - - - 3 21 Notes: Category Size Cut-offs: 2, 5, 10, 25, + °° 77 Table 22 Manufacturing: Mean, Standard Deviation and Number of cohort survivors 1995 Employment Size (age 10) by Age 9 and Age 0 Leverage Class Categories Age 9 Size Class 1 2 3 4 5 Age 0 1 1.1 3.9 8.6 17.6 156.3 Leverage 0.6 3.1 3.9 11.4 173.0 Class 14 11 5 10 11 2 1.2 2.5 8.4 16.1 77.3 0.6 1.4 4.7 9.5 56.3 21 11 18 26 16 3 1.3 4.1 7.2 12.5 70.8 0.8 1.6 2.6 5.8 51.2 15 18 17 23 22 4 1.2 3.6 7.2 15.4 51.6 0.7 2.3 3.6 7.4 34.4 21 24 14 24 16 5 0.8 3.3 6.3 17.9 93.6 0.4 1.9 2.1 5.8 61.9 20 23 18 25 21 Notes: Category Size Cut-offs: 2, 5, 10, 25, + oo , Category Leverage Cut-offs: .5, .75, .9, 1, + ° ° 78 Table 23 Test for mean independence of E[S]0 \ Sg,...,S9_k,S},<pm =l] onSj, Manufacturing (Data: 1 9 8 5 cohort and t = 1 0 , Size Cut-offs: 2 , 5 , 1 0 , 2 5 , + oo ) H°: Unconditional H°M : Weak Increasing H\: Mean independence Mean Independence Monotonicity Conditional on HM k Df x\ p-value a C b XM p-value a C b x\ p-value 1 16 34.9 0.00 16 7.5 0.48(0.05) 16 21A 0.00(0.00) 2 24 37.0 0.04 24 19.9 0.09(0.03) 24 17.0 0.16(0.03) 3 20 22.6 0.31 20 12.6 0.29(0.05) 20 10.0 0.41(0.05) aThis is a simulated estimate of the true p-value, and the number in parenthesis is the estimate of the standard error of this estimate. Twenty simulation draws were used to calculate the estimated p-values. b C provides the number of comparisons across cells that are being made. Table 24 Test for mean independence of E[Si0 | S 9 , . . . ,S 9 _ t ,S 1 ,0 l o =l] on S i , Retail (Data: 1985 cohort and t = 10, Size Cut-offs: 2, 5, 10, 25, +QQ ) HT : Unconditional HM : Weak Increasing H\ : Mean independence Mean Independence Monotonicity Conditional on HM k Df X°r p-value C b XM p-value a C b Zz p-value a 1 14 272.7 0.00 14 2.7 0.89(0.10) 14 270.0 0.00(0.00) 2 21 225.4 0.00 21 6.8 0.73(0.14) 21 218.7 0.00(0.00) 3 23 185.8 0.00 23 4.6 0.93(0.07) 23 181.2 0.00(0.00) "This is a simulated estimate of the true p-value, and the number in parenthesis is the estimate of the standard error of this estimate. Twenty simulation draws were used to calculate the estimated p-values. b C provides the number of comparisons across cells that are being made. 79 Table 25 Test independence of E[Sm \ S9,...,Sg_k,levo,0xo = l] from lev0, Manufacturing (Data: 1985 cohort and t = 10, Size Cut-offs: 2, 5, 10, 25, +°° , Leverage Cut-offs: .5, •75, .9, 1 , + O Q ) Hj: independent oflevp K DF x\ p-value 1 20 47.2 0.00 2 28 67.6 0.00 3 24 56.6 0.00 80 8. Appendix: Maximum Likelihood Estimates Our parametric model is given by ln(empit ) = x<emPu-\) + Pi HemPu-i) + A M.empIA ) + (3.A1) The first hypothesis to test is whether current conditional size depends on initial size. This hypothesis tests H0:P3=0 against the alternative that H.-.p^O. If we fail to reject the null hypothesis, then we estimate \n(empit) = 10 + A, \n(empit_x) + X2 \n(empjt_2) + X^levifi + uit. (3.A2) and test the null of We measure growth only for surviving firms. This may introduce a bias and an inconsistency into the least squares estimation. We control for the possibility of selection bias with the following procedure. Let the discrete variable SURV; t = 1 if the firm survives until time t conditional on the firm surviving until time t - 1 and SURV; t = 0 if the firm does not survive until t conditional on the firm surviving until time t - 1 . Further, let Sj t be the size of firm i at time t. Again, we are focusing on production decisions, so we have two measures of firm size: employment and sales. We wish to determine the impact initial financial state of a firm has on growth and survival of firm in period t conditioning on the set of firms that have survived until period t. Since growth in period t is only observed for those firms that survive through period t we can only 81 measure growth for those firms that survive. The probability that firm survives until t given it survives until t - 1 is represented by a probit equation. The expectation of SURVj t is given by the following: E[SURVit\Xit] = Vx[eit>-V[Xit)] (3.A3) = F[v(Xit)] where V(.) is a function determining the value of a firm, Xj, are determinants of survival, ej t is a normally distributed random variable with mean zero and unit variance, and F(.) is the cumulative normal distribution with unit variance. V(.) will be approximated by a linear function. Equation (3.A3) along with the growth equation given by: log(empit) = X i tp +uit • (3.A4) form a sample selection model. We assume that u i t and are distributed jointly normal with mean zero and covariance matrix Q with 2 2 CJi P CT, pa] i where the variance of the error term in the selection equation has been normalized to unity. Consistent estimates can be obtained for the two equations using maximum likelihood methods. We will use this approach. The determinants of survival will be the same as the determinants of growth. This means that identification occurs through functional form or the non-linearity of the inverse Mills term in the growth equation, since we do not have variables that determine survival but not growth. Finally, heteroskedasticity could be a potential problem. Consistent estimates of standard errors will be obtained using White's (1982) method. 82 Table 26 Maximum Likelihood regression results, Manufacturing Dependent variable: Log(empio) Initial Size Initial Leverage Variable Size Survival Size Survival Log(emp9) 0.919*** 0.026 0.918*** 0.031 (0.051) (0.191) (0.519) (0.217) Log(emp8) 0.166*** 0.288 0.133** 0.134 (0.056) (0.210) (0.055) (0.226) Log(emp!) -0.036* -0.232 (0.022) (0.147) Lev0 0.016 -0.058 (0.068) (0.292) Rho 0.179* -0.534** (0.095) (0.192) Wald statistic 6680.80 5548.35 Number of firms 472 472 Notes: White (1982) standard errors are reported in brackets. ***, **, * denotes significance at 1%, 5%, and 10%, respectively. Table 27 Maximum Likelihood regression results, Retail Dependent variable: Log(empio) Initial Size Initial Leverage Variable Size Survival Size Survival Log(emp9) 0.813*** 0.989*** 0.815*** 0.996*** (0.063) (0.227) (0.063) (0.229) Log(emp8) 0.185*** -0.696*** 0.188*** -0.803*** (0.066) (0.249) (0.064) (0.245) Log(empi) 0.008 -0.152 (0.017) (0.112) Lev0 -0.053** -0.203* (0.024) (0.105) Rho 0.062*** -0.057*** (0.017) (0.018) Wald statistic 6751.52 6552.58 Number of firms 637 637 Notes: White (1982) standard errors are reported in brackets. ***, **, * denotes significance at 1%, 5%, and 10%, respectively. 83 Chapter 4 Does Gibrat's Law Hold? Evidence From Canadian Retail and Manufacturing Firms. This paper investigates the validity of Gibrat's Law holding for firms in manufacturing and retail trade sectors. The object is to expand our knowledge of Gibrat's Law to include non-manufacturing firms. A unique longitudinal firm-level database that contains information on Canadian incorporated establishments enables the inter-industry comparison. The findings of the analysis are that Gibrat's Law is violated in both manufacturing and retail sectors. Violations of Gibrat's Law for both sectors include (i) growth rates that depend on firm size (ii) growth variability that depends on firm size and (iii) a negative persistence of firm growth. Finally, age effects or selection effects are not the causes of these violations. 1. Introduction Gibrat's Law has become the focus of a large number of empirical studies in industrial economics. Robert Gibrat, in his book Inegalites Economiques, sought a model of firm and industry dynamics that would explain his finding that firm size distributions within an industry were highly skewed and appeared to be approximately lognormal. His simple explanation for this finding is the law of proportionate effect or what has become known as Gibrat's Law. The law constitutes the hypothesis that firms (within an industry) draw growth rates from a distribution that is the same for all firms regardless of their current size or previous size history. From this, it follows that growth rates are 84 independent of firm size or as Sutton (1997) states, "the expected value of the increment to a firm's size in each period is proportional to the current size of the firm." There have been a number of empirical examinations testing Gibrat's Law. However, almost all have focused on the validity of Gibrat's Law holding exclusively for manufacturing firms. Non-manufacturing firms, such as service or retail sector businesses, have largely been ignored. This is unfortunate for two reasons. First, we have limited information about growth and industry dynamics for non-manufacturing firms. Second, manufacturing and service/retail firms differ in fundamental ways. Service firms contain fewer employees, experience higher entry and failure rates, have lower sunk costs and invest in less capital. Manufacturing firms are typically characterized as large, capital intensive firms. These differences create a greater discrepancy between large and small firms in the manufacturing sector than compared to large and small firms in the service sector. Small manufacturing firms must grow and realize scale economies or face the consequence of lower probability of survival. In contrast, small service sector firms do not face such survival problems because of the lack of capital intensity and small economies of scale.44 This paper partially fills the gap in the Gibrat's Law literature by examining the size-growth relationship for retail and manufacturing firms. Given the differences between service sector industries and manufacturing industries, we test whether Gibrat's Law is valid for a group of manufacturing firms and a group of retail firms operating over the 4 4 The growth process might differ between manufacturing sector and non-manufacturing sectors, such as retail trade, because of impacts of general events occurring in the Canadian economy. One such event is the business cycle. A recession began in Canada in 1989 with a slight recovery occurring in 1992 and 1993. The Canadian economy did not fully recover from this recession until 1996. We complete analysis for different years to control for the business cycle effects. 85 same period. The results of the analysis are used to show if any differences occur for the growth process in the two sectors. We further split firms in each sector into two age categories: (i) firms that existed before 1985 and (ii) firms that entered in 1985. The age groupings allow for two things. First, age effects are accounted for by analyzing firms with the same age. Group (ii) in each sector provides such a group. Evans (1987a,b) notes that theories of firm dynamics generate growth patterns that vary with the age of the firm.45 If young firms are characterized by fast growth and a smaller average size then analysis of all firms taken together may produce a negative relationship between size and growth even though such a relationship does not exist when looking at individual age cohorts. Second, we provide analysis of the post-entry performance of new retail and manufacturing firms. The paper is organized as follows. The next section contains a brief discussion of previous studies of Gibrat's Law. Section III discusses testing Gibrat's Law and sample selection issues. Section IV contains a discussion of the data and measurement issues. A longitudinal database that tracks Canadian firms between 1985 and 1995 is used. Section V presents empirical findings. Section VI concludes. The paper reports the following finding. Gibrat's Law does not hold for Canadian retail and manufacturing firms. 2. Previous Studies The previous literature on Gibrat's is large and too extensive for a survey here. Audretsch, Klomp, Santarelli and Thurik (2002) provide an extensive review of the previous investigations of Gibrat's Law. 4 6 The authors list 51 empirical studies on firm 4 5 Jovanovic (1982) provides such a life cycle theory. 4 6 Further, Sutton (1997) provides a critical discussion of both empirical investigations and related theoretical implications of industry and firm dynamics. 86 growth rates. We note the following details about this list. Firstly, Audretsch, Klorhp, Santarelli and Thurik (2002) point out that most of the evidence concerns manufacturing firms. There are only four studies, which limit attention to service sector firms. Fourteen studies look at a sample that includes both manufacturing and service firms. The rest of the studies contain only manufacturing firms in their sample investigated. Second, generally Gibrat's Law fails to hold. There are 27 studies, out of the 51 studies listed, which reject Gibrat's Law. A further 16 studies find mixed results, with rejection or acceptance of Gibrat's Law depending on the industry chosen and sample of firms chosen.47 Typically, rejection occurs in these studies because of one of three reasons. One reason for rejection is that often studies find that smaller firms grow at a larger expected rate than compared to larger firms. Examples of studies that find such a result include Kumar (1985) and Dunne and Hughes (1994) for UK firms and Evans (1987a,b) and Hall (1987) for US manufacturing firms. Alternatively, a second reason for rejection is that other studies find growth favours larger firms. Singh and Whittington (1975), and Hart and Prais (1956) provide examples where growth is positively related to firm size. A final reason for the rejection of Gibrat's Law is that the assumption of no serial correlation in firm growth fails to hold. For example, Chesher (1979) examines growth persistence for UK manufacturing firms while Kumar (1985) looks at growth persistence for UK manufacturing and service firms. These studies find a positive serial correlation, which is the norm when growth correlation is found. One exception is Contini and 4 7 Sample of firms refers to whether the sample includes (1) all firms, (2) surviving firms or (3) large firms. For example, Mansfield (1962) looks at firms in three manufacturing industries (steel, petroleum refining and rubber tire). He finds that Gibrat's Law is rejected in 7 out of 10 cases when looking at the sample of firms that includes all firms. When examining survivors, Mansfield rejects Gibrat's Law in 4 out of 10 cases. Mansfield finds that growth patterns for large firms are consistent with Gibrat's Law. 87 Revelli (1989), who find negative growth correlation for Italian manufacturing firms. Alternatively, Tschoegl (1983) finds that growth rates are serially uncorrelated when looking at a sample of large international banks. Audretsch, Klomp, Santarelli and Thurik (2002) investigate Dutch firms in the service sector. This study generally finds that growth persistence does not occur for the sample of Dutch service sector firms. The third detail regarding the list of previous Gibrat's Law studies is that there is a small amount of evidence on the firm size-firm growth relationship for new firms. The list includes eleven studies on new firms. These studies are concerned with post-entry performance of new firms by linking future survival prospects and growth rates to industry and firm characteristics at the time of firm birth.48 With the exception of Wagner (1994), these studies find evidence that smaller start-up firms have a higher growth rate than larger start-ups. Therefore, Gibrat's Law does not hold for new firms, because of an inverse firm size-firm growth relationship. 3. Testing Gibrat's Law The Law of Proportionate effect, or Gibrat's Law, says that a firm's size change is proportionate to its size 4 9 Alternatively, a firm's growth is independent of its size and the logarithm of firm size follows a random walk. Gibrat's Law implies that the moments of the firm growth distribution do not vary with firm size. If Gibrat's Law holds then three main propositions are valid: (i) that firms of different sizes have the same expected proportionate growth; (ii) that the variance of growth rates is independent of a firm's size; and (iii) that there is no serial correlation in firm growth rates. Each proposition can be 4 8 Examples include Dunne, Roberts and Samuelson (1988), (1989) for U.S. firms, Wagner (1994) for German establishments, and Audretsch, Santarelli and Vivarelli (1999) for Italian firms. 4 9 Sutton (1997) provides a formal description. 88 tested with firm size data. Rejection of any one of these propositions is a rejection of Gibrat's Law. Mansfield (1962) notes that the chosen sample of firms could lead to different conclusions. Slow growing firms exit. However, it is possible that slow growing small firms are more likely to exit than compared to slow growing large firm because the smaller firms are closer to an exit threshold. An inverse size-growth relationship could be the result of survival effects with slow growing small firms exiting quickly and slow growing large firms slowly moving toward their death. In order to control for such effects, Gibrat's Law has been tested on three different populations in the literature: (1) all firms, (2) only surviving firms and (3) firms that are larger than the Minimum Efficient Scale (MES) level of output. The third group represents the large firms in an industry. Previous studies have looked at large firms based on the belief that Gibrat's law is valid for large firms. We are interested in comparing the growth patterns between a set of young firm and a set of old firms. The majority of young firms are small and well below the MES. For this reason, attention is restricted to the first two samples of firms. The combination of the two groups of firms, all firms and survivors only, with the three Gibrat's Law propositions leads to the following hypotheses that are being tested on retail or manufacturing firms: HI: The growth rate of each surviving firm over a period is independent of its size H2: The growth rate of each firm (surviving and non-surviving) over a period is independent of its size H3: The variability of growth rates for surviving firms is independent of a firm's size H4: The variability of growth rates for all firms is independent of a firm's size 89 H5: The growth for surviving firms over a period does not exhibit persistence The rejection of HI or H3 provides evidence against Gibrat's Law holding for surviving firms. Similarly, the rejection of H2 or H4 provides evidence against Gibrat's Law holding for the sample of firms that includes survivors and exits. Again, sample selection creates the distinction. The test of growth persistence or H5 applies to only surviving firms, as pointed out by Audretsch, Klomp, Santarelli and Thurik (2002), "it is not possible to analyse persistence of growth for firms that leave the industry during the observation period." It is difficult to know what growth persistence means for firms that exit an industry. Death is an absorbing state, so growth persistence is meaningless for exiting firms. 4. Data and Measurement Issues 4.1. Data This section provides a brief description of the data set and the variables used to measure firm size. The data are taken from the T2LEAP database. This database was created by Statistics Canada. The database contains annual employment and balance sheet information on incorporated employer enterprises within Canada. The sample period is 1984 through to 1996. We analyze growth performance of Canadian firms that exist in 1985. Each firm is tracked using a business registry number (BSNUM). Exit and re-entry by the same firm does not occur when a firm that changes its name, since the BSNUM does not change for this firm. Firms are broken into two groups for analysis. The choice of sample period allows for the identification of one age group: firms that enter in 1985. For simplicity, we refer to 90 this group throughout as the entrants. A firm is part of the entrants if it meets the following criteria. First, the firm must hire employees for the first time in 1985 and, second, the firm must have an incorporation date between January 1, 1985 and December 31, 1985, inclusive. The entrants group provides a set of firms with the same age. The second group contains those firms that were in existence before 1985. We call this group the incumbents. The incumbents contain all firms that first hired employees before 1985 and have an incorporation date before January 1, 1985. We split each entrant and incumbent groups into retail (600-699) and manufacturing (101-399) samples by three-digit Standard Industry Classification (SIC) number. Any non-manufacturing and non-retail firms are dropped from analysis 4.2. Measurement Firm employment measures firm size. The measure of annual employment is called "average labour units" or ALUs. ALUs for a firm are computed by dividing the total annual payroll of an enterprise by the average annual income for workers in the relevant province, size class, and industry at the 3-digit SIC level. This means that the reported ALUs for a given firm can be thought of as the number of "standardized employees" working for a firm during that year. Partial reporting is possible in the first and last operating year of a firm. A firm under reports its annual payroll when it operates for a partial portion of a year. This leads to an under-reporting of the number of ALUs for the firm. Partial reporting could be a problem for the entrant firms in 1985. Further, partial reporting could be a problem entrant and 91 incumbent firms in 1996, since exit is possible in that year.50 For this reason, we examine the growth process between 1986 and 1995 for the sample of firms.51 For most of the analysis firm growth is measured by the following formula: G r = Empimi -Empim6 EmPnm where Gr denotes growth rate and Emp is employment size. If a firm exits between 1986 and 1995 the growth rate over this period is equated to -1 when we examine growth for surviving and exiting firms.52 5. Empirical Results 5.1. Are Firm Growth and the Variance of Firm Growth Related to Firm Size? The analysis of firm growth begins by dividing firms into size classes based on their 1986 size, and comparing growth rates of firms across different size classes. A series of two tests are performed on the surviving firms sample and the survivors plus exits sample. The first test compares the mean growth rates across size classes. This test is a joint difference of means test. If firms of different size classes have similar growth rates then differences in mean growth rates across size classes are zero and the first part of Gibrat's Law holds. The second test compares the variance of growth rates across size 5 0 A firm's exit year is defined as the last year that it hires employees. We cannot identify those firms that exit in 1996 since we would need 1997 information to determine i f 1996 is the last year, a firm hires employees. 5 1 Partial reporting is similar to the measurement error problem, which has been analyzed by Hall (1987). 5 2 A potential difference between manufacturing and retail trade sectors is that manufacturing firms enjoyed preferential tax treatment. Changes were made in the tax system beginning in 1987 to remove the advantage manufacturing firms received. The analysis looks at firm growth between 1986 and 1995. Growth rates across the two sectors may differ, since there are tax policy changes that affect both sectors differently. The previous preferential treatment enjoyed by manufacturing firms promoted the creation of large manufacturing. The removal of such special treatment may mean that growth favors small manufacturing firms as opposed to large manufacturing firms. 92 classes. If variances are the same across size classes then the second part of Gibrat's Law holds. The size classes are chosen to have a common cut off for all samples of firms. This does not mean that roughly equal numbers of firms are placed in each group. Retail firms tend to be smaller than manufacturing firms, while younger firms tend to be smaller than older firms. Therefore, it is impossible to have common size cut-offs and equal numbers of firms in each size class for the different age and industry groups. Common size cut-offs are chosen. Table 28 presents the mean and variance of growth rates from 1986-1995 for firms that survive until 1995. Two general patterns emerge from the table that foreshadow the results of future analysis. First, growth decreases with firm size. With a few exceptions, firms in larger size classes have lower growth rates on average. Second, growth rate variances are quite different across size classes with firms in larger size classes tending to have lower variability of growth rates. In all cases, extreme growth and variability of growth occurs for firms in the lower size classes. Entrant firms have higher growth rates and variability of growth compared to incumbent firms in both industries. Thus, age effects cause differences in growth patterns between age groups, which is consistent with the predictions life-cycle models such as the Jovanovic (1982) learning model. Firm growth is also broken down into three-three year intervals. Table 29 presents a breakdown of growth rates between 1986 and 1989 for survivors over this period. Similarly, Table 30 displays breakdowns for growth between 1989 and 1992, while Table 31 shows breakdowns for growth between 1992 and 1995. Two patterns emerge from these tables. First, growth and growth variability is larger in the earlier years and tapers 93 off in later years. This is again due to age effects. Second, growth rates and variability of growth are generally higher for firms at the bottom end of the size distribution in the respective years. However, the differences of growth patterns across the size distribution are not as great in the later years as they are in the early years, so that no clearly monotonic relationship between firm growth and firm size occurs when analyzing growth between 1992 and 1995. Growth rates do continue to vary with firm size as a non-monotonic u-shaped relationship emerges between 1992 size and growth between 1992 and 1995. Table 32 presents the mean and variance of growth rates from 1986-1995 for all firms. Exiting firms are given a growth rate equal to -1. Again, the patterns remain similar to those in Table 28. Average growth rates decrease when moving up size classes with a few more exceptions compared to Table 28. Variability of growth rates tends to be smaller for firms in larger size classes. Growth and growth variability does not vary greatly for incumbent manufacturing and retail firms in the upper three size classes. Table 32 also shows that entrant firms continue to grow at a rate greater than incumbents even when exits are included in growth calculations. Similar calculations are made over shorter intervals. Table 33 presents analysis for growth between 1986 and 1989, while Table 34 looks at growth analysis between 1989 and 1992. Finally, Table 35 restricts attention to growth between 1992 and 1995. The patterns remain the same as those found in Tables 29, 30, and 31. Growth and variability of growth fall with age for all groups. Second, growth does vary across the size distribution with differences across the size distribution failing over time. 94 Next, we move on to formally test equality of means. Let //,. be the mean growth rate for those firms belonging to size class i . HI or H2 can now be stated as the following hypothesis: H0 : fix = ju2 = //3 = ju4 = ju5 vs. H] : //,. * pj for some i * j . This test is now can be expressed as a joint difference of means test. Therefore, we write: ~MX -MI "o" Mi -Ms 0 Mi -MA 0 MA ~Ms_ 0 Rencher (2002) shows that the test statistic is given by Z2=n(R]u)XRSRY(RM) where n is the number of observations, /J is a vector of sample estimates of ju, S is the sample variance matrix and R is matrix that defines H0 given by: Y -1 0 0 0" 0 1 - 1 0 0 R = 0 0 1 - 1 0 0 0 0 1 -1 The test statistic is distributed as xl • The tests of HI and H2 using firm growth from 1986 to 1995 are presented in Table 36. In all cases, HI and H2 are rejected. Firm growth does depend on firm size. The results provide evidence against proposition (i) of Gibrat's Law holding. Growth differs for firms belonging to different size classes. This result holds when the sample includes only survivors and when the sample includes survivors and exits. Further, if we control 95 for industry or if we control entrant versus incumbents has no relevance in the rejection of proposition (i).5 3 Now, the methodology turns to comparing the variability of growth rates across size classes. In a similar manner as with means comparisons, an equality of variance test is used. We let a) be the variance for the firms belonging to group i . H3 or H4 can be stated as the following hypothesis Hv: o\ - a\ = o\ =o\= a] vs. HvX : cr, * for some i * j . From Rencher (2002), we have a test statistic, which is approximately distributed as xl > given by: m c where c = l + - 1 3 ( * - l ) 1=1 ( 5 \ and m v,=i j Xv,. ln52-2(mv,K2 i=i s] are sample variances with vt degrees of freedom. Tests of H3 and H4 using firm growth from 1986 to 1995 are presented in Table 37. In all cases, H3 and H4 are rejected. The result provides evidence that the variability of 5 3 Dunne, Roberts, and Samuelson (1988), (1989) focus on firms with more than 5 employees. For a comparison, we repeat the above analysis for more than 5 employees. HI and H2 are rejected at the one percent level of significance for all groups with the exception of retail entrants. Thus, proposition (i) does not fail to hold because there are a large number of small firms moving up and down the size distribution. 96 firm growth rates do vary across size classes. Proposition (ii) of Gibrat's Law does not hold for various samples of firms considered.54 As a robustness check, we repeat the equality of means tests and equality of variance tests using alternative cut-offs on the size classes. Rejection of the null hypotheses HI, H2, H3 and H4 occurs with the alternative size cut-offs. These results are robust to varying the limits on the size classes. 5.2. Growth Persistence The methodology to test growth persistence is different from the previous methodology. We move from a methodology, which compares growth rates and growth variability across size classes to a regression framework. The reader is reminded that attention is limited to surviving firms since growth persistence for exiting firms cannot be analyzed. We have \n(Sit) = a + fi\n(Sil_,) + eil (4.1) where t is an index for time, i is an index for the firms, Sit is the employment size of firm i at time t and eu is a random error with zero mean and finite variance. Equation (4.1) provides a framework to test proposition (i) of Gibrat's Law. The proposition is not rejected when fi = 1 in the above regression. If fi < 1 then expected growth rates are higher for smaller firms, while if fi > 1 then expected growth rates are higher for larger firms. 5 4 Again, analysis is repeated for firms with more than 5 employees. H3 and H4 are rejected for all groups. One could argue that proposition (ii) fails to hold because small firms with highly variable and turbulent growth rates dominate results. This result shows that turbulence growth of small firms is not the cause for failure of proposition (ii). 97 If proposition (iii) of Gibrat's Law holds then eit are serially uncorrelated. However, if eit are serially correlated then firm growth in one period affects firm growth in the next period. Following Chesher (1979), growth correlation is modelled as eit having a first order autoregressive process, so that: ea=Pett-\+uu (4-2) where uit is assumed to be a zero mean, finite variance and serially uncorrelated random variable. If we substitute between (4.1) and (4.2) then we obtain ln(S„) = (1 - p)a + ((3 + p) ln(S„_,) + (-#>) ln(S„_2) + u„. (4.3) Equation (4.3) is specified in such a manner, so that both proposition (i) and (iii) of Gibrat's Law can both be tested. These two propositions are valid if the joint hypothesis of = 1 and p = 0 is accepted. Proposition (iii) is valid if p = 0 is accepted. Table 38 reports the nonlinear least squares estimation results for equation (4.3). Three years, 1989, 1992 and 1995, are chosen for brevity and to represent different parts of the business cycle. These years also allow for age comparisons. The growth correlation patterns may be different for younger and older firms. Comparisons are made between entrant firms and incumbent firms, and comparisons are made for different years across the two groups. The following important results emerge from Table 38. First, growth persistence occurs. In all cases, p is negative and statistically different from zero with one borderline case (entrant retail firms in 1992). From Table 38, the growth correlation coefficients typically vary between -0.1 and -0.2. This result contrasts the results of previous studies listed in Audretsch, Klomp, Santarelli and Thurik (2002) review. Contini 98 and Revelli (1989) provide the only study from the review, where Gibrat's Law is rejected because of negative serial correlation in firm growth. The second result is that the coefficient values of fi vary across years. The patterns are similar across industry and age groups. In 1989, fi is less than one and statistically different from one for all groups. In 1992, fi is less than or equal to one for all groups, but fi is statistically different from one for only one group - incumbent manufacturing firms. Finally, in 1995, fi is greater than one for all groups and statistically different from one for entrant manufacturing firms, incumbent manufacturing firms, and incumbent retail firms. These results do not reflect age effects, since the patterns are similar across incumbent and entrant groups. One explanation is that these differences across periods reflect different stages of the business cycle. The Canadian economy entered a recession in the first quarter of 1990, which lasted until the first quarter of 1992. A period of recovery occurred after 1992. However, the results concerning the autocorrelation coefficient (p) do not change greatly across years.55 6. Conclusions This paper looks at the validity of Gibrat's Law holding for retail and manufacturing firms. A sample of new firms is created for retail and manufacturing sectors to control for age. Gibrat's Law holds for a sample of firms if three characteristics are valid for the sample. First, firm growth must be independent of firm size. Second, the variance of firm growth must be independent of firm size. Finally, firm growth is independent across time. These three propositions are tested for each of the four samples of firms. 5 5 We repeated estimation of equation (4.3) with the panel that included the years 1988-1995. Year dummy variables were added as controls. The estimate of p was around -0.10 for each of the four groups of firms. 99 The results are quite clear and consistent across Canadian manufacturing and retail firms at two different age classifications. Gibrat's Law fails to hold for these firms. The results of this paper are summarized by three findings. First, smaller firms tend to have higher growth rates on average than do larger firms. The variability of firm growth varies with firm size, so that the variability of growth tends to be larger for smaller firms. Finally, there is a negative growth correlation between growth rates across time, which means that firm growth exhibits negative growth persistence. Taken individually, the three propositions of Gibrat's Law are rejected. The results presented here do appear to be consistent with previous studies, since Gibrat's Law is rejected. Audretsch, Klomp, Santarelli and Thurik (2002) provide a comprehensive review of previous Gibrat's Law studies. Most of these studies look at manufacturing firms or a combination of large manufacturing and service sector firms. The total number of studies listed is 51. There are 8 acceptances of Gibrat's Law, 27 rejections of Gibrat's Law, and 16 with mixed results. Gibrat's Law is also rejected for Canadian retail and manufacturing firms. Industry dynamics are similar across the two sectors. 100 Table 28 1986-1995 Growth and Variance of Growth by 1986 Size Class, Survivors. Mean Growth Rate Standard Deviation Number of Firms 1986 Size Class Group 0-2 2-5 5-10 10-25 >25 Manufacturing: Entrants 6.05 1.77 2.30 0.94 0.74 (26.75) (4.03) (5.60) (2.10) (1.70) 108 132 94 75 35 Incumbents 2.16 0.35 0.20 0.20 0.27 (20.07) (1.90) (1.95) (1.59) (1.57) 1229 2848 3377 4662 5540 Retail: Entrants 2.05 0.56 0.52 0.69 0.36 (3.44) (1.70) (1.50) (2.53) (0.86) 207 225 109 69 27 Incumbents 1.07 0.40 0.03 0.09 0.24 (4.70) (16.00) (0.84) (1.20) (0.93) 3090 8129 8064 6311 3179 Notes: Growth is measured as the change in firm employment for the period 1986-1995 divided by employment in 1986. Table 29 1986-1989 Growth and Variance of Growth by 1986 Size Class, Survivors. Mean Growth Rate Standard Deviation Number of Firms 1986 Size Class Group 0-2 2-5 5-10 10-25 >25 Manufacturing: Entrants 7.95 0.85 0.92 0.55 0.19 (66.71) (1.42) (1.73) (0.95) (1.07) 163 200 127 99 56 Incumbents 1.53 0.36 0.25 0.20 0.13 (24.61) (1.15) (0.78) (0.73) (0.53) 2044 3881 4389 6027 6989 Retail: Entrants 1.49 0.38 0.32 0.20 0.21 (2.90) (0.77) (0.82) (0.63) (0.69) 320 344 163 98 40 Incumbents 0.74 0.29 0.09 0.08 0.12 (3.34) (13.92) (0.49) (0.50) (0.47) 5750 12101 10791 8118 3880 Notes: Growth is measured as the change in firm employment for the period 1986-1989 divided by employment in 1986. 101 Table 30 1989-1992 Growth and Variance of Growth by 1989 Size Class, Survivors. Mean Growth Rate Standard Deviation Number of Firms 1989 Size Class Group 0-2 2-5 5-10 10-25 >25 Manufacturing: Entrants 0.84 -0.02 0.26 0.05 -0.00 (2.84) (0.60) (0.88) (0.52) (0.51) 72 132 103 135 81 Incumbents 0.43 0.04 -0.05 -0.09 -0.11 (2.53) (1.26) (0.53) (0.47) (0.63) 1372 2927 3521 5305 6823 Retail: Entrants 0.58 0.13 0.04 0.10 0.09 (1.90) (0.54) (0.48) (0.67) (0.35) 160 289 184 107 49 Incumbents 0.38 0.04 0.01 0.01 -0.01 (2.91) (0.86) (0.71) (0.46) (0.42) 4161 9294 9308 7459 4139 Notes: Growth is measured as the change in firm employment for the period 1989-1992 divided by employment in 1989. Table 31 1992-1995 Growth and Variance of Growth by 1992 Size Class, Survivors. Mean Growth Rate Standard Deviation Number of Firms 1992 Size Class Group 0-2 2-5 5-10 10-25 >25 Manufacturing: Entrants 0.49 -0.07 0.09 0.18 0.40 (3.09) (0.63) (0.65) (1.29) (0.84) 68 106 71 116 83 Incumbents 0.46 -0.07 -0.06 0.02 0.20 (2.63) (0.79) (0.71) (0.65) (1.66) 1506 2752 3190 4659 5549 Retail: Entrants 0.20 -0.04 -0.06 -0.00 0.13 (0.69) (0.43) (0.36) (0.45) (0.49) 122 214 156 95 50 Incumbents 0.32 -0.07 -0.10 -0.07 0.05 (2.79) (0.58) (0.43) (0.41) (0.39) 3395 7391 7491 6636 3860 Notes: Growth is measured as the change in firm employment for the period 1992-1995 divided by employment in 1992. 102 Table 32 1986-1995 Growth and Variance of Growth by 1986 Size Class, Al l Firms. Mean Growth Rate Standard Deviation Number of Firms 1986 Size Class Group 0-2 2-5 5-10 10-25 >25 Manufacturing: Entrants 2.30 0.51 1.11 0.17 -0.18 (18.58) (3.28) (4.74) (1.88) (1.45) 231 242 147 125 74 Incumbents 0.37 -0.15 -0.18 -0.17 -0.08 (13.36) (1.64) (1.71) (1.43) (1.46) 2810 4538 4932 6699 7645 Retail: Entrants 0.45 -0.15 -0.15 -0.02 -0.22 (2.82) (1.47) (1.35) (2.09) (0.94) 435 413 196 119 47 Incumbents -0.23 -0.23 -0.33 -0.23 -0.05 (3.03) (11.90) (0.84) (1.12) (0.97) 8318 14769 12259 8971 4171 Notes: Growth is measured as the change in firm employment for the period 1986-1995 divided by employment in 1986. Firms that exit between 1986 and 1995 have a growth rate equal to - 1 . Table 33 1986-1989 Growth and Variance of Growth by 1986 Size Class, Al l Firms. Mean Growth Rate Standard Deviation Number of Firms 1986 Size Class Group 0-2 2-5 5-10 10-25 >25 Manufacturing: Entrants 5.32 0.53 0.66 0.23 -0.10 (56.13) (1.47) (1.74) (1.05) (1.06) 231 242 147 125 74 Incumbents 0.84 0.16 0.11 0.08 0.04 (21.01) (1.16) (0.84) (0.77) (0.60) 2810 4538 4932 6699 7645 Retail: Entrants 0.83 0.15 0.09 -0.01 0.03 (2.72) (0.87) (0.89) (0.73) (0.77) 435 413 196 119 47 Incumbents 0.20 0.06 -0.04 -0.02 0.05 (2.89) (12.62) (0.58) (0.57) (0.54) 8318 14769 12259 8971 4171 Notes: Growth is measured as the change in firm employment for the period 1986-1989 divided by employment in 1986. Firms that exit between 1986 and 1989 have a growth rate equal to - 1 . 103 Table 34 1989-1992 Growth and Variance of Growth by 1989 Size Class, Al l Firms. Mean Growth Rate Standard Deviation Number of Firms 1989 Size Class Group 0-2 2-5 5-10 10-25 >25 Manufacturing: Entrants 0.33 -0.20 0.00 -0.11 -0.14 (2.54) (0.66) (0.94) (0.61) (0.59) 100 162 130 159 94 Incumbents -0.03 -0.13 -0.17 -0.19 -0.21 (2.19) (1.22) (0.59) (0.53) (0.66) 2018 3511 4039 6023 7739 Retail: Entrants 0.16 -0.05 -0.14 -0.06 -0.08 (1.77) (0.64) (0.59) (0.74) (0.51) 218 342 221 126 58 Incumbents -0.05 -0.14 -0.11 -0.09 -0.10 (2.50) (0.88) (0.75) (0.53) (0.49) 6040 11230 10554 8286 4530 Notes: Growth is measured as the change in firm employment for the period 1989-1992 divided by employment in 1989. Firms that exit between 1989 and 1992 have a growth rate equal to - 1 . Table 35 1992-1995 Growth and Variance of Growth by 1992 Size Class, All Firms. Mean Growth Rate Standard Deviation Number of Firms 1992 Size Class Group 0-2 2-5 5-10 10-25 >25 Manufacturing: Entrants 0.14 -0.22 -0.11 0.06 0.29 (2.77) (0.68) (0.72) (1.27) (0.89) 89 127 87 130 90 Incumbents 0.05 -0.20 -0.16 -0.07 0.11 (2.32) (0.80) (0.73) (0.69) (1.63) 2099 3211 3543 5118 5977 Retail: Entrants -0.14 -0.24 -0.20 -0.11 -0.03 (0.80) (0.55) (0.47) (0.52) (0.60) 171 270 184 106 58 Incumbents -0.16 -0.24 -0.21 -0.15 -0.03 (2.32) (0.64) (0.50) (0.47) (0.46) 5319 9087 8524 7270 4161 Notes: Growth is measured as the change in firm employment for the period 1992-1995 divided by employment in 1992. Firms that exit between 1992 and 1995 have a growth rate equal to-1 . 104 Table 36 Test of size-growth independence, 1986-1995 Growth Chi-Square Value Hypothesis Level of Significance HI H2 Manufacturing: Entrants 13.47 15.57 0.01 0.01 Incumbents 28.15 21.52 0.00 0.00 Retail: Entrants 38.73 18.05 0.00 0.00 Incumbents 26.95 27.07 0.00 0.00 Notes: A l l tests are Chi-Squared with four degrees of freedom Table 37 Test of size-growth variance independence, 1986-1995 Growth Chi-Square Value Hypothesis Level of Significance H3 H4 Manufacturing: Entrants 757.13 1206.42 0.00 0.00 Incumbents 33577.31 46056.21 0.00 0.00 Retail: Entrants 142.70 269.28 0.00 0.00 Incumbents 70585.40 95598.15 0.00 0.00 Notes: A l l tests are Chi-Squared with four degrees of freedom 105 Table 38 Empirical results for persistence of growth (1989, 1992, 1995) Dependent Variable: Emp(t) Industry/Age Class 1989 1992 1995 Manufacturing - Entrants P 0.947** 0.981 1.051** (0.013) (0.011) (0.012) P -0.114** -0.200** -0.133** (0.040) (0.042) (0.042) Manufacturing - Incumbents P 0.983** 0.990** 1.035** (0.001) (0.002) (0.002) p -0.151** -0.129** -0.195** (0.007) (0.008) (0.009) 0 0.964** 0.980 1.002 Retail - Entrants (0.011) (0.011) (0.013) p -0.117** -0.064* -0.195** (0.032) (0.031) (0.058) B 0.990** 1.000 1.007** Retail - Incumbents H (0.001) (0.001) (0.002) n -0.096** -0.159** -0.076** H (0.005) (0.005) (0.008) Notes: Asymptotic Standard Errors are given between parentheses. * The hypothesis fi = 1 or p = 0 is rejected at the 5 percent level of significance. ** The hypothesis fi = 1 or p = 0 is rejected at the 1 percent level of significance. 106 Chapter 5 Conc lus ion The dissertation aims to contribute to the understanding of firm and industry dynamics. The study looks at the development of firms. I have focused on a cohort of entrants, which has lead to three investigations: the size and financial dynamics of the entrants and how these compare with the dynamics of incumbent firms, growth dynamics for the entrants and incumbents, and the impact early debt has on the growth dynamics of the entrants. In Chapter 2, I examine the dynamics for a cohort of entrants during the first-ten years of life. Canadian firms identified as starting in 1985 form the entrant group. The study looks at the distributions of sales, employment, assets and debt-asset ratio for the cohort and how these distributions change with age. There is also a comparison of entrant distributions to incumbent distributions. A start-up, entrants have fewer employees, less assets and sales, and higher debt-asset ratios than do incumbents. These differences remain at the end of the ten-year period. However, there is a reduction in discrepancy between the two groups with the entrants catching up to incumbents as the result of having greater movements in the distributions of the variables. Two forces are at work causing the improved distributions for entrants: higher failure rates for firms at the bottom of the employment, assets, and sales distributions, and at the top of debt-asset distribution. Chapter 3 tests whether the long-term growth for the 1985 entrants is independent of its initial debt structure. I look at entrants in the retail and manufacturing sectors. The test involves a two-step process. First, I test whether the stochastic process governing size 107 dynamics does not have initial size dependence. The first test is done to rule out a world where the underlying structure of the firm does not change. The second step of the test, which is only done when we have a world where the stochastic process governing size dynamics does not exhibit initial size dependence, examines whether size at age ten conditional on a lagged size history is independent of initial debt-to-asset ratio. Both retail and manufacturing sectors have size distributions, which are weakly stochastically increasing with age. For retail firms, size at age ten is increasing in initial size even after controlling for a size history. Alternatively, for manufacturing firms, size at age ten is independent of initial size after controlling for a size history. The process governing size dynamics for retail and manufacturing firms does differ. These results mean that I complete the second step of the testing process for only manufacturing firms. Finally, I find that age ten size of these manufacturing firms does depend on their initial debt-asset ratio even after controlling for a size history. For these firms, debt-asset ratio contains information about the future long-term growth of a firm. In Chapter 4, I investigate the validity of Gibrat's law holding for Canadian firms operating in 1985. Attention is limited to firms operating in manufacturing and retail industries, and a comparison is made across the two industries. Within each industry, firms are further split into two groups: (i) 1985 entrants and (ii) 1985 incumbents. Gibrat's Law constitutes that firm growth is random and independent of firm size and past growth. The distribution of growth rates for small firms is identical to the distribution of growth rates for large firms. The results are clear and very similar across the four groups. Gibrat's law does not hold. Smaller firms have higher growth rates and higher variability of growth compared 108 to larger firm. One concern is that hot accounting for the higher failure rates among smaller firms biases the results. The results do not change when the analysis group includes exiting firms. Thus, growth and variability of growth does vary with firm size. One final finding is the presence of negative growth correlation. The finding of negative growth correlation means the rejection of proposition (iii) for each set of firms. Thus, the rejection of each proposition means that Gibrat's law does not hold for these firms. 109 Bibliography Audretch, D. (1991), "New Firm Survival and the Technological Regime," Review of Economics and Statistics 73, 441-450. Audretsch, D.B., E. Santarelli, and M . Vivarelli (1999), "Start-up Size and Industrial Dynamics: Some Evidence from Italian Manufacturing," International Journal of Industrial Economics 17, 965-983. Audretsch, D.B., L. Klomp, E. Santarelli, and A.R. Thurik, "Gibrat's Law: Are Services Different?" Working Paper, Tinbergen Institute, 2002. Baggs, J. 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Essays in firm dynamics Petrunia, Robert John 2004
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Title | Essays in firm dynamics |
Creator |
Petrunia, Robert John |
Date Issued | 2004 |
Description | This thesis comprises three essays that analyze financial and non-financial aspects of firm and industry dynamics. The first essay investigates the evolution of a cohort of entrants during their first ten years of life. The study looks at the distributions of sales, assets, employment and debtasset ratio for these firms over time and compares how these distributions change relative to distributions for incumbent firms. Entrants are smaller in terms of employees, assets and sales, but have a higher debt-asset ratio when compared with incumbents. These differences lessen over time because entrants have higher growth rates and smaller entrant firms have higher failure rates than compared to larger entrants. The second essay investigates whether long-term growth of a firm is independent of initial financial structure. I look at a panel of Canadian retail and manufacturing firms born in 1985. The analysis involves a two-part testing process. The first part tests whether firm growth exhibits initial size dependence. The growth process for retail firms exhibits initial size dependence, while the growth process for manufacturing firms does not. The second part looks at whether growth of ten-year old manufacturing firms is independent of initial debt-asset ratio. The result rejects independence with the finding that age ten conditional size of a manufacturing firm has a non-monotonic relationship with initial debt-asset ratio. The final essay examines whether Gibrat's law holds for groups of Canadian firms operating in manufacturing and retail sectors. Gibrat's law holds when firm growth and variability of growth are independent of firm size and firm growth is independent across time. Firm growth and variability of growth depend on size for each set of firms, which leads to violations of Gibrat's law. The source of these two violations is not survival bias, since the violations occur with the inclusion or exclusion of failing firms. A further violation is that negative growth persistence exists. Finally, I look at possible failure because of age effects. I examine a group of new firms with a common age and find the violations continue to occur for this group. |
Extent | 5131475 bytes |
Subject |
Business enterprises -- Canada -- Management Industries -- Canada -- Management Retail trade -- Canada -- Management New business enterprises -- Management Organizational change Business failures Success in business |
Genre |
Thesis/Dissertation |
Type |
Text |
FileFormat | application/pdf |
Language | eng |
Date Available | 2009-11-27 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0099791 |
URI | http://hdl.handle.net/2429/15845 |
Degree |
Doctor of Philosophy - PhD |
Program |
Economics |
Affiliation |
Arts, Faculty of Vancouver School of Economics |
Degree Grantor | University of British Columbia |
GraduationDate | 2004-11 |
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UBCV |
Scholarly Level | Graduate |
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