Competitive Strategy of Long Lived Small Firms

8/13/2019 Competitive Strategy of Long Lived Small Firms

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Performance, Firm Size and the Heterogeneity of Competitive Strategy

for Long-lived Small Firms: A Simultaneous Equations Analysis

Bernadette Power+and Gavin C Reid

Abstract

This paper examines the relationship between firm size, competitive strategy and

performance, for the long-lived small firm in Scotland. It uses structural modelling to test the

hypothesis that small firms need to remain small if they are to be long-lived. In a three-

equation simultaneous model, performance, size and the dimensions of the competitive

strategy of the firm are jointly determined. Econometric estimates of the three equations are

reported, using 2SLS and iterated 3SLS. A trade-off is found to exist between firm size and

performance. Further, we find that to attain higher equilibrium values of performance, a

varied competitive strategy needs to be adopted. Our prescription is that small firms need to

adjust downwards in size, and to cultivate a more varied competitive strategy, if there the

entrepreneurs are to have a positive influence on performance, thus promoting longevity of

their firms.

Keywords: Performance, Small Firms, Size, Competitive Strategy, Simultaneity

JEL: C42, D21, G33, L2, M13, M21

* Author for Correspondence: Professor of Economics, and Director, Center for Research into Industry,Enterprise, Finance and the Firm (CRIEFF), Department of Economics, University of St. Andrews, St.Salvators College, St. Andrews, Fife, Scotland, KY16 9AL, UKe-mail: [email protected]

Phone/Fax: (+44) (0) 1334 462431 (personal); (+44) (0) 1334 462438 (CRIEFF)www: http://www.st-and.ac.uk/~www_crieff/CRIEFF.html

+Lecture in Economics, Dept. of Economics, University College Cork, Cork, Ireland e-mail: [email protected] Phone: (+353) (0) 21 4902986

Fax: (+353) (0) 21 4273920 www: http://www.ucc.ie/ucc/depts/economics/staff/power.html


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1: INTRODUCTION

The paper explains the tendency of small firms to remain small. It is a micro-

econometric analysis of the relationship between size, competitive strategy and performance

for long-lived small firms. We use a simultaneous equations model to estimate three

endogenous relationships: performance, size, and heterogeneity of competitive strategy. Our

evidence suggests that a trade-off exists between the firms size and performance. Increases

(decreases) in firm size reduce (raise) the performance of the firm, and it is this which tends

to limit the size of the firm. This trade-off encourages owner-managers of small firms to

reduce headcount to achieve greater efficiency. Such efficiency gains arise from greater

labour productivity, often with an increase in human capital of the core workforce. The

substitution of capital (including human capital) for standard labour inputs is another

potential source of efficiency gain. To achieve higher levels of performance, the

heterogeneity of the competitive strategy of the small firm was also found to be important.

Based on this evidence, our prescription is that small firms need to cultivate more varied

competitive strategies, in niche or localised markets, to improve their long-run performance

prospects.

The study is fieldwork based and uses evidence from face-to-face interviews with

owner-managers of mature small firms in Scotland. Performance is measured by a likert

scale over 28 distinct attributes. The latter incorporated aspects of: competitive environment;financial management; organisational structure; and business strategy. Size is measured by

full-time equivalent employees, and the heterogeneity of competitive strategy by a count

variable of strategies pursued by the small firm in their principal market. Section 3 provides a

detailed account of how we measured these variables.

Our econometric estimates used 2SLS and I3SLS. The three equations were estimated

using data collected on 63 long-lived small firms. We define long-lived small firms as

businesses that have been trading for more than 10 years. They were classified as small firms

at inception if they employed less than 100 people. In fact, the small firms in this study were

often much smaller, typically having 10 employees at inception. Today, our long-lived small

firms had 13 employees, on average, indicating some, but not substantial growth since

inception.

Some small firms enjoy high performance, and growth. Storey (1994) describes them as

ten per centers because they are few, and Birch (1996) describes them as gazelles because

of their apparently effortless higher performance. However there is a tendency for most small

firms to remain small. In becoming long-lived, small firms in our sample have passed the


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long run test of economic survival. In surviving the market selection process, they are not

necessarily laggards, unless the markets in which they were operating were uncontested.

Indeed, we would expect that only the fittest firms survive in a competitive market, facing a

market selection test every period (Gould, 1993). However, given that the average age of the

long-lived small firm in the sample (26 years, over a full generation) it is difficult to imagine

that inefficiencies in the market could have allowed these firms to clear the first hurdle of

survival for this length of time. This suggests that there are other reasons preventing these

firms from clearing the second hurdle of growth in firm size.

Evidence of a negative relationship between growth and profitability was found by

Cubbin and Leech (1986) and Dobson and Gerrard (1989). Reid (1993, 1995) confirmed this

for a sample of small business start-ups within a simultaneous framework. This evidence

suggests that there are diminishing returns to increasing the size of the firm and that a

negative relationship is expected between firm size and performance. This study seeks to

embed this trade-off in a larger model; and to extend the analysis to incorporate: (a) the

heterogeneity of the firms competitive strategy; and (b) performance over the long term.

Thus it is recognised that other inherent attributes of the firm could explain the tendency of

the small firm to remain small. Candidates for this include: the size of the market for its

product (e.g. local service); the firms organisational capability; the level of differentiation of

the product (e.g. extent of customisation); and potential risks to the income of the ownermanager (e.g. as a result of cashflow difficulties, overinvestment).

Briefly the development of our ideas is as follows. Section 2 examines the simultaneous

equations model to be estimated. Section 3 discusses the primary source data on which this

study is based, and describes the variables used in estimation. Section 4 reports on Durbin-

Wu-Hausman type tests of endogeneity, employed to examine whether simultaneities exist

between firm size, the heterogeneity of the firms competitive strategy and small firm

performance. In this Section we also discuss appropriate techniques for system estimation.

Our position is that it is often hard to disentangle one relationship from the other using single

equation estimators as they are often dogged by "lack of identification" which may not even

have been investigated. Section 5 reports the results of two appropriate system estimation

techniques (two stage least squares, 2SLS, and iterated three stage least squares, 3ISLS),

which are known to be relatively robust in the face of specification error. Using these

techniques we report on estimates of the behavioural relations between firm size, competitive

strategy and performance. This Section also examines behavioural patterns in the size


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adjustment, heterogeneity of competitive strategy, and performance within the context of the

simultaneous system. Finally, Section 6 summarises our principal results.

2: THE MODEL

We adopt a type of simultaneous equations model with industrial economics

applications. Other recent examples include Jans and Rosenbaum (1997), Beccarello (1996),

and McDonald and Bloch (1999). Jans and Rosenbaum (1996) use nonlinear three stage least

squares to estimate quantity and price equations. Beccarello (1996) used three stage least

squares to estimate mark-up equations. McDonald and Bloch (1999) use instrumental

variables to estimate spillover effects of industrial growth/performance trade-off model. We

use 2SLS and I3SLS to estimate a three-equation growth/performance trade-off model.

This section explains how our key hypotheses are addressed. The central hypothesis

examines behavioural relations between size, competitive strategy and the performance of the

long-lived small firm. A number of papers examine the relation between growth and

profitability or size and growth. However, none explicitly examine a model where firm size,

the heterogeneity of the competitive strategy and performance are jointly determined. Early

work on this relation by Penrose (1959) examined the influence of external competitive

pressure on the growth/profitability trade-off. However this was not examined empirically.

Penrose (1959) stated that external constraints to growth arise from a combination of

increasing market saturation and more intensive competitive pressure. She stated that as a

result of heightened competitive pressure higher growth can only be achieved through higher

advertising expenditure and/or lower prices. This will result in a negative relationship

between growth and profitability (or performance). In this case, the financial cost of these

types of competitive strategies is a hidden cost to growth. Our analysis differs in that rather

than measuring competitive pressure we examine the heterogeneity of the competitive

strategy of the firm.

There are a number of competing models of the performance of the firm. Variants of

the structure-conduct and performance paradigm in industrial economics are examined by

Reid (1987). According to this reasoning industries have structural characteristics (e.g. entry

barriers, product differentiation), which suppress rivalry and raise the profitability of

incumbent firms (Bain, 1956). More recently, the market efficiency school proposed that the

firms stock of resources enable it to extract above normal profits as oppose to structural

barriers or market power (Demsetz, 1973; Lippman and Rumelt, 1982). These worksspawned a number of other studies examining the persistence of industry versus firm effects


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(Schmalensee, 1985; Dierickx and Cool, 1989; Rumelt, 1991). Much of this effort focussed

more on the performance of large firms rather than on small firm performance.

Earlier work on small firms concentrated on firm size, particularly on the relationship

between growth and firm size originating in the Law of Proportionate Effect (or Gibrats

Law). This states that growth rates are independent of firm size and its past growth history.

All firms grow at the same rate over an interval of time, regardless of their initial size.

Conflicting evidence exists on the relationship between growth and size. A number of

empirical studies suggest a negative relationship between growth and size, indicating that

smaller firms have higher and more variable growth rates which reduce their survival rate

(Mansfield, 1962; Hall 1987, Mata, 1994) while other studies (Singh and Whittington, 1975)

have found a positive relationship. These models are mechanistic methods of explaining the

relationship between firm size and growth.

Managerial theories of the firm explicitly examined trade-offs between the growth of

the firm and performance (Penrose, 1959; Marris, 1964; Richardson, 1964; and Slater 1980).

Hidden costs to growth are identified in the literature by Penrose (1959), where she describes

the nature of the managerial limit. This has become known as the Penrose effect (e.g. new

managers are drawn in, who require training to be integrated into the existing framework of

the firm). If the Penrose effect is indeed a source of dynamic scale economies, one would

expect the underlying constraints on growth to induce a negative relationship between growthand profitability. Slater (1980) captured some key features of her approach in a formal model,

which shows that the rapid recruitment of management, which accompanies faster growth,

leads to an increase in marginal cost. Richardson (1964) also discussed this functional

relationship between the organisational efficiency of a firm and its rate of growth. He said

that the former would decline after a point as the latter rises (Richardson 1964:11), that is,

there is ultimately a growth efficiency trade-off.

Evidence of a negative relationship between growth and profitability was found by

Cubbin and Leech (1986), and Dobson and Gerrard (1989), and this was confirmed by Reid

(1993, 1995) for a sample of small business start-ups, within a simultaneous framework. The

latter work examined the relations between growth and performance, rather than that of size

and performance, the novel concern of this paper. The second innovation of this paper is to

test explicitly for simultaneities between competitive strategy, firm size and performance. We

report on the results of the size/performance trade-off, using a new behavioural relation,

which is expanded to account for the intensity of the firms competitive strategy. In general

terms, our three-equation model is specified as follows:


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P = f (S, C, X1) (1)

S= g (P, X2) (2)

C= h (P, X3) (3)

Here, P is a measure of performance, S is a measure of size, C is an index of the

heterogeneity of the firms competitive strategy and the Xirepresent exogenous variables in

the system (discussed explicitly in Section 3). In equation (1) size is expected to affect

performance negatively (assuming a trade-off exists between increasing firm size and

performance), whereas C is expected to influence performance positively. The latter arises

from Porters (1985) ideas on good competitors: these are competitors who, by engaging in

sharp and challenging rivalry, actually promote the efficiency and innovativeness of

incumbent firms, and hence improve their prospects of staying in business. The overall effect

on performance depends on the relative sizes of these effects. X1here represents attributes of

the financial structure of the firm, and aspects of its market and age. Equation (2) represents

size as a function of performance, and other exogenous variables. A negative relationship is

expected here between size and performance. X2incorporates lagged performance variables

and other variables like the resources of the firm (hidden costs to increasing firm size).

Equation (3) represents competitive scope as a function of performance and other exogenous

variables. The sign of the performance effect upon competitive scope is unknown. X3

incorporates market structural variables to approximate the extent of external competitive

pressure in the firms principal market.

Essentially this three-equation model allows us to examine: (a) whether a trade-off

exists between the size of the firm and its performance; and (b) the influence which the

heterogeneity of the firms competitive strategy has on this trade-off. In general, it is

expected that the greater the diversity of the firms competitive strategy, the higher the firms

performance. To survive, the mature small firm becomes leaner, more efficient and provides

a more customised service. The consequence of this is that there is tendency for the firm to

remain small, using differentiated strategies to target localised or niche markets.

3. DATA AND VARIABLES

This section presents information on the database and the variables used in econometric

estimation. It also provides summary statistics on the key variables used in equations (1), (2)


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and (3) above (see Table III below). An account is provided of how these variables are

defined, and an explanation is given of how these variables were measured in the survey

instrument. We also provide some amplification of the specification of each of the structural

equations, considered as part of the overall simultaneous system.

3.1 Database

Briefly, the data set that we used for econometric estimation was based on interview

evidence obtained from 63 owner-managers of long-lived small firms in Scotland. They were

obtained from a sample frame of 90 mature small firms (a response rate of 70%). The latter

were extracted from three parent samples of Scottish small business enterprises. These will

be described as the Leverhulme (1985-1988), Telephone Survey 1991 and Leverhulme

(1994-1979) parent samples, for exposition purposes (see Table II). The owner managers

of businesses in these three parent samples were interviewed by one of the authors in the

1980s and 1990s. The activity fieldwork behind the Leverhulme (1985-1988) sample

involved gathering data by face-to-face interviews with the owner managers of 86 new

business starts in the late 1980s. Of these 86 firms, 25 (29%) survived and 20 of these agreed

to be re-interviewed for this study.i Data on the second sample frame of 160 mature firms,

were attained from the list of members of the Federation of Small Business (FSB) in

Scotland. These data were collected by structured interviews over the telephone in 1991. Atthat time, 113 firms agreed to be interviewed. Fifty, of the original 113 firms from this parent

sample were still in business in 2001 (a survival rate of 44%)ii. Thirty of these firms agreed to

be re-interviewed. From the Leverhulme (1994-1997) sample, our third parent sample, this

time of 150 firms, we found that just 20 were long-lived small firms aged 10 years or more.

In the last case this original sample was intended to be of new business starts. These were

interviewed originally using face-to-face interviews from 19941997. Fifteen out of twenty

firms aged 10 or more were still trading (a survival rate of 75%) iii. Thirteen of these agreed

to be re-interviewed.

[INSERT TABLE I HERE]

The three parent samples are known to be fairly representative of the relevant

populations of small firms in Scotland at the time of selection. They provided a secure set of

known sources upon which further fieldwork could be built. Considerable benefit was

derived from previous contact with entrepreneurs, in terms of access to the field. Generally,

owner-managers were happy to be looked up again, after a long lapse of time.


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In total we gathered data on 63 long-lived small firms, by face-to-face interviews,

between October 2001 and February 2002. The administered questionnaire we created for

this purpose examined the following characteristics of the long-lived small firm: changes in

its scale and scope; pivotal changes in its running since start-up; factors which fostered its

survival; and its level of innovation and technical change. General statistical features of the

database were as follows.

3.2 General Characteristics of Long-lived Small Firms

The firms examined were mature (25 years on average; median age of 22). Almost

all sectors, by SIC code, were represented in the sample, running through from agriculture

(01) to domestic services (99). The main sectors, by SIC codes were: 32, mechanical

engineering (4.8%); 43, textile industry (4.8%); 61, wholesale distribution (4.8%); 64, retail

distribution (23%); 66, hotels and catering (4.8%), 67 repair of consumer goods and vehicles

(6.3%); and 83 business services (9.5%). Thus, the modal firm was a retailer. The sample

proportions between extractive/manufacturers (SIC 01-60) and services (SIC 61-99) were

40% and 60% respectively. These proportions were similar across the extracted and

interviewed parent samples, although they differed across the three parent samples (see

Table II).

[INSERT TABLE II NEAR HERE]Of the 219 firms in the three parent samples 84 (38%) were in manufacturing (SIC

01-60) and 135 (62%) were in services (SIC 61-99). Figures from the Department of Trade

and Industry, for the UK as a whole, indicate that 27% were in extractive/manufacturing and

73% were in services. Thus there is a slight bias towards extractive/manufacturing firms in

our sample. This is partly explained by the slower progression of the Scottish economy to

becoming service based, compared to the UK as a whole. It is also probably partly explained

by the fact that part of the parent samples were drawn from the caseloads of Enterprise

Trusts, which, at the time of early enterprise policies tended to favour manufacturing

enterprise. This proactive behaviour, indeed positive discrimination towards manufacturers,

disappeared from enterprise policy, as fears of de-industrialisation abated and, were replaced

by a new enthusiasm for knowledge based enterprise. The following regions were

represented: Aberdeen, Argyll, Aryshire, Banff, Caithneas, Cumnock, Dundee, Fife,

Glasgow, Inverness, Isle of Skye, Lanarkshire, Lothian and Edinburgh, Midlothian, Moray,

Orkney, Perth, Renfrewshire, Ross and Stirling. These represent well the locational diversity

of long-lived small firms in Scotland.


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Of the sample of 63 long-lived small firms, one (1.6%) was a sole trader operating

from home, fifteen (23.8%) were sole traders operating from business premises, nineteen

(30.2%) were partnerships and twenty-five (44.4%) were private limited companies. This

pattern is very different from what you would expect early in the lifecycle. Then, sole

proprietors would dominate. At the other end of the life cycle, private companies

predominate. Eighteen (28.6%) firms changed their legal form during the life of the business.

There is general evidence of changes in organisational form, from the sole proprietorship

form, to the partnership and private limited company forms, over the lifetimes of the firms,

cf.Reid (1998). The number of full-time equivalent (FTEs) employees, which is one indicator

of the size of these small business enterprises, varied from 1 to 130 with the average and

mode being 13.55 and 6 respectively. The average size of firms (and the corresponding

standard deviation) in terms of full time equivalent employees were as follows: 5.94 (5.85),

sole proprietorship; 7.91(4.08), partnership; and 22.19 (27.69), private company. Size,

measured by turnover for the last trading year, also varied widely by business type. Average

turnover (and its standard deviation) was: 219,813 (143,025) for sole proprietorships;

557,526 (455,994) for partnerships; and 1,372,821 (1,885,391) for private companies

(all figures in 2001 prices). Thus changes from sole proprietorship, to partnership, to private

company, are generally associated with increases in size.

3.3 Variables

This subsection is concerned with the key variables used in the system estimation. We

provide a detailed explanation of how they are defined, and of how the questionnaire design

was used to generate these variables. The endogenous variables in the system are examined

initially, namely, performance, P (measured in three alternative ways), firm size, S, and the

scope of the firms competitive strategy, C. Exogenous variables within the system are then

examined for each structural equation in the system. These exogenous variables can broadly

be grouped into market and strategy variables. The variables are then used in the estimation

reported upon in Section 5. Table III lists these key variables, and their summary statistics.

[INSERT TABLE III NEAR HERE]

3.3.1 Performance

Several approaches to measuring performance in small firms are possible. For

example Smith (1997) and Reid and Smith (2000) identify three. In particular, they contrast

an objective measure (e.g. quantitative measures like profitability and rate of return) with a

subjective measure (e.g. a judgmental evaluation of performance, drawing on both


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quantitative and qualitative evidence). In this paper we adopt the latter approach. It is both

more comprehensive, and more compatible with our evidence base. The requirement for a

comprehensive measure of performance is consistent with the literature on entrepreneurship

and management accounting as applied to the small firm e.g. Wickham, (2001, Ch. 20).

Essentially, it recognises that the proper control of the firm requires a comparison of current

performance to a predetermined plan or objective. This is the basis for the so called variance

analysis in management accounting. This approach would see there being an indissoluble

link between the setting of performance standards, and the control of the firm by the owner-

manager. The most commonly conceived performance standards relate to budgets. However

there are many other forms, including those relating to human factors, like responsibility, and

to technological ones, like hitting research milestones. As regards the compatibility of the

evidence base, our own subjective measure of performance evaluation allows us to undertake

modelling which would otherwise be impossible given our complex sample construction. The

problem is that each parent sample typically offers distinct objective performance measures

gathered at different points in time. There is an intrinsic lack of comparability of these

measures across our sample. Using a new performance measurement approach breaks this

impasse. Our measure is common to the three parent samples, which allows us to proceed

with empirical work on a uniform basis.

Our quantitative indicator of performance was multidimensional, involving 28 items,each of which was calibrated on a 100-point scale. We argue that naturally there are many

dimensions to performance. Our indicator examined these dimensions of performance under

main headings like strategic (9 items), financial (4 items), and organisational (4 items) and

environmental forces (11 items).iv We hold that our approach has advantages over the use of

conventional financial data. These are limited by accounting conventions (e.g. the reporting

protocol). Further, lifecycle effects may make them difficult to interpret in sensible

economic terms. For example up to three years of losses may be assumed early in the life

cycle. Further, accounting profit is not readily related to economic profit. Thus rate of

return, or profitability, which may both seem suitable quantitative indicators for assessing the

performance of the mature small firm, may fail to grapple with quite simple aspects of reality.

For example, profit itself may be ill-defined in many small firms, as owner managers do not

always make a clear distinction between profit and income. We could, of course, have

substituted a simple, single question on self-appraisal of performance, for the more

conventional type of question on rate of return. However, we would argue that our

multidimensional approach has two main advantages over the single question approach.


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First, it produces detailed measurement across wide spectrum performance-relevant variables,

rather than a single variable. Second, by diluting variable specific effects, it produces a more

comprehensive (and stable) measure of what is meant by performance, allowing common

influences to come through (DeVellis, 1991).

The key performance question put to owner-managers was as follows: Wed like to

know what has kept you in business down the years. Some things are good for business and

some things are bad. What effect have the following had?. The owner-managers were

asked to rateveach of the 28 items on a scale of 0 to 100 where 100 is good, and 0 is bad and

50 is neutral. They did so by placing a cross on a line, of length 100 units. In this way, we

calibrated the influence they judged this item to have had, based on their actual experience of

running the business. If an item was not applicable they were asked to say so. An extract of

the scale is reproduced in Figure I.

[INSERT FIGURE I HERE]

We found that owner-managers of our long-lived small firms were readily able to

draw on their experience of running their businesses, in self-appraising the influence that

each of these items had on their performance. In doing so, the owner-managers had in their

minds a large body of qualitative and quantitative evidence, on which they could base their

judgements of performance. To illustrate, over time they had learned how best to combine

their factors of production to exploit market opportunities; and they had learned how to

respond to threats in a way that improved their performance, and enhanced their survival.

Given that owner-managers comfortably juggle these various performance measures in their

own minds, we consider it logical to seek explicit measures of how this juggling act is

sustained. Thus our measuring exercise provides us with a new form of empirical evidence,

based on judgements, which nevertheless is useful in econometric estimation. From the self-

assessment of each items influence on the performance of the firm, we obtained a measure of

overall performance, by summing the individual item scores. Thus an overall score for

performance (Perform) was calculated for each firm, based on the summation of ratings for

factors, normalised to take account of those items that were not applicable. This measure is

not age related, as each dimension may assume a greater or lesser importance at any point in

the lifecycle.

It is envisaged that changes in this judgement of firm performance will lead the firm

to modify factors like its size and its management processes to enhance performance. The


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consequences of this will in turn modify performance judgements. Thus this variable is

expected to be endogenous within our simultaneous equations framework.

3.3.2 Firm Size

The second endogenous variable in this framework is firm size, S. Here, it is

approximated by the number of full-time equivalent employees. As with performance, there

are several ways approaches to measure firm size. Our analysis was repeated using assets and

sales as size measures, and similar results were found to those reported in Section 5. As

measured in 2001, these mature small firms were, on average, just above the micro-firm

upper rangeof 10 employees. They generated 835,000stg in turnover and had using assets

valued at 330,000stg. The predominant firm type was still the micro-firm, and the average

size was somewhat raised by the existence of a few large firms in the sample. Essentially, the

size distribution observed for these small firms is something like a Pareto distribution: that is,

one branch of an hyperbola in the first quadrant, with unity as the lower bound. When

investigating the early life of the small firm, in a single equation model, Reid (1993) found

that size measures like assets and number of full time employees had less clear consequences

for survival than the employment measure. Here, Reids (1993) approach is extended to

examine the interrelationship between size, the heterogeneity of the firms competitive

strategy and long run performance, all in a larger simultaneous equations system. In thisway, we hope to gain a better understanding of inter-relationships between firm size and

performance, and the tendency for new business start-ups to remain small.

3.3.3 Competitive Strategy Space

The third endogenous variable in our model measured the size of the competitive

strategy space of the firm, C. This variable is calibrated by a count of the number of forms of

competition used by the firm This variable may range from 1 to 8 where 1 indicates that the

small firm competes on just one dimension of the competitive strategy space (e.g. price

alone), and 8 indicates that it competes across many dimensions (e.g. price, quality,

delivery). To measure this C variable, the owner managers were asked: What form of

competition is used in your principal market?Options included price, quality, volume, after

sales service, new product development, advertising, tying up suppliers, delivery and

marketing. On average our small firms competed on 4.5 dimensions. Over three quarters of

them competed on price, 87% on quality, 58% after sales service and 63.5% on delivery. It

was less common to compete on advertising (28.6%), tying up suppliers (25.4%) and volume


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performance growth relationship: the age of the mature small firm is also a determinant of its

growth rate as well as its size. The average age is about 26 years, (roughly one generation)

and no firm was younger than 10 years old. The maximum age in the sample was 90 years

(over three generations).

M, is a categorical variable, which identifies the main market for the principal product

group. It ranges from 1 to 4, where 1 denotes more local markets and 4 denotes national or

international markets. Typically, our mature small firm operated in localised markets. Nearly

a half (46%) operated in local markets, few (3.2%) in just regional markets, over a quarter

(28.6%) in Scottish markets, about one fifth (19%) in the UK and few (3.2%) internationally.

More than 50% operated outside local markets, with typically selling to the Scottish market.

Over a quarter (47.6%) stated that their main market had changed since start-up. Typically

firms expanded their market extent.

Initially, other variables were considered in the performance equation including

institutional variables like industrial sector and legal status, and structural variables like

market share, number of major rivals, and degree of competition in the principal market.

These were dropped if they were insignificant.

3.3.4.2 Equation (2) S= g (P, X2)

The exogenous variables (X2) in equation (2), the size equation, represent attributeslike: the level of technical change in the industry, T; the organising capability of the firm,

OC; and the labour productivity at start-up, LPSt. Labour productivity early in the life of the

firm (LPSt), is a ratio of sales to employees in the first interview at constant 2001 prices. It is

predetermined and assumed to be exogenous. It is a measure of the operational efficiency of

the firm earlier in its lifecycle. Firms, which generate more sales per fulltime equivalent

employees, are assumed to be more operationally efficient. Greater operationally efficiency,

early in the lifecycle of the firm, indicates a superior performer at this stage. Superior

performance would often be expected to lead to growth in size. This may not be the case,

however, as firms grow faster earlier in their lifecycle, compared to later. On average, firms

generated sales per full-time equivalent employees of 113,489stg. at this stage in their life in

2001 constant prices.

Our measure of the organising capability of the mature small firm (OC) is a count

variable of its functional activities (e.g. production, accounting, it support, sales, marketing,

product innovation, strategic planning etc.). According to Ghoshal, Hahn, Moran (2000),

administrative reorganisation is often necessary if the firm is to grow over time, and to retain


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its market share in a dynamic environment. Reorganisation often involves rebundling

activities, and may also lead to internalising the various stages of the value chains of goods

and services. To undertake such activities, a firm requires organising capability. Our variable

increases with the level of organising capability. On average, our firms engaged in seven

functional activities. Typically the larger number of these functional activities, the greater is

division of labour required, and the larger is the expected firm size.

3.3.4.3 Equation (3) C= h (P, X3)

The exogenous variables (X3) in equation (3), our competitive strategy equation,

represent attributes of the firms principal market. The number of major rivals, Mriv, is an

index of competitive pressure. In general, the greater the number of major rivals, the greater

the competitive pressure. Even with an average of just 26 major rivals this pressure can be

intense. Indeed, at extremes it can be destructive (Reid, Jacobsen & Andersen, 1993).

Product differentiation, Diff, is a self-appraised measure of product variety. It represents a

directly measured alternative to tricky measures like the cross elasticity of demand, which

require evidence from estimated demand functions. It was scaled to be greater, the greater

the product heterogeneity. In this sample the mature small firm typically sold similar but not

identical products to its competitors. They tried to differentiate their products. Out of the

total sample, only an eighth of firms (17.5%) sold identical products or services tocompetitors. Over a half (52.4%) sold similar products and just over a quarter (25.4%)

produced different products. The question seems to have been well understood, as less than

five per cent (4.8%) 'could not say'.

4. ESTIMATION OF SIMULTANEOUS EQUATION MODEL

The principal relations between size, competitive strategy and performance examined

in our three-equation model are outlined in equations (1) to (3) above. This outline model is

amplified here in equations (4) to (6). This now explicitly incorporates the exogenous

variables discussed above. In (4) to (6), the functions f(.), g(.) and h(.) of (1) to (3) are

expressed in linear forms with additive disturbance terms ui (i =1, 3). The structural

equations to be estimated were as follows:

Pt= 0 +1St +2Tt +3Ct +4Dt +4Mt +5At +6At^2 +u1(4)

St= 0 +1Pt +3LPSt +4OCt +5Tt +u2(5)


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Ct= 0 +1Pt +2Mrivt +3Difft +u3 (6)

Initially, a priori considerations were used to classify variables as either exogenous or

endogenous. Indeed the selection ofP, S and C as endogenous arises as much from the extant

literature, as from statistical considerations. However, once a priori knowledge has been

incorporated in the model, its legitimacy needs to be explored econometrically. Therefore,

formal tests for endogeneity within the system are examined immediately below, in Section

4.1.

4.1 Tests of Endogeneity

This Section reports on two matters: (a) Durbin-Wu-Hausman type tests of

exogeneity, to examine whether simultaneities exist between firm size, competitive strategy

and small firm performance; and (b) ways in which a system of equations can be estimated.Concerning the later, one method would account for contemporaneous correlations between

the errors of the structural equations in the system, using seemingly unrelated regression or

SUR estimation. Another method would account for simultaneities between two or more

endogenous variables, which are determined jointly within the system. We prefer the latter.

4.1 Tests of Endogeneity

Here Durbin-Wu-Hausman type tests are applied to investigate whether the set of

estimates of the structural equations obtained by least squares are consistent or not.vi If the

null hypothesis that OLS estimates are consistent is rejected, endogeneity (not every

regressor is asymptotically independent of the disturbances) is present and the IV estimator is

preferred to the least squares estimatorvii(Davidson and MacKinnon, 1993 p237). Failure to

reject the null hypothesis suggests that there is no need for structural modelling, but failure to

reject it may or may not imply endogeneity. Only under very special conditions (see

Geroski, 1982 p.58, for example) in industrial economics willfailure to reject be compatible

with exogeneity. Hence it is convenient to regard failure to reject as only indicative of

exogeneity.

Using Durbin-Wu-Hausman Tests some evidence of endogeneity was found between

S=g(P) and C=h(P). The F statistics (and associated probability values in parentheses) for

testing the null hypothesis that the coefficients on the fitted values of relevant test variable

(obtained from regressions against all the exogenous variables in the system are zero) were as

follows:


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Test for Evidence of Endogeneity

EQN (4) EQN (5) EQN (6)Test Variable S t Ct Pt PtF-value (1, 53) 2.12 0.99 F(1, 57) 8.2 F(1, 58) 3.35

Prob >F (0.1511) (0.3236) (0.0058) (0.0722)

Test for Evidence of Exogeneity Given that St, Ct and Ptare assumed to be endogenous.

EQN (4) EQN (5) EQN (6)Test Variable Dt Mt Tt Tt OCt Mrivt Difft.F-value 1.58 1.12 0.02 0.41 6.671 1.51 3.30

Prob >F 0.214 0.2954 0.8794 0.5228 0.0119 0.2241 0.0746

This statistical evidence confirms our a priori reasoning. As a result, theoretical and

statistical criteria can be invoked to support system estimation. Labour productivity earlier in

the life of the firm, LPst,and age, At,are predetermined within the system and are known to

be exogenous. Testswere performed for the exogeneity of the other variables in the system,

namely, the level of liabilities of the firm,Dt, the main market of the firm,Mt, the organising

capability of the firm, OCt, the number of major rivals,Mrivt, andthe level of differentiation,

Difft. These tests lead us to regard Dt,MtandMrivtvariables as clearly exogenous. There is

some evidence of endogeneity of OCtat the 5% levelviiiandDifftat the 10% level

ixbut this

seems to be unidirectional in nature and thus is not explicitly modelled here. Sample size

prohibits us from examining all sources of endogeneity in this system.

4.2 System Estimation

The available methods of estimating simultaneous equations vary, based on their

treatment of information, and their use of different estimators (maximum likelihoodxversus

instrumental variables). Single equation methods, like two stage least squares (2SLS), and

limited information maximum likelihood (LIML), estimate the model parameters of each

equation at a time, whereas full-system estimators, like three stage least squares (3SLS) and

full information maximum likelihood (FIML), estimate all the parameters at once.

Two system estimation techniques are adopted in this paper, namely two stage leastsquares (2SLS) and three stage least squares (3SLS), here for comparative purposes given the

evidence of endogeneity. In the presence of endogeneity 3SLS, a full system estimator, is

likely to have an efficiency advantage over the single equation methods, such as 2SLS. We

report the results of iterative 3SLS because these results converge to those of FIML

estimation for all parameters. The work of Jans and Rosenbaum (1996) illustrates the use of a

3SLS (in non-linear form) estimation to estimate another industrial model in which

endogeneity is intrinsic.


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Davidson and MacKinnon (1993, p234) state that it is generally desirable for a model

to be somewhat over identified in order to ensure good finite sample properties, for the use of

instrumental variable (IV) estimation,of which 2SLS and 3SLS are examples. For equation

(4), the number of excluded exogenous variables and included endogenous regresses are four

and two, respectively; for equation (5) they are six and one, respectively and in equation (6)

they are seven and one, respectively. The order condition for identification therefore

suggests that each of the three equations is over identified, and that there are thirteen over

identifying restrictions in total within the system.

5. RESULTS

To examine whether there are tradeoffs between firm size, competitive strategy and

performance for the sample of 63 long-lived small firms we estimated the system of structuralequations (4)-(6) using 2SLS and the I3SLSxi estimation techniques. These two estimation

techniques were adopted for reasons of statistical efficiency, and to examine the robustness of

the results. Each of these techniques place different restrictions on the data and have different

merits, which overcome the failings of other techniques particularly in finite samples.

Efficiency is not the overriding concern, as we also wish to limit finite sample bias. The

results are reported in Table IV and V below. The estimates of the behavioural relation

between firm size, competitive strategy and performance are discussed below in subsection

5.1. Finally, patterns of adjustment of size, competitive strategy and performance within the

simultaneous systems are examined in subsection 5.2.

5.1 Equation Estimates

[INSERT TABLE IV NEAR HERE]

An initial examination of the estimates suggest that the results are robust across the

performance and size equations, under both estimation techniques, (see Table IV). In TableIV, the three equations are set out under each other with performance at the top, size in the

middle, and competitive strategy at the bottom. These are the estimated versionsof equations

(1), (2) and (3) above. Coefficients are as in equations (4), (5) and (6) above. The t-values are

shown under each coefficient. These estimates indicate that a trade off indeed exists between

firm size and performance. For the I3SLS estimates, size has a significant negative influence

on performance, P=f(S), f


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though its sign suggests a trade-off. We regard the I3SLS estimates as being superior, in

terms of econometric properties.

We need to ask why an increase in size, here measured by full-time equivalent

employees reduces the performance of the small firm. Perhaps these reductions in

performance arise from reduction in labour productivity. This could be because these are

increased costs associated with hiring more employees, with rising effort being expended in

recruiting and training new staff. Thus the small firm sacrifices increases in profits or

performance to grow. Viewed the opposite way, the performance equations suggests that

reductions in firm size lead to increases in performance. As the small firm reduces in size

performance increases, due to increased efficiencies (i.e. increased labour productivity caused

by the substitution of labour for capital and a leaner cost base), and a relative increase in the

human capital at work in the small firm. Thus by becoming a leaner organisation, the

survival and the long run prospects of the small firm are promoted. However, one would

expect there to be diminishing returns to a survival strategy of this sort. At the limit, one-

man outfits will find it difficult to compete in the same league as dominant players in the

market unless their goods are very specialised i.e. niche products. Certainly, if we assume

that the goal of the entrepreneur is to raise his firms performance our trade-off relationship

suggests that downsizing may be the principal way to gain improvements in performance.

The properties of the behavioural relation between the strategy space of the firm andperformance are less clear. Estimation by both 2SLS and I3SLS techniques indicates that the

competitive strategy space has a positive and significant effect on performance, in the

empirical version of equation (1) in Table IV. In the empirical versions of equation (3), the

coefficient on performance is negative in sign (suggesting a trade-off), but it is insignificant.

Causality is perhaps unidirectional, i.e. P=f(S,C) but Cg(P). That is, the competitive

strategy of the small firm has a significant positive influence on performance, but its

performance does not significantly influence the heterogeneity of the competitive strategy,

C=g(P). If again here we assume that the goal of the owner manager is to raise performance,

the model points to improvements in performance if the small firm reduces its size and

competes strongly, using a wide variety of strategies.

5.2 Elasticities

[INSERT TABLE V NEAR HERE]

We now turn to examine each equation, by reference to elasticities at the mean, so

presented in Table V. Our goal now is to focus more on the quantitative impact of variables,rather than on their significance per se. In the performance equation a 1% increase in firm


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size leads to a 0.03% fall in performance and visa versa. Thus, increases in the size of the

small firm reduce its performance, but the impact is small. By contrast, the competitive

strategy, Ct, has the largest impact on performance. A 1% increase in the strategy space of

the firm leads to a 0.15% increase in performance. Should a small firm be operating in an

industry which is subject to technical change, (Tt) this experience has a significant positive

effect (see Table IV) on performance and its impact is a quitelarge (elasticity is 0.12%). Thus

industry level technical change seems to have an important effect on promoting the long run

survival (and prospects) of the small firm.

The more liabilities (Dt) the small firm is exposed to, the lower its performance,

though the size of this effect is not significant in the I3SLS estimation. A 1% increase in the

forms of liabilities of the firm lowers performance by 0.3%. Reid (1993) shows that gearing

has a crucial impact on many key aspects of the young small firms existence: medium term

viability, growth and profitability. Excessive levels of liabilities may be detrimental in the

medium term. Here (Table IV) the effect has a negative sign, but it is not significant predictor

of long run survival in the full system estimation (I3SLS). The effect of greater exposure to

external liabilities in the latter part of the firms life is uncertain. If equity finance is a

cheaper source of finance capital, the optimal strategy for highly geared small firms is to

retire debt early in its lifecycle (Reid, 2003). However later in its lifecycle other structures of

finance capital could be appropriate. Thus Power and Reid (2003) found that gearing wasinsignificant in explaining long run survival.

The geographic extent of the small firms main market (Mt) had a positive effect on

firm performance, but this effect was not significant. Less dependence on local markets, or

put another way greater the markets extent, the greater the performance of the small firm,

other things being equal.However Reid (2001) found that unless firms start with marketing

intentions, which are explicitly aimed at national or international markets, the small firm

would never make this their main market, which perhaps explains why this effect is

insignificant.

The effect of age (At) on performance was insignificant. Age squared was significant

at the 10% level using 2SLS but not significant under I3SLS. There is therefore a weak

suggestion that as the small firm gets older its performance falls but at a decreasing rate.

Performance is a convex function of age. This is a plausible result, in that, if performance fell

at an increasing rate the long run survival of these mature small firms would be very fragile.

Such a result would not encourage the continuous investment in these firms which we have

observed.


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In the size equation, (middle equation in Table V) performance had the largest impact

on size. A 1% increase in performance leads to as much as an 11% fall in size (measured by

full-time equivalent employment). This effect is of considerable magnitude compared to the

inverse influence of size on performance (elasticity of 0.03%) in the first equation. This

finding demonstrates why there is a tendency for these mature small firms to reduce their

headcount and to become leaner, to gain further improvements in performance. Here also, a

firm operating in an industry, which is subject to technical change, experiences a significant

positive effect on firm size (elasticity is 1.4%). In response to technical change in the industry

the firm grows in size. Greater headcount is required to respond to technical changes (i.e. the

firm may require to increase the human capital of the firm etc.)

The effect of labour productivity (LPst) earlier in the life of the firm on size was

negative, but not significant in the I3SLS estimation. Firms, which generate more sales per

fulltime equivalent employees, are more operationally efficient. Greater operationally

efficiency earlier in the life of the firm indicates a superior performer at this stage. Superior

performers would be expected to grow in size. This may not be the case however, as firms

grow faster in size earlier in their lifecycle, than in the latter part of their life. Thus this

finding is indicative of early lifecycle effects in labour productivity. Younger small firms

grow faster, in response to increases in labour productivity than mature small firms. It had

the lowest influence on size (elasticity is -0.09%). The organising capability of the firm, OC,had a positive and significant effect on the size of the firm at the 10% level using I3SLS. A

1% increase in organising capability of the firm raises firm size by 0.72%. This result is

consistent with the discussion of Ghoshal, Hahn, Moran (2000) on administrative

reorganisation. To engage in a larger number of functional activities, a greater division of

labour is required.

In the competitive strategy equation (equation 3) performance had a negative and

insignificant effect on the heterogeneity of the firms competitive strategy. This is not

surprising, as many factors other than performance may be determining the size, or scope, of

the firms competitive strategy. Thus we are not concerned about this. Higher levels of

product differentiation had a positive and significant effect on the dimensions of the

competitive strategy of the firm. The size of the elasticity of this effect was 0.29 and 0.48 for

the I3SLS and the 2SLS estimation, respectively. To the extent that product heterogeneity

(Diff) confers local monopolistic advantages on the small firm, it increases the dimensions on

which the firm competes to protect these advantages. This finding supports evidence that

small firms usually seek to cultivate mild forms of product differentiation, especially by


22/34


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identifying restrictions is equal to 2*[-558.894-(-616.1646)] = 2*(57.2706)= 114.5212, which

is much larger than the 0.05 (0.01) chi-square critical value of 22.36 (27.688), suggesting that

the over-identifying restrictions are not consistent with the data (see Berndt, 1991, p.554). As

the results of the system estimation seem robust across the two system estimation techniques

the next subsection analyses the adjustment path of the behavioural relation between size,

dimensions of competitive strategy and the multi-dimensional measure of performance.

5.4 Adjustment Paths

A final interpretation of the model can be undertaken by examining the relationships

between jointly determined variables in the system; firm size, dimensions of competitive

strategy and performance. Suppose all the exogenous variables in equations (4) and (5) are

assigned to their mean values, the functions for the performance equation P=f(S, C)and forthe size equation S=g(P) can be linearly approximated and examined in a two dimensional

graph. The stability of these behavioural relations can then be examined.

Using the estimated coefficients of Table IV, and the mean values for exogenous

variables, these functions are approximated as follows;

Pt= 59.938 - 0.17544St + 2.1594 Ct(7)

Pt= 69.742 - 0.17544St(7a)

St= 160.668 - 2.1831Pt(8)

It is informative to graph equations 7(a) and 8, as in Figure II. Solving out these two

expressions, the equilibrium values (S*, P*), which denote the equilibrium point E is (13.639,

67.349) are close the mean values for firm size and the multidimensional measures of

performance in the sample which were 13.6508 and 67.3467 respectively (see Table III). It is

to be further noted that the equations indicate a stable equilibrium point. Thus starting from a

performance level of 69.742 on the horizontal axis a convergent path to the equilibrium point

E can be traced. Similarly starting from a size of 160 full-time equivalent employees on the

vertical axis another convergent path to E can be traced.xvAs E is close to the relevant mean

size and performance values in the sample, the typical mature firm in the sample has reached

this equilibrium point. The relative size of the adjustments for S=g(P)is much larger that the

relative magnitude of the adjustments for P=f(S). In response to increases in performance,there is a strong tendency for the small firm to adjust downwards in size. Therefore, to


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24

improve the long run survival prospects of the small firm they need to become leaner, and

more efficient in size. Thus the trade-off between firm size and performance implies that

there is a strong performance driven effect to remain small or to reduce in size. We now turn

to the effect of the dimensions of competitive strategy on this trade-off.

[INSERT FIGURE II NEAR HERE]

Figure III illustrates shifts in the performance function as a result of a change in the

dimensions competitive strategy of the firm. If the firm increases the heterogeneity of the

competitive strategy it undertakes the performance function shifts to the right and a new

equilibrium point E* is reached where E* represents higher values of performance and lower

values of firm size. The magnitude of this increase in performance could be reduced if

improvements in performance feedback into the heterogeneity of the firms competitive

strategy. However this effect was insignificant across both system estimation techniques andthus is not given much emphasis here. In essence this figure is suggesting that the long run

prospects of these small firms can be promoted through further specialisation of the

dimensions by which they compete. Competing on a diverse range of attributes of the firms

product, price, service enables the firm to achieve a higher equilibrium performance. This

perhaps explains why small firms usually seek to cultivate mild forms of product

differentiation, especially by customer service and delivery etc. Strongly differentiated

products can only be sold in very limited niche markets, especially if they are constructed on

a customer specified (i.e. bespoke) basis. However economies of scope perhaps exist for

these small firms, in the pursuit of these strategies in more localised or niche markets, Reid

(1993).

[INSERT FIGURE III NEAR HERE]

6. CONCLUSIONS

This paper examines behavioural relations between firm size, the heterogeneity of the

firms competitive strategy and the performance of the long-lived small firm in Scotland. The

latter two variables are measured in novel ways. In this work we find there is a strong

tendency for the small firm to remain small on two fronts. First as a trade-off exists between

firm size and performance, the mature small firm must become leaner and more efficient over

time if it is to survive. The small firm adjusts downwards in size by a considerable amount to

achieve further increases in performance. Second to attain higher equilibrium values of

performance a varied competitive strategy needs to be adopted. This can be achieved through

producing customised or specialist products but also through increasing the aggressiveness of

its competitive strategy to defend market niches such as raising advertising and marketing


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25

efforts. Survival of small firms is linked to product differentiation, as typically small firms

are niche players. The tendency in this instance is to become more specialised and localised

and to seek economies of scope, to improve the long run prospects of the firm. The firm must

also be proactive in defending its niche in the market. Acting in these ways, entrepreneurs

can have a positive influence on the long run performance of the small firm.

Two system estimation methods were employed to estimate the behavioural relation

between firm size, the heterogeneity of the firms competitive strategy and performance; two

stage least squares and iterated three stage least squares. The similarity of the results across

these two estimation techniques suggests the robustness of the results.


26/34


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27

Figure I

Response Format for Performance Indicator

4.1 We'd like to know what has kept you in business down the years. Some things are

good for business and some things are bad. What effect have the following had?

[Show with a cross whether the effect was good or bad.]

N/A Bad Neutral GoodTechnology

0 25 50 75 100

N/A Bad Neutral GoodRival's Innovation

0 25 50 75 100

N/A Bad Neutral GoodRegulation 0 25 50 75 100

Table III

Endogenous and Exogenous Variables

Variable N Mean Std. Dev. Min. Max.P 63 67.3467 8.1036 49.11 90.43

S 63 13.6508 19.8488 1 130

C 63 4.5397 1.8035 1 8

Endogenou

s{

LPSt 63 113489 125103 1780 549577

OC 63 7.2381 2.1381 3 11

S 63 13.6508 19.8488 1 130

A 63 25.5397 15.7284 10 90

Sector 63 1.6349 0.48532 1 2

LegalStatus 63 2.1905 0.8203 1 3

Mriv 63 26.0318 126.1867 0 1000

M 63 2.2698 1.2599 1 4

D 63 1.8254 1.4429 0 4

Diff 63 2.1746 0.7733 1 4

C 63 4.5397 1.8035 1 8

Exogenous

{

T 63 0.8254 0.3827 0 1


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Table IV

Results of System Estimation

Estimation 2SLS I3SLS

Equations Coefficient Coefficient

(t stat) (t stat)

Pt= 0 53.113 54.996 (8.059) (10.65)

+1St -4.65E-03 -0.17544 (-0.6040E-01) (-2.87)

+2Tt 8.6902 10.09 (3.706) (4.46)

+3Ct 2.8866 2.1594 (2.015) (1.83)

+4Dt -1.9571 -0.91728 (-2.31) (-1.402)+5 Mt 0.61294 0.14136 (0.7171) (0.2378)

+6 At -0.28142 -0.14165 (-1.536) (-1.099)

+7 At^2 3.78E-03 1.77E-03 (1.874) (1.204)St= 0 146.71 133.08

(2.758) (2.71)

+1 Pt -2.4254 -2.1831 (-3.023) (-2.896)

+2 Tt 25.869 23.049 (2.742) (2.738)

+3 LPSt -5.44E-05 -1.14E-05 (-2.433) (-0.7666)

+4 OCt 2.0858 1.3618 (1.615) (1.747)

Ct= 0 4.6964 7.3857

(1.393) (2.122)

+1 Pt -3.01E-02 -5.95E-02 (-0.5928) (-1.139)

+ Mrivt -3.56E-03 -7.54E-03 (-1.951) (-4.361)

+3 Difft 0.90142 0.62544 (3.2) (2.463)

Table V

Elasticities at Mean


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29

Estimation 2SLS I3SLS

Pt= 0 0.7886 0.8166

+1St -0.0009 -0.0356+2Tt 0.1065 0.1237+3Ct 0.1946 0.1456+4Dt -0.0530 -0.0249+5 Mt 0.0207 0.0048+6 At -0.1067 -0.0537+7 At^2 0.0503 0.0235St=

0 10.7475 9.7491+1 Pt -11.9657 -10.7703+2 Tt 1.5642 1.3936+3 LPSt -0.4519 -0.0945+4 OCt 1.1060 0.7221Ct= 0 1.0345 1.6269+1 Pt -0.4459 -0.8833+ Mrivt -0.0204 -0.0432+3 Difft 0.4318 0.2996

Figure II

Size Performance Trade-off

Figure III

Impact of an Increase in the Diversity of Competitive Strategy


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Endnotes

This research has been undertaken with the generous support of Enterprise Ireland, to whom

the authors make grateful acknowledgement. We should also like to thank many owner-

managers of small firms in Scotland. They gave generously of their time, over the period

2001-2, allowing us to collect high quality data in the field.

iSee Jacobsen (1986).

iiSee Reid and Andersen (1992).iii

See Smith (1997).ivThe factors were generated from theory and empirical evidence from studies examining differences in the

performance of long-lived small firms.vRating factors along a continuum is a much easier task than ranking the list of factors from top to bottom

especially for long lists of factors. The ranks can be tied when the factors are rated. The consistency whichowner-managers rate factors on each scale item is also improved by defining the meaning respondents shouldassign to middle alternatives using adjectival labeling of points which is undertaken here.viIn practice the test is implemented as follows: Suppose a structural equation is

uyXy 211 ++= where y1and y2 are vectors of suspected endogenous variables, X1is a matrix of exogenous and predetermined

variables, and u a vector of error terms. Let 2y be the vector of fitted values of y2 from a reduced form

regression of y2 against all the exogenous and predetermined variables in the system. The DWH test is simply

an F test that the coefficient on 2y is equal to zero (i.e. test 0 = ) in an estimation of the following

regression uyyXy 2211 +++= .vii

As it happens least squares is the preferred estimator as the asymptotic covariance matrix of the least squaresestimator is never larger than that of IV estimator, it will actually be smaller unless endogeneity exists (seeGreene, 2000 p.383). viiiF(1,60)statistic = 0.17 for Ho

could not be rejected

ix

F(1,60)statistic = 0.57 for Ho

could not be rejected

xMaximum likelihood methods are invariant to reparametrisation whereas instrumental variables are not.


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31

xiWhen higher that 2 iterations are used the significance of the performance and size variables increase rapidly

due to rounding errors.xii

Single R2measures are not appropriate in an equation system. The R2 from a particular equation computedcould be negative since with system estimation in general it is not the case within each equation the sum of theresiduals is zero. The numerator could be larger than the denominator that is the unexplained variation can be

larger than the total variation implying a negative R2. This is because single equation systems minimises ee and

therefore maximises the R2 in general. System estimation methods do not minimise ee. The maximumlikelihood estimator minimises the determinant of the residual cross products matrix; that is ML minimises detEE. Hence ML does not maximise the individual equation R2 values. Since single equation R2measures areflawed in the equation system context a different goodness of fit measure should be employed.

yy

EER

'

'1

~2=

The system2~R reported in Shazam is defined as

( ) ( )YYYYR = '/1~

where Y is an n x k matrix andYcontains the sample means.xiii

The Chi-square statistic is

( )( )22 ~1log RN =xiv The Lagrange Multiplier statistic reported on SHAZAM is computed as

=

=

=k

i

i

j

ijrN2

1

1

2 with

squared correlation coefficient of residuals given by

jjii

ij

ijr

22

=. Under the null hypothesis of a

diagonal covariance structure the statistic has an asymptotic2

)2/)1(( MM distribution.xv

This stability condition can be expressed:(dP/dS)7a= -0.17544 > -0.45806 = (dP/dS)8

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Competitive Strategy of Long Lived Small Firms

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