Productivity measurement in gambling: plant-level evidence from the United Kingdom.
Paton, David ; Siegel, Donald S. ; Williams, Leighton Vaughan 等
1. Introduction
As predicted in a seminal article by Baumol (1967), the service
sector has continued to grow at a more rapid pace than the goods sector
in advanced industrial economies. Given that service industries now
constitute a large proportion of economic activity, assessment of
productivity in such sectors has become an even more important aspect of
the public policy agenda. However, as noted in Griliches (1994) and
Nordhaus (2002), it is notoriously difficult to measure productivity in
service industries (mainly due to problems with output deflators) and in
some cases, even in defining the relevant output.
Gambling is one of the fastest-growing service industries. While
there has been considerable attention paid to the rise in gambling
revenue, there have been virtually no studies of total factor
productivity (TFP) in this sector. The purpose of this article is to
fill this gap, based on an analysis of U.K. establishment-level data.
These data are derived from the Annual Respondents Database (ARD) file,
constructed by the U.K. Office for National Statistics (ONS), consisting
of individual establishment records from the Annual Census of
Production. The ARD file contains detailed data on output, capital,
materials, employment, and numerous plant and firm characteristics and
is quite similar to the U.S.-based Longitudinal Research Database (LRD).
This information can be used to construct measures of TFP.
The use of plant-level data offers two key advantages. One
advantage is that deflation is not likely to be a serious problem, since
plants in the same industry are likely to face similar factor prices.
The ARD also contains data on relatively homogeneous plants. Thus,
measurement errors relating to difference in output mixes are not likely
to be as severe. A second advantage is that the use of plant-level data
allows us to assess and explain (with additional plant and firm
characteristic) relative productivity. We are especially interested in
assessing the relationship between proxies for investment in information
technology and TFP. There is limited evidence on the impact of
information technology on economic performance in services.
The remainder of the article is organized as follows. In section 2
we discuss some general productivity measurement issues. Section 3
presents some background information on the U.K. gambling industry, and
section 4 describes the rich, longitudinal data set of gambling
establishments. Section 5 presents the econometric method used to assess
and explain the relative productivity of these facilities. Section 6
contains our empirical results, and section 7 presents caveats and
preliminary conclusions.
2. Productivity Measurement in Services
General Issues
To compute real output, data are required on turnover or receipts,
as well as a price index to deflate nominal output. (1) Unfortunately,
producer or wholesale price indexes are not available for the outputs of
many service industries, due to the great difficulty in defining
measurable units of output and adjusting for quality changes. We
consider the latter issue first. Changes in quality result from
heterogeneous inputs and outputs and shifting weights in the use of such
inputs and outputs. They also arise from the introduction of new
products and services and the disappearance of old ones. An increase in
the rate of technological change (for example, the rise in the rate of
investment in computers) can potentially exacerbate difficulties in
adjusting prices for changes in quality.
Although it is usually relatively easy to identify the resources
used to produce services (that is, capital, labor, and materials), there
is still the problem of deflation of inputs. Academics have been
especially frustrated at the difficulty in constructing accurate
measures of capital input, which would be used in constructing estimates
of a capital productivity index as well as a TFP index. Therefore, many
researchers have resigned themselves to the analysis of labor
productivity, typically measured as real output divided by the number of
employees or hours worked. The benefit of labor productivity is that it
is likely to be measured with greater precision than TFP. However, labor
productivity measures do not take account of the possibility that
companies may substitute capital for labor, as is likely in an industry
experiencing rapid technological change. Still, McGuckin and Nguyen
(1995), Disney, Haskel, and Heden (2000), and Foster, Haltiwanger, and
Krizan (2001) have made inferences regarding overall economic efficiency
based on labor productivity indexes.
There is a disadvantage associated with using the simpler
productivity measure. As noted by Perloff and Wachter (1980, p. 116),
the use of Q/L, or the average product of labor, as a measure of
productivity has "numerous serious, if not quite fatal conceptual
flaws". Christiansen and Haveman (1980, p. 3) assert that
"although [these] productivity measures ... have serious
weaknesses, the picture of productivity change which they yield is not
greatly different from that of more complete measures."
Three flaws can be enumerated. First, to ensure reliability, output
and input measures must be consistent--that is, they must refer to the
same production activity. Because there are many production activities
implicitly underlying any aggregate measure of output, a meaningful
composite measure must be formulated by denominating the value of each
output measure by an appropriate price index. However, when labor is
denominated in hours, conceptual problems arise because a labor-hours
measure corrects for only one of the many heterogeneous aspects of
workers, namely and obviously the number of hours each works. Additional
adjustments are needed. For example, the age/sex/skill composition of
the labor force varies over time as well as from sector to sector. Since
average labor productivity indexes are primarily used for inter-temporal
comparisons, changes in the composition of the workforce will affect
measured Q, but will not be reflected accurately in a Q/L index unless
the changes are perfectly correlated with the way L is measured. This
conceptual problem can be overcome by adjusting L for the heterogeneity
of the labor force, and thereby, creating an index with efficiency labor
units in the denominator.
Chinloy (1980) describes one method for constructing such an index
based on methods used by the U.S. Bureau of Labor Statistics (BLS). This
index is calculated on the basis of changes in both number of hours
worked and hourly wages earned by different types of workers, classified
by age and education level. Similar indexes of labor productivity or
quality have been used by Jorgenson, Gollop, and Fraumeni (1987) and
Dean, Kunze, and Rosenblum (1988) in studies of aggregate economic
growth. It is important to note that these indices are also based on the
assumption that labor markets are perfectly competitive, as noted in
Chinloy (1980).
Chinloy (1980) defines labor quality, LQ, changes as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where [h.sub.it] is hours worked by the ith type of labor in year
t; [v.sub.it] is the share of total compensation paid to the ith type of
labor; and {[b.sub.it] = ([h.sub.it]/[m.sub.t])} is the share of total
hours worked devoted to the ith labor type. The discrete approximation
for Equation 1 is as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [QUALIND.sub.t] is a quality index that approximates the
left-hand side of Equation 1. In constructing these indices, the key
data requirements are a set of employment attributes to identify each of
the i different types of labor.
Several ways are used to aggregate over heterogeneous outputs in
either partial factor productivity or TFP indexes. The base-year
approach adjusts output values by the price of each product in the base
year. The deflated price approach adjusts the value of each product by a
current average price index. The choice between the two approaches is
important. According to Baumol and Wolff (1984), the base-year measure
is a defensible index for productivity growth comparisons. However, the
authors point out that it is not a useful indicator of inter-industry or
inter-sectoral differences in absolute levels of productivity.
Similarly, the deflated price index is meaningful for intra-industry
comparisons of absolute levels of productivity over time, but it, too,
fails to provide meaningful cross-sectional comparisons. The search for
a valid cross-sectional index of absolute production still continues.
A second problem with labor productivity measures is that the
average product of labor could be related to the business cycle. Thus,
such measures may be capturing effects that are unrelated to technical
progress. In this regard, Gordon (1979) contends that firms retain more
workers in the last stage of a business cycle than is justified ex post
by the future level of output. As a result of such biased ex ante
expectations, Q/L will decline absolutely until firms adjust their
hiring patterns to their corrected expectations about future demand.
A third and perhaps the most serious concern regarding labor
productivity measures is that neither labor nor capital is the sole
source of productivity improvements. Labor-saving improvements resulting
from other factors of production are improperly attributed as an
improvement in labor productivity when these other factors are not held
constant. A major problem with the use of labor productivity as a metric
for economic performance is that it measures the efficiency of only one
input and does not control for the possibility that the plant, firm, or
industry can substitute capital, materials, or services for labor. Many
shun partial factor productivity indices precisely for this reason. A
useful and meaningful productivity framework must therefore identity the
source of the productivity improvement and their interaction with other
factors of production, such as capital, materials, and services in the
overall production process. Along similar lines, Craig and Harris (1973)
show that partial factor productivity measures do not quantify the
impact of technical substitution. If, for example, a new technology is
embodied in capital, Q/L could rise as a result of capital for labor
substitution, ceteris paribus. But if the cost of the new
capital-embodied technology equals the cost savings from fewer workers,
then total production costs are unchanged and the initial movement in
Q/L is misleading with regard to actual productivity gains. In light of
these concerns, we deemed it prudent to present econometric findings
based on TFP and labor productivity measures.
The consideration of measurement errors in the service sector is
not new. In many service industries, the output price index is a
Tornqvist average of input price changes, based on input-output tables.
(2) The use of input-based indices, however, does not take into account
changes in the production process. Therefore, the use of the
input-output tables may be a source of measurement error. In addition,
as noted in previous sections of this report, input indexes are not
immune from the problem of properly accounting for the effects of
changes in quality.
As a result, it is perhaps not surprising that Baily and Gordon
(1988), in their seminal study of productivity in services, identified
severe errors of measurement in service sector prices. However, they
also concluded that there is no evidence to suggest that such
measurement errors are getting worse over time. Siegel (1994, 1995,
1997) presents similar findings, using multiple indicators of price
changes. More specifically, he examined the incidence of measurement
errors in output prices caused by incomplete adjustments for quality
change. Estimating several variants of a latent variables model, he
found that these errors appear to be constant over time. These findings
are highly relevant to our work because we will estimate service sector
productivity growth using panel data.
In addition to concerns regarding the accuracy of input and output
prices, domestic and foreign outsourcing is also a potential source of
measurement error (see Siegel and Griliches 1992). That is, levels and
changes in productivity could be driven by systematic underestimation of
input growth caused by increases in foreign and domestic outsourcing.
Thankfully there does not appear to be a compelling reason to believe
that outsourcing exacerbates errors of measurement of service sector
productivity. The provision of services (for example, health care) is
mainly a local phenomenon, and there does not appear to be substantial
outsourcing across industries, as there is in manufacturing.
Indeed, some authors have asserted that outsourcing leads to
systematic understatement of input growth, and thus, overstatement of
productivity growth. But even in manufacturing, there is considerable
evidence (see Siegel and Griliches 1992; Siegel 1995; ten Raa and Wolff
2001) suggesting that outsourcing cannot "explain" the recent
acceleration in manufacturing productivity growth. Still, we must be
mindful about the potential effects of measurement error on our
empirical results.
We have reason to believe that the measurement difficulties cited
in this section can be overcome, given the availability of
establishment-level data. The primary focus of our analysis will be on
assessing levels of relative productivity. The quality-change problem is
more severe in computing absolute or relative productivity growth. We
propose to undertake an analysis of productivity in gambling at two
levels of aggregation. The first unit of analysis will be the industry,
in which case we will examine changes in productivity over time. The
apparent constancy of measurement errors bodes well for the accuracy of
such productivity growth measures.
Most importantly, however, the primary unit of observation will be
the establishment or plant. The use of establishment-level data allows
us to measure and "explain" relative productivity, and thus,
conduct analysis of "best practices." This is a critical
feature of our empirical analysis and allows for a much richer and much
more accurate assessment and explanation of productivity. For example,
it seems highly reasonable to assume that plants in the same industry
face the same factor prices and generate similar output mixes. While
there may be regional differences in wages, our use of regional dummy
variables in the econometric specification controls for such variation.
Measurement Issues in Gambling
In common with many service industries, gambling presents
considerable difficulties in defining and measuring real output (see
Griliches 1987 and Siegel and Griliches 1992). That is, it is not
precisely clear what is being sold or the nature of the output.
In the context of banking, Fixler and Zieschang (1992) argue that
there are three alternative methods for measuring output: the asset,
user cost, and value-added approaches. Under the asset approach, banks
are only considered as financial intermediaries between liability
holders and those who receive bank funds. In this framework, the outputs
of a bank are its loans and other assets. In contrast, the user cost
approach assesses whether a financial product is an output or input on
the basis of its net contribution to bank revenue. When the financial
return on an asset is greater than the opportunity cost of funds, or if
the financial costs of a liability are less than the opportunity costs,
then the instrument is a financial output. Otherwise, it is an input.
The third method is the value-added approach, which allows each asset
and liability category to potentially have some output characteristics,
rather than distinguishing inputs from outputs in a mutually exclusive
way. The researcher uses operating cost allocations (for example,
expenses) to determine which categories have substantial value added.
These are then identified as the key outputs.
Triplett and Bosworth (2004) provide a review of the long-standing
debate between proponents of the "gross premium" and "net
premium" approaches in the insurance industry. In the gross premium
method, insurance claims are treated as business costs. Gross output
would then equal the total value of premiums. Under the net premium
approach, gross output is defined as premiums less the value of claims.
This distinction can easily be applied to the gambling industry. The
equivalent of the gross premium method is to define gross output as
total gambling stakes or turnover. The equivalent of the net premium
approach would be to define gross output as total stakes less returns to
winning customers (net turnover or gross profits).
The relationship between these two concepts can be formally shown
as follows. First, we define total stakes as Q and gross profits as GP.
Further, we follow the convention and define the amount of a 1 [pounds
sterling] stake that a bettor would expect to lose to the bookmaker as
P, the price of gambling. We then have
P x Q = GP,
where Q is the total number of unit stakes placed by gamblers,
which can be viewed as the total quantity of bets. Based on this
formulation, it seems clear that the counterpart to output in
manufacturing is Q--total stakes, suggesting that the gross premium
approach is the right one for gambling. On the other hand, Akerlof
(cited in Triplett and Bosworth 2004, p. 14) has argued that margins are
a more appropriate measure of output in gambling on the grounds that
this measures the entertainment value of the good to the consumer.
There are also practical issues of relevance here, particularly
given the shift from the tax on gambling turnover to the tax on gross
profits that occurred in the middle of the sample period. For example,
consider the case of an operator who pays out the same revenue as he
receives. The value of gross profit is zero and, under the net premium
approach, this would imply a turnover of zero, despite the fact that
gambling activity has taken place. Indeed, if the operator pays out more
than he receives, this implies a negative turnover!
The same logic applies to the sector as a whole. Similarly, if
margins fall due to increased competition, and more is bet in absolute
stakes, employment may rise. However, turnover under this definition has
fallen. Therefore, if we use gross profits to measure output, we would
conclude that output per unit employment has fallen; that is, labor
productivity has fallen, and we would still obtain this result (though
to a lesser extent) even if employment was unchanged. At the same time
as the labor productivity has apparently fallen, bettors have lost a
lower proportion of the money they staked and more money has been
gambled. The only way in which productivity has fallen is that output as
measured by turnover has fallen. If margins remain constant, output is
unchanged, and this measure is fine as a measure of productivity. If
margins rise, output as measured rises, and productivity appears to
rise. This is also unsatisfactory. In conclusion, this measure is
potentially flawed at least insofar as there are significant changes in
margins over the period of measurement.
On the other hand, if stakes are used to measure output, then a
reduction in margins means an increase in stakes. With a given level of
employment, this means more output for the same employment or higher
labor productivity. This is intuitively correct. If margins remain
constant then stakes will not vary substantially, and it is likely that
employment will not change much either. Note that this is equivalent to
constant productivity. However, there is also a practical problem with
using stakes to measure output. In recent years, betting shops have
increasingly promoted betting on Fixed-Odds Betting Terminals (FOBTs)
over traditional wagering on events such as horseracing. In contrast to
horserace betting, FOBT betting tends to be characterized by high volume
and low margins. Bettors may spend the same amount of money over the
same period of time, but they do so by "repeat" betting. Using
the gross premium approach would lead to us observing a large increase
in gambling output, whereas it is, in fact, debatable that output has
really increased.
In the light of this discussion, we report estimates using both
approaches to measure gross output. Note that as Triplett and Bosworth
(2004) demonstrate this debate is not relevant for the measurement of
gross value added, which is the same in both cases.
3. Background Information on the U.K. Gambling Industry
A fundamental trend in the United Kingdom has been the rise in
gambling activity outside the traditional betting parlour, via telephone
or Internet access, including betting exchanges and interactive TV
betting. The remarkable growth in the incidence of virtual gaming
machines (FOBTs) in betting shops has served to reinforce this trend.
On the financial side, there was a radical change in tax rates and
structure of taxation in October 2001 (see Paton, Siegel, and Vaughan
Williams 2002), moving away from a tax on gross revenue to a tax on
gross profits and effectively halving the incidence of taxation on
bookmakers. This has enhanced the competitiveness of U.K. firms and also
caused a shift towards low-margin, high-turnover, capital-intensive
products, such as FOBTs, which offer "virtual" betting
products such as roulette.
A notable shift in the structure of gaming towards video-based
technology and machine-based gaming has occurred in the casino industry.
The impact of new technology on the gaming machine market has been
limited by consumer resistance to video-based reels in the core
Amusements with Prizes market and the club/jackpot sector, but it has
had a significant impact on the Skill with Prizes sector. A key growth
area for bingo operators in recent years has also been in machine income
and high-margin mechanised cash bingo (MCB) income. There has also been
rapid growth in offshore Internet gaming sites, especially Internet
casinos, which are reliant on capital-intensive technology.
The U.K. betting market (as distinct from the gaming market) can be
divided into five sectors: off-course betting at licensed outlets (the
dominant venue for betting); on-course betting; betting by telephone
(through deposit or credit accounts, or via debit cards); Internet
betting; and interactive (via TV) betting. Betting can be further
subdivided into fixed-odds betting with bookmakers, pool (parimutuel)
betting with the Horserace Totalisator Board (the Tote), "spread
betting," and bet brokerage ("exchange" betting). In
Table 1, we provide a breakdown of gambling turnover in the United
Kingdom by betting medium.
The remote betting sector has grown rapidly, particularly since
2000, as the technology for placing bets has become increasingly
integral to consumers' everyday lives--notably the Internet,
interactive TV (as the digital sector has grown), and the latest
developments in handheld mobile access technology. Table 2 presents data
on the growth of Pay TV in the United Kingdom, which includes gambling
activity. There has also been a steady growth in the number of
multi-telephone-line households and broadband connections, enabling easy
access to Internet betting opportunities. A significant growth in
offshore betting turnover placed by U.K. citizens can also be traced to
the independent bookmaker Victor Chandler, who in the late 1990s set up
a tax-free (though not commission-free) operation in Gibraltar.
Another change has been the growth in the number and variety of
betting operators who establish operations with no shops but simply as a
remote betting entity (for example, Betfair, Betdaq, and Sportingbet).
Driven by the likely consequences for the competitive base of U.K.-based
bookmaking and associated tax revenue implications, a tax based on the
turnover (revenue) of betting operators was replaced in October 2001 by
a tax based on their "gross profits" (that is, the difference
between what they receive from bettors and what they return to bettors).
The gross profits tax essentially replaced a tax on quantity with a more
allocatively efficient tax on price. This was accompanied by the larger
U.K. bookmakers repatriating offshore operations and the abolition of
deductions levied on bettors' stakes or winnings. Since 2001,
betting turnover has grown substantially, although margins have fallen.
Betting turnover placed with offshore bookmakers was in significant part
repatriated on-shore.
Internet access has also grown rapidly during the past seven years.
Research published by Mintel (2005) finds that Internet betting is the
most popular method of remote betting with 9% of bettors having placed a
bet with an online bookmaker while just 5% used a telephone service.
Sixty percent of adults are now online, almost double the number in
2001, and further growth can be expected in other methods of remote
betting as other digital media platforms become established.
In terms of the off-course market, an attempt by Ladbrokes to take
over the betting shops of Coral Racing was blocked by the then
Monopolies and Mergers Commission, although the dominance of the big
bookmaking chains (Ladbrokes, William Hill, Coral, and Tote) has
essentially continued. The monopoly pricing of the Computer Straight
Forecast offers an important perspective on this structural framework
(see Paton and Vaughan Williams 2001).
In the following section, we describe the rich longitudinal data
set used to assess and explain the relative productivity of gambling
establishments.
4. Assessing Gambling Productivity Using the Annual Respondents
Database
The Annual Respondents Database (ARD) is a plant-level file based
on the Annual Business Inquiry (ABI), a survey conducted by the ONS.
Information is collected on a range of variables covering output,
employment, investment, and expenditure for samples of businesses across
the range of industrial sectors. Some variables, such as those relating
to the firm's Internet presence, are not collected on an annual
basis.
Firms are selected for inclusion in the ABI from the
Inter-Departmental Business Register (IDBR) at the ONS. Sampling is
based on size by employment on the Register. The probability of being
selected for the ABI increases with employment size and the largest
firms (currently over 250 employees) are surveyed every year. The ABI is
carried out at the level of reporting unit, which is typically at the
enterprise level. However, a significant number of enterprises have more
than one reporting unit. Selected firms have a statutory duty to provide
data to the ABI. In Table 3 we report the numbers of selected and
non-selected gambling firms included in the ABI for each year from
1997-2003 and also a breakdown by number of employees.
A limited amount of data (on employment and turnover) are held for
all reported units on the IDBR. There is some evidence (Haskel and
Khawaja 2003) that the employment data in the IDBR are more reliable
than the turnover data. For this reason, our productivity analysis is
based on the ABI data alone, with the exception that IDBR employment
data are used to derive appropriate weights. Data on the service sector
(with Standard Industrial Classifications [SIC] within sections G P) are
available from 1997 2002, albeit with a somewhat more limited set of
variables than for the production sector.
Our empirical approach consists of two stages. In the first stage,
we calculate a series of labor productivity measures for the gambling
sector. These are broadly comparable with the Experimental Productivity
Measures currently published for some service industries (but not
gambling) by the ONS and reported in Daffin, Reed, and Vaze (2002). In
the second stage, we estimate stochastic frontier models. These
exploratory models allow us to test hypotheses relating to the
determinants of levels and changes in productivity.
We report labor productivity estimates for gambling using two
measures of production, gross output and value added, and two measures
of labor. We consider these in turn.
Gross Output
Direct measures of gross output (GO) are not available in the
gambling sector as they would be in a conventional manufacturing
industry. Reflecting the discussion above on whether output in gambling
should be defined as total stakes or as total stakes less payouts to
winning customers, we construct two measures of gross output, GO1 and
GO2. (3)
GO1 = turnover+ change in work in progress + change in stocks
brought for resale + work of a capital nature by own staff.
GO2 = turnover--payouts to winning customers + change in work in
progress +change in stocks brought for resale + work of a capital nature
by own staff.
Gross Value Added
Similarly, direct measures of gross value added (GVA) are not
presented in the ARD file for services. We compute it as follows:
GVA = turnover + change in work in progress at start and end of
year--total purchases.
Labor Input Measures
We measure labor input using the employment measures reported in
the ARD. The first measure is total employment (question q50). This
includes part-time work. With the second measure, we adjust for
part-time employment, assuming that one part-time employee is equivalent
to 0.5 full-time employees. Part-time employment is given in questions
q52 and q54, so the second measure is calculated as q50-0.5 q52-0.5 q54.
In calculating these measures, we have three methodological
measures to consider: deflation, reporting period, and weighting for
non-selected firms.
There are several possible deflators, including the GDP deflator,
Producer Price Index (PPI), and the Retail Price Index (RPI). Here we
choose to deflate all variables by the Consumer Price Index for
Recreation & Culture published by the ONS (series CHVS) with the
base year of 1996. Given that we are focusing on a single industry, the
choice of deflation measure is less important than with cross-industry
studies. Reassuringly, however, our gambling results are relatively
robust to different inflation indicators.
For some firms, the reporting period for the data does not cover
the standard annual month period. To control for this, we multiply each
variable by the number of days in the reporting period divided by 365.
We base our productivity estimates on data from the firms selected for
the ABI. It is important to control for the fact that larger firms have
a greater chance of being selected. We control for this by weighting the
observations, using as a basis the employment data from the IDBR
following the methodology of Haskel and Khawaja (2003).
For some firms, the reporting period for the data does not cover
the standard annual month period. To control for this, we multiply each
variable by the number of days in the reporting period divided by 365.
We base our productivity estimates on data from the firms selected for
the ABI. It is important to control for the fact that larger firms have
a greater chance of being selected. We control for this by weighting the
observations, using as a basis the employment data from the IDBR
following the methodology of Haskel and Khawaja (2003).
5. Econometric Model
To assess relative productivity, we use a stochastic frontier
analysis (SFA) method developed independently by Aigner, Lovell, and
Schmidt (1977) and Meeusen and Van den Broeck (1977). SFA generates a
production (or cost) frontier with a stochastic error term that consists
of two components: a conventional random error ("white noise")
and a term that represents deviations from the frontier, or relative
inefficiency.
SFA can be contrasted with data envelopment analysis (DEA), a
non-parametric estimation technique that has been used extensively to
compute relative productivity in service industries. (4) DEA and SFA
each have key strengths and weaknesses. DEA is a mathematical
programming approach that does not require the specification of a
functional form for the production function. It can also cope more
readily with multiple inputs and outputs than parametric methods.
However, DEA models are deterministic and highly sensitive to outliers.
SFA allows for statistical inference, but requires somewhat restrictive
functional form and distributional assumptions.
In SFA, a production function of the following form is estimated:
[y.sub.i] = [X.sub.i] [beta] + [[member of].sub.i], (3)
where the subscript i denotes the ith university; y represents
output; X is a vector of inputs; [beta] is the unknown parameter vector;
and [member of] is an error term with two components, [[member
of].sub.i] = [V.sub.i] - [U.sub.i], where [U.sub.i] represents a
non-negative error term to account for technical inefficiency, or
failure to produce maximal output, given the set of inputs used and Vi
is a symmetric error term that accounts for random effects. The standard
assumption (see Aigner, Lovell, and Schmidt 1977) is that the [U.sub.i]
and [V.sub.i] have the following distributions:
[U.sub.i] ~ i.i.d. [N.sup.+] (0, [[sigma].sup.2.sub.u]), [V.sub.i]
~ i.i.d. N (0, [[sigma].sup.2.sub.v]) [U.sub.i] [greater than or equal
to] 0.
The inefficiency term ([U.sub.i]) is assumed to have a half-normal
distribution--establishments are either "on the frontier" or
below it. An important parameter in this model is [gamma] =
[[sigma].sup.2.sub.u]/([[sigma].sup.2.sub.v] + [[sigma].sup.2.sub.u]),
the ratio of the standard error of technical inefficiency to the
standard error of statistical noise, which is bounded between 0 and 1.
Note that [gamma] = 0 under the null hypothesis of an absence of
inefficiency, signifying that all of the variance can be attributed to
statistical noise.
In recent years, SFA models have been developed that allow the
technical inefficiency term to be expressed as a function of a vector of
environmental or organizational variables. This is consistent with our
argument that deviations from the frontier (which measure relative
inefficiency) are related to environmental and organizational factors.
Following Reifschneider and Stevenson (1991), we assume that the
[U.sub.i] are independently distributed as truncations at zero of the
N([m.sub.i], [[sigma].sup.2.sub.u]) distribution with
[m.sub.i] = [Z.sub.i][delta], (4)
where Z is a vector of environmental, institutional, and
organizational variables that are hypothesized to influence efficiency
and [delta] is a parameter vector. (5)
To implement this model, we estimate the following Cobb-Douglas
production function:
log([Q.sub.it]) = [[beta].sub.0] + [[beta].sub.1] log([K.sub.it]) +
[[beta].sub.2] log([L.sub.it]) + [[beta].sub.3] log([M.sub.it]) +
[[upsilon].sub.it] - [U.sub.it] (5)
where
Q = output of firm i in year t.
K = capital stock
L = labor
M = materials
[[upsilon].sub.it] = a standard, "white-noise" error term
[U.sub.it] = inefficiency of firm i at time t, assumed to follow
the truncated normal distribution.
As explained above, the SFA technique allows us to simultaneously
estimate the production frontier and the determinants of relative
efficiency of establishment. We conjecture that the technical
inefficiency ([U.sub.it]) term in Equation 13 can be expressed as
follows:
[U.sub.it] = [[delta].sub.0] + [summation over k]
[[delta].sub.k][TECH.sub.i] + [[delta].sub.S] log([S.sub.it]) +
[[mu].sub.i], (6)
where TECH refers to a vector of technology indicators and S is
market share.
There is a long-standing theoretical and empirical literature (see
Griliches 1979, 1994; Lichtenberg and Siegel 1991) linking proxies for
investment in technology (TECH) and productivity. Market share (S) is
included in the regression to avoid bias in factor estimates from
heterogeneous pricing across firms due, for example, to market power
(see Carstensen 2004). The relative efficiency equation we actually
estimate is as follows:
[U.sub.i] = [[delta].sub.0] [[delta].sub.1] [COMP.sub.i] +
[[delta].sub.2][TELEPHONE.sub.i] + [[delta].sub.3][INTERNET.sub.i] +
[[delta].sub.S]log([S.sub.it] + [[mu].sub.i] (7)
where COMP and TELEPHONE are the ratios of expenditures on
computers and telephony, respectively, as a proportion of total
turnover; INTERNET is a dummy variable that is equal to 1 if the firm
operates via the Internet and equals 0 otherwise; and time subscripts
have been suppressed for simplicity. Note that information on Internet
operations is available only since 2000. Thus, we estimate the model
separately with and without that variable. Regional and year dummies are
also included as potential determinants of inefficiency.
We estimate two panel-data based variants of the production
function model. The first variant is a time-varying decay production
function, which allows us to formally test whether there are efficiency
changes over time. The second variant involves simultaneous estimation
of the production function and the determinants of relative efficiency
using a one-stage maximum likelihood procedure.
6. Empirical Results
Descriptive Data and Trends from the ABI
In Table 4, we present data on the number of enterprises, turnover,
employment, gross value added, and net capital expenditure from the ABI,
as published by the ONS, for the years 1996-2003. A full description of
these variables and summary statistics is provided in the Appendix. For
comparative purposes, we also report data for all firms in Section O
("Other community, social and personal service activities") of
the SIC, for all firms in Division 92 (Recreational Cultural and
Sporting Activities) and for firms within class 92.71 ("Gambling
and betting activities"). Several stylized facts emerge from this
table. Firstly, the number of gambling enterprises has decreased by 21%
since 1996, whilst employment (from 1998), turnover, and value added
have all increased significantly.
The pattern of data before and after the change to betting taxation
in 2001 is also of interest. Comparing the years immediately before and
after the change (2000 and 2002), turnover increased by 38.3% and GVA by
74.8%. In the following year, turnover increased even more, whilst GVA
reduced slightly. (6) There are two reasons why turnover responded to
the betting tax change. Firstly, the effective tax rate was lowered
significantly, which might be expected to lead to an increase in the
demand for betting. Although some of the demand may have come from other
gambling sectors, there is clear evidence (Paton, Siegel, and Vaughan
Williams 2002) that the tax decrease led to an expansion in total
gambling. Secondly, many businesses decided to repatriate phone and
Internet business to the United Kingdom from offshore locations in
response to the tax decrease. There are, however, two particularly
striking features of the increase in gambling activity.
The first is that between 2000 and 2003, GVA increased less than
turnover. This is consistent with a view that the shift to gross profits
tax enhanced competition in betting and reduced margins (Paton, Siegel,
and Vaughan Williams 2002). (7)
The second striking feature of the increase in turnover and GVA is
that employment increased by just 2.3% between 2000 and 2002. Thus, the
substantial expansion of gambling investment and activity appears to
have been undertaken without any increase in employment. Obviously there
are employment considerations that may be of interest, but, for the
purposes of this report, this is prima facie evidence of a large
increase in gambling productivity between 2000 and 2003.
Note also that capital expenditure declined from 236 mil [pounds
sterling] to 185 mil [pounds sterling] between 1999 and 2000, before
rising to 383 rail [pounds sterling] in 2002 (an increase of 84% on the
1996 figure) and 315 mil [pounds sterling] in 2003. Thus, there is some
evidence that uncertainty regarding the regulatory and tax environment
prior to 2001 severely limited investment in the gambling sector.
However, after the more-favorable tax regime was announced in early
2001, investment began to accelerate.
We now report findings from our analysis of the establishment-level
data relating to estimates of productivity and the determinants of
relative productivity.
Labor Productivity Estimates 1997-2003
In this section, we present the labor productivity estimates for
1997 to 2003 using the different productivity measures as described in
section 4, weighted for non-selected firms.
The estimates using both gross output measures (GO1 and GO2) and
gross value added (GVA) are summarized in Table 5. The top panel
contains results for total employment, whilst the bottom panel presents
findings based on full-time equivalent (FTE) employment. The general
pattern is similar for most measures. Labor productivity increases up to
1999, then decreases sharply through 2001, followed by a recovery in
2002 and 2003. The post-2001 increase is most dramatic for GO1 for which
the 2002 and 2003 figures are significantly higher than for any previous
year. The estimates using GO2 and GVA show similar trends, but in each
case labor productivity in 2002 is estimated to be below the 1997 value.
There are no significant differences between the trends for total and
FTE employment.
Of course, these results relate only to labor productivity. We have
argued above that investment in technology has been of particular
importance in this industry. It may be that ignoring changes in capital
inputs will lead to incorrect inferences regarding productivity trends
in gambling. Thus, in the next section we present the more formal SFA
analysis of productivity and determinants.
Stochastic Frontier Analysis of Productivity
Productivity Changes over Time
As a first cut, we estimate Cobb-Douglas production functions for
GO and GVA. The basic models are reported in the first three columns of
Table 6. There are some notable differences between the results based on
GO1, GO2, and GVA. For example, the Coelli (1995) test provides strong
evidence of the presence of an inefficiency term for GO2 and GVA but not
for GO. Note also that for GO, the coefficient on labor (an estimate of
the output elasticity of labor, given our log-linear specification) is
0.293 (standard error 0.023), the coefficient on capital is 0.669
(0.019), while that for materials is 0.056 (0.017). For these values, we
cannot reject the null hypothesis of constant returns to scale. For GO2,
the coefficient on labor is higher at 0.370 (0.028), while that for
capital is much smaller at 0.360 (0.023). For GVA, the coefficient on
labor is even higher and that for capital even lower. In the case of
GO2, there is evidence of decreasing returns to scale. Thus, it is clear
that, as expected, the choice of output measure is important in this
context.
We retrieve the efficiency scores and summarise these year-by-year
in Table 7 and by employment group in Table 8. There is no discernable
trend in the scores using GO2 and GVA. However, GO1 efficiency appears
to have increased considerably both between 1998 and 2003 and between
2000 (immediately prior to the tax change) and 2003. The results in
Table 8 suggest some evidence that the very small firms (below 20) are
less efficient than the largest firms when using GO1 to measure output.
There does not appear to be a monotonic relationship between size and
efficiency. Further, even this relationship is not observed when using
GO2 or GVA.
We provide several formal tests of the hypothesis of changing
productivity following the 2001 tax change. First, we estimate the
time-varying decay model. These results are reported in the last three
columns of Table 6. Note that the coefficient on the decay parameter is
positive for all three output measures, although significant only for
GVA. The interpretation of a positive coefficient is that the
inefficiency component is decreasing over time. In other words, we find
some evidence that efficiency has increased over time, but only
significantly so when measured by GVA.
Secondly, we conduct Chow tests for each model, splitting the
sample into pre- and post-tax change periods. The results of the Chow
tests indicate that a structural break occurred after 2001. For example,
for GO1, the chi-square test statistic with four degrees of freedom is
59.46. For GO2, the chi-square statistic is 36.75 and for GVA, it is
23.31. In each case, the p-values are zero.
Another aspect of interest is to compare how gambling firms have
performed relative to all firms within SIC 92, "Recreational,
Cultural and Sporting Activities". Consequently, we re-estimate our
model for the whole of this category. We retrieve the efficiency scores
from this model for all firms and for gambling firms. The scores using
GO2 and GVA are reported in Table 9 and, in both cases, gambling
productivity appears to increase faster than in the rest of the
recreation sector. Note that for non-gambling firms, GO2 and GO1 are
equivalent.
Explanations of Varying Productivity
We have observed that there was a significant increase in the
productivity of gambling after 2001. Productivity differentials across
firms are also of interest. In this regard, we consider the results of
including three factors on expected efficiency levels: regional effects,
intensity of expenditure on computer equipment, and intensity of
expenditure on telecommunications. Our expectations are that there will
be significant regional differences in efficiency and the computers and
telecommunications expenditure will be positively associated with
efficiency. The results are reported in Table 10. Note that a
significantly positive coefficient in the inefficiency equation means
that variable is associated with greater inefficiency (lower
efficiency).
The first point of interest is that the dummy variable for the
post-tax years is always negative and sometimes significant. This
provides additional evidence of an increase in efficiency after the 2001
tax changes.
We find only modest variation in regional efficiency, while the
results on technology are mixed. The ratio of spending on computing is
associated with higher relative efficiency, although this result is not
statistically significant. The ratio of spending on telecommunications
is found to be to be associated with significantly greater inefficiency
for GO1 and greater efficiency for GO2 and GVA. In the second half of
Table 10, we report the results using the indicator variable for whether
or not the firm receives orders on the Internet. This may be
particularly important in this industry, where virtually all activity of
some firms is carried out online. Note that information on this variable
is only available from 1999 and so the sample size is considerably
reduced. We find that Internet operations are associated with lower
inefficiency (more efficiency) for all three output measures,
significantly so for GO2 and GVA.
To summarize, our evidence suggests that productivity in gambling
increased following the 2001 tax change. We find little evidence of
significant regional productivity differences among firms, while we find
consistent evidence that gambling establishments operating online are
closer to the frontier (that is, more efficient) than comparable
establishments.
We conducted several robustness checks of our key results,
including using different error specifications for the SFA results,
using a translog functional form, and using fixed and random effects
panel data estimators. To conserve space, we do not report the results
of these experiments here. In general, they indicate that our main
findings are quite robust. Full details are available from the authors
on request.
7. Preliminary Conclusions and Caveats
Our empirical analysis is based on plant-level data on the number
of enterprises, turnover, employment, gross value added, and net capital
expenditure from the Annual Business Inquiry for the years 1996-2003. We
find that the number of enterprises decreased by 21% since 1996 while
employment (from 1998), turnover, and value added all increased
significantly. Comparing the years immediately before and after the tax
change (2000 and 2002), turnover increased by 38.3% and GVA increased by
74.8%.
Significantly, despite the increase in turnover and GVA, employment
increased by just 2.26% during the period 2000-2003. Thus, the huge
expansion of gambling investment and activity appears to have been
undertaken without any increase in employment. Moreover, the "Total
Net Capital Expenditure" series declines from 236 to 185 between
1999 and 2000, before rising to 383 in 2002, an increase of 84% on the
1996 figure, and decreasing to 315 in 2003. Thus, there is some evidence
that uncertainty over the regulatory and tax situation prior to 2001
severely limited investment in the gambling sector. However, after the
more-favorable tax regime was announced in early 2001, investment
started to accelerate.
Next we estimated Cobb-Douglas production functions using two
measures of gross output (GO1 and GO2) and gross value added (GVA). We
provide formal tests of the hypothesis of changing productivity after
the 2001 tax change by estimating the time-varying decay model and by
conducting Chow tests of structural stability. We find consistent
evidence that gambling productivity increased following the 2001 tax
change.
We then assessed the effects of three factors on expected
efficiency levels: regional effects, intensity of expenditure on
computer equipment, and intensity of expenditure on telecommunications.
We find only limited evidence of regional variations in efficiency.
However, we find consistent evidence that internet operations are
associated with lower inefficiency (greater efficiency). These findings
are consistent with a large body of empirical evidence in manufacturing
industries indicating that computers enhance productivity. (8)
A key caveat must be noted. In the current version of the article,
we have eschewed consideration of the possible endogeneity of factor
inputs. It is now common in production function literature for authors
to employ some form of instrumental variables (for example, generalized
method of moments) or the Olley-Pakes (1996) and Levinsohn and Petrin
(2003) semi-parametric methods, due to the well-known concern regarding
simultaneity. Olley and Pakes (1996) note that unobserved productivity
shocks can result in correlation between factor inputs and the error
term, which can be controlled for by using investment as a proxy for
these shocks. Levinsohn and Petrin (2003) propose an alternative
estimator based on intermediate inputs as the proxy, which they assert
does a superior job of addressing this simultaneity problem.
Thus, the simple approach used in this version of the article could
have generated inconsistent estimates of the production function
parameters. In future research, we will implement the Olley-Pakes (1996)
and Levinsohn and Petrin (2003) estimators and include additional
robustness checks suggested by Van Biesesbroeck (2007).
Appendix: Variable Description and Summary Statistics
Mean
(000
[pounds Standard
Variable Description sterling]) Deviation
Gross Output log(turnover + change in 8.529 2.525
(GO1) work in progress + change
in stocks brought for
resale + work of a
capital nature by own
staff)
Gross Output log(turnover - payouts to -- --
(G02) winning customers +
change in work in
progress + change in
stocks brought for resale
+ work of a capital
nature by own staff)
Gross Value log(turnover + change in 7.513 2.325
Added (GVA) work in progress at start
and end of year
- purchases)
Capital Log(capital stock) 8.658 2.742
Labor Log(total number of 4.221 2.099
employees)
Labor1 Log(total number of 3.969 2.110
employees - half number
of part-time employees)
Share log(firm IBRD -2.406 1.974
employment/total industry
IBRD employment)
Computer ratio Ratio of computer & 0.255 0.558
related service costs to
other costs
Telephone ratio Ratio of computer & 0.821 1.865
related service costs to
other costs
Internet sales = 1 if goods and orders 0.766 0.424
are received via the
Internet.
North Dummy variable = 1 if 0.316 0.465
firm is located in
Yorkshire, North East,
Lancashire, or Cumbria
West Dummy variable = 1 if 0.149 0.356
firm is located in West
Midlands or South West
East Dummy variable = 1 if 0.153 0.360
firm is located in East
Midlands or East Anglia
Scotland/Wales Dummy variable = 1 if 0.174 0.380
firm is located in Wales
or Scotland
London Dummy variable = 1 if 0.209 0.407
firm is located in London
or South East
Summary statistics are calculated using the GVA sample, N = 478.
All variables are deflated to 1996 constant prices using the CPI
for Recreation & Culture, series CHVS, with the exception of
capital stock, which is calculated by ONS and deflated to 1995
prices.
Source: ONS.
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David Paton, * Donald S. Siegel, ([dagger]) and Leighton Vaughan
Williams ([double dagger])
* Professor of Industrial Economics, Nottingham University Business
School, Wollaton Road, Nottingham NG8 1BB, United Kingdom: E-mail
David.Paton@Nottingham.ac.uk.
([dagger]) Dean and Professor, School of Business, University at
Albany, SUNY, 1400 Washington Avenue, Albany, NY 12222, USA; E-mail
DSiegel@uamail.albany.edu.
([double dagger]) Professor of Economics and Finance, Nottingham
Business School, Nottingham Trent University, Burton Street, Nottingham
NG1 4BU, United Kingdom; E-mail Leighton.Vaughan-Williams@ntu.ac.uk.
We thank participants at the Social Sciences and Humanities
Research Council international Conference on Index Number Theory and the
Measurement of Prices and Productivity in June 2004 in Vancouver, the
Royal Economic Society Conference in April 2006 at the University of
Nottingham, the 2006 NBER Summer Institute, the 2008 Conference on
Gambling and Prediction Markets at Nottingham Trent University, and
especially, Amil Petrin and Kam Lu for comments and suggestions on an
earlier draft of this article. This work contains statistical data from
the Office for National Statistics (ONS), which is Crown copyright and
reproduced with the permission of the controller of Her Majesty's
Stationary Office and Queen's Printer for Scotland. The use of the
ONS statistical data in this work does not imply the endorsement of the
ONS in relation to the interpretation or analysis of the statistical
data.
(1) As we will discuss later in this report, deflation is not as
serious a problem when researchers have access to establishment-level
data.
(2) Gullickson and Harper (1987) report that producer prices are
available only for some selected services, such as repair services and
real estate and rental.
(3) Further to our discussion above regarding the treatment of
payouts to winning customers, a further ground for caution arises from
the fact that for some companies, Box 424 (Amounts Paid to Winning
Customers) is left blank. We speculate that this is at least partly due
to betting exchanges that do not formally pay out winnings to customers.
However, there may also be some a small number of firms who
(incorrectly) report net stakes (gross profits) as turnover.
(4) See Charnes et al. (1994).
(5) Battese and Coelli (1995) have recently extended this model to
incorporate panel data.
(6) The reason for focusing on these two years is that the tax
changes took place during the course of 2001. Specifically, the changes
were announced in April 2001 and were introduced in October of that
year.
(7) A complicating factor in understanding this trend is the
growing impact of two segments of the market: betting exchanges and
FOBTs. It is very difficult to draw meaningful comparisons between
betting exchanges or FOBTs and conventional betting using turnover
measures. Indeed, even across different betting exchanges there are
differences in how firms measure turnover sometimes it is the amount
matched (adding up the back and lay sides of the bet), sometimes it is
the amount at risk on the lay side. A consequence of this is that the
turnover series reported by the ONS must be viewed in a different light
to that of bookmakers" turnover in estimating the actual growth of
gambling activity, Like betting exchanges, FOBTs are another example of
the trend towards low-margin, high-turnover betting facilities. These
machines, which offer the opportunity to play virtual casino-type games,
notably roulette, generate profit on the basis of rapid turnover
compared to traditional bookmaker-based betting, but lower margins.
(8) See Indjikian and Siegel (2005) for a comprehensive review of
these empirical studies.
Table 1. U.K. Gambling Stakes by Segment, 1998-2002
1998 2002
([pounds ([pounds % change,
sterling] m) % sterling] m) % 1998-2002
Betting 7109 29 17,502 49 +146.2
Gaming machines 8489 34 8585 24 +1.1
National lottery 5207 21 4640 13 -10.9
Casinos 2669 11 3850 11 +44.2
Bingo 1041 4 1200 3 +15.3
Football pools 264 1 130 0 -50.8
Total 24,779 100 35,907 100 +44.9
Source: HM Customs & Excise/Gaming Board for Great Britain/Mintel
(2003).
Table 2. U.K. Pay-TV Households, by Platform, 1998-2003
1998 (m) 1999 (m) 2000 (m)
Analogue satellite 3.8 1.7 0.4
Digital satellite 0.3 2.5 4.7
Analogue cable 2.9 3.2 2.6
Digital cable -- 0.1 0.8
Terrestrial digital 0.1 0.5 1.0
Other free-to-air -- -- --
Total 7.1 8.0 9.5
% Penetration 29 33 38
2001 (m) 2002 (m) 2003 (a) (m)
Analogue satellite 0.1 -- --
Digital satellite 5.3 6.3 6.4
Analogue cable 2.1 1.3 1.2
Digital cable 1.5 2.1 2.1
Terrestrial digital 1.1 1.7 1.6 (b)
Other free-to-air -- -- 0.7 (c)
Total 10.1 11.4 12.0
% Penetration 40 44 48
Source: Mintel (2003).
(a) As of March 2003.
(b) Freeview subscribers.
(c) The estimated number of Sky digital viewers that watch
freeview channels only and do not pay for packages.
Table 3. IBRD Data for Gambling Firms
1997 1998 1999 2000
Non-selected
Enterprises 1861 1860 1818 1681
Mean Employment 24.98 20.46 23.13 16.29
100+ 48 31 35 30
50-99 69 46 60 61
20-49 186 173 162 142
10-19 320 292 284 263
<10 1238 1318 1277 1185
Selected
Enterprises 96 113 94 105
Mean Employment 318.85 346.96 384.27 479.12
250+ 20 20 18 23
100-249 15 22 20 17
50-99 <10 19 12 14
20-49 15 18 15 16
10-19 <10 17 12 14
<10 29 17 17 21
2001 2002 2003
Non-selected
Enterprises 1592 1542 1500
Mean Employment 13.22 11.56 13.4
100+ 31 16 36
50-99 51 52 38
20-49 138 126 128
10-19 232 231 197
<10 1137 1117 1101
Selected
Enterprises 123 120 112
Mean Employment 531.4 546.9 582.7
250+ 24 25 21
100-249 20 20 13
50-99 21 16 18
20-49 24 26 23
10-19 11 13 15
<10 23 20 22
Source: ONS.
Table 4. Summary Data from ABI for Other Services, Recreation,
and Gambling
Total GVA
Turnover Basic
([pounds Prices
Number of sterling] ([pounds
SIC Description Year Enterprises Million) sterling] m)
O Other 1996 148,924 52,511 21,721
community, 1997 145,797 58,751 24,270
social, and 1998 168,046 65,284 25,991
personal 1999 170,495 72,057 30,238
service 2000 170,562 77,891 31,947
activities 2001 172,761 84,078 34,751
2002 173,589 91,240 36,336
2003 172,158 102,131 36,955
92 Recreational, 1996 62,450 35,313 12,184
cultural, 1997 63,674 40,542 13,656
and 1998 65,261 41,353 13,494
sporting 1999 68,009 45,383 16,031
activities 2000 69,378 50,930 18,331
2001 70,736 54,306 19,382
2002 71,549 61,619 20,866
2003 71,383 71,408 21,133
92.71 Gambling 1996 2240 11,849 1462
and betting 1997 2061 13,229 1907
activities 1998 2076 13,938 1834
1999 2009 14,831 2329
2000 1878 16,503 2620
2001 1814 16,805 2385
2002 1719 21,572 3081
2003 1770 28,290 2787
Total Net
Total Capital
Employee Spend
Total Costs ([pounds
Employees ([pounds sterling]
SIC Description Year ('000) sterling] m) Million)
O Other 1996 -- 7874 4089
community, 1997 -- 9381 5767
social, and 1998 1132 13,085 5774
personal 1999 1212 15,042 6642
service 2000 1271 16,580 6163
activities 2001 1323 17,393 6218
2002 1351 19,763 6158
2003 1347 20,711 6217
92 Recreational, 1996 -- 4866 1650
cultural, 1997 -- 6198 2555
and 1998 524 6714 2253
sporting 1999 581 7925 2621
activities 2000 638 9098 2688
2001 638 9543 2763
2002 672 11,087 2696
2003 682 11,673 2520
92.71 Gambling 1996 -- 708 208
and betting 1997 -- 708 262
activities 1998 76 760 202
1999 77 751 236
2000 88 1111 185
2001 90 1069 318
2002 90 1178 383
2003 90 1257 315
Source: ONS.
Table 5. Weighted Mean Labor Productivity in Gambling, 1997-2003
1997 1998 1999 2000
Total Employment
GO1 216.09 227.60 256.75 206.59
GO2 95.61 101.87 113.32 83.96
GVA 75.09 83.46 94.94 69.00
FTE Employment
GO1 255.93 254.95 296.49 245.37
GO2 111.21 114.79 129.29 96.77
GVA 85.81 93.11 108.58 78.61
2001 2002 2003
Total Employment
GO1 196.56 262.18 315.21
GO2 75.12 99.86 89.29
GVA 61.23 67.69 60.42
FTE Employment
GO1 228.24 318.61 391.34
GO2 85.22 116.79 106.62
GVA 69.57 79.06 70.66
Source: Derived by the authors from ONS data.
Table 6. SFA Gambling Production Functions, 1998-2003
Dependent Variable
GO1 GO2
Coefficient on:
Labor 0.293 *** (0.023) 0.370 *** (0.028)
Capital 0.669 *** (0.019) 0.360 *** (0.023)
Materials 0.056 *** (0.017) 0.218 *** (0.021)
Constant 1.583 *** (0.091) 2.291 *** (0.229)
Time decay (a) -- --
N 587 580
Log likelihood -533.87 -623.65
Wald [chi square] 11,126.9 *** 5506.62 ***
Inefficiency (b) -0.701 4.129 ***
CRS test (c) 2.25 12.31 ***
Dependent Variable
GVA GO1
Coefficient on:
Labor 0.604 *** (0.030) 0.291 *** (0.027)
Capital 0.378 *** (0.023) 0.638 *** (0.022)
Materials -- 0.098 *** (0.016)
Constant 1.702 *** (0.299) 42.07 (27.29)
Time decay (a) -- 0.0022
(0.0014)
N 677 587
Log likelihood -873.96 -492.86
Wald [chi square] 4393.6 *** 5672.3 ***
Inefficiency (b) 3.752 *** --
CRS test (c) 1.18 2.85 *
GO2 GVA
Coefficient on:
Labor 0.354 *** (0.032) 0.560 *** (0.035)
Capital 0.362 *** (0.025) 0.382 *** (0.027)
Materials 0.223 *** (0.018) --
Constant 8.516 (19.26) 6.719 *** (0.909)
Time decay (a) 0.0137 0.015 ***
(0.040) (0.004)
N 580 677
Log likelihood -558.96 -716.86
Wald [chi square] 2990.8 *** 1799.5 ***
Inefficiency (b) -- --
CRS test (c) 9.61 *** 6.04 **
All production function variables are specified in logs.
*** indicates significance at the 1% level; ** at the 5% level;
* at the 10% level.
(a) "Time Decay" is an estimate of how the degree of inefficiency
is changing over time. When Time Decay > 0, this indicates that
inefficiency is decreasing over time.
(b) The inefficiency term is assumed to follow a truncated normal
distribution. "Inefficiency" indicates test statistics for the
presence of an inefficiency term using the Coelli (1995) one-sided
test.
(c) CRS test" indicates a two-sided test of the null of
constant returns to scale.
Table 7. Mean SFA Efficiency Scores, 1997-2002
GO1 GO2 GVA
1998 0.364 0.335 0.578
1999 0.350 0.335 0.577
2000 0.316 0.335 0.577
2001 0.299 0.335 0.576
2002 0.289 0.334 0.576
2003 0.267 0.334 0.576
The figures are minus the natural log of technical efficiency;
that is, larger scores indicate greater inefficiency. Figures
for GO2 and GVA have been multiplied by 1000 for ease of
presentation.
Table 8. Mean SFA Efficiency Scores by Employment Group
Employees GO1 G02 GVA
250+ 0.282 0.334 0.576
100-249 0.328 0.335 0.577
50-99 0.303 0.335 0.577
20-49 0.317 0.335 0.577
10-19 0.356 0.335 0.577
<10 0.303 0.334 0.577
The figures are minus the natural log of technical efficiency;
that is, larger scores indicate greater inefficiency.
Table 9. Mean SFA Efficiency Scores: All Recreation and Gambling,
1997-2002
GO2 GVA
All Recreation Gambling All Recreation Gambling
1998 0.728 0.912 0.725 0.718
1999 0.708 0.807 0.706 0.612
2000 0.693 0.791 0.699 0.580
2001 0.677 0.756 0.653 0.567
2002 0.640 0.662 0.625 0.552
2003 0.603 0.653 0.582 0.494
The figures are minus the natural log of technical efficiency; that
is, larger scores indicate greater inefficiency. "All Rec" refers
to all firms within SIC 92, "Recreational, Cultural, & Sporting
Activities."
Table 10. SFA Conditional Mean Production Functions, 1998-2002
Dependent Variable
GO1 GO2
Coefficient on:
Labor 0.288 *** (0.024) 0.377 *** (0.028)
Capital 0.651 *** (0.020) 0.389 *** (0.024)
Materials 0.070 *** (0.017) 0.197 *** (0.021)
Constant 2.260 (44.40) 2.330 *** (0.113)
Inefficiency Equation
Computer ratio -0.0019 (0.007) -0.031 (0.030)
Telephone ratio 0.047 *** (90.013) -0.093 *** (0.036)
Internet sales -- --
North 0.109 (0.070) 0.144 * (0.088)
West 0.093 (0.089) 0.019 (0.122)
East -0.055 (0.085) -0.182 (0.111)
Scotland/Wales 0.104 (0.078) 0.041 (0.100)
Post-tax change -0.368 *** (0.059) -0.125 (0.080)
Constant 0.862 (44.40) 0.455 *** (0.108)
N 587 580
Log likelihood -517.75 -596.31
Wald [chi square] 8643.8 *** 4744.2 ***
Dependent Variable
GVA GO1
Coefficient on:
Labor 0.596 *** (0.030) 0.332 *** (0.029)
Capital 0.412 *** (0.023) 0.619 *** (09.024)
Materials -- 0.073 *** (0.021)
Constant 1.663 *** (0.133) 2.049 (61.05)
Inefficiency Equation
Computer ratio -0.039 (0.038) --
Telephone ratio -0.057 * (0.030) --
Internet sales -- -0.027 (0.073)
North 0.154 (0.098) 0.182 ** (0.091)
West 0.068 (0.128) 0.188 * (0.112)
East -0.222 * (0.128) -0.021 (0.108)
Scotland/Wales 0.008 (0.118) 0.200 ** (0.097)
Post-tax change -0.148 (0.103) -0.149 ** (0.062)
Constant 0.443 *** (0.122) 0.473 (61.05)
N 673 413
Log likelihood -831.53 -378.32
Wald [chi square] 3939.2 *** 6187.8 ***
GO2 GVA
Coefficient on:
Labor 0.386 *** (0.032) 0.619 *** (0.038)
Capital 0.349 *** (0.026) 0.341 *** (0.028)
Materials 0.206 *** (0.023) --
Constant 2.668 *** (0.166) 2.355 *** (0.225)
Inefficiency Equation
Computer ratio -- --
Telephone ratio
Internet sales -0.147 * (0.089) -0.279 *** (0.100)
North 0.009 (0.101) 0.168 (0.127)
West -0.171 (0.163) 0.261 * (0.154)
East -0.499 * (0.264) -0.173 (0.172)
Scotland/Wales 0.020 (0.107) 0.275 ** (0.134)
Post-tax change -0.327 *** (0.083) -0.186 ** (0.087)
Constant 0.533 *** (0.159) 0.493 ** (0.220)
N 408 412
Log likelihood -412.11 -506.9
Wald [chi square] 3785.0 *** 2466.6 ***
All production function variables are specified in logs. Regional
dummies are specified using London as the reference area. Year
dummies are specified using 1997 as the reference year. When
Internet is included as an explanatory variable, 2002 is the
reference year. In these specifications, the inefficiency term
is modelled as a linear function of variables. A significantly
negative coefficient implies that variable is associated with an
increase in inefficiency. *** indicates significance at the 1%
level; ** at the 5% level; * at the 10% level.
