Is There A Piracy Kuznets Curve?
Gilles Grolleau1
Sana El Harbi (lecturer )2
and Insaf Bekir3
Abstract : We investigate empirically the relationship between software piracy
and GDP per capita and show that piracy follows a Kuznets-like curve.
Concretely, piracy first increases with the level of GDP per capita, reaches a
maximum and then decreases at higher levels of income. Making people richer
can be the best way to decrease piracy at the long term horizon. Intellectual
property rights holders should not aim the decrease of piracy per se but the
decrease of piracy in circumstances where it is the most likely to be substituted
by legal sales.
Keywords: Income; Panel data analysis; Piracy.
JEL: O34; O38
1
LAMETA, UMR1135 SupAgro Montpellier.E-mail : [email protected]
2
University of Sousse, Sousse, Tunisia E-mail : [email protected]
3
University de Sousse, Sousse, Tunisia E-mail : [email protected]
1
Is There A Piracy Kuznets Curve?
1. Introduction
Softwares are frequently perceived as unaffordable for most people in
developing countries and even for subgroups of the whole population in
developed countries. For example, ‘the retail price Microsoft charges for
signature products such as Windows and Office — as much as $669, depending
on the version — can rival the average annual household income in some
developing countries’ (Piller, 2006). In these countries, people frequently
consider that the only remaining option is piracy. Interestingly, Piller (2006)
also argues that piracy when income per capita is low can be strategically used
by software companies to create an ‘addiction effect’ by locking-in people on
certain products and collect revenues later when the income level will be
sufficiently high 4 . In sum, they expect to transform today’s pirates in
tomorrow’s payers. Several developing countries exhibit a ‘Robin Hood’
mentality, by being reluctant to enforce anti-piracy laws that will harm poor
people to make rich software creators richer. If this rationale is true, one can
expect that an increase in income can lead to lower levels of piracy. In other
terms, does income increase lead to piracy decrease?
Most extant economic studies on the relationship between income and piracy
have examined the causes of piracy (Ginarte & Park, 1997; Andrés, 2006;
Marron and Steel, 2000; Depken & Simmons, 2004; Papadopoulos, 2003) or
focused on the impact of the strength of IPR on the economic growth (Gould
and Gruben, 1996; Rushing and Thompson, 1999). In general, the findings of
4
It is arguable that software companies can price discriminate to eliminate piracy in developing countries. That
would create the same or similar lock in effect but still earn positive revenues along the way. A possible and
plausible answer is the fear of grey market arbitrage (reimportation into rich countries).
2
these papers support the existence of a negative relationship between income
and piracy. Nonetheless, the formal literature on the relationship between
income and piracy is scant because only few studies deal with the potential
existence of a non-linear relationship between income level and piracy (Maskus
and Penubarti 1995; Kim, 2004). Moreover, because piracy is a function of
income, yet income is itself likely to be a function of piracy, these studies are
subject to potential endogeneity problems. Besides, not only do these studies
diverge significantly in terms of the number of countries included, the period of
analysis, the explanatory variables included, but also they rely mainly on crosssectional estimation methods.
The purpose of this paper is to add empirical evidence regarding the relationship
between software piracy and income per capita. Using panel data analysis on
software piracy on a large number of countries for the period from 1996 to 2007,
we test whether the relationship between piracy and GDP per capita follows a
Kuznets-like curve, which implies that piracy first increases with an income
increase, reaches a maximum and then decreases when income still increases.
The contribution of this study is at least fourfold. First, the paper shed light on
the possible theoretical arguments of why piracy is likely to follow a Kuznetslike curve. Second, we test empirically whether the relationship between piracy
and GDP per capita follows a Kuznets-like curve, with piracy first increasing
then later declining as the level of per capita income increases. Third, the study
explicitly addresses the potential endogeneity problem in the relationship
between piracy and per capita income by using an instrumental variables
approach. Finally, the empirical analysis uses panel data method rather than
cross-section one on a larger set of countries
3
In the next section, we present the theoretical arguments explaining why piracy
is likely to follow a Kuznets-like curve. In section 3 we present the econometric
model and the data used in the empirical analysis. Empirical findings are
presented in section 4. We conclude with some policy implications in section 5.
2. Piracy Kuznets’s curve: Theoretical consideration and Hypothesis
We describe in this section some mechanisms that can explain why piracy is
likely to follow a Kuznets-like curve.
The first phase of a Kuznets-like curve involves that when income increases the
piracy increases too. First, income increases are more likely to be used to satisfy
(more) basic needs in accordance with the Maslow’s hierarchy-of-needs theory.
Moreover, a higher income is more likely to be used to acquire material goods
that are less subject to piracy such as computers, printers, scanners and so forth.
Moreover, these successive income increases can remain insufficient in
comparison to the level required to purchase original softwares. At the same
time, software become more and more desirable and useful because developing
country consumers become better educated and are increasingly exposed to
western lifestyles, resulting in a higher demand for software products, regardless
of their legal prices.
Another argument regarding this ‘piracy increase’ stage can be formulated in a
cost-benefit analysis. People do not pirate because they are moral incompetents,
but they pirate because the perceived benefits of piracy exceed the perceived
costs. In sum, people pirate because it is the strategy from which they expect the
highest net returns compared to legal purchases. This strategy at the individual
level can be supported by developing countries governments and even by firms
that design original softwares. Developing countries governments can exhibit a
Robin Hood mentality seeking to steal from the rich (software designers mainly
located in western countries) to help their own poor. Consequently they are
4
reluctant to enforce intellectual property rights in a way that will ‘harm’ their
citizens (e.g., loss of jobs related to piracy activities, reduced access to
technology necessary for development, loss of subjective well-being because
restricted access to certain goods, opportunity cost of resources incurred to fight
piracy) to make foreign creators richer (Kopczynski, 2009; see also Marron and
Steel, 2000). Moreover, piracy can generate a ‘learning by pirating effect’ and
help a country to acquire useful skills. Recently, during a joint conference with
Bill Gates, the Romanian President Basescu stated that pirated Microsoft Corp
software helped Romania to build a vibrant technology industry. "It helped
Romanians improve their creative capacity in the IT industry, which has become
famous around the world ... Ten years ago, it was an investment in Romania's
friendship with Microsoft and with Bill Gates." (Reuters, 2007). Original firms
can also benefit from piracy by (i) generating a competitor enter barrier effect
products and (ii) creating an addiction effect, making software users locked-in
and dependant on their products. Once these consumers enjoy sufficient income,
these firms can lobby to get better enforcement of their intellectual property
rights and charge these richer consumers, transforming yesterday pirates in
today payers. According to Piller (2006), this strategy has been used by
Microsoft in China, especially to prevent Linux diffusion.
Now, let us discuss the second part of the piracy Kuznets curve. Without
purporting to be exhaustive, several rationales could explain the fact that piracy
decreases when GDP per capita increases, beyond a given level. The most
intuitive argument is that richer people can afford original softwares. Consumers
can also be interested in acquiring related products and services tied to original
versions, increasing the perceived benefits of original products. Moreover,
governments and firms’ policies regarding the enforcement of intellectual
property rights can change the cost-benefit analysis of pirates, making the
purchase of original products the most profitable option. Governments can
5
decide to better enforce intellectual property rights because the collective
benefits (e.g., development of domestic creative sectors, tax collected, attracting
foreign direct investments, employment) overcome the costs, which was not the
case before. For example, if the developing country has now a skilled domestic
industry that innovates and seeks protection against piracy, the government can
invest more in effective enforcement of intellectual property rights with spillover benefits for domestic and foreign creators. Once consumers are locked-in
and can pay, intellectual property rights holders can lobby to convert pirates into
payers (Piller, 2006). Another explanation for the decrease in piracy as GDP
increases can be expressed as follows. If we assume a monetary fine for detected
piracy, an indigent person is undeterred but rich people and firms will rationally
substitute toward legal purchases. As a complementary explanation, if GDP rises,
then tax revenues increase and the government has more resources to enforce
intellectual property laws. So enforcement increases as users' sensitivity to
financial penalties increases as well. Last but not least, pirated software is not an
exact substitute for legitimate software in that the latter receives constant
updates and support (Leibowitz, 2005). Budget constraints can explain why
wealthier consumers are willing to pay more to acquire those additional features.
Based on the previous arguments, we would expect an inverted U-shaped
relationship between per capita income and piracy rate.
3. Model and Estimation method
3.1 Dependent and independent variables
To test the existence of piracy Kuznets curve, we specify a regression equation
using piracy rate as the dependent variable.
As regards the independent variables, as hypothesized in section 2, income per
capita constitute the main variable of interest in our understanding of the
expected inverted U-shaped relationship between per capita income and piracy
rate. For this purpose, we consider the natural log of per capita GDP (LGDP)
6
and its squared term (LGDP²) on the expectation that the coefficient in income
term will be positive, while its quadratic term will be negative.
To test the robustness of our model and to shed greater light on the determinants
of piracy, we introduce other explanatory variables.
Because trade in a country constitutes an important factor explaining the IPR
violation variation (Gould and Gruben, 1996), the share of high technology
exports in total exports is introduced as a control variable to capture the
technology level in an open country. Previous studies advance that the higher
the level of technology, the more likely unauthorized production and distribution
of copyright based materials will take place since the skills and related
technologies will be available (Marulidharan and Phatak, 1999; Ostergard,
2000). Hence we expect a positive relationship between the share of high
technology exports in total exports and piracy rate
The importance of institutional aspects in explaining the variation of piracy has
been well recognized in the literature. To this effect, we include two different
measures to capture some of the potentially significant institutional influences
on software piracy variation. We use the trade-freedom as a proxy for the level
of economic freedom. The effect of economic freedom is found to be ambiguous
(Banerjee et al, 2005, Bezmen and Depken, 2006; goel and Nelson, 2009) On
one hand more economic freedom may lead to lower piracy rate due to lower
prices of legal software from improved competition making illegal software less
attractive. On the other hand, improved market competition might lead to greater
piracy due to the relative simplicity of obtaining business permits by potential
pirates. Moreover, greater economic freedom may imply less government
participation in the economy and this may result in less resources being
allocated to the deterrence of piracy (Goel and Nelson 2009). Given that more
than one influence is at work with respect to this variable, the overall effect
depends upon the relative strength of different influences. Although the effect of
7
economic freedom is ambiguous, we expect that an increase in the trade freedom
will lead to a decrease in the piracy rate.
More corruption in the customs authority, police and judiciary will result in a
lower probability of detection as pirates can bribe to avoid punishment.
Alternately, there is likely to be less social shame attached to unlawful actions in
nations where corruption is culturally embedded. This leads to an increase in
pirates expected profit and thereby to an increase in the level of piracy rate.
Furthermore, already corrupt individuals (bribe takers and bribe givers) are more
likely to produce and purchase counterfeit software. To capture these influences
we include an index of corruption. For all these reasons, we expect a positive
correlation between corruption and software piracy. Indeed, previous empirical
research (Ronkainen and Guerrero-Cusumano, 2001; Papadopoulos, 2003)
corroborates the positive relationship between corruption and piracy.
Legal system and regulations in domain of IPRs protection may equally impact
the occurrence of software piracy. The strength and efficacy of legal institutions
could affect both the buyers and the sellers of pirated software. Since countries
have obligations derived from the extensive restructuring of the international
arrangements for the treatment of IPRs, transnational factors are, also, identified
to be important determinants of intellectual property protection. Countries that
signed unilateral, bilateral and multilateral treaties or conventions for IPRs
protection and have membership in international organizations for intellectual
property rights protection tends to have lower software piracy rate. We therefore
expect that membership to an international copyright convention will result in
lower Piracy rate.
3.2 model specification
Let us assume that the main motive of piracy is a lack of resources leaving
people, (especially in developing countries where the budget constraint is very
8
severe) with the only option of pirating software products. Consequently, we
expect that an increase in resources will ultimately lead to a piracy decrease. In
order to investigate the relationship between piracy and income, we use a panel
data approach. More precisely, we estimate the following equation:
2
Pr it = α i + β 0 + β 1 Y it + β 2 Y it + β 3 Z it + u it (1)
Where Pr it is the piracy rate in a country i (i = 1, 2,…, N) at period t (t = 1,
2,…,T). The Y it is the natural logarithm of income per capita at time t in
country i. The αi reflects the unobserved heterogeneity, and the uit are the
idiosyncratic
errors.
The
regressor
is
strictly
exogenous,
E (u it / Yi1 ...YiT , Z i1 ...Z iT , α i ) = 0 . Equation (1) symbolizes the predicted piracy
Kuznets curve hypothesis expressing Piracy rate as a function of per capita
income and including a quadratic income term. It contains, as well, Z, a vector
of additionally explanatory variables considered by previous researches in
explaining the determinants of software piracy. These include the Share of high
technology exports (High-techex); Trade freedom (tradefree); corruption
(corrupt) and International copyright convention membership (membership).
3.3. Instrumental variables
Eq. (1) suffers from potential endogeneity problems since piracy is a function of
income, yet income is itself likely to be a function of piracy 5 . As a result,
income should be instrumented in Eq. (1).
To avoid any interactions with the piracy rate, the choice of the potential
instrumental variable should refer to other variable categories except economic
5
Previous scholars have found a strong relationship between per capita income and piracy by examining the
impact of per capita income on piracy (Ginarte & Park, 1997; Andrés, 2006; Marron & Steel, 2000; Depken &
Simmons, 2004; Ronkainen & Guerrero-Cusumano, 2001; Papadopoulos, 2003) in one hand and the impact of
IPR on per capita income in other hand (Rushing and Thompson 1996, Gould and Gruben, 1996, Kim, 2004 )
9
ones. Different variables have been used in the literature to instrument the
income, some of them are likely geographical others linguistic (Hall and Jones
1999; Theil and Finke 1983; Kravis et al 1982; Cole, 2007).
The geographical variables refer to the distance from the equator, whereas the
linguistic variables relate to the use of European languages namely English.
Hall and Jones (1999) argue that because Western Europe recognised the
importance of property rights and the importance of checks and balances within
government, countries strongly influenced by Western Europe were, ceteris
paribus, more likely to have a favourable institutional environment and a higher
income level.
We use in this empirical analysis the proportion of the population that speaks
English as an instrumental variable that captures the Western influences.
To be a successful instrument, this variable must be correlated with the income
level without being correlated with the error term in eq (1). That is, it must be
the case that European influence was not targeted towards high income regions
which is obviously the case.
3.4 data and estimation
The data sample includes 900 observations describing 75 different countries in a
balanced panel covering 12 years (from 1996 to 2007). Table 1 provides
background information on the variables used in our analysis.
The software piracy rate is collected from the Business Software Alliance
(SBA). The piracy rate is determined as the percentage of total software
installed that was not legally acquired. Analysts determine how much PC
packaged software was deployed and how much PC packaged software was
legally acquired in a given year, and then subtract one from the other to get the
amount of pirated software.
10
To get the amount of the pirated software, SBA proceeds to the difference
between the amount of PC packaged software that was deployed and the amount
of PC packaged software that was paid for legally acquired 6 . As the first
available report of the SBA backs to 1996, we were not able to go back in time
beyond 1995. Per capita GDP is the gross domestic product based on
purchasing-power-parity per capita and is collected from the World Bank World
Development Indicators table7. As GDP per capita is expressed in thousands of
dollars while the endogenous variable (piracy rate) is a percentage, then, for
reasons of data adequacy, we have carried out the regressions by considering the
logarithmic transformation of this independent variable.
The other explanatory variables used in our analysis are the percentage of high
tech export in the total export, trade freedom level and the corruption level,
International copyright convention membership
Table 1 includes a grid of all these study variables, their sources and a brief
description of each.
[Insert table 1 around here]
A review of the data was employed to help ensure quality of the overall analysis.
Table 2 reports the descriptive statistics of the variables used in the empirical
analysis.
[Insert table 2 around here]
6
7
For further information see http://global.bsa.org/idcglobalstudy2007/studies/2007_global_piracy_study.pdf.
The
International
Monetary
Fund,
World
Economic
Outlook
Database,
April
2008,
http://www.imf.org/external/pubs/ft/weo/2008/01/weodata/download.aspx.
11
4. Econometric results
4.1 existence of Piracy Kuznets curve
Table 3 provides estimates of piracy rate. Model (A1) corresponding to the first
column begins by expressing piracy rate simply as a function of per capita
income. In this model, per capita income is treated as being exogenous with
regard to piracy rate and hence is not instrumented. Models (A2-A6) then
include additional explanatory variables that have been tested in previous studies.
These variables are corruption (Corrup) ; share of high technology exports
(High-techex) ; Trade freedom (Tradefree) ; international copyright convention
membership (membship) defined as a dummy variable taking 0 or 1 depending
whether the country signed or not a particular treaty which protect IPRs. In
model (A6), per capita income is instrumented.
The coefficient of determination R² measures the proportion of the variation in
the dependent variable explained by the regression model. The results reported
in table 3 suggest that in all regression models included variables explained
between 60.04% and 67.82% variation in the software piracy rates.
As conjectured, by our first and main hypothesis, there appears to be a nonlinear
relationship between per capita income and piracy. In all models the coefficient
of the income term is found to be significantly positive while the coefficient of
the quadratic income term is found to be significantly negative. We note the
persistence of the nonlinear relationship between income per capita and piracy
after successive introduction of both institutional quality and legal system
measures. Interestingly, the instrumentation of per capita income does not cause
a drop in the significance of the per capita income variables compared to other
models, as the simple and quadratic coefficient remain significant at 1 per cent
level.
12
The estimation results indicate that illegal copying tends to increase in national
income initially, but once certain threshold value of income per capita is attained
a decline in piracy rates is observed. These results reveal an inverted U-shaped
relationship between per capita income and piracy rate. Since this relation is
similar to the well-known environmental Kuznet’s curve (EKC) there are sound
reasons to name this relationship the piracy Kuznet’s curve (PKC).
[Insert table 3 around here]
By considering the results obtained by the model (A6) where per capita income
was instrumented, the level of piracy rate increases as income increases, reaches
a turning point when per capita income per year equals 2416.31 $ and after that
piracy decreases with increase of GDP per capita income. The piracy Kuznets
curve relationship between piracy and income is depicted in Figure 1.
[Insert figure 1 around here]
4.2 controlling for other factors
Concerning the other variables of interest, table 3 summarizes the different
regressions outcomes
The High-tech export coefficient is negative in all our models, that is the higher
the share of high-technology in total manufactured exports, the less software is
pirated. The interpretation of this relationship which is in contradiction with
previous studies is that open countries with high level of technology export are
more careful to protect their technology. They seek to preserve the uniqueness
of their domestic industries assets. Indeed, when the domestic industry of an
economy in transition becomes skilled and innovative, it seeks protection
against piracy; hence the government can invest more in effective enforcement
13
of intellectual property rights which leads to a decrease of the piracy level.
These countries are more careful to protect their technology from piracy to avoid
that foreign firms take advantage of this IPR violation and construct or develop
their own industries.
The significance and negative sign of the corruption coefficients, across all our
proposed models suggest that the higher is the level of corruption the higher is
the piracy rate8. These findings are consistent with results presented in other
empirical
piracy
studies
(Ronkainen
&
Guerrero-Cusumano,
2001;
Papadopoulos, 2003) and confirm our hypothesis. However, the coefficient of
trade freedom was found to be negative, as predicted, but not significant in all
models that included this variable.
The non significance and the instable sign of the membership variable did not
support our hypothesis that membership to an international copyright convention
will result in lower Piracy rate.
Summing up, the empirical results indicate that there is an inverted U-shaped
relationship between per capita income and piracy. This relationship appears to
be robust to the inclusion of additional institutional and legal control variables.
5. Policy implications and concluding remarks
The immediate policy implication of our finding is the following: grow first and
then let piracy decrease. Consequently, a ‘one-size-fits all’ policy against piracy
offenders is likely to be inadequate. Policies that target countries (or
subcategories of the population) that are close to the turning point can offer the
best return on investment, even if these countries are not the worst offenders. As
a direct consequence, the lobbying and enforcement across countries should be
in relation not with the piracy level per se but with the income per capita level.
8
Note that higher values of the corruption index imply less corruption as our corruption variable represents
freedom from corruption where 0 indicates very corrupted government
14
So, the worst offenders are not necessarily those to be targeted. Put differently,
intellectual property rights holders should not aim the decrease of piracy per se
but the decrease of piracy where it is most likely to be substituted by legal sales.
In sum, ignoring the development stage of offenders of intellectual property
rights can lead to flawed policy prescriptions. Therefore, designing and
implementing effective anti-piracy strategies must take into account the
development stage of the considered countries. The previous arguments are also
consistent with a growing literature on procedural utility where people obtain
satisfaction not only from outcomes, but also from the conditions which lead to
these outcomes (e.g., Benz et al., 2004; Frey and Stutzer, 2005). From this
perspective, the disutility of stealing rich [software firms] when you are ‘poor’ is
likely to be smaller than the disutility of stealing rich [software firms] when the
individual is himself and to a relative extent ‘rich’.
Although we have offered new empirical evidence regarding the relationship
between income per capita and piracy, we have not identified precisely the
contribution of each mechanism to the overall impact. Moreover, we have not
investigated whether these results are robust to other industries affected by
piracy such as music, game and movie industries. Among promising issues that
remain unexplored, we consider investigating in future research whether piracy
is conducive or detrimental to economic growth. The related argument where the
original firm tolerates intentionally piracy at low levels of income per capita to
create an addiction effect transforming today’s pirates into tomorrow’s payers
also deserves further attention.
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17
18
Countries list
Argentina, Australia, Austria, Bahrain, Belgium, Bolivia, Brazil, Bulgaria,
Canada, Chile, China, Colombia, Costa Rica, Croatia, Cyprus, Czech Republic,
Denmark, Dominican Republic, Ecuador, Egypt, El Salvador, Finland, France,
Germany, Greece, Guatemala, Honduras, Hungary, India, Indonesia, Ireland,
Israel, Italy, Japan, Jordan, kenya, Kuwait, Lebanon, Malaysia, Mexico,
Morocco, Netherlands, New Zealand, Nicaragua, Nigeria, Norway, Oman,
Pakistan, Panama, Paraguay, Peru, Philippines, Poland, Portugal, Romania,
Russian Federation, Saudi Arabia, Singapore, Slovakia, Slovenia, South Africa,
Spain, Sweden, Switzerland, Taiwan, Thailand, Turkey, UAE, Ukraine, United
Kingdom, United States, Uruguay, Venezuela, Vietnam, Zimbabwe
Table 1. Data Information
Variable
Pr
Definition
Piracy rate
Source
Software
Business
Software Alliance
Y
Gross domestic product based World
on
Economic
purchasing-power-parity outlook
per capita GDP
International
Monetary Found
Engspeak
The fraction of the population Hall
that speaks English
and
Jones
on
Hunter
(1999)
based
(1992)
and Gunnemark
(1991)
19
World Bank
High-techex
High- technology exports, as a
percentage
of
manufactured
exports
Tradefree
Trade freedom: a composite Heritage foundation
measure of the absence of tariff and
and
non-tariff
barriers
Wall
Street
that Journal
affect imports and exports of
goods and services.
Corrupt
Freedom from corruption: a Heritage foundation
score that measures the level of and
Wall
Street
corruption where 100 indicates Journal
a very little corruption and 0
indicates
a
very
corrupt
government
Membship
Membership
in
the
“trade- World
Trade
related aspects of intellectual Organization
property rights
agreement”
(TRIPS)
Table 2. Descriptive statistics
Variable
N
Mean
Stand dev
Min
Max
Piracy rate
900
59.59
20,11
20
99
GDP per capita
900
14779.44
11637.34
188,4
53152.39
Engspeak
540
44.23
31.23
0.08
98.37
High-techex
857
12.92
14.28
0
75
Tradefree
900
69.59
13.11
13.2
90
20
Corrupt
900
50.92
24.52
7
100
Membership
900
0.25
0.43
0
1
Table 3. Empirical Results
Yit
Yit²
(A1)
(A2)
(A3)
(A4)
(A5)
(A6)
RE
RE
FE
FE
RE
2SLS
60.34***
61.78***
60.39***
60.66***
61.26***
83.38***
(8.53)
(8.92)
(10.43)
(10.98)
(8.73)
(43.67)
-4.28***
-4.34***
-4.34***
-4.33***
-4.25***
-5.35***
(0.47)
(049)
(0.57)
(0.6)
(0.48)
(2.28)
-0.10***
-0.10***
-0.08***
-0.11***
(0.04)
(0.05)
(0.04)
(0.098)
-0.06***
-0.07***
-0.07***
-0.16***
(0.02)
(0.02)
(0.02)
(0.04)
-0.02
-0.07
(0.03)
(0.10)
-2.30
0.63
(2.98)
(3.04)
High-techex
corrup
tradefree
membership
-128.48***
-136***
-120.23***
-122.69***
-132.13***
-234.79
(38.21)
(39.97)
(47.50)
(50.08)
(39.08)
(201.57)
Observations
900
900
900
900
900
900
R-squared
0.6004
0.6163
0.6148
0.6304
0.6343
0.6782
R-squared within
0.2846
0.2855
0.2899
0.2925
0.2921
0.4146
R-squared between
0.6411
0.6290
0.6575
0.6453
0.6502
0.7079
F
37.71
38.69
Prob > F
0.000
0.000
Constant
Haussman test
1.78
1.5
46.19
26.96
Prob > Chi²
0.4111
0.6820
0.000
0.000
Breusch-Pagan test
1164.59
1411.34
1181.86
1434.76
1236.47
Prob > Chi²
0.0000
0.0000
0.0000
0.0000
0.0000
Wooldridge test
161.461
140.736
163.585
142.735
144.225
Prob > Chi²
0.0000
0.0000
0.0000
0.0000
0.0000
Standard errors in parentheses. In models A1 to A5 per capita income is treated as being exogenous with to piracy rate and is therefore not instrumented. In
models A6 per capiat income is instrumented using 2SLS. ***; ** and * denote significance at 99%, 95% and
90%, respectively.
21
Figure 1. The piracy rate-GDP per capita relationship
22