Relationship between bribery and economic growth: an empirical analysis.Abstract
Examining measures of bribe taking and the real gross domestic product (GDP) of 20 countries over a twelve year period, it appears that higher incidences of bribery do adversely affect the rate of economic growth of nations. However, the rate of growth of real GDP does not have a similarly strong impact on reducing bribery levels. Furthermore, for individual countries, the relationship between these two variables varies considerably, indicating that country-specific factors explain both the prevalence of bribery and the pace of economic growth.
Keywords: Bribery; economic growth; corruption perceptions index; international business; public policy
The issue of bribery in international business has been receiving increasing attention from national governments, inter-governmental bodies, non-governmental organizations, chambers of commerce, civic institutions, business executives, and civil society in general. The attention stems from a recognition that bribery imposes costs on doing business, distorts competition, misallocates resources, undermines market efficiency and predictability, encourages illegal and unethical conduct, erodes public respect for the rule of law, undermines development projects, and retards economic growth, particularly so in developing countries where poverty is widespread (Lambsdorff, 1998, Mauro, 1995).
Rapid economic growth offers the surest means to free mankind from poverty. Rising incomes not only allow for increased consumption but also generates the resources needed to invest in vital social and physical infrastructure (e.g., education, health, roads, and electricity) which in turn stimulates further economic activity. Economic activity is often enhanced by international trade and inflows of foreign investment to supplement domestic resources. To the extent that bribery discourages such activities and flows, resources available for development are reduced and thus hurt the rate of economic growth of a country.
The focus of this paper is on examining this relationship between bribery and rate of economic growth to determine (a) whether the level of bribery in a country affects the rate of its economic growth and (b) whether the rate of economic growth in a country affects the level of bribery in that country. In other words, do higher levels of bribery retard economic growth and conversely, do higher rates of economic growth reduce the levels of bribery. Thus, this paper seeks to ascertain the relationship between these two variables as they impact each other.
II. DEFINING BRIBERY & BRIBERY IN INTERNATIONAL BUSINESS
Bribery is defined as "the offering, promising or giving something in order to influence a public official in the execution of his/her official duties" (OECD Observer, 2000). Bribes can take the form of money, other pecuniary advantages, such as scholarship for a child's college education, or non-pecuniary benefits, such as favorable publicity. In the international context, bribery involves a business firm from country A offering financial or non-financial inducements to officials of country B to obtain a commercial benefit.
Transparency International defines corruption as "the abuse of public office for private gain." The non-profit organization produces annually its survey of countries ranked on the basis of how corrupt they are perceived to be. Known as the Corruption Perceptions Index (CPI), it is based on "the misuse of public power for private benefit, with a focus, for example, on bribe taking by public officials in public procurement" (www.transparency.org). The CPI has emerged as a prominent measure of the extent of bribery in international business and is increasingly used by scholars to empirically ascertain patterns and relationships with other variables to understand this subject. The focus of this paper is on bribery, which is a major form of corruption. Thus, this paper does not consider political corruption or collusion among private parties as bribery.
The enormous growth in international trade and investment over the past fifty years has been accompanied by an increase in bribery. The newspapers regularly report bribery scandals in the conduct of international business (e.g., Crawford, 2008). The World Bank estimated that five per cent of the exports to developing countries go to corrupt officials (Moss, 1997). It is estimated that more than US$1 trillion is paid in bribes each year (Labelle, 2006). The chairman of the U.S. branch of Transparency International, the non-governmental organization dedicated to combating corruption, has noted that many analysts feel "there has been a gradual escalation. At one point, five per cent (of a contract price) was standard. That's crept up gradually until now it's in the twenty to thirty per cent range" (Andelman, 1998). If bribery is a burden to international firms, it is even more costly to the countries where they are prevalent. It has been estimated that money lost to bribery is the largest potential source of funding available to many new democratic governments aside from foreign direct investment (Hamra, 2000). The World Bank believes that tackling bribery can lead to significant increases in national income and faster economic growth and to improvements in quality of life issues such as child mortality rates (The Costs of Corruption, 2004).
The seriousness of the issue has prompted governments, intergovernmental bodies, non-governmental organizations, and commercial firms to control and discourage bribe giving and bribe taking. The U.S. was the first industrialized country to address this issue when, in 1977, it enacted the Foreign Corrupt Practices Act (FCPA) making it a crime for any American firm (and foreign firms which issue negotiable securities on U.S. stock exchanges) to offer, promise, or make payments or gifts of anything of value to foreign officials, politicians, and political parties with the intention of changing policies or to secure the suspension of a legal norm (U. S. Department of Justice). In 1999, the OECD Convention on Combating Bribery of Foreign Public Officials in International Business Transactions signed by the 30 member countries of the Organization for Economic Cooperation and Development (OECD) and six other nations came into effect (OECD, 2002). The main goals of the treaty are to prevent bribery in international business transactions by requiring countries to make it a criminal offence to bribe a foreign public official, to have in place adequate sanctions and reliable means for detecting and enforcing the offence, and prohibit bribes from being considered a business expense and thus tax deductible. Financial agencies such as the World Bank, Asian Development Bank, and International Monetary Fund have linked aid disbursements to improvements in administrative practices to eliminate corruption (Lewis, 1997, Rose-Ackermann, 1997). The World Bank has barred firms which engage in bribery from doing business with it. It has established a program to let firms that have worked on bank-funded projects to voluntarily disclose and has found that a number of companies admitted to paying bribes (Corpwatch, 2006). The World Bank has created aggregate governance research indicators for 213 countries around six dimensions, one of which is control of corruption. These annual figures provide beth a snapshot and a trend line of the quality of governance in individual countries and on a comparative basis (Kaufmann, Kraay, and Mastruzzi, 2006). Non-governmental organizations such as Transparency International, through their annual rankings of perceived corruption among countries, spotlight this subject. Many businesses and industry groups have become conscious of their ethical conduct and the need to comply with the emerging web of laws. Consequently, they have created codes of conduct for their employees. Private trade associations such as the Business and Industry Advisory Committee to the OECD and the International Chamber of Commerce have developed anti-bribery programs (Yannaca-Small, 1995). Thus, there have been worldwide efforts to address both the demand for and supply of bribes.
III. REVIEW OF EXTANT LITERATURE
Three strands of literature are reviewed here. They are (a) determinants of bribery and (b) determinants of economic growth. The World Bank has developed a simple formula to describe bribery: C = M + D-A-S where C standards for corruption, M for monopoly, D for discretion, A for accountability, and S for salary. The formula indicates that bribery tends to be high in societies where public officials earn low salaries but have a lot of discretion and limited accountability. Highly regulated economies create conditions for corruption to thrive. Businesses offer bribes and officials seek bribes to suspend the regulations.
Husted (1999) examined the role of economic and cultural variables and found that a significant inverse relationship exists between perceived levels of bribery in a country and the per capita income in purchasing power parity terms. Cultural dimensions--using Hofstede's classification--of masculinity and power distance were significant factors (Hofstede, 1980). Sanyal and Samanta (2002) confirmed Husted's findings and found that income distribution in a country was another significant economic factor. Similarly, Getz and Volkema (2001) found that bribery in a country was related to wealth and so was power distance and uncertainty avoidance. Uncertainty avoidance moderated the relationship between economic adversity and bribery. Thus, there is an empirical basis to suggest that certain economic and cultural factors determine perceived levels of bribery. Sanyal and Samanta (2003) have also found that economic freedom and level of human development are associated with levels of perceived bribery in a country with open economies and high level of human development inversely related to bribery. All these studies found that per capita income is inversely related to bribery.
Determinants of Economic Growth
The level of economic development in the world is very uneven. This is reflected in per capita gross national income (formerly gross national product) in purchasing parity terms of as high as $42,000 in the U.S.A. and as low as $830 in Yemen. Table 1 provides an overview of this worldwide disparity.
Worldwide, between 1990 and 2004, the proportion of people living in extreme poverty fell from nearly a third to less than one-fifth. Economic growth in the developing world has averaged 4.8 per cent a year since 2000, more than double the rate of growth in high-income economies, which averaged 2.0 per cent a year. The decline in poverty has been limited in countries that have experienced slower (or sometimes none at all) economic growth, usually measured by changes in the gross domestic income (GDI) from one period to another. Countries such as China, India, and Vietnam which have exhibited strong economic growth--between 1990 and 2003, the average annual GDP increases for these countries were 9.6, 5.9, and 9.5 percentage respectively--have been able to pull millions of people out of absolute poverty. In contrast, in Sub-Saharan Africa, where the growth rate was 2.8 per cent, in 2002, 300 million people lived on less than $1 a day, an increase of 139 million people over 1981. This is in sharp contrast with East Asia, where the number of extremely poor people fell by 580 million people, to 12 per cent of the population. World Development Indicators data indicate that economic growth is linked to sound policies, well-targeted aid, better governance, and a good investment climate (World Bank, 2006).
The relationship between economic growth and bribery has been examined extensively in the literature, beginning with Mauro (1995). In general, the studies find a negative correlation between bribery and economic growth (Bardhan, 1997). Fisman and Svensson (2000) uses evidence from Uganda to confirm that bribery retards development at the micro level. They studied the relationship between bribe payments, taxes, and firm growth in Uganda for the period 1995-97 and found that a one percentage point increase in the bribery rate was associated with a three percentage point reduction in firm growth.
Trade has proven to be an engine for growth in East Asia, equal to 81 per cent of the region's GDP, which far outstrips trade's 55-per cent share of GDP at the global level. Rapid expansion of China's trade has not only sustained its growth, but has also helped its regional trading partners integrate faster into global manufacturing. Experts of goods and services grew by 10 to 28 per cent in Malaysia, Thailand, the Philippines, Vietnam and Cambodia, and contributed to economic growth rates over six per cent in 2004 in all of these countries. In contrast, trade plays a much smaller role in Latin America and the Caribbean, making up barely 52 per cent of total output. Exports from Latin American countries have expanded by only 4.5 per cent a year since 2000, less than one-third the growth of exports by East Asia and less than half the growth of exports from South Asia and Europe and Central Asia.
Foreign direct investment (FDI) is another engine of economic growth. A study by Habib and Zurawicki (2002) looked at aggregate investment flows from seven countries among themselves and 82 other countries over a three year period (1996-98) and related those flows to the individual country's CPI. They concluded that "corruption is a serious obstacle to investment". They also found a negative effect due to the difference in bribery levels between home and host countries suggesting that investing firms are reluctant to deal with the conditions prevalent in an operating environment with a different level of bribery. In an undated World Bank document, Smarzynska and Wei studied the impact of bribery in a host country on the preference of foreign investors for a joint venture or a wholly-owned subsidiary. They conclude, based on firm-level data, that bribery reduces FDI and shifts the ownership structure towards joint ventures. They also report that U.S. firms are more averse to joint ventures in corrupt countries than investors of other nationalities. This latter finding is consistent with that of Hines (1995) who attributed the reluctance of U.S. multinational firms to avoid joint ventures in high bribe countries to the prohibitions embedded in the FCPA. In another study on the effect of bribery on FDI, Wei (2000) looked at bilateral investment from 12 source countries to 45 host countries and found that a rise in bribery in a country affected inward FDI there. The study also noted that while U.S. firms were averse to bribery in host countries, they were not necessarily more so than average OECD country, in spite of the FCPA. Sanyal and Samanta (forthcoming), in a study of U.S. outward FDI found that while high levels of bribery in recipient countries discouraged U.S. investment there, there were important exceptions. Countries with huge domestic markets (e.g., China) continued to attract U.S. FDI irrespective of the level of bribery.
As noted earlier, the World Bank has reported that good governance (of which lack of bribery is a key component) can bring significant improvement in the standards of living in developing countries. These improvements are facilitated by several factors, one of which is increased international investment (Capua, 2005).
IV. THEORETICAL FRAMEWORK
While extant research, as discussed above, indicates that economic growth is affected by many factors, there is ample evidence that prevalence of bribery is a barrier to economic growth. Consequently, reduction of bribery can only have a salutary effect on the economic environment and in conducting economic activities. Countries with lower levels of bribery, ceterus paribus, are likely to exhibit rapid economic growth. This is because bribery is one of the deterrents to trade, investment, and commercial activity in a country. Countries with higher levels of economic development also have the resources to provide its civil servants (the regulators of government policies) with high salaries and benefits (which reduce the temptation to seek bribes) and are likely to have acquired the mechanisms and civil society necessary to enforce laws against bribery.
Studies unequivocally show that bribe taking is much lower in countries with high incomes. Thus, if high incomes can inhibit bribe taking and high prevalence of bribery retards economic growth, it would suggest that these two factors--economic growth and bribery levels--affect each other both unidirectionally as well as simultaneously. Thus the following propositions can be advanced--
1. Prevalence of high levels of bribery retard economic growth.
2. High levels of economic growth will reduce the prevalence of bribery.
3. Bribery and economic growth can exist concurrently. Bribery prevents incomes from rising and rising incomes reduce the prevalence of bribery. This is because there are cultural, political, and legal factors affect economic growth and the prevalence of bribery in a country.
The aim of this study is to analyze the nature and extent of the relationship between these two variables.
V. DATA AND METHODOLOGY
Two sets of data were collected over a twelve year period, 1995-2006, for twenty countries. These countries are members of OECD (Organization for Economic Cooperation & Development) (www.oecd.org). The availability of the data for these countries for these time period influenced the scope of this study. The time frame is sufficiently long to detect trends and changes with respect to the data for both these variables.
The level of bribery, as measured by the Corruption Perception Index (CPI), was obtained for each of these countries from Transparency International. The measure of the rate of economic growth--annual per cent changes in the gross domestic product (GDP)--were calculated from data obtained from the International Monetary Fund.
CPI scores for individual countries have been used as measurement of bribery in the country. The Index, based on a survey of surveys, is devised from data collected over the previous three years from a wide variety of sources (www.transparency.org). By being a single composite score, the CPI has increased the reliability of the data of each individual source and best captures the perception of the level of bribery in a country as it affects the international businessperson. The CPI is computed on a scale of 10.0 to 0.0. A country rated 10.0 means the country is perceived to be virtually bribe-free; a score of 0.0 means bribery is rampant.
The CPI has gained acceptance amongst economists, academicians, businesspersons, and the media as a credible measure of extant bribery. It is widely reported in the media when it is announced annually. It should be noted that CPI scores report perceptions of bribery within countries not actual levels of bribery. The perception is about the extent of bribe-taking among public officials and politicians in individual countries with respect to conducting business. The CPI does not account for bribery in the private sector or other forms of corruption (e.g., electoral fraud). It is recognized that these scores, constructed from experts' assessments of overall corruption in a country, raises an additional concern about perception biases. However, when CPI scores are compared with other indices of bribery, there is a very high degree of correlation (Svensson, 2005).
GDP data are calculated in U.S. dollars and compared from year to year to measure the rate of economic growth. The GDP is a widely used measure of the size of a national economy. It indicates the level of economic activity in the country and influences the size of investments. The GDP, reported in national currencies, were converted into US dollars using an average exchange rate for the year (International Financial Statistics, 2007).
A regression method, vector autoregressive models (VAR), to test for the causal relationship of these two variables, has been used to analyze the data. A technical note in the appendix describes the model. The empirical results of these statistical tests are presented in the next section.
VI. RESULTS AND ANALYSIS
The data were subjected to two statistical treatments. In the first treatment, two sets of regression analysis were run on each of the two variables for country specific data and for the entire data taken together to test for two-way causality. In one regression, CPI was the dependent variable; in the other GDP was the dependent variable. The results are presented in Tables 2 and 3.
The overall results are mixed. For four countries--Denmark, Ireland, New Zealand, and Spain--the results indicate the two way causality of both the variables. That is, both economic growth rate and levels of bribery are affected by each other. To elaborate, for these countries, an increase in CPI (recall that a high CPI score means less bribery) causes increase in their GDP. Simultaneously, an increase in their GDP has led to an increase in their CPI.
However, in other countries--Canada, France, Greece, Italy, Portugal, and U.K.-the increase in CPI is related to the increase in their GDP but not vice versa. In two countries--Austria and Finland--the direction of the effect is the reverse: the rate of economic growth has led to an increase in their CPI or reduction in perceived bribe taking. However, there is no statistical relationship the other way around. Finally, in eight countries--Australia, Germany, Japan, Netherlands, Norway, Sweden, Switzerland, and the U.S--there is no significant relationship between these two variables in either direction.
In the second treatment, panel estimation was used to examine the relationship of these two variables for the entire data set of 20 countries over 12 years together. Panel data estimation can be used to control for some unobserved omitted variables that differ across countries but may remain constant over time. Table 3 shows the results for both the fixed effects model and the random effects model using time lags of 3 year periods and 4 year periods. (With annual data, the number of lag is typically small 2 or 3. However, we assume that the effect of bribery on real GDP may linger on further. So, we have considered lags of 3 and 4 periods here.) The use of lags is justified since it is likely that there is a time gap between the occurrence of bribery and its subsequent impact on economic growth.
As indicated in Table 3, the overall results indicate that the level of bribery in a country has a significant impact on the changes of the real GDP for that country. F statistics for the causality between CPI and GDP (i.e. CPI causes GDP) is significant at less than 1% level of significance with three year period lag and significant between 5% and 1% at four year period lag. Since these are annual data, it seems that three year period lag is probably more appropriate than four year period lag. (In these countries four period lags refers to four year time period, where government may and can change in many cases.) In contrast, the impact of the rate of economic growth on the level of bribery is much milder; F statistics are much smaller and they are significant at 5% level of significance. This would indicate categorically that bribery has a significant effect on retarding economic expansion. Although at the same time economic expansion does reduce the level of bribery in the country, this relationship is not as strong. These results do confirm the existence of bidirectional causality.
Despite these aggregate results, the relationship of these two variables play out quite differently in different countries, as presented in Table 2. In the U.S., for instance, there is no relationship between these two variables whereas in New Zealand, there is strong two-way causality. In Canada, it is the CPI that affects GDP whereas in Finland, it is the reverse. Given this wide ranging pattern, it seems that country-specific variables and other factors are at play which explains the relationship between level of corruption and the rate of economic growth in individual cases. Other studies on bribery have indicated that cultural factors (e.g., acceptance by the population of hierarchical differences in society), the level of human development (e.g., education attainment of the population), other economic variables (e.g., openness of the economy), and political and legal conditions (e.g., economies in transition and presence and enforcement of anti-bribery laws) significantly affect the level of corruption in a country. In short, however, the findings do provide substantially support for the propositions advanced in the early part of this paper.
VII. POLICY IMPLICATIONS AND LIMITATIONS
The results reported here offer useful guides to both public policy makers and international business executives. These include-
* In evaluating business opportunities, executives need to focus on country specific attributes and not generalize across countries. Every country needs to be assessed on its own particularities for business and investment purposes. A country with a high perceived level of bribe taking may still be a desirable place to conduct business. Similarly, there may be many other deterrents to doing business in a particular country and bribery could be only one, and that too not very crucial.
* While in general businesspersons may expect to encounter low levels of bribery in high income countries, they should not be surprised if this is not true in particular countries and in particular situations. In some high growth countries, it may be that bigger bribes may be expected.
* In formulating strategies for economic growth, policy makers need to tailor them to the specific economic and social conditions of the specific country. A strategy that works in one place may not be appropriate for implementation elsewhere. Policy makers may have to acknowledge that bribe taking may not be a significant hurdle to rapid economic growth in a particular country. Other factors may be more serious detriment to growth. Thus, scarce resources and efforts may be more usefully deployed to removing those hurdles rather than be focused on curbing bribery.
* While eradicating bribery may be a desirable social and economic goal, doing so may not be enough to stimulate higher levels of economic growth if other barriers to trade and investment are not dismantled.
* Rapid economic growth should not relax the authorities from seeking to keep bribery under control. The evidence is that in some cases, economic growth can lead to continued bribery.
It is worth noting however, that these countries in the study are considered as high income where bribery levels are in general lower compared to less developed countries. That significant relationship exists for 12 of the 20 countries suggest that bribery, even if lower, still exists and is associated with continued economic growth. In half of the countries iu the sample, the CPI does affect the GDP. This also indicates how stubborn the prevalence of bribery is in the organization and culture of human society and the difficulty of eradicating it completely.
As the sample of countries in the study is all developed nations; future studies can expand this sample to include developing countries. Some developing countries (e.g., China and Vietnam) have reported high levels of economic growth in recent years despite being perceived as places where bribe-taking is widespread. At the same time, many developing countries remain desperately poor with low rates of economic growth. A more heterogeneous sample of countries can serve to test the validity of the results reported here. As more data on bribery from more a diverse set of countries become available over time, such studies will become easier to conduct.
The measure for bribery is the annual index reported by Transparency International. This is a measure of perception of bribery in a country, as opposed to actual levels. The Index focuses on bribery in the conduct of international business; it may underreport the prevalence of bribery and other forms of corruption occurring in the domestic realm which could influence economic growth in a country.
While this study was exclusively focused on the relationship between two variables, it is well reported that many factors affect both the level of bribery in a country as well as its rate of economic growth. Here is a scope for a more ambitious study that considers many of these influencing variables with a larger sample of countries. This paper does isolate the impact of bribery--the variable of interest--on economic growth, irrespective of the impact of other factors. We acknowledge that other factors may be more important than level of bribery in impacting economic development in specific countries and the results reported here indicate no relationship between the two for many countries.
The aim of this study was to examine the conundrum--does corruption retard economic growth and does high economic growth curb corruption. The results reported here provide some further clarification on this relationship. While there is a significant relationship between the two, it is stronger in one direction--the impact of CPI on GDP is greater than the impact of GDP on CPI. While this is true in the aggregate, the relationship between the two differs markedly across individual countries indicating country-specific attributes.
It is beyond the scope of this paper to examine every country's unique characteristics to explain the prevalence of bribery and the factors propelling economic growth there. But it is clear that this is an area worth investigating, in the form of country case studies. The fact that models of success in some countries have not been easily transferable to other countries further emphasize that national peculiarities need to be understood.
The major findings of this paper are that bribery and economic growth impact each other both unidirectionaly and simultaneously. However, the impact of lower levels of bribery on economic growth is stronger than the impact of higher economic growth rate on reducing bribery. It was also found that there may not exist any relationship among these two variables in some countries. These varied findings suggest that unique country specific factors explain the prevalence of bribery and pace of economic growth; universal explanations need to be hedged.
The findings suggest that concerted efforts to reduce bribery must remain a desirable policy for national governments, international agencies, and non-governmental organizations. Reducing the prevalence of bribery would contribute to a higher rate of economic growth and that in turn could further accelerate the decline in bribe taking a virtuous cycle that can contribute to the economic well-being of more of the world's people. Concurrently, policies that enhance economic growth need to be put in place and implemented to arrest bribery.
APPENDIX NOTE ON STATISTICAL METHODOLOGY
Of late, vector autoregressive models (VAR) have been used to identify and establish relationship among the variables. The simplest VAR process that can be formulated in this context of CPI (denoted by [y.sub.1t]) and the real GDP (denoted by [y.sub.2t]) is a bivariate VAR as described below:
[y.sub.1t] = [[beta].sub.10] + [[beta].sub.11] [y.sub.1t-1] + .... + [[beta].sub.1k] [y.sub.1t-k] + [[alpha].sub.11] [y.sub.2t-1] + ... [[alpha].sub.1k] [y.sub.2t-k] [u.sub.1t] (1)
[y.sub.2t] = [[beta].sub.20] + [[beta].sub.21] [y.sub.1t-1] + .... + [[beta].sub.2k] [y.sub.1t-k] + [[alpha].sub.21] [y.sub.2t-1] + ... [[alpha].sub.1k] [y.sub.2t-k] [u.sub.2t] (2)
where [u.sub.it] is a white noise disturbance term with properties E([u.sub.it]) =0 ([i=.sub.1,2]) and E([u.sub.1t] [u.sub.2t]) = 0.
In equations (1) and (2), current values of [y.sub.1t] and [y.sub.2t] depend on different combination of the lagged k values of both variables. When the VAR model includes many lagged values of the variable, it will let us know which set of variables have significant effects on each dependent variable. So, we can set up different types of testing of hypotheses regarding the parameters: [[beta].sub.10], [[beta].sub.20], [[beta].sub.11], [[beta].sub.12], [[alpha].sub.11], [[alpha].sub.12], [[alpha].sub.21] etc. One such testing process is the Granger Causality test. This causality tests seeks to find out whether changes in [y.sub.1] causes changes in [y.sub.2] and vice versa. It is assumed that if [y.sub.1] causes [y.sub.2], then lags of [y.sub.1] should be significant in the equation of [y.sub.2], equation (2) (i.e. this rejects the hypothesis that lags of [y.sub.1] do not explain current values of [y.sub.2] or [[beta].sub.21] = [[beta].sub.22] = ..... [[beta].sub.2k] = 0 ). If this is the case and not vice versa, then it can be concluded that [y.sub.1] "Granger causes" [y.sub.2], or there exists unidirectional causality from [y.sub.1] to [y.sub.2]. On the other hand, if [y.sub.2] causes [y.sub.1], lags of [y.sub.2] should be significant in the equation of [y.sub.1], (i.e., it rejects the hypothesis that [[alpha].sub.11] = [[alpha].sub.12] = [[alpha].sub.1k] = 0 in equation (1)). If both are true, then it can be concluded that there exists bidirectional causality or bidirectional feedback between [y.sub.1] and [y.sub.2]. Tests of such joint hypotheses can easily be formulated with F- test, since each individual set of restrictions involves parameters from one equation. The equations (1) and (2) can be estimated separately to obtain the unrestricted sum of squared errors. Next, we impose the restrictions and obtain the restricted sum of squared errors and compute the traditional F-statistic to derive the inference about the following hypotheses:
[H.sub.0] : [[beta].sub.21] = [beta].sub.22] = ... = [[beta].sub.2k] = 0
[H.sub.a] : Not [H.sub.0]
[H.sub.0] : [[alpha].sub.11] = [[alpha].sub.12] = ... = [[alpha].sub.1k] = 0
[H.sub.a] : Not [H.sub.0]
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Table 1 Per Capita Gross National Income (PPP) In US Dollars 2006 Region/Country Income World 9,489 High Income 32,824 Canada 32,770 Middle Income 7,252 Upper Middle Income 10,861 Mexico 10,560 Lower Middle Income 6.399 Gabon 6,280 Low Income 2,470 Ghana 2,450 Source: World Bank Indicators database. May 1, 2007. Washington, DC: World Bank. Table 2 Relationship Between CPI and GDP by Country Direction of Causality CPI [right arrow] GDP [right arrow] GDP CPI Country F value P value F value P value Australia 53.51 0.100 4.01 0.21 Austria 4.07 0.203 40.91 0.024 * Canada 12.97 0.008 * 0.06 0.978 Denmark 53.55 0.000 * 8.06 0.023 * Finland 3.11 0.127 7.06 0.03* France 7.73 0.025 * 2.27 0.198 Germany 0.13 0.938 0.21 0.886 Greece 12.82 0.009 * 2.57 0.167 Ireland 52.85 0.000 * 9.56 0.016 * Italy 5.40 0.050 * 4.33 0.074 Japan 0.63 0.632 2.67 0.159 Netherlands 0.35 0.796 13.85 0.068 New Zealand 13.91 0.007 * 13.19 0.008 * Norway 0.15 0.923 0.64 0.623 Portugal 27.58 0.001 * 1.03 0.452 Spain 6.19 0.039 * 7.33 0.028 * Sweden 0.86 0.52 0.74 0.571 Switzerland 0.49 0.705 0.55 0.669 United Kingdom 7.41 0.027 * 1.38 0.349 U.S.A. 3.5 0.105 0.52 0.685 * significant at the 0.05 level Table 3 Panel Estimation of The Relationship Between CPI and GDP F values Direction of Causality 3 period lag 4 period lag Fixed effects model CPI [right arrow] GDP F(3, 152) =5.81 * F(4,130) = 2.316 ** p-value < 0.01 0.05 < p-value < 0.1 GDP [right arrow] CPI F(3,154) = 2.169 ** F(4, 132) = 2.10 0.05 < p-value < 0.1 p-value < 0.1 Random effects model CPI [right arrow] GDP F(3,171) = 6.742 * F(4, 149) = 2.507 * p-value < 0.01 0.05 < p-value < 0.1 GDP [right arrow] CPI F(3, 173) = 2.509 * F(4,151) = 2.65 * 0.05 < p-value < 0.1 0.05 < p-value < 0.1 * significant at 0.05 level ** significant at 0.10 level