GDP per capita and the privatization of
copper mines in Zambia:
a time series analysis of unit root with structural breaks
Author: Mark Hellsten (940925)
Autumn 2019
Independent Project, Advanced Course, 15 Credits Subject: Economics
Örebro University School of Business Supervisor: Linda Andersson Järnberg Examiner: Magnus Lodefalk
Abstract
This thesis investigates the privatization of copper mines and GDP per capita in Zambia using time series analysis. A structural break is a sudden, lasting change in mean or trend of a time series. Potential structural breaks are identified, analysed and discussed. The possible breaks are compared to the most significant events in the economic history of Zambia, gathered in interviews from a qualitative field study. The empirical test also investigates structural breaks in the neighbouring region of Zambia and a Granger test for causality analyses the relationship between the price of copper and GDP per capita in Zambia. The study finds a possible break in Zambian GDP per capita around the year 1998, slightly before the privatization of the copper mines were finalized, in the year 2000. A likely scenario is that several events led to a potential structural break in the Zambian economy around the year 1998. The price of copper may affect the Zambian economy, but it did not seem to cause the 1998 potential break in Zambian GDP per capita. The Granger test for causality also found the price of copper to be a poor forecaster for Zambian GDP per capita. In conclusion, the possible structural break in Zambian GDP per capita was probably caused by a stabilization in the market following a period of wide public reforms, with other events such as the price of copper, the privatization of Zambian copper mines and the HIV pandemic coming under control possibly contributing to the post-break growth to some extent.
Acknowledgements
I would like to express my gratitude to my supervisor Linda Andersson Järnberg for the immense help with choosing the right methodology and for continuous feedback and encouragement for the duration of the project.
Further, I would like to thank Salim Kaunda and Caesar Cheelo, who took time to share their knowledge through interviews, contributing to building a picture of the Zambian economy which would not have been possible without them. I would like to thank the staff at the Policy Monitoring and Research Centre and the Zambia Institute for Policy Analysis and Research for arranging and making the interviews possible.
Contents
1. Introduction ... 1
2. Institutional Background ... 3
2.1. Zambia as part of the international market for copper ... 5
2.2. The case of the privatization of Zambian Consolidated Copper Mines Ltd. ... 6
2.3. Significant events in the economic history of Zambia ... 8
3. Theory ... 10
3.1. Potential benefits for transitional economies ... 11
3.2. The relation between privatizations and economic growth ... 12
3.3. Summary of possible macroeconomic effects of the privatization of ZCCM ... 14
4. Previous research ... 14
4.1. Privatizations and economic growth in developing countries ... 15
4.2. Case studies of the privatization of ZCCM ... 17
4.3. Firm-level studies on privatizations ... 18
5. Data ... 19
6. Empirical methodology ... 21
6.1. Motivation for the choice of methodology ... 22
6.2. Unit roots ... 24
6.3. Structural breaks ... 26
6.4. Multiple structural breaks ... 27
6.5. Zambia’s dependence on copper: Granger causality ... 28
6.6. Qualitative field study: Interviews ... 29
7. Results ... 31
7.1. Augmented Dickey-Fuller test of a unit root, without structural break ... 31
7.2. Zivot-Andrews test of unit root with one structural break ... 32
7.3. Clemente, Montañés and Reyes test for multiple breaks ... 36
7.4. Granger test for causality ... 38
8. Discussion ... 38
8.1. Structural breaks in the neighbouring region ... 39
8.2. Fluctuations in the price of copper ... 40
8.3. Relation to theory and defining moments in the Zambian economy ... 42
9. Conclusions ... 44
References ... 46
Appendix A. Variable list ... 51
Appendix B. Autocorrelation plots ... 52
Appendix C. Transcript of cited parts of interview with Salim Kaunda ... 53
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1. Introduction
In the late 1980’s, privatization programmes were widely adopted around the world (Kikeri & Nellis 2004). The basic notion is that the private sector is more efficient, as government institutions often lack competition. Privatization programmes have since been commonly adopted by developing countries. Developing countries are often faced with unique economic challenges. Large public debts are common, meaning that a large share of the budget must be allocated to debt-servicing (Campbell, White & Bhatia 1998). Underdeveloped private sectors can hamper a capacity to facilitate fast growth. A public sector with limited means can lead to poorly functioning state-owned enterprises. Privatization programmes have been common among developing nations as the reforms have the benefit of reducing fiscal strains, along with other potential benefits.
Zambia’s implementation of privatization reforms was started as a possible solution to economic problems related to a very large, but unsustainable public sector (Limpitlaw 2011). The size of the public sector was a result of policymaking in the centralized one-party state that had been governing Zambia since its independence in 1964. Performance of state-owned enterprises decreased up until the early 1990’s where a multi-party system was adopted and a wide privatization reform was undertaken, amongst them the largest company in Zambia, Zambian Consolidated Copper Mines Ltd (ZCCM).
The wider reforms in Zambia are sometimes hailed as among the most successful privatization programmes enacted by a developing country (Campbell, White & Bhatia 1998). This success came as a result of many factors. The privatization was well prepared, the process was transparent, and was well supported by public institutions. The reason this study is undertaken, is to contribute towards the mapping of the privatization. An area that has not had much research, is on the topic of macroeconomic effects of the privatization. The purpose of this thesis is to investigate the relationship between the privatization of ZCCM and Zambian GDP per capita.
Previous studies consist, among others, of cross-sectional data analysis on the relationship between privatizations and growth in developing countries (Jones 1997; Barnett 2000; Cook & Uchida 2003). A time series analysis on a gradual process of privatization is also included (Shukurov, Maitah & Smutka 2016) as well as a case study on post-privatization performance among Zambian firms (Serlemitsos & Fusco 2003). The privatization of the Zambian copper mines could be used as the basis for designing similar undertakings in other countries. Because
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of this, it is important to map all potential effects that this programme had on the Zambian economy, including the subject of this thesis. The methodology used by the previous research is unsuitable for evaluating a single, significant privatization, as in the case of the privatization of ZCCM. The differing methodology used in this thesis allows for the detection of potential macroeconomic effects that could not be established by previous research on the subject, contributing with filling a gap left by these papers.
The thesis uses quantitative data, a qualitative field study and established theory on the subject to discuss whether the privatization of the Zambian copper mines influenced Zambian GDP per capita, and its growth. Aside from this, the empirical test also sheds some light on other interesting topics such as the relation between economic growth and the demand for copper, as well as the relation between the Zambian economy and the surrounding region. The main question addressed in this thesis is:
Can the privatization of ZCCM be related to structural breaks in Zambian GDP per capita? The quantitative analysis is based on macro-level time series data for the period 1955-2017. The empirical tests involve different methods of testing for unit root, i.e. if a time series returns to a constant mean or if economic shocks have permanent effects. The focus within this theoretic approach lies in finding potential structural breaks. A structural break is defined as an event in a time series resulting in a permanent change the mean or trend, at some point in time. The presence of such a break can often give misleading results in a test for unit root. Variants of these tests are run on Zambian time series with the purpose of detecting whether effects from the privatization of Zambian copper mines seems to have had a macroeconomic effect. Various Zambian time series derived from GDP per capita are used to detect structural breaks, for example, expenditure and output side GDP per capita, its log form, and growth rate. To control for exogenous factors playing a role in the GDP per capita of Zambia, tests are also conducted on variables that could have an effect on the Zambian economy. This is done in order to see if potential structural breaks in Zambian GDP per capita coincide with breaks in other indicators. The first group of exogenous variables consist of six of Zambia’s neighbouring countries, the idea being that these countries are interdependent on each other as, among other things, they serve as a trade link for each other. The other exogenous factor is the price of copper. Zambia is a natural resource dependent country, which could mean that the demand for copper has a significant effect on the output of the country. In addition, to investigate the relationship between the copper market and the Zambian economy, a Granger test for causality is also run.
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The Granger method tests whether the price of copper is a good tool for forecasting Zambian GDP per capita.
The results show that there is a possible structural break in the Zambian GDP per capita around the year 1998, although it is hard to attribute any change to the privatization of ZCCM. Wide public reforms as well as other factors occurred around the year 1998, pointing towards the break being a result of several shocks to the economy of Zambia. The region surrounding Zambia does not seem to affect Zambian GDP per capita enough for a structural break to spill over from the neighbouring countries. The price of copper shows a possible structural break around the year 2003, where prices rose dramatically. This may have affected the Zambian GDP per capita but cannot be the sole cause of the potential structural break as it occurs after the Zambian Break. The limitations in the relationship between the price of copper and the Zambian economy is further supported by the Granger test for causality, showing that the price of copper is not a good forecaster for Zambian GDP per capita.
The thesis is outlined as follows. Section 2 presents an institutional background of the country Zambia, and its place in the international market for copper. Theoretical aspects on privatization and growth are discussed in Section 3, and previous studies are presented in Section 4. Section 5 offers a walkthrough of data and includes a discussion on data sources used and how they were prioritized, as well as which economic indicators were used and why. The empirical methodology in Section 6 presents the econometric tests used in the time series analysis, the qualitative methodology used in the field study, covering ethical matters and methods of conducting an interview. After this, the results of the empirical tests are presented in Section 7 and are discussed in Section 8. The thesis concludes with Section 9.
2. Institutional Background
Prior to independence, Zambia was a British territory called Northern Rhodesia (Central Intelligence Agency 2019). Development was driven by mining of natural resources, among others, copper, cobalt, zinc, lead and other minerals. Zambia is historically one of the most politically stable countries in Africa (AfDB/OECD 2003). Gaining independence in 1964, Zambia saw a long period of one-party rule under President Kenneth Kaunda. Under this period, markets were centralized, and the focus of the state-owned enterprises was to keep high employment rates, rather than profitability (Limpitlaw 2011). The end of one-party rule in
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Zambia came in 1991, when the Movement for Multi-Party Democracy won the election (AfDB/OECD 2003). The new government committed to readjusting Zambia into a market economy, both by deregulation and privatization. In 1992, large scale privatization programmes were enacted to reduce the enormous public sector. This privatization encompassed 280 companies and was overseen by the Zambia Privatization Agency (ZPA). Most of these companies were sold to Zambian residents, many of whom encountered problems related to a poorly functional credit market which hampered much needed investments into the newly privatized companies. The separate project of privatizing the copper mines did not succeed in selling the mines at first, which led to a delay until the end of the 1990’s.
Other significant events include the AIDS pandemic, which hit Zambia hard during the 1990’s (AfDB/OECD 2003). Life expectancy decreased by ten years during the pandemic. The Zambian economy is periodically hampered by draughts, damaging agriculture output. Because Zambia is prone to draughts, the country is vulnerable to climate change and have no real methods of handling it (Cheelo 2019). Zambia is also currently experiencing a power crisis (Kaunda 2019). Not enough energy is being produced which leads to regular black outs during some seasons of the year. The power cuts have significant impact on Zambia’s industry. In the year 2011, policymaking in Zambia shifted to a more expansionary approach, with large infrastructure projects. Cheelo (2019) argues that a recent downturn in economic growth could be a result of inefficient government spending, which increases public debt and does not benefit the private market’s role in leading economic growth in Zambia.
Table 1. Developments in the Zambian economy
1965 1996 2017
Value added, agriculture 19% 28% 8%
Value added, industry 33% 28% 33%
Value added, services 48% 44% 58%
Formal employment rate (age 15+) unavailable 67% 69%
Source: World Bank Open Data (2020).
Note: Value added given as share of the sum of agriculture, industry and services sectors.
Table 1 is an overview of the economic sectors in Zambia. Agriculture rose in the period leading up to 1996, falling to eight percent in 2017, with an increase in the services industry. The industry sector is relatively stable throughout the period. In summary of the Zambian economy, agriculture is an important part of the Zambian economy (AfDB/OECD 2003). Aside from natural resources, Zambia has access to more fertile lands and bodies of water suitable for
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fishing than the countries in the neighbouring region. A large share of the agricultural sector consists of traditionally run farming, with a lack of industrialization leading to inefficiencies in the operation of farms (AfDB/OECD 2003). During the one-party era, the public sector was involved in agriculture and encouraged corn-farming. The industry sector is, apart from mining, made up of manufacturing. The manufacturing is partly made up of the processing of minerals, but also some production of goods (Zambia Development Agency n.d.). The goods are mostly sold domestically, with a small amount being exported to the surrounding region. Tourism is a large contributor to the service sector. Improvements in infrastructure allowing for a higher capacity of tourism to attractions in Zambia has led to this being a growing sector in Zambia.
2.1. Zambia as part of the international market for copper
What sets copper apart from combustible natural resources such as coal and oil is that it to a large extent is not used for final consumption. Around one third of all consumed copper is recycled (Geology and Earth Science News and Information n.d.). A large proportion of the mined copper is also locked into long-term infrastructure, such as buildings. This leads to a figure of at least 65 percent of all historically mined copper still being in use today (European Copper Institute n.d.). This means that some base demand will be met even without mining of new copper. Copper mining instead satisfies increases in demand and production of goods. Being a finite natural resource, extraction of copper will start decreasing with time at some point. This point has not been reached yet and global copper production is still rising yearly (Brininstool 2017). Substitutes for copper include steel, aluminium, titanium, optical fibre and plastic.
Fluctuations in copper prices appear, as one would expect, based on the supply and demand for the resource (Guzmán & Silvia 2018). There are also more complex factors in play, such as monetary liquidity in large customer countries of final goods made of copper having a positive relation with prices. This can be explained by rising monetary liquidity increasing the demand for goods and thereby indirectly raising the demand for copper. Copper being used as a speculative asset can also impact prices. Output of copper seems to be relatively stable, meaning that changes in demand is normally the driver of price changes. Guzmán and Silvia (2018) argues that two significant events have affected copper prices in the past 20 years, namely the rising demand for copper in China and the financial crisis of 2007-2008. Around 2003, the price of copper entered an upwards trend. This can be explained by a demand shock called the
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Chinese boom. This increase in demand was kept steady for multiple years. The failure, or lack of capacity of global copper mining to meet the increase in demand led to a sharp increase in the price of copper in this period, with prices settling at around three times its pre-shock levels. The second shock came in 2008 as a result of lower global demand following the economic crisis, which started a year earlier. This was initially recorded as a temporary negative spike in prices, followed by a long-term downwards trend.
Table 2. Copper mining factsheet for 2016
Global copper production, in tons 19,400,000
Zambian copper production, in tons 740,000
Zambian copper production as a share of global production 3.8 % Value of produced copper in Zambia, as a share of GDP 15.5 % Estimated unexploited global stock of copper, in tons 5,600,000,000
Source: United States Geological Survey (2017); Penn World Table 9.1 (2015).
Zambia is the eighth largest producer of copper in the world and the second largest in Africa, after the Democratic Republic of the Congo. Even though Zambia is a large producer, the sheer amount of output in the highest producing nations in South America means that Zambia only accounts for roughly four percent of the global production; see Table 2. This should indicate that Zambia has limited power in terms of pricing on the market, but this is grounds for further research.
The copper mines are so important to the Zambian economy that the performance of the country is linked to the output of the copper mines and the demand for copper (Sikamo, Mwanza & Mweemba 2016). In 2016, the value of the produced copper in Zambia was around 16 percent of GDP; see Table 2. Considering the price of copper can change significantly from year to year, the 2016 value of copper as a share of GDP suggests just how much the price and demand for copper can influence the Zambian economy. Thus, a change in the operation of the Zambian copper mines following the privatization may have had consequences significant enough to be recorded as macroeconomic effects.
2.2. The case of the privatization of Zambian Consolidated Copper Mines Ltd.
The copper mines in Zambia were not always state owned prior to privatization (Limpitlaw 2011). The mines were nationalized in 1969 as a mean of guaranteeing employment and to develop rural areas of the country. The state-owned company Zambia Consolidated Copper
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Mines Ltd. was formed. While ZCCM was not entirely owned by the Zambian government, all “A”-Shares were owned by the government, corresponding to a total of 60 percent of the shares (ZCCM Investments Holdings Plc 1996).
Table 3. Zambia Consolidated Copper Mines Ltd. factsheet
ZCCM 1996 1995
Zambian GDP 4,345,176 3,289,248
Revenue 1,591,158 1,121,301
Fixed assets and mineral reserves 1,935,996 1,852,006
Revenue, as % of GDP 37% 34%
Value added, as % of gross value added 13% 13%
Total number of employees 42 081 Unknown
Source: World Bank Open Data (2019); Zambia Consolidated Copper Mines Limited Annual Report (1996). Note: All monetary values given in current millions of Kwachas.
After the nationalization reform, profitability of the mining industry fell (Limpitlaw 2011). To some extent, this can be traced back to falling copper prices, but there are other factors as well. Investments needed to compensate for depreciating infrastructure were not made and thereby decreased output further. The mining operations also had a structure with roots in the colonial time where most social services in a mining town were provided by the mining company, further straining profitability. In 1986, the decrease in output had reached a point where several mining operations had shut down. The decision to sell ZCCM was made and the process begun in 1992 but did not successfully start until 1996. At this point, mining output had reduced to less than half of its pre-nationalization level.
The Zambian government faced the question of how the privatization should be done in practice. This was a complicated affair considering the size of the company (Craig 2001). The World Bank was involved in the process via funding the so-called Kienbaum report, which advised a plan based on breaking up ZCCM into smaller assets that could be sold, as reported by Craig (2001). The primary motivation of this unbundling strategy was that the buyer’s influence on the government would be reduced if there were multiple owners, as opposed to one large actor controlling the entire mining sector. The Kienbaum report also advised the government of Zambia to sell the majority of the shares of ZCCM to private owners, while retaining a minority share in each asset. Craig (2001) explains that a report prepared by the bank N.M. Rothchild and the lawyer firm Clifford Chance further developed the ideas of the Kienbaum report. This new report formulated a strategy for ZCCM to divide and sell the
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majority shares of its assets as in the original plan. After the assets were sold, a second phase of privatization would begin where ZCCM was transformed into a holding company for the remaining minority shares in the assets, and then the government would sell most of the shares in the holding company. Further, the government demanded that the new companies would be registered in Zambia and monitored by Zambian institutions (Craig 2001). The advantages of this newly developed approach were that it would strengthen investments and diversify ownership in the economy.
The plan developed by N.M. Rothchild and Clifford Chance was adopted but ground to a halt when ZCCM failed to sell any of the divided assets by 1995, resulting in help being sought from the World Bank (Craig 2001). This led to a restructuring of ZCCM as well as the separation of one of the most important assets, Konkola deep, from ZCCM. The remaining assets were divided into 10 parts, and bidding started in 1997. The plan was originally to complete the privatization in about two years. In mid-1998, the assets producing most of the copper in Zambia were still unsold. Falling copper prices were a cause for concern that made several potential buyers reconsider their positions.
The South African conglomerate Anglo-American company, hereafter referred to as AAC, was a large shareholder of ZCCM prior to the privatization and the company acquired Konkola Deep when it was separated from ZCCM in 1996. AAC now indicated interest to acquire the largest assets of ZCCM. Negotiations were slow and dragged on through 1999. In March 2000, all the assets of ZCCM were sold. Contrary to the early privatizations of state-owned enterprises in Zambia, the new owners of the copper mines consisted of a wide range of mostly foreign companies. The companies that bought the asset packages were based in the United States, Canada, South Africa, China, India, Switzerland and the United Kingdom (Craig 2001). Following this, the second stage of the plan proceeded and ZCCM was turned into a holding company called ZCCM Investment Holdings PLc., which still exists today.
2.3. Significant events in the economic history of Zambia
Zambia has been through multiple defining moments for the economy. The mapping of these events, seen in Table 4, is done in order to relate to the empirical analysis in Section 7 of structural breaks.
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Table 4. Summary of important events in the economic history of Zambia
Event Year Expected effect on
economic growth Independence, Kaunda is elected president 1964 negative Nationalization of copper mines 1969 negative Extensive public reforms 1992-2000 temporarily negative Market stabilizing after reforms 1998 positive
Privatization of ZCCM 1996-2000 unknown
HIV pandemic stabilizing 2000-2004 positive
Source: Kaunda (2019); Cheelo (2019); Limpitlaw (2011); Sikamo, Mwanza & Mweemba (2016); AfDB/OECD (2003). Note: Expected effect on economic growth is based on an interpretation of listed sources and is not empirically tested or proven.
Beginning with independence in 1964, this event could have many economic effects. One effect of President Kaunda getting elected during independence represented a shift in policymaking to a planned economy, which, according to Limpitlaw (2011) had negative consequences in terms of development through a change in focus towards mass employment, rather than growth. The nationalization of the Zambian copper mines in 1969 is the next big event, which was a result of President Kaunda’s policymaking. The production volumes of copper in Zambia started declining after this date. A second effect of the nationalization was that revenue from the mines were being used to fund other public projects. Draughts and deteriorating infrastructure strained the economy further during the 1980’s. This led to a decline in economic performance in Zambia after independence, when effects of the public policies were being felt. The performance was further negatively affected after the nationalization of mines and during the hardships of the 1980’s.
Following the introduction of the multi-party system, extensive public reforms were undertaken, between 1992 and 2000. These reforms consisted of removing monetary controls on prices, interest rates and exchange rates. Privatization shifted the leadership in the market to the private sector. The size of the public sector was also reduced. Cheelo (2019) argues that the persistence of the public reforms was what made it so successful, but also that it hampered growth in the economy under the duration of the reforms. This effect came as a result of an unstable market, leading many firms into liquidation. A negative effect on growth during the reforms is further supported by the privatization curve outlined by Serlemitsos and Fusco (2003), which recorded that performance of the firms generally suffered during the process of privatization. The market stabilized around 1998 (Cheelo 2019). The stability following the reforms is projected to be the main reason behind the most significant shift in the Zambian economy.
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Between 1996 and 2000, ZCCM was privatized (Craig 2001). The observable effects from this was that investments increased in the years immediately following the privatization (Sikamo, Mwanza & Mweemba 2016). There was also an increase in mining output, although this is not proven to be related to the privatization (Limpitlaw 2011). Nevertheless, the privatization fundamentally changed how the mining industry was being operated in Zambia (Craig 2001). In 1996, the value added by ZCCM was around 13 percent of the total value added in Zambia, suggesting how important the company was to the Zambian economy and how a change in its operation could have effects significant enough to be recorded as a change in the economic performance of Zambia; see Table 3.
Zambia was hit hard by the HIV pandemic (AfDB/OECD 2003). It is not possible to determine an exact date when the crisis started and ended. It affected Zambia the hardest during the 1990’s. From an economic point of view, the pandemic was primarily a human capital shock, as life expectancy decreased and even went so far that schools did not have enough teachers. The economic development was further negatively impacted because the government had to divert focus and resources to managing the pandemic (Cheelo 2019). Between 2000-2004, Zambia was able to manage the crisis with more success. The government’s ability to refocus on policymaking geared towards economic growth marked the end of the projected negative effect, as reported by Cheelo (2019).
3. Theory
The theory behind the topics of GDP per capita, economic growth and privatization programmes serve as a reference point to compare with the empirical findings. The history of widely adopted privatization programmes across the globe started during the late 1980’s (Kikeri & Nellis 2004). Before this, policymakers could only speculate about the potential benefits of privatization of public enterprises. One potential benefit of privatization before the facts were in was that state-owned activities often lack competition, which thus means that they could be operating in an inefficient way. It was only after these programmes were finalized though that they could be assessed, and the effects empirically tested. There are some potential downsides to privatization programmes (Kikeri & Nellis 2004). While social welfare could increase, Kikeri and Nellis (2004) explains that critics often bring up that these benefits could be unequally distributed, and the welfare of the average consumer could potentially decrease. Increased inequalities could hamper GDP per capita growth as low income earners may have less access
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to loans that would be used for investments, as this part of the population would have less assets to use as collateral (Bourguignon 2015).
The effects of privatization have been more easily assessed in developed countries (Kikeri & Nellis 2004). A large extent of the research has focused on the changes in production and investment related to the privatization of assets. The effects that have been found range from increased total welfare to growth and fiscal benefits. In turn, the main downside of privatization is potentially increased unemployment in the industry as the new owners scale down or streamline the activities of the new firms. Increased unemployment would make less income available for consumption and investments, thereby hampering GDP per capita (Gottfries 2013). The changes in unemployment related to privatizations tend to be small in proportion to the total unemployment rate of the country (Kikeri & Nellis 2004). It is important to note that the benefits of privatization depend on the type on industry that is subject to a change in owners.
3.1. Potential benefits for transitional economies
Kikeri and Nellis (2004) state that a large share of the privatization programmes was conducted in developing countries. There are a multitude of studies done on the benefits of privatization in developing countries that can explain why privatizations tend to be more prevalent in these settings. One important explanation is the fiscal benefits mentioned earlier. Campbell, White and Bhatia (1998) finds that the most common goal of privatizing in African countries is reducing the fiscal burden. Public debt is created when government expenditure is larger than income. A high public debt-to-GDP ratio means that a large proportion of the budget will be allocated to paying interest on the loans (Gottfries 2013). Privatizations alleviates the fiscal burden via generating income from the sale of public assets. It also reduces the budget by removing expenditures associated with operating the enterprises (Campbell, White & Bhatia 1998). Reduced fiscal strains can lead to one of two things. It could allow the government to reduce taxes, which would allow the population to spend a larger proportion of their income on consumption and investments, thereby increasing GDP per capita (Gottfries 2013). Reduced debts could also mean more capital is available for government consumption, which would also increase GDP per capita, although this could lead the central bank to increase the interest rate, leading to a crowding out of a proportion of the increase in GDP per capita. Reduced tax or increased public spending could lead to more revenue being available for use by the public or private sectors, allowing for a permanent higher level of consumption or investment.
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The other reasons are mostly related to creating a stronger private sector (Campbell, White & Bhatia 1998). This means that privatization could have positive effects on the education levels, market competition and expanding the capital market by shifting ownership of certain assets from public to private. A better functioning capital market could increase investments as a larger share of the population has access to loans (Restuccia & Rogerson 2017). More competition in the market will force the firms to operate efficiently and will also lead to increases in real wage since market competition will decrease the mark-up of prices available to firms (Gottfries 2013). An increase in the real wage would allow for higher consumption and investment by the labour force, while better education would primarily benefit economic growth, explained in section 3.2.
3.2. The relation between privatizations and economic growth
The relation between the potential effects of privatisation programmes and the theory on both GDP per capita and its growth rate is the primary interest of this thesis. Thus, some insights into theories on GDP per capita growth at the macroeconomic level are required to establish how GDP per capita and its growth could be affected by the privatization. The theory established by Solow (1956) and models derived from it can help explain why a reform like the privatization of ZCCM could impact the growth of the country. The primary driver of long run growth in the basic Solow model is technological improvements. The concepts of transitions and sustainable growth are important. Aside from the ongoing growth of technology, a country will only experience growth per worker temporarily as a shock to the parameters, e.g. a change in investment rate, and transition the economy to a new steady state output level. Relating this to the topic of privatizations, this means that potential effects of a privatization programme can take two forms. It could lead to a transition to a permanent new income level but with no lasting effects on growth. This transition could be the result of the economic reform shifting the amount of investments in the economy. The other possibility is one where it affects the permanent growth rate of the economy, which could be a result of a faster growth rate of technology in the economy. In a time series, a transition would be represented by a change in intercept, while a permanent change in growth rate would be recorded as a change in slope.
Being a developing country, there are some additions to the theory on economic growth that could represent Zambia better. A development of the exogenous growth rate of technology suggests that the technology level will be determined more by the ability to adopt already
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existing technology, as opposed to developing it (Jones & Vollrath 2013). The country can only adopt the technology its inhabitants are able to use, with the degree of education being the determinant of how much technology an individual can use. The inclusion of education into the equation leads to the conclusion that technology adoption must grow at the same rate as the technology development of the frontier countries. Intellectual property rights are an important driver of technology as it incentivises research via securing the right to profit of an invention. These rights may or may not extend outside of the technological frontier. Further, some newly developed technologies are designed for a market ready to adopt them, possibly making them unusable or ineffective in developing countries. Since the indicator being investigated in this thesis is GDP per capita, production by foreign-owned companies operating inside the borders of the country are included in the measurement. If a foreign company sets up business in Zambia as a result of a privatization, it could bring new technologies with it. Foreign educated workers moving in from countries with a higher level of technology to work with a newly bought company could also affect the ability of the labour force to use new technology, thereby affecting economic growth. A foreign company’s willingness to establish itself in a developing country could also be influenced by if the exclusive rights to their technology is protected or not.
Another perspective to consider is that Zambia is a natural resource dependent country (Sikamo, Mwanza & Mweemba 2016). Because a large portion of the economy relies on a diminishing stock of a finite natural resource, economic growth will slow down with time (Jones & Vollrath 2013). The natural resource is also being divided over more workers as population grows, further straining growth. While the consequences on dependency on natural resources are useful to keep in mind, Zambia has not reached a point where copper production seems to be diminishing (Sikamo, Mwanza & Mweemba 2016). Output of copper is still rising and there are areas suitable for new copper mines that have not yet been exploited (Schuler & Lokanc 2015). There is also the consideration that the total stock of natural resources is not known, with a likelihood that more copper will be found in Zambia, if explorations are made. If the privatization of ZCCM led to more copper being discovered by the buyers, the effect could be a higher level of, still diminishing, economic growth. The higher GDP per capita growth relies on the assumption that a constant share of the natural resource is being used each year, with a share of a now larger of stock of copper after the discovery, reducing the strain on growth.
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3.3. Summary of possible macroeconomic effects of the privatization of
ZCCM
GDP per capita and its growth could be affected by the privatization of ZCCM via the theories in section 3.2. and 3.1. The effects could either be a change in consumption, investments or government spending, or it could be via a change affecting the growth theories. While consumption, investment and government spending measures total output and not per capita output, it retains the same effects on output per capita, if the population is assumed to remain unchanged as a result of the effects.
Table 5. Macroeconomic effects of privatizations
Potential cause Projected effect Resulting in
Increased competition Increases in productivity, lower mark-ups increasing real wage
Temporarily higher growth, consumption and investment levels increase
Reduced fiscal burden Either reduce taxes or increases available government revenue
Increases in government spending, investment or consumption levels Unequal distribution Reducing opportunities among low-income
earners
Decreases in investment level Increases in human capital Allows adoption of more advanced
technologies
Temporarily higher growth Better capital market Better access to loans Increases in investment level Increased unemployment Less income available to consumers Decreases in investment and
consumption levels Discovery of new copper A higher stock of natural resources being
available for exploitation
Permanent higher level of output Foreign companies setting up Influx of investments, human capital and
technology
Temporarily higher growth, increase in investment level
Note: Based on all effects and results outlined in section 3, 3.1 and 3.2
Summarizing all the possible effects of a privatization outlined in section 3, 3.1 and 3.2, most effects are found to be positive; see Table 5. The macroeconomic effects become more understandable when considering the privatization of ZCCM consisted of 13 percent of the economy being shifted into private hands; see Table 3.
4. Previous research
Most studies done on the relationship between GDP per capita and privatizations investigates the growth rate and not the total GDP per capita. There are three major papers (Plane 1997; Barnett 2000; Cook & Uchida 2003) that have investigated the relation between privatization
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and growth in developing countries at a macroeconomic level. These have in common that they use a cross section of countries to test their hypotheses. This section also presents an example of a study using time series analysis to investigate the relationship between privatizations and economic growth (Shukurov, Maitah & Smutka 2016). While the empirical tests of the four papers are fundamentally different in their methodology, the question they ask is similar to that of this thesis. The macroeconomic studies are presented below in sub-section 4.1, while case studies of ZCCM and similar cases, as well as a sample of microeconomic studies, are presented in sub-section 4.2 and 4.3.
4.1. Privatizations and economic growth in developing countries
Plane (1997) investigates the relationship between economic growth and privatization programmes in 35 developing countries from all over the world with a stated intent to privatize. The empirical test uses a Probit and Tobit model for the period 1988-1992. The aim was not only to establish if privatizations benefit growth, but also to explore what makes a successful privatization. The results show that privatizations have a positive effect on growth. The positive effects are projected to arise from strengthened institutions, a more transparent economy and the market’s ability to stabilize prices in the country. It also indicates that privatizations seem to have a bigger economic impact if they take place within the infrastructure or industry sector. Plane (1997) also mentions that a lot of research has been made on the topic of privatizations but very few studies focus on the macroeconomic level. Zambia is included among the countries in the cross section, but the period analysed is before the Zambian privatizations started. An IMF working paper written by Barnett (2000) looks at macroeconomic effects of privatization. The study uses 18 countries during their privatization reforms. The countries are developing countries of no specific continent. The first of the two questions that are covered by the paper is if privatization revenue is spent or saved. The second is whether privatizations have a macroeconomic effect on an economy. The empirical test consists of a regression where revenue generated from privatizations, as well as total amount of privatization, are the explanatory variables. Barnett finds a strong and robust correlation between economic growth and privatization. The positive effect of privatizations seems to be recorded instantly with a diminishing lagged effect over time, potentially representing a transition in the economy to a new higher output level. Opposite to what critics of privatizations argue, Barnett finds that there is a negative relationship between privatizations and unemployment. Barnett does, however,
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advise caution to his findings because other political reforms and more efficient policies being implemented at the same time could be captured within this correlation.
A paper by Cook and Uchida (2003) uses a cross section of 63 countries and performs an extreme bounds analysis. The sample is larger than in the other two papers and are picked from developing countries. The results of this paper contradict the ones by Plane (1997) and Barnett (2000) as it points towards a negative relationship between growth and privatization. Cook and Uchida admits that the methods used cannot rule out the problem established by Barnett (2000) related to other policies being captured by the privatization variable.
Following the fall of the Soviet Union, extensive privatization reforms were implemented in the former Eastern Bloc. The reforms in the Eastern economies can be related to the privatization of ZCCM as the Zambian economy were in a similar process of reforms following the move to multi-party democracy. One of the studies was made by Shukurov, Maitah and Smutka (2016), which investigates the gradual privatization of the economy of Uzbekistan using time series analysis. The impact of privatizations was measured on the log of GDP per capita growth. A gradual process of privatization in Uzbekistan made the estimated model suitable as an annually changing level of privatization could be compared to other factors affecting economic growth. The privatization index used as a variable showed an insignificant effect on GDP per capita growth. The development of the capital market and share of the private sector, which could both be an affected by the privatizations, were found to be significant. In summary of the methodology of the previous research, the methods involving a cross-section of data between countries used by Plane (1997), Barnett (2000), Cook and Uchida (2003) has the main advantage of being able to establish the general patterns of the effects of privatization programmes. A cross-sectional study of macroeconomic effects between countries is, however, less suitable for investigating the effects of individual privatizations, especially over time. A time series analysis using multiple regression is a useful method for measuring the macroeconomic effects within one country over time. This method, used by Shukurov, Maitah and Smutka (2016) can investigate a gradual process of privatization taking place over many years, while accounting for other factors influencing the dependent variable. A weakness of running a regression on time series data is, not unlike that of the regular cross-sectional study, that it can only measure a privatization’s immediate or lagged effect on economic performance. This makes the time series multiple regression method less suitable for measuring lasting effects of a single, large privatization.
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4.2. Case studies of the privatization of ZCCM
Not many peer reviewed papers have been published that study the effect of the privatization of ZCCM. There are, however, a few relevant papers that should be mentioned.
Craig (2001) explains how the privatization of ZCCM was conducted in practice and which other options existed for the Zambian government. The paper explains how a number of factors, such as deteriorating infrastructure and the outstanding debts of ZCCM shaped the process of privatization. Craig presents a historical background to the case without making any conclusions about post-privatization effects. Nevertheless, the paper highlights how complicated the process of privatization was.
A post-privatization study by Serlemitsos and Fusco (2003) investigates the effects of the privatization programme in Zambia on the micro level. The study covers the changes in performance of Zambian firms during, and following, the privatization. The firms in question are not copper mines, but companies that were privatized along with, and before, ZCCM in the early stages of the public reforms that started in 1992 and are related to the copper mines via their differing levels of dependence on the copper mines. The results show that most companies experienced poor performance during the period of the privatization, with smaller firms often experiencing negative growth rates, in terms of revenue. The firms appeared to follow a trend where performance dropped during the privatization, recovered the year after and then stagnated during the third year. Assets purchased by foreign investors performed better than domestic ones, possibly a result of Zambians preferring to invest in companies that later were more affected by the market liberalization. Export oriented companies were also affected by privatizations. The firms with a moderately strong dependence on the mines were negatively affected, possibly as a result of the newly privatized copper mines reassessing and changing their suppliers. The performance of firms with a strong relation to the mines had a performance that was more tied to how the mining sector was performing, rather than following the trends experienced by other privatized firms. The study by Serlemitsos and Fusco was conducted just a few years after the privatization was concluded and so does not follow up on more than a couple of years following the finalisation of the reforms.
A paper formed as a summary of established research on the subject of privatization includes some points related to the privatization of ZCCM (Parker & Kikpatrick 2005). Parker and Kikpatrick discuss methodological problems related to quantitative studies on privatizations. One of the problems is that it is impossible to know what would have happened if a reform was
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not undertaken i.e., the counterfactual. This is a concern also highlighted by the studies by Plane (1997), Barnett (2000), Cook and Uchida (2003), where it is difficult or impossible to prove that the changes in economic performance is a result of a privatization and not some other reform or event that happened at the same time. An alternative to studies with a cross-section of countries, is case studies. However, a case study faces other limitations. The researcher in a case study has more influence over the result of the study. This is because a case study most often cannot test a hypothesis empirically and has to rely on the researcher’s own interpretation of events. It is critical to keep this in mind throughout this thesis to avoid claiming a causality that cannot be proven empirically.
There are also problems related to the scope of studies. A privatization can have a large number of effects outside of the performance of firms. Establishing other effects, such as effects on the income distribution can be hard. There is also a problem mostly related to developing countries where some data can be unavailable or hard to interpret. Changes in unemployment could represent changes in the number of jobs available, but it could also be a result of people previously outside the system of formal occupation, entering the work force. Parker and Kikpatrick (2005) highlights that the success of a privatization reform depends on how it was prepared and implemented, which gives hints as to what can be expected from a case study.
4.3. Firm-level studies on privatizations
Studies on the effects of privatizations have also been made outside the field of macroeconomics. When studying effects on the microeconomic level, performance of individual firms that were privatized or related to the privatized firms is the primary interest. The methodology and conclusions of microeconomic papers have a weak but important connection to the topic of this thesis. A summary of a selection of microeconomic papers could be useful to explain which changes occurs within the individual firms and industries, which in turn could partly explain how the potential macroeconomic effects arise. Empirical evidence of the microeconomic effects lends weight to the sources that describe the effects compiled in Table 5. The three following papers represent a diverse view on privatization and microeconomics, covering a general study, a study in a developing setting as well as one set in an environment in a state of economic transformation.
D'souza and Megginson (1999) investigated the change in performance among 85 firms from both developing and developed nations. The definition of performance lies in the investigated
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variables, among them changes in employment, efficiency and output, which are variables that could lead to macroeconomic effects. The empirical test finds that output and efficiency increased after privatization, while the effect on employment within the firms is negative but statistically insignificant.
Porta and López-De-Silanes (1999) investigates one of the early major privatization programmes, the privatization of Mexican state-owned enterprises of the late 1980’s. The paper does not investigate whether there was an increase in performance among privatized firms, but what the causes of increased performance could be. A contribution towards the question of whether increased total benefit comes at the cost of increased inequalities, as firms could increase prices, lower wages or decrease their employment levels following privatizations. The study finds that most of the inequalities are caused by decreasing employment, but also that this is a relatively small contributor to the increased performance of firms, which is largely attributed to increases in productivity.
Compiling papers published on the topic of privatization in transitional economies, Djankov and Murrell (2002) examined firm performance in eastern Europe and the Commonwealth of Independent States (CIS) following the fall of the Soviet Union. The majority of the research show that post-privatization performance increased in eastern Europe but not in the CIS region. In the CIS, ownership often passed to managers and other employees after the privatization, as opposed to the, mostly foreign, investors acquiring privatized firms in eastern Europe. The cause for the lacking change in performance in the CIS was attributed to the assumption that a managerial ownership is as inefficient as state-ownership. This further highlight how important the design and implementation of the privatization process is to its success.
5. Data
The variables investigated are primarily real GDP per capita and its growth rate. The choice of using GDP per capita instead of total GDP is motivated by their different reactions to population growth rates. Constant population growth would be recorded as a positive influence on GDP, even though it has no real effect on the level of output per person (Jones & Vollrath 2013). GDP per capita is affected by shocks in the population growth rate, a shock means that the capital stock is divided by more workers, which lowers output per worker. GDP per capita is not, however, affected by a constant rate of population growth, as capital is invested to keep the
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capital stock per worker constant. A change in GDP per capita from one year to another translates to GDP per capita growth, which means that the causes and determinants affects GDP per capita via its growth rate, leading to the decision of including both GDP per capita and the growth rate of GDP per capita in the empirical tests.
Data on GDP per capita is available from sources such as Penn World Table, World Bank and the Zambian Central Statistics Office. Because of the nature of the econometric tests, having as many datapoints as possible gives a more reliable result. In an ideal world, quarterly data would be used to increase the length of the series. This, however, is unavailable for any significant time period for Zambia. When determining which source to use, priority is given to the time series with the highest number of recorded data points. In the end, most data were taken from the Penn World Table version 9.1 (Feenstra, Inklaar & Timmer 2015). The Zambian indicators in the Penn World Table generally start around 1955. Because both expenditure and output side GDP per capita were found for Zambian GDP per capita, both are included for the empirical test. To test different ways a structural break could appear, GDP per capita was divided into three different formats. The first one is real GDP per capita as purchasing power parity. Second, the growth rate of GDP per capita is included. Since this is what determines the change in level of GDP per capita, a break could also appear in this data, with different implications. Third, the log of GDP per capita is taken. Since GDP per capita often grows exponentially as a result of sustained growth, the log could linearize the GDP per capita and make a trend break easier to detect. All variants of Zambian GDP per capita uses a time series starting in 1955 and ending in 2017.
A group consisting of Zambia’s neighbouring countries is also included in the analysis to compare if results of the empirical test appear to be similar in other countries in the region, and thereby if it is likely that changes in the Zambian economy is a result of endogenous changes, such as policymaking. This group includes all countries with a border to Zambia excluding Angola and the Democratic Republic of the Congo. The Democratic Republic of Congo was excluded due to conflicts in the country likely interfering with general trends of the region. Angola was left out due to lack of data, with a time series starting in 1970. All data measuring GDP per capita in the neighbouring region uses a time series starting in 1960 and ending in 2017.
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Figure 1. Zambian GDP per capita and price of copper
Source: Penn World Table 9.1 (2015) & World Bank (2019).
Figure 1 shows real Zambian GDP per capita and the price of copper, and the possible correlation between them. In periods with spikes in the price of copper, GDP per capita of Zambia seems to follow. There seems to be a change in the trend of both the Zambian GDP per capita and the price of copper around the turn of the century, which raises the question whether the price of copper can be used to explain the economic performance of Zambia. To investigate a potential relation between the copper market and the Zambian economy, the price of copper is included in the analysis. The time series on the price of copper starts in 1960 and ends in 2018.
6. Empirical methodology
As outlined in section 4, there is a variety of previous research conducted on the subject of macroeconomic effects of privatisations. Choosing the methodology most suitable for the empirical tests of this thesis is done by discussing the strength and weaknesses from the methods used in the previous research, as well as alternative approaches.
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 1 9 6 0 1 9 6 3 1 9 6 6 1 9 6 9 1 9 7 2 1 9 7 5 1 9 7 8 1 9 8 1 1 9 8 4 1 9 8 7 1 9 9 0 1 9 9 3 1 9 9 6 1 9 9 9 2 0 0 2 2 0 0 5 2 0 0 8 2 0 1 1 2 0 1 4 2 0 1 7 P rice p er to n ( co n stan t u sd ) GDP p er ca p ita (p p p ) Year
Zambian GDP per capita and price of copper
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6.1. Motivation for the choice of methodology
For a case like the privatization of ZCCM, where a single, though dominant firm is being investigated, a different approach to the ones presented in the research in section 4.1 is needed as the radical change takes place within a single or a few time periods. One test could involve representing time periods after the privatization of the firm with a dummy variable which tests if there is a change in the dependent variable following the privatization, while accounting for other factors using other variables with an effect on the dependent variable. A problem with this approach is that time series data needs to be stationary to give reliable results in a multiple regression (Wooldridge 2016). Many economic indicators being investigated will be turned stationary by using its first difference instead of their absolute values, i.e. the annual change of the variables. This means that if the privatization for example causes a large, instant change in GDP per capita level, it will only be recorded in the data being tested as a single period of higher or lower GDP per capita growth, even though there could be a lasting effect in the form of a permanent different output level. Another problem is the exogenous choice of where the dummy variable is placed. A dummy variable placed at any year around the start of a period of high growth would likely give a statistically significant result, even though it may not be the actual year that marked the start of high growth. A final problem revolves around the need to include dummy variables for other events affecting the dependent variable. The number of events makes the multiple variable analysis more unfeasible and poses the question of whether there is a method that could instead choose a significant date in the time series endogenously, which could then be related to important economic events afterwards.
Using a methodology involving tests for structural breaks solves the problems of unclear or inconclusive results caused by the requirement for stationarity and exogenous choosing of a time for the tested event. A structural break is a sudden, lasting change in the trend or mean of a time series, explained in detail in section 6.3. There are methods of detecting these kinds of breaks endogenously. Tests for structural breaks could find if there is a permanent effect of an event, something that could not be investigated via a multiple regression. It would also find the most likely point in time for a break, which would be a more credible result than the researcher simply testing for a permanent change in his or her own point of interest using a dummy variable. With this in mind, tests for structural breaks are chosen as the method for investigating the effects of the privatization of ZCCM in this thesis.
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Using the methodology of structural breaks contributes to filling the gap in the analysis of the macroeconomic effects of privatizations left by the methods used by Plane (1997), Barnett (2000), Cook, Uchida (2003), Shukurov, Maitah and Smutka (2016). This is done by identifying potential structural breaks in the indicators outlined in section 5 with the purpose of finding out if there are any breaks around the time of the privatization of ZCCM. This section will provide a walkthrough of which tests are used to accomplish the purpose and how they work.
A structural break could be caused by any major change within, or outside the economy (Libanio 2005). A significant difficulty is therefore the question of whether a potential structural break is actually caused by the event in question, in this case the privatization of ZCCM, or by some other event or combination of events taking place at the same time. The purpose of the qualitative field study is to gather events in the economic history of Zambia that could be alternative causes to potential structural breaks. Since there is no way of setting up a testable hypothesis with the aim of supporting whether the privatization of ZCCM caused a structural break or not, it is important to support the discussion with as much information about alternative causes as possible.
The potential alternative causes could be investigated and discussed, although empirically proving any cause for a possible structural break in a time series is not possible. Investigating every possible alternative cause for a structural break would also be impossible, and mostly limited to speculation because of the lack of testable data. There are, however, a few possible causes that could be investigated due to them being recorded by a matching time series, on which the same tests for structural breaks could be applied to. A structural break appearing at the same time, or in a few periods before a Zambian break could mean it is a possible cause. A structural break appearing at a time after the Zambian break would logically rule the indicator out from being the sole cause of the break.
A structural break represents a significant shift in an economy that is unlikely to be caused by a small policy adjustment, such as a change in interest rate (Perron 1989). This leads the search for possible causes to something that defines and determines the state of the Zambian economy. The Zambian economy’s reliance on copper is assumed to be one of these. The relationship between the Zambian economy and demand for copper is explained in section 2.1. The price of copper could be a reasonable cause for a Zambian structural break if the break would take place at the same time as a sudden, long term change in the price of copper. Further, instead of relying
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on the claim that the price of copper is a major influence on the Zambian economy, the relationship is tested to aid in the discussion of a possible break having a significant effect on the Zambian Economy. Secondly, Zambia being a landlocked country means that the country could be reliant on the performance of its neighbours, mainly due to the trade relationship with these countries (Kaunda 2019). If structural breaks would appear in many of the indicators of neighbouring countries at the same time as a Zambian break, a change in the economic performance in the region could be a possible cause.
6.2. Unit roots
The econometrics implemented in the empirical test is based on theory on stationarity, unit roots and structural breaks. Stationarity of a time series is important to consider when running most sorts of statistical tests in time series analysis (Wooldridge 2016). This is because getting reliable results often relies, among others, on the assumption of the variable in question being stationary over time. If one were to run a regression on a nonstationary time series the results would often be misleading, with unrealistically high 𝑅2 values and t-statistics (Libanio 2005). A variable is defined as stationary if its properties does not change over time (Wooldridge 2016). This means that in a stationary time series, the mean and variance of the sample are constant in all periods included. The alternative to a stationary time series is a nonstationary one. A nonstationary time series is described as having a unit root present (Libanio 2005). In a stationary series, a shock will not have a permanent effect on the variable. Instead, it will revert to its mean in the long run. The presence of a unit root means that the values of the time series will not return to a long term mean after a shock.
𝑦𝑡= 𝜇 + 𝛿𝑡 + 𝑒𝑡 (1)
Equation (1) explains a process with a trend in the 𝑦 values of the series, where 𝜇 is the intercept, or the mean if the model is completely stationary, 𝑡 is a time trend and its parameter 𝛿, 𝑒𝑡 is the random error term of the period. Equation (1) is called a trend-stationary process. This series will grow or decrease over time, but the mean will return to its trend in the long run.
𝑦𝑡= 𝜇 + 𝜃𝑦𝑡−1+ 𝑒𝑡 (2)
Equation (2) explains a process of a random walk with drift. The variable 𝑦𝑡 is determined by the last period’s 𝑦 as well as the error term (Libanio 2005). A shock to the error term in time
25
period t-1 will affect 𝑦, and this then carries over to the next period where the effect of the shock is still present in 𝑦𝑡, thereby causing a permanent effect of a one-time shock in the error term. Because 𝜇 is carried into the next period by 𝜃𝑦𝑡−1, the definition of a random walk with nonzero drift is similar to a trend in that it moves with a slope, determined by the drift term 𝜇. The drift means that if a unit root is present, 𝑦𝑡 will depend on both the drift term and the sum of the past error terms, meaning the series does not return to the trend line like the trend-stationary process. This is called a difference-trend-stationary time series.
The two types of processes are named based on how to convert the data into stationary series, i.e. by detrending or differentiating. 𝜃 and 𝛿 are parameters, determining if 𝑦𝑡−1 and 𝑡 have an effect on 𝑦𝑡, and thereby also if there is a unit root present. If 𝜃 is less than one, the effect of the past values of 𝑦 will dissipate over time. A parameter 𝜃 will rarely have a value greater than one, as this would mean 𝑦𝑡 explodes over time. Because 𝜃 is assumed to be one or less than one, all the methods included in this thesis testing the parameter 𝜃 are one-sided tests.
A common test for unit root is the Augmented Dickey-Fuller (ADF) test. It is developed on the previous definition of a unit root in equations (1) and (2) and is based on estimating the following equation.
𝑦𝑡 = 𝜇 + 𝛿𝑡 + 𝜃𝑦𝑡−1+ ∑ 𝛾𝑗∆𝑦𝑡−𝑗 𝑝
𝑗=1
+ 𝑒𝑡 (3)
To make the model robust to serial correlation, additional lags in the explanatory variable are added. These lags gather up the potential serial correlation present in the model, where 𝑝 is the number of additional lags included in the test. The number of additional lags included depends on the nature of the data and the size of the sample. For annual data, one or two lags are most commonly chosen as including more lags will reduce the usable sample (Wooldridge 2016). Serial correlation, or autocorrelation, is a characteristic where there is a correlation between a variable and a past time period’s value of the same variable. The presence of serial correlation in a regression breaks the OLS time series assumption of no serial correlation.
The hypothesis set up by the ADF test for trend-stationarity or difference-stationarity depends on the parameters 𝜃 and 𝛿. A statistically significant lagged time coefficient 𝜃 means that the series is difference-stationary. If the trend coefficient 𝛿 is significant and different from zero, the model is trend-stationary. The ADF test can be done in different variants. One of them tests for unit root under a constant slope. The other version is a drift test that sets up the null
