An Examination of the Impact of Power Sector Reform on Manufacturing and Services Sector in Nigeria: an Empirical Analysis

Received Jan 25, 2018 Revised May 2, 2018 Accepted May 28, 2018 The main objective of this study is to empirically examine the impact of Power Sector Reform on Manufacturing and Services Sector in Nigeria between 1999-2016. The study employed secondary annual time series data sourced from World Bank database (2016). The methodology adopted for the study was Augmented Dickey-Fuller (ADF); a test for long-run relationship using ARDL Bounds Testing approach with analysis of long-run and shortrun dynamics in the model. A striking revelation from the study is the inverse relationship that exists between manufacturing output and electricity consumption in Nigeria within the period referenced. This negative relationship is not unconnected with widespread allegation of misappropriation of budgeted funds for the Power Sector by successive administrations in Nigeria since 1999. It must be stated in clear terms that constant and consistent electricity generation, transmission and distribution is sine-qua-none for the growth of the national economy. Virtually all sectors of the economy depend on the supply of electricity to do business and so the lack of this vital ingredient of growth contributes in no small measure in stagnating economic growth and development. Efforts at reforming the power sector can only be fruitful when ALL stakeholders in the power sector including the political class put away their personal agendas and take the bull by the horn towards rescuing the nation from the looming danger of stagnant economic growth. Furthermore, there is the need for the Nigerian government to come up with new, better and alternative ways of improving energy generation and supply, as well as proper maintenance of electricity infrastructure in the country. Keyword:

INTRODUCTION 1.Background to the Study
Electric energy is an important factor of production and crucial for industrialization and economic growth of any nation. The quest for rapid and sustainable economic growth of an economy is a function among other variables, of not just adequate power supply but a sustainable and reliable distribution of energy, particularly electricity for economic growth and development [1]. In fact, no economy will develop without having an efficient and functioning energy consumption platform. In Nigeria, energy serves as the pillar of wealth creation. It is the nucleus of operations and engine of growth for all sectors of the economy. The output of electricity in the country usually consolidates the activities of other sectors which provide essential services to direct production activities in agriculture, manufacturing, mining, commerce etc. Nigeria is endowed with abundant energy resources but suffers from perennial energy crisis which has defied solution. Successive administrations in Nigeria have invested humongous amount of money (in billions of American dollars) towards revitalizing this all-important sector upon which the economic success and prosperity of Nigeria depends, with little or nothing to show for it [2].

Background to the Study
The disagreement on the association connecting electricity consumption with gross domestic product (GDP) was adequately investigated in energy economics literature [3,4]. Diverse empirical findings were maintained and in many instances found to be contradictory. A lot of factors have contributed to these disagreements and discrepancies, among which are methodologies adopted and the period of study chosen. In some cases, such works studied the energy sector overall without giving definite and particular attention to electricity consumption which is the core index for measuring energy consumption in Nigeria. It is in view of these inconsistencies that this paper seeks to empirically examine the impact of Power Sector Reform on Manufacturing and Services Sector in Nigeria The study is deliberately designed to cover the period 1999-2016, a seventeen years period for specific emphasis on the Fourth Republic democratic dispensation. The choice of scope is further motivated by the fact that it was during these periods (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016) that Nigeria invested billions of US dollars in investment to make the power sector efficient and effective towards contributing to overall economic growth and development. The value of the federal government's investment in these enterprises for the period studied is mind-boggling and it is not an exaggeration to state that the power sector has steadily absorbed a large share of public finances without commensurate benefits to the economy, hence this study is timely. The following research questions are expected to be answered at the end of the study (a) what is the effect of power sector reform on manufacturing output in Nigeria? (b) what is the impact of electricity consumption on services sector of the Nigerian economy?

Study Objectives
In specific terms, the study aims at achieving the following objectives: a. Examine the effect of Power Sector Reform on manufacturing output in Nigeria; b. Examine the impact of Electricity consumption (proxy for power sector reform) on services sector in Nigeria;

Research Hypothesis
The study shall examine the veracity of the following hypothesis: Ho1: Power Sector Reform has no significant effect on manufacturing output in Nigeria; Ho2: Electricity consumption has no positive impact on services sector in Nigeria; This study proceeds as follows. Section II reviews previous literature on Power Sector Reform in Nigeria, Economic Growth, etc. Section III develops an empirical model for analyzing the effect of power sector reform on economic growth in Nigeria and describes the data utilized in this study. Section IV presents and discusses the results of the empirical model, while Section V provides conclusion and policy recommendations.

LITERATURE REVIEW 2.1. An Overview of Privatization of Power Sector in Nigeria 2.1.1. Historical Overview
Electric power came to Nigeria in 1898 with the establishment of the first generating plant by the British colonial government [5,6]. The management of the generating plant was named the Public Works Department (PWD). Thereafter, the then Federal Government of Nigeria passed an ordinance in 1950, establishing the Electricity Corporation of Nigeria (ECN) saddled with the responsibility of generating, transmitting, distributing and sale of electricity in Nigeria. Other bodies like the Native Authorities and the Nigeria Electricity Supply Company (NESCO) had licenses to produce electricity in some locations in Nigeria [5]. In 1962, the Federal Government by an act of Parliament established the Niger Dam Authority (NDA). The authority was responsible for the construction and maintenance of dams and other works in the River Niger and elsewhere, generate electricity by water power, improve navigation and promote fisheries and irrigation. The electricity produced by NDA was sold to ECN for distribution and sales at utility voltages. In April 1972, by a decree, Electricity Corporation of Nigeria and Niger Dam Authority were merged to form National Electric Power Authority (NEPA). The reasons given for this merger include: vesting of production and distribution in one company and that it will bring about more efficient utilization of the human, financial and other resources available to the electricity supply industry in the country [7]. In 1973, NEPA became operational and was responsible for generating, transmitting and distributing of electricity to all parts of the federation. Starting with only four power stations namely Ijora, Delta, Afam thermal stations and Kainji hydro power station with a total installed capacity of 532.6MW serving more than two million customers, which has grown to 5,958MW in year 2000 with the establishment of additional power stations namely Jebba, Shiroro hydro power station Egbin, Sapele, Delta thermal power station in the early eighties having a combined installed generating capacity of 2940MW (PHCN, 2010. Nigeria @50:Status of Power sector). In 1988 NEPA was partially commercialized and supported by an upward review of the tariffs. This was aimed at attracting investors to the sector. Due to increase in the population of the country and the absence of additional power plants the available facilities became overstretched and this led to the reform of the power sector.

Power Sector Reform In Nigeria
With the return of civil rule in 1999, the federal government embarked on power sector reform. This culminated in the Electric Power Sector Reform (EPSR) Act 2005. This is contained in a Federal Government of Nigeria Gazette and it stipulates the reforms in the electricity power sector and how they are to be implemented. The Power Sector Reform was embarked upon on March, 2005 due to the inadequate supply of electricity, high demands and issues with bills. The main goal of the reform is to accomplish full deregulation of the Electricity Supply Industry (ESI) in two years after its implementation. The objectives include making electricity generation and supply available to consumers, making the sector investor-friendly and dismantling NEPA's monopoly. This was achieved through the passage of the Electric Power Sector Reform (EPSR) Act which came into being on the 11th of March, 2005. The reasons given for the reform include: introduction of competition in the industry as a means of improving industry efficiency that will result in providing lower energy prices to end users, lack of price transparency in utility operations hence consumers and regulators demand price transparency and declaration of cross subsidies among different users, like many other public owned institutions, corruption, inefficiency and managerial incompetence prevailed and the electricity industry showed inconsistent policy direction and lack of strategy framework for its sustainable development, policy decisions by past government in the ESI were based on political or administrative interest instead of efficient resource allocation and cost recovery necessary for economic development and the strategic energy policy for the country was never implemented [5].
The Act repealed the earlier law establishing NEPA, consequently, the Power Holding Company of Nigeria, (PHCN) was set up and charged with the responsibility of providing power supply. It also restructured the power sector from a vertically integrated structure into eighteen unbundled autonomous companies comprising one transmission company called TransCo, six generation companies known as GenCos and eleven distribution companies-DisCos respectively. The Act focused on the liberalization and privatization of the sole power provider-PHCN while introducing Independent Power Producers IPPs. The EPSR Act nurtures a wholesome market starting with a single buyer of electricity produced by PHCN and the IPPs for onward sale to the eleven DisCos that would also be offered for sale. Eventually the single model would be discarded for a bilateral contract model with suppliers and buyers free to contract between themselves.
The Act further provides for the establishment of the Nigeria Electricity Regulatory Commission (NERC) which is charged with the following [8]. Regulate tariffs and quality service; oversee the activities of the industry for efficiency; institutional and enforcement of the regulating regime; licensing of Generation, Distribution, Transmission and Trading companies that result from the unbundling of NEPA; legislative authority to include special conditions in licenses; provision relating to public policy interest in relation to fuel supply, environmental laws, energy conservation, management of scarce resources, promotion of efficient energy, promotion of renewable energy and publication of reports and statistics; providing a legal basis with necessary enabling provisions for establishing, changing, enforcing and regulating technical rules, market rules and standards.
In November, 2005 Nigeria Electricity Regulatory Commission was inaugurated and took full responsibility. Other aspects of the reform provided for the management of the Rural Electrification Agency (REA), the National Electric Liability Management Company (NELMCO) which is a special purpose entity created to manage the residential assets and liability of the defunct NEPA after privatization of the unbundled companies. The Act also provided for the establishment of a Power Consumer Assistance Fund (POLAF) to subsidize under-privileged electricity consumers.

Empirical Studies on Electricity Supply and Demand in Manufacturing Sector in Nigeria
For any meaningful improvement in the productivity of manufacturing sector to take place in any economy, the supply and demand of electricity must remain uncompromising elements of the process. This submission was corroborated by Iwayemi [9] and Odell [10] as cited in Olayemi [11]. While Iwayemi [9] argued that, for Columbia as a nation to industrialize, electricity supply and demand are crucial factors in the process, Odell [10] also averred the importance of energy sector in the socio-economic development of Nigeria. He further submitted that strong demand and increased supply of electricity would stimulate increased income and higher living standards in Nigeria.
Ndebbio [12] agreed with this contention, noting that electricity supply drives the growth of manufacturing sector. He argued that one important indicator to show whether a country's manufacturing sector is growing or not is the megawatt of electricity supplied and consumed. According to him, a country's electricity consumption per capita in kilowatts per hour (Kw/H) is proportional to the state of the growth of the industrial sector of the country.
In another study, Adenikinju [13] also supported the various arguments from Iwayemi [9], Odell [10], as well as Ndebbio [12], by providing a strong argument to further support the overwhelming importance of energy supply to the Nigerian economy. The poor nature of electricity supply in Nigeria, according to him, has imposed significant cost on the manufacturing sector of the economy. This argument is also in line with the survey of the Manufacturers Association of Nigeria (MAN) in 2005, where it was revealed that the cost of generating power constitute about 36 percent of production cost in the sector. Accordingly, Ekpo [14], in his own opinion, elaborated on the cost of running a generator economy and its adverse effects on investment. He strongly opined that for Nigeria as a nation to accelerate the pace of the growth of manufacturing sector, the country should consider fixing power supply problem.
Furthermore, Adenikinju [13] examined the cost of electricity shortages on the Nigerian manufacturing sector using the data obtained from a nationwide survey. The study confirms that the cost of electricity failures to the Nigerian manufacturing sector is quite high and very alarming. Nigerian firms were found to incur costs on the provision and maintenance of expensive back-up such as generators and other diesel-powered machines to minimize the expected outage costs. This constitutes high cost diesel and gas with the average costs as huge as three times the cost of government-supplied electricity. The marginal cost estimates also indicates that the cost of Kwh of unserved electricity is very high. These teething challenges in the sector have led to lot of multinational corporations closing their firms and relocating to nearby countries that enjoy uninterrupted electricity supply.
Okonkwo [15], submitted that regular supply of all forms of energy in an economy is regarded as essential oil for lubricating or propelling the wheels of economic activities, aimed at increasing growth of aggregate output. Energy, apart from serving as a pillar of wealth creation in developing economies, serves as an engine of growth for all sectors of the economy; electricity development and utilization therefore has pervasive impact on industrial development of every nation.
Finally, in an attempt to explore the area of the impact of electricity, numerous literatures only revealed the relationship between economic growth and electricity supply, with some only on manufacturing output, with little empirical attention on the effect of electricity on the various sectors of the economy. This could lead to fallacy of composition because economic growth is only a function of the performance of different sectors which certainly differ in their need for electricity. In response to this perceived gap, this study explores the effect of Power Sector Reform on manufacturing output and services sector in Nigeria.

STUDY METHODOLOGY
The analysis began with the unit root test to determine whether the time series data were stationary at levels or first difference. The unit root test was conducted on each variable in the model, namely, MAN, Serv and E-consump. The Augmented Dickey Fuller (ADF) unit root test were used to test for the stationarity of the variables. A stationary time series refers to the series with a constant mean, constant variance, and constant autocovariances for each given lag. After determining the order of integration of each of the time series, and if the variables were integrated of the same order, the ARDL Bounds Testing approach to cointegration test was used in this study to determine whether there is any long-run or equilibrium relationship between E-consump and the other independent variables in the model. If the variables were found to be cointegrated, then an error correction mechanism (ECM) through ARDL approach would be estimated to model the short-run dynamics.

Model Specification 3.1.1. Augmented Dickey-Fuller Unit Root Test Model
To study the stationarity properties of time series, the Augmented Dickey-Fuller test (ADF) [16] is employed in this study. The test involves estimating the regression. The model for the ADF unit root framework is as follows: In the above equation, α is the constant and ρ is the coefficient of time trend. X is the variable under consideration. In this study, the variables include log(FDI), log(GDP-pc), log(INVT), and log(MAN). Δ is the first-difference operator; t is a time trend; and ε t is a stationary random error. The test for a unit root is conducted on the coefficient of Xt-1 in the above regression. If the coefficient, β, is found to be significantly different from zero (β ≠ 0), the null hypothesis that the variable X contains a unit root problem is rejected, implying that the variable does not have a unit root. The optimal lag length is also determined in the ADF regression and is selected using Akaike information criterion (AIC).

Estimation Techniques: ARDL Modelling Approach
The estimation technique adopted for this work is based on Auto-regressive Distributed Lag (ARDL) approach and Error Correction Mechanism (ECM). The ARDL modeling approach popularized by Pesaran [17], Pesaran [18], and Pesaran [19] has numerous advantages. The main advantage of this approach lies in the fact that it can be applied irrespective of whether the variables are I(0) or I(1) and that none of the variables is stationary at 1(2) and beyond [17]. Another advantage of this approach is that the model takes sufficient numbers of lags to capture the data generating process in a general-to-specific modelling framework. Moreover, a dynamic error correction model (ECM) can be derived from ARDL through a simple linear transformation. The ECM integrates the short-run dynamics with the long-run equilibrium without losing long-run information. It is also argued that using the ARDL approach avoids problems resulting from non-stationary time series data. This study illustrates the ARDL modelling approach by considering the following equation:
The ARDL approach uses the F-test to determine the presence (or not) of a cointegrating relationship between variables, although the asymptotic distribution of the F-statistic in this context is not standardized without taking account of whether the variables are I(0) or I(1). The critical values of this distribution are given in Pesaran [17], and Pesaran [19]. Two sets of values are presented in the form of a table. The first set assumes that all the variables are I(1), while the second set assumes that all the values are I(0). This makes it possible for the variables to be stationary and first-order integrated. If the value of the calculated F-statistic is higher than the highest value of this region, the null hypothesis is rejected, thus indicating the presence of cointegration between variables without taking account of whether they are I(1) or I(0). If the value of the F-statistic falls below this region, the null hypothesis of no cointegration cannot be rejected, whereas an F-value lying within the region implies that the result of the test is indeterminate.
If the existence of a long-run relationship between the variables is borne out, the second stage in the analysis consists in estimating the short-run and long-run parameters, using the ARDL approach. Once the long-run relationship between the variables is determined, then the estimates of the long-run ARDL can be obtained. If a long-run relationship between the variables exists, then there also exists an error-correction representation. Consequently, the error correction model is estimated in the third step; it indicates the speed of adjustment to long-run equilibrium following a short-run shock.
A general error-correction representation of equation is formulated as follows: (4) where, φ = Speed or rate of adjustment; δ 1 , Π 2 , α 3 , represents the coefficients of the variables respectively; Δ is the difference operator, m is the lag length of the variables; ect t-1 denotes the residual from the cointegration equation (the error correction term), and ε t is the uncorrelated white noise residuals.

Economic Apriori
This specifically has to do with sign expectation set by economic theory and it is expected that parameters in this model have the correct signs and sizes that conform to economic theory. If they carry the expected signs, then the hypothesis is accepted otherwise they are rejected. Explicitly put, it is expected a priori that an increase in electricity consumption will result to a rise in manufacturing output and more resultoriented services sector, ceteris paribus.

Diagnostic/Stability Test
At the end of the study, the VECM would be subjected to the statistical diagnostic tests, namely, normality, serial correlation, heteroskedasticity and the inverse root of Auto-Regressive characteristic Polynomial tests to ascertain its statistical adequacy.

DATA ANALYSIS AND INTERPRETATION 4.1. Augmented Dickey-Fuller Unit Root Test
In the first step of the analysis, we will use both the ADF unit root test to identify which variables in the models have a unit root. In other words, we would like to determine whether variables in the models are stationary or non-stationary. Prior to carrying out ARDL bounds test, it is expected to first test for the stationarity of all the variables in the model to determine the order of integration for each variable. This is a necessary step to ensure that variables are not second-order stationary (i.e., I(2)) and to avoid fallacious results. According to Ouattara, the calculated F-statistics which Pesaran [19] provide are not valid in the presence of I(2) variables, since the bounds tests are based on the assumption that variables are either I(0) or I(1). Below is the Table 1 showing the order of stationarity of the series examined. The results of the Augmented Dickey-Fuller (ADF) unit root test as presented above revealed that no variable attained stationarity at its level form until it was differenced. Therefore, the null hypothesis of nonstationarity cannot be rejected at levels. However, at first difference, all variables were stationary. That 123 means at first difference the variables were integrated of order I(1), hence it is concluded that E-consump, MAN and Serv are first difference stationarity. Having met the prerequisite for estimating cointegration test, the study proceeds to estimate the ARDL Bounds Testing as popularized by Pesaran [17], Pesaran [18], and Pesaran [19].

Augmented Dickey-Fuller Unit Root Test
To determine the existence (or not) of a long-term relationship between the variables using the ARDL technique is to test for the presence or otherwise of a longrun relationship by applying Bounds test developed by Pesaran [19] The cointegration test results are reported below. Notes: The critical values are taken from Pesaran [17] with five regressors. ** denote rejecting the null at 5% level of significance. The range of the critical value at 5% and 1% are 3.1-3.87; 4.13-5.0 respectively. The ARDL Bounds testing approach to cointegration result above implies the rejection of the null hypothesis that no long-run relationship exists between the variables, thus concluding that evidence of a longrun relationship exists between electricity consumption in Nigeria, manufacturing sector output and services sector output respectively between 1999 to 2016. Precisely, cointegration is achieved if and only if it is reported that the calculated F-statistics of the joint null hypothesis that there is no long-run relationship between the variables is greater than the lower and higher bound of the 95 percent critical value interval. From the above table, the F-statistic value of 6.430694 is greater than the lower and higher bound of 95 percent critical value (3.1-3.87), thus leading to the rejection of the formulated null hypothesis of no cointegration.

ARDL Unrestricted Error Correction Model Estimate
The estimate of the generalized unrestricted error correction model is as shown in Table 3. The choice of ARDL model (4,1,1) selected is based on Akaike Information Criterion (AIC). From the model, both the R-Squared and adjusted R-Squared are 90%. This means that the regressors can explain about 90% of the variation in the model within the model. The Durbin Watson test statistic of 2.5 indicates the absence of first-order autocorrelation of residuals in the model. The F-test for the model is equally significant at conventional significance levels. The model meets all specifications of the diagnostic tests in Table 3. The Table 3 and graphs in Figure 1 and 2 reveals that there is absence of first order serial autocorrelation in the model or the residuals are not serially correlated; there is the absence of heteroscedasticity, therefore, the errors are homoscedastic. Furthermore, the normality test adopted is the Jarque-Bera (JB) statistics, the study observes that the residual are normally distributed. The result of CUSUM/CUSUMQ stability test indicates that the model is stable. This is because the CUSUM/CUSUMQ lines fall in-between the two 5% lines.   The result of the estimated long-run and short-run dynamic estimates is shown in Table 4 and 5 above. All independent variables in the model (manufacturing output and service sector output) revealed a long-run significant relationship with electricity consumption in Nigeria. The reverse is however the case in the short-run as both variables (MAN and Serv) are statistically insignificant in relationship to the dependent variable (electricity consumption) in the short-run. The coefficient of MAN has an inverse relationship with the dependent variable both in the long and short-run while that of (Serv) appeared with a positive sign (i.e. it is positively related to the dependent variable-electricity consumption) also in the long-run and in the shortrun within the period studied. The parameter estimate of (MAN) is statistically significant at 0.01 significance level with a long-run elasticity of -0.276748, that is, for every 1% decrease in electricity consumption in Nigeria, manufacturing sector output declines or falls by approximately 28%. This result is in agreement with the findings of Olayemi [11] who opined that electricity generation and supply in Nigeria under the reviewed period impacted negatively on the manufacturing productivity growth, due to unnecessary government's spending on non-economic and unproductive sectors. On the other hand, the coefficient of service sector output (Serv) is positively related to the dependent variable and as well statistically significant in the model. Empirical evidence reveals that for every percentage rise in electricity consumption in Nigeria there is approximately 70% rise or increase in output from the different services sector of the Nigerian economy in the long-run, all things being equal. Short-run dynamic analysis revealed similar outcomes.

Estimate of Short-run Dynamics
The estimated coefficient of the error correction term ECM (-1) has the expected negative sign, and it is also statistically significant at 0.01 level. The speed of adjustment is too high, and leaves much to be desired. It shows that only about 172% of the disequilibrium within the model in the previous year is subsequently corrected in the current year. The speed of adjustment of the variables in the model in response to a deviation from its long-run equilibrium path is 172%. The result of the error correction term provides strong evidence that there is indeed a long-run equilibrium relationship between the exogenous variables (manufacturing sector output, and services sector output) and E-consump which is a proxy for electricity consumption.

CONCLUDING REMARKS
The main objective of this study is to empirically examine the impact of Power Sector Reform on Manufacturing and Services Sector in Nigeria. The study employed secondary annual time series data sourced from World Bank database (2016). The methodology adopted for the study was Augmented Dickey-Fuller (ADF); a test for long-run relationship (ARDL Bounds Testing), and an ARDL approach to long-run and short-run to examine the effect of the dependent variable (electricity consumption) on the explanatory variables (manufacturing sector output and services sector output). Evidence revealed that series employed in the model are stationary at first difference and exhibit long-run relationship within the period studied. That is, both dependent and independent variables (E-consump, MAN and Serv) can walk together without deviating from an established long-run path.
One striking revelation from the study is the inverse relationship that exists between manufacturing output and electricity consumption in Nigeria within the period referenced. This negative relationship is not unconnected with widespread allegation of misappropriation of budgeted funds for the Power Sector by successive administrations in Nigeria since 1999. At the advent of the present democratic dispensation in 1999, the then President, Chief Olusegun Obasanjo carried out massive reforms in the Power sector accompanied by huge budgetary allocations but with little or no visible results noticed. The Late Umar Musa Yar'adua and Goodluck Jonathan continued in the reform process but darkness and gross darkness in our businesses / homes has remained our lot. In fact, the key sectors that drive economic growth such as industries and manufacturing has continued to groan and operate under an unfavourable climate of epileptic power supply for a larger portion of Nigeria's seventeen years of democratic experimentation, despite billions of US dollars appropriated to the Ministry of Power. Many manufacturing outfits have taken flight and relocated to neighbouring West African states as they could no longer cope with the exorbitant cost of running diesel-powered machines for the survival of their businesses. This is in line with the view of a survey by the Manufacturers Association of Nigeria (MAN in 2005), that the cost of generating power constitute about 36 percent of production. This huge cost is enough to discourage investors in the real sector of the economy.
It must be stated in clear terms that constant and consistent electricity generation, transmission and distribution is sine-qua-none for the growth of the national economy. Virtually all sectors of the economy depend on the supply of electricity to do business and so the lack of this vital ingredient of growth contributes in no small measure to stagnating economic growth and development. It is also imperative to note that Nigeria's story of incessant power outages is not in any way connected to lack of funds; but to the endemic and systemic corruption that is threatening the corporate existence of the country From year to year, very promising and enviable plans, policies and programmes are designed, aimed at taking the nation to the Promise Land of 24/7 era of electricity supply, but alas, the cankerworm of corruption, nepotism, lack of patriotism etc keep pulling us backward from achieving our goal of a stable power supply. The attitude of our leaders towards salvaging this catalyst of growth has remained lackluster and uninspiring, to say the least. Efforts at reforming the power sector can only be fruitful when ALL stakeholders in the power sector including the political class put away their personal agendas and take the bull by the horn towards rescuing the nation from the looming danger of stagnant economic growth.
Finally, there is the need for the Nigerian government to come up with new, better and alternative ways of improving energy generation and supply, as well as proper maintenance of electricity infrastructure in the country. Deliberate efforts by the government to improve power infrastructure will result in the country being able to increase electricity production threefold and thus optimally utilize its installed generating capacity to something in the region if 10,000 mega-watts. When this feat is eventually attained, Nigeria can then stand shoulder high with other emerging economies in the world in terms of growth in output in key sectors of the economy.


Life Micro Insurance in Assam-A Case Study

Micro insurance is a tool for investment, savings and as a measure of social security to the poor. It increases the livelihood of the poor where they can eat well, have good health since they wouldn’t have to save as much for emergencies. This research paper discuss about growth of microinsurance in India as well as in Assam. The micro insurance providers are seventeen in number in India. The numbers of micro insurance agents are in growing trend both in LIC of India and in private insurers too. The study concludes that the growth rate micro (life) insurance sector is not positive through the years as started it.

The Indian regulator (IRDA) has bought in specified micro insurance regulations in November 2005, in which the regulator has undertaken the product design, specifying a distribution channel in form of NGO, Self Help Group or a MFI and the pricing mechanism to insurers. Insurance Regulatory Authority of India (micro insurance) Regulation 2005 has been stated mainly two types of micro insurance: General micro insurance product: General micro insurance product means any health insurance contract, any contract covering the belonging, such as hut, livestock, or tools or instruments or any personal accident contract, either on individual or group basis, as per terms stated in schedule-I appended to the regulations, Life micro insurance product: Life micro insurance product means any term insurance contract with or without return of premium, any endowment insurance contract or health insurance contract, with or without an accident benefit rider, either on individual or group basis, as per terms stated in schedule-II appended to the regulations.

Micro Insurance Products in India:
There are 24 life insurance companies are present in India but only 17 companies are providing micro insurance products this clearly give an idea of low attraction of majority of companies towards these products. Below is the list of micro insurance products along with the name of companies: Note: All Micro-insurance products and products falling within the parameters prescribed under the IRDA (Micro-insurance) Regulations, 2005, but launched prior to the said Regulations.

Need of study:
Insurance plays the important role in the economic development of the country. It helps for the mobilization of savings of people, specially from middle and lower income group. But any research has not been taken yet in promoting activities and implementing plans of micro insurance in Assam. The trends of micro insurance in Assam are still remaining as unknown. The researcher intends to focus a picture on the growth of life micro insurance on Assam.

OBJECTIVES OF THE STUDY:
1. To study the awareness level of micro insurance among the poor people of Assam. 2. To study the growth of life micro insurance in India as well as in Assam.

LITERATURE REVIEW:
The present study embodies a brief review of the research done in the area of micro insurance. The purpose of reviewing the earlier studies is to economize the historical and present prospective of the present work and the related studies which have been taken cognizance of one or more variables includes in the study. Dr. Ashfaque Ahmed (2013) 1 in his study "perception of life insurance policies in rural India" reveled that there is low level of awareness and understanding of life insurance products. There are various factors that influence consumer thinking when they are planning to invest in insurance scheme. Most of the customers show their interest in life insurance having higher risk coverage and also for good return with safety. The roles played in perception of life insurance policies in rural market by members of the family varies with knowledge parameters as well as with the typed of products and sometimes with the company name also. While a number of psychological variables are useful in obtaining into consumer's perception towards buying life insurance policies in rural areas. The insurance company name also plays an important role in purchasing. Ramanathan, K.V. (2011) 2 research has resulted in the development of a reliable and valid instrument for assessing customer perceived service quality, awareness level, and satisfaction level of customers towards life insurance industry. Here, service quality needs to be measured using a six dimensional hierarchal structure consisting of assurance, competence, personalized financial planning, corporate image, tangibles and technology dimensions. Syed Abdul Hamid& Roberts & Paul Mosley (2010) 3 in the study shows that there is a positive impact of micro health insurance in the reduction of poverty among rural households of Bangladesh. Micro health insurance has a significant beneficial effect on food sufficiency of poor's and has a dynamic improvement in the health status of poor rural households. Gunita Arun Chandhok (2009) 4 The result of study indicates that there is a huge untapped market for micro health insurance and majority of population are aware and understand the importance of micro health insurance. Thus, micro insurance will go a long way in eradicating poverty. If the various micro insurance models are implemented effectively by Insurer, MFI"s, SHG"s, NGO"s, Health institutions, Donors and Co-operatives the BPL population will lead a peaceful and secure life.

FINDINGS AND ANALYSIS:
The data are first edited, coded and tabulated for analyzing by using diagrams, graphs, charts, pictures etc. Data analysis is the process of planning the data in an ordered form, combining them with the existing information and extracting from them. Interpretation is the process of drawing conclusions from the gathered data in the study. In this research the researcher has analyzed the data using percentages and graphs. The various attributes were analyzed separately and the importance to each was calculated on the basis of the percentage. The rank having the maximum percentage was taken to be preferred importance to the particular attribute.

Growth of micro insurance in India:
The micro insurance business in India cannot make a continuous progress in both public insurance and private insurance companies. More life and group operations and many fresh policies have been launched by the insurance companies. The distribution system of policies has also been strengthened substantially, and the new business of micro insurance has shown a sufficient growth though the mass is still very low.  Table clearly revealed that public insurance companies have increased the percentage of policies in first six years but in the last two years it is negative growing rate. On the other hand, private insurance companies have increased percentage policies not less than 400% whether it is some time increased or decreased. Similarly public insurance companies have increased growth rate for premium from the first six year satisfactory but in the last two years the growth rate of premium is very low. But the private insurance companies have maintained a satisfactory growth rate in case of the premium amount. Therefore, the tables reveal that in case of individual micro insurance business the overall policies issued by private insurance companies is more than public insurance company but the premium collection rate of public insurance companies is higher. Similarly in group micro insurance business private insurance companies overall growth rate is higher in number of schemes issued and premium collection but negative in lives covered then public insurance companies.  The Table-  In table-6 it is clearly revealed that the Life insurance Company of India, Guwahati Division insurance agent increased from 27 in the year 2010-11 to 126 in the year 2016-17 but only 23 insurance agents are working actively in the year 2016-17. It focuses that the public insurance company cannot attract the mass people to micro insurance in Assam.

CONCLUSION:
Micro insurance is just one of the several risk pooling tools available to low income people. Micro insurance sector can play a vital role in developing of our economy. But all the insurance companies except LICI have reduced working on micro insurance because of many people not came forward to act as agents or intermediaries for providing life micro insurance. Micro insurance providers should begin by training and educating key intermediaries in the idea of promoting insurance and private insurers should also begin developing relationships with existing delivery channels The insurance companies should innovate products and distribution beyond the regulatory requirement to conduct business in the low income segment.


extfieldsofstudy: Economics Mathematics

text:
The Italian Pension Gap: a Stochastic Optimal Control Approach

We study the gap between the state pension provided by the Italian pension system pre-Dini reform and post-Dini reform. The goal is to fill the gap between the old and the new pension by joining a defined contribution pension scheme and adopting an optimal investment strategy that is target-based. We find that it is possible to cover, at least partially, this gap with the additional income of the pension scheme, especially in the presence of late retirement and in the presence of stagnant career. Workers with dynamic career and workers who retire early are those who are most penalised by the reform. Results are intuitive and in line with previous studies on the subject.

Introduction
During the last few decades, several countries across the world have faced the ageing population problem. It is well known that the ageing of the population threatens the sustainability of Pays-As-You-Go pension systems, that is essentially based on a sufficiently high ratio workers to pensioner. To tackle this issue, many governments have introduced new reforms that lead to deep changes into the pension systems.
In particular, in Italy, the Dini reform (introduced in 1995) instituted a completely different pension system for the new classes of workers. Before the reform, the public pension was provided through a defined benefit salary-related system. Namely, the pension provided was simply a service-based percentage of the last salary of the worker. After the reform, the public pension has been provided through a contribution-based system, where the worker contributes by himself to build his pension. This remarkable change generated two different classes of workers, the pre-reform workers and the post-reform workers, and lead to a pension gap between their corresponding pension rates and replacement ratios. The aim of this paper is to illustrate a possible way to fill this pension gap investing optimally in a defined contribution (DC) pension fund during the working life. In order to achieve the goal, a stochastic optimal control problem with suitable annual targets is solved. We consider two different salary growths to represent two different classes of workers: a linear salary growth (blue-collar workers) and an exponential salary growth (white-collar workers). A numerical section illustrates the practical application of the model. Our results are in line with previous results on the comparison between the old pre-reform Italian pension and the new post-reform one, see Borella & Coda Moscarola (2006) and Borella & Coda Moscarola (2010). We find that the gap between salary-related pension and contribution-based pension is larger for workers with dynamic career than for workers with a stagnant career. A slow salary increase associated to late retirement can produce a new pension that is almost equal to (or even exceeds) the old pension. Expectedly, the gap is easier to cover in the case of late retirement, and vice versa. Interestingly, the gap increases when the rate of growth of the salary increases.
The reminder of the paper is as follows. In Section 2 we introduce the milestones of the Italian pension system and the consequences of the Dini reform. In Section 3 we build the model and the corresponding stochastic optimal control problem. In Section 4 we derive the closed-form solutions to the problem for the two different salary growths considered. In Section 5 we carry out some simulations in order to test the model and show the behaviour of the optimal investment strategy and the optimal fund growth in a base case scenario. In Section 6 we make sensitivity analysis of the pension distribution with respect to retirement age. In Section 7 we investigate the break even points that lead the "new" pension to equal the "old" pension. Section 8 concludes.

The Italian pension provision
The Italian pension system has been modified through a series of legislative measures taken by different governments during the 90s. We only hint at the Dini reform which is useful in order to understand the following model. The Dini reform (law 335, 1995) has changed the system for the calculation of the pension from a salary-based system to a contribution-related system. The workers shifted from one system to the other depending on the contributions paid at the end of 1995. Therefore, three different situations were created: 1. The workers with at least eighteen years of contributions on 31/12/1995 remained under the salary-related system and therefore they were not touched by the reform.
2. The workers with less than eighteen years of contributions on 31/12/1995 were subjected to a mixed method.
3. The workers who were first employed after 31/12/1995 are subjected to the contributionbased system.
In this paper, we compare the method for the calculation of the public pension before the Dini reform with the "new" method for the calculation of the public pension in Italy after the reform.
The formula for the pension rate P o before the Dini reform was where S(T ) is the final salary and T indicates the number of past working years. In the following, we shall call the pension rate (1) the "old pension". The old pension is a percentage of the product of the last salary by the years of service, and the related net replacement ratio -which is the ratio between the first pension rate received after retirement and the last salary perceived before retirement -is given by In contrast, the new formula for the pension rate P n is described by where • β is the conversion coefficient between a lump sum and the annuity rate, and its choice should reflect actuarial fairness. If it does, then β = 1/ä x , whereä x is the single premium of a lifetime annuity issued to a policyholder aged x, i.e., where ω is the extreme age, v = 1/(1 + r) is the annual discount factor and n p x is the survival probability from age x to age x + n.
• c is the contribution percentage for the calculation of the pension rate (supposed to be constant during the whole working life and, for the employees, set by law to 33%).
• T indicates the number of past working years.
• w is the mean real GDP increase.
In the following, we shall call the pension rate (2) the "new pension". Compared to the old pension, the new pension is given by a complicated formula and depends not only on all the salaries but also on other parameters. Its related net replacement ratio is

The optimization problem
The main idea of this paper is the following. We assume that the worker was firstly employed after 31/12/1995 and will receive the new pension (2) from the first pillar (i.e., the public pension), but he wants to integrate it with additional income from the second pillar (i.e., the private pension funds) to obtain a pension rate that is as close as possible to the one that he would have obtained with the old pension rule (1). Since the Dini reform, and apart from a few exceptions accessible only by self-employed (not considered in this paper), pension funds in Italy are defined contribution (DC) and not defined benefit (DB). This means that the contribution to be paid into the fund is fixed a priori in the scheme's rules and the benefit obtained at retirement depends on the investment performance of the fund in the accumulation period.
We assume that at time 0 the worker joins a DC pension scheme and has control on the investment strategy to be adopted on the time horizon [0, T ], where T is the retirement time.
The financial market consists of two assets, a riskless asset B = {B(t)} t≥0 and a risky asset Z = {Z(t)} t≥0 , whose dynamics are described by where r is a constant rate of interest and {W (t)} t≥0 is a standard Brownian motion defined and adapted on a complete filtered probability space (Ω, F , {F t } t≥0 , P). We assume that the contribution c(t) paid into the fund at time t is a fixed proportion of the salary of the member where k ∈ (0, 1) and S(t) is the salary of the member at time t. Finally, the proportion of portfolio invested into the risky asset at time t ∈ [0, T ] is y(t). Hence, the dynamics of the wealth are described by the following SDE where x 0 ≥ 0 is the initial wealth paid into the fund (it can also be a transfer value from another pension fund). Because the aim of the worker is to reach a pension rate that is as close as possible to that of the salary-related method, we assume that there exist annual targets {F (t)} t=0,1,2,...T that he wants to achieve, and that his preferences are described by the loss suffered when the targets are not met. Thus, we introduce the following quadratic loss (or disutility) function analyse and discuss the link between "utility-based" approach and "target-based" approach. From a theoretical point of view, the quadratic loss function also penalizes any deviations above the target, and this can be considered as a drawback to the model. However, the choice of trying to achieve a target and no more than this has the effect of a natural limitation on the overall risk of the portfolio: once the desired target is reached, there is no reason for further exposure to risk and therefore the surplus becomes undesirable. This is in accordance also with the fact that the mean-variance approach to portfolio selection has been shown to be equivalent to the minimization of a quadratic loss function: see the seminal papers by Zhou & Li (2000) and Li & Ng (2000), and, in the context of DC pension schemes, Vigna (2014). The idea that people act by following subjective targets is also accepted in the decision theory literature. For instance, Kahneman & Tversky (1979) support the use of targets in the cost function, and Bordley & Li Calzi (2000) investigate and support the target-based approach in decision making under uncertainty.
We now need to define the targets. Recalling that the worker's goal is to reach the old pension pre-Dini reform, we set as final target F (T ) the amount that the retiree aged x should pay to an insurance company in order to fill the gap between the previous pension rate and the current one, i.e., whereä x is the price of the annuity given by (3) to a retiree aged x, P o is given by (1), P n is the continuous formulation of equation (2), which means The interim targets F (t) for t ∈ [0, T ) are set to be the compounded value of fund plus contributions using the interest rate r * that matches a continuity condition between interim targets and final target, i.e.
with r * such that 1 The worker's goal is to minimize the conditional expected losses that can be experienced from the fund until retirement where ρ > 0 is the (subjective) intertemporal discount factor.
As usual in optimization problems in DC pension schemes, the contribution rate is not a control variable, and the only control variable for the worker is the share of portfolio y(t) to be invested into the risky asset at time t ∈ [0, T ]. To formulate the optimization problem, we define the performance criterion at time t with wealth x, i.e., and the admissible strategies.
The minimization problem, then, becomes over the set of admissible strategies.

Solution
In order to solve the optimization problem (12), the value function is defined as Remark 2. In this work, we neither set boundaries on the values that the fund X(·) can assume, nor set boundaries on the share y(t) to be invested in the risky asset. The existence of a minimum finite bound on X(t) would be desirable, as well as proper boundaries on the investment strategy. The former would be intended to protect the retiree from outliving his asset and not being able to buy a minimum level of pension at time T , the latter to comply with the usual forbiddance of short-selling and borrowing. However, adding restrictions to the state variable and the control variable means adding boundary conditions to the problem and this makes it extremely hard (and often impossible) to solve analytically. Among the few works that treat optimization problems with restrictions in DC pension schemes, see Di Giacinto, Federico & Gozzi (2011) and Di Giacinto, Federico, Gozzi & Vigna (2014).
We write the HJB equation x) is the infinitesimal operator and the functions b(·) and σ(·) are the drift and the diffusion terms of the process X = {X(t)} t≥0 defined by (6). Substituting into (14), we obtain with the boundary condition To have an easier notation, let us define Thus, equation (15) becomes The first and second order conditions are Therefore, (19) becomes Moreover, condition (20) is satisfied if and only if We will show later that this condition is actually satisfied, so that the solution is a minimum. By substituting (21) into (18), we obtain the non-linear PDE We guess a solution of the form From the boundary condition (16), we obtain The partial derivatives of V are and substituting them into (21), we derive the optimal investment strategy at time t with wealth x, i.e., Substituting the partial derivatives of V (·, ·) into (23), we have where λ := (µ − r)/σ is the Sharpe ratio of the risky asset.

Solution of the problem with two different salary evolutions
Two different salaries are compared: a linear salary and an exponential salary where S 0 is the initial salary and g i (i = l, e) is the mean real salary increase.
The contribution in the two cases is Remark 3. We have selected two simple models for the salary growth for analytical tractability and the aim of providing closed-form solutions for the optimal investment strategy. 2 The two different salary growths may represent two different categories of workers, the exponential growth being associated to white-collar workers with dynamic salary increase, the linear salary increase being associated to blue-collar workers with smooth salary increase. The distinct k ′ s reflect the assumption that the savings capacity of white-collar workers is higher than the savings capacity of blue-collar workers.
Therefore, there are also two different families of targets.
For the linear salary case (for notational convenience, in the following we will write g and k in the place of g l and k l ): where Π l n is the net replacement ratio for the new public pension with linear salary. For the exponential salary case (for notational convenience, in the following we will write g and k in the place of g e and k e ): where Π e n is the net replacement ratio for the new public pension with exponential salary. Solving the system (28) in both cases, we find the following solutions Substituting these solutions into (26), we obtain the two optimal investments y * l (t) and y * e (t), t ∈ [0, T ].

Simulations
We have carried out several numerical simulations in order to investigate some quantities of interest to the pension fund member when the model is implemented in the practice. In particular, we have investigated to what extent the gap between the old pension and the new pension is filled. We have first considered a base case, and then made some sensitivity analysis.

Base case: Assumptions
The assumptions for the base case are the following: • the initial fund is X(0) = 1; • the public pension contribution is c = 33%; • the mean GDP growth rate is w = 1.5%; • the riskless interest rate is r = 1.5%; • the drift of the risky asset is µ = 6%; • the diffusion of the risky asset is σ = 12%; • the intertemporal discount factor is ρ = 3%; • the annuity value is calculated with the Italian projected mortality table IP55 (for males born between 1948 and 1960); it isä 65 (1.5%) = 17.875; therefore, the conversion factor from lump sum to annuity is β = 1/ä 65 (1.5%) = 0.0056; • the age when the member joins the scheme is x 0 = 30; • the time horizon is T = 35 meaning that the retirement age is x T = 65; • the initial salary is S(0) = 1.
We have considered two different salary growths, with different values for the annual salary increase g and the annual contribution rate k: • exponential salary: S e (·) as in formula (30) with g e = 6% and salary contribution percentage k e = 10%; • linear salary: S l (·) as in formula (29) and g l = 8% and salary contribution percentage In the simulations, we have discretized the Brownian motion with a discretization step equal to two weeks (∆t = 1/26), and we have simulated its behaviour over time in 1000 different scenarios. At each time point, we have not applied the optimal unconstrained investment strategy y * (t), because short-selling and borrowing are likely to be forbidden.
We have, instead, implemented the "sub-optimal" constrained investment strategies, which are constrained to stay between 0 and 1. In particular, the sub-optimal y so (t) is defined as where y * (t) is the optimal investment strategy. 3 The adoption of constrained investment strategies leads, as a desirable consequence, the fund not to run under 0. Constrained suboptimal strategies of this type are not new in the literature and they are good approximations of the optimal investment strategies. They were applied, e.g., by Gerrard et al. (2006) and Vigna (2014) in the context of DC pension schemes with a constant interest rate, and they proved to be satisfactory: with respect to the unrestricted case the effect on the final results turned out to be negligible and the controls resulted to be more stable over time. In each scenario of market returns, the sub-optimal value y so (t), t ∈ [0, T ], has been calculated and then adopted for the fund growth.

Base case: Results
Regarding the investment strategy adopted and the evolution of the fund over time in the base case, we present the following results: • Table 1 reports, for both cases of exponential and linear growths, the old pension P o , the new pension P n , the old net replacement ratio Π o , the new replacement ratio Π n , the rate of growth of the targets r * and the last salary S(T ); • the two graphs of Figure 1 report some percentiles (graph on the left) and mean and standard deviation (graph on the right) of the distribution, over the 1000 scenarios, of the investment strategy y so (t) for t ∈ [0, T ], for the exponential salary growth; • the two graphs of Figure 2 report some percentiles (graph on the left) and mean and standard deviation (graph on the right) of the distribution, over the 1000 scenarios, of the fund X so (t) for t ∈ [0, T ], for the exponential salary growth; • the two graphs of Figure 3 report some percentiles (graph on the left) and mean and standard deviation (graph on the right) of the distribution, over the 1000 scenarios, of the investment strategy y so (t) for t ∈ [0, T ], for the linear salary growth; • the two graphs of Figure 4 report some percentiles (graph on the left) and mean and standard deviation (graph on the right) of the distribution, over the 1000 scenarios, of the fund X so (t) for t ∈ [0, T ], for the linear salary growth.  We observe the following: 1. as expected, with exponential salary growth the final salary is significantly larger (more than double) than that with linear salary growth; therefore, despite the old replacement ratio (that does not depend on the salary growth) is the same (70%), the old pension is much larger with a dynamic career than with a smooth one; 2. the investment strategy for the exponential growth is remarkably riskier than that for the linear growth: for the exponential growth in almost 75% of the cases the portfolio is entirely invested in the risky asset for all t, while for the linear growth all percentiles of y so (t) (apart from the 95th one) decrease gradually from 1 to 0 over time; 3. the larger riskiness of the strategy for the exponential growth is due to the larger gap between the old and the new pension: the old replacement ratio is 70% in both cases, but the new replacement ratio (that does depend on the salary growth) is 32% for the exponential growth and 51% for the linear growth; the larger gap to fill in for the exponential increase entails riskier strategies, and the smaller gap to fill in for the linear increase entails less risky strategies; these results seem to suggest that the new reform affects to a larger extent workers with a dynamic career than workers with a smooth career; 4. with both salary increases, on average the investment in the risky asset decreases over time and approaches 0 when retirement approaches; this result is in line with previous results on optimal investment strategies for DC pension schemes (see e.g. Haberman & Vigna (2002)) and is consistent with the lifestyle strategy (see Cairns (2000)), that is an investment strategy largely adopted in DC pension funds in the UK.
Finally, because the aim of this work is to reduce the gap between the old and the new pension, it is fundamental to investigate to what extent the gap is reduced. If the worker joins the pension fund for T years, then at retirement he will receive the new pension P n plus the additional pension P add provided by the pension fund. Therefore, his total pension will be P tot , given by P tot = P n + P add where P add = X so (T ) a 65 (1.5%) .
In order to compare the old pension with the total pension, • Figure 5 reports, in the case of exponential salary growth, the distribution, over the 1000 scenarios, of the final pension P tot that the retiree will receive; the old pension P o is also indicated, as a benchmark; • Figure 6 reports, in the case of linear salary growth, the distribution, over the 1000 scenarios, of the final pension P tot that the retiree will receive; the old pension P o is also indicated, as a benchmark.
Pension distribution with x T =65 and T=35 for exp salaries We notice that • in the case of exponential salary growth, the final pension is distributed more uniformly between 3.3 and 5.6 (the old pension being 5.7), while for the linear salary growth there is a large concentration of the final pension on the immediate left of the target, between 2.5 and the target 2.66; • what observed above is due to the fact that it is easier to reach the target in the case of linear increase than in the case of exponential increase, because (as observed in point 3. above) the gap between the old and the new pension is larger with the exponential increase than with the linear increase; • the fact that it is relatively easy to approach the target with the linear increase is consistent with the rate of increase of the annual targets r * = 4.86% (see Table 1).
This rate lies between the return on the riskless asset (1.5%) and the expected return on the risky asset (6%); opposite, with exponential salary increase the rate of increase of annual targets is r * = 7.76% that is larger than the expected return on the risky asset.

Changing the retirement age
In Section 5.2 we have set the retirement age equal to 65. It is clear that results strongly depend on the retirement age. In this section we consider different retirement ages, namely 60, 63, 65, 67 and 70, and investigate how the distribution of the final pension P tot changes accordingly. Table 2 reports, for each retirement age considered x T = x, the annuity valueä x , the conversion factor from lump sum into pension β x , and, for both cases of exponential and linear growths, the old pension P o , the new pension P n , the old net replacement ratio Π o and the new net replacement ratio Π n . The graphs in Figure 7 report the pension distribution with the different retirement ages considered in the case of exponential salary growth, while the graphs in Figure 8 report those related to the linear salary increase. showing the larger chance of approaching the target in the case of linear increase.
• With both salary increases, we observe that it is easier to reach the target with an older retirement age: higher retirement age means lower gap between the old and the total pension. This is intuitive and expected, and is due to different reasons: (i) because of actuarial fairness principles, the highest the retirement age, the lower the price of the lifetime annuity; (ii) a higher retirement age also means that the fund grows for a longer time, meaning a higher lump sum to be converted into pension. These two factors imply that the higher the retirement age, the higher the final pension, everything else being equal.
• In the extreme case of linear salary increase and retirement age equal to 70, the difference between the old and the new pension is so small that investing in the riskless asset for the entire working life (40 years) is sufficient to cover the gap, and the final pension P tot = 3.464 turns out to be higher than the old pension P o = 3.36 in 100% of the cases.

Break even points
In the previous sections we have seen that, expectedly, with both salary growths the old pension is larger than the new pension. This result heavily depends on the choice of the parameters and may no longer hold if some parameters change.
We have calculated what values of some key parameters would equate the old pension to the new pension, leaving the values of the remaining parameters equal to those of the base case. In particular, we have calculated the break even points for the parameters w, β and g. Figure 9 reports the six plots of the quantity P o − P n (difference between the old and the new pension) as a function of β, g and w, in both cases of exponential and linear salary. In particular, figures 9a, 9e and 9c report the exponential salary case, while figures 9b, 9f and 9d report the linear salary case. The red point is the base case, the green point on the x−axis is the break even point that equals the old pension to the new pension. (f) Break even point for g (lin salary) Figure 9: Break even points w.r.t. β, g and w for exponential and linear salary.
We notice the following: • the difference between the old and the new pension decreases with β, i.e., it increases with the price of the annuity 1/β. This is obvious, because the old pension is not affected by the price of the annuity, while the new pension is affected by β and it increases with it; therefore, the higher β the higher P n , the lower P o − P n . With exponential increase, the old and the new pension are equal when β = 0.12, that corresponds to price of the unitary annuity equal to approximately 8.33, against the base value of 17.785; with linear increase, the old and the new pension are equal when approximately β = 0.078, that corresponds to price of the unitary annuity equal to 12.82, against the base value of 17.785; • the difference between the old and the new pension decreases with w. This is again obvious, because the old pension is not affected by the mean GDP growth rate w, while the new pension is affected by w and it increases with it; therefore, the larger w the larger the new pension, the lower the gap between the old and the new pension. With exponential increase, the old and the new pension are equal with a mean GDP of approximately w = 6.5%, with linear increase, the old and the new pension are equal with mean GDP of approximately w = 3.5%; • the difference between the old and the new pension increases with g. This result is interesting, because both the old pension and the new pension are positively correlated with the salary growth g, but to a different extent: the old pension is affected by it only via the final salary that is used to calculate the pension income, the new pension is affected by it via the yearly contributions that are paid into the fund and accumulated until retirement. Figures 9e and 9f seem to suggest that the impact of g on the old pension is larger than that on the new pension, leading to a larger gap in case of increase of g; • the break even point for the salary increase rate is about g e = 1% for exponential salary increase, about g l = 1.5% for linear increase. This result indicates that with sufficiently small salary increase the old pension and the new pension coincide. In the presence of salary increase rates smaller than the break even point, the new pension is larger than the old one. This is consistent with what observed in point 3. in Section 5.2: the effect of the pension reform is more considerable for workers with dynamic career than for workers with smooth career.

Conclusions
In this paper, we have tackled the issue of the gap between an "old" pre-reform salary-related pension and a "new" post-reform contribution-based pension. We have investigated to what extent the gap can be reduced by adding to the state pension another pension provided by a DC pension scheme. We have used stochastic optimal control and a target-based approach to find the optimal investment strategy suitable to cover the gap between the salary-related and the contribution-based pension. The numerical simulations suggest that the gap between the salary-related pension and the contribution-based pension is larger for workers with dynamic career than for workers with a stagnant career, meaning more difficulties for the first class of workers to fill in the gap than for the second class of workers, even by assuming a higher savings capacity. Intuitively, the gap is easier to cover in the case of late retirement, and vice versa. This result is consistent with results in Borella & Coda Moscarola (2010). A slow salary increase associate to late retirement age can produce a new pension that is almost equal to (or even exceeds) the old pension. Expectedly, the gap reduces when the mean GDP increase and when the price of the annuity increases. Interestingly, the gap increases when the rate of increase of the salary increases.


Replicating “Predicting the present with Google trends” by Hyunyoung Choi and Hal Varian (The Economic Record, 2012)

In this note, the author describes different ways one could try to replicate Choi and Varian (Predicting the present with Google trends, The Economic Record, 2012). (Published in Special Issue The practice of replication) JEL A1 C1 C8 C53

In this note, I describe different ways one can replicate a paper and illustrate these ways by applying them to Choi and Varian (2012).
A replication can consists of 3 steps.
Step one is checking whether one can replicate the results of the paper using the data and code provided by the authors. One would expect that with the help of the authors one can replicate the various estimates reported in a paper. Such exact replication could be considered as successful if the vast majority of coefficients in a paper can be replicated exactly, with typos explaining deviations.
Second, one can try to collect the data and write the code based on the description in the paper one attempts to replicate. Ideally such replication would lead to the exactly the same numerical estimates though given the likely presence of implicit assumptions, small unreported data manipulations, updated data sources or misunderstandings by the person doing the replication, a replication could be deemed successful even if numerical estimates are not exactly replicated but qualitatively conclusions (i.e. statistical and economic significance) would be confirmed.
The two abovementioned approaches to replication are important as knowing this kind of checks can happen provides an incentive to researchers to spend more efforts on avoiding mistakes, to double and triple check their own results and ideally, to make their code, data and details on how these were created, publicly available. At the same time, these two approaches to replication are rather narrow: they only check whether one get similar results if one does exactly the same thing for the same time period and the same country and the same data source. However, since most people will only read abstracts, introductions and/or conclusions, and since we all have the tendency (and wish) to extrapolate results of studies of specific situations to general laws of economics, 'broader' replication is also needed.
These more comprehensive checks would be replication attempts of the overall conclusions of paper one wished to replicate rather than of the exact numerical estimates reported in the paper. That is, does one find that for many countries, or series, or time periods, the general conclusion still holds. Such replication attempts are important as they provide an incentive for researchers to avoid cherry picking results and to do various robustness checks. In addition, such checks should push researchers to be very careful in their conclusions and make it clear to the reader that their results are for a specific dataset and setting rather than should be seen as an illustration of an economic law that is true always and everywhere. Such comprehensive replication efforts are similar in nature to what meta-analyses or literature surveys are doing.
Let's now turn to the paper we will use to illustrate the above steps, the paper by Choi and Varian (2012) Choi and Varian (2012) includes 4 examples of macroeconomic statistics that can be forecasted more accurately if time series, reflecting the search intensity of terms related to the macroeconomic statistics, are included in the regression used to forecast the macroeconomic statistics. They show for example that if one augments an autoregressive model of U.S car sales, with series that reflect the evolution of search intensity for 'Trucks and SUVs' and "Auto Insurance" 1 , both in-sample and out-of-sample forecast accuracy improves by about 10%. Other examples focus on the forecasting of US unemployment benefits claims, visitor arrivals to Hong Kong and Consumer confidence in Australia. Choi and Varian (2012) has 1189 citations in Google Scholar. This is substantially more than Ettredge et al.(2005), the paper identified by Choi and Varian (2012) as the first to suggest using web search data in forecasting economic statistics, and substantially more than the early survey of this literature by Goel et al. (2010), also cited by Choi and Varian (2012). Ettredge et al.(2005) has 141 citations in Google Scholar while Goel et al. (2010) has 385 citations in Google Scholar. One possible explanation for the relative popularity of this paper is the fact that it has been written by two authors with Google as affiliation, and hence could be seen as some kind of 'official' paper connecting economic forecasting and web search intensity. An alternative explanation is that the Choi and Varian paper (2012) is more optimistic about how useful search intensity can be for prediction. Choi and Varian (2012) conclude: 'We have found that simple seasonal AR models that include relevant Google Trends variables variables tend to outperform models that exclude these predictors by 5 per cent to 20 per cent.' While Goel et al. (2010)'s conclude: 'We conclude that in the absence of other data sources, or where small improvements in predictive performance are material, search queries provide a useful guide to the near future".
The Choi and Varian (2012) paper can be replicated in the various ways described above, each way having a different goal in mind. Table 1 compares the results reported in the paper with various alternative approaches, focusing on the example of forecasting US car sales. Table 1 about here Column II checks whether one can replicate the results of the paper using the data and code provided on Varian's website 2 . In this case, using Choi and Varian (2012)'s data and code for the US car sales I get exactly the same results. If a further check of the other examples in the paper would also result in this conclusion, the first step of our replication would be deemed successful.
In column III of table I, I make an attempt to collect the data and write the code based on the description in the Choi and Varian's paper, rather than using the code and data they provide on Varian's website. For papers based on Google's search intensity, this kind of replication is unlikely to lead to exactly the same numerical estimates. As Choi and Varian (2012) note in their paper: "Note that Google Trends data is computed using a sampling method, and the results therefore vary a few per cent from day to day." Hence, it's unlikely that 6 or so years after Choi and Varian created their search intensity series, T get exactly the same series as they got. For the same reason, this replication will not be replicable as on different days I get slightly different numbers when downloading the search intensity series. Similarly, the US Sales series data available from the link provided in the paper are slightly different from the data provided on Varian's website 3 . Column III shows that when I use the data I downloaded 1 These are categories of searches rather than specific search terms, hence this is the evolution of the intensity for search terms that fall into the category 'Trucks and SUVs' and "Auto Insurance". 2 http://www.sims.berkeley.edu/~hal/Papers/2011/Data.zip from Google Trends I get slightly different estimates but the coefficients are sufficiently similar, both in the statistical and economic sense, suggesting that the Choi and Varian (2012) paper would also pass this second replication step.
Somebody reading only the conclusion of Choi and Varian (2012) that "We have found that simple seasonal AR models that include relevant Google Trends variables tend to outperform models that exclude these predictors by 5 per cent to 20 per cent" might well be convinced that Google Search helps to predict everything and everywhere. Hence, the third step in our replication plan tries to check whether Choi and Varian (2012)'s conclusion survives when applied to other settings than those checked in the paper.
In column IV, I extend the dataset from 2011 to 2017, and find that the predictive impact of adding search intensity terms gets weaker. While the coefficients of the search intensity variables are significant, the adjusted R 2 increases by less than 5%. Similarly, using Choi and Varian's model and time period on NZ car sales data shows insignificant coefficients for both search intensity variables, though the increase in adjusted R 2 is still more than 5% (column V). Extending the data up to 2017 for NZ further shows only a negligible increase in adjusted R 2 (column VI). Of course these are just some counterexamples 4 . Varying the countries or time periods further, one might find that differences due to the longer period or the NZ data are the exception rather than the rule. Hence, a replication should check systematically, varying one aspect of the original study, whether adding Google search intensity series adds predictive power.
For example, one could start by collecting data for a given series for many countries and estimate for all countries the same model suggested by Choi and Varian (2012), i.e. add search intensity data for 'Trucks and Suvs' and for 'Auto Insurance' to an AR(1,12) model 5 . This would allow to investigate to what extent there is heterogeneity in the contribution of these two search intensity series. And if such heterogeneity is found, one could try to explain this heterogeneity. For example, in countries where there is a greater number of searches (like the US) the predictive contribution of search intensity series could be bigger than in countries with a smaller number of searches (like New Zealand).
Similarly, one could vary other aspects of the Choi-Varian (2012) paper. One could continue to focus just on the US but check how changing the model affects the contribution of the search intensity series. One could for example, include additional autoregressive terms or lags which gives the "Adjusted Monthly Sales for Retail and Food Services" and the adjustment coefficients which are rounded at 3 digits. Multiplying these two quantities gives what should be the unadjusted series used by Choi and Varian (2012). The unadjusted time series of the estimates can also be obtained from the Census bureau https://www.census.gov/econ/currentdata/dbsearch?program=MARTS&startYear=1992&endYear=2017&cate gories%5B%5D=441&dataType=SM&geoLevel=US&notAdjusted=1&submit=GET+DATA&releaseScheduleId=] These two 'unadjusted' series are not exactly the same but very similar, differences could be related to rounding. Both series are slightly different from the data provided on Varian's website. The search intensity data on Varian's website are also standardized in a different way than the one's available from Google Trends. 4 These counterexamples are only based on in-sample forecasting performance. Choi and Varian (2012) also check out-of-sample forecast performance. 5 One example of a step in this direction is Tuhkuri (2016) who studies not only how Google Search can help predict unemployment at the US level but also at the level of the various different US states. of other series. Or one could vary the time period of the analysis, applying the Choi-Varian (2012) model to shorter or longer periods of data, or to non-overlapping various sub-periods.
It is hard to predict what the outcome of this third replication step would be though my guess is that Choi and Varian (2012)'s results would be true not just for the examples they tested, but rather would be true for some places and some time periods, rather than always and everywhere. Choi and Varian (2012)'s conclusion is written such that it allows for some uncertainty: 'relevant Google Trends variables tend [bold added] to outperform models that exclude these predictors by 5 per cent to 20 per cent' 6 . So the result of the third step replication would help to quantify the 'tend [bold added] to outperform' from Choi and Varian's conclusion. That is, once the study's internal replication is successful (step 1 and 2), we know that under some circumstances, adding search intensity series improves forecasts. If step 3 would come to the conclusion that adding search intensity series improves forecasts only for the cases they describe in the paper, one could argue that step 3 of the replication was not successful, that their results are not externally replicable. However, just like it is unlikely that a single study will consider all possible circumstances, it is unlikely that any replication would be able to consider all possible circumstances. Hence, rather than leading to a binary conclusion (the external replication is successful or not successful), the replication would estimate how often, and in what circumstances, adding search intensity series improves forecasts.
So far, I have focused on a three steps replication plan, where the first two steps focus on the internal validity of the paper, while the third step focuses on the external validity of the paper. These three steps are all focusing on 'academic' replication, however. But replication could also leave the ivory tower and check whether a paper is replicable in 'real life', that is, are the conclusions of a paper, after the paper has been made public, actually used by decision makers? In the case of Choi and Varian (2012), even if academic studies find Google Search can help forecasting, the ultimate 'replication' would be that there are businesses and government that actually use this knowledge in real life, and because of this, have a competitive advantage. That would be the 'real' proof that the predictive power of Google search intensity, is not just an academic gimmick but does provide an economic meaningful advantage to forecasters. Mui (2014) writes that 'The Bank of Israel and the Bank of England incorporate Google analytics into some of their forecasts.', suggesting adding Google Search intensity might even pass this advanced replication benchmark. At least, in some cases, that is. *** means significant at 1% significance level, * means significant at 10% significance level.
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