Carl Grekou
email: g.grekou@u-paris10.fr

Romain Perez
email: romain.perez@oecd.org

Child Mortality in sub-Saharan Africa: Why Public Health Spending Matters

Keywords: JEL Classification: H51, I12, I18, O15 Millennium Development Goals, MDGs, Under-5 mortality rate, sub-Saharan Africa, Public expenditure on health

Since 2000, child mortality has dramatically decreased in Africa. Based on an econometrical analysis over 45 sub-Saharan African countries, this paper analyses the determinants of such evolution, and shows that urbanization, sanitation improvement and GDP growth per capita played a critical role in this overall improvement over 2000-2011. The increase in public health expenditures proved to be also decisive, though the elasticity with mortality rate is much weaker. Reaching the Abuja target of 15% of public health expenditure in total public expenditures would have decreased the under-5 child mortality rate by 9% over 2001-2011. It could further reduce this rate by 14% over 2012-2021, and allow Africa to save 19.8 million of children lives. It would also help the region to achieve the Millennium Development Goal on child mortality (reduce by two thirds under-5 child mortality over 1990-2015) by 2022-23, while it would not be reached before 2027 otherwise, according to our estimates.

Introduction

Reducing child mortality in Africa has been recognized as a major priority by the international community and African governments. Therefore, the reduction by two thirds of under-five (child) mortality (U5MR)1 between 1990 and 2015 is the fourth goal of the eight United Nations Millennium Development Goals (MDG). The African Union Assembly has consistently reiterated its commitment to this MDG by recommending concrete actions since then, and pledged to allocate at least 15% of government expenditures to health under the 2001 Abuja Declaration. With the introduction of Poverty Reduction Strategy papers (PRSPs) and the heavily Indebted Poor Countries (HIPC) Initiative in 1996 and its enhanced version in 1999, the support to the public health sector has gradually increased in sub-Saharan Africa, reaching 36.6 USD billion (3.06% of GDP) in 2011 versus 8.2 USD billion in 2000 (and 2.15% of GDP).

Progress has been noticeable in terms of health outcomes, with a drop by 39% in U5MR between 1990 and 2011. Though the MDG4 (-66%) appears out of reach for 2015, progress has been continuous and widespread, including every African country but one.2 Thirteen countries out of forty-nine have reduced their U5MR by more than 50%, while other health and mortality indicators have improved significantly. 3However, the causes of this general improvement remain debated leading to an overall uncertainty on the prospect of health conditions and mortality rates in Africa in coming decades. The role of public authorities and international donors in these results is often pointed out not only to account for improvements but also to explain the failure of African countries to reach MDG4. Indeed, the Abuja target has still not been met at the end of 2011, public health expenditures representing only 10.43% of total public expenditures in Sub-Saharan Africa (versus 8.69% in 2000). By contrast, "non-political" factors -such as economic growth, access to water and sanitation, urbanization -are often highlighted as the real determinants to this gradual improvement in child health. According to some studies, the relationship between public health expenditures and health conditions is even non-existent or so weak that increasing public expenditures should not be considered as a priority.

The question is to know whether more public resources should be allocated to health systems in order to achieve MDG4 and save children lives in Africa, or whether these rare resources should be allocated to other public priorities, considering that the real determinants of public health and children mortality are not linked to public health expenditures.

Beyond this, this analysis is also critical to understand why MDG4 will not be achieved in time; when this goal can be realistically achieved; and which target could be considered beyond 2015, given existing trend in mortality reduction. In a nutshell, should African governments keep the Abuja target as a political priority in the perspective of the MDG4?

What implications would have a dramatic increase in health expenditures -and possibly ODA -allocated to health budget in Africa on children lives? Here are some issues tackled by this paper.

Thus, the aim of this paper is to analyze socio-economic determinants of child and neonatal mortality in sub-Saharan Africa over the 2000-2011 period. It considerably differs from other analyses in the extent that it also focus on the implications of the Abuja target on child mortality. Also, in a forecast exercise based on a number of assumptions (on change in public health spending, GDP growth, urbanization, . . . ), we develop a series of projections of under-5 mortality rate which, given the scenario, allow us to determine the MDG4 achievement year and therefore children lives saved or lost.

The paper is organized as follows. Sections 2 and 3 respectively present the review of literature and the methodological approach. In Section 4, we present the key results.

Section 5 is devoted to the importance of public health spending in achieving the Millennium Development Goal on child mortality. Finally, Section 6 concludes.

Review of literature

The determinants of health conditions -and child mortality -in Africa remain a controversial topic in academic literature. Some factors are widely recognized as essential, such as GDP per capita growth, access to water and sanitation and female education. Others are more uncertain. The role of public health expenditures has been questioned, though the most recent literature tends to show a positive correlation between health outcome improvements and expenditures.

2.1 GDP growth, female education and health conditions are closely related Economic growth and general health improvement are generally recognized as closely linked. Growth has several possible direct and indirect effects on health, provided that it benefits to the majority of people: increase in purchasing power and better access to food, water, sanitation and health services; better access to education and birth control means. . . Additionally, economic growth is generally associated with higher public revenues, and leads to improved public health infrastructure and public health service coverage, stimulating demand for health services [START_REF] Cutler | The Determinants of Mortality[END_REF].

In return, healthier individuals will affect the economy in different ways, as shown by [START_REF] Bloom | The health and wealth of nations[END_REF]2003), with more productive workers, less sickness absence or early retirement, more investment in education, and greater expectation of a longer life, which stimulate savings available for investment in the economy. Therefore, [START_REF] Gupta | Does Higher Government Spending Buy Better Results in Education and Health Care?[END_REF] showed that the population's health status improves as per capita incomes rise, with lower under-five and infant mortality rates. The World health Organization (WHO) estimates that an increase of life expectancy at birth by 10% will boost economic growth rate by 0.35% a year.

In the same vein, female literacy and gender equality are acknowledged as important determinants of health conditions, in particular of children (see [START_REF] Baldacci | Social Spending, Human Capital, and Growth in Developing Countries: Implications for Achieving the MDGs[END_REF]World Bank, 1993). Women tend to play a more important role in family health and sanitation, therefore educating mothers helps improving nutrition and their children's health [START_REF] Zakir | Factors Affecting Infant Mortality Rates: Evidence from Cross-sectional Data[END_REF]Wunnava, 1997, Currie and[START_REF] Currie | Mother's Education and the International Transmission of Human Capital: Evidence from College Openings[END_REF]. Studies have consistently found a strong relationship between women education and child health, as illustrated by [START_REF] Sastry | Family-level Clustering of Childhood Mortality Risk in Northeast Brazil[END_REF] in Brazil, where mothers with at least three years of school education were found to have 32% lower mortality risk among their children than mothers with less education. In a study of several African countries, [START_REF] Madise | Heterogeneity of Child Nutritional Status between Households: A Comparison of Six Sub-Saharan African Countries[END_REF] came to similar conclusions. [START_REF] Magadi | Status of women and infant/child health in Kenya with particular reference to the high mortality zone in Nyaza Province[END_REF] complemented this stream of work, highlighting that father's education was also significantly associated with child health in the case of Kenyan communities, where mothers do not have much access to education.

2.2

The role of public health expenditure is more controversial

The relationship between public health expenditures and health outcomes has been extensively studied. Early studies offered a rather contrasted perspective on this relationship. Some (see [START_REF] Kim | More Resources, Better Health? A Cross-National Perspective[END_REF][START_REF] Musgrove | Public and Private Roles in Health[END_REF][START_REF] Burnside | Aid, the Incentive Regime, and Poverty Reduction[END_REF] find no evidence that total spending on health (public plus private) has any impact on child mortality or that it is not the dominant driver of child mortality outcomes [START_REF] Filmer | Child Mortality and Public Spending on Health: How Much Does Money Matter?[END_REF]. [START_REF] Carrin | Exploring the Health Impact of Economic Growth, Poverty Reduction and Public Health Expenditure[END_REF] studied the influence of poverty reduction and public health expenditure on health status based on a sample of 40 developing countries and covering the period [1985][1986][1987][1988][1989][1990]. Their methodology relied on estimating an equation where the dependent variable is health status, captured by life expectancy, infant mortality and under-five mortality. Each of these variables is regressed on public health expenditure to gross national product (GNP) ratio, incidence of total absolute poverty and the GNP per capita. The empirical results indicate that GNP per capita is positive and highly related with health status while the reduction of poverty is directly associated to health. However, public health expenditures are not statistically significant. This latter result is in line with that of [START_REF] Filmer | The impact of public spending on health: does money matter?[END_REF] which examined the impact of both public spending on health and non-health factors (economic, educational, cultural) in determining child (under-5) and infant mortality. Based on a multivariate regression they concluded to a very weak impact of public spending on health. According to them, change in public health expenditures would explain less than one-seventh of change in under-five mortality, and these results were not statistically significant. [START_REF] Gupta | Does Higher Government Spending Buy Better Results in Education and Health Care?[END_REF] also stated that the evidence of the relationship between health expenditures and health outcomes is not robust. Non-robustness as the authors acknowledged may be linked to the fact that the data on public health expenditure and mortality are un-likely to be comparable across countries. Secondly, non-robustness as suggested by [START_REF] Temple | The New growth Evidence[END_REF] and [START_REF] Durlauf | Growth Econometrics chapter 8 in[END_REF] may be due to the fact that most of these studies suffer the problems common to cross-country regressions, particularly, unobserved heterogeneity that might be correlated with the variable of interest.

Using a model similar to that of [START_REF] Filmer | Child Mortality and Public Spending on Health: How Much Does Money Matter?[END_REF][START_REF] Temple | The New growth Evidence[END_REF], [START_REF] Wagstaff | The Millennium Development Goals for Health: Rising to the challenge[END_REF] show that good policies and institutions (as measured by the World Bank's Country Policy and Institutional Assessment or CPIA index) are important determinants of the impact of government health expenditures on outcomes. In particular, as the quality of policies and institutions improves (as the CPIA index rises), the impact of government health expenditures on maternal mortality, under weight children, under-five and tuberculosis mortality also increases and is statistically significant. However, they conclude that the impact of government expenditures on under-five mortality remains not significantly different from zero.

Similarly, [START_REF] Rajkumar | Public spending and outcomes: does governance matter?[END_REF] used annual data for 1990, 1997 and 2003 and an ordinary least square regression for 91 developed and developing countries to assess the social outcomes of government spending on health status. Their results indicated that public expenditure on health has a greater negative impact on child mortality in countries with good governance, high quality of bureaucracy and low corruption levels. Public spending on health care alone does not guarantee improved social outcomes, good quality governance tools such as well-functioning budget formulation, execution and monitoring are essential in order to produce a better health position.

More recent literature tends to demonstrate a positive relationship between spending on health and health outcomes. The extension of data collection and coverage, as well as the joint improvement in health outcomes and public health expenditures in recent years, could account for this change in perspective.

Following [START_REF] Gupta | The effectiveness of government spending on education and health care in developing and transition economies[END_REF], [START_REF] Gupta | Helping Countries Develop: The Role of Fiscal Policy[END_REF] reached the conclusions that government spending on health care does improve country's health status. They underlined the necessity of efficient assignment of resources. They also found that health care is also affected positively by per capita income, urbanization, adult literacy, access to water and sanitation, and private spending. [START_REF] Anyanwu | Health Expenditures and Health Outcomes in Africa[END_REF] provided econometric evidence linking African countries' per capita total as well as government health expenditures and per capita income to infant mor-tality and under-five mortality in Africa between 1999 and 2004. They concluded that total health expenditures, including the public component, are important contributor to health outcomes, while ethnolinguistic fractionalization and HIV prevalence are also affecting significantly these outcomes. They also discussed the implications of these results in the debate over the means to attain the targets envisioned by the Millennium Development Goals. [START_REF] Novignon | Health and vulnerability to poverty in Ghana: evidence from the Ghana Living Standards Survey Round[END_REF] used panel data from 1995 to 2010 covering 44 countries in Sus-Saharan Africa as well as fixed and random effects panel data regression models to show that health care expenditure significantly influences health status through improving life expectancy at birth, reducing death and infant mortality rates. Both public and private health spending were showed correlated to these outcomes, even though the impact of public health expenditures were shown to be stronger. As [START_REF] Anyanwu | Health Expenditures and Health Outcomes in Africa[END_REF], they stated that increasing health care expenditure is still required to achieve the Millennium Development Goals, while effective public-private partnership in allocating health care expenditures were also needed.

Similarly, the importance of urbanization is discussed

Mortality rate is generally higher among rural households than in their urban counterparts as access to health is typically better, and private cost of health (such as transportation costs) tends to lower in urban areas, as shown by Schulz (1993). Besides, urbanization plays an important role in health conditions as it contributes to an epidemiological transition that affects the pattern of mortality. With urbanization, non-communicable diseases such as depression and heart disease, as well as road traffic deaths, are gradually replacing the traditional causes of disability and premature death in rural areas, such as infectious diseases and malnutrition. This process, of great importance for child mortality, is particularly important in developing regions, where the WHO estimates that non-communicable diseases will account for seven out of every ten deaths by 2020, compared with less than half today.

Despite rapid urbanization in sub-Saharan Africa, few case studies have been conducted on changes in mortality pattern, especially due to the epidemiological transition. Agyei-Mensah and de-Graft (2010) presented evidence to illustrate the nature and speed of this transition in Accra, Ghana. They demonstrated that it transition is polarized across social class: wealthy communities experience higher risk of chronic diseases, while poor communities experience higher risk of infectious diseases and a double burden of infectious and chronic diseases.

The views on the relationship between urbanization and health remain contrasted. Unplanned rapid urbanization has been identified as a health hazard, as more than a third of the population in sub-Saharan Africa are classified as urban dwellers -this proportion could exceed 50% by 2035. However, [START_REF] Leon | Cities, urbanization and health[END_REF] showed in its exhaustive review of literature that there is no clear indication that people, including children, are worse off than people living in non-urban settings. Data available would suggests that in most instances child mortality is lower in urban than in rural areas and that there is no urban penalty in child health in low and middle income countries. [START_REF] Fotso | Urban-rural differentials in child malnutrition: trends and socioeconomic correlates in sub-Saharan Africa[END_REF] showed that in sub-Saharan Africa the prevalence of child growth stunting is lower in urban compared with rural areas. Three series of factors are generally said to explain this phenomenon: absolute poverty and malnutrition remain mainly rural phenomena (1), vaccination coverage rates are generally higher in urban populations than in their rural counterparts and (3) dissemination and uptake of effective interventions such as oral rehydration therapy are likely to be more effective in an urban setting. Lastly, most of the growth in urban population observed and projected to occur in coming decades will be in small and medium-sized towns and cities of fewer than 1 million inhabitants.

Despite this bulk literature, on the link between public health spendings and health status -namely child mortality -very few research have sought to tackle this issue under the MDGs scope. Indeed, a considerable number of studies addresses the issue of health status determinant, child mortality being one of the most important indicators. However, to the best of our knowledge, there are no studies attempting to analyze the role of public health spendings as the main channel to reduce child mortality as suggested by the Abuja's target and the MDG4. In this paper, we focus on the role played by changes in public health expenditure in the evolution of child mortality rate. More specifically, after determining the elasticity of child mortality to public health spendings, we tried to assess the effects of the Abuja commitment (a comparative analysis between the observed rate of mortality versus that would be observed if the commitment was respected). We also address the issue of the year to which the MDG4 could be reached. Obviously, given the mortality rate path, this objective will not be completed in 2015. Finally, we analyze the effects of such delay, namely in terms of lives saved / lost.

Data and Methodology

Data

In this paper, we have retained neonatal and under-5 mortality rates (per thousands) as health status indicators. This is in line with existing literature. The under-5 mortality rate is a target fourth goal of the United Nations Millennium Development Goals, while the neonatal mortality rate4 is often used to measure the quality of health services.

The data used are mainly extracted from the World Development Indicators database (World Bank) and cover the period 2000-2011. Our sample consists in 45 sub-Saharan African countries (see Appendix A.2 for more details). The rest of the dataset contains public spending on health (expressed as share of GDP) which is our interest variable and a set of control variables such as GDP per capita (PPP), urbanization rate, water and sanitation improvements, private expenditure on health, and Official Development Assistance (ODA).

Table A.3 in Appendix A summarizes and gives further details about the data.

Descriptive statistics: health expenditures and health outcomes

Since 2000, the level of public expenditure on health (as share of GDP) in SSA countries increased from 2.15% to 3.06%. Private expenditure on health also increased even, and as a consequence, total expenditure per capita almost tripled, from US$ 42 to US$ 117.7. In the meantime, life expectancy increased dramatically, while mortality rates declined. The largest decrease is that of the under-5 mortality rate which fell from 136.5 (per 1,000) in 2000 to 102.28 in 2011, a 25% decrease, followed by the infant mortality rate decrease (-21.7%).

Neonatal mortality rate followed the same trend, but in lesser extent with a decline of 13.63%.

Econometrical approach

The econometrical approach is based on panel data regressions. The basic equation (in logarithm) examines the direct impact of public expenditure on health outcomes, as proxied by neonatal and under-5 mortality rates. We specified the model as follows:

M ortality it = α i + βP ubExp it + φX it + it (1)
where M ortality is our health outcomes (neonatal or under-5 mortality rates), P ubExp are the public expenditure on health, X and φ are respectively the vector containing the control variables and estimated coefficients of these control variables. i = 1, . . . , N t = 1, . . . , T and are respectively the individual and temporal dimensions of the panel, α i the country fixed effects and it the error term.

In line with existing literature, we include the income level (GDP (PPP) per capita). As emphasized by [START_REF] Filmer | The impact of public spending on health: does money matter?[END_REF], the inclusion of income is necessary to control for the impact of income on health which works through a variety of indirect channels (better nutrition, better housing, better sanitation,. . . ). We therefore expect a negative relationship between the mortality rates (neonatal and under-5) and income levels.

We also integrate female literacy rate. Indeed, as stated above, it is often argued that female literacy is an important children health status determinant. One can argue that in Africa, women play an important role in family health and well-being. Furthermore, as stressed by [START_REF] Currie | Mother's Education and the International Transmission of Human Capital: Evidence from College Openings[END_REF], educated mothers are more likely to be aware of nutrition and children health.

We Finally, we added urbanization (defined as the percentage of the urban population in the total population). As recently stressed by the World Bank's Global Monitoring Report (GMR, 2013), urbanization helps pulling people out of poverty and advancing progress towards the Millennium Development Goals (MDGs). Given the fact that living in an urban area can somehow 5 facilitate access to health care, we expect a negative relationship between mortality rate and public health expenditure.

As stated above, the econometric approach is based on panel data regressions. We consider three different estimation methods to ensure robustness of our analysis. The two first estimation methods consist respectively in applying fixed-effects (FE) and random effects (RE) estimation techniques to model 1 (i.e. equation 1). These two techniques can handle systemic tendency of individual specific components to be higher in some units than others (individual effects) and possible higher in some time periods than others (time effects).

Another advantage of these two techniques is that they adjust for heteroskedasticity. 6 Given that GDP per capita is potentially endogenous, we rely on Instrumental Variable (IV) to 5 See previous section.

6 Unlike previous studies, we do not apply Ordinary Least Squares (OLS) on the pooled data since the OLS estimator is likely to generate highly biased coefficients by ignoring both country specific effects and possible endogeneity of the right hand side variables. Even if they still require assumptions to be satisfied (such as strict exogeneity), the fixed-effects and random effects estimators are therefore preferable to the pooled OLS estimator.

deal with this possible endogeneity issue. Instrumental variable methods allow consistent estimation when the explanatory variables are correlated with the error terms of a regression relationship. 7 IV regression consist in instrumenting an explanatory variable (that supposed to be endogenous) by another variable (the instrument), correlated with the "endogenous" variable but not with the error term. In our study, we have instrumented GDP per capita using its lagged value (second lag).

4 Key results: estimating the main economic determinants of child mortality reduction in sub-Saharan Africa 4.1 Urbanization, GDP growth and improvement in sanitation accounted for most of the improvement in child mortality in Africa According to our results (see Table 2), the main determinant to child mortality over 2000-2011 was urbanization. The estimated elasticity varies between -0.33 and -0.72 and is statistically significant for all models (see Tables 2 and3). Similarly, GDP per capita change is another critical and statistically reliable determinant to account for under-5 child mortality variation over this period of time. Our estimates range from -0.23 to -0.36: a 1% increase in the income level (GDP per capita), leads to a reduction of under-5 mortality rate between 0.23% and 0.36%. Improvement in sanitation facilities (% population with access) is also an important determinant for under-5 mortality rate. The estimated impact varies between -0.19 and -0.24 and is statistically significant at 10% confidence level. 8 Female enrollment in secondary is also negatively linked with under-5 mortality rate but this relationship does not appear statistically significant. Finally, we found that net O.D.A (Official Development Assistance) received per capita negatively impact the under-5 mortality rate but marginally only (a 1% increase in O.D.A. would lead to a reduction of U5MR around 0.04%).

7 Such correlation may occur when the dependent variable causes at least one of the covariates ("reverse" causation), when there are relevant explanatory variables that are omitted from the model, or when the covariates are subject to measurement error. 8 We do not mention the FE-IV estimate since it is not statistically significant.

4.2

The role of public expenditure increases was less determinant, but statistically significant

From the three estimations (FE, RE and FE-IV), public expenditure on health is found to be negatively correlated with under-5 mortality rate and statistically significant. The correlation is however small. The elasticity coefficient varies between -0.06 for the FE-IV estimation and -0.10 for the RE estimation, which mean that a 1% increase in public health expenditure leads to a reduction between 0.06% and 0.10% of the under-5 mortality rate.

Our results also show a negative but not statistically significant relationship between private expenditure and under-5 mortality rate. Indeed, private expenditure appears to be significant at lower confidence level than the conventional ones. 9

The analysis is similar for neonatal mortality rates

Neonatal mortality rates, which dropped less significantly than U5MR, appear to have similar determinants, as shown in Table 3. Estimated elasticities are however smaller, due to the magnitude of neonatal mortality change. Once again, urbanization, GDP per capita and sanitation appear to be the main factors to mortality rate reduction. The effects of public expenditures is more marginal, but still significant. To sum up, the income level (GDP per capita), improvements in sanitation access, urbanization, O.D.A and public expenditure on health are important determinants in reducing the neonatal and under-5 mortality rate. Moreover, our results suggest that increasing public expenditures does help bringing down children mortality rate, though the correlation coefficient is weaker than for structural determinants such as income level.

5 Achieving MDG4 in Africa: the importance of public health expenditures

As it can be seen in Figure 1, under-5 mortality rate in SSA fell from 178 (per thousands) to 108.3 between 1990 and 2011. This decrease represents a decline of 39.1% in two decades, which is significant but far from the target set for the MDG4 (reducing child mortality by two third between 1990 and 2015). As a result, it is clear that SSA countries will not reach the MDG4 by 2015. We have estimated that the under-5 mortality rate should be around 93.5 (per thousands) by then. This is far from the target of 60 per thousands (i.e. the 1990 rate's third).

From this perspective, an interesting issue is to know when SSA countries would reach the "MDG 4". Based on projections, we estimated that the MDG4 could be reached in 2027, if everything remains unchanged. This result should be interpreted cautiously since there is a certain level of uncertainty on key assumptions, including on GDP growth in Africa over this period. What if Abuja's commitment was respected?

In 2001, African countries committed to devote 15% of their budget to health expenditure, under the Abuja Declaration. However, this commitment has not been generally respected: from 2000 to 2011, the share of government expenditure devoted to health expenditure in total public expenditure increased from 8.7 to 10.4% (see Table 4). In the previous section, we found that the impact of public expenditure on health is relatively weak, with elasticities varying between -0.06 and -0.10. However, given the gap between the Abuja target and the effective level of public health expenditure, the increase in expenditures could be important for child health if African governments were to meet their commitment. This is all the more true given that capital spending in public expenditures have long-term effects that cumulate over time.

Based on the econometric work presented in section 3, and a simple projection exercise (described in Appendix C.3), we have analyzed the implications of such increase in public health expenditures. In terms of under-5 child mortality rate, reaching the Abuja target would have implied an average drop of 9% per year from 2001 to 2011, allowing Africa to save a total of 16.3 million of children lives over this period of time, as shown in Table 5 (exhaustive results are presented in Appendix C.2). On average, public health expenditures should have been increased by 52%, which explains the magnitude of the impact on U5MR.

Reaching the Abuja target could have much stronger effect as time goes by, while proving easier to reach. As a result of the increasing trend in public expenditure, the gap between this target and the effective level of expenditure narrows, so that the annual cost of reaching the Abuja target would represent 1.2% of GDP beyond 2012 (vs. an average of 1.3% over [2001][2002][2003][2004][2005][2006][2007][2008][2009][2010][2011]. As health systems benefit from the accumulation of capital, the effects of the long term increase in public spending are magnified, so that child mortality rate would be on average 14% lower over 2012-2021, representing a total of 19.8 million of lives saved over this period. These results raise several questions related to the importance and priorities of health policies in Africa. On the one hand, we see that committing more public resources would have a dramatic impact on health, allowing Africa to save almost two million children per year in the coming decade and significantly contributing to the achievement of the MDG4.

On the other hand, the financial burden of the Abuja target should not be underestimated, and it remains challenging to identify how these additional resources could be mobilized given that other development priorities (education, infrastructures, . . . ) also require more public spending. In this perspective, the improvement in the efficiency of public spending could play a critical role in the reduction of child mortality.

In the same vein, the role of capital public health spending should be pointed out. As a result of their lasting effect, their increase has dramatic effects on child mortality and proves much more important than recurrent public spending. Of note, the WHO ( 2010) estimates that at least 50% of medical equipment in developing countries is either partly usable or totally unusable.

Conclusion

Our study confirms the importance of structural factors -such as urbanization and longterm growth -in the evolution of child mortality in Africa over the period 2000-2011. This shed some lights on the challenge to reach MDG4 in Africa by 2015. However, it also points out the statistical significance of the relationship between public health expenditure and under-5 child mortality rate, in line with the most recent literature on this topic. This relationship is of critical importance for African development, despite the weakness of the correlation coefficient between U5MR and public expenditure. Indeed, the MDG4 target, which aims at reducing child mortality by two-third, could be achieved in 2022 if African governments were to respect the commitment made in 2001 and increase the share of their health public expenditure to 15%, while the target would not be met before 2027 otherwise.

On the field this increase in public expenditure would dramatically change the pattern of child mortality, allowing Africa to save almost 20 million of children lives between 2012 and 2021. The cost of reaching the Abuja target would amount annually to 1.2% of African GDP, which obviously shows the limitations of this commitment. However, the human and social effects of such increase appear to be of such magnitude that it could deserve further attention.

Another avenue that was not explored in this paper concerns the improvement in the efficiency of public health expenditures. Undoubtedly, this qualitative improvement could also play a major role in helping African countries in their efforts to cut child mortality and achieve Millennium Development Goals. In 2000, Lesotho, Rwanda and Sierra Leone spent respectively 3.95%, 1.65% and 3.59% of their GDP as health expenditure. Their under-5 mortality rates were respectively 117.3, 183 and 240.6. In 2011, health public expenditure for Lesotho, Rwanda and Sierra Leone respectively corresponds to 9.45%, 6.10%, 3.39% of their GDP and the under-5 mortality were respectively 86, 54.1 and 185.3. The striking fact is the considerable drop (-70.4%) of the under-5 mortality rate in Rwanda. In a lesser extent, we also note the reduction in under-5 mortality in Lesotho. In general, all countries increased their public expenditure on health and have, despite the heterogeneity, and all but one recorded a decrease in the under-5 mortality rates.

C. Key results

C.1. Causality tests

Results displayed in Table C.1 are those obtained from the test proposed by [START_REF] Dumitrescu | Testing for Granger non-causality in heterogeneous panels[END_REF]. For brevity, we do not present the details. Note however that under the null of Homogenous Non Causality (HNC), there is no causal relationship for all the cross-units of the panel. Under the alternative, there is a causal relationship for at least for one cross-unit.

Figure 1 :

 1 Figure 1: Under-5 mortality rate in SSA (observed and forecasted)

  According to our estimate, increasing health public expenditure to 15% of the total public expenditure would allow African economies to reach the MDG4 by 2022-2023 instead of 2027, but would clearly not suffice to meet the 2015 deadline.

Figure 2 :

 2 Figure 2: Under-5 mortality rate: observed and Abuja engagement

B

  . Graphics: Public expenditure and mortality rates in SSA For illustrative purposes, we presented in Figures B.1 and B.2, the level of our health outcomes and the level of the public expenditure on health. The scatter plot representations allow us to observe the dispersion around the trend. B.1. Public expenditure and Under-5 mortality rate in SSA With respect to the under-5 mortality rate, as Figure B.1 (a and b) shows, we can observe the diversity of the situations. The decreasing trend reflects the fact that, overall, an increase in the public expenditure could lead to a decrease in the under-5 mortality rate. Only a few countries present "low" levels of under-5 mortality rate (Seychelles, Mauritius, Cape Verde. . . ).

Figure

  Figure B.1.a: Public expenditure on health and under-5 mortality rates in SSA (2000)

Figure

  Figure B.1.b: Public expenditure on health and under-5 mortality rates in SSA (2011)

Figure

  Figure B.2.b: Public expenditure on health and neonatal mortality rates in SSA (2011)

Table 1 :

 1 Descriptive statistics

	2000	2011	Mean	Std.dev Min	Max
			(2000-2011)

Note: Values reported correspond to average for all African considered countries. *= 2010's value

Table 2 :

 2 Under-5 mortality rates and public expenditure on health

	Dependent variable		Under-5 mortality rate
	GDP per capita	-0.23*** -0.28***	-0.36***
		(-4.45)	(-5.99)	(-4.81)
	Public expenditure	-0.08*** -0.10***	-0.06**
		(-3.56)	(-4.47)	(-2.54)
	Private expenditure	-0.04	-0.03	-0.04
		(-1.38)	(-1.05)	(-1.10)
	Urban	-0.72*** -0.33***	-0.53**
		(-4.33)	(-2.88)	(-2.44)
	Sanitation	-0.24**	-0.19**	-0.13
		(-2.60)	(-2.51)	(-1.04)
	Female secondary	-0.09	-0.18	-0.16
		(-0.65)	(-1.39)	(-1.00)
	O.D.A	-0.04*** -0.05***	-0.04**
		(-2.86)	(-3.57)	(-2.53)
	Constant	10.16*** 9.51***	10.39***
		(16.80)	(17.54)	(15.35)
	R-squared	0.63	0.62	0.61
	Estimation method	FE	RE	FE -IV
		Within	GLS	TSLS
	Note: * * * , * * and * respectively denote significance at 1%, 5% and 10%. t-statistics are reported
	in parentheses.

9 Significant at 20%.

Table 3 :

 3 Neonatal mortality rates and public expenditure on health

	Dependent variable		Neonatal mortality rate
	GDP per capita	-0.13*** -0.16***	-0.17***
		(-5.09)	(-6.37)	(-4.68)
	Public expenditure	-0.03*** -0.04***	-0.02*
		(-2.86)	(-3.59)	(-1.76)
	Private expenditure	-0.05*** -0.04***	-0.05***
		(-3.16)	(-2.71)	(-2.86)
	Urban	-0.37*** -0.23***	-0.29***
		(-4.44)	(-3.33)	(-2.76)
	Sanitation	-0.14*** -0.12***	-0.11*
		(-3.02)	(-3.04)	(-1.83)
	Female secondary	-0.06	-0.10*	-0.13*
		(-0.94)	(-1.66)	(-1.64)
	O.D.A	-0.01	-0.01	-0.00
		(-0.92)	(-1.22)	(-0.55)
	Constant	6.52***	6.35***	6.65***
		(21.30)	(21.69)	(20.20)
	R-squared	0.64	0.64	0.63
	Estimation method	FE	RE	FE -IV
		Within	GLS	TSLS

Note: * * * , * * and * respectively denote significance at 1%, 5% and 10%. t-statistics are reported in parentheses.

Table 4 :

 4 Public expenditure on health in SSA countries

		2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
	% Gov.	8.69 8.73 9.12 9.65 10.27 10.70 10.58 10.66 10.30 10.17 10.06 10.43
	expenditure
	% GDP	2.15 2.26 2.34 2.50	2.64	2.70	2.69	2.74	2.76	2.98	2.93	3.06

Source: World Bank (WDI)

Table 5 :

 5 Increasing public health spending to 15% of total public spendinghealth and financial implications

		U5MR WDI:	U5MR Results	Difference in	Children	Increase in
		observations	(Abuja target)	U5MR	lives saved	public health
		and estimates				spending
		(after 2011)
	2000	153.39	144.49	-6%	979,355	73%
	2011	108.34	95.52	-12%	1,828,477	44%
	2016	90.19	77.48	-14%	1,997,792	37%
	2021	74.36	62.82	-16%	1,972,071	27%
	Source:Authors' calculations

Table C .

 C 1: Causality tests between public health spending and the mortality rate indexes Public spending to X" indicates that we test the null hypothesis of Homogenous Non Causality (HNC) from Public spending to X. "*" indicates rejection of the null at the 5% significance level.C.2. Abuja target and under-5 mortality rateTableC.2: The effects of increasing public health spending to 15% of total public spending (Abuja target) on U5MR

	Children lives	saved	(C)		1,224,194	1,418,311	1,501,279	1,536,696	1,537,231	1,564,883
	Children lives	saved	(B)		734,516	854,680	906,379	928,579	929,071	946,547
	Children lives	saved	(A)		979,355	1,203,361	1,270,470	1,299,019	1,299,191	1,321,308
	Difference in	U5MR	(C)		-0.07	-0.08	-0.09	-0.09	-0.09	-0.09
	W HN C Difference in	U5MR	(B)		Public spending to Under-5 mortality rate K=1 K=2 K=3 11.41 3.64 6.55 -0.04 -0.05 -0.05 -0.06 -0.06 -0.06	Public spending to neonatal mortality rate K=1 K=2 K=3 18.48 5.86 8.92
	Z HN C ZHNC U5MR after U5MR after U5MR after Note: "WDI: U5MR Difference in	observations Abuja -FE Abuja -FE-IV Abuja -RE U5MR	and estimates (A) (B) (C) (A)	(after 2011)	54.08* 40.00* 153.39 144.49 146.71 142.26 149.19 138.53 141.62 136.63 144.99 134.01 137.16 132.02 140.92 129.96 133.09 127.96 -0.06 -0.07 -0.08 -0.08	136.89 126.19 129.24 124.23 -0.08	132.81 122.17 125.19 120.21 -0.08	12.12* 3.12*	31.96* 4.96*	90.86* 67.66*	28.41* 8.66*	53.36* 9.18*
					2000	2001	2002	2003	2004	2005	2006

The probability of dying between birth and age five years expressed per 1000 live births.

Swaziland, with a U5MR of 104 at the end of 2011 is 24% above the level reached in 1990, despite a large drop since 2000.

See Table 1 in Section 3.2 for further details.

Neonatal mortality rate is the number of neonates dying before reaching 28 days of age, per 1,000 live births in a given year.

We surveyed the literature and set β to 18% (see[START_REF] Elmendorf | Health Expenditures, Services, and Outcomes in Africa: basic data and cross-national comparisons 1990-1996[END_REF].

We proceeded in a similar manner for the following period, continuing to subtract the impact of recurrent expenditure of the previous period.

Appendix

A. Data appendix

A.1. Sub-Saharan Africa statistics α and β are respectively the share of public expenditure allocated to Capital and Recurrent expenditure.

To evaluate the effects of Abuja commitment, we proceeded as follows:

where M ort.rate it is the under-5 mortality rate obtained in period 1 if the Abuja's commitment was respected; M ort.rate it is the observed mortality rate and m/G the estimated elasticity of under-5 mortality rate to public expenditure (see section 3). Ġ1 is the variation of public expenditure to reach the Abuja's target. Equation C.2 therefore allows us to approximate the mortality rate in period 1 if Abuja's commitment was respected.

We proceeded in a similar manner to obtain the under-5 mortality rate in period 2. The main difference here is that we subtracted the effect of recurrent expenditure on health.

Indeed, we assume that only capital expenditure have a persistent effect on the mortality rate. The share of recurrent expenditure on health is given by in equation C.

where g = M ort.rate 2 -M ort.rate 1 M ort.rate 1 is the observed decline rate in under-5 mortality rate and Ġ2 the variation of public expenditure between period 1 and 2 to reach the Abuja's commitment.

Equation C.3 can be rewritten as follows:

M ort.rate i2 = M ort.rate i1 × [1 + g + m/G (β Ġ1 -Ġ2 )] (C.4)


Ha-Thu Nguyen
email: hathunguyen12@gmail.com

Default Predictors in Credit Scoring -Evidence from France's Retail Banking Institution

Keywords: Auto Loans, Credit Risk, Credit Scoring, Logistic Regression. JEL Classification. G3, C51, C52

The aim of this paper is to present the set-up of a behavioral credit-scoring model and to estimate such a model using the auto loan data set of one of the largest multinational financial institutions based in France. We rely on a logistic regression approach, which is commonly used in credit scoring, to construct a behavioral scorecard. A detailed description of the model building process is provided, as are discussions about specific modeling issues. The paper then uses a number of quantitative criteria to identify the model best suited to modeling. Finally, it is demonstrated that such model possesses the desirable characteristics of a scorecard.

Introduction

"Credit-scoring technologies have served as the foundation for the development of our national markets for consumer and mortgage credit, allowing lenders to build highly diversified loan portfolios that substantially mitigate credit risk. Their use also has expanded well beyond their original purpose of assessing credit risk. Today they are used for assessing the risk-adjusted profitability of account relationships, for establishing the initial and ongoing credit limits available to borrowers, and for assisting in a range of activities in loan servicing, including fraud detection, delinquency intervention, and loss mitigation. These diverse applications have played a major role in promoting the efficiency and expanding the scope of our credit-delivery systems and allowing lenders to broaden the populations they are willing and able to serve profitably." Alan Greenspan, U.S. Federal Reserve Chairman, October 2002 Speech to the American Bankers Association 2 Given the key role played by credit in all economies, evaluating its associated risk is a crucial issue. The traditional way to evaluate credit risk, which relies on human analysis of a borrower's financials and future prospects, has been subject to critics. Various credit-related biases indeed exist, making human analysis less reliable. 3 In particular, agents tend to be too confident about their knowledge [START_REF] Alpert | A Progress Report on the Training of Probability Assessors[END_REF]). In addition, as shown by [START_REF] Barber | The Courage of Misguided Convictions: The Trading Behaviour of Individual Investors[END_REF], agents' overconfidence bias is aggravated by the importance of the task, and by the fact that they tend to neglect past failures and focus on past successes. Libby (1975) shows that judgmental decisionmaking based on a batch of ratios allows bankers to predict firms' bankruptcy in a three-year horizon with a 74% accuracy, whereas using a simple method based solely on the liability/asset ratio actually 2 improves this percentage. This result is in line with [START_REF] Meehl | Clinical versus Statistical Prediction: A Theoretical Analysis and a Review of the Evidence[END_REF], according to whom the human capacity to integrate complex and diverse sources of information is questionable. Anecdotal feedback (as opposed to statistical feedback) is given in lending institutions, making improving inductive reasoning difficult [START_REF] Nisbet R | Improving Inductive Inference[END_REF]).

The method of credit scoring is an attempt to address these concerns. Credit scoring is the methodology that scores accounts as to their likelihood of the outcome of, for example, becoming delinquent. It is often performed by lenders and financial institutions to access a person's creditworthiness. Consequently, credit scoring relies much more on a quantitative model in which the criteria as well as their relative importance are well defined. This is of course not to say that credit scoring does not need human judgment, but it leaves less room for human error. For instance, in some retail finance, the sole results of a scoring model cannot be used for decision-making purpose. Compliance departments always require at least some degree of human judgment in the decision making process.

As a matter of fact, credit scoring was first used in the 1960s and is still widely used by banks and lending institutions for several reasons. First, credit scores help automating manual decisions and are based on the following statistical principle: If past trends indicate towards future trends, then a score leads to better decisions than manual ones because there is no subjectivity involved for the majority of decisions. Second, scores are also cost-effective because they reduce turnaround time, and potentially, headcount requirement. As a result, credit scores help lenders in assessing risk more fairly because they are consistent and objective. Third, consumers also benefit from this method: No matter who the clients are, their credit score only reflects their probability to repay debt obligation, based on their past credit history and current credit status. Thus, credit scores improve performance substantially while keeping costs down. Progress in technology and in the sharing of information, namely the establishment of Credit Bureau in the United States and similar institutions in other countries, have contributed to the rise of credit scoring in every kind of lending [START_REF] Altman | Credit Risk Measurement: Developments over the last 20 years[END_REF].

The use of credit scores presents undoubtedly the greatest value in the decision-making process, when the underwriter must define clear scenarios based on scores and policies. The score allows the lender to answer questions such as whether to accept or reject a loan, or what are the maximum loan amounts, the applicable interest rates, the terms of the loan, etc. Credit scores may have different types, depending on where and how they are used. Some of these types are application scores, behavior scores, collections scores, fraud scores, etc. These names differ by the emphasis placed on different aspects of the scores, such as the source of information, the tasks being performed or what is being measured.

Credit scoring is an applied domain and has seen regular contribution from various authors. Early treatments of the scoring problems are Bierman and Hausman (1970) and Dirickx and Wakeman (1976), as well as Srinivasan and Kim (1987) among others. Most credit scoring models use past data to estimate risk for new applicants by assuming that past risk correctly predicts future risk. The number of factors taken into account has significantly increased with later models. [START_REF] Hand | Construction and Assessment of Classification Rules[END_REF] and Thomas, Edelman and [START_REF] Thomas | Credit Scoring and its Applications[END_REF] present credit scoring and its application in various lending activities. [START_REF] Hand | Construction and Assessment of Classification Rules[END_REF] also handles the issue of evaluating the effectiveness of credit scores ("scoring the score").

Various statistical methodologies have been investigated to construct credit scoring models over the last 50 years. With time, academic researchers focused more and more on credit scoring techniques, then replaced the first oversimplified univariate analysis. [START_REF] Beaver | Financial ratios predictors of failure[END_REF] and Altman (1968)4 examined a multiple discriminant analysis (MDA) by using financial ratios as predictors of failure.

Several years later, the MDA was still the dominant statistical technique, and was further investigated by [START_REF] Deakin | A discriminant analysis of predictors of business failure[END_REF][START_REF] Edmister R | An Empirical Test of Financial Ratio Analysis for Small Business Failure Prediction[END_REF], [START_REF] Blum | Failing company discriminant analysis[END_REF][START_REF] Altman | Zeta-analysis: A New Model to Identify Bankruptcy Risk of Corporations[END_REF][START_REF] Taffler R | Going, Going, Gone -Four Factors Which Predict[END_REF], Altman et al. (1995), and[START_REF] Lussier R | A non-financial business success versus failure prediction model for young firms[END_REF]. Nevertheless, most of these authors mentioned in their researches that two basic assumptions of MDA are often broken when applied to the failure prediction.5 Further discussions on this topic are presented by [START_REF] Barnes | Methodological implications of non-normality distributed financial ratios[END_REF], Karels & Prakash (1987) and Leay and Omar (2000). Regarding these issues, the conditional logit model has been employed for the first time by [START_REF] Ohlson | Financial ratios and the probabilistic prediction of bankruptcy[END_REF]. By using this methodology, the restrictive assumptions of MDA are not required and the conditional logit model permits dealing with categorized data. The logistic model also returns a score between zero and one, which easily can be converted to the probability of default (PD). Another advantage is that the estimated coefficients can be interpreted one by one as the importance of each of the independent variables in the explanation of the PD. [START_REF] Wiginton | A Note on the Comparison of Logit and Discriminant Models of Consumer Credit Behavior[END_REF] in his research found that logit model outperforms discriminant analysis. Following Ohlson and Wiginton, many researchers such as Campbell and Dietrich (1983), [START_REF] Zavgren | The prediction of corporate failure: the state of the art[END_REF], [START_REF] Gentry | Classifying bankrupt firms with funds flow components[END_REF], Aziz et al. (1988), Gardner and[START_REF] Gardner | Evaluating the Likelihood of Default on Delinquency Loans[END_REF] Other statistical techniques have also been suggested to improve the prediction quality of credit scoring models such as Bayesian methods, neutral network, decision tree, k-nearest neighbor, survival analysis, fuzzy rule-based system, support vector machine, and hybrid models. However, the logistic regression still remains the most popular method. Nowadays, even in the largest financial institutions in the world, logistic regression is always considered as one of the main approaches to predict defaults.

Our paper falls into this strand of the literature by providing an empirical analysis of credit scoring in the case of auto loans. From a methodological point of view, the paper focuses mostly on the creditscoring process using different statistical techniques. From an applied perspective, we provide an application on real data of a France-based retail bank. The behavioral scorecard developed in the paper is a key element of the research. In fact, application scorecards have been investigated in different academic papers whereas behavioral scorecards have not received as much attention by researchers. Additionally, the presentation of real behavioral credit-scoring process is something occasionally encountered, and nothing is done in a form similar to the paper. Finally, it should be noticed that our credit-scoring model has been successfully implemented in the bank which provided the data, hereafter called bank A.

The rest of paper is organized as follows. Section 2 presents the credit scoring development process. Section 3 describes our case study model. Section 4 is devoted to the model application and its results. Section 5 concludes the paper.

Credit Scoring Development Process

Data Preparation & Gathering

Data is of paramount importance to the scorecard development process. Data preparation is timeconsuming and consists of the following four main activities:

-Characteristic identification: Scorecards are based on characteristics, which are in turn translated into questions that the underwriter asks a customer. The questions depend on the type of scorecard, product, market, local compliance and laws. Thus, each characteristic has varying importance and predictive power in the model.

-Selecting the development sample:

There are two basic types of data that can be used in the scorecard: demographic data (data collected at the time of application) and performance data (data that covers total historical delinquency performance since time of opening). Different data will be used depending upon the type of scorecard. For example, an application scorecard uses only demographic data captured at the time of application, while a collection/ behavior scorecard is unlikely to use much demographic data, but will rather concentrate on using performance data.

-Checking data quality: After collecting data, the underwriter needs to check data quality. Data need to be complete (contains all relevant information), accurate (being true) and the processing of data needs to be robust (able to withstand changes in the environment).

-Good/ Bad definition: Good/ Bad account definition determines whether accounts are likely to roll to write off or not. For instance, good accounts are likely to repay fully and are those that have always been past due of at most 30 days but no more, whereas bad accounts are those that have been delinquent for 90 days or more. However in every case, it is recommended to carry out the analytical method called "Roll Rate Analysis" in creation of the good/bad definition [START_REF] Naeem | Credit Risk Scorecards: Developing and Implementing Intelligent Credit Scoring[END_REF]).6

Data transformation: Fine & Coarse Classing

Following the preparation of data, the underwriter has clean data in a form ready to use for modeling. The next step is to analyze the characteristics suitable for being modeled in the data preparation stage. The purpose is to identify the characteristics (or questions) that can separate good accounts from bad ones. Hence, a predictive characteristic contains attributes that display clearly different levels of risk for different attributes. There are two stages in this process: Fine and Coarse Classing.

(i) Fine Classing

In fine classing step, each attribute is broken down and analyzed. Fine classing presents an opportunity to review the data in a summarized form. It is the first step along the road to coarse classing data and identifying characteristics to be included in the scorecard.

At this stage, the underwriter determines if there are any characteristics that have such low predictive power that there is no benefit in including them in any further analysis. To do this, firstly the underwriter calculates the good/bad odds. It is defined as:

ݏܱ݀݀ ൌ ݀ܩ% ݀ܽܤ%

The Odds measure the proportion of good accounts to bad accounts. If this ratio is zero, then there is equal chance of an account with that attribute being good or bad. If it is less than 1 then there are more Bads than Goods.

With the good/bad odds, we can now calculate weights for all fine classes. Weight is a measure of how good or bad the accounts are within a particular attribute:

ݐ݄ܹ݃݅݁ ݂ ݁ܿ݊݁݀݅ݒ݁ ൌ ݈݃ሺܱ݀݀ݏሻ

A weight shows whether there are more Goods than Bads for a given attribute, or vice versa. If the weight is negative, this means there are more Bads than Goods, and if it is positive, it means there are more Goods than Bads. If it is close to zero then there are similar numbers of Bads and Goods.

The weights are then used to calculate the Information Value (IV) of a characteristic. This is first done for all attributes of a characteristic. These are then totaled to give an information value for the characteristic as a whole. ܸܫ ൌ ݐ݄ܹ݃݅݁ ൈ ݀ܩ%ሺ െ %݀ܽܤሻ

The Information Value measures the ability of a characteristic to separate between good and bad accounts. Information Value is always greater than 0 but is generally less than 2.

Using the IV, the underwriter can exclude non-predictive variables. Following is one of the most frequently used rules:

:݁݀ݑ݈ܿݔܧ ܸܫ ൏ 10% :ݕݎݐ݂ܿܽݏ݅ݐܽܵ 10% ܸܫ 100% ݕ݈݄݃݅ܪ :݁ݒ݅ݐܿ݅݀݁ݎ ܸܫ 100%
A characteristic with a very low information value is considered to be non-predictive. Calculation of fine classes with information value and exclusion of non-predictive variables is the first step in the process of coarse classing. Obviously, each lending institution has its own policy regarding the exact threshold less than which ݏܸܫ are considered non-predictive.

(ii) Coarse Classing

The objective of coarse classing is to combine the small fine classes into larger groups so that the number of accounts in each group is significant enough. This optimizes the discriminatory power of attributes and ensures the model is stable. The underwriter should look for similar bad rates as shown by the weights when deciding which groups to put together. This process in reality tends to be manual and requires significant human judgment by the credit officer.

Modeling Techniques

Once the final coarse classes have been decided, the next step is to model the relationship between the variables, which may be usually either linear or logistical. A linear regression is used for a continuous outcome variable, whereas a logistic regression is retained for a binary outcome variable. Input to regression model comes from coarse classing output.

Scorecards are based on multiple regression which analyzes several variables to predict an outcome.

There are three types of regression: forward selection, backward elimination and stepwise regression. Forward selection starts with an empty model, and then adds a new variable at each step, only stops adding when no further benefit from additional variable. In contrast, backward elimination starts with model containing all possible variables, and then removes a variable at each step, only stops removing when we see deterioration of model performance. Finally, stepwise regression is a combination of these two previous regressions.

Generally, the underwriter should use 5% or 10% significance level but also consider adjusting the significance level to remove/add variables so that the number of variables should be as relevant as possible.

Checking for Correlation

The underwriter needs to check the correlation between every pair of variables in our model, and considers removing one of the variables if correlation is higher than 0.5 in absolute value (i.e. if the two variables are "too" correlated). The choice of the rule is not rigid and can vary according to the modeler's personal opinion if this preserves the model's stability and performance.

Analyzing Model Performance

Score validation provides a measure of the performance of the scorecard. There are several different measures that can be used to assess the effectiveness of a scorecard before it is implemented, as well as during the monitoring phase. These measures are summarized in Table 1. A good KS is normally superior to 35% and higher is better.

A higher KS value indicates that the scorecard is doing a better job of separating Goods from Bads, and thus, rank-ordering risk.

A Gini coefficient higher than 40% is considered to be satisfactory.

The higher the Gini, the better the model since again, Goods are better separated from Bads.

The ideal score distribution is the one with no score having more than 5% of accounts in it.

If the rule is violated, the scorecard will make no sense.

Implementation and Use

The implementation analysis starts by comparing the performance of the new scorecard to that of the existing one. If the new scorecard cannot discriminate better between Goods and Bads then it is unlikely that it would be implemented. The underwriter should compare the scorecards by looking at their respective KS and Gini statistics.

A scorecard is built upon a data sample taken from the past, and the performance of the scorecard is therefore reliant upon the assumption that the past will accurately represent the future. Since the past and the future normally will not be the same, it is important that the underwriter monitors the portfolio to identify and incorporate any differences into the scorecards as quickly as possible.

Monitoring is also an important part in understanding the portfolio and how it is performing, and ensuring that the scorecard is making optimal decisions given the available information.

This section outlines the entire credit scoring process and also demonstrates that credit scoring is not simply a mathematical model of predicting defaults. In reality, it requires an important degree of human judgment during its development and implementation process. In fact, by finding considerable differences between the implied loss distributions of the two banks with equal regulatory risk profiles, Jacobson et al. (2006) prove that the formal design of a rating system and the way in which it is implemented can be quantitatively important for the shape of credit loss distributions. Moreover, if the loan officers use unique data based on hard information to develop credit scoring models, and they are volume-incentivized, Puri et al. (2013) show that loan officers increasingly use multiple trials to move loans over the cut-off, both in a regression-discontinuity design and when the cut-off changes. Another relevant research to address the incentives of financial intermediaries is presented by Keys et al. (2010). Their empirical result proposes that securitization, by converting illiquid loans into liquid ones, could reduce lenders' incentives to screen borrowers, thus limiting the utility of credit scoring.

Model Description

The behavioral credit-scoring model presented in this paper is used, for the first time, to estimate the probability of default of all individual automobile loans in bank A, based mostly upon the customers' financial, family standing and payment behaviors. This scorecard will be applied for each current loan in the individual automobile loans portfolio so as to assess the quality of the portfolio.

The model is developed in the SAS language, using the assumption that future performance will reflect past one. The model is then expected to be stable over time. However, substantial changes in macroeconomic environment, government regulation, product specifications, and population might affect scorecard stability.

Variables used in this scorecard include both application and behavior data. Application data presents some of the following characteristics: employment seniority, house ownership, marital status, family income, rent amount, and other comprehensive expense amount. Behavioral data includes worst delinquency in last three months, number of month-in-default, time since last delinquency, and other payment behavior variables. Hence, all data comes from loan application forms, collected during the lifecycle of customers. There is no use of external data, like credit bureau data or market information.

All available data from the observation window was used for the development sample (80% of outcome periods) and validated in the validation sample (20% remaining outcome periods). Three observation dates have been chosen: 01/2010, 04/2010, and 07/2010; and three outcome periods have been considered:

• February 2010 to January 2012

Application and Results

The model development begins with data gathering and processing. This phase aims to understand the data and its quality in order to define the scope of study.

The scorecard development process is summarized in Figure 1.

Data preparation

The model depends totally upon data, and there are many data considerations during the scorecard development and use. Data is then verified to make sure of its transparency, its quantity and its quality.

Application and behavior data

As previously mentioned, application data are those collected at time of application such as marital status, residential status, age, income, and other comprehensive expense amount. In addition, some variables included in application data may not be used in their raw format but used to generate other variables. The following are example of generated variables:

•

Generated cross-variables

These variables are created for the purpose of having new variables with a stronger information value.

Examples of cross-variables include age-revenue, loan term-loan amount.

A total of 32 variables are initially selected for inclusion in the behavioral scoring model. These variables are listed in the first column of Length of the longest spell of arrears ( 9) Group 1: Customer's personal characteristics (age, sex, religion, marital status, education, employment sector and place, etc.) Group 2: Data on the enterprise (type, professional skills, number of employees, productivity, profitability, etc.) Group 3: Profitability (main and secondary revenue, revenue stability) Group 4: Amount and composition of assets (total assets including money and deposits) Group 5: Financial situation (initial and current amount of loans received, defaults, loans granted) Group 6: Investment plans (presence of investment plan, other sources of finance) Group 7: Customer's relationship with bank (past loans with bank, savings account with bank, etc.) Group 8: Bank's control of credit risk (loan destination, disbursement form, method collateral, contractual conditions on interest rates, etc.)

Fine & Coarse classing

The fine and coarse classing step needs to be done before modeling the score. This step aims at building homogeneous classes in terms of risk or bad rate, and also identifying the characteristics that can better separate the Goods out from the Bads.

For each variable, we apply the "IV" (Information Value) method:

ൌ ሺ ሻ ൌ ൬ % % ൰ ൌ ቆ ൈ ∑ ∑ ቇ ൌ ൈ ሺ% െ % ሻ
This method is first applied to continuous variables and then to categorical variables. We categorize continuous variables as suggested by Thomas et al. (2002). First, the range of values for each continuous variable was split into ten categories, based on the assumption that all categories should have the same number of observations. Second, odds ratios and information values were computed for each category (fine classing) and categories with similar values were joined together (coarse classing). This step was also performed for categorical variables.

Let us now present a number of examples for both types of variables.

Example of a continuous variable: loan term

A common approach for the initial fine classing of a continuous variable is to create a standard number of equally sized groups. In this case, the variable is sorted and classed into at most 10 intervals. Tables 3 and4, as well as Figures 2 and3 summarize the results obtained for loan term. In the coarse classing step (Table 4), we look at the similar bad rates, and then create three homogeneous classes for the variable. Coarse classing gives us more visibility even if we lose a little bit of significance.

Example of a categorical variable: Residential status

Loan term

Weight Tables 5 and6 and Figure 4 summarize the analysis of residential status within the behavioral scorecard development. Once fine classing is done, the next stage is to combine the small fine classes into larger groups so that the number of accounts in each group is significant enough.

However, there are two opposite purposes when implementing coarse classing. On the one hand, it is better to represent the characteristic with as few coarse classes as possible. The reason is the smaller the number of classes, the less complicated and over-fitting the model. On the other hand, having too few coarse classes can make lose valuable information because the smaller the number of potential coarse classes, the less powerful the variable, and vice versa.

Thus, for residential status, the goal is to reduce the number of classes as much as possible, but with a minimal information loss. In this case, merging different fine classes into two larger coarse classes, which are owner and others, reduces the IV from 43.9% to 41.6%.

The information values of all candidate variables can be found in Table 7. Obviously, the most significant variables are all behavioral ones. They are those that characterize historical bank-client relationships, a finding that is in line with the comprehensive overview in Anderson (2007). The remaining variables are significant for the most parts.

Modeling

Before entering in the modeling step, it is necessary to review characteristics for possible inclusion in a scorecard. There are some primary factors to be considered:

• The variables need to be relevant.

• They have a significant degree of predictive power (through their Information Value).

• They have a low correlation with each other (through Cramer's V & Pearson's test). 7

At this step, only the variables that are adapted to these criteria for modeling are selected. Next, to model the relationship between the variables, the logistic regression method works best for binary criterion (Good/Bad) and is recommended by bank A's global banking policy. Such regression is estimated using the Maximum Log-likelihood method.

Logistic regression requires some assumptions as follows: (i) categorical target variable; (ii) linear relationship, with the log odds functions; (iii) independent error terms; (iv) non-correlated predictors; and (v) use of relevant variables.

We have tested 8 models, each with a different combination of variables. To this end, we rely on automated selection routines, such as forward selection, backward elimination and stepwise regression.

Compared to the other two techniques, the backward elimination method has notable advantages. First, a set of variables could have a significantly higher predictive power even if any subset of them does not. This is a default of forward selection and stepwise regression, which do not admit a variable into the model simply because its individual predictive power is not good enough. Furthermore, backward elimination measures the model's joint predictive power as a whole because it starts with all of the variables. Thus, the backward method is selected.

Model Performance Measures

7 Cramer's V shows the degree of association in tables which have more than 2x2 rows and columns. It is

calculated as ܸ ൌ ට ఞ మ ேሺିଵሻ
, where ߯ ଶ is derived from Pearson's test, ܰ is the the total number of observations and ݇ is the number of rows or columns in the table. Cramer's V may vary between 0 and 1. A value close to 0 indicates little association between variables and vice versa.

Once the modeling step is done, we assess the model performance. At this stage, all candidate models need to be passed through performance tests.

First, the candidate model is rejected if one of the following criteria is violated: i. KS is generally higher than 35%. ii. Gini is normally superior to 40%. iii. Regarding to score distribution, no score has more than 5% of accounts. iv. The bad rate decreases when the score increases and the good/bad odds increase when the score increase. v. There is no significant change (ideally less than 1%) in the criteria values above of the development sample and ones of the validation sample.

Second, we keep only models that satisfy the criteria, and then choose the best model by comparing the criteria values of different models.

Finally, we need to make sure that the final model can validate every performance criterion.

As a result, we have tested 8 models, following the three steps presented above, and have finally found one model which outperforms the others. The final model contains 10 variables which are presented in Table 8. We provide below performance measurement results of our best model.

KS & Gini

Table 9 and Figures 5 to 7 display the results regarding KS statistic and Gini coefficient. As shown, we observe a small variation in KS and Gini in the development and validation samples. KS and Gini are also greater than 50%. These elements confirm the power and the stability of the model in the whole population. The Lorenz curve (Figure 7) shows the cumulative percentage of good against the cumulative percentage of bad in the development and validation samples. The green line indicates the distribution of good and bad under random scoring where every customer has a 50-50 chance of being good (or bad), whereas the red (validation sample) and blue (development sample) lines show the plot using our Figure 8 shows that the bad rate decreases as the score increases and the good/bad odds increase as the score increases. This is obviously a desirable characteristic of the model.

Score Distribution

Figure 9: Score distribution

The score distribution (Figure 9) shows our expected result. This is a well-distributed plot with no score having more than 4% of accounts. In other words, the scores given by the model is rather homogeneous and not concentrated.

All these results confirm the performance of our selected model.

Calibration & Implementation

Calibration

Score must now be calibrated and presented in the proper unit. In other words, calibration is a way of aligning our scorecard so that the odds by score relationship are consistent across all scorecards.

Let ݂ ௧௧ be the calibrated (target) score. The alignment process is simply given by: ൌ ࢻ ࢻ ൈ

As the result of applying to our specific model, score calibration is presented as follows: The FinalScore value represents the final score that is consistent across all scorecards of the bank, regardless of the country where those scorecards are established.

Finally, we can sort the population based on this metric. Five credit ratings are proposed to tally the population into groups of varying credit risk degrees. The result is shown in Table 10:

Implementation

Before a model can be put into use, an independent model-validation unit must document if model validation results are correct. Internal audit will then verify that each model enters production with formal approval by the validation unit.

The validated model will be now used to assess the portfolio's quality. To achieve this, we must first apply the final equation to score every present accounts. These observations after calibration will be tallied into five credit ratings (CR) as shown above, as well as into a number of groups based on the accounts' default probability (ܲܦሻ. The expected gross value of losses can be estimated by the following relationship:

ݏݏݎܩ ݀݁ݐܿ݁ݔܧ ݏݏܮ ൌ ܦܲ ൈ ݃݊݅݀݊ܽݐݏݐݑܱ ݐ݊ݑ݉ܣ ே ୀଵ
The expected net value of losses is calculated by taking into account the recovery rate: ݐ݁ܰ ݀݁ݐܿ݁ݔܧ ݏݏܮ ൌ ݏݏݎܩ ݀݁ݐܿ݁ݔܧ ݏݏܮ ൈ ሺ1 െ ݕݎ݁ݒܴܿ݁ ܴܽ݁ݐሻ These measures allow us to calculate the provision amount corresponding to the cost of risk of the portfolio. One can therefore determine the evolution of the portfolio's risk and analyze its quality.

Conclusion

The objective of the paper is to show how scorecards are built within a lending institution by giving a detailed development process of a real behavioral scorecard. We have provided a glimpse of the credit risk management process and how loans are classified, what are the data needed for scoring and how they are selected, and finally how the models are implemented, checked for validity and compared between themselves. Our paper is mostly in line with existing researches, and has the additional advantage of describing how credit scoring is applied in real life.

This paper may be extended for further research. First, it would be interesting to compare the result of the logistic regression with the results of other statistical techniques. Second, we should extend the current credit process to collection/fraud by developing a collection/fraud scorecard for the purpose of being more efficient in optimizing the net expected loss and then improving the portfolio management process. Third, analyzing the advantages/defaults of different performance indicators (such as KS, Gini, Score distribution, etc.) used to assess scorecard power would be a promising extension.

,

  Platt et al. (1990), Lawrence and Arshadi (1995), Becchetti (2003), Kleimeier et al. (2007), Avery et al. (2012) also used logit models to predict default. Recently, Charitou, Neophytou and Charalambous (2004) demonstrated once again that the logit method outperforms other methods based on their empirical results.

Figure 1 :

 1 Figure 1: Scorecard development process

  Time with bank = Date of situation -Date of first account opening (in years) • Time at present address = Date of situation -Date of entry to the house (in years) Behavioral data are essential to have an overall look at the history of delinquency performance since time of opening, in order to predict future clients' payment behaviors and portfolio quality. The following are examples of behavioral generated variables: • Maximum bucket (or number of days past due) in the last 12, 6 and 3 months • Number of unpaid months in the last 12, 6 and 3 months

Age

Postcode

Figure 2 :

 2 Figure 2: Fine Classing of loan term Figure 3: Coarse Classing of loan term

Figure 4 :

 4 Figure 4: Fine and Coarse Classing of Residential status

Figure 5 :Figure 6 :

 56 Figure 5: KS of the development sample

Figure 7 :

 7 Figure 7: Gini Curves Comparison

Table 1 : Principal Performance Measurements with Decision-making Rules

 1 Bads in the i th class is noted cp . Similarly, the cumulative percentage of Goods in the i th class is noted cp ୋ .

	1. Kolmogorov-Smirnov statistic	2. Gini coefficient		3. Score distribution	4. Bad rate and Good/
							Bad Odds by Score
	The KS measures the widest spread	Like KS, the Gini coefficient	Score distribution is	This measurement is
	between cumulative Goods and	is a quantitative measure of	another measurement	necessary to verify if
	cumulative Bads.	how	well	the	model	that the underwriter	the	bad	rate	is
	The divergence between the two	discriminates between Goods	looks for a well-	decreasing as the score
	curves determines the strength or	and Bads, but by looking at	distributed plot.	increases	and	the
	weakness of the scorecard to	actual discrimination versus		good/bad odds increase
	differentiate good customers from	perfect discrimination.			as the score rises.
	bad customers. In other words, the	Like KS, the calculation of
	higher KS, the better the model since Goods are more separated from Bads. Calculation: If we divide the sample into 10 classes by descending risk level, the	the Gini is presented below: D ୋ୧୬୧ ଵ ൌ ൛൫cp ୋ -cp ୋ షభ ൯൫cp ୧ୀଵ cp షభ ൯ൟ -1
	cumulative percentage of The calculation of the KS indicator
	is presented as follows:
	D ୗ ൌ Max ୧ ൛|ܿ െ ܿ ீ |ൟ

Table 2 : Comparison of candidate variables commonly used in credit scoring models through different researches Nguyen (2014) -France Kocenda and Vojtek (2011) -Czech Kleimeier et al. (2007) -Vietnam Schreiner (2004) -Bolivia Vigano (1993) -Burkina Faso Crook et al. (1992) -UK

 2

	Group 1: Customer's personal	Socio-demographic	variables:
	characteristics (marital status,	Education (1), Marital status (2),
	age, region, residential status,	Years of employment (3), Sector
	job, time at present address,	of employment (4), Gender (5),
	number of children, time at	Date of Birth (6), Type of
	present employment, time at	employment (7), Number of
	bank)			employments (8), Employment
	Group 2: Loan characteristics	position (9), Credit ratio 1 (10),
	(type of credit, vehicle type,	Credit ratio 2 (11), Region (12)
	vehicle condition, vehicle
	price, loan amount, loan	Bank-client relationship variables:
	duration, client's contribution-	Own resources (13), Amount of
	to-vehicle price ratio, client's	loan (14), Purpose of loan (15),
	initial contribution, existence	Length of client/bank relationship
	of a co-borrower)		(16), Date of account opening
	Group 3: Financial situation	(17), Deposit Behavior (18), Loan
	(income, debt-to-income ratio,	Protection (19), Type of product
	troubled debt restructuring)	(20), Number of co-singers (21),
	Group 4: Other behavioral	Date of loan (22).
	variables (number of months
	in bucket 0, max bucket in the
	past 12/6/3 months, number of
	months of non-payment in the
	past	12/6/3	months,
	delinquency status)
	Group 5: Generated cross-
	variables (age-revenue, loan
	term-loan amount, marital
	status-revenue)

Table 3 : Fine classing of loan term Loan term (months) %Good %Bad Odds Weight IV Bad Rate

 3

	0 -35	3.6%	2.0%	1.8	0.6	1.0%	4.0%
	36-48	19.9%	15.5%	1.3	0.2	1.1%	4.1%
	49 -59	6.4%	6.1%	1.1	0.1	0.0%	5.8%
	60 -72	68.1%	75.6%	0.9	-0.1	0.8%	5.8%
	>=73	2.0%	0.8%	2.4	0.9	1.0%	2.3%
	Total					3.9%

Table 4 : Coarse classing of loan term Loan term %Good %Bad Odds Weight IV Bad Rate

 4

	<= 48	23.5%	17.5%	1.3	0.3	1.8%	4.0%
	49 -72	74.5%	81.7%	0.9	-0.1	0.7%	5.8%
	> 72	2.0%	0.8%	2.4	0.9	1.0%	2.3%
	Total					3.5%

Table 5 : Fine classing of residential status

 5

	Residential status	%Good %Bad Odds Weight	IV	Bad Rate
	Owner	59.8% 28.4%	2.1	0.7	23.4%	2.9%
	Live with parents	10.7% 13.8%	0.8	-0.3	0.8%	7.4%
	No answer	0.2%	0.2%	0.9	-0.1	0.0%	6.8%
	Live with employer	2.1%	2.6%	0.8	-0.2	0.1%	7.2%
	Tenants	27.2% 55.0%	0.5	-0.7	19.6%	9.9%
	Total					43.9%

Table 6 : Coarse classing of residential status Residential status %Good %Bad Odds Weight IV Bad Rate

 6

		Loan term
	1,0		87,1%		1,0			87,1%
	0,8				0,8
		60,1%
	0,6				0,6
	0,4			Weight	0,4	29,6%
		25,0%
	0,2				0,2
		5,8%
	0,0	0 -35 36-48 49 -59 60 -72	>=73		0,0	<= 48	49 -72	> 72
	-0,2	-10,5%			-0,2		-9,2%
		Owner	59.8%	28.4%	2.1	0.7	23.4%	2.9%
		Others	40.2%	71.6%	0.6	-0.6	18.2%	8.4%
		Total					41.6%

Table 7 : List of candidate variables with Information Value Variables Fine classing Coarse classing IV > 10 % 2% < IV <= 10 % IV > 10 % 2% < IV <= 10 %

 7

	Marital status	15,58%	12,27%
	Residential status	43,9%	41,6%
	Type of credit	2,37%
	Vehicle condition	1,15%
	Vehicle type	2,04%
	Region	6,19%	5,92%
	Existence of co-borrower(s)	1,77%
	Troubled Debt Restructuring	45,99%
	Job	20,41%	19,01%
	Loan duration	3,9%	3,5%
	Time at present address	11,17%	9,52%
	Loan amount	23,48%	14,80%
	Income	13,88%	12,97%
	Number of children	2,30%	2,29%
	Time at present employment	18,39%	14,91%
	Age of the client	13,93%	12,82%
	Client's Initial contribution	41,40%	37,39%
	Client's contribution-to-vehicle price ratio	48,05%	43,56%

Table 8 : List of variables in the selected behavioral scoring model

 8

	1. Marital status
	2. Residential status
	3. Troubled debt restructuring
	4. Job
	5. Client's contribution-to-vehicle price ratio
	6. Debt-to-income ratio
	7. Number of months in the bucket 0
	8. Max bucket in the past 6 months
	9. Months of non-payment in the past 6 months
	10. Delinquency status

Table 9 : Comparison of KS and Gini in the development and validation sample Development sample Validation sample

 9

	KS	Gini	KS	Gini
	58.94%	74.64%	58.74%	74.39%

rate and Good/ bad odds by score Figure 8: Bad Rate and Odds in the development and validation samples Development sample Validation sample

  of the samples. Also, there is only a nearly imperceptible difference between the Lorenz curve of the development sample and that of the validation sample. The performance of the model is thus confirmed.

	80,00% 100,00% model in each Bad					60,00% 70,00%					KS
							50,00%
	60,00%		KS = 58.94 %		40,00%
	40,00%						30,00%
							20,00%
	20,00%					CumG
						CumB	10,00%
	0,00%						0,00%
	0	2	4	6	8 10 12 14 16 18 20	0	2	4	6	8	10 12 14 16 18 20
	100,00%						70,00%
	90,00%						60,00%
	80,00%
	70,00%						50,00%				KS
	60,00%						40,00%
	50,00%		KS = 58.74 %
	40,00%						30,00%
	20,00% 30,00%					CumG	20,00%
	10,00%					CumB	10,00%
	0,00%						0,00%
	0 2 4 6 8 10 12 14 16 18 20		0	2	4	6	8	10 12 14 16 18 20
							-10,00%
						GINI Curves
					100%
					80%
			Cumulative Bad		40% 60%
					20%					Development
										Validation
					0%					Random
					0,00%	20,00%	40,00%	60,00%	80,00%	100,00%
						Cumulative Good

Table 10 : Credit Rating

 10

	Credit Rating	Condition	Frequency
	A+ A B C D	݁ݎ݈ܿܵܽ݊݅ܨ 750 700 ݁ݎ݈ܿܵܽ݊݅ܨ ൏ 750 650 ݁ݎ݈ܿܵܽ݊݅ܨ ൏ 700 600 ݁ݎ݈ܿܵܽ݊݅ܨ ൏ 650 ݁ݎ݈ܿܵܽ݊݅ܨ ൏ 600	33,35% 28,92% 24,39% 7,62% 5,72%

In the original Z-score model, Altman combined a set of five business ratios: EBIT/Total Assets, Net Sales/Total Assets, Market Value of Equity/Total Liabilities, Working Capital/Total Assets, and Retained Earnings/Total Assets.

The multiple discriminant analysis technique is based on two restrictive assumptions: (i) Multivariate normality of independent variables and (ii) Equal covariance matrices of groups (default/non-default).

Roll Rate Analysis helps to predict losses based on delinquency, involves comparing worst delinquency in a specified previous buckets with that in the next buckets, and then computing the percentage of accounts that maintain their worst delinquency, or get better, or roll forward into the next delinquency buckets.