Alexis Brenon
email: alexis.brenon@imag.fr

François Portet
email: francois.portet@imag.fr

Michel Vacher
email: michel.vacher@imag.fr

Using Statistico-Relational Model for Activity Recognition in Smart Home

Keywords: Activity Recognition, Markov Logic Network, Factor Graph, Smart Home

This paper presents the use of a model which mixes logical knowledge and statistical inference to recognize Activities of Daily Living (ADL) from sensors in a smart home. This model called Markov Logic Network (MLN) has different implementations and we propose to compare three of them, from the widely used Alchemy 1 to the new generic framework DeepDive 2 . Finally, we discuss the interest these software products can have for real time activity recognition.

Introduction

Smart home, as described by De Silva [START_REF] De Silva | State of the art of smart homes[END_REF], is a home-like environment (home, flat, etc.) equipped with sensors and actuators. These devices can be used to provide various facilities to the inhabitants through ambient intelligence and automatic controls. As listed by Peetoom et al. in their literature review [START_REF] Peetoom | Literature review on monitoring technologies and their outcomes in independently living elderly people[END_REF], many laboratories have built their own smart home to study how technologies can make life easier for people. Among those, researchers are interested in identifying Activities of Daily Living (ADL) to characterize the user's context.

The context is a generic term which generally regroup the location of the user, its current activity, etc. [START_REF] Dey | Understanding and using context[END_REF][START_REF] Coutaz | Context is key[END_REF] It is used by context-aware services, and so, activity recognition is crucial to allow context-aware applications to provide more active services.

Activity recognition has been studied for a while and many techniques have been used. One of them relies on computer vision which leads to ethical, acceptance and computational problems. To get around this issue, many projects use only simple and ubiquitous sensors [START_REF] Peetoom | Literature review on monitoring technologies and their outcomes in independently living elderly people[END_REF] and more recently, a project used microphones to extract information from the audio stream [START_REF] Chahuara | On-line human activity recognition from audio and home automation sensors: comparison of sequential and non-sequential models in realistic smart homes[END_REF].

Given all these kinds of data, inference have been done following two main approaches. On the one hand, a set of rules can be defined by a domain expert to infer high-level information from low-level sensors' data [START_REF] Skillen | Ontological user modelling and semantic rule-based reasoning for personalisation of help-on-demand services in pervasive environments[END_REF]. On the other hand, machine learning and statistical models learned on corpus can be used to generalize already seen behaviors [START_REF] Cook | Casas: A smart home in a box[END_REF]. A third approach, explained in Section 2, unifies the logical models and the statistical ones [START_REF] Domingos | Unifying logical and statistical ai[END_REF].

Main implementations of statistico-relational model will be compared in Section 3 against a multi-modal corpus. Finally, we will discuss the different perspectives considered in Section 4.

Statistico-Relational Models

Markov Logic Network (MLN) is one of the statistico-relational models, primarily introduced by Domingos et al. [START_REF] Domingos | Unifying logical and statistical ai[END_REF]. It is a template model to construct Markov networks (also named Markov random fields) from a set of weighted first-order logic formulas. Based on both of these pillars, MLN combines their advantages to handle at the same time the complexity and the uncertainty of a representation of the real world. As Domingos et al. explain in their paper, the MLN formalism subsumes many other probabilistic models allowing it to be more concise and to handle easily non-independent and identically distributed models.

MLN is used to infer the most probable state of a world given some evidences which is called Maximum A posteriori Probability/Most-Probable Explanation (MAP/MPE) inference. This can be easily done using a SAT solver able to handle the weights of the formulas [START_REF] Domingos | Unifying logical and statistical ai[END_REF]. Another task of MLN is to compute the probability that a formula is true in a specific world. This is done thanks to the Markov Chain Monte Carlo inference algorithm.

With the logical models, a domain expert is needed to transfer its knowledge. MLNs take a step to avoid this expensive phase, allowing it to learn the weights from an annotated corpus. In the same way, some attempts have been made to learn the structure of a MLN using Inductive Logic Programming techniques.

It exists different implementations of MLN. The most well known is Alchemy [8] developed by the University of Washington. It makes it possible to define MLNs based on a defined syntax similar to Prolog and to proceed to weight learning and inference on given data. Developed in C++, Alchemy is, to best of our knowledge, no longer maintained since 2013. Nevertheless, it is still widely used by researchers, as in the previous study made in our team. That is why we decided to use it as a baseline to compare other implementations.

Then, Stanford University launched another project, called Tuffy3 , using a similar implementation to Alchemy moving from C++ to Java and relying on PostgreSQL. Usage of an external relational database management system (RDBMS) improves dramatically the time and space efficiency of Tuffy inference phase [START_REF] Niu | Tuffy: Scaling up statistical inference in markov logic networks using an rdbms[END_REF]. In 2014, Tuffy development stopped in favor of DeepDive.

DeepDive is the new project of the Hazy Research group 4 . It is a generic framework primarily designed for knowledge base creation (KBC) which can handle many problems [START_REF] Wu | Incremental knowledge base construction using deepdive[END_REF]. Born out of the ashes of Tuffy, DeepDive also

First Results on ADL Recognition

Until now, we have measured the learning performance of the different available software. The learning performance is the score of the system when it infers on the exact same data set than the learning one.

In our case, we use a multi-modal corpus which regroups a full range of sensors values, some computed higher level data (room where the user stayed the longest, agitation level, etc.) and the actual activity of the user. This corpus is composed of 26 hours of experiments on 21 persons, divided into 1 minute long time windows, represented by 94 values [START_REF] Chahuara | On-line human activity recognition from audio and home automation sensors: comparison of sequential and non-sequential models in realistic smart homes[END_REF]. For our first approach, the MLN structure (logical knowledge) is very naive, as we suppose that all the feature values are relevant. Thus, every value implies an activity with a certain degree of truth. This is not optimal but gives us a first baseline to beat.

We ran the following experiments: (1) weight learning and inference with Alchemy; (2) inference with Tuffy (based on Alchemy learning); (3) weight learning and inference with DeepDive. We used Alchemy 1.0, Tuffy-0.3 and DeepDive-0.6.0 on a computer with 24 Intel Xeon CPUs at 2.4GHz with 145GB of RAM running Debian 8 (Jessie) in all of our experiments.

As you can see in Table 1, the execution time of Tuffy and DeepDive is improved by an order of magnitude compared to Alchemy. The small differences in F1-score let's suppose that the three approaches are comparable in performance. We also extract the weights learned by Alchemy and by DeepDive. The correlation between the two sets of weights is about 0.69, highlighting a quite high positive linear correlation which can confirm that both systems work the same way, and that their results can be seen as equivalent.

Perspectives

One of the goals of our project is to build a system able to give context information to artificial intelligence. As explained in the Section 1, the user activity is one of the context components.

To do so, our system must be able to infer user activity in real time (the user must not feel a lag because of computation time) and to adapt itself to the user, all along its life. Sensor values are coming all along the day, and so our system must be able to handle on-line classification or incremental learning. DeepDive is designed as an incremental framework, and can execute the next learning and inferring phases in less time than the one measured in a one shot test (see Table 1) as shown in its description paper [START_REF] Wu | Incremental knowledge base construction using deepdive[END_REF].

Then, we will try to implement a reinforcement learning algorithm, decreasing weight of irrelevant formulas. This raises different questions, as in which proportion can we change the weight? Can we change only one weight, or does the modification must impact other weights? How to know which weights to modify?

Finally, we would like the user be allowed to add or remove some formulas without any technical skills. Once these formulas are added to our model, how can we take them into account? Does our model must be fully re-learned?

Table 1 .

 1 Execution time and F1-score of different implementations of statisticorelational models use the external RDBMS PostgreSQL to manage the data. But DeepDive does not use the exact MLN definition of Domingos et al. to handle the logical and statistical parts of the model. Its implementation is based on Factor Graphs (FG) instead of Markov networks. FG is a very generic graphical model which can handle many other problems solved with different graphical models [11].

		Learning time	Inferring time	F1-Score
	Alchemy	+3 days	3h 45'	89 %
	Tuffy		3'51"	90 %
	DeepDive	23"	10"	91 %

http://i.stanford.edu/hazy/tuffy/

https://twitter.com/HazyResearch

⋆ This work is part of the CASSIE project founded by a Projet Investissement d'Avenir (2014)(2015)(2016)(2017)(2018)


Djédjé Hermann Yohou
email: dher.yohou@gmail.com

Catherine Araujo Bonjean

Yannick Bouterige

Constantin Compaoré

Coulibaly Aïssata

Eric Relwendé

Aristide Mabali

Cyril Chalendard

Antoine Cazals

The advantages and disadvantages of Economic Crises, where earlier version was presented under the

Keywords: Fiscal space, Efficiency of public spending, DEA, Africa JEL codes C14, H40, H50, H60, H62, O1

Taking advantage of African experience, this paper proposes to enrich empirically the issue of fiscal space. Africa has markedly achieved significant economic progress since the 80's decade crisis. However, this progress has been proven insufficient to curb dramatically the infrastructures gap and poverty because of the shortage of funding. While several ways are being looked for creating a sustained fiscal space, this paper argues that improving the quality of public spending remains the key avenue. It then derives fiscal space by computing Data Envelopment Analysis (DEA) efficiency scores of public spending using a group of 62 African and non-African countries over the period 1980-2013. The results indicate that on average African countries are less efficient than their peers. The average efficiency score of public spending for African countries relatively to their peers is 0.585 suggesting that they could reduce their spending by 41.5% to achieve the same results. This results in a lost fiscal space of about 11.5% of GDP equivalent to 43.8% of the outlay used and 3/4 of the current level of tax revenues. However, they have achieved a substantial improvement in efficiency change over time. Moreover, the results evidence that this estimated lost fiscal space is tied to the other indicators of fiscal space. In particular, larger lost fiscal space is positively correlated with foreign aid and external debt inflows but negatively with tax capacity.

Introduction

Africa has markedly made headway since the end of the 80's decade crisis. The continent is one of the world's fastest-growing region in spite of a context of harsh global imbalances and financial crisis. Over the last decade, African economy increased by more than 5% per year. Some human development indicators have set some encouraging progress. For instance, the global infant mortality rate fell from 168.1 deaths per 1,000 live births over the period 1990-1995to 100.6 over 2010-2015(United Nations, 2013). The gross rate of secondary school enrollment in Sub-Saharan Africa (SSA) has doubled between 1985 to 2009 1 . According to many institutions, these results arise from better good governance and fiscal affairs management [START_REF] Panel | Grain, fish, money: financing Africa's Green and Blue Revolutions[END_REF].

The policies associated to the debt reduction initiatives, the increase and the improvement in aid systems have certainly released greater fiscal space. This suggests that governments have benefited from more budget room that allows them to fund their priorities without worsening their solvency and the stability of the economy [START_REF] Heller | Back to Basics-Fiscal Space: What it is and how to get it[END_REF].

However, the continent continues to face huge challenges. The recent Ebola outbreak has revealed that the current performances are vulnerable. The gap of infrastructures remains important and continues to retard a fair development of the different economic sectors. A study of AICD 2 reported by OECD (2012) states that the annual funding gap is estimated to US$ 93 billion.

As a result, the strong growth has not generated a significant poverty reduction in the region leading it to adopt an inclusive growth (IG) agenda for 2063. Meanwhile, it has to cope with a recent emergence of terrorism to alleviate the investors' concerns.

The region therefore needs more financial resources to strengthen its recent progress and support its IG agenda. But the financial contribution of the domestic private sector is currently limited because of a low financial depth and a difficult access to the international capital markets. Creating a wider fiscal space becomes therefore inescapable. In practice, countries can expand their fiscal space by increasing tax revenues, borrowing from domestic and international markets, 1 http://www.uis.unesco.org/Education/Documents/ged-2011-fr.pdf.pdf 2 Africa Infrastructure Country Diagnostic (AICD). It is a project designed to expand the worlds knowledge of physical infrastructure in Africa and supported by the World Bank, the African Union, the Agence Française de Développement, the Department for International Development (U.K.), the European Union, the New Economic Partnership for Africas Development, and the Public-Private Infrastructure Advisory Facility.

seigniorage, mobilizing foreign aid, or by increasing the efficiency of their spending [START_REF] Heller | The prospects of creating 'fiscal space'for the health sector[END_REF][START_REF] Debrun | Making Fiscal Space Happen: Managing Fiscal Policy in a World of Scaled-Up Aid[END_REF][START_REF] Melecky | Fiscal responses after catastrophes and the enabling role of financial development[END_REF]. Nevertheless, there is a strong evidence that the use of some of these instruments is limited by the potential noxious consequences they may involve. The recent sovereign debt crisis in the world and the ongoing one in Greece highlight that public debt may pose serious concerns for fiscal sustainability and economic growth, as the theories of debt overhang and intolerance predict. In Africa with a limited domestic saving, funding public spending through domestic borrowing may seriously crowd out private investment. Because potentially inflationary, seigniorage may induce huge macroeconomic uncertainties. Now, it is less used since most of the countries have adopted inflation targeting. Regarding aid, although it has been an important funding option for the continent, it has declined during the last decade. Moreover, the current tightening fiscal policies in donor countries do not guarantee a further surge in aid for next years. Aid unpredictability may also harm a good medium-term budget planning. Taxation and improving the efficiency of spending remain the two potentials to harness fully. But, despite a recent greater attention to taxation, most of the countries have difficulty in reaching the minimum level of 20% of GDP of tax revenues as recommended by the United Nations. Rather than increasing funding, fiscal space literature emphasizes that improving the quality of public spending, i.e. improving efficiency, is the best way to address the shortage of resources without compromising the sustainability of public budget. But it does not pay much attention to the estimation of this "fiscal space", i.e. here the potential progress in improving public spending (the same public service delivery with less money), assuming given revenue unchanged as the constraint. This paper therefore estimates the fiscal space African countries could have mobilized by improving the quality of public spending. The quality of public spending is measured by computing Data Envelopment Analysis (DEA) efficiency's scores. This approach allows to estimate the amount of spending a country would have saved in order to reach the same level of output in comparison with its peers. As outputs, I use a set of human and sectoral development indicators that are close to the Millennium Development Goals (MDGs). Countries' performances are then assessed closely to their own defined objectives.

The present approach enriches the existing measures of fiscal space. [START_REF] Ghosh | Fiscal fatigue, fiscal space and debt sustainability in advanced economies[END_REF] propose the gap between the observed value of debt and a potential debt limit from which fiscal solvency is of concern. [START_REF] Aizenman | What is the risk of European sovereign debt defaults? Fiscal space, CDS spreads and market pricing of risk[END_REF] refer to the number of tax-years a country would take to repay its debt. [START_REF] Brun | Evaluation de l'espace budgétaire des pays en développement[END_REF] emphasizes on the deviation of domestic tax level from its potential. In spite of the relevance of these approaches, the inconclusiveness of the fiscal policy literature [START_REF] Rogoff | Growth in a Time of Debt[END_REF][START_REF] Minea | Is high public debt always harmful to economic growth? Reinhart and Rogoff and some complex nonlinearities[END_REF] is illustrative that an additional variable is necessary in assessing fiscal space. The alternative proposed in this paper is built on the meaningful assumption that inefficiency of public spending matters. This paper is not the first to assess the efficiency of public spending in Africa. [START_REF] Gupta | The efficiency of government expenditure: experiences from Africa[END_REF], [START_REF] Chemli | Efficience du financement des services publics et croissance économique dans les Pays en développement: Analyse en coupe transversale[END_REF] and [START_REF] Pang | Efficiency of public spending in developing countries: an efficiency frontier approach[END_REF] have yet done similar exercises by focusing on some specific areas such as education and health. In contrast, the present paper clearly analyzes the challenges of the quality of public finances for building a sustainable fiscal space and poverty alleviation in African region. Moreover, it considers the two major components of public budget, investment and consumption, as inputs. Indeed, the structure of public spending is identified in literature as a starting-point of its quality; investment is typically seen as productive and consumption not. But the issue is still on debate. Some recent findings from IMF staff [START_REF] Dabla-Norris | Investing in public investment: an index of public investment efficiency[END_REF]International Monetary Fund, 2015) indicate that high investment does not necessarily mean increased productivity. Here, I analyze investment and consumption as complements since they often need each other to be effective. In addition, the paper uses an updated dataset of 45 African countries over 1980-2013. This extensive panel data aids to catch the dynamics between countries' performances and the quality in public affairs management over comprehensive sub-periods.

The remainder of the paper is structured as follows. Section 2 defines the concept of fiscal space adopted and its measurements. Section 3 explains the methodology. Section 4 presents the results. Section 5 concludes.

Economists and decision-makers are increasingly paying attention to the concept of "fiscal space". [START_REF] Heller | Back to Basics-Fiscal Space: What it is and how to get it[END_REF] has defined it as room in a governments budget that allows it to provide resources for a desired purpose without jeopardizing the sustainability of its financial position or the stability of the economy. The World Bank and the International Monetary Fund have put on this definition by stating that "fiscal space exists when a government can increase expenditure without impairing its fiscal solvency, i.e. without impairing its capacity to service its debt.", [START_REF] Committee | Fiscal policy for growth and development: An interim report[END_REF]. For [START_REF] Roy | Fiscal Space: Policy Options for Financing Human Development[END_REF], this definition of fiscal space focusing on sustainability is limited by the fact it does not stress on the key actions to mobilize resources for MDGs' funding. They then define fiscal space as: "concrete policy actions for enhancing domestic resource mobilization, and the reforms necessary to secure the enabling governance, institutional and economic environment for these policy actions to be effective". The literature identifies several ways to gauge fiscal space depending on the focus of the paper. [START_REF] Ghosh | Fiscal fatigue, fiscal space and debt sustainability in advanced economies[END_REF] define fiscal space as the distance between the current debt level and the debt limit beyond which fiscal solvency is in doubt. Drawing on the works of [START_REF] Bohn | The behavior of US public debt and deficits[END_REF]Bohn ( , 2008) ) as well as those of [START_REF] Mendoza | International evidence on fiscal solvency: Is fiscal policy "responsible"?[END_REF] and [START_REF] Ostry | Primary Surpluses and sustainable Debt Levels in Emerging Market Countries[END_REF], the debt limit is determined by estimating a primary fiscal balance reaction function which uses the squared and cubic debt terms besides some other control variables. [START_REF] Aizenman | De facto fiscal space and fiscal stimulus: Definition and assessment[END_REF] and [START_REF] Aizenman | What is the risk of European sovereign debt defaults? Fiscal space, CDS spreads and market pricing of risk[END_REF] define fiscal space, called de facto, as the inverse of the tax-years it would take to repay the public debt. Specifically, it measures the outstanding public debt relative to the de facto tax base, where the latter measures the realized tax collection, averaged across several years to smooth the business cycle fluctuations. [START_REF] Brun | Evaluation de l'espace budgétaire des pays en développement[END_REF] adopt a tax effort approach and derive fiscal space as the ratio of the current level of revenues to potential tax revenues, based on structural indicators such as GDP per capita and sectoral values added.

In this present paper, I derive fiscal space by the quality of public spending by linking its use to its outcomes. Whatever the definition considered, the key point in fiscal space concept is how much a country can dispose some room for fiscal maneuver. This begins by improving the quality of the existing revenues in achieving the goals. The better it gets, the lower is the need of borrowing and the risk of fiscal insolvency. Moreover, the quality of public service delivery may encourage tax compliance and consequently the domestic revenue collection.

The concept of "quality of public spending" cannot be separated from that of the whole public finance including revenues. Borrowing from [START_REF] Barrios | The quality of public finances and economic growth[END_REF], it comprises the policies that ensure sound budgetary stances, long-sustainability and those that increase the production potential and facilitate the economy to adjust to shocks. The achievement of these outcomes requires an efficient and effective use of public revenues while creating incentives for an efficient functioning of labor, goods and services markets. The inconclusiveness of the literature on the effect of government size on growth has led to establish that this effect varies across countries and over time depending on its level and its quality. In terms of size, common thinking is that low unlike high levels of government are associated with increased sustained growth because it likely generates less tax distortion and eviction of the private sector. This quality is approximated by two aspects: the structure and the efficiency. The structurerelated-quality hypothesis distinguishes between the categories of spending that potentially promote growth from those that harm it. Thereby, government consumption and military spending are viewed as counterproductive while investment in infrastructures development, in education or in health are growth-enhancing. Nonetheless, the empirical evidence remains mixed suggesting that the composition assumption is not sufficient. The results depend on the fiscal size and the conditions (macroeconomic policies, governance, corruption etc.) under which they are spent.

In the case of African countries, [START_REF] Devarajan | Low Investment Is Not the Constraint on African Development[END_REF] find that they do not suffer of any problem of underinvestment but of efficiency constraints. On the contrary, [START_REF] Fosu | Optimal public investment, growth and consumption: evidence from African countries[END_REF] show that they are hit by underinvestment. Recent findings of [START_REF] Dabla-Norris | Investing in public investment: an index of public investment efficiency[END_REF]International Monetary Fund (2015) stress that the key point of investment's productivity is its efficiency.

The efficiency-related-quality hypothesis looks for the way resources are used to reach their goals.

The latter definition also makes a crucial distinction between 'effectiveness' and 'efficiency'.

Public spending is effective if it reaches its outcome independently of how much is invested. In contrast, efficiency questions whether countries could achieve better outcomes at current levels of spending (Verhoeven et al., 2007) or whether the same outcomes could be obtained with lower levels of spending. In that case, efficiency is superior than effectiveness to the extent that it includes the latter. The current paper considers quality of public spending as good if the latter is efficient.

Efficiency is generally measured as the distance to a production frontier through non-parametric and parametric methods. The non-parametric approaches are the Free Disposal Hull (FDH) and the Data Envelopment Analysis (DEA). They relate multiple inputs and outputs to account for the gap between potential output allowed by given quantities of inputs and the level of output currently achieved with the same quantities. Each country's efficiency is therefore evaluated relative to its peers distinguishing best practices from lower ones. Countries that are efficient than others get a score of one whereas the less efficient ones are rated lower. For instance, an input efficiency of 0.7 for a country means that the latter could reduce the level of input by 30%

to get the same level of output or to be efficient. Thus, the non-parametric approaches allow for estimating the level of wasted resources of the producer.

The parametric methods consist in estimating a stochastic efficiency frontier assuming a functional form of production such as Cobb-Douglass or translog [START_REF] Barrios | The quality of public finances and economic growth[END_REF].

Unlike non-parametric approaches, parametric ones dissociate the exogenous effects from the efficiency ones by decomposing the residual into two components: a random error term and an inefficiency term. They also allow to test the standard statistical properties. Parametric approach allows to correct the sensitivity of the results to the existence of outliers. However, they require strong assumptions and a large number of observations. Especially, they outperform non parametric approaches only when the estimated stochastic frontier is close to the assumed technology [START_REF] Rayp | Measuring and explaining government efficiency in developing countries[END_REF]. Moreover they are usually suitable for micro-level data whereas some authors question their ability to effectively decompose noise and inefficiency [START_REF] Banker | A Monte Carlo comparison of two production frontier estimation methods: corrected ordinary least squares and data envelopment analysis[END_REF][START_REF] Ruggiero | Efficiency estimation and error decomposition in the stochastic frontier model: A Monte Carlo analysis[END_REF][START_REF] Rayp | Measuring and explaining government efficiency in developing countries[END_REF].

A number of studies use the non-parametric approaches to compare the performances of public spending among countries. Thus, [START_REF] Gupta | The efficiency of government expenditure: experiences from Africa[END_REF] resort to FDH to assess the efficiency of public expenditure on education and health of 37 African countries relative to each other and also to Asia and the Western Hemisphere over the period 1984-1995. Their findings indicate that on average African countries are less efficient than the latter regions although their efficiency has been improved during this period. They also find that among African countries, the least performant ones (like Cote d'Ivoire and Botswana) record better income distribution than the most efficient ones like Ethiopia and Lesotho. According to these authors, inefficiency is caused by high wages practices in the education sector and intra-sectoral misallocation of resources. [START_REF] Chemli | Efficience du financement des services publics et croissance économique dans les Pays en développement: Analyse en coupe transversale[END_REF] use DEA approach to calculate the scores of efficiency of public spending in education and health of 45 developing countries including African countries over the period 1990-2002. Their calculations show a weak efficiency about 30%. Further regressions point out that these spendings do not support economic growth due to the low level of their quality. [START_REF] Pang | Efficiency of public spending in developing countries: an efficiency frontier approach[END_REF] using FDH and DEA techniques in a sample of 140 developing countries over the period 1996-2002 come to similar conclusion. Countries with larger size of government and in particular with larger share of wage bill of the total budget are less efficient. Furthermore, [START_REF] Afonso | Public sector efficiency: an international comparison[END_REF] find, from DEA approach, that the most efficient members of OECD spend on average 30% less than their European partners to achieve the same performances. Afonso et al. (2010) analyze public sector efficiency in the new EU member states compared relative to emerging markets. DEA computations show that expenditure efficiency across the former as compared to the group of top performing of the emerging market in Asia is diverse.

Methodology

The public spending efficiency scores

Building on Afonso et al. (2010), the general relationship that I am testing can be given by the following function for each country i :

Y i = f (X i ), i = 1...n (1)
where Y i is a composite indicator reflecting the output measure; X i denotes the different components of public spending or inputs in country i. For an actual output Y < f (X i ), country i exhibits inefficiency. For the observed input level, the actual output is smaller than the best attainable one and inefficiency can then be measured by computing the distance to the theoretical efficiency frontier.

Following the common practice in macroeconomic literature [START_REF] Barrios | The quality of public finances and economic growth[END_REF], the efficiency scores will be computed by a DEA approach originating from the seminal work of [START_REF] Farrell | The measurement of productive efficiency[END_REF] and popularized by [START_REF] Charnes | Measuring the efficiency of decision making units[END_REF] (Afonso et al., 2010). This preference relatively to the stochastic approach is grounded in the difficulty to determine the a priori technological function of the government at macroeconomic level. As stated before, DEA is a non-parametric mathematical programming approach which calculates efficiency in production.

It constructs an envelopment frontier over the data points such that all the observations lie on or below the production frontier [START_REF] Coelli | A guide to DEAP version 2.1: a data envelopment analysis (computer) program. Armidale: University of New Engaland[END_REF]. The program is computed under the assumption of constant return scale (CRS) or variable return scale (VRS). Unlike CRS, VRS is convenient when the Decision Making Units (DMU's) are operating at a non-optimal scale environment [START_REF] Coelli | A guide to DEAP version 2.1: a data envelopment analysis (computer) program. Armidale: University of New Engaland[END_REF]. Due to constraints on resources, difficulties to access to international funding in particular to the private one, I can assume that African countries are not operating at an optimal scale environment. So, VRS is the appropriate hypothesis to hold in this work.

Choosing input or output orientation is another assumption when computing DEA. The input orientation aims at determining how much input quantities (spending) can be proportionally reduced without changing the quantities of the output produced. In contrast, the output orientation maintains unchanged the input and looks for the maximum output to attain. Since the rationale of the paper is to measure the amount of fiscal room countries can free up to support their progress, I use the former orientation. Another reason in favor of the input-orientation is that governments have most control over their spending than the outputs. Program ( 2) is that of VRS with an input-orientation.

                       M in θλ θ st -y i + Y λ ≥ 0 θxi -Xλ ≥ 0 N 1 ′ λ = 1 λ ≥ 0 (2)
where Y (M *N ) is the matrix of outputs and X(K*N ) is that of inputs. K, M are respectively the number of the inputs and outputs. N is the number of the decision making units i (DMUs, countries). θ is a scalar and measures the efficiency score. It must satisfy θ ≥ 1. For θ = 1, the country is on the frontier and hence technically efficient while (1 -θ) is the level of public spending which would be reduced to achieve the same efficiency without changing the output.

λ is a N *1 vector of constants that measures the weights used to compute the location of an inefficient country if it were to become efficient. The inefficient country would be projected on the production frontier as a linear combination of those weights, related to the peers of the inefficient country. N 1 is an n-dimensional vector of ones.

With a panel data, it is interesting to measure the productivity change and its main driver in a particular period. This is possible via a Malmquist total factor productivity (TFP) index.

m o (y t+1 , x t+1 , y t , x t ) = [ d t o (x t+1 , y t+1 ) d t o (x t , y t ) × d t+1 o (x t+1 , y t+1 ) d t+1 o (x t , y t ) ] 1/2 (3)
A m o index greater than one indicates positive TFP growth from period t to period t + 1. An index inferior to 1 means a decrease. When equal to 1, there is no change. The four component distance functions d t+a o ; a = 0...n are linear programs problems like that of the program (2) (see [START_REF] Coelli | A guide to DEAP version 2.1: a data envelopment analysis (computer) program. Armidale: University of New Engaland[END_REF] for an extensive development). Programs ( 2) and ( 3) must be jointly solved N times once for each country in the sample.

Data

I use a panel of 45 African countries over the period 1980-2013. However, the effects of some public choices may be perceptible over more than a year later. For instance, the building of infrastructures like roads and bridges, health and school infrastructures is often made over several years. In order to circumvent a such "annual bias", I average data over five years with the exception of the last period 2010-2013 which is four years average. This also helps to circumvent the data unavailability on some years for some countries. Let's us mind one that DEAP is applicable only for a balanced panel data. In addition, DEA approach compares countries of the same sample. Since, this may lead one to conclude that a potentially-inefficient country is efficient, I tried to include a large set of non-African emerging and developing economies following IMF's classification. But, due to data availability and quality I limit the number of non-African countries to 17. The empirical studies are very often bound to such a limited sample because of data limitations (see for instance [START_REF] Rayp | Measuring and explaining government efficiency in developing countries[END_REF] and [START_REF] Rahmayantia | Expenditure Efficiency and the Optimal Size of Government in Developing Countries[END_REF]). However, this approach is also relevant to compare where African countries are ranked and/or progressed relatively to the other countries. In fact, in the light of the considerable progress of Brazil, Russia, India, China and South Africa, most of the African countries have recently and increasingly targeted "emergence". In terms of economic policy, this is equivalent to manage public affairs so as to create at least the same performances or progress of these countries.

I do not consider developed countries because of significant differences with developing countries.

Especially, the outputs indicators for developed countries vary little and are close to the maximum while their priorities are different with those of less developed ones. Finally, in terms of policy implications, it seems more relevant for a developing country to target closed performers rather than pursuing unrealistic goals.

Using a fine decomposition of public spending would have been interesting to link each sector to the corresponding outputs indicators as it is often done for the education and health sectors.

Unfortunately, there is not such a comprehensive dataset on public spending for our sample. I then use two major components of public spending as inputs: the share of public investment in GDP and the share of general government final consumption expenditure in GDP. Although the analysis of discretionary choices of a government tends to oppose the growth-enhancing effects of public investment to the retarding-effects of public consumption, there are some advantages to use these expenditures. The trade-off between investment and consumption cannot be reduced to a perfect substitution. As stated before, the composition of public expenditure matters for the efficiency of a type and the whole of expenditure. Specifically, spending in infrastructures may require some given amount of government consumption components to be effective and vice versa. For example, building new hospitals and schools will be effective if there is a sufficient and appropriate number of nurses, doctors and teachers and working material. In many cases, this may involve a recruitment of new employees, new salaries, wages' increase and new public Despite the fact that DEA is an interesting tool to assess countries performances, it imposes some constraints to be efficient. Its discriminatory power is weak in the case of a large number of inputs and/or outputs. For instance, drawing from Simar and Wilson (2000) and Groskopff (1996), [START_REF] Pang | Efficiency of public spending in developing countries: an efficiency frontier approach[END_REF] note that too many outputs may biase efficiency scores towards one, increase the variance of the estimators and reduce their speed of convergence to the true efficiency estimators. This problem can be overcome by using the variables that provide essential component of production eliminating one of the pair of factors that shows a strong positive correlation. Some authors estimate different scores alternating the number, the quality of inputs and/or outputs. This generally yields contrasting results with a difficulty in interpreting the discrepancies in scores and ranks. I use here a simple and meaningful approach by summarizing the nine outputs in two single indexes applying a Principal Component Analysis (PCA).

The human capital indicators constitute the first index (HAI-Human Asset Index) while the production indicators form the second index (PI-Production Index). Each index is obtained by carrying all of the correspondent variables weighted by the associated coefficients of the first PCA component. Details are in appendix. Furthermore, it is worth noting that this approach is more relevant than estimating scores separately since the same inputs are used for producing the outputs at the same period. Otherwise, one should face an overestimation or underestimation of the scores. Finally, I augment the input ratios by 1 because of the null values of the investment ratio for some countries. This affine transformation on inputs does not affect the results since the individual performances are gauged relatively to the peers. In short, the table shows that African countries tend to have relative higher government size than the other economies but have lowest economic performances. But, this conclusion is not always true in the light of the case of Seychelles. The next section provides estimates of the DEA efficiency scores.

Results

Efficiency scores and the lost fiscal space

Table 2 reports the efficiency scores of the VRS analysis for the whole of the seven periods for each country and group of countries. It also reports the average of efficiency scores (Average) over the period and the number of times (Times) the country has been on the frontier as well as the average of the resources level that would be saved if the country were efficient.

The results indicate that African countries on average are not efficient in comparison with the non-African countries. The average efficiency score of public spending for African countries over the span of the study is 0.585 against 0.825 for the non-African. This implies that on average African countries should reduce their spending by 41.5% to achieve the same performances whereas non-African countries should reduce theirs by 17.5%. The results also show that there is no discrepancy in efficiency among Maghreb and sub-Saharan African regions. Indeed, both record the same efficiency score. The analysis of figure 1 shows that there is no significant shift in the trend of the efficiency scores. Efficiency has steadily increased from 0.575 to 0.697 for the whole sample. This upward tendency is mainly due to that of the non-African countries yet retarded by the slight progress of African performances. Taking African economies specifically, the results evidence that the sub-Saharan region is the main driver of the African tendency. The North region presents an evolution by jerks and jumps. The breaking in the increase tendency in Sub-Saharan Africa over the two last periods may be explained by the recent food prices crisis that has caused a significant increase in public spending to mitigate its consequences but with Nevertheless, the ranking according to the number of times may hide some heterogeneities in efficiency progress of certain countries. The ranking according to the average level of efficiency's .5

.6

.7

.8

.9 1985-1989 1995-1999 2005-2009 . . Period

Non-Africans Maghreb Sub-Saharan Africa

Overall Africa Overall Sample Source: Author's estimations score does not always follow the same path as the former particularly in the case of Africa. With an average score of 0.849, Seychelles remains the most African efficient economy. It is followed by Zimbabwe (0.79), Cameroon (0.77), Mauritius (0.765), Sierra Leone (0.76). The recent progress of Equatorial Guinea is balanced by the inefficiency of the four first periods leading to a rank of 15th with an average score of 0.642 while Nigeria is now ranked 22th with a score of 0.565.

The difference in the two rankings suggests that over time some countries become more efficient and others did not. The less five efficient countries are Angola (0.429), Burundi (0.404), Burkina Faso (0.392) Botswana (0.38) and Lesotho (0.287). South Africa as the most advanced African economy is ranked 8th. Figure 2 depicts the correlation between the efficiency scores and the ratio of public spending across the main group countries. The correlation is negative suggesting that larger public spending does not provide returns irrespective the region considered and the type of public spending. This finding is in line with a number of studies investigating the efficiency of public spending [START_REF] Gupta | The efficiency of government expenditure: experiences from Africa[END_REF][START_REF] Pang | Efficiency of public spending in developing countries: an efficiency frontier approach[END_REF][START_REF] Afonso | Public sector efficiency: an international comparison[END_REF][START_REF] Chemli | Efficience du financement des services publics et croissance économique dans les Pays en développement: Analyse en coupe transversale[END_REF]Verhoeven et al., 2007;Afonso et al., 2010;Vierstraete, 2012).

As suggested before, loss in efficiency creates loss in public resources. The lost of fiscal space computed through table 2 has been generated by multiplying the level of resources used by the difference between the maximum efficiency score (1) and the estimated efficiency score (θ).

Let's remind that (1 -θ) corresponds to the proportion of the used resources a country should reduce in order to realize the same amount of outputs, i.e. to be efficient. Then, a country's loss of fiscal space is estimated relatively to the efficiency of the peers of a country. The lost fiscal space when a country is efficient is zero. The analysis of the two tables shows that on average for the full sample, total factor productivity improves substantially. The change is equal to 1.165 suggesting a rise in TFP by 16.5%. This increase results mainly from that in efficiency which rises by 12.2% whereas technology change improves slowly by 4%. African regions record the biggest amelioration due to a significant increase in efficiency by 14.1% and a slight increase in technology by 4.1%. This result suggests that the improvement in the quality of public resources management is the main driver of TFP by up to more 75%. In addition to this analysis, I spur my curiosity to see how this improvement in efficiency is correlated with the waste of resources. Trivially, the negative correlation in figure 3 supports the idea that better quality of fiscal management throughout time helps country to create more resources.

A striking outperformance of 4.42 is noted by Chad over 2005-2009 after a decrease in the previous period due to a significant fall in public spending ratio over 2005-2009. However, as demonstrated by figure 3, the exclusion of this value from the data does not affect the negative correlation between efficiency change and unsaved fiscal space. On average, the African countries that have decreased in efficiency improvement are Angola, Gabon, Ghana, Lesotho, South Africa and Zimbabwe. However Angola, Ghana and partially Lesotho have recorded significant progress to become productive while the more recent decline in Gabon and South Africa points some In general quality of public spending has been thus improved in Africa but with some disparities among countries and over time. This stage of my results does not confirm those of [START_REF] Gupta | The efficiency of government expenditure: experiences from Africa[END_REF] who find that increase in the productivity in Africa is driven by outward shifts in the efficiency frontier. This progress may be attributed to the Public Finance Management Reforms undertaken under the donor pressures in the frame of Structural Adjustment Programs and strengthened in the frame of the Heavily Indebted Poor Countries (HIPC) initiatives. However, the fact that they are still inefficient involves other critical challenges in terms of ensuring a sustainable fiscal space for poverty reduction.

Rebranding quality of public spending and fiscal building for better performances

This section depicts how the unsaved fiscal space is connected to other aspects of fiscal space.

The three first are interesting in the relationship between waste and tax capacity building using Dataset on government revenues from International Center for taxation and Development (ICTD) [START_REF] Prichard | The ICTD Government Revenue Dataset[END_REF]. Building a sustainable taxation in developing countries like Africa is doubly important. It would serve not only for curbing the shortage of poverty alleviation funding but also to leave the fragility in which they are. Domestic taxation has clearly been identified as a certain way to induce much broader improvements in state administrations capacity [START_REF] Brautigam | Taxation and state-building in developing countries: Capacity and consent[END_REF][START_REF] Prichard | Does reliance on tax revenue build state capacity in sub-Saharan Africa?[END_REF]. Moreover, reliance on domestic taxes instead of foreign assistance is pro-governance by generating incentives to build strong social contract and accountability between state and its citizens [START_REF] Moore | Death without taxes: Democracy, state capacity, and aid dependence in the fourth world[END_REF][START_REF] Knack | Sovereign rents and quality of tax policy and administration[END_REF]. This implies in some extent a high degree of tax compliance. The first three figures intend for showing that poor quality management of existing resources is one of the engines of the weak results of taxation reforms in Africa. When citizens are sure that their efforts are poorly managed and find difficult to be provided good public services, their trust in government reduces and they become less encouraged to pay taxes. The social bargaining therefore weakens and the level of the collected taxes remains structurally low. Tax capacity is often measured by the level of the potential stable domestic revenues, i.e. excluding resources revenues. When considering the first figure, a positive correlation between overall government revenues and waste in public outlays surprisingly seems to exist. But, the decomposition into non resource tax revenues and resource tax revenues provides a different picture. Tax capacity ratio is negatively associated with waste in public spending. In contrast, there is a positive correlation between waste in public spending and resource revenues suggesting the well-documented problem of "resource curse".

Low levels of domestic tax capacity and resource curse induced by poor quality of public resources are conducive to foreign assistance dependence and concerns on fiscal sustainability. Figure 5 shows that the inability of governments to create room by improving efficiency of spending is negatively related to domestic saving. When domestic saving is low, prospects of economic growth become pessimistic and incentives to invest decline compromising future rebuilding of saving. To

Fitted values

Lost fiscal space in Africa(% of GDP)

Source: Author's estimations, World Bank and ICTD.

finance its activities, governments may try to create fiscal space through new borrowing or mobilization of foreign assistance [START_REF] Committee | Fiscal policy for growth and development: An interim report[END_REF]. Figure 5 shows that the loss in fiscal space is positively associated with foreign aid and net flows on external debt in Africa. The effects of foreign aid on the recipient countries are still debatable. Although, many African countries benefit from a concessional debt, the risk of change remains prominent and may cause sovereign insolvency. With a limited room due to government inefficiency and low institutional development, the fiscal adjustment would be more disastrous. Figure 6 reconciles the fiscal space approach of IMF that emphasizes on efficiency of public spending and fiscal sustainability and that of [START_REF] Roy | Fiscal space for what? Analytical issues from a human development perspective[END_REF]. As one would expect, the more a country loses because of inefficiency, the more public stance worsens, suggesting that quality of public finances is associated with fiscal sustainability. In terms of outcomes, the figure shows that economic growth is negatively correlated to the loss of fiscal space although the link seems to be weak. However, the Malmquist index decomposition of the inefficiency shows that African countries have achieved a substantial improvement in the quality of spending in comparison with the other countries involving a reduction in the waste of revenues. But this improvement remains insufficient to become more efficient than the non-African countries. This suggests improving government management and governance remains an absolute factor of significant progress in Africa. These results urge that strengthening the good governance reforms are highly of importance in order to deepen the current progress in a sustainable way as highlighting the connection between the lost fiscal space and the other fiscal space policies. Indeed, the results show that larger waste of fiscal space is positively correlated with foreign aid, external debt flows, fiscal deficit but negatively with tax capacity. Moreover, there is a positive correlation between resource tax and the lost fiscal space while the negative correlation between African efficiency level and per capita economic growth seems to be weak.

In spite of these logical results, some cautions should be pointed in interpreting the findings.

Although I have paid a great attention to the data treatment, the issue of data quality of public spending notably of investment remains. This problem is not new but closely related to the low institutional development in developing countries. For instance, [START_REF] Fosu | Optimal public investment, growth and consumption: evidence from African countries[END_REF] have pointed this kind of problem in their study. The databases of the World Bank and the African Development Bank that I use in this study are currently the most developed ones to my knowledge. Another point due to data availability is the limitation of the sample size which may affect the respective ranks if additional countries are introduced. Moreover, the impact of government spending on some output indicators may drag on several periods so that the observed inefficiencies may be the result of the previous decision-makings [START_REF] Gupta | The efficiency of government expenditure: experiences from Africa[END_REF]).

Finally, one may apply alternative methods of efficiency evaluation such as stochastic methods to provide additional robustness to the present findings. 1984-89 1990-1994 1995-1999 2000-2004 2005-2009 2010

  It decomposes the TFP index into technical change and technical efficiency change. Clearly, a positive technical efficiency change means that the efficiency improvement results from a better management of the resources with the current technology over a period of time. A positive technical change suggests that the efficiency improvement results from innovation (new scientific and technical knowledge, products and techniques in the provision of the output services (Kirigia et al., 2011)).

  purchases. Using public investment and consumption allows to include both the consumption and the infrastructures of the set of sectors. I then account for the phenomena of composition and complementarity in explaining public efficiency.Public investment is proxied by the gross fixed capital formation expenditure of the public sector.I had three possibilities. Indeed, The World Bank Group has developed a dataset of public gross fixed capital formation expenditure for African Economies through African Development Indicators (ADI) while the African Development Bank (AfDB hereafter) reports two datasets using the World Development Indicators (WDI) of the former institution and the World Economic Outlook (WEO) of the International Monetary Fund (IMF). The three datasets show a slight difference for most of the countries but with some huge differences for few countries. In order to allow a more consistent comparison among countries both African and non-African, I subtract the gross fixed capital formation expenditure of the private sector from the total one using WDI. The resulted dataset is also close to the three former ones. Where data are missing, I complete with the three latter by using the one which presents the same figures with the calculated existing ones for each country. For minor cases, I do not have any possibility of using the above construction. So I use data from the articles IV of IMF 3 . Data on government consumption are from UN Database. Regarding outputs, in line with the common practice in the related literature, I consider human capital indicators. They comprise two indicators of health: the five-year infant mortality and the undernourished prevalence indexes and two education indicators: the gross secondary enrollment and the literacy indexes from the Foundation for International Development Study and Research (FERDI)[START_REF] Closset | Human Assets Index Retrospective series: 2013 update[END_REF]. The higher the value of each index, the higher the quality of human capital. In addition, I account for the sectoral economy productivity since there is a strong evidence that too high government size may harm economic performances. However, the African governments through the Poverty Reduction Strategy Papers have engaged to promote an harmonious economic sectoral development including agriculture, industry and infrastructures.The reforms undertaken might reduce the threat of "too" government size. Hence, I use the US$ real per capita values added of agriculture, manufacture, construction, transport and the wholesale and retail trade as additional outputs. I do not use the global industry value added which includes mining sector since the resources from the latter are unstable and may suddenly overestimate the country performances. My concern is clearly to look for the sustainable efficiency of the countries in close with their engagements. In order to avoid a "measurement bias" among the outputs which may influence the scores, I normalize these last outputs indicators by using a Max-Min formula in such a way that the higher the value the higher the performance. Data on these indicators derive from the United Nations database. This database provides data on former Ethiopia and Ethiopia respectively including and excluding Eritrea since the independence of the latter in 1993. It also separates Zanzibar from Tanzania. In both cases, I consider a single country in order to stay coherent with the other datasets. Ethiopia includes the former and Ethiopia excluding Eritrea since 1993. I add data for Zanzibar to those of Tanzania since the former is still considered as a region of the latter.

  low amelioration in the outputs indicators. Thus, the results do not show a significant change in the quality of public spending in Africa and particularly in sub-Saharan Africa suggesting that the claim of expansion of public spending to boost progress in the frame of the Millennium Development Goals' launch does not necessary create a sustained fiscal space.The individual analysis of the countries shows that only a few African countries have been situated on the frontier at least once. Seychelles is the best ranked African country in terms of the number of times to reach the efficiency frontier. It has reached the frontier five times consecutively since the 1990's. It is followed by Equatorial Guinea, three 3 times, since 2000's and Zimbabwe over1985-1989 and 2005-2009. Cameroon, Cote d'Ivoire, Ethiopia, Ghana, Libya, Niger, Nigeria and Togo achieve this performance only once. On the contrary, the group of non-African countries provides the most efficient countries. Bangladesh, Mexico and Uruguay have always been on the frontier while Brazil and Guatemala present inefficiency only once. Peru is efficient since 2000's, Philippines since the period of 2005-2009 while Sri Lanka met efficiency over1980-1984's period.

Figure 1 :

 1 Figure 1: Evolution of Efficiency scores in group of countries

Figure 2 :

 2 Figure 2: Efficiency scores and the level of public spending

Figure

  Figure 3: Loss growth and Efficiency change

Figure 4 :

 4 Figure 4: Lost fiscal space and tax capacity development in Africa

Figure 5 :

 5 Figure 5: Lost fiscal space, domestic saving and external financing in Africa

Figure 6 :

 6 Figure 6: Lost fiscal space, fiscal balance and economic growth in Africa

Table 1

 1 reports the average levels of the public expenditure composition and the constructed indexes across the sample countries over the covered period. Countries tend to spend much in consumption than in investment, with three exceptions including Bangladesh, Egypt and Equatorial Guinea. Consumption is on average twice greater than investment. Africa reports the highest ratios both of consumption and investment. Public investment in this continent is on average 8.9% of GDP against 17.2% of GDP for consumption expenditure. The sub-Saharan region, with shares of 7.8 and 16.5% in GDP respectively of investment and consumption, spends less than the Maghreb with respectively 9.9% and 17.9%. Meanwhile the share of investment in GDP in non-Regarding the output indexes, the picture is quite different. The non-African countries show highest levels for both outputs indexes. They report 139.4 for HAI and 36.7 for Production Index while Africa reports respectively 105.6 and 28.3. The bad performances in Africa are mainly drawn by those of sub-Saharan region with 79.5 for HAI and 21.8 for PI. The five highest ranked countries in terms of HAI are Bulgaria (185.7), Uruguay (183.9),Seychelles (183.8), Fiji (174.8) and Libya (172.52) whereas Chad (23.1), Burkina Faso (33.9), Burundi (33.9) Ethiopia (34.3), Mozambique (37.3) show the lowest levels. For the PI, Seychelles and South Africa are the only African countries among the best five rated countries.

	African countries is on average 5.7% against 12.6% for consumption. Moreover, the disparities
	in expenditure ratios among countries are huge ranking from 2.4% to 17.3% for investment and
	from 4.8% to 31% for consumption. In terms of investment, the head of the most spending coun-
	tries quantile are constituted of Equatorial Guinea (17.3%), Lesotho (15%), Burundi (13.9%),

Table 1 :

 1 Output Indexes and Public expenditure (% of GDP) in sample countries

	Country	HAI Index	Product Index	Public Investment	Public Consumption	Total expenditure
	Bangladesh	84.902	6.885	5.972	4.873	10.845
	Brazil	163.429	64.397	2.375	17.264	19.640
	Bulgaria	185.724	61.938	3.831	16.864	20.694
	Fiji	174.795	61.804	6.571	16.883	23.453
	Guatemala	110.067	42.005	2.868	7.913	10.781
	Honduras	133.893	26.914	6.441	13.684	20.124
	India	100.882	12.393	8.735	11.440	20.175
	Iran, Islamic Rep.	147.649	34.677	9.282	14.175	23.457
	Jordan	170.030	27.646	8.084	23.665	31.749
	Nepal	83.812	6.303	5.921	9.037	14.958
	Pakistan	78.423	14.323	6.738	11.190	17.928
	Peru	149.954	42.091	4.780	9.719	14.498
	Philippines	156.692	24.582	4.127	9.891	14.018
	Sri Lanka	159.790	23.211	4.479	11.402	15.881
	Thailand	146.011	49.048	7.439	11.598	19.036
	Uruguay	183.860	88.901	3.963	12.616	16.579
	Non-African	139.370	36.695	5.725	12.638	18.364
	Algeria	141.189	35.555	11.567	16.307	27.874
	Egypt, Arab Rep.	137.002	21.703	12.943	12.760	25.704
	Libya	172.528	48.720	12.985	23.924	36.909
	Mauritania	78.979	19.650	8.979	20.670	29.650
	Morocco	114.689	35.536	5.217	17.457	22.675
	Tunisia	145.795	48.238	7.873	16.402	24.274
	Arab Maghreb Union	131.697	34.900	9.927	17.920	27.847
	Angola	48.871	21.433	7.154	31.004	38.158
	Benin	61.615	11.988	7.834	13.000	20.834
	Botswana	127.232	38.693	10.786	23.401	34.187
	Burkina Faso	33.855	7.766	9.787	19.782	29.570
	Burundi	33.874	3.752	13.893	17.441	31.333
	Cabo Verde	134.761	40.448	7.935	20.054	27.989
	Cameroon	76.922	19.692	4.370	11.191	15.561
	Central African Republic	37.822	10.283	5.461	12.926	18.387
	Chad	23.149	7.507	6.852	16.125	22.977
	Comoros	70.670	23.841	9.825	20.459	30.284
	Congo, Rep.	93.187	19.912	11.768	16.724	28.492
	Cote d'Ivoire	70.392	21.706	4.941	11.737	16.678
	Equatorial Guinea	89.847	24.359	17.253	16.726	33.979
	Ethiopia	34.333	2.385	8.256	11.058	19.314
	Gabon	128.048	58.798	6.763	14.317	21.079
	Gambia, The	69.028	9.993	8.739	15.756	24.495
	Ghana	98.895	21.502	8.092	11.119	19.211
	Guinea	48.735	3.368	5.825	9.695	15.520
	Kenya	100.716	11.781	7.084	17.128	24.213
	Lesotho	104.064	7.519	14.992	30.755	45.748
	Malawi	67.075	5.726	9.054	16.686	25.740
	Mali	40.849	10.216	8.881	12.181	21.062
	Mauritius	164.129	70.425	7.462	13.497	20.960
	Mozambique	37.302	4.451	11.314	11.659	22.973
	Namibia	119.857	47.784	7.859	26.521	34.380
	Niger	37.387	6.147	5.392	13.865	19.257
	Nigeria	71.097	24.068	6.731	15.935	22.666
	Rwanda	57.792	5.952	8.147	11.630	19.778
	Senegal	66.787	12.369	4.886	15.885	20.771
	Seychelles	183.809	116.389	10.039	29.181	39.219
	Sierra Leone	39.994	11.227	4.799	9.642	14.441
	South Africa	158.900	64.344	4.861	19.105	23.967
	Swaziland	111.704	37.396	6.424	17.639	24.063
	Tanzania	67.427	8.887	6.714	14.385	21.098
	Togo	76.281	9.801	6.173	12.810	18.983
	Uganda	66.575	7.487	4.756	11.330	16.086
	Zambia	62.466	13.471	6.049	18.381	24.430
	Zimbabwe	107.362	4.423	2.835	18.011	20.846
	Sub-Saharan Africa	79.548	21.771	7.894	16.546	24.440
	Overall Africa	105.622	28.336	8.911	17.233	26.144
	Overall sample	116.871	31.122	7.849	15.701	23.550
	Max	185.724	116.389	17.253	31.004	45.748
	Min	23.149	2.385	2.375	4.873	10.781
	Source: Author's construction, FERDI, World Bank, IMF and UNDATABASE.

Table 2 :

 2 Summary of DEA scores and average lost fiscal space (waste)

	Country	1980-84	1985-89	1990-94	1995-99	2000-04	2005-09	2010-13	Average	Times	Lost Fiscal spa
	Bangladesh	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	7.000	0.000
	Brazil	1.000	1.000	0.752	1.000	1.000	1.000	1.000	0.965	6.000	0.756
	Bulgaria	1.000	1.000	1.000	1.000	0.866	0.751	0.944	0.937	4.000	1.390
	Fiji	0.651	0.703	0.661	0.689	0.681	0.979	0.982	0.764	0.000	5.947
	Guatemala	0.940	1.000	1.000	1.000	1.000	1.000	1.000	0.991	6.000	0.114
	Honduras	0.585	0.585	0.673	0.778	0.668	0.649	0.769	0.672	0.000	6.670
	India	0.582	0.506	0.522	0.502	0.642	0.618	0.651	0.575	0.000	8.643
	Iran, Islamic Rep.	0.405	0.514	0.667	0.691	0.754	0.746	0.951	0.675	0.000	8.333
	Jordan	0.394	0.435	0.483	0.456	0.585	0.605	0.745	0.529	0.000	15.562
	Mexico	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	7.000	0.000
	Nepal	0.650	0.634	0.680	0.615	0.886	0.788	0.834	0.727	0.000	4.220
	Pakistan	0.530	0.479	0.464	0.513	0.851	0.774	0.895	0.644	0.000	7.041
	Peru	0.766	0.816	1.000	0.895	1.000	1.000	1.000	0.925	4.000	1.227
	Philippines	0.974	1.000	0.943	0.809	0.956	1.000	1.000	0.955	2.000	0.711
	Sri Lanka	1.000	0.870	0.994	0.955	0.993	0.686	0.738	0.891	1.000	2.089
	Thailand	0.619	0.679	0.798	0.846	0.860	0.805	0.814	0.774	0.000	4.327
	Uruguay	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	7.000	0.000
	Non-African	0.770	0.778	0.802	0.809	0.867	0.847	0.901	0.825	72.131	3.943

  Thus, the loss in fiscal space created by the inefficiency of public spending in Africa is about 11.5% of GDP equivalent to 43.8% of the outlay used. It is 11.3% of GDP, about 46.3% of the allocated resources for SSA and 45.4% for the Maghreb. Rationally, non-African countries exhibit less lost fiscal resources. The leakage for the non-Africans is around four times less than that of the African region. An insight in individual countries shows that how much the country is hit by the inefficiency depends on the level of outlays confirming the premise that larger public sector is more harmful when efficiency Until now, the findings are analyzed in a static way considering whether a country becomes closer to or farther away from the efficiency frontier[START_REF] Aubyn | Study on the efficiency and effectiveness of public spending on tertiary education[END_REF]). Let's now examine the efficiency in a dynamic way assuming that the frontier itself is not static since I am dealing with panel data. My concern is to determine how productivity has grown and what drives this improvement: amelioration in the quality of public management (change in technical efficiency) or a movement of the production frontier (technological change). For that, I use Malmquist index to decompose the total factor productivity (Tfpch) into its efficiency (EFFCH) and technological (techch) components over time. This exercise is important since almost all African countries record a steady growth of some indicators especially those of human capital while those of non-African economies tend to stagnate at high levels. This may suggest that African countries have grown fast and substantially relatively to non-African ones although they are inefficient. Table3sums up these indexes, more details are provided in table 8 of appendix.

	is missed. For instance, Seychelles loses much room (6.56%) than Cameroon (3.97%), Mauritius
	(4.96%), Zimbabwe (4.91%) and Uganda (5.29%) although it has the best practice in Africa
	because it spends much. The efficiency of Seychelles is then explained by the fact it outperforms
	in terms of outputs. With a high government size but low level outputs, the inefficiency of
	Lesotho translates into the highest loss estimated up to 33.06%.

Table 3 :

 3 Malmquist index summary of countries means

	Country	Effch	Techch	Pech	Sech	Tfpch	Country	Effch	Techch	Pech	Sech	Tfpch
	Bangladesh	1.132	1.047	1.000	1.132	1.186	Comoros	1.216	1.037	1.160	1.049	1.261
	Brazil	0.973	1.060	1.000	0.973	1.031	Congo, Rep.	1.031	1.071	1.030	1.001	1.105
	Bulgaria	0.999	1.044	0.990	1.009	1.043	Cote d'Ivoire	1.148	1.055	1.128	1.018	1.211
	Fiji	1.073	1.042	1.071	1.002	1.119	Equatorial Guinea	1.418	1.065	1.298	1.093	1.511
	Guatemala	1.068	1.030	1.010	1.057	1.101	Ethiopia	1.124	1.026	0.937	1.199	1.153
	Honduras	1.075	1.034	1.047	1.027	1.112	Gabon	0.992	1.039	0.981	1.012	1.031
	India	1.072	1.025	1.019	1.052	1.099	Gambia, The	1.410	1.038	1.209	1.166	1.463
	Iran, Islamic Rep.	1.180	1.034	1.153	1.024	1.220	Ghana	0.951	1.029	0.925	1.029	0.979
	Jordan	1.117	1.031	1.112	1.005	1.152	Guinea	1.096	1.026	1.030	1.064	1.124
	Mexico	1.000	1.031	1.000	1.000	1.031	Kenya	1.046	1.025	1.043	1.003	1.072
	Nepal	1.178	1.022	1.042	1.130	1.203	Lesotho	0.936	1.014	0.934	1.003	0.949
	Pakistan	1.127	1.020	1.091	1.033	1.150	Malawi	1.098	1.029	1.039	1.057	1.131
	Peru	1.061	1.033	1.045	1.015	1.096	Mali	1.148	1.032	1.026	1.119	1.185
	Philippines	1.006	1.025	1.004	1.002	1.031	Mauritius	1.034	1.030	1.031	1.003	1.065
	Sri Lanka	0.947	1.010	0.951	0.996	0.957	Mozambique	1.219	1.046	1.019	1.196	1.274
	Thailand	1.063	1.030	1.047	1.015	1.095	Namibia	1.054	1.051	1.051	1.003	1.108
	Uruguay	1.022	1.041	1.000	1.022	1.063	Niger	1.112	1.045	0.979	1.136	1.162
	Non-Africans	1.079	1.036			1.115
							Nigeria	1.072	1.039	1.012	1.059	1.114
	Algeria	1.040	1.028	1.011	1.028	1.069	Rwanda	1.205	1.037	1.043	1.156	1.249
	Egypt, Arab Rep.	1.168	1.036	1.126	1.037	1.210	Senegal	1.104	1.046	1.050	1.052	1.155
	Libya	1.002	1.025	1.005	0.997	1.027	Seychelles	1.082	1.073	1.150	0.941	1.161
	Mauritania	1.219	1.053	1.199	1.016	1.284	Sierra Leone	1.040	1.050	0.968	1.074	1.092
	Morocco	1.103	1.037	1.050	1.050	1.143	South Africa	0.972	1.028	0.966	1.006	0.999
	Tunisia	1.158	1.035	1.128	1.027	1.199	Swaziland	1.085	1.033	1.096	0.990	1.121
	Maghreb	1.148	1.037			1.191
							Tanzania	1.045	1.022	0.984	1.062	1.068
	Angola	0.964	1.034	1.035	0.932	0.997	Togo	1.206	1.031	1.118	1.078	1.243
	Benin	1.131	1.044	1.029	1.099	1.181	Uganda	1.025	1.024	1.001	1.025	1.050
	Botswana	1.092	1.031	1.067	1.024	1.126	Zambia	1.027	1.024	1.069	0.961	1.052
	Burkina Faso	1.121	1.029	0.991	1.131	1.153	Zimbabwe	0.967	1.072	0.977	0.990	1.037
	Burundi	1.050	1.038	0.892	1.177	1.090	SSA	1.140	1.042			1.185
	Cabo Verde	1.078	1.075	1.040	1.036	1.158	Mean	1.085	1.037	1.038	1.045	1.125
	Cameroon	1.017	1.031	0.976	1.042	1.048
	Central African Rep.	1.170	1.030	1.104	1.059	1.205
	Chad	1.122	1.033	0.965	1.163	1.158
	Note: All Malmquist index averages are geometric means

Table 7 :

 7 Principal components(eigenvectors: sectoral productive values added)

	Variable	Comp1 Comp2 Comp3 Comp4 Comp5 Unexplained
	Agriculture(agri)	0.3455	0.9026	0.2156 -0.0207 0.1381	0
	Construction(constr)	0.4773 -0.1958 -0.3681 -0.5073 0.5839	0
	Manufacture(manu)	0.4691 -0.0403 -0.4770 0.7401 -0.0547	0
	Transports(trans)	0.4945 -0.0756 -0.0167 -0.3856 -0.7751	0
	Whole and retail trade (trade) 0.4338 -0.3737 0.7682	0.2139	0.1902	0
	Sources: UN DATABASE and World Bank. Number of observations: 427
	Index product=Agri*0.3355+Constr*0.4773+Manu*0.4691+Trans*0.4945+Trade* 0.4338

Table 8 :

 8 Malmquist index decomposition full results

	Country Period

The different datasets are available upon request.

This work was supported by the LABEX IDGM+ (ANR-10-LABX-14-01) within the program "Investissements d'Avenir" operated by the French National Research Agency (ANR).

A Composite Index construction of the outputs The European Journal of Comparative Economics,9,[425][426][427][428][429][430][431][432][433][434][435][436][437][438][439][440][441][442][443]


Fabrice Bouquet
email: bouquet@lifc.univ-fcomte.fr

Stéphane Debricon
email: debricon@lifc.univ-fcomte.fr

Bruno Legeard
email: legeard@leirios.com

Jean-Daniel Nicolet
email: jean-daniel.nicolet@etat.ge.ch

Extending the Unified Process with Model-Based Testing

Keywords: Unified Process, Model-Based Testing, Class Diagrams, Statecharts, OCL, Model specialization

The Unified Process (UP) is a software development technique that includes modeling of specifications and testing workflow. This workflow is achieved by information interpretation of specification to produce manual tests. In this paper, we extend the UP with model-based testing (MBT) where models resulting of the UP will be used for MBT. We describe how model-based testing introduces new test design activities in parallel with the application design activities. We give guidelines to derive the test model from the analysis model produced by the UP. We illustrate this tailored process with the example of a Geneva State taxation.

Introduction

Model-based testing (MBT) exists as a process [START_REF] Utting | Practical Model-Based Testing -A tools approach[END_REF], describing each step needed from creating a test model, automatically generating test cases and executable test scripts from that model. MBT can then be viewed as an independent process in the development life cycle. To make it more efficient and widely used, our purpose is to include MBT in an existing and recognize process, that is to extend the Unified Process (UP) to support model-based testing key features. The UP is a software engineering process. Its goal is to transform requirements into software. To realize this transformation we model requirements, using for example the Unified Modeling Language (UML). And then models evolve to be more and more precise and finally an implementation of the system is made. We propose guidelines to specialize model produced by the UP into model suitable for test generation. The new process called UPMBT will then support the usual manual writing of test cases, but also the automatic generation of tests from a new artefact called test model. This is a key concept of UP, the ability to be tailored. The most famous version of the UP is the RUP (Rational Unified Process), which comes with tools and support. There are also other example of tailored UP such as the EUP (Enterprise Unified Process) [START_REF] Ambler | Introduction to the enterprise unified process[END_REF]. In this paper we define an extension of the UP to include the model-based testing process. In the first section we will introduce the unified process, and the model-based testing process. In the second section we will describe how the UP evolves to support MBT. We also explain benefits and gains expected in the development process. Then we will propose a way to produce a test model from a model provided by the UP. The last section will present a case study based on the life cycle of a taxation in Switzerland.

Overview of the Unified Process and Model-Based Testing

In this section we introduce in more details UP and MBT.

The Unified Process (UP)

We want to consider a software development technique called the Unified Process.

The goal of the UP is to define who does what, when and how. The UP is strongly tied to UML [START_REF]UML Resource Page[END_REF], but they are actually independent. The UP is the methodology explaining how to transform requirements into software. UML is the visual language necessary to the methodology. Note that UML has been standardized by the OMG. A meta-model exists for both, each of which being an instance of the meta-meta-model named Meta-Object Facility (MOF), defined as the nearly universal root from which several other meta-model derive, like for example XMI (the XML format used to store UML models) and CWM (Common Warehouse Metamodel). The meta-model used for the UP is called Software Process Engineering Metamodel (SPEM). First research leading to the creation of the UP have been done by Ericsson (the Ericsson approach 1967) and Rational (the Rational Objectory Process, 1996 to 1997) now a part of IBM. In addition it is also based on other best practice and guidelines such as managing requirements, visual modeling of software, component-based architectures, iterative development, verifying software quality and managing changes of software.

The UP is organized into four phases, often with several iterations happening inside some of these phases [START_REF] Arlow | UML 2 and the Unified Process, Second Edition, Practical Object-Oriented Analysis and Design[END_REF]. The phases are:

Inception: The goal of the inception phase is to have an overview of the overall project; this phase should establish feasibility, from technical prototyping to functional behavior modeling. Stakeholders and project management should end up with an agreement on the scope of the project. Major risks have been identified and a business case expressing how the project delivers benefits to the business is available. The inception phase should evaluate the cost and produce a schedule for the project.

Elaboration: The goal of the elaboration phase is to produce a working skeleton of the architecture of the project. This skeleton will capture some of the most risky functional behavior expressed in the requirements. By the end of this stage, most of the use cases have been written, the hard engineering decisions have been made and the final commitment of whether or not continue with the project can be made.

Construction:

The goal of this phase is to build the product. The construction phase is usually a series of development iterations that flesh out the functionality of the skeleton into a deliverable product. Each iteration goes for one to two months, has a fixed deadline and produce a release that can be tested and evaluated by users.

Transition: The goal of this phase is to deliver the finished product to the users. This includes deployment, beta-testing, completion of the user documentation, training of the end users and reacting to user feedback. A project review is done to evaluate the process.

Model-Based Testing (MBT)

The objective of testing is to find defects in software. To achieve this goal, one must be able to find differences between an implementation and what stakeholders expressed in requirements.

One way to do this is to use model-based testing; it relies on a behavior model, precise enough, of the requirements. The testing model should capture the expected behavior with sufficient abstraction; we don't want to consider every detail.

An implementation should offer an adequate solution to every requirement expressed whether they were formal or not. In fact, if we consider a model as detailed as the System Under Test (SUT), we would rather validate the implementation.

Abstraction is a necessity for model-based testing, but any omission will lead to the impossibility to generate tests for the omitted part. It is a question of choice, for the modeler, whether he wants tests for a requirement or not. Models should be abstract but precise and complete enough to generate the required test case and the expected results (the test oracle). The models we consider are universal rather than existential abstractions -e.g. state machine diagrams or pre-post conditions as opposed to sequence diagrams [START_REF] Utting | A taxonomy of model-based testing[END_REF].

We will consider a template for a process conducting the generation and execution of tests on a SUT as shown in Fig. 1.

Step 1 A model of behavior is deduced from requirements and specification documents. Abstractions will be made at that point; it can range from output abstraction (we don't care about a specific result) to functionality abstraction (a part of the SUT is excluded).

Step 2 This step of the process should defined test selection criteria. Arguably, a good test case is one that is likely to detect severe and likely failures at an acceptable cost, and that is helpful at identifying the underlying fault [START_REF] Utting | A taxonomy of model-based testing[END_REF]. This definition is too general and does not explicit a way to define relevant test selection criterion. A good practice is to relate test selection criteria to a specific functionality in the SUT. The ability of the testing engineer is of great importance for the choice of criteria regarding the test suite that should be generated.

Step 3 Test selection criteria are then transformed into test case specification. They formalize the notion of test selection criteria and render them operational. The set of test case that satisfy a test case specification can be of any cardinality: it is empty if there is no satisfying test case; usually, they are many test cases that satisfy it.

Step 4 With the testing model and the test case specification, a test suite can be produced. The difference between a test case specification and a test suite is that the further is intentional while the latter is extensional: all tests are explicitly enumerated. This work is done by a test case generator taking the model and the test case specification to produce tests.

Step 5 Tests produced in the previous step will now be executed on the implementation of the SUT. But first we need to add some kind of interface between our test and the implementation. Remember that we made some abstraction on the model, so we can assume that it will not be possible to execute directly the tests produced. We need to add what is called an adapter to bridge those different levels. The goal of this module is to concretize inputs and then to pass them to the implementation and record the output produce by it. Those results will be used to give a verdict on the test case. A verdict is the comparison result of the output of the SUT with the expected output as provided by the test case. There are 3 distinct verdicts: pass, fail and inconclusive. A test passes if outputs defined by the test case and produced by the SUT are equivalent. It fails if they are different. The inconclusive verdict applies to non determinist system.

Extending the Unified Process with Model-Based Testing

In this section we will extend the UP to support a MBT process, and we describe what benefits could be expected.

Evolutions in the UP phases

As we introduce MBT in the UP, we also have to describe what impacts can be expected on phases of the UP. The inception phase is not impacted by this approach. Changes mainly concern the elaboration and the construction phase.

During those phases the system will grow from a prototype to a final product and the associated tests artifacts will evolve with iterations. The elaboration phase will produce a test model for basic functionalities, an adapter and an adapter layer. By the end of the phase, those artifacts should be mature enough and the adapter layer architecture should be precisely defined. The focus for this phase is on the structure of the adapter layer that should be able to map the implementation.

During the construction phase, artifacts will only evolve with the addition of new functionality that might produce new question to be elicited. Each iteration made within the elaboration and construction phase will augment the number of test suite. System testers and users will have a complete testing framework and suitable tests.

Benefits of MBT will be the production of corrections in the analysis and design model earlier in the process. Following iterations introducing them in the implementation model. More important a defect might be found before the effective execution of a test. Manual and generated test scripts, produced by the entire process, will be executed in the transition phase. They will be included to the beta-testing for the software.

Evolutions in the UP workflows

We consider a typical construction iteration of the UP as described earlier. We propose to introduce the MBT activities right after the UP analysis workflow that is in the design process. From the MBT viewpoint, the first activity is the production of a test model. This requires the analysis model to be available.

From this point on, we extend the UP by adding a new artefact for the design workflow, so that two different kinds of model are produced. The first model is the usual design model of the UP, while the second one is a test model. Both are derived from the analysis model and the requirements documents. The design workflow needs to be divided into two parallel processes. A development team will take in charge the execution of the usual design process and a test team will follow a model-based testing process. Those two point of view on the same analysis model may lead to deviation between models. This will be the result of a different or partial interpretation of specification present in the analysis model. The unified process recommends assigning a team that will go through the entire process for a given functionality, rather than splitting team for a given activity.

For testing activity it's a good practice to have a dedicated team, first because they must have specific skills and to be relevant a testing model must be independent enough. Obviously a team will be made of workers endorsing a role depending of the workflow or the phase. Team independence during this workflow is crucial. Any question raised while modeling for test, should be elicited by the system analyst or a stakeholder but not by the development team. A good independence ensures a good accuracy of the generated tests. This parallel process is shown in Fig. 2.

The next workflow in the UP is the implementation. The development team will have to produce an implementation for the design model. Meanwhile the test team will have to produce an adapter to interact with the SUT, that is to implement the generated test cases into executable test scripts. Both developments will occur approximately at the same time and they must be carefully coordinated. The interface must have been well defined for test scripts to interact with the SUT. They are called control and observation points. They must be available for the test team to apply scripts and get output from the SUT. The test workflow needs to be described for each team with more details. This workflow will gather, for the development team, all activities of usual testing; that are: creating test case, evolving existing test scripts, running tests and reporting any defects detected. The goal of this workflow, for the test team, is to generate test scripts from the adaptation layer and the generated test cases. Test cases have been generated during the previous activity using a MBT test generator. Any changes made on the model during the design phase will be integrated to the newly generated test The next activity will be the execution of those tests under the system. Defects will not be reported directly as they can be produced by the model or the implementation (or both). A control of the model must be done before reporting the defect. If the failure is proved to be relative to the implementation, then a good diagnostic can be (issued from our test cases).

Specializing an analysis model into a test model

We mentioned earlier that UML can be used as the modeling language for the unified process. It can also be used to generate tests (e.g. [START_REF] Offutt | Generating tests from UML specifications[END_REF]), various works have been done [START_REF] Kansomkeat | Automated-generating test case using uml statechart diagrams[END_REF],[BBM + 01], [START_REF] Hartmann | Uml-based integration testing[END_REF], [START_REF] Briand | A uml-based approach to system testing[END_REF],[KHC + 99] and they all have in common the subset of UML used. Models should represent the system structure and its expected behavior. The analysis model reflects the system structure with class diagrams. Those diagrams contain classes, with attributes and operations, and relations between classes. The system behavior will be captured by statecharts and sequence diagrams. The first one is made of states and transitions linking them. And the second one expresses messages exchange between actors. An analysis model may contain unnecessary informations (we probably does not want to test every functionality of the system) and in the same time be lacking of crucial informations in regards of our testing process. Those reasons explicit why we need to specialize our analysis model into a new one, the test model. A test model derives from an analysis model. That means that classes and relations (from class diagrams), states and transitions (from statecharts) will be re-used in our test model. However those items cannot be used directly because abstraction is a necessity when modeling for test on a real system [START_REF] Prenninger | Abstractions for model-based testing[END_REF]. This is precisely the step 1 of the process described in section 2.2 Models should not contain every classes of the analysis model, only a subset of classes representing the function to be tested should appear. But on the other side, we need to add information to the test model. The goal of the model is to produce test based on what is expressed. The analysis workflow does not produce a model complete enough. A model should contain class operation with a minimum amount of information about the system behavior. The description can be placed on class diagrams, using pre-and post-conditions, or in state machines using transition effects. We suggest the use of OCL [START_REF] Warmer | The Object Constraint Language, Second Edition, Getting your models ready for MDA[END_REF] to express those informations. OCL is a formal language, non ambiguous and is part of the UML2.0 specification. Any relevant information expressed in an informal way on the analysis model should be specified using the OCL notation in diagrams used for tests.

Case Study: RTAXPM

To illustrate the need for specialization of an analysis model, we will introduce in this section a case study. This is a tax record life cycle of the Geneva State AFC (fiscal administration). The AFC is using RUP in combination with IBM Rational tools, which gives us a nearly complete and well structured model of the system. The functionality under test for this case study is a taxation life cycle. We only focus on the analysis model, the life cycle is described using three kind of diagram in the AFC model: use case diagram (Fig. 3), statechart diagram (Fig. 4) and class diagram. Our purpose is to generate tests from this model. We will use all provided diagrams to produce a model suitable for test. All informal informations will be added on diagrams using OCL. Taking into account the type of diagrams and the formal language used, its availability at the LIFC, we choose to generate test cases with the MBT test generator LEIRIOS Test Generator for UML (LTG)1 . The test model have been made with Borland Together Designer 2006 for Eclipse, then exported and processed by LTG.

A taxation life cycle

Specializing the AFC analysis model into a new test model

In this section we will describe all changes induced by the specialization.

-We add 'taxer ' and 'group leader ' classes. Those classes appear in the model as actor (c.f. Fig. 3), and are issued of the security policy defined for the application framework. This information was clarified by the use case diagram and by an explanation of the project manager. In addition the use case explicit that a group leader is the only taxer being able to stamp or suppress a taxation. This will be introduce in the statechart diagram by new states, representing a login and logout from the system. -We transform informal notation such as 'user allowed to stamp' and 'stamp needed', into formal notation: First the ability for stamping is defined as an attribute of taxer class. Added to this, the need for stamp is more complex to introduce. A use case (not included in this paper) describes in an informal way, how to define if a stamp is needed on a taxation. It depends on computation on a taxation record data. This rises a problem of choice:

• we can either put computation rules in the model, it allows the use of exact guard on transitions. • or we can use a boolean-like value defining if a stamp is needed or not, and leave the computational work to the adaptation layer. We choose to use a boolean value. We place the following OCL guards in the test model: [taxer.allow_stamp=true or taxation.stamp_needed=false] and [taxer.allow_stamp=false and taxation.stamp_needed=true] -We retain all attributes of the analysis class in our 'taxation' class. They will not be all used for the test of the life cycle but can be useful for other test generation.

-We add, in our 'taxation' class, operation needed for the transition on the statechart diagram. They will capture the behavior of our taxation life cycle. It is described by a taxation status (e.g. 'in taxation', 'controlled' or 'to stamp'). The taxation status will be our control point for the test oracle.

Figure 5 is the model produced by the specialization of an analysis model into a test model. For each test target, the LTG tool computes, if possible, one or more test cases. We set up the tool with a depth-first algorithm and a search depth of 10.

Generated test cases for the taxation life cycle

For our case study, 16 test cases were produced covering the 9 operations of a taxation.

Figure 6 is a screen shot of a test case example for the 'stamp' operation and its oracle. This test case is transformed into a test script using the adapter. The produced test script is then ran on the AFC framework through the adaptation layer. The result returned by the framework is compared to the oracle which gives the verdict of our test case.

Conclusions

In this paper, we propose to extend the UP with MBT activities. This allow the automatic generation of validation test cases from a test model that inherits from the analysis model. Then, adapters are developed to be used for generating executable test scripts from the abstract generated test cases. Including MBT into a software engineering process will accelerate its adoption, giving industrials a defined framework to introduce tests from models in their development process. One of the great difficulty of MBT, so far, is to keep the testing model alive. Specifications or design model evolve during a development life cycle and the test model will be useless if not modified. This is where the iterative feature of UP ensure that both models are at an identical state. The chosen case study at the AFC gives us the first support for this approach, but we need to explore links between analysis, test and design models.

This UP process extended with MBT has been used in the real context of the development of a taxation system at the Geneva State (Switzerland).

The main benefits of the integration of MBT activities into the UP are the reusability of the analysis models to develop the test model, and the automatic generation of validation test cases for the considered application functionalities. Moreover, the development of the test model, which implies to formalize the expected behavior of the system under test, leads to a direct feedback on the analysis models (and design models) that help their validation.

This integration of MBT activities in well recognized and used software development process is a key issue for the dissemination of the MBT approach in the software development practices.

Fig. 1 .

 1 Fig. 1. model-based testing process

Fig. 2 .

 2 Fig. 2. Packages produced by the UP extended with MBT

Fig. 3 .

 3 Fig. 3. Use cases (extract from the model).

Fig. 4 .

 4 Fig. 4. Taxation life cycle (extract from the model).

Fig. 5 .

 5 Fig. 5. Taxation life cycle for MBT.

Fig. 6 .

 6 Fig. 6. Test cases for the stamp operation.

For more information about the model-Based testing tool LTG, see www.leirios.com

Acknowledgments. The authors would like to thank the CTI and Mark Utting for their participation.