Ablam Estel Apeti

Jean-Louis Combes

Eyah Denise

Eyah Denise Edoh

Entrepreneurship in developing countries: can mobile money play a role?

Keywords: JEL Classification: G23, G32, L26, O32 Mobile money, entrepreneurship, entropy balancing, developing countries

Entrepreneurship in developing countries: can mobile money play a role?

Introduction

Entrepreneurship is generally recognized as an important component to stimulate economic growth, innovation, and competitiveness, promote development, and may have social effects such as reducing poverty or unemployment [START_REF] Schumpeter | The theory of economic development[END_REF][START_REF] Acs | Innovation in large and small firms: an empirical analysis[END_REF][START_REF] Acs | Entrepreneurship, economic development and institutions[END_REF][START_REF] Pennisi | Understanding entrepreneurship in developing countries[END_REF][START_REF] Haltiwanger | Who creates jobs? small versus large versus young[END_REF][START_REF] Qin | Access to credit and entrepreneurship: Evidence from china[END_REF][START_REF] Asturias | Firm entry and exit and aggregate growth[END_REF]. While developing countries face economic and social challenges, the evolution of entrepreneurship that can help them initiate solid growth or absorb a growing labor force remains shy. Indeed, in contrast to the 7% level of enterprise creation in advanced countries, the average level of entrepreneurship in developing countries is 3%, a difference of 4 percentage points or 56% (World Bank, 2021a).

The existing literature offers a rich analysis of the factors that may hinder enterprise creation, among which access to finance is the most salient issue [START_REF] Pennisi | Understanding entrepreneurship in developing countries[END_REF]World Bank, 2021b). For example, in the context of China, [START_REF] Qin | Access to credit and entrepreneurship: Evidence from china[END_REF] document the role of improved access to finance following the 2006 Postal Savings Bank of China launch in encouraging business creation. [START_REF] Beck | Finance and growth for microenterprises: evidence from rural china[END_REF] conducted a study on China using the Rural Finance Survey conducted in 2009 to show that access to finance increases entrepreneurship. The link between access to finance and entrepreneurial capacity is also shared by authors such as [START_REF] Allen | Law, finance, and economic growth in china[END_REF][START_REF] Levine | Finance and growth: theory and evidence[END_REF][START_REF] Pennisi | Understanding entrepreneurship in developing countries[END_REF][START_REF] Beck | Who gets the credit? and does it matter? household vs. firm lending across countries[END_REF][START_REF] Han | The link between credit markets and self-employment choice among households in rural china[END_REF][START_REF] Cai | The relationship between credit constraints and household entrepreneurship in china[END_REF][START_REF] Ma | Credit accessibility, institutional deficiency and entrepreneurship in china[END_REF][START_REF] Herkenhoff | The impact of consumer credit access on self-employment and entrepreneurship[END_REF][START_REF] Tian | Do place-based policies promote local innovation and entrepreneurship[END_REF][START_REF] Charfeddine | Financing new entrepreneurship: Credit or microcredit?[END_REF] and supported also by statistics of World Bank (2021b). In this paper, we analyze the effect of a "recent" financial innovation in developing countries, namely mobile money, 1 on entrepreneurship.

The development of digital transactions and mobile payments has transformed the financial landscape in developing countries, making it easier for many people to access basic financial services. Since the success story of M-PESA in Kenya in 2007, mobile money has emerged in developing countries as the most effective way to provide (poor) households with access to financial services on the one hand and to modernize financial transactions on the other, in context of a strong preference for cash.

Mobile money has received considerable attention in the existing literature in recent years. Early studies, essentially microeconomic, present mobile money as a welfare tool by promoting financial inclusion, increasing consumption and household income (Jack andSuri, 2014 Munyegera and[START_REF] Munyegera | Mobile money, remittances, and household welfare: Panel evidence from rural uganda[END_REF][START_REF] Suri | The long-run poverty and gender impacts of mobile money[END_REF][START_REF] Riley | Mobile money and risk sharing against village shocks[END_REF]. In addition, other studies explore the effect of mobile money on the ability of households to obtain well-paying jobs, receive remittances, invest, and on firm performance [START_REF] Suri | The long-run poverty and gender impacts of mobile money[END_REF][START_REF] Gosavi | Can mobile money help firms mitigate the problem of access to finance in eastern sub-saharan africa[END_REF][START_REF] Islam | Does mobile money use increase firms' investment? evidence from enterprise surveys in kenya, uganda, and tanzania[END_REF][START_REF] Aggarwal | Cashing in (and out): Experimental evidence on the effects of mobile money in malawi[END_REF][START_REF] Patnam | Real effects of mobile money: Evidence from a largescale fintech expansion[END_REF][START_REF] Lee | Poverty and migration in the digital age: Experimental evidence on mobile banking in bangladesh[END_REF]. At the macro/cross-country level, some studies identify mobile money as a mechanism for economic formalization [START_REF] Jacolin | Informal sector and mobile financial services in emerging and developing countries: Does financial innovation matter?[END_REF], inequality reduction [START_REF] Asongu | The impact of mobile phone penetration on African inequality[END_REF], monetary policy efficiency via low inflation, and better macroeconomic performance [START_REF] Adam | Mobile money and monetary policy in East African countries[END_REF][START_REF] Aron | Inflation forecasting models for uganda: is mobile money relevant?[END_REF][START_REF] Dunne | Financial innovation and money demand: Evidence from sub-saharan africa[END_REF][START_REF] Kipkemboi | The impact of mobile money on monetary and financial stability in sub-sahara africa[END_REF][START_REF] Mawejje | Macroeconomic effects of mobile money: evidence from uganda[END_REF]. In the same perspective, recent studies by Apeti (2023a) and [START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF] respectively show that mobile 1. It allows more than half of the population previously excluded from the formal financial system to have access to financial tools. money improves household welfare by reducing consumption volatility and improves government revenues by increasing tax collection. Despite the evolution of the literature on mobile money and its effects on development, little, to the best of our knowledge, is said concerning the capacity of this financial innovation to boost entrepreneurship in developing countries. This paper aims to fill this gap by analyzing whether adopting digital financial services such as mobile money can help developing countries improve their level of entrepreneurship.

To identify the effect of mobile money, we rely on an impact analysis method, namely entropy analysis developed by [START_REF] Hainmueller | Entropy balancing for causal effects: A multivariate reweighting method to produce balanced samples in observational studies[END_REF] and recently used by Apeti (2023a) and [START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF] to analyze respectively the effect of mobile money on household consumption volatility and on tax revenue. Using a sample of 105 developing countries over the period 2006-2020, we show that mobile money adoption increases entrepreneurship in developing countries. This result is robust to several robustness tests, including changing the definition of mobile money, the definition of entrepreneurship, the placebo tests, adding additional control variables, altering the sample design, and alternative estimation methods such as panel fixed effects, and GMM system. Furthermore, the heterogeneity tests performed show that: ithe effect of mobile money may depend on the intensity of mobile money use, iieffect of mobile money may depend on some structural factors such as democracy, conflict, quality of regulation, corruption, financial development, internet, and education.

The rest of the paper is organized as follows. The next section presents the theoretical considerations. Section 3 presents the methodology. Section 4 presents the data and descriptive statistics. The results are presented in section 5, with robustness analysis in section 6. Section 7 presents the heterogeneity tests. Section 8 concludes.

Theoretical considerations

In this section, we discuss the arguments that support the effect of mobile money on entrepreneurship.

First, mobile money facilitates business creation by easing financial constraints or barriers for firms/households. Access to finance plays a key role in households' decision to start a business or take risks [START_REF] Beck | Finance and growth for microenterprises: evidence from rural china[END_REF][START_REF] Qin | Access to credit and entrepreneurship: Evidence from china[END_REF]. However, access to finance in developing countries is challenging due to information asymmetry issues [START_REF] Stiglitz | Credit rationing in markets with imperfect information[END_REF] and the concentration of services in urban areas, leaving nearly half of individuals outside the traditional financial system. However, mobile money innovation provides a "new" opportunity for households in developing countries to access financial services at a lower cost. Evidence currently exists regarding the ability of mobile money to promote access to finance and reduce financial market imperfections such as information asymmetry. For example, [START_REF] Dalton | Epayment technology and business finance: A randomized controlled trial with mobile money (revision of CentER DP 2019-032[END_REF] in a Randomized Controlled Trial (RCT) with small and medium-sized enterprises in Kenya estimate the causal impact of an electronic payment technology on business finance. The authors show that e-payment technology or mobile money increased access to mobile loans-in number of loans, as well as amount borrowed-by at least 50% through the reduction of information asymmetries resulting from increased digital transactions. This conclusion is in line with [START_REF] Ahmad | Mobile money, financial inclusion and development: A review with reference to african experience[END_REF]Beck et al., 2015 which show that users' mobile money transactions can be used to establish credit scores which can help them get loans to finance their investments. Also, as highlighted by Suri and Jack, 2016, mobile money can change financial behavior-increasing financial resilience and savings-and promote efficient labor allocation, resulting in poverty reduction and ultimately a shift from agriculture to business. Finally, by facilitating remittances [START_REF] Suri | The long-run poverty and gender impacts of mobile money[END_REF][START_REF] Riley | Mobile money and risk sharing against aggregate shocks[END_REF], mobile money can reduce households' financial pressure allowing them to use these funds directly for entrepreneurial activities or indirectly through the development of (formal) financial inclusion [START_REF] Anzoategui | Remittances and financial inclusion: Evidence from el salvador[END_REF][START_REF] Shapiro | Remittances, entrepreneurship, and employment dynamics over the business cycle[END_REF]Yavuz and Bahadir, 2021).

Secondly, mobile money can encourage risk-taking and therefore entrepreneurship through its ability to smooth (idiosyncratic) risks or reduce loss aversion but also by reducing transaction costs. Indeed, uncertainty is one of the major concerns for business creation [START_REF] Gulen | Policy uncertainty and corporate investment[END_REF]. For example, as [START_REF] Boudreaux | Natural disasters and entrepreneurship activity[END_REF] show, negative shocks such as natural disasters penalize entrepreneurial activities. Indeed, natural disasters can hinder entrepreneurial activity by increasing entrepreneurial uncertainty and fear of failure by damaging infrastructure, disrupting supply chains, and affecting business performance. In addition, natural disasters can hinder the return to normal operations and thus decrease productivity [START_REF] Boudreaux | Weathering the storm: How foreign aid and institutions affect entrepreneurship activity following natural disasters[END_REF]. Therefore, by helping to smooth risks [START_REF] Jack | Risk sharing and transactions costs: Evidence from kenya's mobile money revolution[END_REF][START_REF] Riley | Mobile money and risk sharing against aggregate shocks[END_REF][START_REF] Koomson | Mobile money adoption and response to idiosyncratic shocks: Empirics from five selected countries in sub-saharan africa[END_REF]Apeti, 2023a), digital financial instruments such as mobile money can increase house-holds motivation to conduct entrepreneurial activity. Evidence on the effect of mobile money on risk but especially on business dynamics is offered by [START_REF] Patnam | Real effects of mobile money: Evidence from a largescale fintech expansion[END_REF] in India. Using granular transaction data from Paytm, one of India's largest mobile money providers with over 400 million users, the authors analyze the effect of mobile money on business outcomes in India. Drawing on the period surrounding the demonetization policy, which led to a sharp increase in mobile money adoption, they analyze how mobile money affects traditional risk-sharing arrangements. First, the authors find that the use of mobile money increases resilience to shocks by mitigating the impact of rainfall on nightlights-based economic activity and household consumption. Second, by conducting enterprise survey around a progressive targeting intervention that incentivized enterprises to adopt mobile payments technology, they conclude that firms that adopt mobile payments have improved sales after six months of use, compared to other firms. In addition, when they ask businesses about their subjective expectations for future sales, they find that mobile payments adoption is associated with lower subjective uncertainty and greater sales optimism.

Another aspect of risk that can increase the risk of loss and therefore the fear of entering into entrepreneurial activities comes from the lack of digitalization of transactions. Indeed, the limited capacity to make transactions digitally pushes households to carry cash for the provision of intermediate goods needed from their suppliers but also after the sale of products on the (domestic) market which exposes them to the risk of theft/robbery. Thus, by offering digital savings/transactions opportunities, mobile money can help limit insecurity such as theft and potential production losses for entrepreneurs, thereby increasing the willingness to engage in entrepreneurial activity, while lowering transaction costs will reduce production costs and consequently reduce the minimum capital requirements for engaging in entrepreneurial activities [START_REF] Beck | Payment instruments, finance and development[END_REF][START_REF] Suri | Mobile money[END_REF].

Finally, infrastructure (both physical and human) and institutions are crucial elements for business creation [START_REF] Van Der Sluis | Education and entrepreneurship selection and performance: A review of the empirical literature[END_REF][START_REF] Chowdhury | Institutions and entrepreneurship quality[END_REF][START_REF] Chauvet | Taxation, infrastructure, and firm performance in developing countries[END_REF]Boudreaux et al., 2022a). Accordingly, by providing an opportunity for governments to better collect taxes [START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF]-necessary for infrastructure financing [START_REF] Chauvet | Taxation, infrastructure, and firm performance in developing countries[END_REF])-, facilitate investment in human capital [START_REF] Ahmed | Mobile money and healthcare use: Evidence from east africa[END_REF][START_REF] Rotondi | Mobile money and school participation: Evidence from africa[END_REF], and by creating the opportunity for a strong institutional quality [START_REF] Krolikowski | Can mobile-enabled payment methods reduce petty corruption in urban water provision?[END_REF][START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF], mobile money can help foster business creation. Putting these arguments together, we assume that mobile money-a financial innovation that promotes financial inclusion by connecting a sizable section of previously unbanked people-helps to promote entrepreneurial activity.

Methodology

This study analyzes the effect of mobile money adoption on entrepreneurship-measured by new business density rate defined as the number of newly registered corporations per 1,000 working-age people-in mobile money countries (treatment group) compared to non-mobile money countries (control group). Mobile money adoption is far from being a random feature (Apeti, 2023a;[START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF]. It may depend on several factors, including economic performance, level of development, access to cell phones, and access to traditional financial services. These factors-which may also affect entrepreneurshipmake mobile money adoption endogenous (not random) through the problem of selection bias [START_REF] Allcott | Site selection bias in program evaluation[END_REF]. To circumvent this problem and identify the effect of mobile money, we follow Apeti (2023a) and [START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF] using an impact analysis method in particular entropy balancing-a method developed by [START_REF] Hainmueller | Entropy balancing for causal effects: A multivariate reweighting method to produce balanced samples in observational studies[END_REF]. This approach is also used by several authors in the economic literature including [START_REF] Neuenkirch | The impact of us sanctions on poverty[END_REF] to assess the impact of U.S. sanctions on poverty, [START_REF] Ogrokhina | The effect of inflation targeting and financial openness on currency composition of sovereign international debt[END_REF] to assess the effect of inflation targeting on the international debt denomination, [START_REF] Caselli | Heterogeneous effects of fiscal rules: The maastricht fiscal criterion and the counterfactual distribution of government deficits[END_REF] to evaluate the effect of fiscal rules and by [START_REF] Apeti | Sovereign debt default and inequality[END_REF] to analyse the effect of sovereign debt default on inequality. A similar approach is adopted by [START_REF] Riley | Mobile money and risk sharing against village shocks[END_REF] to assess the effect of mobile money on risk-sharing, and [START_REF] Munyegera | Mobile money, remittances, and household welfare: Panel evidence from rural uganda[END_REF] to assess the effect of mobile money on the welfare of a panel of 846 rural Ugandan households.

Entropy balancing allows us to identify the effect of mobile money by comparing mobile money and non-mobile money countries (or units) that are similar in observable characteristics, while controlling for time and country fixed effects. This method offers some advantages compared to concurrent impact analysis methods 2 such as propensity score matching (PSM) or difference-in-differences. First, it allows for a high degree of balance between the treatment and control groups by creating a synthetic group as close as possible to the treatment group. Second, unlike other impact analysis methods such as PSM, it does not require an empirical model for mobile money adoption, thus limiting specification and multicollinearity problems. Third, unlike classical matching methods, entropy balancing uses a more flexible reweighting approach by keeping the weights closer to the base weights to avoid information loss. Unlike conventional matching, which is based on the assumption of conditional independence, the fourth advantage is that entropy balancing allows us to exploit the panel aspect of our data and control for time and country-fixed effects in the second stage of our regression.

The approach used in this study is based on the principle that mobile money adoption is the treatment and entrepreneurship is the outcome variable. The units of observation are country-year observations. The observations with mobile money are the treatment group, and those without mobile money are the control group. The treatment effect on the treated (ATT) is defined as follows:

AT T = E[Y (1) |T = 1] -E[Y (0) |T = 1] (1)
where Y (.) is the outcome variable measuring the entrepreneurship. T indicates whether the observation unit is subject to mobile money adoption (T = 1) or not (T = 0).

E[Y (1) |T = 1] the entrepreneurship during the mobile money period, E[Y (0) |T = 1]
is the counterfactual result for countries that had adopted mobile money, i.e. the entrepreneurship in countries that had adopted mobile money if they had not.

The issue is that E[Y (0) |T = 1] is not observable due to the non-random nature of mobile money adoption. If this were the case, the ATT could easily be identified by comparing entrepreneurship in mobile money countries with non-mobile money countries.

Identifying ATT then requires a good proxy for E[Y (0) |T = 1]. To do so, we match mobile money units with non-mobile money units that are as close as possible on observable characteristics that meet two criteria: correlated with mobile money adoption and entrepreneurship. Under the condition that the non-mobile money units are fairly close to the mobile money units, any difference in entrepreneurship is attributable to mobile money adoption. Based on these different elements, we can rewrite equation (1) as follows:

AT T = E[Y (1) |T = 1, X = x] -E[Y (0) |T = 0, X = x] (2)
where X = x is a vector of observable covariates that may affect both the decision to adopt mobile money and entrepreneurship, E[Y (1) |T = 1, X = x] is the entrepreneurship of mobile money units, and E[Y (0) |T = 0, X = x] is the expected entrepreneurship for the synthetic control units. Estimating the ATT by entropy balancing involves two steps.

The first is to compute weights for the control group (non-treated group). These weights may satisfy pre-specified balanced constraints involving sample moments of observable characteristics (X). Following [START_REF] Neuenkirch | The impact of us sanctions on poverty[END_REF], we choose balance constraints that impose equal covariates means between the treatment and control groups.

In doing so, we want to ensure that the control group, on average, has non-treatment units that are as similar as possible to the treated units. 3 The second uses the weights from the first step in a regression analysis where entrepreneurship is the dependent variable. In the second step, we control for the covariates employed in the first step. This is equivalent to including control variables in a randomized experiment and increases estimation efficiency. In addition, time-and country-specific effects are included in the second step to respectively account for time-specific effects such as the Global Financial

Crisis or pandemics and country-specific heterogeneity arising from, for instance, differences with regard to political, economic, institutional environments, or country-specific entrepreneurial culture.

Despite the various advantages of entropy balancing discussed above, we note that this approach may have some limitations. Indeed, entropy balancing may fail to control for the potential endogeneity biases resulting from unobserved time-varying factors that may affect both mobile money and entrepreneurship, and on the other hand, to successfully deal with the inertia of entrepreneurship. Consequently, to test the robustness of our conclusions, we complete the entropy balancing by alternative estimation methods such as Ordinary Least Squares (OLS), and two-step system-GMM dynamic panel estimator.

Data, and descriptive statistics 4.1 Data

To analyze the effect of mobile money on entrepreneurship, we use panel data covering 105 developing countries over the period 2006-2020. The study focuses on developing countries as the adoption of mobile money is specific to them. In other words, no developed country has adopted this policy to date. The choice of the sample and time period is primarily dictated by the availability of reliable data. Specifically, our sample begins (ends) in 2006 (2020) since this is the first (last) year of available data on entrepreneurship. Summary statistics and the list of countries used in the paper are available in the Appendix.

For our dependent variable, we follow previous studies on entrepreneurship [START_REF] Klapper | The impact of the financial crisis on new firm registration[END_REF][START_REF] Ayyagari | Who creates jobs in developing countries?[END_REF][START_REF] Boudreaux | Weathering the storm: How foreign aid and institutions affect entrepreneurship activity following natural disasters[END_REF][START_REF] Qin | Access to credit and entrepreneurship: Evidence from china[END_REF][START_REF] Tian | Do place-based policies promote local innovation and entrepreneurship[END_REF], by using data from the World Bank's Entrepreneurship Database (WBED). Specifically, we use the new business entry density which is defined as the number of newly registered firms per 1,000 working-age people (ages 15-64) per year. The WBED also provides information on total business density defined as the total number of registered businesses per 1,000 working-age persons (ages 15-64) and closed business density defined as the number of written-off businesses per 1,000 working-age persons (ages 15-64) that we use for robustness tests.

Our main variable of interest is mobile money. Following previous studies [START_REF] Munyegera | Mobile money, remittances, and household welfare: Panel evidence from rural uganda[END_REF][START_REF] Riley | Mobile money and risk sharing against village shocks[END_REF]Apeti, 2023a;[START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF], we measure mobile money as a dummy variable taking 1 when a country i at date t adopts mobile money and 0 otherwise, using GSMA's mobile money deployment tracker. 4 Regarding the control variable, we select the control group of units with no mobile money that is on average as similar as possible to the treatment group of mobile money units in terms of relevant pretreatment characteristics. Following previous studies, we include a set of control variables that prior literature identifies as relevant determinants of mobile money adoption. These variables include: real GDP per capita, mobile cellular, urban population growth, rule of law, investment freedom, education, and globalisation index.

We expect a negative correlation between real GDP per capita and mobile money 4. https://www.gsma.com/mobilemoneymetrics/#deployment-tracker

given that mobile money is considered to be a low cost solution for low-income countries compared to relatively high-income countries, which would have access to a variety of payment methods [START_REF] Jacolin | Informal sector and mobile financial services in emerging and developing countries: Does financial innovation matter?[END_REF]. We expect a positive sign for mobile cellular and urban population growth as the deployment of mobile money is fundamentally linked to the cell phone market's dynamism [START_REF] Jacolin | Informal sector and mobile financial services in emerging and developing countries: Does financial innovation matter?[END_REF]Apeti, 2023a;[START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF] and that mobile money transactions are mainly from urban to rural areas. We also expect a positive correlation between mobile money and the level of education as individuals with higher education are more likely to easily adapt to financial innovations, such as mobile money services, than less educated individuals [START_REF] Seng | The mobile money's poverty-reducing promise: Evidence from cambodia[END_REF][START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF]. As highly globalized countries may have access to international "best" practices, which can support the widespread adoption and increased efficiency of mobile money, we expect a positive correlation between mobile money and the globalization index. Finally, the rule of law and investment freedom are included to capture countries' institutional framework. Hence, we expect a positive sign for the rule of law and investment freedom as non-restrictive regulatory environments and the lack of investment barriers are important incentives for mobile money adoption [START_REF] Jacolin | Informal sector and mobile financial services in emerging and developing countries: Does financial innovation matter?[END_REF]. Finally, to contain the reverse causality we lag these variables by one period (see for instance, Neuenkirch and Neumeier, 2016; Apeti, 2023a; Apeti and Edoh, 2023 for similar exercise). 5 Finally, as part of the robustness checks, we add to these variables a large number of other potential determinants of mobile money and entrepreneurship. We provide a detailed description of all variables used, and their sources in Appendix. discussed above, show the importance of selecting an appropriate control group when estimating the treatment effect of mobile money in order to avoid spurious treatment effect estimates.

Descriptive statistics and covariate balance

In Table 2, we present in columns [1] and [2] the mean values for country-year observations after weighting between the treated and the synthetic control groups. Column [3] shows the difference in mean between the treated and the synthetic control groups.

A comparison of the average pre-treatment characteristics of the treatment group to those of the synthetic control group reveals the efficiency of entropy balancing as no statistically significant difference in the mean values remains. Consequently, entropy balancing allows us to construct a perfect control group that is closely similar to mobile money countries in terms of the mean values of the pre-treatment covariates.

To provide a first idea on the relationship between mobile money and entrepreneurship, we compute average entrepreneurship in mobile money and non-mobile money countries. 6 The results are presented in Table 3. A closer look at this table shows that when comparing the control group, i.e. the non-mobile money countries, to the treatment group before the introduction of mobile money, i.e. the pre-mobile money situation, we observe similar entrepreneurship dynamics. Indeed, the average number of new businesses created or entrepreneurship in the treated countries before the introduction of the treatment, i.e. mobile money countries before the introduction of mobile money, is 1.26% compared to 1.29% for the control group. The mean comparison test performed-to compare 1.26% and 1.29%-between these two groups reveals a p-value of 0.8159 highlighting that the control group countries and the pre-mobile money situation of the treated countries are similar i.e. entrepreneurship is similar in these two groups. Next, we compare the situation after the treatment introduction with the control group. The observations show that the adoption of mobile money improves the level of entrepreneurship in the treated countries (1.67% vs. 1.29% with a p-value of 0.0340).

Finally, we complete our analysis by comparing the level of entrepreneurship before and after the adoption of mobile money in the treated countries. The results highlight a rise in the level of entrepreneurship after the adoption of mobile money captured by a new business creation rate of 1.26% before the implementation of mobile money compared to 1.67% after, a difference of 0.4 percentage points. 7 These different observations, al-6. A similar approach is adopted by [START_REF] Neuenkirch | The impact of us sanctions on poverty[END_REF]. 7. This difference is statistically significant at 10% level (p-value: 0.0634).

though "purely" descriptive, provide a first picture of the relationship between mobile money and business creation/entrepreneurship.

Robustness checks

In this section, we conduct several robustness checks to verify the validity of our results.

Alternative specifications

We start this section by excluding the Global Financial Crisis (GFC) episodes and the Covid-19 crisis from our sample to isolate the potential impact of crises on entrepreneurship [START_REF] Klapper | The impact of the financial crisis on new firm registration[END_REF]. Results compiled in Table A1, (columns [1]-[2]) in Appendix show a similar result to our baseline conclusions.

Second, we test the robustness of our results to alternative measures of entrepreneurship. Although our main dependent variable is new business entry density we also consider total business density rate and closed business density rate as alternative measures of entrepreneurship by re-estimating our baseline model using the same covariate as in Table 4. These alternative variables are from the World Bank's Entrepreneurship Database. Results are provided in [3] and [4] Table A1 in Appendix. We find that mobile money increase the number of total business density. However, the coefficient of closed business density is negative and statistically significant which is quite normal. Thus, we could argue that changing the definition of our dependent variable produces conclusions consistent with those previously discussed.

Third, we make some adjustments regarding our treatment variable, mobile money.

We begin with the possible concern about a potential endogeneity problem that could bias our results. Indeed, mobile money adoption can lead to a change in the economic, political or institutional environment of countries that have adopted it. Consequently, the effect we capture might not be driven by mobile money adoption but by any change in the institutional, political, social, or economic conditions after its adoption. In addition, since no country has abandoned mobile money after its adoption, any feature that may determine the deployment of mobile money can potentially be a source of endogeneity.

To circumvent these problems, we construct a treatment variable defined over a window from one year before adoption to the year of adoption [START_REF] Neuenkirch | The impact of un and us economic sanctions on gdp growth[END_REF]Apeti, 2023a;[START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF]. Then, we re-estimate our baseline model with this new variable assuming that this time window will provide a more robust effect of mobile money on entrepreneurship as the institutional, political, social, and economic environments-which generally change very slowly-is likely to be more stable over a narrow time period. The result in column[4] of Table A2 in Appendix underlines findings consistent with our baseline results: mobile money increases entrepreneurship. Second, we change the definition of our treatment variable by removing mobile money services provided by banks and the first year of mobile money adoption (Apeti, 2023a;[START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF]. Finally, we exclude non-mobile money countries from our sample and keep only the treated group as mobile money countries may differ from non-mobile money countries in ways that go beyond the country and time fixed effects [START_REF] Neuenkirch | The impact of un and us economic sanctions on gdp growth[END_REF]. The results are compiled in Table A2, columns [1]-[3] in Appendix.

Altering the mobile money variable does not affect our previous finding: the estimated coefficients of mobile money remain positive, and statistically significant.

Fourth, we perform a placebo (falsification) test in two different ways. First, we define placebo or arbitrary dates for mobile money by randomly assigning an adoption date to the countries in our sample (Apeti, 2023a;[START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF] can impact new entrepreneurs in several ways. First, inflation can increase prices in the marketplace. Second, higher inflation will also lead to higher wages as with a higher cost of living, workers are more likely to demand higher wages to limit the erosion of their purchasing power. Also, higher inflation can also lead to higher borrowing costs and create a liquidity constraint for businesses by reducing accounting profits for leveraged firms [START_REF] Madsen | Inflation and investment[END_REF]. 8 Public expenditure allows the financing of basic public services (health, education), which are favorable to the development of entrepreneurship. Therefore, we control the effect of public expenditure by including current expenditure and public investment. Variables related to the regulatory environment such as tax payments, the number of procedures to register property, start-up procedures, and start-up costs for a new business are also included. Tax payments are the total number of taxes paid by businesses. The number of procedures to register property is the number of procedures required for businesses to secure rights to property. Start-up procedures are those required to start a business, including interactions to obtain necessary permits and licenses and to complete all inscriptions, verifications, and notifications to start operations. The start-up costs for a new business are measured as a percentage of the respective country's income per capita. These variables are included in the model to control for their potential influence on the entrepreneurial activity as the existence of administrative barriers reduces nascent entrepreneurship [START_REF] Dreher | Greasing the wheels? the impact of regulations and corruption on firm entry[END_REF][START_REF] Chambers | Regulations, institutional quality and entrepreneurship[END_REF][START_REF] Boudreaux | Weathering the storm: How foreign aid and institutions affect entrepreneurship activity following natural disasters[END_REF]Boudreaux et al., 2022a).

For example, [START_REF] Klapper | Entry regulation as a barrier to entrepreneurship[END_REF] show that the costs of entry measured in terms of 8. [START_REF] Gillman | Inflation, investment and growth: a money and banking approach[END_REF] also note the negative effect of inflation on investment and, by extension, on entrepreneurship. money outlay, reduce the fraction of new firms significantly. Fisman and Sarria-Allende ( 2004) also find that in countries with high levels of entry regulation, industries respond to growth opportunities through expanding existing firms rather than creating new firms. We also included climate-related variables such as disaster intensity, climate vulnerability, and resilience, to control the effect of climate shocks. Natural disasters can damage infrastructure, disrupt supply chains, and affect firm performance, thereby hindering entrepreneurial activity by increasing uncertainty and fear of failure [START_REF] Monllor | Natural disasters, entrepreneurship, and creation after destruction: A conceptual approach[END_REF][START_REF] Boudreaux | Natural disasters and entrepreneurship activity[END_REF]Boudreaux et al., 2022a[START_REF] Boudreaux | Weathering the storm: How foreign aid and institutions affect entrepreneurship activity following natural disasters[END_REF]. In addition, natural disasters can impede the return to normal operations and thus decrease productivity [START_REF] Grube | Embedded entrepreneurs and post-disaster community recovery[END_REF][START_REF] Boehm | Input linkages and the transmission of shocks: Firm-level evidence from the 2011 tōhoku earthquake[END_REF][START_REF] Boudreaux | Weathering the storm: How foreign aid and institutions affect entrepreneurship activity following natural disasters[END_REF]. However, natural disasters can also generate entrepreneurial opportunities as destruction generates market inefficiencies and reduce the market entry requirement by reducing the opportunity cost of capital if other business opportunities become unprofitable (Boudreaux et al., 2022a[START_REF] Boudreaux | Natural disasters and entrepreneurship activity[END_REF]. Like natural disasters, financial crises can also undermine entrepreneurial activity as shown by [START_REF] Klapper | The impact of the financial crisis on new firm registration[END_REF]. However, these variables may also drive significant adoption of mobile money since mobile money can protect households in times of crisis or disaster [START_REF] Riley | Mobile money and risk sharing against village shocks[END_REF].

As sound government policies or "institutions" can promote and support entrepreneurship in a country, we assume that countries with greater political stability are likely to have a higher degree of entrepreneurial activity. In addition, politically stable nations will have lower risk and transaction/contracting costs, and higher levels of government transparency, predictability, and accountability [START_REF] Dutta | Entrepreneurship and political risk[END_REF], which may favor the development of entrepreneurship. Financial development can significantly affect entrepreneurship. Indeed, better credit availability might push some self-employed individuals into formal employment and others into formal entrepreneurial activities as shown by [START_REF] Boustanifar | Finance and employment: Evidence from us banking reforms[END_REF] and [START_REF] Qin | Access to credit and entrepreneurship: Evidence from china[END_REF]. Financial development can also impact mobile money adoption. Indeed, countries with high financial development would not be interested in adopting mobile money as they have a multitude of formal financial services such as banks. On the other hand, financial development may also be positively correlated to mobile money adoption as less restrictive regulatory environments and investment barriers are important incentives for mobile money adoption [START_REF] Jacolin | Informal sector and mobile financial services in emerging and developing countries: Does financial innovation matter?[END_REF]. We also control for self-employment, as [START_REF] Faggio | Self-employment and entrepreneurship in urban and rural labour markets[END_REF] show that a higher incidence of self-employment positively and strongly correlates with business creation and innovation. Next, we include GDP growth. The effect of growth on entrepreneurship is unclear. Indeed, while [START_REF] Ovaska | Entrepreneurship in post-socialist economies[END_REF] find no significant impact on the number of new enterprises per 1000 inhabitants, [START_REF] Parker | Explaining international variations in selfemployment: Evidence from a panel of oecd countries[END_REF] for their part, show that growth may increase entrepreneurship. However, others authors such as [START_REF] Noorderhaven | The role of dissatisfaction and per capita income in explaining self-employment across 15 european countries[END_REF], [START_REF] Wennekers | Uncertainty avoidance and the rate of business ownership across 21 oecd countries, 1976-2004[END_REF], [START_REF] Bjørnskov | Economic freedom and entrepreneurial activity: Some cross-country evidence[END_REF], claim that economic growth reduces entrepreneurial activity. Finally, external financing such as aid and remittances can also enhance entrepreneurial activity as they contribute to technology transfers, facilitates building infrastructure, and promotes productive capacities. The results are reported in Table A3, column [1]- [19] in Appendix and support the result of our baseline findings. We find that all the estimated effects are positive, and statistically significant with a magnitude comparable to the baseline one, providing evidence that our results are robust to potential omitted covariates.

Finally, we control for country-Specific time trends. Indeed, controlling for countryspecific linear time trends allows us to remove distinctive trends in the entrepreneurial activity in individual countries that might otherwise bias our estimates if they accidentally coincided with other mobile money-related changes [START_REF] Saka | Epidemic exposure, financial technology, and the digital divide[END_REF]. Results compiled in column [20] of Table A3 (Appendix) show findings in line with our baseline conclusions.

Alternative estimation methods

To ensure that our findings are independent of the chosen estimator, we further compute the effects of mobile money on entrepreneurship using panel fixed effect and system GMM methods. The results of these exercises are reported in Appendix.

Table A4 presents the results of the estimates based on the Blundell and Bond, 1998 two-step system-GMM dynamic panel estimator controlling for the baseline entropy balancing covariates. This method allows us to include a lag of the dependent variable to account for entrepreneurial dynamism and to address the lack of valid external instruments for estimating the causal effect of mobile money on entrepreneurship while controlling for the Nickell bias that arises when estimating a dynamic panel with fixed effects. We find that the GMM regression provides results that are qualitatively consistent with the entropy balancing's finding. The estimated effect of mobile money is positive and statistically significant at the 10 percent level. Finally, we note that entrepreneurial activity is fairly persistent as the lagged entrepreneurship is positive and statistically significant with a coefficient of 0.92.

We conclude this section by panel regression controlling for the baseline entropy balancing covariates, and country and year fixed effects. The results are presented in column [1] of Table A5 and the effect of mobile money remains positive and statistically significant. We test the robustness of the panel regressions by augmenting the baseline specification one at a time and simultaneously with the same additional control variables used in the robustness section of the entropy balancing approach. The results compiled in columns [2]-[20] of Table A5 show a consistent result to our baseline results.

Heterogeneity

In this section, we performed some heterogeneity tests by analyzing whether the positive effect of mobile money on entrepreneurship is influenced by the intensity of mobile money usage and by some structural characteristics describing countries' political and economic environment. To ease interpretation, we report all the results in Figure 1, 2, and 3.

Intensity of mobile money usage

First, we hypothesize that, the effect of mobile money on entrepreneurship may depend on the intensity of mobile money usage or adoption. Indeed, one of the main constraints of using dummy variables in a cross-country study is that it fails to capture the depth of mobile money use [START_REF] Ogrokhina | The role of inflation targeting in international debt denomination in developing countries[END_REF]Apeti, 2023a;[START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF]. For that purpose, we interact our binary mobile money indicator with four variables: 9 the number of active mobile money accounts per 1,000 adults, the value of mobile money transactions in percentage of GDP, the number of mobile money transactions per 1,000 adults, and the average number of transaction per active mobile money accounts. Figure 1 graphically illustrates the result of the marginal effect of mobile money relative to those variables that take into account the intensity of mobile money use. We observe that the effect of mobile money on entrepreneurship increases with the 9. The interaction approach is also used by [START_REF] Ogrokhina | The role of inflation targeting in international debt denomination in developing countries[END_REF] to test the intensity of policy adoption. number of active mobile money accounts per adult, the value of mobile money transactions, the number of mobile money transactions per adults, and the average number of transaction per active mobile money accounts. These results thus provide support for our hypothesis that the effect of mobile money may depend on the intensity of the use of mobile money.

Structural factors

In this subsection, we analyze whether the positive effect of mobile money may depend on some structural characteristics that may affect the efficiency of mobile money.

First, we analyze the sensitivity of our results to the political and institutional environment of the treated countries. Indeed, it can be argued that mobile money can be more efficient in a political environment characterized by strong democratic institutions, high-quality of regulation, and less corruption, since good institutions are likely to promote reform efficiency.To test this, we interact the binary mobile money indicators with a variable depicting the quality of the political/institutional environment. The first three graphs of Figure 2 illustrate the marginal effects of mobile money on entrepreneurship relative to democracy, quality of regulation, and the level of corruption.

Indeed, the figure shows that the effect of mobile money increases when the political environment of countries is favorable, i.e. when institutions are more democratic, when the quality of regulation is sound, and when the level of corruption is low. Next, we assume that the effect of mobile money would be less effective in an environment where individuals are more exposed to conflict. Indeed, [START_REF] Blumenstock | Violence and financial decisions: Evidence from mobile money in afghanistan[END_REF] provides evidence that violence affects how people make financial decisions. The authors show that individuals who are exposed to violence are less likely to adopt and use mobile money, a new financial technology, and are more likely to retain cash on hand. We test this hypothesis by interacting our mobile money indicator with a conflict intensity variable.

The last graph of the Figure 2 shows that the effect of mobile money on entrepreneurship decreases with the intensity of the conflict and becomes non-statistically significant around a score of 7, thus supporting our assumption.

Second, we test if the effect of mobile money depends on some characteristics such as education, internet usage, and (formal) financial institutions. First, individuals with higher levels of education are likely to adapt more easily to financial innovations, such as mobile money services, than those with less education [START_REF] Seng | The mobile money's poverty-reducing promise: Evidence from cambodia[END_REF][START_REF] Apeti | Tax revenue and mobile money in developing countries[END_REF]. Accordingly, the effect of mobile money would be more efficient with higher levels of education. Second, countries with high internet access are more likely to have access to formal financial services such as banks, thus making the adoption of digital financial services like mobile money less attractive [START_REF] Owusu-Agyei | Internet adoption and financial development in sub-saharan africa[END_REF]. Moreover, countries with high internet access may already have a high level of entrepreneurship [START_REF] Hjort | The arrival of fast internet and employment in africa[END_REF][START_REF] Luo | How does broadband infrastructure promote entrepreneurship in china: Evidence from a quasi-natural experiment[END_REF], and therefore the marginal effect of mobile money would be less in such conditions. Taken together, we assume that the effect of mobile money would be less efficient in countries with high internet. Third, the effect of mobile money would be less efficient in high financial development conditions as countries with high financial development already have access to a multitude of formal financial services thus the adoption of mobile money in these countries would be less attractive. The last three graphs in Figure 3 illustrate the results. We find that as the level of financial development and internet adoption increases, the marginal effect of mobile money on entrepreneurship decreases. However, we find that the effect of mobile money is greater when the level of education is high, thus corroborating our above hypotheses. Entrepreneurship is identified as a driver of development, growth, innovation, and welfare. Given that developing countries-which face crucial challenges such as low growth, low innovation, high poverty, and high unemployment-entrepreneurial activities are "very" weak compared to developed countries, looking for instruments to foster entrepreneurship seems necessary to help these countries boost their development/growth process. Consequently, mobile money-a "recent" financial innovationcould be a valuable tool for these countries to promote business creation/entrepreneurship.

In sum, mobile money could offer economic growth and prosperity benefits for developing countries by promoting entrepreneurship. Yavuz, R. I. and Bahadir, B. (2021). Remittances, ethnic diversity, and entrepreneurship in developing countries. Small Business Economics, pages 1-22.

  . of transaction per active mobile money accounts Dashed lines give 90% confidence interval.

Figure 1 -

 1 Figure 1 -Entrepreneurship and mobile money: intensity of mobile money

Figure 3 -

 3 Figure 3 -Entrepreneurship and mobile money: structural factors

Table 1 (

 1

columns [1]-[2]

) shows the sample means of all matching covariates before weighting for country-year observations for the treatment group (with mobile money) and the control group (without mobile money). Column [3] reports the differences in means between both groups and their statistical significance. The findings reveal that mobile money countries are characterized by ilow real GDP per capita, iihigh mobile cellular, iiihigh rule of law, ivhigh urban population growth, vhigh investment freedom, vihigh education, and viihigh globalisation. These descriptive statistics, which are consistent with the expected relationship between mobile money and the covariates 5. Robustness tests conducted and not reported in the paper show similar results without lagging these variables.

Table 1 -

 1 Covariate balance before weighting.

		[1]	[2]	[3]=[2]-[1]
		Mobile money No mobile money Difference
	Lag GDP per capita (Log)	7.65	7.76	0.11*
	Lag mobile cellular	91.63	62.48	-29.15***
	Rule of law	-0.48	-0.59	-0.11***
	Lag urban population growth	3.00	2.74	-0.26*
	Investment freedom	52.45	45.60	-6.85***
	Lag education	38.95	38.58	-0.37
	Lag globalisation	54.42	51.76	-2.66***
	Observations	531	282

*** p<0.01, ** p<0.05, * p<0.1.

Table 2 -

 2 Covariate balance after weighting.

		[1]	[2]	[3]=[2]-[1]
		Mobile money No mobile money Difference
	Lag GDP per capita (Log)	7.65	7.65	0
	Lag mobile cellular	91.63	91.63	0
	Rule of law	-0.48	-0.48	0
	Lag urban population growth	3	3	0
	Investment freedom	52.45	52.45	0
	Lag education	38.95	38.95	0
	Lag globalisation	54.42	54.42	0
	Observations	531	282
	Total of weights	531	531

  Table4report the baseline results. With the synthetic controls of Table2, we estimate the effect of mobile money on entrepreneurship (ATT) using the weighted least squares method. In column [1], we only show the association between our key variable of interest (mobile money) and entrepreneurship while controlling with country and yearfixed effects. The estimated coefficient is positive and statistically significant at the 5%

	Table 4 -Entrepreneurship and mobile money
		[1]	[2]
	Entrepreneurship Entrepreneurship
	Mobile money	0.243**	0.351***
		(0.1113)	(0.1215)
	Covariates	No	Yes
	Year fixed effect	Yes	Yes
	Country fixed effect	Yes	Yes
	Observations	622	622
	Unreported constant included. Robust standard errors in brackets. *** p<0.01, ** p<0.05, * p<0.1.
	bile money, its entrepreneurial activity increases by 0.35 percentage points compared
	to non-mobile money countries. This result is economically meaningful as it represents
	18.42 percent of the average of entrepreneurship in our sample. Compared to the con-
	trol group, this coefficient represents 26.52 percent of their non-conditional average of
	entrepreneurship, i.e. 1.32 percent.

level. In column

[2]

, we present our baseline specification that contains all matching covariates used in the first step to construct the synthetic group as well as country and year fixed effects. It is important to note that including the matching covariates in the second stage of entropy balancing increases the quality of the estimation (as in a randomized experiment) while controlling for country and year-fixed effects eliminates any country-or year-specific effects.

Based on our complete specification that includes both fixed effects and matching covariates (column [2]), we observe that the effect of mobile money on entrepreneurship is positive and statistically significant at 1%. The magnitude of the coefficient is 0.35 percentage points

(column [2]

). In other words, when a country adopts or uses mo-

Table A2 in

 A2 . Second, we define a placebo date for mobile money by computing a mobile money variable that incorrectly assigns the mobile money start date before the actual start date, i.e. one year before the actual mobile money date of each mobile money country in our sample. The intuition behind these tests is that, if our baseline findings are due to mobile money adoption, Appendix. The non-statistically significant results of the placebo variables suggest that our results are robust, especially with respect to measurement error.Five, we check if our result is sensitive to the inclusion of additional covariates that may affect both mobile money adoption and entrepreneurial activity. For this purpose, we include one at time and then simultaneously a set of additional controls to our base-

	line model. These variables include: inflation, public investment, current expenditure,
	tax payments, procedures to register property, start-up procedures to register a business,
	cost of business start-up procedures, disaster intensity (in log), climate vulnerability, re-
	silience, political stability, financial development, self-employment, financial crisis, GDP
	growth, labor force, Official Development Assistance (ODA), and remittances. Inflation

using placebo dates should produce a non-statistically significant estimate, otherwise this would indicate a misspecification of the entropy balancing estimate. Results based on entropy balancing using these placebo dates are reported in the last columns [5]-[6] of

Table A3 -

 A3 Entrepreneurship and mobile money: additional control Unreported constant included. Robust standard errors in brackets. *** p<0.01, ** p<0.05, * p<0.1.

		[1]	[2]	[3]	[4]	[5]	[6]	[7]	[8]	[9]	[10]
		Inflation	Public investment	Current expenditure Tax payments	Procedures to	Procedures to	Costs of starting Disaster intensity Climate vulnerability Resilience
						register property start a business	a business
	Mobile money	0.360***	0.351***	0.342***	0.342***	0.360***	0.392***	0.390***	0.350***	0.345***	0.323***
		(0.1250)	(0.1117)	(0.1178)	(0.1219)	(0.1211)	(0.1316)	(0.1322)	(0.1233)	(0.1212)	(0.1172)
	Covariates	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Year fixed effects	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Country fixed effects	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Observations	585	610	597	582	580	542	542	622	622	622
		[11]	[12]	[13]	[14]	[15]	[16]	[17]	[18]	[19]	[20]
		Political stability Financial development	Self employment	Financial crisis	Growth	Labor force	ODA	Remittances	All covariates	Time trend
	Mobile money	0.351***	0.380***	0.355***	0.353***	0.377***	0.349***	0.361***	0.351***	0.287***	0.280**
		(0.1213)	(0.1209)	(0.1225)	(0.1215)	(0.1277)	(0.1222)	(0.1163)	(0.1223)	(0.1094)	(0.1145)
	Covariates	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Year fixed effects	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Country fixed effects	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Observations	622	574	622	622	583	622	610	604	479	622

Table A4 -

 A4 Entrepreneurship and mobile money: GMM-system

		[1]
		Entrepreneurship
	Lag entrepreneurship	0.923***
		(0.0649)
	Mobile money	0.221*
		(0.1302)
	Log GDP per capita	0.239
		(0.2661)
	Mobile cellular	0.003
		(0.0029)
	Rule of law	0.299
		(0.3995)
	Urban population growth	-0.033
		(0.0486)
	Investment freedom	0.001
		(0.0060)
	Education	0.014
		(0.0237)
	Globalisation	-0.013
		(0.0168)
	Fixed effects	Yes
	Hansen test p-value	0.712
	Numb. of instruments/numb. of countries	45/60
	Observations	599

Unreported constant included. Robust standard errors in brackets. *** p<0.01, ** p<0.05, * p<0.1.

Table A5 -

 A5 Entrepreneurship and mobile money: Panel fixed effects

	Entrepreneurship	[1]	[2]	[3]	[4]	[5]	[6]	[7]	[8]	[9]	[10]	[11]	[12]	[13]	[14]	[15]	[16]	[17]	[18]	[19]	[20]
	Mobile money	0.154*	0.172*	0.187**	0.171*	0.170*	0.179*	0.212*	0.210*	0.157*	0.156*	0.155*	0.154*	0.168*	0.158*	0.154*	0.165*	0.157* 0.188** 0.156*	0.212*
		(0.0918) (0.0974) (0.0939) (0.0966) (0.0963) (0.0947) (0.1088) (0.1086) (0.0927) (0.0915) (0.0895) (0.0919) (0.0992) (0.0930) (0.0918) (0.0984) (0.0920) (0.0950) (0.0947) (0.1194)
	Inflation		-0.013																		-0.025**
			(0.0092)																		(0.0104)
	Public investment			0.524***																	0.553***
				(0.1847)																	(0.2055)
	Current expenditure				-0.713																0.487
					(0.6440)																(0.7743)
	Tax payments					0.001															0.007*
						(0.0036)															(0.0039)
	Procedures to register property						-0.052														0.130
							(0.0986)														(0.1069)
	Procedures to start a business							0.026													-0.018
								(0.0286)													(0.0312)
	Costs of starting a business								-0.000												-0.001*
									(0.0002)												(0.0004)
	Log disaster intensity									-0.002											-0.002
										(0.0077)											(0.0091)
	Vulnerability										3.649										6.964
											(6.8738)										(7.5578)
	Resilience											5.542***									19.625***
												(1.0316)									(4.0390)
	Political Stability												0.006								-0.079
													(0.0739)								(0.1028)
	Financial development													-0.670							-2.195
														(3.0579)							(3.6573)
	Self-employed														-0.008						-0.006
															(0.0134)						(0.0145)
	Financial crisis															0.006					-0.016
																(0.1314)					(0.2525)
	Growth																-0.205				-2.615
																	(0.8834)				(1.9832)
	Labor force																	-0.542			0.058
																		(0.7242)			(0.9265)
	ODA																		-0.022		-0.051
																			(0.0163)		(0.0322)
	Remittances																			-0.014	-0.008
																				(0.0109) (0.0142)
	Covariates	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Year fixed effects	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Country fixed effects	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
	Observations	622	585	610	597	582	580	542	542	622	622	622	622	574	622	622	583	622	610	604	453

Unreported constant included. Robust standard errors in brackets. *** p<0.01, ** p<0.05, * p<0.1.

Table B2 -

 B2 Mobile money country

	Albania	Indonesia	Niger
	Argentina	India	Nigeria
	Armenia	Iran, Islamic Rep. Nepal
	Benin	Jamaica	Peru
	Burkina Faso	Jordan	Paraguay
	Bangladesh	Kazakhstan	Qatar
	Bolivia	Kenya	Rwanda
	Brazil	Kyrgyz Republic	Senegal
	Botswana	Cambodia	Sierra Leone
	Central African Republic Sri Lanka	El Salvador
	Colombia	Lesotho	Chad
	Dominican Republic	Morocco	Togo
	Egypt, Arab Rep.	Madagascar	Thailand
	Fiji	Mexico	Tajikistan
	Gabon	Mali	Tunisia
	Georgia	Myanmar	Turkey
	Ghana	Mongolia	Tanzania
	Guinea	Mozambique	Uganda
	Guatemala	Mauritania	South Africa
	Guyana	Malawi	Zambia
	Haiti	Namibia	Zimbabwe

[START_REF] Hainmueller | Entropy balancing for causal effects: A multivariate reweighting method to produce balanced samples in observational studies[END_REF], using Monte Carlo simulations as well as empirical applications, demonstrates that entropy balancing outperforms other matching techniques, such as propensity score matching and genetic matching, in terms of estimation bias and mean square error.

This procedure ensures that once the weights are generated, mobile money and non-mobile money countries exhibit similar trends in their outcome variable over the pre-treatment period (see[START_REF] Ogrokhina | The effect of inflation targeting and financial openness on currency composition of sovereign international debt[END_REF].

Conflict Intensity

Dashed lines give 90% confidence interval. Internet: individuals using the internet (% of population). Source: WDI


Dana Codreanu
email: codreanu@irit.fr

André Péninou

André Peninou
email: peninou@irit.fr

Florence Sedes
email: sedes@irit.fr

Modélisation de trajectoires cible/caméra : requêtes spatio-temporelles dans le cadre de la videosurveillance

Introduction

Le nombre de caméras de vidéosurveillance installées dans le monde augmente chaque jour. En France, le système de la RATP déployé sur Paris comprend 9000 caméras fixes et 19000 mobiles. Lors de faits particuliers (e.g., agressions, vols), les opérateurs de vidéo surveillance se basent sur les indications spatiales et temporelles de la victime et sur leur connaissance de la localisation des caméras pour sélectionner les contenus intéressants pour l'enquête. Deux grands problèmes peuvent alors survenir : (1) le temps de réponse est long (jusqu'à plusieurs jours de traitement) et (2) un risque important de perte de résultats à cause d'une mauvaise connaissance du terrain (appel à des opérateurs extérieurs). Le but de notre recherche est de définir des outils d'assistance aux opérateurs qui puissent, à partir d'une trajectoire donnée, sélectionner de façon automatique les caméras pertinentes par rapport à la requête.

Contexte de la vidéosurveillance et problématique

Dans un système de vidéosurveillance le contenu est acquis par des caméras fixes et mobiles installées dans des contextes différents (à l'extérieur ou à l'intérieur des bus, des stations de métro, dans les rues, etc.).

Lorsqu'une victime d'une agression porte plainte, on lui demande de décrire les éléments qui pourront aider à trouver les segments vidéos pertinents. Les éléments d'une telle description sont : la Localisation (e.g., Paris), la Date et l'Heure (e.g., 10 octobre 2013 entre 10h et 11h), l'Événement recherché (e.g., vol de sac), et la Trajectoire de la victime avant et après l'événement (e.g., Rue de Rivoli, de la sortie du musée du Louvre jusqu'à l'entrée de la station de métro Chatelet). Les opérateurs, en se basant sur les aspects spatiaux et temporels de la requête et sur leur propre connaissance de la localisation des caméras, sélectionnent les caméras qui auront référencé r des informations concernant la trajectoire de la personne pour ensuite analyser les enregistrements vidéo.

Le but et de définir un(des) nouveau(x) opérateur(s) prennant comme entrée une trajectoire cible définie comme un ensemble d'unités u k (segments cartographiques de la rue de Rivoli) et un intervalle temporaire et qui calcule la liste d'extraits vidéo pertinents pour la requête :

hasSeen : u 1 , u 2 , ..., u n , [t 1 , t 2 ] =>    c 1 : t 1 start -> t 1 end , u k (1 <= k <= n) ... c m : t m start -> t m end , u k (1 <= k <= n)
ce qui équivaut à dire que la caméra c i a potentiellement "filmé" le segment u k de la trajectoire de la requête entre

t i start et t i end , avec t 1 <=t i start <=t 2 et t 1 <=t i end <=t 2 .
3 Modélisation des prises de vue de caméras et des trajectoires de déplacement

Afin de pouvoir effectuer les requêtes nécessaires pour assister les opérateurs, nous proposons un modèle intégrant d'une part les réseaux routier et de transport et d'autre part : (1) les caméras fixes et leur position sur le réseau routier, (2) les changements des champs de vue des caméras fixes dans le temps et (3) les caméras mobiles et leur attachement à un objet mobile.

Dans notre approche nous proposons un modèle à quatre couches indépendantes : (1) Réseau routier, (2) Réseau de transport, (3) Objets, (4) Caméras.

La couche Réseau Routier est basée sur l'approche de modélisation sous forme de graphe consacrée dans la littérature (Liu et al., 2012). Le réseau routier est un graphe G= (N, A), dans lequel les noeuds sont les croisements des rues et les arcs sont les rues. Le Réseau de Transport est aussi modélisé sous forme de graphe. A ce niveau, les noeuds sont constitués par des stations de bus qui sont situées sur des segments de rues. Des séquences ordonnées de noeuds de transport forment des lignes (e.g., des lignes de bus). La couche Objets modélise les positions des objets fixes et mobiles par rapport aux couches sous-jacentes. Chaque Objet Mobile transmet périodiquement sa position en fonction de différentes stratégies (e.g., chaque fois que l'objet change de segment) que nous ne traitons pas dans ce papier. Nous supposons que nous avons au moins une mise à jour de la position par segment de rue. L'ensemble de points avec les timestamps associés forment leur trajectoire (Gutting et al., 2006).

Au-dessus de toutes ces couches, nous modélisons les Caméras de Vidéosurveillance. Un schéma simplifié de cette couche est illustré dans la Figure 1. Cette couche est composée des caméras fixes et mobiles. Les caméras fixes ont une position 2D fixée au moment de l'installation. Les caméras mobiles sont associées à un objet mobile (e.g., bus) et leur trajectoire est la même que celle de l'objet.

La nouvelle génération de caméras a des capteurs GPS incorporés et même des boussoles. Les technologies développées autour de ces caméras rendent possible l'extraction automatique des caractéristiques de prise de vue, par exemple : l'orientation, le zoom, la distance focale, etc. En se basant sur ces éléments, il est possible de modéliser le champ de vue et de tracer ces modifications dans le temps (Arslan Ay et al., 2010).

Conclusion et perspectives

Afin d'aider les opérateurs, nous proposons une approche de modélisation spatiale et temporelle des caméras de vidéosurveillance dans le cadre d'un réseau routier, modélisation basée sur des informations spatiales et des trajectoires des objets mobiles. A partir de ce modèle on peut sélectionner la liste des caméras qui qui ont potentiellement "filmé" la trajectoire d'une personne. Nous envisageons d'étendre le modèle pour prendre en compte les réseau de caméras à l'intérieur de stations de métro ou de train.Un autre aspect concerne l'ordonnancement des résultats en fonction de la distance des caméras par rapport aux segments de la requête.

Références

Arslan Ay, S., R. Zimmermann, et K. SeonHo (2010). Effective map-matching on the most simplified road network. Multimedia Systems 16, 105-125.

Gutting, R., V. Almeida, et Z. Ding (2006). Modeling and querying moving objects in networks. VLDB Journal 15, 165-190. Liu, K., Y. Li, F. He, J. Xu, et Z. Ding (2012). Effective map-matching on the most simplified road network. In Proceedings of the 20th International Conference on Advances in Geographic Information Systems, 609-612.

Summary

Our work concerns the assistance to the operators of videosurveillance in the search for partiular videos (e.g., attack of persons, lost object) by the automatic identification of a set of cameras likely to have filmed a required scene. This paper presents a multi-layer modeling (cameras fixed and mobile, road network, public transport network) whose characteristic consists in rather including calculation data of the geometry of the cameras viewpoints on the network layer than to store this geometry as such.

FIG. 1 -

 1 FIG. 1 -Modélisation UML de la couche Caméras

  La requête sélectionne les caméras dont la géométrie du champ de vue (calculée à partir des caractéristiques stockées dans la table FOV et de la position de la caméra par la fonction geometry(F, C.POSITION)) intersecte la géométrie du segment de rue donné (SDO_RELATE est un opérateur spatial qui vérifie si deux géométries ont n'importe quel type d'intersection (paramètre anyinteract)) dans l'intervalle recherché. Q2 : Sélectionner les caméras mobiles dont la trajectoire a intersecté un segment donné : SELECT MC.IDMC FROM < EDGES E, MO, MC> WHERE { SDO_RELATE(E.SEGMENT, MO.POSITION), 'mask=anyinteract')='TRUE' AND t 1 <= MO.TIMESTAMP AND MO.TIMESTAMP<= t 2 AND MO.IDOBJ=MC.IDOBJ AND E.ID=idSegmentRequete } La deuxième requête sélectionne les caméras mobiles associées aux objets mobiles dont la trajectoire a intersecté le segment donné entre t 1 et t 2 .

	IDFC FROM < EDGES E, FC C, FOV F>
	WHERE {
	SDO_RELATE(E.SEGMENT, geometry(F, C.POSITION),'mask=anyinteract')='TRUE'
	AND C.IDFOV=F.IDFOV AND E.ID=idSegmentRequete
	AND ((F.TIMESTAMP<= t 2 AND F.TIMESTAMP >= t 1 ) OR
	(F.TIMESTAMP<t 1 AND NOT EXISTS (SELECT F1.TIMESTAMP FROM FOV F1
	WHERE F1.TIMESTAMP>F.TIMESTAMP AND F1.TIMESTAMP<=t 1
	AND F1.IDFOV=F.IDFOV))) }
	1. http ://iapg.jade-hs.de/personen/brinkhoff/generator/


Jiaxin Xu

R Ô M E Bobin

Anne De

Vismes Ott

Christophe Bobin

Paul Malfrait

Analysis of gamma-ray spectra with spectral unmixing -Part I: Determination of the characteristic limits (decision threshold and statistical uncertainty) for measurements of environmental aerosol filters

Keywords: gamma-ray spectrometry, characteristic limits, full spectrum analysis, spectral unmixing

Poisson-statistics based spectral unmixing has previously been shown to be an efficient analysis tool for the activity estimation of radionuclides from gammaray spectroscopy measurements. In this paper, we present the quantification of characteristic limits (decision threshold, detection limit and limits of the coverage interval) for the metrological use of such spectral unmixing algorithms.

The proposed approaches are evaluated and validated with simulated spectra of HPGe and NaI measurements by comparing the results to characteristic values calculated from Monte Carlo simulations.

. Introduction

The gamma-ray spectrum analysis problem has been tackled with spectral unmixing in [START_REF] Xu | Sparse spectral unmixing for activity estimation in γ-ray spectrometry applied to environmental measurements[END_REF], [START_REF] Paradis | Spectral unmixing applied to fast identification of γ-emitting radionuclides using NaI(Tl) detectors[END_REF]. These studies show that such new algorithms based on the full spectrum analysis and the Poisson statistics underlying the gamma-ray detection process provides a more sensitive analysis of radionuclides than standard peak-based algorithms. In this work, we focus on the metrological use of the spectral unmixing algorithms, which further ne-cessitates quantifying the characteristic limits associated with the measurement result.

The characteristic limits generally consist of the decision threshold, the detection limit and limits of the coverage interval, are essential for decision making purposes of the measurement results. While the calculation of these limits have been well studied in peak-based analysis, new calculation approaches are needed for the spectral unmixing algorithms due to their different estimation procedures. More, precisely, contrast to peak-based algorithms, the spectral unmixing is an analysis tool that identifies and quantifies radionuclides from the full energy spectrum (i.e., peaks and their associated continua) of a gamma-ray measurement. The problem can be generally written in the matrix formulation as follows :

x ∼ Poisson (Φa + b) (1)
With the aim of decomposing a measured spectrum x ∈ R M ×1 (composed of M channels) into a linear combination of radionuclides' spectral signatures Φ ∈ R M ×N (containing N radionuclides' spectral signatures) and a background spectrum b ∈ R M ×1 , the spectral unmixing estimates radionuclides' mixing weights a ∈ R N ×1 that are proportional to radionuclides' activities. Therefore, we focus on the calculation of characteristic limits of the mixing weights estimated with Poisson-statistics based spectral unmixing algorithms.

The paper is organized as follows: Section 2 presents the concept of characteristic limits for radioactivity measurements. In Section 3, we describe the data used in this work and present how the characteristic limits can be calculated from Monte Carlo simulations. Section 4.2 explores the calculation of the decision threshold. Next, we discuss the assessment of the coverage intervals in Section 5. Section 6 provides conclusions of this work.

Characteristic limits in radioactivity measurements

Refer to ISO 11929, the notations below are used in the description of the characteristic limits:

• Y : Measurand, the quantity of interest.

• y: Determined value of the measurand Y (i.e., the estimate of Y ).

• ỹ: True value of the measurand.

We first present the classical statistical hypothesis framework used for decision making in gamma-ray spectrum analysis. It is commonplace to consider testing hypotheses with the two alternatives (associated with type I error and type II error described in Table 1):

• H 0 : the null hypothesis, where a given radionuclide is not "active". The standardization document ISO 11929 defines the determination of the characteristic limits, namely the decision threshold, the detection limit, and limits of the coverage interval for ionizing radiation measurements. It provides a framework for the computation of the characteristic limits. Referring to [START_REF] Weise | Determination of the detection limit and decision threshold for ionizingradiation measurements: fundamentals and particular applications[END_REF], [START_REF] Michel | Measuring, estimating, and deciding under uncertainty[END_REF], the definition and interpretation of the characteristic limits for some estimate y of a measurand Y are as follows:

• Decision threshold (DT) allows a decision to be made on whether or not the physical effect quantified by the measurand is present.

The determination of DT is related to the Type I error described in Table 1. When the quantity y exceeds the critical value (DT), the null hypothesis H 0 should be rejected with respect to a given false positive rate (FPR).

It can be described with:

α = P (y ≥ DT |ỹ = 0) (2)
where ỹ is the true value of the measurand and α is the desired critical FPR.

• Detection limit (DL) indicates the smallest true quantity value of the measurand, which can still be detected with the applied measurement procedure.

The determination of DL is related to the Type II error described in Table 1. It is selected with respect to a desired false negative rate (FNR) based on the decision threshold level.

More precisely, the detection limit (DL) is the smallest value that provides a desired Type II error probability β:

β = P (y ≤ DT |ỹ = DL) (3)
where the DT is given and ỹ is the true value of the measurand.

• The coverage interval for the estimate y is an interval that has a probability γ of containing the true value ỹ.

Data description and the characteristic limits assessment with

Monte Carlo simulations

In this work, the investigations are based on the following gamma-ray spectra simulations:

• Simulated aerosol filter measurement of an HPGe detector cylindrical (60 %relative efficiency) [START_REF] Xu | Sparse spectral unmixing for activity estimation in γ-ray spectrometry applied to environmental measurements[END_REF], which corresponds to the energy response of gamma-emitting radionuclides from 20 keV to 1640 keV composed in 16384 channels. This mixing scenario consists of 10 radionuclides: In this context we focus on the assessment of characteristic limits for 4 radionuclides: 7 Be, 22 Na, 137 Cs, 212 Pb, since these radionuclides cover the whole energy range and different statistic regimes. The simulation model of 10 radionuclides and the contribution of these 4 radionuclides are displayed in Figure 1. A traditional approach to quantify the characteristic limits for some estimation method is to make use of Monte-Carlo simulations. In the following paragraphs, we present how the characteristic limits of the spectral unmixing method can be calculated from Monte Carlo simulations.

Decision threshold from Monte Carlo simulations. Monte Carlo simulations that mimic the mixture under the null hypothesis of a radionuclide allows quantifying the false positive rate of this radionuclide, thus the decision threshold. For each radionuclide, 1000 simulations are performed with this radionuclide set to zero and other radionuclides set to their actual levels. The spectral unmixing algorithm is subsequently applied to estimate radionuclides' mixing weights from these simulated spectra. The distribution of the estimated mixing weight of this radionuclide allows computing a decision threshold with respect to some false positive rate from the according percentile of the distribution.

Coverage interval from Monte Carlo simulations. In practice, and assuming that some estimate of the mixing weights have a limited estimation bias or error, a coverage interval with respect to a given probability γ and for individual radionuclides can be derived by performing Monte-Carlo simulations.

More precisely, we first perform 1000 Monte Carlo simulations that mimic the actual mixing scenario of radionuclides. Next, the spectral unmixing algorithm is applied to estimate mixing weights from these simulated spectra. Finally, the coverage intervals of radionuclides can be derived from the distribution of their estimated mixing weights.

In practice, Monte Carlo simulations are seldom used to analyze gammaray spectra in routine analysis procedures. The main drawback is their massive computational cost since Monte Carlo simulations are needed for each new spectrum to be analyzed. In the next sections, we focus on computationally cheaper and yet precise alternatives to derive the characteristic limits without resorting to Monte-Carlo simulations.

Quantifying the decision threshold

Decision threshold in peak-based analysis

In gamma-ray spectrum analysis, the decision threshold is usually derived from some statistical test based on the measured spectrum. This amounts to evaluating how much the estimated quantity associated with a radionuclide's activity departs from the background (i.e., other contributions composed in the measured spectrum) and is therefore statistically consistent or not with this background.

In the peak-based analysis, the activity is associated with the net counts. It is the total number of counts measured in a given ROI, which further corrected by the average number of counts of the background:

N n = N g -N 0 (4)
where N n is the net counts number associated to the activity, N g is the observed gross number of counts and N 0 is the number of background counts.

Recall the definition of DT in Section 2, the DT level of the measurand (i.e., net counts number) is derived from:

α = P(N n ≥ DT | Ñn = 0) (5)
where α and Ñn stands for the desired FPR and the true value of the net number of counts respectively. The estimated number of N g and N 0 , noted Ng and N0 respectively. In practice, the DT is derived from some statistical test of the quantity Ng -N0 under the hypothesis of Ñn = 0, which has:

• mean value equal to zero.

• variance according to 2 N0 , since both of N g and N 0 follow the Poisson statistic thus their mean value are equal to their variance, and

N g = N 0
under the hypothesis of Ñn = 0.

Decision threshold in spectral unmixing analysis

The DT determination in peak-based analysis considers that the background spectrum N 0 is well estimated and provides a mean value of the distribution under the null hypothesis, from which the DT can be derived based on a desired FPR. Now, we aim to investigate the DT in the spectral unmixing approach,

where the measurand associated with a radionuclide's activity is the number of counts in the full spectrum range. The DT can be derived with the same idea of statistical test based on a "background", but adapted to the full spectrum analysis.

Recall that the spectral unmixing decomposes a gamma-ray spectrum into individual spectra of radionuclides. To determine the decision threshold of a single radionuclide indexed by j in the unmixing model, we reformulate the true linear mixing model with this radionuclide and an equivalent background:

Φa + b → φ j a j + m (6)
where φ j a j represents the individual spectrum of the j th radionuclide, while the other radionuclides and the background spectrum b compose an equivalent background:

m = l =j φ l a l + b
In the spectral unmixing analysis, the activity of the j th radionuclide is associated to the mixing weight a j . Recall the definition in Section ??, the DT level of the measurand (i.e., a j ) is derived from:

α = P (a j ≥ DT |ã j = 0) (7)
Recall that, the measured spectrum x is composed of M channels, ∀i ∈ 130 [1, ..., M ], the observed counts in each channel of the spectrum follows a Poisson distribution with mean value:

λ i = [φ j a j ] i + m i .
The DT can be derived from a standard hypothesis testing procedure test under the null alternative of H 0 : ãj = 0, which leads to

λ i = m i for ∀i ∈ M .
This can be generally formulated with some statistical test T as follows:

α = P T ≥ T (λ)|∀i, λ i = m i (8)
For this purpose, we propose to make use of statistical test based on different assumptions as follows:

a. Test based on the sum of observed counts:. a simple statistical test to consider is based on the total number of counts, as measured by the sum of observed counts under the null hypothesis H 0 . Thanks to the statistical independence of each channel, this quantity should follow a Poisson distribution with mean value m (i.e., estimated equivalent background).

i x i ∼ Poisson i mi (9)
Therefore, the DT (noted a * j ) of the estimated activity for the j th radionuclide with a given false positive rate α, can be derived from the cumulative distribution function (CDF) of the following distribution:

α = P i∈C x i ≥ i∈C [φ j a * j ] i + i∈C m i ( 10
)
where C is some set of observed channels. The total number of counts from the full spectrum is a special case where C defines all the observed channels.

While it allows to account for the full information carried out by the spectrum, it however poorly distinguishes the radionuclide to be tested from the background.

We rather use the pre-specified channels in a region of interest, where the equivalent background is better distinguished from the j th radionuclide. (e.g, peak region of the radionuclide).

b. Test based on sum of weighted observed counts:. In order to better distinguish between the radionuclide to be tested and the equivalent background, we further investigate statistical test derived from the sum of weighted counts in different channels written as i w i m i with the following choice of w i :

• Let Ψ = φ j m , the least squares solution of the mixing vector of Ψ can be written as:

â ∈ argmin a 1 2 x -Ψa 2 (11)
for which the solution is â = Ψ † x, where Ψ † = (Ψ T Ψ) -1 Ψ T is the pseudo inverse matrix.

We make use of the the component of Ψ † related to φ j as the weights matrix, noted as w 1 = Ψ † φ . As graphically illustrated in Figure 3, it allows projecting onto the span of φ j parallelly to m.

Nevertheless, the resulting statistical test do not follow a Poisson distribution. Thankfully, since it is defined as a linear combination of a large number of observed channels, one can approximate the distribution to be Normal. The resulting statistical test with observed counts x and estimated equivalent background m will be carried out as follows:

i w i x i ∼ N i w i m i , w 2 i m i (12)
while in each channel, the mean value µ = w i m i and variance σ 2 = w 2 i m i are considered, since both the mean value and the variance of the model equal to m i because of the Poisson statistics. The DT of the estimated activity a * j can be derived from the CDF of Normal distribution:

α 2 = P i w i x i ≥ i w i [φ j a * j ] i + i w i m i (13)
• the weighted background statistical test is further studied with w 2 = Ψ † φ with:

Ψ † = Ψ T diag( 1 φ j a j + m )Ψ -1 Ψ T diag 1 φ j a j + m (14)

Evaluation of the decision threshold determination

For a comparison purpose, by fixing the false positive rate to α = 2.5%,

160
we evaluate the statistical tests proposed in Section 4.2 to assess the decision threshold for HPGe and NaI measurements described in Section 3, while the results are compared to those carried out with Monte Carlo simulations. The evaluations are carried out as follows:

• For each radionuclide, the accurate DT level quantified with respect to

• Decision threshold assessment with different statistical tests for each Monte Carlo simulation:

-the Poisson statistical test based on the sum of counts in peak region. This is used only for HPGe measurements since using the peak regions to analyze NaI measurements is not interesting due to the correlations of spectra, for which it is better to take into account the full spectrum information. Experiments on the described mixing scenario (see Figure 1) of the HPGe measurement considers the following peak regions: 7 Be at 477 keV, 22 Na at 1274 keV, 137 Cs at 661 keV and 212 Pb at 238 keV.

-the Gaussian statistical test based on two choices of weighted sum of counts, noted w 1 and w 2 respectively.

Results

For HPGe spectra, the different statistical tests are compared in Figure 4, 5, 6 and 7. Figure 8, 9, and 10, and 11 for NaI spectra respectively. The results report the distribution of:

• Poisson test based on region of interest (ROI) (green) of x.

• Gaussian test based on sum of weighted counts carried out by w 1 x (blue) and w 2 x (orange).

• For a comparison purpose, the accurate DT level calculated from Monte Carlo (i.e., 1α percentile of the distribution under the null hypothesis)

is displayed with a dotted line (red).

From these results, we can draw the following conclusions:

• Firstly, compared to the Gaussian statistical test based on the sum of weighted counts, the Poisson statistical test based on the sum of the counts in the ROI is less efficient to derive the DT. Since the peaks are not well distinguished from the continua.

• For HPGe measurement, for 22 Na, 137 Cs and 212 Pb, the Gaussian statistical test of weighted counts with w 2 derives similar DT levels comparing to the actual 1α percentile of the distribution (i.e., accurate DT level), which is better than the choice of w 1 . This is not valid for 7 Be due to the fact that 7 Be is predominant in the measured spectrum, while its equivalent background is poorly estimated. However, the determination of accurate DT level for low-level radionuclides is more important for the decision making purpose; in such case, the dominant spectral contribution such as 7 Be can provide a better estimation of the equivalent background thus more accurate DT determination for low-level radionuclides.

• When we further focus on the results of NaI measurements, the choice of using w 2 is shown to be more consistent than w 1 ; it allows better distinguishing a radionuclide from its equivalent background when the spectra are overlapped in the whole energy range.

Confidence interval

The statistical uncertainty of the estimation of a parameter is twofold: the estimation bias and an interval of values that contains the true value of the parameter. In the spectral unmixing approach, the assessment of uncertainties can be carried out from Monte Carlo simulations that mimic the actual mixture of radionuclides as presented in Section 3. The distribution of estimated values provides both the estimation bias and the coverage interval. However, this requires a massive amount of simulations, making this approach hard to implement in practice. Nevertheless, the Poisson-based spectral unmixing is shown to provide accurate activity estimations; we can only focus on determining a coverage interval from the estimated mixing weights.

Fisher information to compute coverage intervals

For the observed variable x distributed as f (x|θ), the maximum likelihood estimator (MLE) can be approximated with a Gaussian distribution:

N θ, I(θ) -1 (15)
where I(θ) is the Fisher information (Fisher ( 1956)) defined as:

I(θ) = E θ ∂ 2 log f (x|θ) ∂θ 2 (16)
The estimation standard error can be obtained by replacing the unknown true value θ by the estimated value θ.

In our activity estimation problem, the investigated Poisson-based spectral unmixing provides a maximum likelihood estimate of the mixing weights, noted â. According to the Poisson likelihood, the Fisher information matrix can be written as:

I(â) = Φ T diag x ⊘ (Φâ + b) 2 Φ (17)
We propose to assess the coverage interval of the estimated mixing weights â by the diagonal elements of I(â) -1 , which approximates the standard deviation of the distribution.

Evaluation of coverage interval in spectral unmixing

In this paragraph, the coverage interval assessment with Fisher information matrix is evaluated with simulations of HPGe and NaI measurements described in the previous section. More precisely, we calculate the standard deviation from the Fisher information matrix and evaluate the results with Monte Carlo simulations.

Firstly, we make use of the Q-Q (quantile-quantile) plots, which compares the distribution of estimated activities of Monte Carlo simulations to the distribution generated from the standard deviation carried out with Fisher information.

The aim is to i), test the normality of the estimator, which allows validating the coverage interval with a standard uncertainty in terms of Normal distribution.

ii), compare the distribution to those obtained with Fisher information.

More precisely, for each radionuclide, we show the Q-Q plot for two data samples noted A 1 and A 2 :

• A 1 for estimated activity values of Monte Carlo simulations.

• A 2 for Normal distribution generated from the Fisher information of the estimation:

N a 0 , σ 2 f where a 0 is the expected mixing weight of the radionuclide and σ f is the standard uncertainty calculated from the Fisher information matrix.

For each value a in a sample (A 1 and A 2 ), quantiles are calculated with:

q = a -µ σ (18)
where µ and σ are the mean value and the standard deviation of the given sample.

The Q-Q plots shown in Figure 12 2 and Table 3 for HPGe and NaI measurements respectively. percentage within a 0 ± 2σ f 96.4 93.9 95.7 95.0 percentage within a 0 ± 3σ f 99.9 99.8 99.8 99.9

Figure 1 :

 1 Figure 1: Spectral unmixing model used to illustrate the evaluation of the characteristic limits. The simulated measurements (gray) are composed of the above 10 radionuclides, while individual spectra of 7 Be, 22 Na, 137 Cs, 212 Pb will be evaluated.

Figure 2 :

 2 Figure 2: Spectral unmixing model of simulations of NaI measurements.

Figure 3 :

 3 Figure 3: Schema of the least squares solution of the equivalent background model.

Figure 4 :

 4 Figure 4: DT assessment for HPGe measurements: 7 Be

  and Figure 13 for the HPGe measurement and the NaI measurement, respectively, display the quantiles of A 2 (Fisher quantiles) as a function of A 1 (Estimation distribution quantiles). Firstly, the results show the normality of activity estimation of Monte Carlo simulations with the straight line of the Q-Q plots and absolute values from 0 to 3. This confirms that the coverage interval of the estimation can be carried out with an approximation of the Normal distribution. Secondly, the Normal distribution generated with spectral unmixing (Maximum likelihood estimation) and Fisher information matrix provides similar coverage intervals comparing to the real Monte Carlo distribution. To further valid this conclusion, we calculate the percentage of the values estimated from Monte Carlo simulations within the interval of:a 0 ± σ f , a 0 ± 2σ f and a 0 ± 3σ f ,where a 0 , σ f stand for the expected mixing weight (i.e., simulated value) and standard error determined by the Fisher matrix. These percentage values are expected to be 68.27 %, 95.45 % and 99.73 % for normal distribution. The results are shown in Table

Figure 12 :

 12 Figure 12: Evaluation for the HPGe simulation: the Q-Q plots for Fisher quantiles versus estimation distribution quantiles for radionuclides.(blue). The theoretical Q-Q plots are shown in red.

Figure 13 :

 13 Figure 13: Evaluation for the NaI simulation: the Q-Q plots for Fisher quantiles versus estimation distribution quantiles for radionuclides.(blue). The theoretical Q-Q plots are shown in red.

Table 1 :

 1 Two types of errors of hypotheses test.

7

  Be, 22 Na, 40 K, 137 Cs, 210 Pb, 208 Tl, 212 Bi, 212 Pb, 214 Bi, 214 Pb. Their

	mixing weights are fixed to values that are customary in real aerosol mea-
	surements.

Table 2 :

 2 Standard deviation from Fisher information matrix comparing to Monte Carlo simulations (HPGe measurements).

60

  Co 134 Cs 137 Cs 152 Eu percentage within a 0 ± σ f

		68.1	66.0	67.5	66.2
	percentage within a 0 ± 2σ f	95.3	95.0	94.0	95.5
	percentage within a 0 ± 3σ f	99.7	99.5	99.9	99.8

Table 3 :

 3 Standard deviation from Fisher information matrix comparing to Monte Carlo simulations (NaI measurements).

	6. Conclusion
	7. Bibliography styles
	References

265

Fisher RA. Statistical methods and scientific inference.

Oliver and Boyd, 1956.

α percentile of the distribution of estimated values from Monte Carlo simulations under the null hypothesis of this radionuclide.