Estimating the demand for informal public transport: evidence from Antananarivo, Madagascar

Informal public transport has been growing rapidly in many developing countries. Because urban infrastructure development tends to lag behind rapid population growth, informal public transport often meets the growing gap between demand and supply in urban mobility. Despite the rich literature primarily focused on formal transport modes, the informal transport sector is relatively unknown. The paper analyzes the demand behavior in the “informal” minibus sector in Antananarivo, Madagascar, taking advantage of a recent user survey of thousands of people. It is found that the demand for informal public transport is generally inelastic. Essentially, people have no other choice but to use this kind of public transport. While the time elasticity is estimated at − 0.02 to − 0.05, the price elasticity is − 0.05 to − 0.06 for short-distance travelers, who may have alternative choices, such as motorcycle taxi or walking. Unlike formal public transportation, the demand also increases with income. Regardless of the income level, everyone uses minibuses. The estimated demand functions indicate that people prefer safety and more flexibility in transit. The paper shows that combining these improvements and fare adjustments, the informal transport sector can contribute to increasing people’s mobility and reducing traffic congestion in the city.


Introduction
In recent years, informal public transport or paratransit has been growing rapidly in many developing countries. It includes a wide variety of transportation services between formal transport normally characterized by mixed traffic with fixed 1 3 routes and fixed schedule and private vehicles. Across countries there are different definitions and names of paratransit services (e.g., Tuk-tuk in Thailand, Jeepney in Manila, Matatus in Kenya, and Dala dala in Tanzania), but informal public transport is typically characterized by more flexible and cheaper mobility services, though less comfortable and sometimes unsafe, than formal public transport, meeting the more customized mobility demand without prefixed routes and schedule in a relatively loosely regulated environment. 1 It is estimated that more than half of the total public transport demand is met by paratransit modes in many large cities in developing Asia (Shimazaki and Rahman (1996)).
Informal public transport is becoming predominant in many African cities, as the region has been experiencing accelerated urbanization (Fig. 1). Africa's urban population was more than doubled from 200 million in 1990 to 548 million in 2018 (UN ESA 2018). It is expected to continue growing. Among others, urbanization is one of the most important driving forces for economic growth (UN ESA 2020). However, urban infrastructure development often lags behind rapid population growth, causing significant urban congestion and informality. Many African megacities, such as Abidjan, Lagos and Nairobi, have already been ranked among the most stressful cities in terms of traffic congestion (Fig. 2). Because of the lack of well-prepared land use plans and sufficient infrastructure capacity, African cities are often found to be disconnected and overcrowded in small areas around the city centers (e.g., Lall et al. 2017). Informal public transport has been growing to meet the people's growing demand for mobility toward urban centers.
Informal public transport has the potential to continue growing further. Of particular note, it is not necessarily substitutable for, but complementary to formal public transport. Kumar et al. (2021) argue that formal public transport, such as bus rapid transit (BRT), is not always a solution and there are different public transport markets in a city. Formal and informal transport modes can coexist under a wellintegrated urban transport system (e.g., Permana et al. 2018). 1 3 different routes. Based on user survey data at 48 informal public transport stops in New Delhi, Behal et al. (2020) show that paratransit users are concerned about safety, while formal bus users are more concerned about reliability. Similarly, based on interview data from users, Tiglao et al. (2020) found five key determinants of paratransit use: vehicle condition, service availability, reliability and convenience, and access to information in the Philippines.
There are only a few studies which adopt more rigorous quantitative methods to analyze the demand behavior for informal public transportation. Applying the discrete choice model, Golub et al. (2009) estimate the welfare impacts of different policy interventions in Rio de Janeiro. It is shown that the demand for "vans," an informal transport service using 10-15 passenger minibuses, as opposed to train and bus transport, is elastic to household income and travel time. Gadepalli et al. (2020) examine socioeconomic characteristics of paratransit users in Visakhapatnam, a port city in Andhra Pradesh situated at the eastern coast of India. Their estimated discrete choice model between formal buses and paratransit modes, including shared auto-rickshaw and three-wheeler services, indicates that women, youngsters and the low-income group have higher preferences for paratransit. The demand for informal transport is also found to be crucially dependent on efficiency, frequency and transitability.
Still, unlike formal public transport, 2 it remains largely unknown in many places how the paratransit demand behaves and how the public transport sector involving informal modes could be improved or should be regulated, if needed. Taking advantage of a recent large user survey carried out in Antananarivo, the current paper attempts to examine the demand for paratransit minibus services, called "Taxi Be," within and around the city. The sample data comprise about 3300 paratransit users. Taxi Be has the potential to contribute to reducing urban congestion and ameliorating people's mobility if the system is better organized. On the other hand, the current chaotic Taxi Be operations may even worsen the city's congestion if proper policy measures are not taken. To better manage the growing paratransit market, it is essential to understand the demand behavior, including basic economic parameters, such as price and income elasticities.
The remaining sections are organized as follows: Section 2 provides a brief overview of the informal public transport sector in Antananarivo. Section 3 elaborates on our methodology and Sect. 4 explains our data. Section 5 presents main estimation results. Section 6 examines different model specifications and discusses policy implications as well as the robustness of the estimates. Then, Sect. 7 concludes.

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Estimating the demand for informal public transport

Overview of Informal Public Transport in Antananarivo
Madagascar is one of the least developed countries in Africa. The GDP per capita is among the lowest in the world, estimated at about US$520. About 21 million Malagasy people or 76.5% of the total population still live under the poverty line. Madagascar has been experiencing rapid urbanization in recent years (Fig. 3). The country's total population is about 26 million, 3 of which about 3.3 million are estimated to live in Greater Antananarivo, the nation's capital. 4 While other secondary cities, such as Toamasina and Mahajanga, are also growing, Greater Antananarivo is growing even faster at an annual growth rate of 2.4-4.2%, depending on the district. As a result, unlike other African countries, the primary city concentration has been increasing in Madagascar (Fig. 4).

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Antananarivo is becoming increasingly congested. Antananarivo is a historic city, which was established in the early 1600s (Wade 2015). Geographically, the city is also surrounded by hilly mountains. In Antananarivo, the land space allocated for transport infrastructure is extremely limited. The share of urban land used for streets is estimated at only 5.7% (Iimi 2019a), far below the international norm: Many large cities in developed countries use 15-25% of built-up areas for transport infrastructure (Angel et al. 2016).
Madagascar has a sizable informal sector in the economy. The literature discusses how the institutional setting and governance would affect the informality of the economy (e.g., Torgler and Schneider 2007). In developing countries, the informal sector or shadow economy tends to grow. In Madagascar, the informal sector accounts for about 38% of total employment (Nordman et al. 2016). In Antananarivo, currently, there is no formal public transportation that is operational. The vast majority of passenger traffic is carried by "informal" public transport, mostly, minibuses, called Taxi Be. There is no official statistics of minibus ridership; however, based on the 2016 household survey in Antananarivo, it is estimated that about 38% of the residents use minibus services (World Bank 2019). The total ridership in the sector is estimated at about 1.3 million rides per day.
Minibuses are loosely regulated by the central and local governments, depending on their service areas. While within-city services are registered at the Antananarivo Urban Commune (CUA), the Ministry of Transport is responsible for licensing other suburban operations that operate across districts and communes (Table 1). Although all operating routes, stops and schedules are in theory supposed to be registered, their actual implementation is not necessarily supervised. Operators only pay a license fee of 35,000 Malagasy Ariary (MGA) (US$10) and a parking fee of MGA120,000 (US$35) per year.
Over 6000 minibuses are currently operating along about 130 routes. Since there is no formal supply-and-demand matching mechanism in Antananarivo, many operators choose to offer their services where the passenger demand is concentrated, i.e., along the major national roads (e.g., RN1, RN2, RN3, RN4 and RN7). Other less populated areas or remote suburban areas are left unserved. Because of the lack of coordination between the two regulatory authorities, within-city and suburban bus services are duplicated geographically, adding to traffic congestion (Fig. 5). The average speed of Taxi Be is only 10-15 km per hour during peak hours. Although minibus fares are relatively cheap at about MGA500 or 15 U.S. cents per ride, many people, especially those who live in suburban areas, spend more than one hour to commute every day. Because of limited and inefficient transport services, a large number of Antananarivo residents are forced to live in limited available resident areas near to the central business district (CBD). About 60% of the total city population is concentrated within 5 km of Lake Anosy, the central part of the city, raising land and housing prices in Antananarivo substantially. The highest price around the CBD exceeds about MGA1 million or US$300 per m 2 (Fig. 6). When the difference in income is taken into account, this translates into the same level of residential land prices in Tokyo. 5 In Madagascar, about 61% of the urban population live in slums. 6 A more efficient transport system needs to be built to assure better accessibility in broader areas and make housing and land prices more affordable.

Methodology
To understand the mobility behavior towards informal public transport services, the following analysis is focused on the minibus (Taxi Be) market. In Greater Antananarivo, there is no other major alternative public transport mode. Although there exists rail infrastructure within or through the city, it is only used for freight purposes. To go to work, the vast majority of people use minibuses, unless they walk (Fig. 7). The low-income group tends to walk to their workplaces, but if they can afford public transport, they almost always use Taxi Be. Even people belonging to the higherincome group use Taxi Be. In Antananarivo, only 5% own individual cars.
Following the traditional trip generation and demand analysis in the literature (e.g., Goulias et al. 1990;Horowitz 1993;Parsons and Kealy 1995;Romano et al. 2000), a simple demand function for Taxi Be services is considered:

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Estimating the demand for informal public transport where Q i is the number of trips that individual i makes per week and P i is the average fare that they pay per trip. The estimation model is suitable to analyze the demand when detailed person-based data, including trip-and individual-specific characteristics, are available, which is the case in this paper. One of the limitations to estimating this demand equation is that the price is potentially an endogenous factor determined by the interaction between consumers and suppliers. As discussed above, the informal bus market in Antananarivo is highly competitive and contestable. Thus, the suppliers' response to consumer demand is considered to be relatively limited. In addition, there may be some omitted variables that potentially affect both price and quantity. To mitigate this risk, our equation includes as many observables as possible. While X represents a set of trip attributes, such as within-vehicle time and transport mode, Z includes other individual characteristics, such as age, gender and income level. The omitted variable tests are used to verify the validity of our specifications.
The price elasticity β is of particular interest because there is little evidence on this in the literature. In the formal public transport sector, there are a number of (1) studies and literature reviews on transport elasticities (see, for example, Goodwin et al. 2004;Litman 2013Litman , 2021Wardman et al. 2018). In the literature, the price elasticities for public bus transport are estimated at − 0.2 to − 0.3 in the short run. The long-term elasticity exceeds 0.5 in absolute terms. There is little evidence on the informal transport side.
For informal transport services, it is often difficult to observe price data by nature. Our data come from a minibus user survey that was carried out around Antananarivo in March 2021. The survey covers 10 zones in 8 Antananarivo districts 7 and 2 adjoining districts 8 where about 3.2 million people live according to the latest 2018 census (Fig. 8). For each zone, about 400 minibus users were randomly surveyed around major bus stops. In total, 4,124 responses were collected, including partial responses.

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Estimating the demand for informal public transport In the informal sector, fares are not necessarily determined systematically. Customers can negotiate prices. The actual prices may vary depending on a subjective judgement of the trip distance, time and traffic congestions. On the other hand, service operators may simply collect a uniform "normal" price (e.g., MGA500 per ride) regardless of the traveled distance. In the informal transport sector, there is no formal fare collection system on board. In the case of Antananarivo, our data shows that the average cost is MGA840 per trip, with a wide variation from nearly zero to MGA24,000 or about US$6 ( Fig. 9).
Understanding fare elasticities is particularly important in the developing country context. From the operator's point of view, the informal transport sector may be under too intense competitive pressure because of the lack of proper price, entry and safety regulations. There is no job security (Tichagwa 2016). From the user's point of view, however, affordability is an issue in many developing countries. The share of household spending on transportation is about 2-8% in Africa (Lozano-Gracia and Cheryl 2014). In Madagascar, transport spending accounts for 4-6% (Fig. 10). The low-income group tends to shoulder the relatively heavier burden than the highincome group. It is an important policy decision whether and how market prices are regulated in the informal public transport sector.
Following the literature (e.g., TRL 2004; Paulley et al. 2006;Litman 2021), a number of trip characteristics are included in X. In-vehicle time, i.e., time spent on board of the vehicle, represents the efficiency of each trip. Access and egress modes are also important from the last-mile connectivity point-of-view (e.g., Brands et al. 2014). Transit or waiting time will be an additional burden for users. More generally, multimodal connectivity determines the people's overall demand for mobility. A better integrated formal and informal transport system stimulates more demand (e.g., Chowdhury and Ceder 2016;Permana et al. 2018). In Antananarivo, two types of minibuses coexist, without coordination (at least in an explicit manner). The majority of passengers only use within-city Taxi Be. About 5% use both within-city and suburban buses (Fig. 11).
In general, quality of service is an important determinant of the demand for public transportation. Although it may be defined by a number of attributes, many people prefer clean, safe and comfortable rolling stocks (e.g., TRL 2004; Chica-Olmo    To measure these aspects, subjectivity cannot be avoided. However, at least two aspects are important to consider: safety and comfort (e.g., Simsekoglu et al. 2015). In Antananarivo, about 20% of the minibus users feel that the services are uncomfortable and unsafe. More women than men feel that minibuses are not safe (Fig. 12).
The demand structure likely differs depending on trip purposes as well. The demand for essential trips, such as commuting to work and school, is normally less elastic than that for nonessential activities, for instance, shopping and recreation (TRL 2004). In Antananarivo, trip purposes differ by gender. More than half of the male passengers use minibuses to get to work (Fig. 13). Female riders use minibuses to not only go to work but go shopping. As a consequence, the level of demand for transportation is also different between men and women. Male passengers travel on average 4.69 times per week, and female 4.43 times per week (Fig. 14). The majority of transit users travel 3-6 times, but some passengers make more than 40 trips per week. This variation is our dependent variable, Q.  To control for other unobserved trip-specific characteristics, the origin-destination pairs can be included as a set of dummy variables. They are expected to capture some common, though unobservable, characteristics to move from a particular location to another, such as traffic congestion levels and frequency of services.
Finally, observed passenger characteristics are included in Z to control for the individual effects, such as gender, age and educational attainment. Income elasticity of demand is another important economic issue. Since transportation is a normal good (Lozano-Gracia and Cheryl, 2014), people with higher incomes are likely to travel more frequently. At the same time, they are more likely to own private cars, though the individual car ownership is still generally limited in Madagascar.
Among minibus users in Antananarivo, male passengers earn more than female (Fig. 15). This is consistent with Iimi (2019b). Women are more likely to commute by minibus, spending more time on board of the vehicle (Fig. 16), yet, they earn less than men. The employment status is also relevant. Among minibus users, the share of those who are not employed is higher for women/ female users. By contrast, the share of people who are formally employed is much higher for men (Fig. 17).
The above-mentioned comparative statistics indicate that there are several potential differences in demand behavior among different types of minibus users. First, the demand may differ depending on the traveled distance. Suburban bus users tend to travel longer than those who use only within-city Taxi Be. The literature shows that the price elasticity tends to be high because people have an option of walking (e.g., Paulley et al. 2006;Kholodov et al. 2021). As shown in Fig. 7, in fact, many people just walk to work in Antananarivo. Second, the demand may behave differently between commuters and non-commuters. The demand for those who commute for work or to school may be less elastic than that for those who make a trip for shopping, recreation and other personal reasons. Third, the demand structure may be different between male and female users.
(2) To examine these potential differences in demand, a structural test is used (Chow 1960). Letting d be a dummy variable representing one of the different groups of users, the coefficients can be differentiated between the two groups, for instance, male and female riders: The null hypothesis that 1 = 2 , 1 = 2 , 1 = 2 , 1 = 2 will be examined by the Chow test.

Data
To analyze the informal transport activities, it is essential to obtain person-based trip data, which are normally difficult and expensive, as pointed out by Huang (2019). Our data are unique and come from a minibus user survey that was carried out in the places where many people embark on and disembark from minibuses in Greater Antananarivo. With observations with missing values and outliers excluded, the following analysis uses 3133 observations. The survey covers Greater Antananarivo, comprising 10 districts. Despite the recognition of disparities in population, our survey attempted to interview the same number of minibus users in each district. To take this into account, each observation will be weighted by the inverse of its probability of being sampled according to the respondent's origin. The sampling weights are calculated based on the total census population.
The data were collected through a relatively simple questionnaire-based survey. In recent years, a wide range of new public transport data have become available from different sources, including big data and remote sensing data (Ge et al. 2021). While georeferenced data tracked by automatic vehicle location systems have great potential for providing the accurate, real-time information on movements of people and freight, automatic fare collection systems can also generate detailed data on travel origin and destination, allowing to analyze the travel behavior and demand. Unfortunately, however, it is still a challenge to collect transit data in the informal sector. In Antananarivo, there is no regulatory framework governing or monitoring daily operations. No centralized fare collection system is used. Revenue data from service operators are unavailable or unreliable. To analyze the informal sector, survey data have the advantage of revealing hidden data that are hardly observable otherwise, although they may be somewhat biased.
The summary statistics are shown in Table 2. In our used sample, minibus users make on average 4.5 trips per week. The raw data has a large variation in this from one to 67. To exclude severe outliers, the analysis only uses observations with 15 trips or less (Fig. 18). 9 The average trip cost is about MGA840 or about 25 U.S. (3) The original data range from 1 to 67, seemingly including some outliers. Thus, the conventional letter values are used to identify outliers. The upper outer fence is 15. Ten observations are considered to be severe outliers outside the outer fence, which make up about two per million of a normal population. Though the regression results remain broadly the same regardless of whether the outliers are included or excluded. cents per trip. Nearly half of the surveyed users take advantage of minibuses to go to work, followed by those who go shopping (about 25%) or go to school (13%). Those who use Taxi Be for escort purposes are used as a baseline. The accessibility before getting on or off the bus looks generally good. While average access time to boarding point (ACC ) is about 9 min, egress time from alighting point (EGR) is on average 16 min. This reflects the fact that many city residents are concentrated around the center of the city where the minibus network is well supported by many routes. For about 56% of the users, both trip origins and destinations are within Antananarivo Urban Commune (i.e., dCUA ).
However, having too many informal buses in limited areas may be causing massive traffic congestion in the city. Minibus users spend on average 50 min on board of the vehicle (TIME) (Fig. 19). This is comparable or greater than the average commute duration in developed countries, for instance, 26 min in the United States. The average commuting time is 53 min in the United Kingdom and 42 min in other European countries (Chatterjee et al. 2020). For some people, it takes more than 4 h to get to their destinations. The average user transfers minibuses 1.3 times per trip (TRS). Thus, at least one transfer is needed to get to a destination, which means that route coordination is important. In the sample, about 5% of the travelers have no transfer. To take the logarithm of the variable with zero values unbiasedly, the Battese's (1997) specification is used: Then, lnTRS * and D TRS are included in the equation, instead of lnTRS. While about 75% use only within-city Taxi Be, 20% use only suburban minibuses (dSUBU). About 5% use both (dBOTH). The within-city bus-only users are set as a baseline. Informal public transport users are not trusting the quality of the services. About 19% feel that minibuses are not safe. Similarly, 21% responded that minibuses are not comfortable.
For individual characteristics, the income level is categorized into seven groups. Half of the respondents earn less than MGA300,000, approximately, US$75 per month. Minibuses are an important means of transportation in Antananarivo or in Madagascar in general. Slightly more than half of the surveyed minibus users are female (dFEMALE). About 40% are considered household heads (dHHH).
In Madagascar, formal job opportunities are limited. About 32% responded that they are employees. While 39% are considered self-employed, 22% of minibus riders are not employed. Self-employees are used as a baseline in the analysis. For household asset ownership, only 6% in the sample own private cars. Motorcycles and bicycles are more prevalent: 17% for the former and 13% for the latter. These modes of transport can potentially be an alternative to informal public transport.

Main estimation results
The ordinary least squares (OLS) regression is first performed ( Table 3). Regardless of the inclusion of the OD pair dummy variables, the estimated results are broadly consistent. From the statistical point of view, the specification with the OD dummy Estimating the demand for informal public transport The dependent variable is lnQ. Robust standard errors are shown in parentheses *, ** and *** indicate statistical significance at the 10, 5 and 1%-level, respectively variables (Model 2) may be more preferable than the one without OD dummies (Model 1). According to the Ramsey RESET test, the hypothesis that there is no omitted variable can be rejected in the specification without the OD pair dummy variables. The test statistic is estimated at 3.92, which is significant at the 1% confidence level. With the OD dummy variables included, the omitted variable test cannot be rejected. The test statistics is 1.93, statistically insignificant. This suggests that in the market that we are analyzing, there are many important unobserved routeor trip-specific characteristics affecting people's informal public transport demand, such as local environment around origins and/or destinations and traffic conditions. Other estimation methods are also performed to confirm the robustness of the OLS results. Since our dependent variable is a nonnegative count variable, a natural alternative estimator is the negative binomial regression model (Models 3 and 4). The results are found to be similar to the OLS results (Table 4). Quantile regression is also performed because our dependent variable is skewed, although some outliers are excluded. The quantile approach has the advantage of being robust against outliers because it predicts the quantiles, such as median, by minimizing the sum of the absolute residuals. By contrast, the OLS is potentially sensitive to outliers. The quantile regression generates broadly similar outcomes (Models 5 and 6). 10 Thus, the following analysis is focused on the OLS models.
The estimated results from OLS (Models 1 and 2) are broadly consistent with our prior expectation; however, there are some important differences from the literature mostly focused on the formal sector. Note that it is difficult to overgeneralize our results. In the literature, there are few studies investigating the informal transit sector. However, it is clear that the demand for informal transport is significantly different from that for formal transportation. First, the price elasticity is found to be relatively modest at − 0.02 and statistically insignificant under these model specifications. The p value of the coefficient of lnP is 0.21. It can be concluded that the demand is relatively inelastic to fares in the informal public transport sector. As will be discussed in the next section, however, the price elasticity seems to vary across different types of passengers. It can be statistically significant in some cases, but the elasticity is small in any way. This is considered to be particularly characteristic for informal public transport in developing countries: there are few alternatives regardless of fares.
Time elasticity is significant but its magnitude is relatively modest. Under the specification with the OD pair dummy variables included, the coefficient of in-vehicle time (TIME) is estimated at − 0.033. Holding everything else constant, people are discouraged to take a trip by minibus when in-vehicle time gets longer. The estimated elasticity is more modest than others found in the literature that often examines the formal transport sector, ranging from − 0.3 to − 0.5 (TRL 2004). Again, there are few alternative modes of transport in Antananarivo. Even though the operational efficiency of minibuses is low, people cannot help but use them.
The estimation results indicate that the minibus demand is particularly strong for those who commute to workplace or school. The coefficients of trip purposes being to work or to go to school are statistically significant and numerically large. It

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Estimating the demand for informal public transport Table 4 Negative binomial and quantile regression Negative binomial regression

Quantile regression
Model (3) Model (4) Model (5) Model (6) Without OD dummy The dependent variable is Q for the negative binomial regression and lnQ for the quantile regression, respectively. Robust standard errors are shown in parentheses *, ** and *** indicate statistical significance at the 10, 5 and 1%-level, respectively Table 4 (continued) Negative binomial regression

Quantile regression
Model (3) Model (4) Model (5) Model (6) Without OD dummy implies that commuting workers and students are crucially relying on this informal transport sector for their everyday mobility. Access and egress times are less relevant in the informal transport sector. In the formal sector, it is often shown that efficiency in a multimodal connection among different modes is important to stimulate the demand for public transportation (e.g., Hensher and Rose 2007). For instance, Brands et al. (2014) find that about 40% of public transport users use bicycles as access mode. In the case of Antananarivo, there is little evidence supporting such a view. Both coefficients of access and egress times are insignificant. In fact, the current minibus network is already comprehensive. Many users may have a fairly good access to minibus stops from their home, offices or schools. As shown above, the average access time to a boarding point is 10 min, and egress time 15 min.
Regarding transit, first, suburban buses to within-city bus transfer are not preferable. The coefficient of dBOTH is found to be significantly negative. This indicates that the sector reform is needed to improve the interface between the two networks by enhancing coordination to make transfers easier. The duplicated regulatory frameworks under the two different authorities should be improved to ameliorate the synchronization of the routes and schedules.
Second, however, transit itself looks important for minibus users. dTRF is negative and lnTRF has a positive coefficient. Thus, the demand increases when people transit more frequently. The result may be understood as the indication that having more transfers does not mean inconvenience but flexibility for users. Unlike traditional formal public transport systems, the current minibus network is not optimally designed to meet the people's real demand. Thus, transfers are unavoidable. Under the circumstances with high route density, it can be more efficient to have a number of short routes. There is some similar discussion in the literature. Deb and Filippini (2013) found that the service quality, defined by density of transport routes, has the highest demand elasticity. A shorter waiting time can also increase the demand for public transportation (e.g., Hensher and Rose 2007).
Safety matters. As discussed, there is a concern about safety of minibus operations in Antananarivo. Over 6500 people died in road crashes in the city in 2016, of which more than 20% involved minibuses (World Bank 2019). The coefficient of dUNSAFE is negative and significant. When minibus operations are unsafe (though judgements are fundamentally subjective), the demand declines. This is consistent with an increasing concern among users. On the other hand, there is no significant result regarding the comfort of minibus operations (dUNCOMF).
For the individual effects, it is found that informal minibus transportation in Antananarivo is a "normal good" (as opposed to inferior good). The estimated coefficients of the income group dummy variables tend to increase with the income level (Fig. 20). This is contradictory to earlier studies in the literature, which generally show that the income elasticity is negative (e.g., Deb and Filippini 2013;TRL 2004;Paulley et al. 2006). In developed countries, the demand for public transportation could decrease with the household income because people with a high income can own and use their private cars. However, in developing countries, such as Madagascar, buying a car is not an immediate, viable option. Private vehicles are still expensive for most people. As shown above, the private vehicle ownership is only 6% in Antananarivo. Therefore, people still tend to continue using minibuses even if their income increases. A policy implication is straightforward: it continues to be important for the Government to make increased efforts toward improving efficiency in this public transport sector.
Still, relatively speaking, private car owners are less likely to use minibuses than those who do not own a car. After all other characteristics, including household income, are taken into account, the coefficient of dCAR is significantly negative. This is consistent with the literature. Naturally, if people own a car, they will likely use it. Bicycles may also be an alternative, but the statistical significance of dBIKE is weaker than car ownership.
For other individual characteristics, our results show that women are less likely to use informal minibuses than men. This is not consistent with earlier findings in the formal public transport sectors. For instance, Hensher and Rose (2007) show that public transport modes, such as rail and bus, are more often selected by women and the youth. The negative coefficient associated with female users in our case may be relevant to the above-mentioned safety concern but also affected by the employment status of the surveyed bus users. More men are formally employed than women. Related to the above discussion about the difference in the trip objective, the transport demand is significantly lower for those who are not employed than self-employees (baseline). All these variables are intertwined with one another.

Discussion
One of the unexpected results in the above baseline estimation is that the price elasticity is not statistically significant, though it is estimated as being negative. As shown above, one general tendency in this sector may be that the demand is really less price-elastic. This is applicable for not only Madagascar but also other countries that have the similar informal paratransit systems characterized by too much competition under the poorly regulated environment. However, another possibility is that the demand structure may differ among groups of users. For instance, the demand may be different between commuting workers and occasional users. As indicated by the literature (e.g., Paulley et al. 2006), the price elasticity may also differ between relatively short-and long-distance travelers. These heterogeneities among users may contribute to resulting in the statistical insignificance of our estimated price elasticity.
To investigate the heterogeneity in demand behavior, first, the difference in demand between short-and long-distance travelers is considered. Our surveyed minibus users are all short-distance travelers by global standards; however, there is an important distinction between those who travel within Antananarivo Renivohitra (CUA), the central part of Greater Antananarivo, and those who travel beyond CUA. From the geographic point of view, the former are basically those who live in the old capital city and travel very short distances. On the other hand, the latter are generally those who live in suburban areas and thus need to commute longer distances. This difference is represented by a dummy variable, dCUA .
This differentiation is also important from the administrative point of view. Recall that there are two different minibus systems in Greater Antananarivo. Short-distance travelers (i.e., dCUA = 1 ) are primarily served by within-city Taxi Be, which is regulated by the city government CUA. Longer-distance travelers (i.e., dCUA = 0 ) use suburban buses or both. Suburban buses are supervised by the Ministry of Transport at the national level. Thus, the differentiated results could have different policy implications to different government entities, although it may not be straightforward because the service areas of the two networks are partially duplicated.
To examine whether the demand behavior is different between short-and longdistance travelers, the interaction term between lnP and dCUA is added (Models 7 and 8). This allows us to differentiate the price elasticity between the two groups. The selected results are shown in Table 5. The full results are presented in the Appendix. The coefficients of lnP are significantly different depending on dCUA : For short-distance travelers (i.e., dCUA = 1 ), the price elasticity is estimated at -0.054, which is significant. For longer-distance travelers ( dCUA = 0 ), the elasticity remains insignificant. Thus, the demand-side management through fare adjustments is only effective for within-city Taxi Be: A 10% increase in fares would reduce the demand by about 5%. This is consistent with the literature: Within the center of the city, people may have alternative modes of transport, i.e., taxi, motorcycle taxi or even walking, because trip distances are likely to be relatively short.
According to the Chow test, the demand structures are considered to be different between the two groups. The estimated test statistic is 1.57, which is statistically significant. Thus, the demand function can be estimated separately between the two groups. The separated models are presented in Models 9 and 10. Again, the price elasticity is only statistically significant in the estimation with data from within-city bus users. The estimated elasticity is − 0.063, still relatively modest. Other coefficients are broadly similar, except for a few. For instance, the negative demand impact by gender is only found in short-distance travels. The potential impact of private car ownership is found to be particularly significant for long-distance minibus users.
The number of transfers is only significant when dCUA = 1 . Flexible connectivity matters only to Taxi Be users. However, the time elasticity is significant for both Taxi Be and suburban buses. The elasticity is larger for the former. This is because traffic congestion is severer within CUA. It is critical to improve operational  (7) Model (8) Model (9) Model (

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Estimating the demand for informal public transport efficiency of Taxi Be for stimulating people's mobility throughout the public transportation system. The number of transfers, which can be interpreted as a proxy of the connectivity among bus routes, is particularly important for travelers within CUA where more bus routes are available. Outside of the CUA, the current suburban bus routes are lineal. The transferability does not matter too much. 11 Travelers within CUA are more worried about safety. Women have the lower demand particularly within CUA. Suburban residents who own a car have a particularly low demand for informal public buses, presumably because they can drive. On the other hand, the vehicle ownership does not seem to affect the demand of city residents for public transport significantly. The vehicle ownership is very low anyway, and people may not use their vehicles within CUA because of the current traffic congestion.
One may also wonder whether the demand behavior may differ between everyday commuters, such as those who go to work or school, and other occasional users, for instance, those who go shopping. The structural test is performed by creating another dummy variable, dWorkSchool, which is set to one when the trip objectives are to get to work or go to school and zero otherwise. The Chow test statistic is estimated at 15.68, which is significant. Thus, the demand structures are considered to be different between these two groups of users.
The estimated coefficients are broadly similar to the above estimates. However, when the sample is divided into the everyday and occasional users (Models 13 and 14), there are certain differences in demand behavior between the two groups. It is clear that the price elasticity is significant only when dWorkSchool = 0 ( Table 6). As expected, the demand by nonessential travelers is highly elastic. The coefficient is estimated to be − 0.062. Their demand can be affected more by fares. On the other hand, the demand looks less price-elastic for everyday commuters. This is because they do not have a choice. In addition, the time elasticity for daily commuters is lower (in absolute terms) than that for nonessential travelers. For the former, they are forced to use minibuses no matter how long they have to be on board. On the other hand, those who travel for other purposes than working or going to school may have some more flexibility in terms of travel time. By the same token, the necessity of using both within-city and suburban buses has a significant impact on nonessential travelers. But commuters do not have such flexibility to avoid a transfer between the two networks.
Finally, the potential difference in demand between male and female minibus users is examined. The Chow test statistic is estimated at 1.48, which is significant at the 5%-level. Thus, the demand structure is systematically different between male and female passengers. The main results from the separated regression are shown in Table 7 (Models 17 and 18). Male passengers seem to be more sensitive to prices. The price elasticity is only significant for male minibus users. Male passengers are also particularly sensitive to travel time. The time elasticity (TIME) is only significant for men. This may be dependent on the difference in trip objectives. The male demand is more influenced by their trip purposes, e.g., work, business and schooling. Table 6 OLS estimation differentiated by trip purposes Only selected coefficients are presented. See the full result in the Appendix. The dependent variable is lnQ. Robust standard errors are shown in parentheses *, ** and *** indicate statistical significance at the 10, 5 and 1%-level, respectively.

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Estimating the demand for informal public transport  (15) Model (16) Model (17) Model ( Only selected coefficients are presented. See the full result in the Appendix. The dependent variable is lnQ. Robust standard errors are shown in parentheses *, ** and *** indicate statistical significance at the 10, 5 and 1%-level, respectively Table 7 (continued)

Separate regression
Model (15) Model (16) Model (17) Model (18 For female users, the demand is more related to nonessential trip purposes, such as personal trip and family visit. Despite our prior expectation, there is no gender-specific impact related to safety or comfort. The household ownership of a vehicle particularly matters to women. If a vehicle is owned, the demand for public buses is reduced significantly.

Conclusion
Informal public transport has been growing rapidly in many developing countries and offers a wide variety of transportation services. Informal public transport is becoming predominant in many African countries where rapid urbanization has been experienced. Because urban infrastructure development tends to lag behind rapid population growth, many African cities are overcrowded and disconnected. Informal public transport is often used to meet the growing gap between demand and supply in urban transport services.
Despite the rich literature primarily focused on formal transport modes, the informal transport sector is relatively unknown and often loosely regulated. The paper focuses on analyzing the demand behavior in the "informal" minibus sector in Antananarivo, Madagascar, taking advantage of a recent user survey of thousands of people.
A number of new findings are discovered, though they cannot be overgeneralized. First, the demand for informal public transport is generally inelastic. The time elasticity is about − 0.02 to − 0.05, probably, one-tenth of the elasticities observed in the formal transport sector in the literature. The price elasticity is also estimated to be small at 0.05-0.06 in absolute terms, which is significantly lower than the norm in the formal sector, i.e., 0.3-0.5. It is found that the demand is price-elastic only for short-distance travelers, who may have alternative choices, such as motorcycle taxi or walking. The demand is also inelastic for everyday users for commuting purposes (employees and students), though their demand is strong. Unlike formal public transportation, the demand increases with income. Regardless of income level, everyone uses minibuses, though some modal shift may be expected for those who own a private car.
The policy implications are mixed. The results indicate the general difficulty to intervene in the market. The demand is rigid no matter how the operational efficiency changes and no matter how much is charged. Essentially, users have no other mode choices. This is especially relevant for developing countries and indicates a particular challenge from the environmental and congestion management point of view. Pricing is not necessarily useful for demand-side management. Even though fares were regulated and forced to be increased, the demand for informal transport would not be contained. However, even though the elasticities are limited, it is important to remind us of the significance of the market size. In Antananarivo, for instance, the minibus sector carries about 600,000 passengers every day. Even small changes in efficiency (i.e., within-vehicle time) or fares could result in a significant change in travel demand as a whole. In addition, the improved operational profitability by increased fares, while not affecting the demand much, could allow operators to maintain their fleet more properly, paying necessary attention to safety and environmental issues.
Importantly, the analysis shows that several other features are important to influence the demand for informal public transport. It is essential to improve informal public transport safety. Users also demand more flexibility of the transit system. Perhaps, the current network design may not be optimal for them, calling for further investigation into the need for bus route restructuring. Especially, using both within-city and suburban buses is found to be a particular burden for users. Their connectivity is particularly poor because of the lack of coordination between the two systems. The duplicated regulatory frameworks need to be ameliorated.
By improving these features, the demand can be stimulated even if fares are increased. The current fares seem to be too low, creating overcompetition in the market, overusing the old and unsafe fleet, and aggravating traffic congestion on the road. By re-organizing the network and imposing stricter safety regulations, the operational efficiency can be improved with reduced total trip times for passengers. The improved benefits can be sufficient to compensate for potential changes in bus fares, potentially allowing proper fleet maintenance and timely fleet renewal.
Estimating the demand for informal public transport  The dependent variable is lnQ. Robust standard errors are shown in parentheses *, ** and *** indicate statistical significance at the 10, 5 and 1%-level, respectively Table 8 (continued)   The dependent variable is lnQ. Robust standard errors are shown in parentheses *, ** and *** indicate statistical significance at the 10, 5 and 1%-level, respectively Table 9 (continued)

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Estimating the demand for informal public transport

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The dependent variable is lnQ. Robust standard errors are shown in parentheses *, ** and *** indicate statistical significance at the 10, 5 and 1%-level, respectively