Informal sector dynamics in times of fragile growth: The case of Madagascar

This article examines the dynamics of the informal sector in Madagascar during the 1995–2004 period, which was characterized by sustained growth that ended due to a major political crisis. As conventionally assumed by simple dualistic models, the informal sector indeed fulfils a labor-absorbing function in times of crisis. However, informal business creation was also a major trend both during macroeconomic growth and during crisis and recovery. Growth in the informal sector was mostly extensive, with little job creation or capital accumulation. Although such a situation would be consistent with the existence of poverty traps, estimated marginal returns to capital are decreasing, which tends to reject this hypothesis.


Introduction
The informal sector is the main source of income and employment for most urban households in the developing world. Traditionally, informal activities were considered the subsistence segment in a dual urban economy that was bound to disappear with economic growth and the development of the modern sector (Lewis, 1954). Recent evidence has shown that the informal sector in fact comprises various forms of production and employment typically in very small enterprises, contradicting the assertion that it will disappear with economic growth (Maloney, 2004). While some of these informal firms may indeed represent a form of urban subsistence production, the informal sector is usually also the host of a number of successful entrepreneurs (Cunningham and Maloney, 2001;Fields, 2004). Such heterogeneity means that there are no straightforward predictions on how the size, structure and performance of the informal sector change during long periods of economic growth or spells of crisis. Yet there is little empirical evidence on the way informal firms react to overall macroeconomic dynamics. This article is an attempt to provide some evidence on the dynamics of the informal sector in Madagascar between 1995 and This period is particularly interesting because it comprises both a sustained period of economic growth and a serious economic and political crisis.
After a long period of economic decline that started with the country's independence in 1960, Madagascar experienced an exceptional period of economic expansion between 1995 and 2001. One factor of growth was the development of Export Processing Zones (EPZ), which attracted foreign industries, in particular textiles, and thus stimulated exports and employment. In Antananarivo, the real average labor income increased by 53 per cent between 1995 and 2001. In the first half of 2002, the major political crisis following the presidential elections of December 2001 reversed this trend, as general strikes, roadblocks and a power vacuum caused a temporary collapse of GDP growth and a massive departure of foreign industries, in particular those located in the EPZs (Razafindrakoto and Roubaud, 2002). The political crisis had disastrous effects on the economy: GDP declined by 12.7 per cent, real incomes dropped by 5 per cent and the unemployment rate nearly doubled (Cling et al, 2005). Despite the severity of the economic downturn, recovery was quick after the end of the conflict (in May 2002), with a GDP growth of 9.8 per cent in 2003 and around 5 per cent in the two following years. Thereafter, household living conditions stagnated: in 2004, earnings were as low as in 2002 (Gubert and Robilliard, 2010).
Several strands of literature can provide a conceptual framework for the description and analysis of transformations that occurred in the informal sector in the decade under review. We rely on a unique data set of four representative and perfectly comparable cross-sectional surveys of informal enterprises in Antananarivo collected in 1995Antananarivo collected in , 1998Antananarivo collected in , 2001Antananarivo collected in and 2004, that is, before and after the 2002 crisis, to study two main questions.
First, is the informal sector counter-cyclical or pro-cyclical? To what extent is its dynamics linked to the overall macroeconomic context? The simple dualistic view implies that the informal sector follows counter-cyclical dynamics. In contrast, if workers are indifferent between sectors at the margin and informal sector employment is in fact voluntary, then wages and employment in both sectors should move together, in a pro-cyclical way (Maloney, 2004). With a more complex view of the informal sector, we can expect pro-cyclical movements in the upper tier and countercyclicality in the lower tier (Bosch and Maloney, 2010). Empirical evidence on the impact of contextual factors, such as the overall macroeconomic environment, on small firm growth in developing countries is scarce. McPherson (2000), for example, examines the impact of structural adjustment in Zimbabwe on changes in the magnitude and structure of the small enterprise sector. Mead and Liedholm (1998) cite studies of the Dominican Republic, Kenya and Jamaica to derive the following hypotheses regarding the relationship between economic expansion and firm growth: in times of macroeconomic growth, informal sector job creation is likely to be channeled mainly through firm expansion, while jobs would be destroyed as workers move to better economic opportunities, such as formal jobs. On the other hand, stagnation would lead to downsizing and more new firm creation. 1 We assess the cyclicality of informal activities by looking at the joint dynamics of the formal and informal labor markets and the evolution of aggregate and average capital stock in informal enterprises ('Informal labor and capital dynamics: Descriptive statistics'). We then run enterprise growth regressions using retrospective data and include in the specification proxies capturing the overall economic conditions to study the impact of GDP growth on informal business growth ('Informal business growth and the macro environment').
Second, is the technology in the informal sector consistent with a poverty trap model? The stagnation of a number of Informal Production Units (IPU) may be a sign of the existence of poverty traps, evidence of which can be found in very low returns at very low levels of capital. Non-convex production technologies combined with imperfect credit markets have been put forward by microeconomic theory to explain this so-called 'poverty trap' (Banerjee and Newman, 1993). However, a number of recent studies from diverse low-and middle-income countries have found very high returns to capital at low levels of capital in small-scale activities, thus contradicting the assumption of low subsistence returns at low levels of capital (McKenzie and Woodruff, 2006;Udry and Anagol, 2006;De Mel et al, 2008;Grimm et al, 2011). Building on this recent empirical literature, we estimate production functions to evaluate capital returns in different segments of the capital distribution and assess the existence of these poverty traps in the Madagascar context ('Returns to capital in the informal sector'). By adding year interactions we study changes in these returns over time to assess whether or not they increase with economic expansion.

Data and Sample Description
We use 1-2-3 Survey data that were collected in Antananarivo between 1995 and 2004 (Razafindrakoto et al, 2009). These surveys were specifically designed to collect information among representative samples of informal firms. The informal sector is defined as employment in unincorporated enterprises that are not registered or do not keep any written accounts. 2 Phase 1 is a labor force survey, conducted every year since 1995, among 3000 households. Principal and secondary activities of every member aged 10 years and over are recorded, including the type and status of the enterprise in which they work (formal/informal), making the establishment of a list of all informal firms headed by any member of a household possible (whether it is the main or the secondary activity). This list serves as the sampling frame for Phase 2, in which around 1000 businesses randomly drawn from the Phase 1 roster are surveyed and which collects information on labor force characteristics (including contributing family workers), sales, profits, investment, expenditures for intermediate inputs, fees and taxes. The stratification scheme, by industry and type of firm (with or without wage workers), as well as an oversampling of the most atypical kind of firms (for example, big manufacturing enterprises), makes sure that the full heterogeneity of the informal sector is captured. Phase 2 has been conducted every 3 years since 1995, and therefore we can use data on four representative and perfectly comparable cross-sections of approximately 4000 businesses surveyed in 1995, 1998, 2001 or 2004. 3 Three key advantages of the 1-2-3 Surveys over other alternative data sets need to be stressed here. First, the mixed household-enterprise survey frame is the only one to ensure full representativeness of the informal sector. Previous studies, especially in Africa, are typically based on enterprise surveys that cover only a part of all informal firms; in general the upper tier of the informal sector in some specific industries, mainly manufacturing. Second, our four rounds of surveys are fully comparable, as the sampling methodology and questionnaires have been maintained constant over time. To our knowledge, this is the first time ever such a series of repeated cross-sections of informal businesses on a representative basis is available in Sub-Saharan Africa. Third, as informal entrepreneurs do not usually keep books, the survey questionnaire has been designed to assist them in establishing, product by product, all their sales and expenses of the previous month or of another, shorter or longer period of time (previous day, week and so on) best adapted to each individual case. 4 This detailed and comprehensive procedure provides reliable data, avoiding the usual underestimation biases caused by more aggregate questions. 5 The same extensive process is used to reconstitute the capital stock evaluated at replacement costs to take into account depreciation. More specifically, the entrepreneur is asked to report all the equipment that he has used in the last year to operate his business and the replacement value of each item. In sum, our data set offers a unique opportunity to obtain insights on the evolution and dynamics of the informal sector over a decade.
In the entire article, value added is a monthly measure and is calculated as the difference between sales and intermediary consumption (raw material and inventory purchases, rent and utilities, and other expenses). Value added therefore corresponds to the sum of capital income, all labor income and entrepreneurial profits. The capital variable is the total stock of capital, measured at the actual replacement value, and includes buildings and land, furniture, vehicles, tools, machines, and other types of equipment. To obtain real values of capital and value added, the Consumer Price Index is used as a deflator. 6 We pool the four cross-sections to describe the main characteristics of informal businesses ( Table 1). To take into account their heterogeneity, we disaggregate the sample along two dimensions: type and sector. The 'type' of business refers to the organization of labor in the enterprise: pure self-employment (70.5 per cent of the total sample), non-wage IPUs, in which workers (mainly family members) help the business owner without receiving a wage, and wage IPUs.
While the average age of the businesses is around 8.7 years, the median age is 3.7 years lower, indicating that there are many very young businesses in the sample, and a few (much) older ones. There are some striking differences across sectors. Textile, other industries, construction and service IPUs are much older on average than catering, food processing and trade businesses. The distribution of wage and non-wage IPUs also appears quite different across sectors. Self-employment is overrepresented in textile, services and transport but it represents less than half of food processing and catering businesses. In certain sectors, such as textile, trade and services, wage workers are almost non-existent. Mean monthly value added is 491 000 MGF (35e) while median value added is only 201 000 MGF (14e), indicating substantial heterogeneity across businesses. 7 This is even more visible in the value of the capital stock, whose distribution is strongly skewed to the right. The mean is over 2 600 000 MGF (189e) but the median is only 341 000 MGF (24e). There are a few businesses operating with a very high-capital stock, while the large majority own very little or no capital at all. In fact, 10 per cent of businesses operate with no physical capital whatsoever.
Although a large majority of businesses are purely self-employed owners operating with a low stock of physical capital, other types of informal businesses are also present in the informal sector. Size and performance indicators are quite variable, particularly across sectors of activity. Over time, this heterogeneity suggests that certain types of businesses may be able to grow and take advantage of favorable macroeconomic circumstances, whereas others would stagnate more. Changes that took place in the informal sector between 1995 and 2004 are examined in the following sections.

Informal Labor and Capital Dynamics: Descriptive Statistics
We first look at the distribution of employment by institutional sector over time ( Table 2) and define three large institutional sectors: the public sector, the formal private sector (including firms operating in EPZ) and the informal sector. Informal sector jobs are divided into two categories: dependent and independent. 8 The informal sector is the main job provider in Antananarivo, totaling more than one out of two jobs, and it seems to follow counter-cyclical dynamics. Reversing a previous process of informalization of the economy, its share steadily decreased between 1995 and 2001, from 57 to 53 per cent of total employment, and this drop was statistically significant after 1998. This drop occurred in a context of public administration and state enterprise downsizing, as part of the structural adjustment program. Therefore, in terms of employment, this process mainly benefited the private formal sector, in particular thanks to the rapid development of EPZs. The average annual growth rate of employment over the period was 27 per cent in EPZs but only 3 per cent in the informal sector (Cling et al, 2005). In Antananarivo this led to a tripling of the share of EPZs in total employment between 1995 and 2001, from 3 to more than 10 per cent, whereas the share of private formal sector jobs remained stagnant at 25 per cent.
However, within the informal sector, we also observe two opposite trends during this period: an increase in the share of independent informal jobs, and a sharp and statistically significant drop in the share of dependent informal jobs. Interestingly, in the period of strongest growth (1998)(1999)(2000)(2001), although dependent informal labor was absorbed in formal enterprises, the absolute number of enterprises continued to increase, more slowly than before, but still faster than the overall growth of the employed labor force (bottom panel of Table 2). This is in contrast with evidence presented by McPherson (2000) on the effect of structural adjustment in Zimbabwe. The retrenchment of civil servants led to an increase in informal sector employment characterized by a rise in the average size of firms. In the case of Madagascar, informal sector employment growth is extensive rather than intensive, as it happens mainly through the creation of new businesses rather than the expansion of employment in existing ones. In addition, a fraction of the fast growth in the number of informal businesses is explained by new entries on the labor market.
The 2002 crisis totally reversed the trend of employment formalization. Between 2001 and 2004, the informal sector reconquered its previous share of the labor market, increasing its share by 5 percentage points, and thus reaching a higher level than in 1995. Informal jobs absorbed both laid-off workers from closing formal enterprises and new entrants on the labor market, deprived of any alternative source of jobs. As the recovery in EPZs was fast, it lost only 1 percentage point of its share of employment over that 3-year period. 9 Recovery of other domestic formal enterprises seems to have been limited. Although both dependent and independent informal employment increased between 2001 and 2004, the growth in the number of informal entrepreneurs was much faster than the overall increase in the number of workers. In the period of crisis and the following recovery, the decrease in formal employment seems to have been mainly compensated by an increase in informal independent labor (its share in total employment increases from 34.2 to 38.5 per cent), rather than informal hired or family labor, suggesting that existing businesses were not able to absorb the surplus labor released by the formal sector, and most of these workers started an informal business.
Turning now to patterns of capital accumulation, Table 3 provides an estimation of the total capital stock of the informal sector by year as well as the average and median stock of capital of IPUs. 10 Overall, the informal sector accumulated capital between 1995 and 2001, and then stagnated. The average and median stock of capital with which IPUs operate increased quite strongly between 1995 and 1998 but subsequently dropped, reaching in 2004 a level inferior to its initial level. The increase in total capital during that period was therefore mainly due to the multiplication of the number of IPUs, another sign of extensive growth in the informal sector. Results shown in Table 3 are rather unexpected, because economic growth was strong until 2001, but we see capital accumulation only until 1998. This suggests that the global macroeconomic context did not completely integrate the informal sector, which seemed to stay outside of the growth process. In addition, we notice that the average stock of capital of firms in 1995 and 2004 was roughly the same. Figure 1 shows box plots of the stock of capital of IPUs disaggregated by type of firm and sector of activity. Whether self-employment, wage or non-wage, all types of IPUs had the same median capital stock in 1995 and 2004 with some differences in the intermediary years. Only non-wage IPUs increased their median capital stock after 1998, rather than after 1995. 11 Although we must be cautious when interpreting such intertemporal comparisons, due to price measurement issues when deflating the capital stock, it is striking to see that as a whole, the informal sector stagnated, and capital accumulation did not really happen. Informal sector growth appears to be extensive both in times of growth and crisis, with a continually expanding number of businesses that seem globally incapable of accumulating capital and creating jobs for workers other then the owner. Our data set provides information that supports this extensive growth pattern. For example, the share of households owning at least one IPU increased from 50 to 60 per cent between 1995 and 2004. Among owners, 21 per cent of households owned more than one IPU, and this share increased by 8 percentage points during the period (results not shown). The survey includes a question on the projected use of a loan if the entrepreneur could obtain one for his activity. A little less than half declared that they would invest it in the existing firm and about 40 per cent declared that they would rather start another business. Investing in a new enterprise rather than expanding an existing one is hence a common strategy.

Informal Business Growth and the Macro Environment Empirical Strategy
Descriptive statistics suggest that there is relative disconnection of the informal sector from the global macroeconomic context. Using data that span a much longer period than what previous studies on the same topic have used, a multivariate analysis of the determinants of small enterprise growth can help assess the role of the macroeconomic environment on growth. 12 This analysis can also provide evidence on which types of enterprises, and in particular which industry, have the most potential to grow. Even though our data set is made of repeated cross-sections, we can make use of retrospective data collected on the number of workers in the IPU when the business was set up. 13 Following previous work by McPherson (1996), we measure enterprise growth as the change in the number of workers over the life of the business. Although growth can be measured through sales or profit, we only have retrospective data on the number of workers at start-up, which is assumed to be somewhat correlated with growth in sales. 14 In addition, as we are interested in the dynamics of informal businesses from a job creation point of view, this is not an unsatisfactory measure. We define the dependent variable Growth j as the annual logarithmic change in employment between the year IPU j was surveyed (Tj ) and the year it was created (t 0 j ): Measuring growth in this manner is subject to several caveats. First, we only know the size of the enterprise at two points in time, at start-up and the year of the survey, which will hide any intermediary changes in the size of the unit. Second, it is a rather lumpy variable that cannot reflect the fact that an entrepreneur may intensify his own effort before actually hiring a new employee. 15 Evidence from developing countries (Cote d'Ivoire, Mexico) suggests that the growth pattern of microenterprises is consistent with the standard results from the theoretical literature on firm dynamics (Sleuwaegen and Goedhuys, 2002;Fajnzylber et al, 2006). We thus estimate the following standard firm growth equation, which is based on the 'learning' model developed by Jovanovic (1982): 16 The Agesize vector includes the logarithms of age and initial size of the IPU, with quadratic and interaction terms: lnAge, (lnAge) 2 , lnSize, (lnSize) 2 , (lnAge)×(lnSize). This specification allows for non-linearity in the effect of age and initial size on growth. The Owner vector is a set of the following owner characteristics: age when started firm, female, marital status, education and multiple IPU ownership in the household. Sector includes seven dummies indicating the sector of activity of the IPU.
Our variable of interest is GDP, defined as the log of the average annual GDP growth rate in Madagascar over the lifespan of the enterprise: where GDPgrowtht is the rate of growth of GDP in year t. 17 We make use of the temporal dimension of the data, which were collected in three different years, 1998, 2001 and 2004, to identify the effect of the macroeconomic context on enterprise growth since the birth of the enterprise and until the time of survey, net of the age effect. To account for possible heterogeneous effects, the model is also estimated with a set of interactions of the sector dummies and the GDP variable.
A potential bias in the estimates may arise from selective survival of firms, based on age or initial size. The size coefficient may be upward biased if small firms that experience negative growth have a higher rate of failure than larger firms. Unfortunately, we cannot control for the selection of failures because our data are retrospective, not longitudinal. While we should keep in mind that such a bias may exist, the fact that our data are representative cross-sections of all firms at a given point in time means that we are carrying out the analysis on a sample of survivors, which is of interest in itself. In addition, studies in other settings have found this bias to be insignificant (McPherson, 1996). Another bias linked to selective exit may arise from the fact that we do not observe informal businesses that have formalized. If these IPUs showed higher employment growth than those that remained informal, our model would underestimate the extent of firm growth and the size coefficient would be downward biased.
The model is estimated using Ordinary Least Squares (OLS) regressions run on the sample of enterprises younger than 20 years of age to reduce recall bias problems (thus dropping 10 per cent of the sample). We distinguish between IPUs that started as pure self-employment, which can only stagnate or grow, and those that started with two workers or more. Descriptive statistics show that the large majority of IPUs that started with only one worker did not grow at all, as only 12 per cent increased in size. The proportion of businesses with several workers at start-up that expanded is also around 12 per cent, whereas contraction is much more frequent, close to 21 per cent (results not shown). Table 4 presents summarized results, showing the sector and GDP growth variables and interactions and the partial derivatives of the age and size variables, evaluated at the sample mean. 18 Consistent with theoretical predictions (Jovanovic, 1982), age and initial size both have a strong negative effect on growth. In the sample of IPUs with two or more workers at start-up, we see that the size-growth negative relationship holds, although it is weaker than in the full sample, but the effect of age on growth becomes positive: as they grow older, IPUs that started 'large' experience a growth rate that does not slow down as fast as for smaller firms. 19 We again find a strong negative relationship between age and growth among IPUs that started with one worker.

Results
Catering, other industrial activities and food processing experienced employment growth. These appear to be sectors with a high growth potential, which obey more an entrepreneurial Informal sector dynamics in times of fragile growth 445 rather than a survivalist logic. Food processing is in fact the only dynamic sector both in terms of employment growth and mean capital accumulation. 20 Service and transport activities have a negative impact on the growth of businesses. Service activities are the worst-performing sectors in terms of value added, which potentially explains their slow growth, but transport businesses have a high average value added and capital stock (see Table 1). However, entrepreneurs in the transport sector are mostly drivers of their vehicles (taxi drivers, rickshaw drivers and cart pullers), which is an intrinsically individual activity, and hiring staff would require very large and often unaffordable investments, such as buying a new vehicle. In the full sample regression, the variable proxying the macroeconomic environment during the life of the enterprise has a positive and significant effect at the 10 per cent level. Enterprises that experienced a higher average GDP growth rate since their birth grew faster than others, whereas a more recessive or stagnant environment would then imply a slower growth. In the full sample, the mean of the variable of interest, GDPj , is 3.18, and the average enterprise annual growth rate is 1.5 per cent. A 10 per cent increase in the average GDP growth rate (from 3.18 to 3.5 per cent) would yield an increase in the annual IPU growth rate of 0.7 percentage points. At that rate, an IPU starting with 2 workers would grow to 3 workers in approximately 8 years, rather than 12.
The set of interactions of the sector dummies and the GDP growth variable are jointly significant at the 5 per cent level, suggesting that the effect of the macroeconomic context is heterogeneous across sectors. Only the catering sector interaction has a stronger positive impact than the reference sector, with a total effect significant at the 10 per cent level. Service IPUs seem to follow a counter-cyclical trend, as the sign of the coefficient is negative and the total effect is significant at the 1 per cent level, indicating that they perform a labor-absorbing function during recession and contract in times of macroeconomic growth. As shown in the descriptive statistics (Table 1), services to households and firms operate with very little physical capital and are mostly owner-only operated. These businesses are able to absorb excess labor because no extra capital is needed by worker. In periods of growth, the workforce can then be easily reduced without leaving capital idle. Such IPUs will quickly shrink in size when there is more employment elsewhere, suggesting that the jobs they offer in times of stagnation correspond to queuing jobs.
In the sample of IPUs that started with two or more workers, we no longer have an effect of the average GDP growth rate, and the sector×GDP interactions are not globally contributive to the model, as indicated by the F-test. However, we can note again counter-cyclical dynamics in the service sector, as well as in transport and construction, the latter being the only significant total effect. As for services, this counter-cyclical effect in construction can also be explained by the labor-intensive functioning of these activities, which can easily use more labor (even if it is not very productive).
Among IPUs that were owner-only operated at start-up, the GDP growth variable has a strong positive effect on enterprise growth, significant at the 1 per cent level, indicating that businesses that started out as pure self-employment were pulling the effect of the macroeconomic context in the full sample regression. Once again, the catering sector benefits the most from growth (or suffers the most during economic recession).
The GDPj variable used in the regressions as a proxy for the global macroeconomic context during the life of the business is an average growth rate. As it is very aggregate in nature, it may hide quite different overall economic dynamics for the same average figure. 21 To address this issue, we refine Specification (1) by introducing a measure of the volatility of GDP growth. Volatility is measured by the standard deviation of GDP growth between the survey year and the birth year of the enterprise. For the full sample and the sub-sample of IPUs that started as owner-only units, results are robust to the addition of this variable, which is not significant (Table 5). Volatility has a significant positive effect on growth of IPUs that started with two workers or more, with the GDP growth variable still non-significant. This suggests a survival effect, as faster-growing, larger enterprises at start-up had better resistancer to large changes in the economy, such as the crisis. This would cause these enterprises to be overrepresented in the data, and explain this positive effect of volatility on their growth. Finally, we include a variable measuring the number of years the IPU experienced a positive GPD growth rate, as a ratio of its age. The effect of this variable is significant only for businesses that started with one worker, for which it is positive (Table 5).

Returns to Capital in the Informal Sector Empirical Strategy
The global macroeconomic context of growth during the 1995-2001 period does not seem to have triggered a more intensive growth process in the informal sector, which mainly continued to grow at the extensive margin. Such a finding of stagnation would be consistent with the hypothesis of extremely low returns to capital in very small-scale activities in developing countries. We seek evidence of the existence of such poverty traps by estimating production functions to analyze returns to capital, using the four cross-sections of data available. Unfortunately, there is no retrospective information on capital accumulation and value added that would enable us to analyze returns to additional investments within each IPU. We therefore have to rely on cross-sectional data to infer these returns.
Let VA j be the monthly value added of IPU j. We estimate the following Cobb-Douglas production function with two factors, capital (Kj) and labor (Lj): Labor is the total monthly number of hours worked by the owner and paid and unpaid workers. Capital is defined, as before, as the total replacement value of all the equipment of the firm. HCij is a set of human capital variables and other owner characteristics (sex, education, experience, age, marital status). IPUij is a set of IPU characteristics, including seven sector dummies and the age and age squared of the IPU. Yearij is a set of three variables indicating the survey year, with 1995 as the reference.
As we wish to test whether informal firms exhibit patterns of decreasing returns consistent with neo-classical theory or, on the contrary, whether poverty traps appear, we follow work by Grimm et al (2011) and estimate the production function on the entire pooled sample and on subsamples of capital stock, defined by the quartile of capital stock to which the IPU belongs. 22 Notes: OLS regression results, *P<0.1, **P<0.05 and ***P<0.01; robust standard errors in parentheses adjusted for clustering at the household level; controls not shown: initial size, characteristics of owner, sector indicators.
We further divide the sample by size (one or more workers) and sector to take the heterogeneity of the informal sector into account. Changes in marginal returns over time are considered by adding year×capital and year×labor interaction terms to the list of regressors.
In Equation (2), β 2 is the elasticity of value added with respect to capital. Marginal returns to capital (MRK) are obtained by multiplying the estimated elasticity by the mean average product of capital in the sample over which the estimation is run: Let us now discuss a few econometric problems common to the estimation of production functions. Although the available data limit what can be done to correct some of these issues, we attempt to present how they might bias the coefficients in the production function. A common issue that arises when using microenterprise survey data is the potential underreporting by the respondent of both profits and capital. However, the effects found at low levels of capital in the next section are strong enough to mitigate the concern that this would bias the estimated coefficient of returns to capital toward zero. In addition, we think there is little reason to assume that respondents would underestimate more the value of their equipment at low levels of capital stock than for high levels of capital. 23 Another problem is the simultaneity of the level of observed inputs and output. Labor and capital are chosen by the entrepreneur and may be correlated with an unobserved productivity shock or an unobserved input, such as managerial ability of the owner. The estimated coefficients of the input variables can therefore be biased upward, in particular labor, which is more flexible than capital and thus more easily adjusted following a shock. In the same vein, an upward bias will be caused by reverse causality between the level of profit and capital. We cannot appropriately tackle this issue with the data at hand, as correcting this bias usually requires instrumenting with input prices or using panel data (Ackerberg et al, 2007).
A third common problem in the estimation of production function is endogenous exit, which introduces a selection bias, an issue that we discussed in the analysis of the determinants of growth. As smaller firms are known to be more vulnerable than larger ones, surviving small firms are likely to be selected and have high levels of outputs. This would tend to bias downward the capital stock coefficient (Ackerberg et al, 2007).
Finally, we consider specification issues. First, IPUs operating with no capital or who have a zero (or negative) value added are excluded from the regression, because these variables are expressed in logarithms. As this could bias the coefficient of the capital variable, we also estimated a modified equation that allows the inclusion of enterprises operating with no capital. Following Battese (1997), in this specification a dummy variable equal to 1 if the IPU runs with zero capital is included and lnK j is modified to be equal to 0 when the zero capital dummy equals 1 (instead of being a missing value). Second, as the Cobb-Douglas production function imposes strong constraints on the technology, we also estimated a translog specification that allows a more flexible functional form. Results were very robust to these changes and are not presented here. Table 6 reports the capital and year coefficients estimated on the full sample and on the four quartiles of capital stock separately. The marginal returns to capital are shown at the bottom of the tables. The time dummies indicate that the increase in value added over the entire period was significant, but, although value added remained higher in 2004 than initially, the difference between the 2001 and the 2004 dummy coefficients is not significant. This result is in line with a crisis effect that slowed down the progress in income and profits in the informal economy. This is true for all quartiles but the third, which is the only one that experienced a significant increase between these 2 years. In fact, in the highest segment of capital stock, value added was lower in 2004 than in 2001. 24 We find an estimated elasticity of capital of 15 per cent, lying between 9 and 35 per cent across quartiles. As shown in the first column of Table 6, the implied marginal returns to capital are 2.5 per cent. However, at low levels of capital, they are much higher, equal to 119 per cent. An 'average' entrepreneur, operating with a stock of capital of 32 000 MGF (2.3e) and realizing a monthly value added of 2 48 000 MGF (18e) would increase his monthly value added by 11 900 MGF (0.86e) if the equivalent of 10 000 MGF (0.73e) were invested in the IPU. The estimated elasticity in the second quartile of capital stock is lower (9 per cent), and the marginal returns are almost 10 times lower. Although the estimated production elasticities are higher above the median of the distribution of capital, implied marginal returns are, with 6.8 per cent and 2.8 per cent for the third and fourth quartiles, respectively, substantially lower than in the lowest segment of the capital distribution.

Results
The sharp drop in returns as we move up the distribution of capital is due to the very strongly decreasing average product of capital. Decreasing returns to capital contradict the standard theory of poverty traps, but are in line with findings from other studies on Africa, Latin America and Asia. We should hence reconsider poverty traps as an explanation of stagnation at subsistence levels for a large share of entrepreneurs. High returns indicate that there is a growth potential, as a small entrepreneur reinvesting part of his gains would reap larger profits, relative to the investment made.
We now look at returns to capital by type of IPU and sector to assess whether this pattern of decreasing returns emerges in every segment of the sector. Table 7 shows the marginal returns to capital calculated using the estimated elasticities from the regressions run on separate size sub-samples (full regressions not shown). We find very high returns to capital (114 per cent) in   the smallest IPUs (owner-only), but these returns are even more sharply decreasing than in the full sample, dropping in the second quartile to 5 per cent only. In IPUs with two or more workers, the pattern is different: returns are not as high in the lowest segment, and are actually increasing between the first and the second quartile. Even in the third quartile, returns remain quite high, over 20 per cent, and only in the highest quartile are returns very low. The relationship between capital and value added in these enterprises is somewhat flatter than in the smallest IPUs, suggesting that in this category of businesses, capital seems to be allocated in a more efficient manner than in the smallest businesses, where returns are extremely heterogeneous. Table 7 also presents marginal returns implied from the sector sub-sample regressions. 25 We find for all sectors the same pattern of decreasing returns to capital. Construction exhibits very high returns overall (25 per cent), followed by catering (8 per cent). We find for the other sectors similar returns to the pooled estimation, around 2-3 per cent. In the least capitalintensive segment, construction and trade have the highest returns, but all sectors exhibit returns above 50 per cent. In the higher segments, returns are very low, and nil in capitalintensive trade firms. What we concluded above for the informal sector as a whole is hence confirmed at the sectoral level: strongly decreasing returns to capital lead to a rejection of the poverty trap hypothesis.
We now discuss the change in marginal returns to capital over time, looking at the results of the regression augmented with capital×year interactions (Table 8). We note that the marginal returns to capital are remarkably stable over time (between 2 and 2.6 per cent). With a few exceptions, in each year, returns to capital roughly follow the same pattern of strongly decreasing returns to capital. In 1998, returns to capital start out much lower than in the other years (35 per cent), due both to a lower elasticity and a higher average stock of capital in the lowest quartile (leading to a lower average productivity of capital). In 2001, an odd pattern emerges in the second quartile, which presents negative returns, due to a negative elasticity of value added with respect to capital.

Conclusion
Little is known about the dynamics of the informal sector in times of growth and crisis in developing countries. This article is an attempt to analyze in detail how the informal sector changed over time, and whether or not it benefited from growth. The context we have chosen, Madagascar between 1995 and 2004, is particularly interesting because it refers to a period of fragile growth, characterizing many African countries today. A first aggregate approach of the informal sector shows that the informal labor market followed a counter-cyclical dynamic, shrinking during growth and absorbing excess labor in crisis. Within the informal sector, however, independent employment increased throughout the entire period. In other words, informal business creation was a major trend both during the first period of positive macroeconomic context and during crisis and recovery. Studying growth at the level of the IPU shows a large amount of stagnation as most enterprises remained very small. In addition, capital accumulation was slow and enterprises mostly operated with little physical capital. Only the smallest, owner-operated enterprises expanded in accordance with the macroeconomic context, while in larger IPUs, growth appears somewhat disconnected from the context. The situation, however, is quite heterogeneous. Some activities appeared counter-cyclical, expanding during crisis and shrinking during growth.
The analysis of such a rich data set reveals many different dynamics, by sector or size, and the heterogeneous character of the sector. However, it appears that growth in the informal sector was mostly extensive, with little job creation or capital accumulation. Although such a situation would be consistent with the existence of poverty traps, estimates of marginal returns to capital tend to reject this hypothesis. On the contrary, with decreasing returns to capital, the informal sector actually exhibits patterns consistent with the neo-classical theory of the firm. An efficient allocation of capital should then direct investment toward the smallest enterprises to reap the gains of these high returns to capital. One question that therefore remains to be answered is: Why are microentrepreneurs not reinvesting their gains in their business if returns are so high at low levels of capital? First, it may be rational for the entrepreneur to stay small and invest his gains to create a new business, thus benefiting from the high returns to capital in very small units. Second, the entrepreneur faces a number of constraints that may explain a behavior different from what would be expected from a rational investor. Capital market imperfections and high risks in conjunction with risk aversion are likely to be important causes of this inefficient capital allocation. Another possibility is that the entrepreneur would rather keep his business small to stay completely in control, rather than hire labor, which could entail high supervision costs. Notes period will be very different from the previous period output. This yields negative age-growth and age-size relationships (Jovanovic, 1982). 17. Source of the GDP growth data: World Development Indicators, the World Bank. 18. Because of lack of space, coefficients of the other control variables are not discussed here. Full results are available upon request. 19. This was suggested by the positive and significant age×size interaction variable coefficient in the full sample regression (not shown). 20. Capital accumulation by sector not shown to save space. 21. However, the magnitude of the negative GDP growth rate in 2002 is sufficient to influence the average for IPUs that experienced the crisis. 22. To avoid composition effects that may be a problem with repeated cross-sections, we defined the quartiles separately for each year. 23. In all regressions, we drop influential outliers from our sample (and sub-samples) that we identify using the DFITS-statistics (Belsley et al, 2004). Applying this procedure, we lose about 5 per cent of the observations. 24. To save space, other controls are not discussed but have the expected sign. In particular, female entrepreneurs are less productive than their male counterparts. The gender performance gap is analyzed extensively in Nordman and Vaillant (2014). Full results are available upon request from the authors. 25. Food processing and other industries are aggregated in a single sector to ensure that the sample size is large enough to obtain a reliable estimate. Given small sample sizes, returns are not estimated in the third and fourth quartiles of capital for the construction sector, nor are they in the first quartile for catering. We do not run this regression on the transport sector, in which capital stock is mostly vehicles and therefore very high and lumpy.