Katharina Wrohlich
email: kwrohlich@diw.de

Empirical Analysis < D1 -Household Behavior and Family Economics < D -Microeconomics

Keywords: child care, excess demand, partial observability model child care, excess demand, partial observability model JEL Classification: J13, C35, D12 child care, excess demand, partial observability model JEL Classification: J13, C35, D12

The extension of publicly provided or subsidized child care is currently one of the priorities of the political agenda in many European countries. In this paper the excess demand for subsidized child care slots in Germany is estimated using a partial observability model. The results show that there is considerable excess demand for child care for children aged less than three years in east and west Germany, even among children with working mothers.

Introduction

Providing suitable child care services has become an important political objective in many European countries. While child care policy has long been a neglected issue, policy makers now see subsidized child care as a multiple-purpose policy instrument that is hoped to affect mothers' labor force participation, fertility and educational outcomes. The importance of child care has also been recognised on the level of the European Union. At the Barcelona summit of the European Council in 2002, EU member states agreed upon harmonized child care targets: By 2010, member states shall be providing child care to at least 90 percent of children between three years and mandatory school age and at least 33 percent of children under three years of age, "taking into account the demand for child care facilities and in line with national patterns of provision". 1 While several countries in the EU already fulfil these targets, many continental and southern European countries are falling behind, as can be seen from Figure 1. Germany is also among these countries. However, the German case is somewhat special: while the provision of child care is high in all parts of east Germany, provision of child care for children below three years in west Germany is among the lowest in Europe. Recently, the German government has introduced legislations that aim at a "demand-oriented" extension of subsidized child care in Germany, especially for children under the age of three years.

[Figure 1 about here] On the European, as well as on the national level, there seems to be the political goal of extending subsidized child care in order to meet the demand. In the 1 See [START_REF] Plantenga | Investing in childcare. The Barcelona childcare targets and the European social model[END_REF]. 3 presence of rationing, however, estimating demand for child care is not trivial. For Germany, micro level data sets with information on explanatory variables necessary to estimate demand for child care, such as the Labour Force Survey (Mikrozensus) or the Socio-Economic Panel (SOEP), only include information on child care utilization, not on child care demand. It is known whether a child is in a child care facility, but if this is not the case, one does not know whether this is because his or her parents did not want the child to attend a child care facility, or whether they applied for a slot but were not offered one. To identify demand and supply of child care services, partial observability models such as those introduced by [START_REF] Poirier | Partial Observability in Bivariate Probit Models[END_REF] and [START_REF] Abowd | Job Queues and the Union Status of Workers[END_REF] and applied to the context of child care in the UK by [START_REF] Chevalier | The Supply of Childcare in Britain: Do Mothers Queue for Childcare?[END_REF] can be used. These models allow estimating the demand for and supply of child care even when only the joint outcome of these two variables, namely child care utilization, is observed.

For the purpose of estimating demand for child care in Germany, I will use a model that combines the advantages of the model by [START_REF] Poirier | Partial Observability in Bivariate Probit Models[END_REF] and the [START_REF] Abowd | Job Queues and the Union Status of Workers[END_REF] model. Since it is known that, for institutional reasons, certain children are not restricted in their access to child care facilities, the sample can be divided into two parts: first, observations which are not restricted and secondly observations which might be restricted. Thus, the estimation of demand and supply of child care slots is based on a likelihood function that consists of two parts, a univariate probit of the demand for child care for the unrestricted part and a bivariate probit of demand and supply of child care for the possibly restricted part of the sample.

Estimation results show that among children aged up to three, a large fraction of children are queuing for child care (24 percent in west Germany and 59 percent in east Germany), i.e. their parents demand a child care slot but are not offered one. 4 Even though availability of child care is higher in east than in west Germany, the excess demand for child care is larger in east Germany since the demand for child care is well above the national average in these regions. For children between three and six years, access restrictions to child care do not seem to be a major problem.

The reminder of the paper is organized as follows: The next section provides some stylized facts on utilization and availability of child care and a short description of the child care "market" in Germany. Section 3 gives a short overview of the relevant literature. In Section 4 the details of the econometric model are presented, while Section 5 describes the data. In Section 6, the estimation results are presented, Section 7 summarizes and concludes.

Stylized Facts and Institutional Setting

Official statistics show that in Germany, availability of child care, usually measured as slots per 100 children in a certain age group, differs between regions and age groups (see Table 1). Overall, availability of child care is much higher in east than in west Germany, especially for the younger age group. This is due to the fact that women's employment (including mothers' employment) was strongly encouraged in the former German Democratic Republic, whereas in west Germany, policy discouraged mothers from working. 2 Given the data on child care availability, it is not surprising that also child care utilization differs considerably between east and west Germany and between children younger than three years and children between three years and school age. 3 2 See [START_REF] Rosenfeld | Gender and Work in Germany: Before and After Reunification[END_REF] for a detailed description of women's employment patterns in the two German states before reunification. 3 Official statistics show that on average, there are 3 slots available for 100 children under the age of three. On the other hand, 6 percent of all households with children under three years in the SOEP report that their child is in a child care facility. This difference might be due to the fact that some facilities take more children than they are officially allowed to. Another explantion would be that some children are in a form of child care that is "instiutional" but not counted by official statistics. The same pattern applies to the employment rates of mothers. 4 Employment among mothers in east Germany is higher than employment among mothers in west Germany, and employment increases with the age of the child.

[Table 1 about here] Another interesting fact is that the correlation between maternal employment and child care utilization in Germany is not as strong as it could be expected. Among all children aged between three and six who are in a child care facility, only about 40 percent have working mothers. The figure is somewhat higher (about 60 percent) for children under three years using child care services. In general, the relatively low employment rate of German mothers can be related to the negative work incentives that result from joint income taxation (see [START_REF] Steiner | Household Taxation, Income Splitting and Labor Supply Incentives -A Microsimulation Study for Germany[END_REF]) and the generous parental leave scheme (see [START_REF] Lauer | Employment of Mothers after Childbirth: A French-German Comparison[END_REF]). The relatively low employment rate of mothers with children in child care institutions is more puzzling and could be explained by the fact that in west Germany, child care, especially parttime care for children aged between three and six years, is primarily seen as preschool education and not necessarily as a means to facilitate mothers' employment.

On the other hand, 17 percent of all children under three, who are not in child care, have working mothers. It is to be assumed that in this case some sort of informal This might particularly be the case in the growing sector of family day care, which is increasingly also subsidized by communities but not counted as slots in child care facilities in the official statistics. Note that child care by private babysitters or childminders is not counted as "in child care" in this table. The "market" for formal child care is highly regulated in Germany. 5 Formal child care is highly subsidized, such that parents' fees only cover about 25 percent of the total costs. Parents' fees are charged according to the parents' income. Admission to child care institutions is regulated through the communities. The usual practice is to favour children with working parents, children with single mothers and children with older siblings who are in the same institution.

In addition to public or private facilities, child care by nannies or childminders is also used, especially for children under the age of three. This sector has traditionally been almost exclusively privately organized, and official statistics about the amount of utilization of child minding in terms of children or hours, as well as on the cost structure, are not available. Estimations based on surveys give utilization of full-time babysitters or child minders of about 4% of all children under the age of three. The costs of child care by a childminder are much higher than in a child care facility, and amount to about 690 Euro per month (Jurczyk et al. 2004). In contrast, parents' fees for a full-time slot in a subsidized child care facility amount to 110 Euro on average. The highest fee reported by parents in the SOEP wave 2002 amounts to 400 Euro per month.

Given that this private market for child care in the form of child minding exists, excess demand for child care really means excess demand for child care at the subsidized price, i.e. in subsidized child care facilities. Considering the large difference between the market price for child care and the parents' fees for a subsidized child care slot, it is not surprising that parents prefer to queue for a subsidized child care slot instead of buying private child care on the market, since the

Literature Review

The demand for child care has already been subject of numerous international studies. There exists a large literature on the demand for child care in the United States and Canada (see, among others, [START_REF] Connelly | Marital Status and Full-time/part-time Work Status in Child Care Choices[END_REF], as well as [START_REF] Joesch | The demand for nonrelative child care among families with infants and toddlers: A double-hurdle approach[END_REF], who provide a detailed literature review), and more recently also for other countries. 8 In most of these studies, demand for child care and labour supply decisions of mothers is estimated simultaneously. Some other studies focus on special characteristics of the demand for child care. For example, Joesch and Hiedemann ( 2002) estimate the demand for child care using a double-hurdle model in order to separate different reasons for zero child care consumption in the US. While they differentiate between zero consumption due to high costs and zero consumption because parents are not interested in non-relative child care regardless of the cost, access restrictions to child care are not modelled as a reason for zero consumption. Access restrictions are explicitly modelled by [START_REF] Chevalier | The Supply of Childcare in Britain: Do Mothers Queue for Childcare?[END_REF] in a study of the demand for child care in the UK. The authors use a partial observability model in the style of Porier (1980) in order to separate demand and supply of child care. They find evidence for considerable excess demand for child care in the UK. 6 There might of course be also other reasons why parents prefer institutional child care over the private sector, for example if they expect the child care quality to be higher in the institutional sector. However, due to lack of data, quality issues are not taken into account in my analysis. 7 The question of why an excess demand exists in the child care market, and whether the supply of child care is endogenous with respect to mothers' employment rates is not analyzed in this paper. Stutzer and Duersteler (2005) provide an interesting investigation of this question for the case of Switzerland.

8 See e.g. [START_REF] Choné | Female Labor Supply and Child Care in France[END_REF] for France, Del [START_REF] Boca | Child Care Choices by Italian Households[END_REF] for Italy, Kornstad and Thorensen (2006) for Norway, [START_REF] Lokshin | Household Childcare Choices and Women's Work Behavior in Russia[END_REF] for Russia. As far as Germany is concerned, the empirical literature on the demand for child care is rather limited. 9 An early study by [START_REF] Merkle | Frauenerwerbstätigkeit und Kinderbetreuung. Eine theoretische und empirische Analyse für die Bundesrepublik Deutschland[END_REF], who uses data from the SOEP, estimates price elasticities for child care demand. [START_REF] Ondrich | Care of Children in a Low Fertility Setting: Transitions between Home and Market Care for Pre-School Children in Germany[END_REF] analyze the determinants of the transition from home to institutional child care in Germany. [START_REF] Büchel | Form der Kinderbetreuung und Arbeitsmarktverhalten von Müttern in West-und Ostdeutschland[END_REF] estimate the effects of socio-economic variables such as education and income as well as parents' ethnicity on the utilization of child care on basis of the SOEP. Although e.g. [START_REF] Merkle | Frauenerwerbstätigkeit und Kinderbetreuung. Eine theoretische und empirische Analyse für die Bundesrepublik Deutschland[END_REF] and Ondrich and Spieß (1998) "control" for rationing of child care slots in the demand estimation by introducing the availability of child care slots on a regional level as a control variable, these studies are either based on the assumption that observed child care utilization can be interpreted as demand or explicitly state that effects on child care utilization are estimated. In the latter case, these studies have no implication concerning the demand for child care.

Econometric Model

The data set I use for estimation contains information about the child care status of the child, i.e. it is known if a child is in a child care facility or not. If a child is not in a child care facility, this can be the case because (i) the parents do not want the child to be in a child care facility, or (ii) because the parents applied for a child care slot but were not offered a slot. This implies that the observed variable "child care status" is in fact the joint outcome of two unobserved variables, namely the demand for child care and the supply of child care slots. In order to calculate the size of the queue for subsidized child care, a model has to be estimated that allows to predict the probability that a child is not given a child care slot (supply = 0), although the parents want the child to be cared for in a facility (demand = 1). On the basis of 9 A detailed literature survey on German studies can be found in [START_REF] Büchel | Form der Kinderbetreuung und Arbeitsmarktverhalten von Müttern in West-und Ostdeutschland[END_REF]. Formally, the model can be stated as follows: The latent variable demand for child care D* depends on child and household characteristics X D and a stochastic part

D , * D D D D X = + (1)
where D is a vector of coefficients. It will be assumed that parents will have realized demand if D* is above a certain threshold, which is set to zero for convenience,

1 if * 0 D D = > . (2)
Therefore, the probability that parents demand institutional child care can be stated as Pr( 1) Pr( )

D D D D X = = > . (3)
Further, it is assumed that parents are offered a child care slot according to some household, child and regional characteristics X S , a vector of coefficients S and a stochastic error term

( ) ( ) 1 2 2 , ; 1 , ; C C D D S S D D S S L X X X X = (8)
where 2 denotes the bivariate normal cumulative distribution function.

This model was used for a joint estimation of demand and supply of child care slots in the UK by [START_REF] Chevalier | The Supply of Childcare in Britain: Do Mothers Queue for Childcare?[END_REF]. In the German case, however, some children are not restricted in their access to child care services. Children who have already been in a child care facility the year before do not have to queue again for a slot in the current year. The data set I use (SOEP) is a panel study, thus information on last year's child care status is available. Secondly, I will assume that

( ) ( ) ( ) ( ) { } 1 1 1 2 2 0 1 , ; 1 , ; C C D D D D NR C C D D S S D D S S NR L X X X X X X = = = (9),
where NR=1 denotes the unrestricted sample and NR=0 denotes the possibly restricted sample.11 Note that identification of the model stated in equation ( 9) is based on exclusion restrictions as well as the estimation of a univariate probit for the unrestricted part of the sample.

Apart from the coefficients, I am particularly interested in the probability that demand equals 1, but supply equals 0, i.e.

( )

Pr 1 0 D S = = .
When grossed up to the population total, this can be interpreted as excess demand for subsidized child care in Germany. The variables used in both the demand (X D ) and the supply equation (X S ), are the age of the child, the mother's marital status and number of siblings in child care facilities. Mother's nationality is also included in both equations, since both, demand patterns as well as the ability to overcome the access restrictions to subsidized child care may differ between Germans and non-German citizens.

The variables that are included in the demand equation only are mother's education, as measured by two dummy-variables indicating high-school degree and university degree. The variable indicating university degree is also interacted with a dummy variable indicating that the child is under the age of three, since high skill mothers may wish to enter the labour market earlier and therefore demand a child care slot earlier than lower skilled mothers. Further, a hypothetical net household income is used that measures net household income in the case that the mother is not working. This income is calculated on the basis of the tax-benefit simulation model STSM (see Steiner et al. 2005) and contains the household's capital income, income from rent and lease and the earned incomes of other household members as well as public transfers such as social assistance, if the household is eligible. This hypothetical net income is used rather than the actual household income, since actual income is potentially endogenous (the decision of the mother to work might be correlated with demand for child care slots). I also think that it is more appropriate to use the hypothetical net household income rather than the actual "other income" (i.e.

husband's labor income, social transfers, income from capital, rent and lease etc.).

Under the German tax-transfer regulations, which include joint taxation of married couples and many means-tested benefits on the household level, the level of "other income" is also influenced by the mother's employment decision.

A dummy variable indicating frequent church attendance of the mother is also used as a variable that possibly captures attitudes towards non-parental child care. In addition to these mother's characteristics and income variables, some variables on household composition are also included in the estimation of the demand equation, such as number of siblings in certain age groups and the presence of another adult household member besides the parents.

In the supply equation, the number of child care slots per child available at the county level is used as an additional explanatory variable. This variable is available for each of the 440 counties and for two different age groups, namely for children under the age of three and for children aged between three and school age.

Chevalier and Viitanen ( 2004) also use the average price for a child care facility at the regional level for identification of the demand equation. For the case of Germany, this variable cannot be used. Official data on prices at the regional level do not exist since facilities are not required to report the prices they charge. However, even if data on parents' fees were available, it would not be possible to include them as explanatory variable in the estimation of the demand equation due to endogeneity problems. This is because the parents' fees depend on the family's income, which is determined by employment of both parents. As has been argued before, mothers' labor force participation is endogenous. Thus, in the German context, it is not possible to control for prices in the demand equation.

Data and Variables

The model described in the section above will be estimated on the basis of data from the German Socio-Economic Panel (SOEP) from the year 2002. The SOEP is a representative panel study of private households living in Germany. 12 While the SOEP usually contains only basic information on child care utilization, the 2002 wave provides detailed information on child care utilization, type of facility, child 12 For more information on the SOEP, see http://www.diw.de/english/sop/. As already mentioned in the section above, for the estimation of the model, regional information on the county level is matched to the individual data. 13 Child care availability ratios (child care slots per child in each county) for two different age groups are matched to the individual child information from the SOEP. These data were provided by the German Youth Institute (Deutsches Jugendinstitut DJI). 14 Additionally, data on the spatial structure of the counties are matched to the individual data using variables from the INKAR data set provided by the Federal Office for Building and Regional Planning (Bundesamt für Bauwesen und Raumordnung). 15 In this data set, all 440 German counties are classified into 1 out of 9 spatial structure types, depending on population density and distance to the next urban centre. Tables 2 and3 provide detailed information on sample size, definitions and descriptive statistics on the variables used in the estimated model.

[Table 2 about here]

[Table 3 about here]

Estimation Results

Table 4 presents the coefficients of the estimated model. All coefficients -if significant -have the expected sign. The demand for child care is positively influenced by the age of the child, by the simulated net household income and the number of siblings who are attending child care facilities. More educated mothers demand more child care for their children, although the coefficient for "mother 13 I thank DIW Berlin for the special permission to use the regional code number at the county level. 14 I would like to thank H. Bayer from the Deutsches Jugendinstitut for the provision of this data. 15 For more information on these data, see Bundesamt für Bauwesen und [START_REF] Raumordnung | Aktuelle Daten zur Entwicklung der Städte, Kreise und Gemeinden[END_REF]. 15 holding a university degree" is significant only for children under three years. 16 The mother's nationality does not influence the demand for child care, however the frequency of her church attendance has a significantly negative effect on the demand for child care. The same is true for the number of siblings and the presence of another adult household member apart from the parents. While the size of the city does not have a significant effect on the demand for child care, living in east Germany leads to a significantly higher demand than living west Germany.

In the supply equation, the availability of child care slots on the county level has a positive influence on the individual probability of being offered a child care slot. The age of the child also has a positive effect. The mother's marital status does not influence the probability of being offered a slot. This is also true for the number of siblings already in child care. However, the mother's nationality does affect the probability of being offered a child care slot: German mothers are more likely to have access to child care services than non-German mothers. This might either be an indication for discrimination by the providers of child care services, or for the fact that for non German parents, it might be more difficult to overcome access restrictions to child care due to communication problems, lack of knowledge concerning official or unofficial channels, etc. Neither the regional variables nor the variable indicating rural area are statistically significant. This is not surprising since differences in the provision of child care slots are already captured by the 'availability of child care slots' variable. The correlation coefficient of the error terms of the demand and supply equations (rho) is positive yet not significant.

[Table 4 about here] 16 This result is not surprising since child care utilization for children older than three years is common in Germany even for children with non-working mothers (see section 2). In order to asses the predictive quality of the estimated model, I compare actual and predicted values of child care utilization. The predicted value is coded as 1 if the predicted probability is higher than 0.5. The model performs well in predicting the joint outcome of child care demand and supply. As Table 5 shows, 90 percent of all observations are predicted correctly according to this rule. For comparison, a model that explains the left-hand side variable by a constant only would predict 54 percent of all cases correctly.

Estimations from the partial observability model allow to predict the marginal probabilities of demand for and supply of child care slots. Table 5 shows these marginal probabilities by regions and age groups. For all age groups, demand for a child care slot is lower in west than in east Germany. The predicted probabilities of supply of child care slots come close to the official statistics on availability.

However, especially for children younger than three years living in west Germany, the marginal probability of being offered a slot is higher than the official availability ratio. This might be explained by the fact that child care facilities are willing to take more than one child per slot and that -at least in some regions -there might actually be more slots available within the family day care system than reported by official statistics.

[Table 5 about here]

The joint probability that parents demand child care for a child but are not offered a slot gives the individual probability of being rationed. These probabilities are presented in Table 6 by age group and region. Although availability of child care slots is much higher in east than in west Germany for children in the younger age group, excess demand for child care is more prevalent in the east. This result is surprising yet can be explained by the fact that not only the supply but also the demand for child care in east Germany is well above the level in west Germany. For children in the older age group, access restrictions to child care seem to be only a minor problem. 17

[Table 6 about here]

As Table 6 shows, excess demand for child care is quite large for children in the younger age group even when only the sample of children with working mothers is considered. Since employment status of the mother is not included as an explanatory variable, these numbers have to be seen as an upper bound for the excess demand for subsidized child care of children with working mothers. Usually, in Germany child care facilities favour children with working mothers; this effect could not be explicitly taken into account in the empirical analysis.

The total size of the queue for child care slots in numbers of children is shown in Table 7. In total, parents of more than 600,000 children up to the age of three years demand subsidized child care but are not offered a slot. Most of these children have non-working mothers, as is shown in Table 8. However, more than 200,000 slots would be needed only for children of employed mothers, including those with mothers in marginal employment. Another 20,000 children who are queuing have mothers who state that they intend to start working "as soon as possible". 18 Note that these numbers are probably the lower-bound of mothers with small children stating that they wish to work in the near future, since they are not 17 It should be noted, however, that rationing of child care services has more than one dimension: in addition to access restrictions to child care services, short opening hours, e.g. only in the morning, also poses a problem in many regions of Germany. This is particularly true for children between three and six years. This dimension of rationing has not been studied in this analysis. 18 In the SOEP questionnaire, non-working persons are asked "Do you intend to engage in paid employment (again) in the future?". The possible answer categories to this questions are "No, definitely not", "Probably not", "Probably" and "Yes, definitely". After that, people are asked "When, approximately, would you like to start with paid employment?", and the possible answers are "As soon as possible", "Next year", "In the next two to five years" and "In the distant future, in more than five years". [Table 7 about here]

[Table 8 about here]

The high number of children with working mothers queuing for child care slots suggests to target public expenditures towards providing child care primarily for this group. However, the positive outcomes of child care on later educational achievements (see [START_REF] Rossbach | Effekte qualitativ guter Betreuung, Bildung und Erziehung im frühen Kindesalter auf Kinder und ihre Familien[END_REF]) might be one reason to subsidize child care independently of the labor force status of their parents.

Summary and Conclusions

In this paper, I have estimated the excess demand for public child care in Germany on the basis of a partial observability model. The model developed here makes use of the advantages of the models proposed by [START_REF] Poirier | Partial Observability in Bivariate Probit Models[END_REF] and [START_REF] Abowd | Job Queues and the Union Status of Workers[END_REF]. Since it is known that certain children are not restricted in their access to child care facilities, the sample could be divided into two parts, into children not restricted and children who might be restricted. The estimation of demand and supply of child care slots is based on a likelihood function that consists of two parts, a univariate probit of the demand for child care for the unrestricted part of the sample and a bivariate probit of demand and supply of child care for the possibly restricted part of the sample.

Estimation results show that among children aged up to three, a large fraction is queuing for child care (24 percent in west Germany and 59 percent in east Germany), i.e. their parents demand child care services but there is no slot available.

  either by the father, grandparents, neighbours etc. or paid babysitters -is used.

5

  For a detailed description of Germany's child care institutions see Ewers et. al. (2005) the mother's (or father's) market wage 6 . Therefore, it is important to keep in mind throughout the paper that by excess demand for child care I really mean the excess demand for child care in subsidized institutions.7

  models, demand and supply for a restricted good can be estimated, even if only the joint outcome of the two unobserved variables, demand and supply, is observed.

  live in a county where availability of child care slots is near to hundred percent in their age group are also part of the unrestricted sample. 10 Drawing on this information, I follow the idea of[START_REF] Abowd | Job Queues and the Union Status of Workers[END_REF] and divide the sample into two parts, namely the unrestricted observations and the possibly restricted observations. For the unrestricted part, the observed variable "child care utilization" can be explained by demand-side variables only. The likelihood function of the model used here therefore consists of two parts: a univariate probit part for the unrestricted sample and a bivariate probit for the restricted sample. Assuming that the coefficients of the demand variables are the same in both parts, the likelihood function of this model takes the following form:

  they intend to work provided they could be offered a child care slot.

  l a n d F r a n c e G r e e c e I r e l a n d I t a l y N e t h e r l a n d s P o r t u g a l S p a i n S w e d e

  As already mentioned above, only the joint outcome of the two variables D and S, namely child care utilization C, is observed. The probability that child care is used is

	S	=	1 if * 0 S > .					(5)
	Thus, the probability of having a child care slot available is
	Pr(	S	1) Pr( = =	S	>	X	S S	)	.	(6)
	F o r 1) Pr( 1 C Pr( S = = =	D	1) Pr( = =	D	=	1) Pr(	S	=	1 |	D	1) = .	(7)
							P
									e
										e r
													R e v
													i e
													w
							S , formally
	S	*	=	X	S s	s + .					(4)
	As in the case of the observed demand a child care slot will be supplied for a certain
	child if S* is above zero,
													10

[START_REF] Poirier | Partial Observability in Bivariate Probit Models[END_REF]

proposed to estimate the parameters of D and S in a bivariate probit model that is identified if each equation excludes at least one exogenous variable appearing in the other equation. The likelihood function of this model is given as

Page 14 of 30 Editorial

  expenditures and informal care arrangements. The 2001 wave of the SOEP is used to get information about last year's child care status.

	Submitted Manuscript
	care hours,
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	P
	e
	e r
	R e v
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	14

Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Tables and Figures Figure 1: Publicly financed/subsidized child care slots for children aged less than three per hundred children in selected countries of the European Union

  This would suggest that, as far as public policy is concerned, public expenditures should be concentrated on the provision of child care for this group. This has in fact been reflected in legislation recently passed by the German parliament.The relevance of the results presented here, however, goes beyond the current political debate in Germany. Since several European countries (e.g. Austria, Switzerland, Italy and other southern European countries) have similar child care institutions as (west) Germany, the results presented here suggest that excess demands for child care exists also in these countries. Furthermore, the results for east Germany suggest that excess demand for child care might also exist in transition economies where public expenditures for child care have been cut, even though the availability of child care might still be higher than in many western European countries. This research project was funded by the Thyssen Foundation in the research project "Labor Market and Welfare Effects of Family Policy in Germany". I would like to thank M. Csillag, P. Haan, C. Langer, M. Myck, C. K. Spiess, V. Steiner, A. Uhlendorff and T. Viitanen, as well as participants of the "Berlin Network of Labour Market Research" seminar for helpful comments and discussions on an earlier draft. The usual disclaimer applies.

	F o r working mothers. F o r STEINER, Viktor, Peter HAAN and Katharina WROHLICH (2005): Documentation of the Tax-Benefit-Microsimulation Model STSM (1999-2002). Mimeo. STÖBE-BLOSSEY, Sybille (2004): Bedarfsorientierte Kinderbeteruung. Teil 1: Arbeitszeit und Infrakstruktur. Vorläufige Auswertung einer Befragung von Müttern mit Kindern unter 14 Jahren. Arbeitspapier des Instituts Arbeit und Technik, Gelsenkirchen. STUTZER, Alois and Reto DUERSTELER (2005): Versagen in der staatlichen Krippenförderung -Betreuungsgutscheine als Alternative. CREMA Working Paper No. 2005-26. Acknowledgements: F o r F o r F o r F o r
	P P P P P P
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	e r e r e r e r e r e r
	R e v R e v R e v R e v R e v R e v
	i e i e i e i e i e i e
	w w w w w w
	Excess demand for subsidized child care is also present among children with
	19 20 23

Source: BMFSFJ (2003) and

[START_REF] Dji | Zahlenspiegel. Daten zu Tageseinrichtungen für Kinder[END_REF]

.

Table 1 : Child care utilization and employment of mothers with young children in Germany Official statistics on availability of child care slots (slots per 100 children)

 1

	Children aged 0-<3	Children aged 3-6
	All	8%	105%
	East Germany	33%	115%
	West Germany	3%	104%
	Child

care utilization (only child care in subsidized facilities) Employment of mother (all children)

		Children aged	Children aged	Children aged	Children aged
		0-<3	3-6	0-<3	3-6
	All	10%	84%	21%	37%
	East Germany	32%	92%	37%	50%
	West Germany	6%	82%	18%	34%
			Employment of mother
		Children in child care	Children not in child care
		Children aged	Children aged	Children aged	Children aged
		0-<3	3-6	0-<3	3-6
	All	58%	39%	17%	23%
	East Germany	69%	54%	17%	0%
	West Germany	46%	37%	16%	24%

Note: Employment of Mother means full-time or part-time employment. Marginal employment ("geringfuegige Beschaeftigung") is not included. Source: SOEP, wave 2002 and DJI 2002.

Table 2 : Sample description Number of children in SOEP wave 2002, aged 0 -6 and not yet enrolled in school 1857

 2 In these cases, there were missing values on variables needed for the calculation of net household income, such as missing information on the income of other household members. Source: SOEP, wave 2002.

	(… these children live in 1426 households)
	Observations lost due to missing values in the variable on local availability of child care facilities	27
	Observations lost due to missing values in the hypothetical net household income variable*	20
	Sample size used for estimation	1810
	… thereof children who are not constrained in their access to childcare	907
	… children who might be constrained	891

*

Table 3 : Variable description

 3

	Variable Name	Description

The reason why in this analysis, the focus is on child care and mother's employment and other characteristics of the mother is the fact that in Germany, in the large majority of all families, housework and child care is still undertaken by the mother and not the father (see, e.g.,[START_REF] Steinbach | Wie Paare sich die Arbeit teilen[END_REF]).

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

There are 440 counties in Germany. It is assumed that children are not restricted in their access to child care slots if there are more or equal to 99 slots per 100 children in the county.

Note that this likelihood function is not the same as the one used by[START_REF] Abowd | Job Queues and the Union Status of Workers[END_REF]. In their application, demand and supply of the possibly restricted part of the sample is specified as the product of the two corresponding probabilities rather than a bivariate distribution.

Table 3 continued Explanatory variables used in the supply equation only availability Availability ratios of child care slots by age group on the local level: Number of child care slots per child

* Only those mothers were considered who answered "Yes, definitely" to the question "Do you intend to engage in paid employment (again) in the future?" Numbers in brackets refer to 95% confidence intervals calculated using the bootstrap method.


Mohammad Niaz

Asadullah Skope

Dr Sanzidur Rahman
email: srahman@plymouth.ac.uk

I21 -Analysis of Education < I2 -Education < I -Health, Education, and Welfare, Q12 -Micro Analysis of Farm Firms, Farm Households, and Farm Input Markets

Keywords: Agriculture, returns to education, stochastic production frontier, Bangladesh. JEL classifications: I21, Q12, N5

This paper reassesses the debate over the role of education in farm production in Bangladesh using a large dataset on rice producing households from 141 villages. Average and stochastic production frontier functions are estimated to ascertain the effect of education on productivity and efficiency. A full set of proxies for farm education stock variables are incorporated to investigate the 'internal' as well as 'external' returns to education. The external effect is investigated in the context of rural neighbourhoods. Our analysis reveals that in addition to raising rice productivity and boosting potential output, household education significantly reduces production inefficiencies. However, we are unable to find any evidence of the externality benefit of schooling -neighbour's education does not matter in farm production. We discuss the implication of these findings for rural education programmes in Bangladesh.

Introduction

Acknowledging the importance of education in the labour market success of individuals, governments all around the world routinely advocate further investment in education.

However, the majority of the population in developing countries depend on agriculture for their livelihood. Knowledge of market returns to education is less useful as a guide to increase educational investment in such agrarian societies. In theory, education is expected to improve productivity in all spheres of activities including agriculture. A positive return to [START_REF] Coelli | Technical, allocative, cost and scale efficiencies in Bangladesh rice cultivation: a non-parametric approach[END_REF] and [START_REF] Rahman | The application of frontier approaches to model the efficiency of rice producers in Bangladesh[END_REF] did not find any significant effect of education on production efficiency. The authors attributed this finding to the fact that the education system in Bangladesh was not agriculturally orientated. The only study that reports a positive education effect on farm efficiency is Sharif and Dar (1996). However, findings of this study are difficult to generalise. The authors use a highly purposive sample which comprises of only 100 households selected from only one village in Bangladesh, and therefore, limit scope for generalisation.

In stark contrast to the current controversy surrounding the returns to education in Bangladesh's agricultural sector, there exists a burgeoning literature documenting the positive impact of education on the welfare of individuals and households in rural areas. An additional year of schooling increases labour market earnings by 5.7% in rural areas (Asadullah, forthcoming). Education also affects household consumption in rural areas.

Using household data for the year 1995-96, [START_REF] Wodon | Microdeterminants of consumption, poverty, growth, and inequality in Bangladesh[END_REF] finds that a household with both the head and the spouse having completed secondary school have an expected per capita consumption 60% higher than that of a similar household with an illiterate head and spouse.

Most importantly, educated heads in rural areas are less likely to experience intergenerational poverty traps [START_REF] Asadullah | Intergenerational economic mobility in rural Bangladesh[END_REF]. In sum, education matters for economic success in rural Bangladesh. With the majority of rural households relying on farm activities for their livelihoods, one would a priori expect a positive impact of education on farm production. A potential explanation for the failure of earlier research on the farm production function using Bangladeshi data to detect an 'education effect' lies in the methodology. Most of the earlier literature employed empirical models that were underspecified in two ways.

First, almost all the studies focusing on internal returns to education preclude the possibility of centralized decision making in farm work [START_REF] Yang | Education in production: Measuring labour quality and management[END_REF]. Consequently, the farm education stock is modelled as either the level of education of the household head or that of an average Given that much of the farm work in agrarian societies is household (instead of individual) specific, such proxies may contain little information and, therefore, undermine the actual returns to education. Earlier research on Bangladesh by [START_REF] Deb | Human Capital and Agricultural Growth in Bangladesh[END_REF], [START_REF] Wadud | Farm household efficiency in Bangladesh: a comparison of stochastic frontier and DEA methods[END_REF] and [START_REF] Rahman | The application of frontier approaches to model the efficiency of rice producers in Bangladesh[END_REF] used farmer education as the sole measure of farm human capital.

Second, the existing studies of farm production in Bangladesh and other developing countries exclusively centre on internal returns to schooling, ruling out the presence of any externality effect of education in improving productivity and efficiency. Three exceptions are [START_REF] Appleton | Education and agricultural productivity: evidence from Uganda[END_REF], [START_REF] Knight | The role of education in facilitating risktaking and innovation in agriculture[END_REF] and Weir and Knight (forthcoming).

Educational externalities arise as uneducated farmers learn from the superior production choices of other educated farmers in the neighbourhood. A similar externality arises when educated farmers are early innovators and are copied by those with less schooling [START_REF] Knight | The role of education in facilitating risktaking and innovation in agriculture[END_REF]. Apart from such social learning, an externality effect could also capture the possibility that uneducated farmers simply access the basic literacy and numeracy skills of their educated neighbours. Partly motivated by such arguments, [START_REF] Appleton | Education and agricultural productivity: evidence from Uganda[END_REF] examine the effect of mean level of education of other farmers in the same enumeration area on agricultural productivity in Uganda. They conclude that the externality benefit of education is sizable: the level of primary schooling of neighbouring farmers enhances productivity of the sample farmer. Weir and Knight (forthcoming), on the other hand, explore the external effect on productivity and efficiency using Ethiopian data. Their analysis reveals the significant externality benefit of education on productivity, but no such benefit is found in improving technical efficiency. They conclude that education externalities affect adoption and spread of innovations, thereby, raising productivity in farming.

Similar education externalities could prevail in farm production in Bangladesh. In the dense and closely-knit society of rural Bangladesh characterized by an extremely low level of literacy, the educational externality could serve as an important non-market determinant of Given the perceived importance of education in raising productivity and efficiency in agriculture, the present study is set out to examine two important issues in Bangladesh. First, we test for the internal effect of education. That is, whether the education level of a household raises farm productivity and efficiency. Second, we test for the presence of any external effect of education. We examine whether, in addition to household's own level of education, farm production is positively influenced by education of others in the residential neighbourhood. We do so by estimating the average production function as well as stochastic production frontier for rice cultivation in Bangladesh with controls for a host of farm inputs, education stock measures and villages-level determinants.

There are three major findings of our study. First, we find a positive effect of the education level of a household on farm production. Such internal returns to education arise through raising productivity, boosting potential output and reducing technical inefficiency.

On the other hand, there is no evidence of an external effect of education on agricultural productivity. Neighbour's education does not matter in reducing production inefficiency either. Lastly, farm production is centralized so that even if the household head is uneducated, productivity and potential output are augmented so long as an educated adult coresides in the same household. The remainder of the paper is organized as follows: section 2 describes the study area, the methodology, the empirical specifications of the production

Methodology

The study area

The farm households in this study belong to the Matlab thana 1 of the Chandpur district in Therefore, most of the farmers in the study area now operate as either smallholders (typically owning less than 1 ha of land) or as sharecroppers.

Similar to other regions of Bangladesh, the majority of adults in the study villages never went to school. This is despite a substantial labour market return to education in the Matlab villages -one year of additional schooling leads to a 7 per cent gain in average earnings for wage workers [START_REF] Berman | Fertility and education in radical Islamic Sects: Evidence from Africa and Asia[END_REF]. This is similar to the overall wage individuals is well-documented for Bangladeshi households [START_REF] Basu | Is literacy shared within households? Theory and evidence for Bangladesh[END_REF]. Our study extends these ideas in the context of farm production.

Modelling internal and external benefits of education on productivity and efficiency

Application of an average production function as well as the stochastic production frontier framework is appropriate to analyze the internal and external benefits of education on productivity and efficiency. In this study, productivity is defined as the ratio of observed output to observed input use with respect to a given level of production technology. On the other hand, the term efficiency refers to technical efficiency in farm production, defined as the ratio of the observed to maximum feasible output, with respect to a given level of production technology and the observed input use (an output oriented measure).

Two basic hypotheses are tested (distinguishing between internal and external effects): whether education affects (a) productivity as well as placement of the frontier (that is, influences production as well as increases potential output), and (b) deviations from the frontier (that is, affects production efficiency). The internal benefit of education on 8 productivity and placement of the frontier is captured by specifying level of education at the household as an independent variable in the average production function and in the stochastic production frontier function respectively. The external benefit of education on productivity and placement of the frontier is captured by specifying neighbourhood level of education as an independent variable in these models.

In this study, the degree of inefficiency in production is measured by the deviation from the frontier. Therefore, the internal and external effects of education on efficiency are examined by placing household-level and neighbourhood-level education in the 'inefficiency effects model' in addition to variables representing farm and village characteristics to explain the underlying causes of deviation from the frontier.

A stochastic production frontier approach, developed by Aigner et al. (1977), is utilized in this study. In this framework, the output (rice production) is treated as a stochastic production process and is defined as:

) 1 ( ) exp( . ) ; ( i i i A x f Q = where + R x
is a (NxJ) matrix of the inputs,

+ R Q
is the (Nx1) vector of output, f(.) is the best practice production frontier, A is the technology parameter vector, and i subscripts individual farm households, respectively.

The error term i is composed of two components:

) 1 ( a u v i i i =
where the component v i s are assumed to be identically and independently distributed The production efficiency of the farm i is defined as:

) 2 ( | ) exp( ] | ) [exp( 1 0 = = = D d i di d i i i W E u E EFF
where E is the expectation operator. This is achieved by obtaining the expressions for the conditional expectation u i upon the observed value of i . The method of maximum likelihood is used to estimate the unknown parameters, with the stochastic production frontier and the inefficiency effects functions estimated simultaneously. The likelihood function is expressed in terms of the variance parameters, [START_REF] Battese | A model for technical inefficiency effects in a stochastic frontier production function for panel data[END_REF].

2 2 2 u v + = and 2 2 / u = (Battese

The empirical model

The production structure of rice farmers in Bangladesh is specified using a single-output, multi-input Cobb-Douglas production function and a stochastic production frontier, respectively. The general form of the production function and the stochastic production frontier for the ith farm is expressed, respectively as:

) 3 ( ln ln ln 1 1 1 0 i J j M m mi m K k ki k ji j i D E X Q + + + + = = = = ) 4 ( ln ln ln 1 1 1 0 i i J j M m mi m K k ki k ji j i u v D E X Q + + + + = = = = where = = + + + = D d i G g gi g di d i a E W u 1 1 0 ) 4 ( F o r P e e r R e v i e w 10
where the dependent variable Q is the aggregate of rice output 2 produced (kg per farm) in all three seasons, 'Aus' (pre-monsoon), 'Aman' (monsoon) and 'Boro' (dry-winter); Xs are the inputs of land cultivated (ha), total value of all purchased inputs 3 (taka), total imputed value of all home supplied inputs 4 (taka), and value of farm-capital assets used in rice production (taka); Es are the variables representing the internal and external benefits of education; and Ds are the village dummies; is the standard two-sided random error in eq (3); v is the twosided random error and u is the one-sided half-normal error in eq (4); and ln is the natural logarithm; Ws in eq. ( 4a) are the variables representing farm-specific characteristics to explain inefficiency and includes age of the farmer (years), tenurial status (1 if owner operator, 0 otherwise), irrigation facilities of the village (1 if have facility in the village, 0 otherwise), level of infrastructural development at the village 5 (number), non-agricultural income share 6 (proportion of total household income obtained from non-agricultural sources), and Es are variables representing internal and external effects of education; is the truncated random variable; k , 0 , j , m , 0 , d and g are the parameters to be estimated. with our neighbourhood education measures, the estimate of the education externality is likely to be biased upwards. We rule out this possibility of upwardly biased estimate of education externality by fully controlling for village fixed effects. This strategy ensures that our estimates of external returns to education are at least not driven by unaccounted village level determinants (both observed and unobserved) of farm productivity. Nonetheless, we cannot rule out the possibility that a similar bias may prevail due to the omission of neighbourhood level unobserved correlates of farm productivity, so that our estimates of externalities are likely to be upwardly biased 9 .

Lastly, exploring externality effects at bari (instead of village) level is appropriate as baris define the relevant social space in rural Bangladesh. The extant studies (for instance, [START_REF] Appleton | Education and agricultural productivity: evidence from Uganda[END_REF] investigate the neighbourhood effect at the lowest administrative level which, in most cases, remains much broader than the social space relevant for farmers in rural areas. [START_REF] Appleton | Education and agricultural productivity: evidence from Uganda[END_REF] use the enumeration area to define a neighbourhood in Uganda, which on an average comprises of as many as 1000 households. It is not clear, a priori, how such administrative boundaries could capture the relevant social space for farmers. Geographical remoteness is likely to inhibit any economically meaningful social interaction. Weir and Knight (forthcoming) is the only study that overcomes this problem by focusing on lower-level neighbourhoods (defined in terms of household clusters instead of some arbitrary administrative boundary) within each survey site in their Ethiopian study. Baris in our study resembles these rural neighbourhoods in Ethiopia.

Therefore, throughout this study, we compare and contrast our estimates of externalities with that reported in Weir and Knight (forthcoming). Matlab thana. Second, households were sampled. If a bari had just one household, it was always selected. In the case of multi-household baris, two households were selected at random from each of the sample baris. This led to a total sample of 4368 households 10 . Since for each household, we know the identity of its bari and village of location, we can account for non-household (that is, external) determinants of agricultural productivity and efficiency using this dataset.

Data

While all the households completed the section on farm production, only 56.5 per cent (2469 households) of them were engaged in agricultural production. After purging this sample of potential outliers 11 , the final sample contained a total of 2357 rice producing households. Of these, the majority (85%) came from multiple-household neighbourhoods where the mean number of households is six. For these households, the externality variable is a measure of education in the other (sampled) household in the neighbourhood. The remaining 352 households (15% of the sample), however, belong to single-household baris so that neighbourhood education is set to zero for these households.

Results

The summary statistics of the variables used appear in Table 1. A number of points can be noted from this Lastly, 50 per cent of household-income is derived from non-agricultural sources.

["Table 1" about here]

Ordinary Least Squares (OLS) regression is used to estimate the parameters of the average production function models. The Maximum Likelihood Estimation (MLE) procedure is used to estimate the parameters of the stochastic production frontier and inefficiency effects models jointly in a single stage 14 using STATA Version 8 (Stata Corp, 2003). All model specifications include four basic farm variables -land, purchased inputs, home supplied inputs and farm capital assets used directly for rice production. Also, all model specifications control for village fixed-effects (to purge the data of the village-level unobserved determinants of farm output) unless mentioned otherwise. A test for the joint significance of fixed-effects in all specifications rejected the null hypothesis of 'no influence' (H 0 : m = 0 for all m) at the 1 per cent level of significance (see Appendix Table A). This confirms that studies dealing with farmers' decision making process at farm-level must dissociate the effects of village-level correlates, which has not been seen in studies using Bangladesh data. 14 account for the internal and external benefits of education in rice production. The OLS model implicitly assumes fully efficient rice farmers, an assumption that will be relaxed subsequently when we proceed to examine the stochastic frontier production function for rice farming. Overall, these six specifications are able to explain 63-65 per cent of the variation in rice production, which is much higher than the explanatory power of the OLS models of the average production functions (with/without fixed-effects) reported in other studies 16 .

Productivity effects of education

["Table 2" about here]

All basic farm variables significantly influence rice production and the estimates are robust irrespective of model specifications. The effect of land is dominant as expected.

Output elasticity of land varies from 0.65 to 0.71, implying that a 1 per cent increase in land area will increase rice production by 0.65 to 0.71 per cent. Since, a Cobb-Douglas model is used, the sum of the coefficients of all the basic farm variables provides a direct estimate of the 'returns to scale' in rice production. This sum varies from 0.83 to 0.87 indicating decreasing returns to scale. [START_REF] Appleton | Education and agricultural productivity: evidence from Uganda[END_REF] and [START_REF] Weir | Externality effects of education: dynamics of the adoption and diffusion of an innovation in rural Ethiopia[END_REF] also reported decreasing returns to scale in cereal production for Ugandan and Ethiopian farmers respectively. Given widespread reporting of scale inefficiency among farmers in developing countries, estimates of 'decreasing returns to scale' seem consistent with expectation.

The internal (household-level) benefits of education in rice production are first explored in the neighbourhood fixed-effects models (1) and ( 2) in Table 2. The motivation underlying joint control for schooling of the household head and that of other household members (Model 2) is that production decisions are likely to be made collectively when farm size is small. The distinction between farm managers and workers is marginal in such a setting. While contributions of all may matter, the highest educated member in the household is likely to play the lead role. We find that the effect of household education is 6.4%, To explore the external (neighbourhood-level) benefits, we re-estimate the production functions with village fixed effects and an additional control for neighbour's education (Models 3-6, Table 2). Model (3) proxies for farm education using head's schooling only.

Model (4) additionally controls for maximum level of education of other household members.

Model (5) jointly controls for schooling of the head and maximum level of education in the neighbourhood. Lastly, Model (6) includes all three measures of education.

We find that an additional year of the household head's education increases rice production by 4 per cent (Model 3). But controlling for maximum adult education in the household, education of the head has no impact (Models 4 and 6). This finding confirms our earlier conjecture that farm production within the household is a centralized activity so that the most educated household member plays the key role in decision making 17 . The external benefit of education, measured by neighbour's education level is weak (Models 3 and 4).

When specified jointly with the household head's education, one year of additional schooling at the neighbourhood level increases rice production by 3 per cent (p<0.10), and is similar to the estimate of [START_REF] Weir | Externality effects of education: dynamics of the adoption and diffusion of an innovation in rural Ethiopia[END_REF] for Ethiopian cereal farmers. However, when we additionally control for maximum schooling among other householders, the neighbourhood effect disappears. We also re-estimated the regressions with alternative measures of neighbour's education (e.g. mean education of adults or education of the head in the neighbouring household). However, our results remained unchanged.

In the next stage we relax the assumption of fully efficient rice farmers and estimate stochastic production frontier models to allow for farm-specific inefficiencies. The test of significance of the inefficiencies in the model rejects the null hypothesis of 'no influence' (H 0 : µ = = 0) at the 1 per cent level, indicating that it is a significant improvement over the A). The predicted farm specific inefficiencies are then modelled as a function of selected farm and village level characteristics. In all specifications, both the stochastic production frontier and inefficiency effects models are estimated simultaneously. These results are summarized in Table 3.

["Table 3" about here]

The influence of basic farm variables on potential rice output is robust and mirrors those obtained from the average production function models. The first four models in Table 3 provide alternative specifications to account for internal and external benefits of education on the placement of the rice production frontier. A positive significant coefficient on the relevant variable will establish the evidence of its influence on outward shift of the rice production frontier. A test of joint significance of the effect of education in shifting the production frontier outward strongly rejected the null hypothesis of 'no influence' (H 0 : k = 0 for all k) at the 1 per cent level, indicating that education does have an influence on increasing potential output (Appendix Table A). Once again, we find strong evidence of the internal benefits of education in shifting the rice production frontier outward. The estimates of the level and magnitude of influence mirror those obtained in the average production function estimation results reported in Table 2. An additional year of schooling of the household head or adult members within the household will shift the rice production frontier by 3-7 per cent.

However, when the education of the head and that of other adult householders are controlled simultaneously, the coefficient on the former becomes insignificant. This is consistent with the argument of centralized planning. To sum up, the most educated member raises farm output not only through boosting average output, but also by shifting the production frontier.

The finding of a positive effect of formal education on potential output is at contrast with Weir and Knight (forthcoming), who using Ethiopian data found no such effects. Turning to the external benefit of education in shifting the rice production frontier, however, evidence is still weak. When included alongside head's education, an additional year of schooling in the neighbourhood seems to shift the rice production frontier by 3 per cent (p<0.10). But with additional control for maximum education of the adult householder, neighbourhood education has no impact.

Our earlier finding that the maximum education of the householder, instead of that of the household head, matters most in farm production suggests that educated householders are substitutes for one another. In order to formally test for this possibility, we also estimated an average production function and stochastic frontier production functions for a sub-sample of households where the household heads are uneducated 18 . Reassuringly, we find robust internal benefits of education (adult household education) on rice productivity and placement of the rice production frontier. The externality effect of neighbourhood education remains absent. Therefore, households where uneducated heads co-reside with educated adult members still experience significant gains in rice production. This finding has important policy implications which we discuss later in the paper.

Next, to detect any non-linearity in returns to the household head's education on rice productivity and placement of the frontier, we categorized his/her education into three levels: up to primary level, up to secondary level, above secondary level (details are given in Table 1). The results are presented in Appendix Table B, Models 1-4. We find that the influence of education on rice productivity and placement of the frontier kicks in only when the head's education level lies between primary and secondary level 19 . Tertiary level of education, perhaps, drives the household head away from rice production allowing him/her to engage in off-farm and non-agricultural activities, which presumably provides higher income when compared with rice farming. However, controlling for maximum schooling in the household, head's education once again has no impact.

Efficiency effects of education

Given robust internal benefits of education in rice productivity and the placement of the production frontier and the missing external benefits of education in the same, we next investigate the influence of education on technical efficiency. Prior to the discussion of these effects, we want to briefly highlight the farm-specific efficiency scores presented in Table 4.

The mean efficiency level varies between 71-73 per cent across specifications, indicating that rice production can be increased up to 27-29 per cent by improving technical efficiency alone with no additional use of resources. The minimum efficiency level is 12 per cent, whilst the maximum is 94 per cent. The results are similar to those reported by [START_REF] Wadud | Farm household efficiency in Bangladesh: a comparison of stochastic frontier and DEA methods[END_REF] and [START_REF] Coelli | Technical, allocative, cost and scale efficiencies in Bangladesh rice cultivation: a non-parametric approach[END_REF] for Bangladesh.

["Table 4" about here]

Models 5, 6, 7 and 8 in Table 3 present the results of 4 alternative specifications of the internal and external effects of education on technical efficiency. Five variables representing farm characteristics and selected village-level characteristics are used to explain farm-specific technical inefficiency, in addition to variables representing the internal and external effects of education (for details, see lower panel of Table 1). A test of joint significance of all variables including education rejects the null hypothesis of 'no effect' (H 0 : d = 0 for all d) at the 10 per cent level in all cases (see Appendix Table A). Non-agricultural income share seems to be the dominant variable in explaining technical efficiency. The significant positive sign on this coefficient points towards a situation where households with a higher opportunity to engage in non-agricultural activities fail to pay adequate attention to their rice production activities and are, therefore, highly inefficient. The result is similar and consistent with the findings of [START_REF] Ali | Profit efficiency among Basmati rice producers in Pakistan Punjab[END_REF], [START_REF] Wang | Production efficiency in Chinese agriculture: evidence from Rural Household Survey data[END_REF] and [START_REF] Rahman | Profit efficiency among Bangladeshi rice farmers[END_REF]. Rice producers also benefit significantly from better infrastructure 20 . Underdeveloped infrastructure has negative effects or not at all. This result corroborates the findings of [START_REF] Ali | Profit efficiency among Basmati rice producers in Pakistan Punjab[END_REF], [START_REF] Coelli | Technical, allocative, cost and scale efficiencies in Bangladesh rice cultivation: a non-parametric approach[END_REF] and [START_REF] Rahman | Profit efficiency among Bangladeshi rice farmers[END_REF], indicating that farmers in remote villages are less efficient after accounting for other correlates of efficiency. Weak evidence that owner operators are relatively efficient compared with tenants is also found.

Turning to our variables of interest, we find weak evidence of the external benefits of education in improving technical efficiency (Models 7 and 8). The coefficient on the neighbour's education variable is significant in Model 7 only. Once we additionally control for adult education within the household, neighbourhood education becomes insignificant (Model 8). Nevertheless the test of joint significance of the inefficiency effect of all education variables strongly rejected the null hypothesis of 'no effect' (H 0 : g = 0 for all g) at the 5 per cent level (Appendix Table A).

Similar results follow when the household head's education is categorized into levels (see Models 5, 6, 7 and 8, Appendix Table B). Beyond secondary schooling, head's education does not matter in reducing production inefficiencies (Model 5). Once, again, the external returns to education are absent net of level of education of adult householders.

Conclusions and policy implications

Like other developing countries, Bangladesh is characterized by low human capital investment. Returns to additional investment are high; schooling is vital to labour productivity. Yet earlier studies eschewed the positive role of education in farm work arguing that formal schooling in Bangladesh is not agriculture-oriented, and hence makes little contribution to improving farm productivity and efficiency. To the extent that schooling raises literacy and numeracy skills and the ability to process agricultural information, an education effect can exist independent of school curriculum design. Returns to such skills are [START_REF] Rosenzweig | Why Are There Returns to Schooling?[END_REF]. This study therefore reassessed the puzzle over low returns to schooling in farm work in Bangladesh using a large dataset of rural rice producing households spread over 141 villages.

Three sets of results follow from our empirical analysis. First, the results espouse the existence of the internal benefits of education in rice production: education matters in raising productivity, boosting potential output and improving efficiency. This is consistent with the fact that farm work in Bangladesh involves modern varieties of seeds and inputs. There are several implications of such a positive education effect. First, similar to labour market returns to education, schooling is relevant even in an agrarian setting where wage work opportunities may be limited. This, therefore, questions the commonly held view that household investment in children's schooling in agrarian societies is discouraged by a lack of a return to education in farm work. Second, the finding that proximity to an educated adult in the household boosts farm productivity implies that not all farmers who are uneducated are worse-off in farm work. Earlier studies (for example, Sharif and Dar, 1996a, b) on the effect of education on rice production inefficiency in Bangladesh probably overstate the efficiency loss suffered by less educated farmers in rural Bangladesh. Given the evidence of a centralized production regime, public policy should therefore aim at targeting farm households where all members are uneducated. How this can be achieved, nevertheless, remains unclear. If the education effect merely reflects the effect of basic literacy and numeracy skills, then a well-designed adult literacy programmes could serve as a potential policy intervention. Providing literacy training to one adult householder would suffice. On the other hand, if education captures the effect of farm-specific lessons acquired during one's school years, then adult literacy programmes may not be sufficient. Our data supports the relative importance of basic education over higher education in agriculture. When household head's education is decomposed by levels of education, the results show that head's primary and/or secondary level of education has a significant impact on productivity (Appendix Table B, Model 1). Farmers who complete secondary schooling also enjoy significant efficiency gains (Appendix Table B, Model 5), suggesting that basic literacy skills, usually attained during primary and secondary schooling, are more relevant in farm production than tertiary education.

The third important finding relates to education externalities. The absence of a 'neighbourhood education' effect in farm production is in contrast with other studies that have tested for similar effects using developing country data (for example, Weir and Knight, forthcoming). The precise reason for this discrepancy is not clear. One possibility is that educational spill-over effects on potential output arise through adoption of high yielding variety (HYV) technologies 21 . But the adoption rate of these HYV technologies is higher in Bangladesh (including the study villages) compared with Ethiopian villages so that returns to education in the form of 'learning-from-others' is likely to be less in Bangladesh.

In conclusion, evidence of a significant household education effect is consistent with the fact that farmers in Bangladesh operate in a modernizing environment (for example, one where there are changes in technology and infrastructure) compared with other regions such as Africa and Latin America where farm production is largely traditional. Despite such returns, the distribution of education stock is sparse in rural Bangladesh. A vast majority of the farming population remains uneducated or lives in isolation from other educated individuals (in own household or in the residential neighbourhood). Consequently, only a fraction of them succeed in appropriating returns from advanced technology in farm work.

Lack of education (or access to it) then partly explains why Bangladesh agriculture has not been able to fully exploit the available technologies. In spite of modernization, total factor 2. We have aggregated the volume of rice produced over all three seasons covering a crop year. This is because our main focus is to determine the internal and external benefits of education on overall rice production (the main staple and dominant crop in Bangladeshi farming) which is unlikely to differ across seasons for the same household. The main difference one usually obtains in parameter estimates of basic production inputs is across varieties of rice produced, as the input mix as well as use rates differ to a large extent between production of traditional and modern rice varieties. Unfortunately, our data do not distinguish between the varieties of rice produced in each season. In this specification, we implicitly assume that the production function is same for both traditional and modern rice.

3. Purchased inputs include seeds/seedlings, fertilizers, pesticides, irrigation, hired labour, and hired animal power services.

4. Home supplied inputs include all family labour, animal power services, manures, and seeds.

5. The index of underdevelopment of infrastructure is constructed using a cost-of-access approach. A total of six infrastructural indicators are used. These are: local market, bank, thana (sub-district) headquarter, bus stop, boat station, and telephone office (for details of construction procedure see [START_REF] Ahmed | Formulation and estimation of stochastic frontier production function models[END_REF].

6. The non-agricultural income share is composed of earnings from selling labour (permanent, seasonal as well as daily labour), revenues from household assets other than farm, non-farm assets and livestock, and earnings from primary and secondary non-agricultural sources. . We only focus on householder (farm) workers. Information on workers hired from outside the household is unavailable and hence not accounted for in our analysis.

8. As discussed later in the paper, we also experiment with other measures of neighbourhood education such as mean education of adults in the neighbouring household and education of the head of the neighbouring household. 9. For a comprehensive discussion of the issue of identification of neighbourhood effect, see [START_REF] Durlauf | Neighbourhood Effects[END_REF].

10. Further details on the MHSS are available in [START_REF] Rahman | Matlab Health and Socioeconomic Survey (MHSS)[END_REF].

11. Outliers in the output variable were identified by examining the ratio of rice output (kg) per decimal unit of land cultivated. Any observation with a ratio less than 2 or greater than 140 (2<x<140) is defined as an outlier and discarded. This is equivalent to restricting the sample to observations that fall within 3 standard deviations of the mean ratio.

12. The neighbourhood variable is constructed by excluding all members of the index household.

13. This, however, does not guarantee that all farmers within the village have full access to irrigation.

14. The single-stage approach is considered superior against the conventionally used twostage approach wherein the first stage involves estimation of the stochastic production frontier and the prediction of inefficiency effects under the assumption that these inefficiency effects are identically distributed with one-sided error terms. The second stage involves specification of a regression model for predicted inefficiency effects, which contradicts with the assumption of an identically distributed one-sided error term in the stochastic frontier [START_REF] Battese | A model for technical inefficiency effects in a stochastic frontier production function for panel data[END_REF]. Translog specification lies in the fact that we control for village level correlates of productivity and efficiency using the least-square dummy variable (LSDV) approach.

This entails inclusion of 139 village dummies so that our variable list ranges from 144 to 149 variables in production frontier models alone. In such a setting, Translog specification is not feasible, owing to the problem of multicollinearity [START_REF] Hsing | On the choice of production functions: the case of US manufacturing industries[END_REF].

Moreover, [START_REF] Kopp | Frontier production function estimates for steam electric generation: a competitive analysis[END_REF] suggest that the choice of functional form has a limited effect on technical efficiency. Consequently, Cobb-Douglas specification is widely used in studies that use large number of independent variables (e.g., Weir and Knight, forthcoming;[START_REF] Rezitis | Measuring technical efficiency in the Greek agricultural sector[END_REF]Xu and Jeffrey, 1998;[START_REF] Dawson | Measuring farm efficiency over time on Philippine rice farms[END_REF]).

16. For example, Weir and Knight (forthcoming) report adjusted R 2 of 0.55 for the OLS models of cereal output with site level fixed effects. The better-off fit of our models perhaps owes to the use of a large number of village dummies to control for village level fixed effects.

17. The choice of maximum education could be problematic if it proxies access to nonfarm cash income, rather than direct access to skills learned at school. We tested for this by additionally controlling for non-farm income of the household. However, it did not drive out the effect of maximum household education.

18. The results are not reported here but available from the authors upon request.

19. This finding is consistent with the experience from other Asian countries, wherein a positive education effect on technology adoption is documented only if farmers have more than four years of schooling [START_REF] Philips | Farmer education and farm efficiency: a meta-analysis[END_REF].

20

. The infrastructure index is defined as the level of underdevelopment of infrastructure.

Hence, a positive coefficient on this variable indicates positive effect on efficiency.

F

  productivity and efficiency. The scope for social interactions is widened by the way the agricultural production system in Bangladesh is organized, particularly, rice production in irrigated areas. Although farmers commonly possess small parcels of land in various locations, each irrigated block of land used for rice production (known as the command area) hosts a large number of farmers who are effectively neighbours and have to grow rice at the same time, if not using the same varieties. Such social proximity could improve knowledge-sharing and generate positive externalities of education of individuals.

  data; section 3 discusses the results; and section 4 concludes and draws policy implications.

  Bangladesh. The Matlab thana comprises of a total of 141 villages. Being criss-crossed by rivers, these villages remain sufficiently remote and well outside urban influence. Actual travel time between the capital city (Dhaka) and the Matlab thana is 5 hours. Therefore, villagers primarily rely on the local economy for their livelihoods. Agriculture constitutes the key source of earnings. Although in recent years, the study area has experienced some expansion of non-farm activities, the farm sector remains the single largest employer of the rural workforce; primary economic activities are agriculture and fishing. Rice is the principal crop in Matlab villages, in terms of its share in total cereal production. Being located in a low-lying area, the study villages are frequently flooded, particularly during the monsoon season. Hence, although unsuitable for homestead use, the flood-plain land of Matlab villages is ideal for rice cultivation. The distribution of land, however, is not homogenous. About 50 per cent of the households are landless. Increases in population growth and density have also led to a reduction in average farm size, as well as increased fragmentation of landholdings.

  The internal benefit of education is measured by two variables: (a) the education level of the household head (completed years of schooling), and (b) the maximum level of education (completed years of schooling) of adult householders (aged 19 years and over) 7 .The external benefit of education is measured by the maximum years of schooling of adult neighbours 8 . Eight specifications were adopted using three types of education variables to examine the internal and external effects of education on farm productivity and efficiency.The productivity effects were analyzed by placing these variables in the production function as well as the stochastic production frontier, while the efficiency effects were analyzed by placing them in the inefficiency effects model. Identification of neighbourhood externality as a causal effect is dubious if there are other determinants of farm productivity and efficiency that operate at the village level. If the positively affect farm productivity and are positively correlated

  study comes from the Matlab Health and Socio-economic Survey (MHSS). The survey was conducted in all the villages of the Matlab thana in the year 1996. The dataset provides a rich description of the agricultural and non-agricultural profiles of the sample households and their asset portfolios along with complete information on the personal characteristics of the householders. The sample households were selected in two steps. First, a random sample of 2678 residential neighbourhoods -baris -was selected from the entire

  labour market returns to education in the study villages. The household head's education, however, has no effect.

  inefficiencies do exist (Appendix Table

  , as farmers may not have the required inputs to use at the correct time,

  a modernizing agricultural sector, where access to advanced technology complements human capital stock

  agriculture has declined at an annual rate of 0.23 per cent per year for the period 1961-1992 mainly owing to dramatically falling efficiency, and this is despite strong technological progress[START_REF] Coelli | A stochastic frontier approach to total factor productivity measurement in Bangladesh crop agriculture, 1961-92[END_REF]. Current policy initiatives of the government to expand educational opportunities in rural areas of the country are therefore well-placed and promise significant long-run returns in terms of bolstering agricultural productivity. is the second lowest unit of local government in Bangladesh.

  rationale behind using Cobb-Douglas specification as opposed to a more flexible

  the household head's education is only 3 years. The maximum average level of adult education in the household is 5.8 years, and the maximum average level of neighbour's education is 6.7 years 12 . The average age of the farmer is 49.2 years, 48 per cent of farmers are owner operators, and 97 per cent of the villages have irrigation facilities 13 .

	average level of
	F o r
	P
	e
	e r
	R e v
	i e
	w
	13

Table.

Farms in our sample are small, with an average size of 0.51 ha. Fortysix per cent of the household heads in our working sample never attended school so that the

Table 2

 2

	F o r
	P
	e
	e r
	R e v
	i e
	w

presents OLS estimates (with fixed effects) of the extended Cobb-Douglas 15 production functions incorporating alternative specifications of the education variables to

Table 1 : Summary statistics of variables

 1 The differences in results, however, could also reflect the possibility that the existing evidences on the externality effects of education are exaggerated. Recent research on human capital externalities in the labour market context suggests that naïve estimates of educational externalities are upwardly biased. And when corrected for endogeneity of education, there is little evidence in support of externalities of education[START_REF] Acemoglu | How large are human capital externalities? Evidence from compulsory schooling laws[END_REF]. Although a similar analysis is yet to be attempted for agricultural production, it is difficult to rule out the prospect of a spurious externality effect of education in farm activities.

	21.
	o r
	P
	e
	e r
	R e v
	i e
	w
	26

Page 32 of 40 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 3 : Estimates of stochastic production frontier (Dependent variable: Natural log of rice produced)

 3

		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Production frontier model
	Constant	3.691	3.636	3.659	3.636	3.710	3.749	3.735	3.752
		(11.00)**	(10.84)**	(10.91)**	(10.83)**	(10.92)**	(11.23)**	(10.99)**	(11.20)**
	Farm variables
	ln Land	0.665	0.657	0.662	0.657	0.665	0.657	0.660	0.657
		(47.63)**	(46.75)**	(47.31)**	(46.73)**	(46.67)**	(45.27)**	(45.97)**	(45.28)**
	ln Purchased inputs	0.114	0.112	0.114	0.112	0.113	0.112	0.113	0.112
		(11.52)**	(11.48)**	(11.56)**	(11.47)**	(11.36)**	(11.20)**	(11.34)**	(11.22)**
	ln Home supplied inputs	0.020	0.019	0.019	0.019	0.019	0.019	0.019	0.019
		(5.11)**	(4.90)**	(5.08)**	(4.90)**	(5.07)**	(4.88)**	(5.02)**	(4.89)**
	ln Farm assets	0.016	0.015	0.015	0.015	0.016	0.015	0.015	0.015
		(4.07)**	(3.89)**	(3.93)**	(3.88)**	(4.13)**	(3.95)**	(3.99)**	(3.92)**
	Education variables
	ln Head's education	0.039	0.011	0.027	0.011
		(3.20)**	(0.77)	(2.05)*	(0.75)
	ln Adult education in HH		0.063		0.063
			(3.80)**		(3.27)**
	ln Neighbour's education			0.028	0.001
				(1.94)+	(0.04)
	Model diagnostics
	Log Likelihood	-1695.00	-1687.83	-1693.13	-1687.83	-1696.36	-1690.08	-1692.07	-1689.52
	Wald 2	6460.96	6529.81	6476.50	6529.27	6123.43	5699.03	5954.83	5703.94
	Prob > 2	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
		0.822	0.821	0.825	0.821	0.792	0.747	0.774	0.748
		(13.20)**	(13.60)**	(13.24)**	(13.55)**	(12.18)**	(10.67)**	(11.42)**	(10.64)**
	2	0.830	0.807	0.839	0.808	0.709	0.576	0.652	0.579
		(2.94)**	(3.07)**	(2.89)**	(3.06)**	(3.41)**	(4.01)**	(3.62)**	(3.96)**
	Inefficiency effects model
	Constant	-2.942	-3.018	-3.055	-3.020	-2.212	-1.470	-1.867	-1.478
		(1.78)+	(1.86)+	(1.78)+	(1.86)+	(1.78)+	(1.71)+	(1.75)+	(1.70)+

Page 35 of 40 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

				Submitted Manuscript
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Age	0.002	0.005	0.004	0.005	0.003		0.006	0.005	0.006
		(0.48)	(1.02)	(0.72)	(1.02)	(0.63)		(1.71)+	(1.29)	(1.73)+
	Head is female	0.347	0.402	0.379	0.402	0.280		0.283	0.310	0.293
		(1.42)	(1.68)+	(1.51)	(1.68)+	(1.43)		(1.84)+	(1.70)+	(1.87)+
	Tenurial status	0.146	0.157	0.160	0.157	0.145		0.140	0.152	0.143
	Irrigation Village infrastructure Non-agril. income share	(1.04) 0.770 (0.77) 0.049 (2.06)* F o r P e e r R e v i e w (1.15) (1.10) (1.15) (1.23) 0.809 0.774 0.809 0.662 (0.82) (0.76) (0.82) (0.80) 0.046 0.049 0.046 0.043 (2.04)* (2.03)* (2.04)* (2.12)* 1.011 0.987 1.014 0.987 0.891	(1.54) 0.467 (0.79) 0.038 (2.33)* 0.730	(1.41) 0.579 (0.81) 0.040 (2.17)* 0.847	(1.56) 0.479 (0.80) 0.037 (2.31)* 0.740
										35

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript F o r P e e r R e v i

e w 38 Appendix Table B: Alternative estimates of stochastic production frontier (Dependent variable: Natural log of rice produced)

		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	Production frontier model
	Constant	3.688	3.626	3.650	3.624	3.696	3.744	3.727	3.748
		(10.98)**	(10.81)**	(10.88)**	(10.80)**	(10.86)**	(11.24)**	(10.97)**	(11.21)**
	Farm variables
	ln Land	0.667	0.657	0.664	0.657	0.667	0.657	0.662	0.657
		(47.86)**	(46.79)**	(47.46)**	(46.80)**	(47.10)**	(45.49)**	(46.31)**	(45.49)**
	ln Purchased inputs	0.113	0.112	0.113	0.112	0.113	0.112	0.113	0.112
		(11.47)**	(11.46)**	(11.53)**	(11.46)**	(11.39)**	(11.21)**	(11.36)**	(11.23)**
	ln Home supplied inputs	0.020	0.019	0.019	0.019	0.020	0.019	0.019	0.019
		(5.12)**	(4.89)**	(5.08)**	(4.89)**	(5.13)**	(4.88)**	(5.05)**	(4.89)**
	ln Farm assets	0.016	0.015	0.015	0.015	0.016	0.015	0.015	0.015
		(4.03)**	(3.87)**	(3.89)**	(3.86)**	(4.10)**	(3.93)**	(3.96)**	(3.90)**
	Education variables
	Primary education (grade 1-5)	0.042	0.004	0.026	0.004
		(1.73)+	(0.16)	(1.00)	(0.14)
	Secondary education (grade 6-10)	0.067	0.006	0.042	0.005
		(2.26)*	(0.17)	(1.31)	(0.15)
	Higher secondary and above (grade 11+)	0.075	-0.004	0.042	-0.005
		(1.38)	(0.07)	(0.75)	(0.08)
	ln Adult education in HH		0.069		0.068
			(4.18)**		(3.51)**
	ln Neighbour's education			0.033	0.003
				(2.27)*	(0.15)
	Model diagnostics
	Log Likelihood	-1696.78	-1688.10	-1694.21	-1688.09	-1696.69	-1688.69	-1691.56	-1688.13
	Wald 2	6454.24	6530.14	6475.66	6533.24	6192.15	5723.25	5996.17	5727.56
	Prob > 2	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
		0.825	0.822	0.822	0.822	0.807	0.747	0.781	0.748
		(13.55)**	(13.43)**	(13.43)**	(13.75)**	(12.44)**	(10.61)**	(11.57)**	(10.59)**

Page 39 of 40 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

			Submitted Manuscript
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
	2	0.840	0.270	0.270	0.264	0.767	0.575	0.672	0.577
		(2.95)**	(0.64)	(0.64)	(0.62)	(3.13)**	(3.98)**	(3.49)**	(3.95)**
	Inefficiency effects model
	Constant	-2.962	-3.042	-3.094	-3.049	-2.575	-1.474	-1.994	-1.469
		(1.80)+	(1.85)+	(1.80)+	(1.88)+	(1.78)+	(1.72)+	(1.77)+	(1.71)+
	Age Head is female Tenurial status Irrigation Village infrastructure	0.003 (0.54) 0.363 (1.47) 0.129 (0.92) 0.766 (0.78) F o r P e e r R e v i e w 0.006 0.004 0.006 0.003 (1.12) (0.82) (1.13) (0.72) 0.421 0.400 0.422 0.307 (1.73)+ (1.57) (1.74)+ (1.40) 0.144 0.147 0.145 0.136 (1.06) (1.02) (1.07) (1.05) 0.806 0.768 0.806 0.736 (0.82) (0.76) (0.82) (0.80) 0.049 0.045 0.049 0.045 0.047	0.007 (1.87)+ 0.297 (1.91)+ 0.127 (1.41) 0.475 (0.81) 0.039	0.006 (1.41) 0.333 (1.73)+ 0.139 (1.26) 0.609 (0.82) 0.042	0.007 (1.89)+ 0.306 (1.94)+ 0.129 (1.43) 0.484 (0.82)
									39

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Acknowledgements

We are thankful to Stefan Dercon, Francis Teal, Sharada Weir and participants at the 2006 Rural Futures Conference (University of Plymouth) and an anonymous referee for helpful comments on an earlier version of the paper. However, usual disclaimers apply.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript