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Economic considerations for analysis of early childhood development programmes

Abstract
Introduction
Analytical frameworks for considering the determinants of and the impact of human resources investments in childhood development
Estimation issues in ascertaining the determinants of and the impact of investments in childhood development
Framework for policy choices related to childhood development
References

Jere Richard Behrman

The author is the W.R. Kenan, Jr., Professor of Economics at the University of Pennsylvania in Philadelphia, Pennsylvania, USA.

Abstract

The first section of this paper presents analytical frameworks for considering the determinants of and the impact of human resources investments in childhood development. These are investments, because resources devoted to child development may have returns not only currently, but in the future. Emphasis is placed on the underlying behaviours that determine such investments by households, given their resources and the prices and programmes that they face. Important implications are that: (1) households have their own objectives and therefore may not make the decisions that policy makers anticipate; (2) households make such decisions together with many other decisions in light of all their resources and current and expected prices and programmes, so there may be important cross-programme effects; (3) for empirical analysis or casual observations, many of the determinants of childhood development investments and many of their impacts include not easily observed variables, so inferences that do not control for such variables may be wrong; and (4) the expected returns and costs may differ substantially, depending on a range of markets, programmes, and macro contexts. The second section considers estimation issues in ascertaining the determinants of and the impact of investments in childhood development: (1) random measurement error, which may bias towards zero the estimated effects of right-side variables; (2) omitted variable bias, which causes the estimated effects of observed variables to be misrepresented because these variables in part are representing the effects of the omitted variables; (3) simultaneity bias of a direction that depends on the model being considered if the right-side variables are determined simultaneously with the dependent variable; and (4) selectivity bias if data are available only on a selected sample. The third section presents a framework for policy choices related to childhood development. The two basic motives for policy interventions are discussed: (1) Efficiency to obtain the maximum output for given resources and technologies and (2) distribution of resources or products among members of society. Illustrations are given, with explicit reference to possible child development policies.

Introduction

Early childhood development programmes are widely considered to be promising means through which society might improve the prospects of future generations of adults in low-income countries, as well as in other societies. This paper attempts to illuminate economic considerations related to analysis of early childhood development programmes and how they relate to what we think we know and to what we might be able to know, about the determinants and the impact of child development and about related policy choices.

Because these issues are inevitably empirical in nature, the tripartite foundations for good empirical analysis is considered, in the particular context of the determinants of and the impact of childhood development and related policy issues: theory, data, and estimation. These three dimensions of empirical social science analysis are critically interrelated. Theory provides frameworks for exploring systematically various dimensions of the determinants of and the impact of childhood development. Theory also points to what data are needed for such explorations, and to some of the probable estimation issues that should be addressed. Data, of course, are essential for empirical analysis, limit the extent to which analyses can be undertaken, and shape most of the estimation problems. Thus, the estimation problems reflect implications of theory and of the data that are available, and often more importantly, of the data that are not available - such as variables that are not observed or measured only imperfectly in the data but that may affect importantly childhood development and other human resource investments as well as subsequent adult productivity and other outcomes of interest.

The first section presents simple analytical frameworks for considering the determinants of and the impact of human resource investments in childhood development - production functions for representing the direct productivity impact of childhood development and reduced-form demand relations for family investments in childhood development and for related behaviours. Illustrations are given of the kinds of questions that can be answered about childhood development and related programmes within these frameworks, and about the difficulties in answering such questions. The second section discusses estimation issues in ascertaining the determinants of and impact of childhood development and related programmes. This section is important not only for analysts of the impact of childhood development, but for users of such analysis so that they can evaluate what we know and what we do not know from available empirical studies and from proposed future studies. The third section considers the basic framework for policy choices related to childhood development programmes, with emphasis on the two basic motives for policy changes - increasing efficiency (productivity with given resources) and changing distribution. Both of these motives are considered in some detail, with emphasis on information issues that are central to a number of possible policy interventions and to their evaluation, and on what policy changes are likely to have high priority.

Analytical frameworks for considering the determinants of and the impact of human resources investments in childhood development

Direct production function impact of childhood development
Household demands for human resource investments such as in child development

Good theories about the determinants of and the impact of human resource investments, such as those in childhood development, abstract the essence of complex empirical phenomena in ways that lead to testable empirical propositions about behaviour and policy choices in the presence of imperfect information. This section begins with a production function that is central to these theories, and then turns to micro theories that underlie some dimensions of the behaviours determining investments in childhood development and other human resources, the returns to those investments, and policy considerations related to such investments.

Direct production function impact of childhood development

Childhood development, of course, is of interest in itself, perhaps because it increases child happiness. It also may be of interest because it has a “production function” impact on other outcomes later in the life cycle directly or indirectly of interest, such as education, health, wages, and productivity. The total impact of child development can be considered the present discounted value of all such effects, each weighted by its appropriate price.¹

A firm production function, for example, can illustrate the (lagged) impact of childhood development (perhaps through its impact on subsequent learning capacities and health) and other characteristics of workers, together with other production inputs such as machinery and equipment, on firm production. A production function is a technological relation that gives the maximum output that can be produced with a given set of inputs by a firm (or by other production units). The production function in itself does not say anything about whether the inputs actually used are the best combination of inputs, given the firm’s objectives. But it is an essential part of models of behaviours related to human resource investments within the larger contexts of objectives that a family has, markets that a family faces, and assets that a family has at the time that decisions related to child development are made.

The production function for firm f highlights the role of attributes of worker i in firm f - including the ability (A_if), education (S_if), health (H_if), and work effort (E_if) of worker i in the production of the firm’s output (Q_f), given similar attributes of other workers in the firm (L_f), capital stock of the firm (L_f), firm management capabilities and organization (M_f), and knowledge (T_f) of technologies relevant to the firm’s production:

Relation (1):

Q_f= Q(A_if, S_if, H_if E_if L_f, K_f, M_f, T_f)

This relation, of course, is the simplification of a complex production process, with all of the variables representing many dimensions. But this simplification points to some important aspects of production and how it might relate to earlier childhood development of current workers. It is important for a number of questions about childhood development to know what is the impact of earlier childhood development (C_if) of worker i on the production of firm f (or to evaluate the economic impact of resources devoted to child development, MQ_f/MC_if). For example, to evaluate the rate of return to increasing resources devoted to child development, it is necessary to have some notion of what long-run effects better child development has on economic productivity (and perhaps on other outcomes). It seems plausible that there is no direct impact of current worker’s earlier child development on production, for which reason relation (1) does not include C_if explicitly. But that does not mean that the marginal product of childhood development on production is zero. To the contrary, it is thought to be positive through affecting direct production inputs such as education, health, and effort.

This has two important implications for the evaluation of the economic impact of resources devoted to child development. First, it may be necessary to have a fairly long time horizon. Decades may pass before the returns to investments in these resources maybe reaped. So such returns must be discounted to reflect the long lag between the investment and the returns. Second, it may be necessary to trace the impact through a number of channels - education, health, and effort in this example. Both of these factors mean that it is difficult to estimate empirically what is the magnitude of the economic impact of resources devoted to child development.

In part for these two reasons, all (or virtually all) of what might be considered production function estimates related to the impact of child development on economic productivity address one or the other of two stages: (1) The impact of child development on intermediate outcomes such as education or health, and (2) the impact of these intermediate outcomes on productivity. The second stage is just the estimation of relation (1). The first stage is the estimation of production functions similar in general form to relation (1), but with the intermediate outcome as the dependent variable that is being produced and resources devoted to child development among the right-side inputs. Relation (2) gives an illustration for education of the ith person (S_i), depending on previous child development (C_i), ability (C_i), health (H_i), nutrition (N_i), school quality (Q_i), and other factors:

Relation (2):

S_i=S(C_i,A_i,H_i, N_i, Q_i,...)

If analysts, whether they be sensible policy makers or high-powered econometricians, had good information on the inputs and outcomes of these production processes, considerable light could be shed on the answers to questions such as are raised in the previous paragraph by estimating the critical parameters in these basic production processes. But there are at least three basic data problems in undertaking such estimates.

First, some critical variables are not likely to be observed by analysts. Examples for relation (1) include individual worker’s abilities A_if, individual worker’s efforts E_if, and the firm’s management capabilities M_i. Examples for relation (2) include abilities A_i and school quality Q_i. The lack of observations on such variables not only means that it is very difficult to assess their impact. It also means that it is difficult to assess the impact of observed variables. If children with more ability are likely to receive more childhood development resources and their abilities are not controlled in estimates of production relations such as (2), for example, the impact of childhood development on education is likely to be overestimated because it is in part proxying for unobserved abilities.

Second, some critical variables are likely to be observed only very poorly by analysts. Resources devoted to childhood development itself are a central example. Therefore most, although not all, empirical studies represent childhood development very crudely, by such measures as duration of participation in formal childhood development programmes, by imperfect test scores, or by family characteristics. If the observed indicator of childhood development that is used for analysis is a noisy representation of true childhood development with the noise random, this aspect of the data, if not controlled in the estimation, results in underestimates of the true effects of childhood development. If the observed indicator of childhood development is systematically related to other variables in the production function as, for example, might be the case with use of parental characteristics such as income and schooling that are likely to be systematically associated with health and nutrition in relation (2), the result is a multiplicity of biases in the estimates of the production technology in relation (2), depending on exactly what is the nature of relation between the observed indicator and the true extent of childhood development.

Third, though relations (1) and (2) are written without reference to time, production processes are dynamic, so longitudinal data on all the relevant variables may be required to understand the production processes, but often data are available only at a point in time or for very limited time periods. This may result in omitted variable biases that lead to misleading estimates of the nature of the production processes.

Household demands for human resource investments such as in child development

Resources devoted to childhood development may have current consumption benefits for the children and for their family and may have future investment effects through production processes such as those that are discussed above. Childhood development and other human resource investment determinants involve for- going current consumption to increase future consumption. Becker’s [1] Woytinsky Lecture provides a simple but very useful framework with which to think about investments in human capital. This framework is considered from the perspective of families making investments in childhood development, basic education, or other types of human capital.

Within this framework, human capital investment demands such as for childhood development reflect the equating of expected marginal private benefits and expected marginal private costs for human capital investments in a given child (fig. 1A).² The marginal private benefit curve depends importantly, inter alia, on the expected private gains in productivities (or perhaps in wages/salaries that maybe related to productivities) due to human capital investments. These benefits depend on the marginal impact of the human capital investment on productivity in a production function such as in relation (1) (and perhaps indirectly through a production function as in relation 2) and on the marginal rewards that accrue to the investor because of that impact. The marginal private benefit curve is downward-sloping because of diminishing returns to human capital investments (given genetic and other endowments). The marginal private cost may increase with human capital investments because of increasing marginal private costs of borrowing on financial markets (if such markets do not permit borrowing for such purposes, at some point the marginal private cost curve may become very steep or vertical). The best human capital investment for this individual is H*, where the two curves intersect, with both the marginal private benefit and the marginal private cost equal to R*. For higher human resource investments than H*, the marginal costs exceed the marginal benefits so there is pressure to reduce the investments to the H* level. For lower human resource investments than H*, the marginal costs are less than the marginal benefits so gains can be made by increasing investments to the H* level. This equilibrium human capital investment at H*, is associated with an equilibrium rate of return, i*, that equates the present discounted value of expected marginal private benefits with the present discounted value of expected marginal private costs. By comparing this rate of return with those on other investments the household can decide whether this investment should be undertaken.

If the marginal private benefit curve is higher for every level of human capital investment as for the dashed line in figure 1B, all else equal, the equilibrium human capital investment (H**) and the equilibrium marginal private benefit (R**) both are greater. The marginal private benefit curve may be higher for one of two otherwise identical individuals (children) except for the difference noted below because one individual (or whoever is investing in that individual, such as the inaividual’s parents)³,⁴ (1) has greater genetic endowments that are complementary with resources devoted to childhood development or other human capital investments; (2) has lower discount rates so that the future benefits of human capital investments have greater value at the time of the investment decision; (3) has human capital investment options of higher quality (e.g., access to higher quality public childhood development programmes or public schools) so that the! marginal private benefits for a given level of private investments are higher, and the equilibrium investments greater;⁵ (4) has better health and a longer expected life due to complementary investments, so that the post-investment period in which that individual reaps the returns to the investment in childhood development is greater and therefore the expected returns greater; (5) has greater marginal private benefits to a given level of such investments because of schooling or labour market discrimination that favours that individual due to gender, race, language, family, village, or ethnic group; (6) has returns to human resources investments that are obtained more by the investor or the relevant decision maker (e.g., if traditional gender roles dictate that children of one sex, but not the other, provide old-age support for their parents, parental incentives maybe greater to invest in children who are likely to provide such support⁶); (7) has greater marginal private benefits to a given level of investment because of being in a more dynamic economy in which the returns to such investments are greater; (8) has greater marginal private benefits to a given level of such investments because of greater externalities from the human capital investments of others in the same economy; or (9) lives in a more stable economy so that the discount rate for future returns is lower (because risk is less) and thus the marginal private benefit of future returns greater.

FIG. 1A. Private marginal benefits and private marginal costs of human resource investments including those in child development

FIG. 1B. Private marginal benefits and private marginal costs of human resource investments, with higher(solid) and lower (dashed) marginal benefits

If the marginal private cost is lower for every level of human capital investment as for the dashed line in figure 1C, all else equal, the equilibrium human capital investment (H**) is greater, with the marginal private benefit (R***) lower at the higher investment level. The marginal private cost might be lower for numerous reasons. Compare two otherwise identical individuals except that one individual: (1) has lower private cost access to childhood development programmes related to such investments because of closer proximity to such services or lesser user charges; (2) has less opportunity costs for time used for such investments (e.g., such costs may have as an important component the costs of mothers’ time in participatory programmes, and such costs may vary among women due to variance in their labour market wages); or (3) is from a household with greater access to credit (or less need for credit) for financing such investments because of greater wealth or status or better connections.

FIG. 1C. Private marginal benefits and private marginal costs of human resource investments, with higher(solid) and lower (dashed) marginal costs

This maximization process leads to demands for childhood development and other human capital investments in individuali that depend on all relevant prices P and on all relevant resources R and on all the parameters of the relevant production functions (including those for the production of human resources) and on preferences:

Relation (3):

H_i = H(P, R I production parameter, preference parameters)

This simple framework systematizes five critical, common sense, points for investigating dimensions of the determinants and the effects of childhood development investments and other human capital investments.

First, the marginal benefits and marginal costs of human capital investments in a particular individual differ depending upon the point of view from which they are evaluated: (i) There may be externalities (i.e., effects on others that are not transferred through markets, such as the knowledge externalities mentioned below) or capital/insurance market imperfections so that the social returns differ from the private returns; and (ii) There may be a difference between who makes the investment decision (e.g., parents) and in whom the investment is made (e.g., children) which may result in gender (or birth-order) differentials in incentives for investments in children given traditional gender (birth-order) roles in old-age care for parents. To evaluate the determinants of human capital investments and their impact it is essential to be clear about from whose perspective the investment decision is being made.

Second, human capital investments are determined by a number of individual, family, community, and (actual or potential) employer characteristics, only a subset of which are observed in social science data sets that are available to analyse childhood development determinants and effects. To identify the impact of the observed characteristics on human capital investments, it is important to control for the correlated unobserved characteristics. For example, households with greater income also may live in areas in which expected rates of returns from human capital investments tend to be greater and learning environments are better. If so and if only household incomes and not expected rates of return nor learning environments are observed in the data, the impact of household income on such investments is likely to be overestimated with usual procedures.

Third, to identify the impact of human capital investments including those directed towards childhood development, it also is important to control for individual, family, and community characteristics that determine the human capital investments and also have direct effects on outcomes of interest. Otherwise the estimated effect includes not only the impact of the human capital investments, but also the effects of individual, family, and community characteristics that directly affect the outcomes of interest and are correlated with the human capital investment because they partly determine those investments. For example, if innate ability affects both investments in childhood development and then schooling and then wages directly due to the impact of ability on production in relation (1) (in addition to any indirect effect through the impact of childhood development on education in relation 2) and if there is not control for innate ability in estimates of the impact of childhood development (whether direct or indirect through education) on wages, the estimated effects are likely to be biassed because the representation of childhood development in relations (1) and (2) (perhaps through education in the former) is partly proxying for innate ability in these estimates.

Fourth, empirically estimated determinants of, and effects of, childhood development investments, basic education, and other human capital investments are for a given macro economic, market, policy, and regulatory environment. The actual returns may change substantially with changes in that environment, such as those associated with changing from administrated to market prices, lessening governmental demands for trained workers, improving markets, opening up an economy more to international markets, establishing greater macro balance, eliminating regulations on migration, or lessening discrimination in labour markets. In a rapidly changing work environment, this means that evaluation of childhood development programmes and other policies from historical data is difficult unless the stable parameters in underlying structural relations determining behaviour (e.g., production functions, preferences) can be obtained in such analysis. Reduced-form relations such as the demand functions in (3) that combine production and preference parameter responses to current and expected future market and other changes are less likely to be stable given such changes, which has implications for evaluation of childhood development-related policies.

Fifth, the impacts of changes in policies may be hard to predict by policy makers and outside analysts. If households face a policy change, they can adjust all of their behaviours in response, with cross-effects on other outcomes, not only on the outcome to which me policy is directed. Provision of food for small children, for example, effectively is an income subsidy to the household, which the household can divert in part at least to whatever use it wishes by cutting back on food provided to the children at home.

Estimation of the demand for childhood development and other human capital investments in relation (3) that is sensitive to these considerations can be informative for addressing a number of relevant questions. For example, how responsive are household childhood development decisions to the prices of | resources or programmes for childhood development? How important are incomplete markets, particularly for capital and insurance, in childhood development decisions? Do limitations in such markets mean that children from poorer backgrounds face relatively severe constraints on childhood development because their families have very limited resources for self-financing childhood development investments and cannot readily finance them through capital markets? What role do information imperfections play in the household childhood development decisions? Are potential household/individual investors in childhood development well-informed about the potential returns to childhood development?

With good information on all of the determinants of childhood development that are embodied in relation (3), good analysts could estimate such relations and illuminate important aspects of childhood development. But the problems in estimating such relations are parallel to those in estimating the production functions in relations (1) and (2). Indeed, they probably are more severe, because the essence of childhood development is investment with future returns rather than current production decisions, with the household making the investment decision frequently not knowing with certainty who employers of the child will be long in the future, but only having partial information about the distribution of certain characteristics of potential employers. Likewise, such decisions are made without certain knowledge about the characteristics of other relevant future markets, but only some prior beliefs about prices and options in those markets.

Estimation issues in ascertaining the determinants of and the impact of investments in childhood development

Estimated relations related to childhood development
Estimation problems in attempting to ascertain the determinants and impact of childhood development
Possible resolutions for estimation problems

Estimation of the determinants of childhood development by family behaviours and of the impact of childhood development is central to the concerns of this workshop. This section considers first different types of relations that might be informative based on the analytical framework above, then some estimation problems, and finally some possible resolutions of these problems. This material is important for analysts who may be involved in undertaking such investigations. It also is of major importance for those who attempted to interpret what we do and do not know about the determinants of and the impact of childhood development from existing studies. Only by having some sensitivity to these estimation problems can good judgements be made to assess empirical studies regarding what we know and where there are gaps in our knowledge.

Before turning to this discussion it is useful to emphasize that any empirical interpretations depend (although too often implicitly rather than explicitly) on some underlying model. It is important to recognize that what we think we know about causality from empirical studies depends, whether we acknowledge it or not, on assumptions regarding the relevant behaviour - particularly if, as usually is the case, behavioural data are used. It is not possible just to look at the data and see what they say about causal effects that determine childhood development, the impact of childhood development or other behaviours of interest, although it is possible to show correlations. Therefore, to clarify what we really know about causality, it is desirable to be as explicit as possible about the assumptions regarding the underlying models of behaviour.

Estimated relations related to childhood development

Implied by analytical frameworks

Family behaviours, including human capital investments in childhood development, are modeled as determined by the investors (families) maximizing their respective objective functions given relevant market prices, resource constraints, production functions, and objective (welfare) functions. These decisions are made sequentially over time - on the basis of stocks (including human resource stocks) reflecting past prices and constraints and expectations concerning the distributions of currently unknown future prices, policies, and production shocks. The constrained maximization of the objective function leads to demand functions in terms of predetermined assets and prices broadly defined, technologies and preferences, and the distributions of critical variables such as prices, policies and production shocks the actual values of which will be revealed only in the future. Resources broadly defined include income-generating physical, financial and human assets, some of which may reflect past investments and some of which (e.g., genetic endowments) are generally considered to be independent of current behaviour. Prices broadly defined include time as well as money costs for privately provided goods and services and for publicly provided goods and services. The implied relations for investigating the determinants of family behaviours related to childhood development are (i) to estimate directly the underlying structural relations that determine childhood development (e.g., childhood development production functions analogous to relation 2 with childhood development as the outcome and the production inputs into childhood development as inputs) and (ii) to estimate demand relations for childhood development or for inputs used to produce childhood development (e.g., expressions that are analogous to relation 3).

Childhood development and other human capital investments that themselves are determined by family and perhaps social programme behaviours are posited to have positive impact on outcomes such as education or labour market productivity. The impact of these human resources can be evaluated by (i) estimating directly the underlying production functions in which childhood development is an input directly or indirectly (e.g., relations 1 and 2) and (ii) estimating net profit and output “demand” relations (relation 3), perhaps conditional on childhood development and on other production stocks at the start of the period of interest as well as on what is known about the distributions of variables the actual values of which will be revealed in the future.

This section briefly considers these alternatives as well as two related approaches to which appeal often is made in the empirical literature on the returns to human capital investments - Mincer-type earnings functions and hedonic price indices. For all of these approaches, the considerations regarding what determines human capital investments are critical not only for estimating the determinants of related household and firm behaviours but also for attempts to estimate what are productivity effects of childhood development and of other human capital investments that are the result of earlier family and social sector programme behaviours.

Structural relations - production functions

Structural relations are the basic underlying relations in the models of family and firm behaviours discussed above. The most commonly estimated structural relations are production functions. A linear approximation to a general production function can be represented with firm output (Q_f) produced by two categories of variables relating to the ith worker in the fth firm (XI) and to the fth firm (X_F) and by an explicit stochastic disturbance term (U_f):⁷ where the a’s are parameters to be estimated that indicate the respective effects on Qf of changing the respective inputs. The stochastic term captures random effects that are not correlated with any of the other predetermined right-side variables. Sources of these stochastic terms might be weather fluctuations or chance snafus in production processes or other production shocks. Although this production function is written for firms, there also are production functions that are analogous in form, which pose the same estimation problems, for the “learning” or “education” produced in part by childhood development in relation (2) with “firm” replaced by social sector services.

Relation (1A):

O_f= a_XI+ a_XFXF+ U_f

Table 1 gives some examples of how variables might fall into these different categories in common data sets for firm production functions, for education (affected by childhood development) production functions, and for wage production functions. Of course exactly into which categories various variables fall in a particular case depends on both the underlying model of behaviour (which determines what is behaviourally determined and what is predetermined within the model⁸) and on the data in the particular data set used (which determines what is observed and what is unobserved). Further, as discussed below, there may be an important distinction for estimation purposes regarding what variables are posited as predetermined in the model and what variables are independent of the stochastic disturbance term in the relation being estimated.

The parameters (a’s) in the production function give the direct impact of the right-side variables - some of which may directly reflect policies - on Qr. With good estimates of the appropriate production functions, the direct determinants of many outcomes determined by household behaviours and the direct impacts of many human capital investments could be evaluated with considerable confidence. Such estimates can help to answer many of the questions raised above. Good production function estimates may be difficult to obtain, however, because of the estimation problems discussed below.

Reduced-form “demand” relations

A second set of relations that can be estimated to explore the determinants of and the impact of family and firm behaviours and of policies related to childhood development consists of “demand” relations. These relations give some behavioural outcome as dependent on all predetermined (from the point of view of the entity - family, or whatever - making the decisions) prices and resources and on the parameters in the underlying production functions and preferences. The outcome may be the demand for some good or service (e.g., the family demand for child development or firm demand for trained workers or for profits), or may be the supply of some good or service (e.g., the supply of firm output). These are the relations that most commonly are estimated in the literature. These demand functions in principle are derived explicitly from the constrained maximization behaviour of families (and of firms) that are discussed above. As such they incorporate all of the underlying structural (e.g., production function) parameters that are involved in that process. But all of the choice variables during the period of interest are substituted out, so the demand functions are not underlying structural relations such as production functions, but so-called reduced-form relations because the maximizing behaviour that determines such variables has been combined and “reduced” to the relations that give the behavioural outcomes as a function of purely predetermined and expected prices and resources. In some empirical studies the underlying structural parameters can be identified from estimation of the demand relations. In most cases, however, demand functions are just posited to result from constrained maximization and the underlying structural parameters are not identified in the estimates, though the demand parameters still are some combinations of these parameters. In such cases demand functions permit the estimation of the total effects of predetermined variables on the behavioural variables of concern, but not estimation of the exact mechanisms through which preferences and technical production functions affect the behavioural outcomes. This means that demand function parameters are less likely to be stable if there are changes in markets or policies or expectations than are production function parameters.

TABLE 1. Illustrative examples of different categories of input variables for different production functions in common models and common household surveys^a

Categories of variablesb			Production functions for
Aggregation	o/u	b/p	Firm production	Education	Wage rates
Individual	o	b	Schooling attainment, training, health, work experience	Schooling attainment, childhood development, health and/or nutrition status	Schooling attainment, work experience, health and/or nutrition status, occupation
	u	b	Nutrients consumed, intensity of effort, on- the-job learning	Time studying, intensity of effort	Intensity of effort, on- the-job learning
	o	p	Age, sex	Age, sex	Age, sex
	u	p	Genetic ability and health endowments, motivation	Genetic ability and health endowments, motivation	Genetic ability and health endowments, motivation
Household	o	b		Learning materials
	u	b		Time other household members help with learning	Time spent by spouse or others that increases productivity
	o	p		Schooling attainment of parents and siblings	Schooling attainment of spouse
	u	p	Household work attitudes and abilities	General household learning environment
Community	o	b
	u	b
	o	p	Weather	Schooling of others in community	Schooling of others in community
	u	P	General work environment	Quality of schools and childhood development programmes, general intellectual environment	General knowledge environment
Firm	o	b	Schooling, formal training, work experience of other workers, products, material inputs		Schooling, formal training, work experience of other workers, products, material inputs
	u	b	Abilities and motivations of other workers, compliance with legal regulations		Abilities and motivations of other workers, compliance with legal regulations
	o	p	Machinery and equipment and other capital inputs		Machinery and equipment and other capital inputs
	u	p	Management capabilities, quality of capital and intermediate inputs		Management capabilities, quality of capital and intermediate inputs

^a. The categorization of variables depends both on the model posited (concerning behavioural versus predetermined variables) and on the data available (concerning observed versus unobserved variables). Therefore it changes for different models and for different data sets.

But the examples given in this study are illustrative of fairly widespread practices.

^b. “b” refers to behavioural variables, “p” refers to predetermined variables within the model, “o” refers to observed variables in the data, and “u” refers to unobserved variables in the data.

On a general level demand functions can be written with a vector of behavioural outcomes (Z) dependent on a vector of prices broadly defined (P) and a vector of resources (R) - with the relevant prices and resources depending on what entity is the demand function. If there are uncertainties regarding relevant future prices, policies, and shocks, then the characteristics known at the time of the decision of interest regarding the distributions of those outcomes should be included instead of their realized values. A linear approximation to the demand function for a family (or firm) facing prices PF and with resources RF and a vector of stochastic terms (V_f) is:

Relation (3A):

Z_f=b_PFPF+b_RFRF+V_f

Conditional demand functions

Conditional demand functions, as contrasted with the unconditional ones in relation (3A), include among the right-side variables some variable(s) that are determined by the behavioural model for the decision-making unit - the family or firm - under examination. If the included behavioural variable(s) on the right side is determined at least in part by past behaviour, its effect may be estimated in such relations.⁹ This might appear to be a conditional demand function with which the impact of current childhood nutrient intakes on current childhood development could be explored. But the coefficient of current child nutrient intakes is merely the ratio of the effect of the price that has been eliminated in relation (3A-1) relative to the effect of that price in relation (3A-2) (i.e., b₃₁ = b₁₁/b₁₂). Thus the coefficient of current child nutrient intake in relation (3A-3) does not reveal anything interesting about the effect of current child nutrient intakes on current childhood development, but only of the relative price effects (for PF₁) in the two demand relations. For example, the current period firm net profit function might be posited to depend on the start-of-the-period stocks of workers with different levels of education and health, both of which reflect in part early childhood development, which depend on all past behavioural decisions related to childhood development and hiring/separating workers. In such a case, the start-of-the-period stocks of workers with different human resources are just other right-side variables that are predetermined with respect to current prices and (other) resources in the demand relation in (3A). That relation also includes all of the current prices. An unbiased estimate of the coefficients of the stocks of workers with different childhood development gives the impact of the start-of-the-period stocks of trained workers on the current-period net profits. That the start-of-the-period stocks of trained workers were determined by past behaviour poses some estimation problems discussed below, but the interpretation of unbiased coefficients of these variables as reflecting their impact on current net profits is clear.

Mincer-type earnings functions

The most common framework for estimating the private rate of return to time spent in school - which again maybe affected by prior child development- - in terms of labour market outcomes is due to Mincer [5]. In the simplest case, once one finishes school and starts to work, earnings depend only on years of schooling. Let Y₀ be wages with no schooling and Y_S be wages with S years of schooling, but with the earnings stream starting S years later due to the time spent in school. In equilibrium, the present discounted values of the earnings from the two options are equated, which implies a semilog earning or wage function:

Relation (4):

In Y_s = In Y₀ + r S

where r is the private rate of return to time spent in school. To estimate this relation (or more extended versions of it) a stochastic term (e) is added (usually without comment). One possible justification for such a stochastic term would be random measurement error in the dependent variable. Another would be that some individuals have better “market luck” than others, independent of their schooling.

There are numerous estimates of such expressions that purport to measure the private rate of return to time spent in schooling. How do these expressions relate to the production function for wages for the general form of relation (1A) that is summarized in table I? Implicitly they assume that the impacts of schooling (and, through schooling, of childhood development) are independent of all other inputs (e.g., ability, motivation, other inputs, technology). Thus strong assumptions are placed on the production technology, such that ability, motivation, and family connections have impact on wages only through their effects on schooling (or childhood development).^10,11

An alternative interpretation of relation (4) is as a “hedonic” (so the market values depend on the individual’s characteristics) wage function. In this case the coefficients are the market valuations of attributes such as schooling, again under the (usually implicit) assumption that there are no effects of variables - such as ability, motivation, and family connections - that are not controlled in the estimation but that may have an effect on both human capital investments and wages.

Estimation problems in attempting to ascertain the determinants and impact of childhood development

There are a number of possible problems in obtaining good estimates of the determinants of, and the impact of, childhood development. Therefore, what are presented as estimates of relations such as those that are discussed above may be biased - i.e., the true determinants of childhood development and the true impact of childhood development are not revealed because of estimation problems. These estimation problems all share a common characteristic: the disturbance term in the relation actually estimated is not simply an element in U_f or V_f or e that is distributed independently of all the right-side variables in the relation being estimated, but instead is correlated with right-side variables (e.g., because it is a compound disturbance term that includes unobserved variables as well as U_f or V_f or e or because of the way that U_f, V_f, and e are defined for the sample used in the estimates).

Measurement error

Measurement error may contaminate any of the observed variables used for estimates of the relations that are discussed above. Random measurement error occurs if what is observed (C*) is not the true childhood development variable (C), but the true variable plus a random error (w):¹²

Relation (5):

C*=C+w

Random measurement error in the dependent variable merely adds to the stochastic disturbance term, but does not bias the coefficient estimate of the right-side variable. Therefore random measurement in childhood development does not cause biases in the estimates of the determinants of childhood development.

Random measurement error in a right-side variable causes bias in the coefficient estimates of interest. Consider, for example, the case in which childhood development C is a right-side variable that is posited to affect education (5). The true relation is:

(1B)	S=bC+v and the relation estimated is:

(1C)	S=bC*+v+bw

Intuitively, because the observed childhood development is a noisy measure of true childhood development, the true dependence of childhood development on education is masked, and the result is an underestimate of the childhood development effect. Formally, the estimate of the childhood development impact is:¹³

Relation (ID):

Because F_C²/(F_C ²+F_V ²) is less than one, the estimate is biased towards zero. The bias is greater the larger the variance in the measurement error relative to the variance in the true value.

Omitted variables

In both production function estimates and demand function estimates, there may be variables that should be included among the right-side variables but that are not observed and therefore not included.¹⁴

For the production function estimates, for example, there may be unobserved inputs such as inherent ability, motivation, and management capabilities. In terms of relation (1A) with the subcategories of variables, the basic estimation problem is that the observed right-side variables (XI^ob, XI^op, XF^ob, XF^op) may be correlated with the unobserved variables (XI^ub, ZI^up, XF^ub, XF^up) that are included in the compound disturbance term with U_f¹⁵ Therefore the estimates of the impact of the observed variables include not only their true effects but also part of the effects of any correlated unobserved variables. As a result, Ordinary Least Squares estimates of their effects are likely to be biased, with the bias either up or down depending on the exact model and magnitudes.

For the demand relations (3A), the compound disturbance term includes, in addition to Vf the other unobserved variables (PF^u, RF^u). If any of me observed variables on the right side of relation (3A) are correlated with any of the unobserved variables, their coefficient estimates are biased, because, in addition to their own effects, they represent in part the effect(s) of the correlated unobserved variable(s). Further, in conditional demand functions in which some variable such as the start-of-the-period health stock discussed above is included among the right-side variables, such predetermined behavioural variables may be correlated with any of the right-side unobserved variables, because such variables entered into the determination of these predetermined behavioural variables in earlier periods. For example, in conditional net profit functions, the start- of-the period stocks of trained workers may be correlated with unobserved workers’ abilities and motivations. Often such possible biases are ignored.

The sign and magnitude of omitted variable bias depends on the effect of the omitted variable(s) and on its correlation with included variables. Consider the case of a simple wage production relation in which childhood development (C_i) and ability (A_i) together with a stochastic term (v_i) determine wages for individual i (Y_i) (with any intervening variable such as education substituted out for this example):

(1E) Y_i=aC_i+bA_i.+v_i

Relation (IF):

a = a + br_C,A

Simultaneity

Simultaneity bias occurs when a variable that is determined in the current period within the model appears as a right-side variable in some other relation. Among the relations discussed above, production functions are the ones for which simultaneity might be a problem. For example, consider a production function for child development parallel to relation (1A) in which one of the inputs is current nutrition inputs consumed by the child. Assume further that there are no problems with measurement errors and no problems with unobserved inputs. In general, nutrients consumed in the current period (and any other right-side variable that is behaviourally determined within the period) are correlated with the disturbance term in this relation. This is the case because for nutrients consumed in the current period (and for all other variables determined within the period) there is a demand function of the form of relation (3A). Included on the right side of that relation is a stochastic term (Vf) that includes the stochastic terms from all of the production function relations in the model - including that for production of child development. This results in a correlation between nutrients consumed in the current period and the stochastic term in the production function for child development that causes biases in the estimated impact of such nutrients on child development. The sign and the magnitude of the bias depend upon the exact structure of the model.

Selectivity

Selectivity bias may result if observations are available only for a selected subset of the sample. Such selectivity may occur for any of the relations that are discussed above. For instance, suppose that tests of cognitive development are administered to children in childhood development programmes, but not all children of the eligible age range are enrolled in such programmes. If it were desirable to know the impact of childhood development program quality on cognitive development, a function of the general form of relation (3A) could be estimated. But this relation can be estimated only for those children enrolled in a programme, because there are test scores only for those children.

Figure 2 provides a simple illustration of selectivity bias. Consider a group of children who are the same age and sex but who have been exposed to childhood development programmes of different qualities (including no exposure for those not enrolled in childhood development programmes). If there were observations on cognitive test scores and childhood development programme quality for everyone in the sample, the true relation in relation (3A) could be estimated. The solid line in this figure represents this true relation between cognitive test scores and childhood development programme quality, with a slope of g. Of course the observations for most individuals do not fall exactly on this line. For a given childhood development programme quality (e.g., C₁), some observations are above the line (e.g., point A), some are below (e.g; point B), and some may be on the line (e.g., point C). But the true line best summarizes the cloud of points of cognitive achievement test scores-childhood development programme quality combinations for all the children in the whole sample.

However, cognitive achievement test scores are not observed for everyone in the sample. In fact such test scores are only observed for children for whom their parents expected the gains from enrolment in childhood development programmes to be sufficiently large to offset the costs. For simplicity, assume that this means that only children whose test scores would have been, were they enrolled, equal to or greater than the horizontal dotted line at R on the vertical axis in figure 2 are in fact enrolled. Therefore the estimate of the programme impact is based only on the test-childhood development programme subsample above this horizontal line. The problem is that this subsample is not randomly selected. For childhood development programme quality levels below the level at which the true relation crosses R (i.e., C2 in the figure), only children who have sufficiently positive disturbances to get them to R or above are selected into the subsample (e.g., for C1, the child at point A, but not the ones at points C and B). For childhood development programme quality levels above the level at which the true relation crosses R, only children who have sufficiently negative disturbances to get them below R are selected out of the subsample (e.g., for C3, the child at point F is selected out of the subsample, but those at points E and D are selected into the subsample). Thus the subsample selection procedure, with its systematic relation between the disturbance term in the true relation and childhood development programme quality, creates a correlation between the disturbance term and childhood development programme quality for the subsample for which estimates of the desired relation can be made. As a result, if this relation is estimated using only this subsample, something like the dashed slope line is obtained, with a biased estimate of the true relation between cognitive achievement test scores and childhood development programme qualities.

FIG. 2. Selectivity bias in estimated relation of cognitive achievement test score to child development program quality

Possible resolutions for estimation problems

More and better data

If more and better data could be obtained at no or little cost, more and better data clearly would be desirable. If information could be collected on more variables that are unobserved in current data sets being used for analysis, the problem of omitted variable bias due to unobserved variables could be lessened.¹⁷ Unfortunately, information on some such variables - e.g., genetic endowments - is likely to be very difficult to obtain. Nevertheless some researchers have made efforts (not without controversy) to obtain such data (e.g., the use of Raven’s test to represent innate abilities in Kenya and Tanzania [14]).

Measurement error bias could be lessened with better data in the sense of more accurate variables. For example, instead of using parent-reported time in formal childhood development programmes, one could obtain the actual time recorded in the records of the childhood development programme(s) attended. For events for which timing in the past is important, one can help fix the timing through reference to significant events in the individual’s life (e.g., major disasters, major rites of passage, major political events). Measurement error bias also could be eliminated with alternative reports on the same variables that could be used as instruments (see below) if the measurement errors in those reports (even if large) are not correlated with the measurement errors in the original variable. To illustrate, schooling reports from adult siblings or from adult children have been used for this purpose, as in some recent studies [7, 9].

But more and better data do not come free or, usually, at little cost (either in terms of money or time or the co-operation of respondents). So decisions always have to be made about the trade-offs, which vary depending on the analyses that data will be used for.

Experiments

A major problem in evaluating policy and other determinants of household and firm behaviours, and in evaluating the impact of childhood development and other human resources on various outcomes, is that the right-side variable, the impact of which is of interest, is not independent of the compound disturbance term (including any unobserved variables) in the relation being estimated. A possible resolution of this problem, at least in some circumstances, is to conduct experiments with random assignment of the “treatment” and a comparison group for control.

For example, in order to evaluate the impact of a new childhood development programme on later schooling success, in principle, participation in such childhood development programmes could be given to a random subset of children of eligible age, with before-and-after comparisons made of changes in the school experiences of those randomly selected for the childhood development programme (and for those not selected). With such an experiment one could obtain an estimate of the household demand response to the new childhood development programme. Note that what is obtained is nor the production function response in relation (1). This is the case because, from the point of view of the household, the new childhood development programme is an added household in-kind resource that can be distributed (at least in part) to whatever use the household wishes (e.g., by reducing other childhood development investments that might have been undertaken in the absence of the programme). For this reason it would be desirable to tie such experiments to household surveys so that the possible effects on other outcomes could be measured.

Well-conducted experiments, thus, would provide additional useful information for evaluation of many policy options, including some related to childhood development. Linking such experiments to household survey data might usefully permit exploration of “spillover” effects and possible selective attrition. But it is difficult in many contexts to conduct such experiments - though families interested in childhood development might be randomly selected into experimental and control groups, those who are not interested cannot be so selected, so the population for which an experimental sample is useful is a selected sample. It also is difficult to assure that the experimental “treatment” in fact is received by all of the experimental group and not (nor some close substitute) by the “control” group. Moreover, “experimental effects” may cause distortions, and it is difficult to devise experiments relating to childhood development in which there is a placebo that can be administered that appears to participants and to administrators to be identical to the experimental treatment of interest. Further, questions of fairness or of ethics may preclude a number of experiments.¹⁸ Finally, conducting experiments usually is relatively costly and often difficult to arrange because of pressures on those administering the experimental treatment to include others than just those in the experimental group.¹⁹

Fixed effects

In fixed effects estimates, dummy variables are included for the unobserved fixed effects at the aggregation level of interest (i.e., individual, family, firm, community). Therefore the correlations between these unobserved variables in the compound disturbance term and the observed variables are eliminated, so this possible source of omitted variable bias is eliminated. To use fixed effects, multiple observations are required that have the same fixed effect in the same relation being estimated (i.e., observations on various children in each of a number of families at a point of time or on the same children in different childhood development programmes over time for family fixed effects).²⁰ These dummy variables control for all the factors that are common and fixed for the level of aggregation for which they are used. Family fixed effects, for example, control for all the observed and unobserved fixed family characteristics that enter into production functions in relation (1) or demand functions in relation (2) - for instance, for fixed but unobserved parental preferences for child quality and parental child-rearing capabilities. Therefore their use eliminates omitted variable bias at the level(s) of aggregation for which they are used.

Limitations of fixed effects estimates include: (1) they can only control for predetermined fixed unobserved variables and not predetermined time-varying unobserved variables; (2) they do not permit estimates of the impact of observed fixed variables for the same aggregation level as are the fixed effects (i.e., with individual fixed effects based on data over time one cannot obtain estimates of the impact of observed individual variables that are fixed over time as, for example is usually the case for adult schooling); and (3) they exacerbate random measurement problems because the estimates for the effect of variables that vary within the group of observations for which there are fixed effects are based on deviations from the means for that group, so random noise is relatively much more important than in level estimates without fixed effects.

Instrumental variables

In instrumental variable estimates, the intent is to replace observed right-side variables that are correlated with the compound disturbance term with their estimated values, based on a set of instruments, that are not correlated with the compound disturbance term. This procedure can thus eliminate correlations between observed right-side variables and the compound disturbance term that arise because of unobserved variables, because of simultaneity in production function estimates, and because of unobserved variables in demand function estimates. The right-side variables that are instrumented generally include behavioural variables within the model in production functions but may also include variables that are considered predetermined within the model in either production function or demand function estimates. If parental schooling levels are among the right-side variables in cognitive achievement production functions and unobserved parental or child (given genetic inheritance) innate abilities are in the compound disturbance term, for example, estimates of parental schooling effects are subject to an omitted variable bias problem just as are estimates of observed right-side variables that are behavioural in the model. That is, the relevant notion of predetermined for estimation purposes is independence from the compound disturbance term, not just what is assumed to be given a priori in the model.

Good identifying instruments have the following properties: (a) they do not appear in the relation being estimated; (b) there is at least one such observed instrument for every observed behavioural right-side variable in the relation being estimatedi²¹ (c) they are independent of the compound disturbance term (which includes all of the relevant unobserved variables) in the relation being estimated; and (d) they are sufficiently correlated with the observed right-side behavioural variables. If instruments are used that have these properties, the correlations between the observed right-side behavioural variables and the compound disturbance term are eliminated by using for the former their estimated values based on the instruments. Primary candidates for identifying instruments in a production function are the right-side variables in the demand relations for the right-side behavioural variables that do not appear in the relation being estimated - basically the predetermined prices and resources broadly defined [with the latter subject to condition (a)] in the demand relations (3) discussed above. For demand function estimates, any variables that are included in the demand functions do not satisfy condition (a). For conditional demand functions with variables predetermined from an earlier period, the natural instruments for these variables are the subset of their past determinants that are independent of the current right-side predetermined variables, such as past price shocks or other shocks.

In practice, finding such instruments is often difficult. In particular for production functions, if there are unobserved behavioural variables (XI^ub, XF^ub) in the compound disturbance term, these depend on the same predetermined variables in the demand relations as do the observed variables, so that set of predetermined variables does not satisfy condition (c). Therefore most instrumental variable estimates of production functions are unbiased conditional on the (often implicit) assumption that there are no unobserved behavioural inputs. But this generally is likely to be a strong assumption, as is suggested by table 1. This particular problem does not exist for demand relations. But for demand relations, as for production functions, the past data necessary to instrument variables that are determined prior to the period of estimation are not available in many data sets. For such reasons, instrumenting for variables determined within the model, and for measurement error and fixed effects for controlling for unobserved fixed variables are combined in a number of studies.

Selectivity control

The basic approach to controlling for selectivity is to incorporate the sample selection decision rule into the analysis. That is, for the case discussed above of estimating the relation between cognitive test scores and child development programme qualities, the approach is to incorporate the decision rule for whether or not a child is enrolled in a child development programme into the analysis. There are various ways of incorporating the sample selection decision rule into the analysis. Perhaps the most widely used method is Heckman’s two-step method. In the first step, the selectivity rule is estimated, and in the second step, the relation of interest is estimated including among the right-side variables a statistic calculated from the first-stage residuals that corrects for the effect of sample selectivity on the original disturbance term (so that it no longer is correlated with the observed right-side variables).²²

Framework for policy choices related to childhood development

Brief definitions of basic motives for policy changes
Specific examples of possible inefficiencies in childhood development
Endnotes

Standard economic rationale for policies includes concerns about efficiency/productivity and about distribution, concerns that interact. This rationale holds for policies related to childhood development and other human resource investments, just as for policies related to other aspects of the economy. This rationale may be of interest for individuals working in childhood development not only to help them think about the nature of policy choices that they want to make, but to make them more effective advocates in debates with others, such as those in the Finance Ministry, about public resources devoted to childhood development.

Brief definitions of basic motives for policy changes

Economic efficiency

A situation is efficient if no one person could be made better off without making someone else worse off.²³ Or, to make the statement in reverse, if there is inefficiency, some people could be made better off with the same resources without making anyone worse off. Or, equivalently, everyone could be made better off with the same resources. It would seem from such statements that inefficiency, all else equal, is clearly not socially desirable.

Some critics claim that efficiency relates to small static gains, not the radical restructuring needed for the process, of development. But even though many of the examples given and estimates made about efficiency are static in that they relate to gains/losses from reallocating production inputs and/or the composition of output at a point of time, there is nothing inherent about the notion of efficiency that limits its applicability to static considerations. Efficiency can be considered with regard to questions of production/consumption/factor use over time as well as at a point of time. Moreover, efficiency in a static sense is likely to be necessary, though not sufficient, for dynamic efficiency.

In the real world, furthermore, information problems are pervasive. These information problems make effective directive policies, including those to restructure radically economies and societies, very difficult to know, implement, and monitor. Given these information problems, in many contexts, the best policies from an efficiency perspective may be ones that assure that the private incentives for behaviour are the same as the social incentives for behaviour, which is just the condition for efficiency.

Inefficiency may arise from “market failures” such as externalities (i.e., effects of one unit that are external to that unit in ways that are not transferred through market prices), increasing returns to scale over the relevant output range (so that prices do not reflect the true marginal social costs), and public goods (in which case the marginal cost of providing marginal benefits is zero, so pricing at marginal costs cannot provide revenues to cover total costs). Inefficiency also may arise from “policy failures” such as restrictions on prices (including wages) so that they do not reflect marginal costs and restrictions on entry and exit so that sellers or buyers can affect the prices that they face (and therefore have incentives to set prices different from marginal costs).

Distribution

Distribution is a major policy motive distinct from efficiency. A very efficient economy might have a very undesirable distribution of command over resources. Society well might want to assure, for example, that everyone has basic education and employment skills even at some cost in terms of efficiency/productivity.

An important question is whether there are distributional reasons to subsidize programmes for children, including childhood development, health, and nutrition programmes, particularly in light of the questions about how choices should be made among policy options.

One argument in favour of such subsidies is that they are a means of getting resources to poorer families. For this to be a justifiable motive for such subsidies, they have to be targeted effectively towards children from poorer families, not towards all children. Most social sector programmes in fact do not succeed all that well in concentrating resource transfers to the poor, so this is not a trivial consideration. Secondly, there has to be a more effective way to transfer resources to poorer families than subsidizing other goods and services used by such families (e.g., basic staples) or simply transferring cash. Again, this is not a trivial concern. If the object is to increase the welfare of the poor as much as possible, for example, it would seem that the most efficient mechanism would be to transfer generalizable resources such as money or earning power to them, not particular goods or services in kind such as subsidized child development programmes.

A second argument in favour of such subsidies is that society has a distributional interest in avoiding extreme poverty for any generation, and the most effective way to lessen the probability of current children living in poverty from experiencing similar poverty when they become adults is to improve their human resources so that their command over resources will be greater when they are adults because of labour market returns to those human resources. An essential part of this strategy, moreover, is establishing the fundamentals of their human resource development through strong child development. As stated, this argument is for subsidizing human resource investments in those children who are at greatest risk of being in poverty as adults, not necessarily children who live in poor households and certainly not all children. But because perceptions are that intergenerational correlations of poverty are high, a major target group for this reason often is children in poor families.

A third argument sometimes made is that society as a whole has more interest in the next generation than do individual parents, so investments in children should be subsidized. Although this argument might have merit on distributional grounds, in most societies it is not a distributional argument in favour of poorer members of society. On the contrary, for most societies the long-run secular positive trend in economic growth means that on the average current children are likely to be better off in economic terms than their parents.

A fourth argument is that better child development will reduce the probabilities of subsequent subsidies for public services such as for health and welfare transfers given current pricing/subsidies for social sector policies. But arguably better child development will increase the probabilities of subsequent subsidies for other public services, such as for schooling, so it is not clear what is the net effect. Moreover, the more fundamental question pertains to pricing all the social sectors correctly in the sense discussed below.

A fifth argument is that children have basic rights that society must guarantee if they are not provided by their own families. This would argue for targeting publicly subsidized child development programmes, to the extent that they are justifiable, on these grounds towards children who otherwise would not have such rights fulfilled, not towards child development more generally.

Choosing among policies

There are a number of reasons why private decisions relating to childhood development and other human resource investments may not be efficient within a particular market and policy environment. Explicit examples are discussed below. There also are ,concerns about distribution - most commonly, the command over resources of the poorer members of society - that often have been among the motives for policies related to childhood development.

If all other markets in the economy are operating efficiently and there are differences between marginal private and social incentives in the human capital investment market for childhood development so that private incentives are to invest at levels other than the efficient levels, policies that changed the human capital investment to the socially efficient levels would increase efficiency.²⁴ However, that still does not indicate what policies would be best to induce human capital investments, including those in child development, at desirable levels. There are a large range of possibilities, including governmental fiats and regulations, governmental provision of childhood development services, price incentives in the market for human capital investments, price incentives in other markets, changing institutional arrangements in various markets, etc.

Three important considerations should guide choices among alternative policy changes.

First, policies have costs - not only the direct costs of implementation and monitoring, but also the distortionary costs introduced by policies that may encourage socially inefficient behaviour. These include the distortionary costs of raising revenues to finance fiscal expenditures that are necessary for policy formulation and implementation, which in some cases are estimated to be considerable (e.g., [16]). In fact the costs may be sufficiently large that it is not desirable to attempt to offset some market failures by policies. But, if it is desirable to do so, there is a case generally for making policy changes that are directed as specifically as possible to the distortion of concern (or as high as · possible in a policy hierarchy defined by increasing distortion costs) because that lessens the distortion costs introduced by the policy. The less well focused are policies, the more widespread and more substantial are likely to be the distortion costs of the policies themselves, in addition to any distortion costs from raising revenues to finance the policies.

Second, there are tremendous information problems regarding exactly what effects policies have, particularly in a rapidly changing world. This is an argument in favour of policies that are as transparent as possible, which probably generally means higher in the policy hierarchy with regard to distortion costs because more direct policies are likely to be more transparent. This also is an argument for considering an experimental approach to evaluating policy alternatives - that is, rather than introducing a reform countrywide, introduce variants of reforms for childhood development programmes, schools, and other social services selected randomly with carefully monitoring of the results (though there are limitations to the use of experimental approaches. The information problems are often an argument for price policies (taxes or subsidies), because if there are shifts in the underlying relations they are likely to be more visible in a more timely fashion if they have impact on governmental resources than if they only change the distortions faced by private entities, as tends to happen with quantitative policies. Furthermore, there is a strong argument for governments to subsidize the collection and provision of more information about childhood development markets more generally, because information is not likely to be provided optimally otherwise by private providers. Information has “public goods” characteristics in the technical sense of that term. The marginal cost of providing more information is very small and possibly declining, so private providers cannot cover their costs of provision except by restricting the quantities provided and charging a price above the low marginal social costs. The relevant information includes not only information about the functioning of human resource markets and possible market failures, but also serious evaluations of governmental policies that are related to childhood development and possible policy failures. Too often policy evaluation is an afterthought at best, with little attention before policy changes to establishing critical baseline data and little attention in the analysis to the incentives created by the policy changes for private behaviours and to the estimation problems that are discussed above.²⁵

Third, as noted above, distribution is a concern separate from efficiency. Moreover, there well may be tradeoffs between policies that increase efficiency and distributional ends. If increasing childhood development for those for whom the rates of return in terms of productivity are highest is efficient, and if there are positive complementarities between childhood development and schooling, as is often claimed, then there is a tradeoff between increasing childhood development for persons for whom the productivity effects are greatest and increasing childhood development for the persons who are poorest.²⁶ Society might have the objective of assuring that everyone (or everyone but those who are disabled or too young or too old) have basic education. But presumably it is desirable to assure that everyone has basic education at as little cost in terms of productivity as possible. Therefore, rather than ignoring efficiency considerations in pursuit of distributional goals, it is desirable to choose policies as high as possible in the efficiency policy hierarchy and still assure that the basic education targets are met. Efficiency considerations play an important role in interaction with the pursuit of distributional goals.

Thus, for efficiency/productivity reasons, particularly given that information is imperfect and changes are frequent, there is an argument generally for choosing price policies as high as possible in the policy hierarchy defined by the extent of distortionary costs - and thereby using interventions that are as focused on the problem as possible in light of the distributional tradeoff and possibly other constraints on policy choices. Note further that this means that if there is a good efficiency/productivity reason for public support for childhood development or for other human capital investments, that does not mean that the best way to provide that support is through governmental provision of the related services. Higher in the policy hierarchy than direct governmental provision of such services, for example, are likely to be subsidies or taxes that work through individuals or firms to create incentives for the efficient provision of these services whether the actual providers are public, private, or some mixture. On the other hand, policies that discriminate against one type of provider - for example, by making the availability of such subsidies dependent on whether the provider is public - are generally likely to be lower in the policy hierarchy than policies that do not have such restrictions. Information problems are likely to be pervasive, finally, and may in themselves warrant policy changes.

Specific examples of possible inefficiencies in childhood development

Related markets, empirical evidence, and policy options

It is useful to consider some explicit respects in which childhood development-related markets might be inefficient in the absence of policy changes. Of course it is impossible to give generalizations that apply to all or even to most countries. For serious policy recommendations, there must be careful consideration of the specific situations in a particular case, with sensitivity to the underlying behaviours and to the problems in interpreting those behaviours, given limitations on information. Nevertheless, there are some general arguments that have been put forth for policy changes related to childhood development that merit attention, even if definitive conclusions about their merits in particular contexts only can be reached with confidence by considering in detail those particular situations.

The private incentives for investments in childhood development and other human resources are largely those that are given by markets that individual units - households and firms - engage in (although there may also be some important incentives other than market incentives, such as those within units such as household or firms, that could lead to inefficiency²⁷). Under standard assumptions regarding production technologies, if prices are “right” in the sense that they reflect the true social marginal benefits and costs and markets are complete, an entity (family, household, farm, household enterprise, factory, trading firm, or whatever) that is maximizing its own revenue net of costs chooses the efficient combination of inputs for each product, efficient quantities of all inputs, and efficient quantities of all outputs. Such production entities, under these assumptions, behave efficiently by following the marginal conditions discussed above, given that from their individual perspectives prices are fixed by markets. Likewise, if prices are right in the above sense and markets are complete, families that maximize their objective functions by satisfying the marginal condition that marginal welfare for the last rupee (peso or whatever) spent on all goods is the same, choose efficient consumption bundles. Inefficiencies thus usually are deemed to reflect “market failures” in the sense that market prices fail to incorporate all social marginal benefits and costs, or that markets are incomplete, or “policy failures” if the reasons that prices do not reflect social marginal benefits lie not in production technicalities but in policies.

Figure 1 can be reinterpreted to consider the question of whether investments in childhood development or in other forms of human capital are efficient. If the private incentives for such investments are the same as the social incentives, the solid curves in figure 1A represent both the marginal private and the marginal social incentives and H* is the privately optimal and the socially optimal (efficient) level of human capital investment. In this case the private and the social rates of return to this investment are the same. Also in this case, even if this rate of return is quite high, there is no efficiency reason for public resources to be devoted to childhood development. Private behaviours result in just the right investments from a social perspective.

Now consider what happens if the private and social incentives differ for human capital investments, first with respect to the marginal benefits and then with respect to the marginal costs. Note that in each of these cases the social rates of return for this investment differ from the private rates of return, which suggests an efficiency argument for a policy change.

Let the dashed line in figure 1B represent the marginal social benefits for human capital investments that are drawn to be greater than the marginal private benefits.²⁸ In this case the private incentives are to invest in H*, which is less than the socially optimal (efficient) level of human capital investment H**. Therefore there is an efficiency argument to consider policies to induce or to require private investments of H ** instead of H*.

Why might marginal social benefits exceed marginal private benefits for human capital investments? Among the most frequent answers to this question are some that primarily reflect market failures (e.g., examples 1-2,4-5, and 9-11 below) and others that reflect policy failures (e.g., examples 3,6-8 below):

1. Private investors in childhood development and other forms of human capital underestimate the true private and therefore social returns from such investments. Policies that would seem to be high in the efficiency policy hierarchy for this reason would be policies that subsidized provision of current information on patterns in expected returns to human resource investments: costs of different types of childhood development investments and schooling, enrolment rates, placement and schooling and job progression of graduates (e.g., tracer studies), education and childhood backgrounds of different types of workers (e.g., reverse tracer studies) - all related to different types of childhood background. As noted, because of the public goods characteristics of information, such information is not likely to be provided sufficiently by unsubsidized private entities. Less high in the hierarchy would be policies that subsidized childhood development per se. And relatively low in the hierarchy would be direct public provision of childhood development programmes. The beneficiaries of such policies might include the poor, but also are likely to be considerably those in the middle- and upper-income classes who have the basic education that permits them to exploit better information about childhood development options.

2. More investment in childhood development, in addition to the direct eventual impact on the individual’s own benefits through facilitating subsequent education and learning capacities, may increase the productivity of others through technological, institutional, and market innovations that are not reflected in the individual’s or firm’s investment returns because information about such innovations is spread other than through markets. There are questions regarding the extent to which childhood development contributes to the development of such capacities. But if basic education is important for the adoption of new technologies, strong child development may be important. In important recent studies, for example, Foster and Rosenzweig [22,23] provide empirical evidence that on-the-job experience interacted with basic education to generate external benefits in the initial spread of Green Revolution agricultural technologies in India. To my knowledge systematic empirical investigations of similar possibilities for basic education in other contexts are not available.²⁹ Although such an externality, if it exists, might rationalize public subsidies for childhood development investments, it would not seem that such subsidies (and much less direct governmental provision of childhood development) would be at the top of the policy hierarchy for dealing with this market failure. Higher in the policy hierarchy would seem to be subsidies directly for experimenting and attempting to adapt new innovations, because that is the direct process that generates externalities through learning. Probably policy changes that are highest in the efficiency policy hierarchy would have unequalizing effects on distribution, or at least not reach the poorer members of society, because early experimenters are likely to be among those better off, or at least not the poorest members of society.

3. Families with children with higher than average unobserved motivation and unobserved abilities, given their characteristics that will be observed by potential employers, are not able to self-finance such human capital investments, because they cannot borrow for such investments. There is considerable indirect evidence consistent with this possibility, in that the characteristics that usually are thought to be readily observed in labour markets - schooling, age, gender, past work experience - are consistent with but a limited part of wage variations. Subsidizing childhood development and other education might be high in the efficiency policy hierarchy for providing a means of signaling such characteristics. There are some studies that suggest that at least in some developing country contexts, formal schooling plays such a signaling role in that its effects remain significant in some empirical wage relations even with control for cognitive skills acquired in part through schooling (e.g., [25, 26]. The policies that would seem to be highest in the efficiency policy hierarchy in this case would be ones that addressed directly the capital market and wage restrictions that preclude self-financing of childhood development and other forms of education (both of which are discussed below). Less high in the hierarchy, but still fairly high, would seem to be various means of certifying skills, abilities, and motivations - although the potential for having useful certification for children of the age in which investments in child development occur would seem to be limited. Subsidies for certification tests might be one such mechanism. Such policies would be likely to benefit some of the poorer members of society (because they are more likely to be constrained from self-financing such investments), but probably not many of the poorest.

4. Uncertainty in combination with households wanting to avoid risk and imperfect or costly insurance options means that the private incentives are to underinvest in childhood development and other human capital from a social point of view, because on an aggregate level such risks are reduced by pooling them across members of society. The considerable dispersions of labour market returns to persons with the same education in most societies are consistent with the possibility that there is considerable uncertainty regarding the returns to human capital investments, although part of these dispersions may reflect variations in abilities and motivations that are observed by people making these investment decisions, although not by policy makers and analysts (so the latter groups’ perceptions may be biased by omitted variable bias. High in the efficiency policy hierarchy to address this possibility would be the development of insurance markets, but the possibility of developing such markets well might be limited because of the standard moral hazard and adverse selection problems. Not quite as high, but still relatively high in the policy hierarchy would seem to be policies that subsidized risky investments in combination with income taxes. If childhood development and other forms of investment in education are relatively risky investments, then they would be covered among other risky investments. Such policies would seem to have the potential of benefiting considerably poorer members of society who are less able to self-insure their investments and may have higher risk aversion (Binswanger’s is a seminal study on the latter [27]).

5. There are social gains beyond the private gains to childhood development and other human capital investments because basic human resources reduce the probabilities of illnesses and unemployment, both of which have social benefits beyond the distributional ones through reducing respectively the stress on public health systems and the probability of illegal activities. Public subsidies for childhood development and other basic human resource investments might be high in the policy hierarchy for such purposes on a priori grounds, although there remains the question of empirical evidence regarding their effectiveness in this regard. Such policies would seem likely to have distributional benefits for relatively poorer members of society.

6. Policies limit price flexibility (e.g., administratively set prices, minimum wages, price floors and ceiling for basic food staples), labour market flexibility (e.g., mandatory termination payments, health insurance and pensions tied to a particular employer) and childhood development programmes (e.g., limiting subsidies to public childhood development programmes) that distort the incentives for childhood development. In recent years, however, there has been some tendency for such regulations to be lessened in many countries. In any case highest in the efficiency policy hierarchy are changes simply to eliminate such policy distortions. The reluctance to do so often is for distributional reasons. Relatively well-off workers with employment in formal sector firms (including providers of child development related services) and relatively well-off governmental employees may have vested interests in maintaining such policies due to the rents they receive from them. There is little evidence that poorer members of society benefit from such policies in most developing countries.

7. Positive marginal income tax rates mean that the private marginal returns to an individual’s human capital investments are less than the marginal social returns. This possibility seems logically to be true ceteris paribus but not very relevant currently for most workers in developing countries and even less relevant for considering child development policies. Furthermore such taxes might be part of a second-best policy package in the absence of insurance markets. In current contexts, removing existing income taxes in developing countries are likely to have benefits primarily for those who already are relatively well off.

8. More investment in childhood development and other forms of human resources may have marginal social benefits above the private wages received because of administratively set wages (e.g., public school teachers, public health workers, public researchers). This appears to be a fairly widespread phenomena in many developing countries. The policy change that is highest in the efficiency policy hierarchy in this case is to pay wages that are competitive with those paid in the private sector. The constraints from doing so often appear to be budgetary in combination with past governmental employment policies that were not oriented primarily towards the efficient provision of governmental services. In many instances steps are under way towards rationalizing the public sector in ways that will lessen this problem, but there are strong vested interests in previous practices. The distributional questions are likely to involve, primarily, who among the relatively well-off members of society will benefit from such restructuring and who will suffer losses.

9. There are incomplete markets for household production of human resources that affect the productivity benefits of childhood development, so different households maximize their welfare functions with regard to different trade-offs rather than the true relative social marginal costs. For an explicit example, in poor populations individuals who are healthier and have better nutritional status maybe more productive, but for many tasks monitoring problems may mean that labour markets do not reward such productivities. Therefore different households effectively make their decisions regarding investments in health and nutrition - that may affect the effectiveness of childhood development - with regard not to the same relative market prices as would be necessary for efficiency, but with regard to different trade-offs. Empirical evidence suggests that this is the case at least in poor rural labour markets (e.g., [28-31]). Policies that would seem to be relatively high in the efficiency policy hierarchy in this case would be ones that improved information about health and nutrition and related productivity of poor people. Possibly childhood development and other educational programmes could serve this purpose, though I am not aware of empirical evidence that is focused on this possibility. If so, the impact would be largely on poorer members of society who are more at risk of not being able to signal their true productivities for such reasons.

10. The productivity benefits of childhood development and other human capital investments are in the future and the social discount rate is less than the private discount rate. Although this is a possibility that has been raised in considerations of whether there are reasons for policies to encourage more investment than individuals would choose on their own, I am unaware of any relevant empirical evidence. Presumably such evidence would have to be based on some weighted responses of a nation’s population that indicated that they would like to give up more current consumption for the purpose of future consumption than they individually decide to do. If this is a reason for public subsidies for childhood development in a particular context, then it would seem that such subsidies for childhood development would not be very high in the policy hierarchy. The basic problem is a very general one about trade-offs between present and future consumption, and not one concerned particularly with childhood development. Higher in the policy hierarchy than policies that directly related to childhood development would be policies that penalized current consumption and encouraged general investment in the future, such as consumption taxes and subsidized interest for investments generally. Probably general policies that discouraged current consumption would, in terms of distribution, be regressive because consumption tends to absorb larger proportions of the income of poorer households. Subsidized interest rates that were available to all, on the other hand, might benefit poorer households who currently do not have access to capital markets (although there remain problems of adverse selection and moral hazards in regard to those markets).

11. There are social gains beyond the private gains to childhood development and other human capital investments because basic human resources for all are viewed by society as inherently valuable in themselves in addition to their effects on individual economic productivity and consumption. Again, as for the previous possibility, while there often is appeal to such a notion, sometimes on nationalistic grounds, it is not clear what empirical evidence is available. Again it would seem that the possible empirical evidence would have to document differences between collective and individual preferences. In this case, however, policies to subsidize childhood development and other human resource investments would seem to be relatively higher in the efficiency policy hierarchy because they more directly address the problem than when the problem has to do with generalized consumption paths. Whether such policies would be equalizing or unequalizing in terms of distribution would depend very much on in what respects human resources are viewed as collectively more desirable than individually. On one hand, everyone having basic human resources might be given emphasis, in which case the policies that are higher in the policy hierarchy would tend to be equalizing or at least pro-poor. On the other hand the goal might be to have world class intellectuals or scientists, in which case the focus would be on the upper end of the distribution, which might be unequalizing (although increasing mobility for a few very bright but poor individuals).

Why might marginal social costs be less than marginal private costs for human capital investments? Among the most frequent answers to this question is one that points primarily to a market failure and one that points primarily to a policy failure:

1. There are capital and insurance market imperfections, more so for childhood development and other human capital investments (in part because human capital is not recognized as collateral) so that the marginal private costs for such investments exceed the true marginal social costs, particularly for those from poorer families who can not relatively easily self-finance and self-insure such investments. Conventional wisdom is that these problems are widespread. Empirical evidence is that childhood development and other educational investments often are constrained by household income, which is consistent with this conjecture if there are not current consumption aspects to such education (e.g., [32]). The first best resolution is to improve these markets, which in many cases may mean public subsidies for improving information about potential borrowers or for providing insurance for them. Less high in the efficiency policy hierarchy, but still probably fairly high (particularly if such problems are greater for educational investments than for many other investments) are public subsidies for childhood development and other education targeted towards poorer members of society. Effective efforts to lessen these problems are likely to benefit relatively poorer members of society who have potential for such education because they are the ones that are most likely to be constrained from undertaking such investments by limited capital and insurance markets.

2. The sectors that provide services related to human capital investments, such as childhood development and schooling, produce inefficiently. This appears to be the case broadly, though the systematic evidence is limited. The insignificance or “wrong” signs of many inputs in many educational production function estimates for developing countries, for example, suggests that the production of these services often is not very efficient (e.g., [33]). High in the policy hierarchy for dealing with this problem would seem to be to create incentives for more efficient production of education by subsidizing information about the value added of alternatives (because such information is a public good, as discussed above), using market pressures to guide production (e.g., through pricing, with vouchers if public subsidies are warranted), and treating all suppliers equally (whether public, private, or nongovernmental organizations) rather than limiting entry or subsidies to certain types of providers. With respect to the distribution of beneficiaries, they would seem to be fairly widespread. But many poorer members of society would be among them because the poor are more likely to be dependent on such institutions and to have been less able to self-finance or use family connections to assure alternative means of acquiring relevant education.

Endnotes

1 Some prices may be easy to observe, such as wages. Others may be difficult to impute, such as the price of child happiness. Discounting makes possible the comparison of two streams of costs and benefits over time by converting them into their present or current values. Discounting is critical for comparing investments in which there are different lags between the investments and the payoff. If the interest rate is r per year, the present discounted value of a rupee received next year is 1/(l+r) rupees, because if one had that much currently, one could obtain an interest rate r and have 1 rupee next year. More generally, the present discounted value of a rupee received or paid in n years is l/(l+r)n. Again of one dollar in 15 years, for example, is worth only $0.47 now if the appropriate discount rate is 5%, only $0.22 if the appropriate discount rate is 10%, and only $0.11 if the appropriate discount rate is 15%. The failure to discount for comparing events that happen at very different points in time, such as for exploring the impact of reducing childhood iron anaemia on adult productivity, can lead to quite misleading results (e.g., overstating considerably the gains from childhood development programmes).

2 These are present discounted benefits and costs (see the previous note).

3 For the last three of these comparisons, the otherwise identical individuals would have to live in different economies.

4 A number of these examples, both on the marginal benefit and the marginal cost side, depend on their being imperfect capital and insurance markets. For example, if capital markets are perfect, heterogeneities in discount rates across households do not have an effect, because all households maximize the present discounted value of their investments at identical market interest rates. Likewise, there is not differential access to financing across households for such investments. If insurance markets are perfect and insurance is costless, moreover, risk does not affect households differentially. But it is widely perceived that capital and insurance markets for human resource investments are missing or quite incomplete.

5 A simple model for the impact of public school quality on household schooling investments is presented and estimated for Brazil in Behrman and Birdsall [2]. If the investor must pay for greater human resource service-related quality, however, investment does not necessarily increase with a higher-quality option. What happens to the equilibrium investment depends upon where the marginal private cost curve for the higher-quality option is, in addition to the location of the marginal private benefit curve.

6 Though this tendency may be offset if, for example, human capital substitutes sufficiently for financial and physical transfers in marriage markets (e.g., Rao [3]).

7 I use linear approximations here because they are the simplest forms that still permit characterization of various estimation issues. Log-linear forms in which all of the variables are replaced by the logarithms of their values (which implies interactions among all the right-side variables) are identical in representation once the variables are redefined. In empirical studies, linear and log-linear specifications are very common, but other functional forms also are used at times. For other functional forms, the essence of the estimation issues is the same. If the functional form that is used is not a good approximation to the true functional form, there is misspecification error that is akin to omitted variable bias discussed below (with the unobserved variable being the variable that would have to be added to transform the assumed specification to the true functional form).

8 For example, all community characteristics usually are assumed to be predetermined. But households, individuals, and firms can change community characteristics by migrating, which is incorporated into some modeling (e.g., [4]).

9 It is not possible, however, to estimate the effect of one behavioural variable determined in the current period on another with demand relations. This point is not always understood, so it is developed briefly in this note. For example, current childhood development may be posited to be determined simultaneously with current child nutrient intakes. Consider the following two demand relations for current childhood development (Z_C) and for current child nutrient intakes (Z_N) as dependent on two prices (PF₁, PF₂), predetermined resources (RF), and stochastic terms (V_c, V_N):

(3 a-1) Z_C = b₁₁PF₁+b₁₂PF₂+b₁₃RF+VC and
(3A-2) Z_N = b₂₁PF₁+ b₂₂PF₂+ba₂₃RF+VN.

These two relations imply:

(3A-3) ZC = b₃₁ZN+b₃₂PF₂+b₃₃RF+V_C’

10 A number, but not all, of recent studies report evidence using twins or other sibling data or direct measures of ability that suggest that usually unobserved endowments have direct effects on wages (e.g., [6-13].

11 To be able to learn about the productivity rather than the earnings impact of schooling, moreover, there must be knowledge of the relation between private earnings and marginal productivities.

12 Usually it is random measurement error that is emphasized; it is discussed here. Measurement error also may be systematically related to the true variable, with implications that depend on exactly what is the nature of the systematic relation.

13 F_C² is standard statistical notation for the variance in C, which is simply a measure of how much the individual observations of C differ from the average (mean) value of C.

14 Conditional on the assumptions for the Mincerian earnings functions, there is not such a problem in this case. But the assumptions on the production technology are quite strong, and some studies suggest that they are not justified in fact (e.g., for estimates of schooling responses to endowments, see [9,10]). Hedonic wages/prices may have an omitted variable problem, because all characteristics of the person/item being priced are not observed. For example, observed schooling may be correlated with unobserved factors that affect wages, such as ability, motivation, and family connections.

15 The compound disturbance term includes all the unobserved variables unless their effects are controlled in some way (see the discussion of fixed effects below).

16 Misspecification of the functional form has similar effects. If there should be interaction terms, for example, but they are not included and they are correlated with any of the included terms, the estimates of the included terms are biased in way that is analogous to omitted variable bias.

17 Strictly speaking, this should read that “the problem of omitted variable bias due to unobserved variables probably could be lessened.” If there is only one cause of bias in an estimate, eliminating that cause eliminates the bias. If there is more than one cause for a bias, eliminating any one cause does not necessarily lessen the bias, because some other bias may have been offsetting the one the cause of which is eliminated. But in the absence of information suggesting that eliminating any particular bias exacerbates the problems due to another counteracting bias, the presumption is that eliminating a particular bias probably lessens the total bias. This is analogous to considerations about efficiency and eliminating distortions that are mentioned briefly below.

18 In some circumstances, such as the introduction of a new programme or a new programme feature, the change cannot immediately be instituted nationwide in any case. Therefore there is potential for introducing it randomly initially, a possibility that has been exploited in a few recent cases.

19 There have been considerable efforts at conducting experiments to evaluate other human resource investments, such as training programmes in the United States. Heckman et al. [15] review these efforts and elaborate on the limitations of these experiments.

20 This means that panel (longitudinal) data generally must be used to control for individual fixed effects (though there are a few exceptions, such as using data on identical twins to control for fixed individual genetic endowments).

21 This statement assumes that identification is by exclusion restrictions, which is the most common assumption, but not the only possibility.

22 Implementation of this method requires that the statistic used from the first stage (the “inverse Mills ratio”) be identified by variables that enter into the decision rule but not directly into the second stage or by functional form. For example, family firm product prices may affect whether a child is enrolled in a childhood development programme, but perhaps not what the child learns if the child does enroll.

23 Note that this is not the same as engineering or scientific efficiency. An engine that is very efficient in the engineering sense, for example, may be very inefficient economically because it uses inputs that have better uses elsewhere.

24 If all other markets in the economy are not operating efficiently, policies that narrow the differences between private and social marginal incentives in the human capital investment market or in some segment of that market do not necessarily increase efficiency and productivity. Clearly, in the real world there are many market failures and incomplete markets, so some distortions may be counterbalancing others. But in the absence of specific information to the contrary (such as on the existence of two counterbalancing distortions), a safe operating presumption is that lessening any one distortion between social and private incentives is likely to increase efficiency.

25 For example, to analyse well the impact of policies, it often must be recognized that policies are not predetermined, but are made by individuals or groups of individuals with various objectives in mind, including accommodating to pressures from and needs of constituents. The failure to control for the determinants of governmental policies may cause substantial misestimates of their effectiveness [17]). The basic intuition is clear from considering the simple example of evaluating the impact on cognitive development of childhood development programmes from cross-sectional data from a number of communities. If the resources devoted to such programmes tend to be concentrated in communities that have greater political power, wealth and better-off children net of their effects, the association between child cognitive development and resources devoted to childhood development programmes overstates the effectiveness of the programmes on cognitive development unless there is control for resource allocation among childhood development programmes in different communities. On the other hand, if the resources devoted to such childhood development programmes tend to be concentrated in communities that have poorer health environments, greater poverty, and less well-off children net of the effects of the childhood development programmes, the association between child cognitive development and resources devoted to childhood development understates the effectiveness of the childhood development programmes on child cognitive development unless resource allocation among childhood development programmes in different communities is controlled for. A number of recent studies both characterize the underlying objective functions for governmental behaviours and find that controlling for such behaviours alters substantially the estimated impact of governmental programmes (e.g., [18,19]).

26 The available studies on the positive relations between productivity (or wage) gains and childhood development - education interactions, however, may overstate the causal effect because of the failure to control for the selectivity of childhood development in the presence of important unobserved (by analysts) attributes, such as ability and motivation.

27 Udry [20] provides a recent empirical study of inefficiencies within African households with regard to the allocation of productive resources, including labour time, between men and women. Other studies are reviewed elsewhere [21].

28 The marginal social benefits also could be lower than the marginal private benefits, in which case the marginal social benefits curve would be below the marginal private benefits curve, and policies to attain efficiency would have to reduce the private incentives to the social levels. The basic analysis would be the same, but with the opposite sign on the differences between the marginal private and social benefits and therefore on the appropriate policies. To keep the presentation as simple as possible in the text, I consider only the case in which the marginal social benefits exceed the marginal private benefits, which is the case usually emphasized in the literature on human resources.

29 The empirical evidence to which reference usually is made regarding educational externalities includes micro individual or firm-level evidence of the economic impact of education on wages or productivity. Most studies are not very sensitive to the estimation issues that arise, because education reflects behavioural choices, so it is hard to know how to interpret such estimates. But even if it is assumed that they are not biased due to such problems, they do provide estimates of the private rates of return to time spent in school (and possibly indirectly childhood development) and estimates of the “social” rates of return that incorporate, in addition to the private costs, the public costs. For low-income countries, for example, the average estimated “social” rates of return to primary, secondary, and tertiary schooling are 23.4%, 15.2%, and 10.6% [24]. Prima facie this might seem to be a strong case for public support for basic schooling in low-income countries. But these “social” rates of return say nothing very useful about differences between social and private rates of return. True, the same source summarizes the average private rates of return to these three levels of schooling to be different from the “social” rates of return, with the average private rates of return, respectively, at 35.2%, 19.3%, and 23.5%. But if the comparison were to be interpreted to tell anything about efficiency motives for policies, the conclusion would be that public schooling subsidies should be reduced to zero to eliminate the differences between the “social” and the private rates of return, not maintained or increased. However, this conclusion does not require any estimates, but follows directly from the way in which the “social” benefits are calculated, i.e., effectively adjusting the estimated private rates of return to include public costs beyond the private costs. These “social” rates of return make no effort to incorporate differences in private and social benefits due to externalities. Thus they provide no basis for concluding that on efficiency grounds there should or should not be subsidies for schooling, nor that on efficiency grounds one level of schooling should be subsidized more than another.

30 The marginal social costs also could be higher than the marginal private costs, so a comment parallel to that in a previous note also applies here.

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