We then exploit a unique feature of child care markets and a unique data set to examine empirically the effects of information provision by public and not-for-profit agencies. In some child care markets, Resource and Referral agencies (R&Rs) provide a centralized source of information on location, price, and observable characteristics of child care. R&Rs are generally grass roots, not-for-profit organizations whose primary function is to help parents find appropriate child care for their children. Consumers in markets with R&Rs can reasonably be assumed to have better information or lower search costs than consumers in markets that are not served by R&Rs. We study the effects of R&Rs on market outcomes using data from a diverse number of sources, including firm-level data from a nationally representative sample of child care centers, various compilations of child care policy variables, and two special surveys carried out for this project.

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### Monthly Archives: June 2014

The market for child care is characterized by vertical differentiation and asymmetric information between buyers and sellers, where buyers incur substantial search costs to learn about variations in prices and care characteristics. Such informational imperfections are common to many markets and have fundamental implications for how product markets function.

The results suggest a number of extensions. Given the limitations in our sample period and the reliance on T-asymptotics to identify the parameters of interest, we have worked with very simple preference specifications. It would be interesting to work with preferences that are a more general the way demographic and labour supply factors are allowed to affect utilities. One possibility would be to estimate these effects using a longer time period and the Euler equation for a relatively safe asset and then check over the shorter period whether the orthogonality conditions hold, given the particular preference structure estimated. More generally, it would also be interesting to consider more flexible forms of preferences, including the non-expected utility preferences of the kind studied by Epstein and Zin (1989) and models with habit formation. The problem with the latter, however, is that they are very hard to study without longitudinal data.

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This paper has looked at the empirical failure of the Consumption Asset Pricing Model in the context of recent secular changes in the number and type of shareholders in the UK. Since the first order conditions for the model only hold as an equality for individuals that are currently participating in asset markets, it is natural to look at the consumption behaviour of these individuals rather than the aggregate population. Pursuing this empirical strategy poses a number of problems. Not only do we need household level information on consumption and on asset ownership, but also we have to deal with the fact that asset ownership is neither a permanent nor an exogenous status for the households in the survey. In addition, the data that are available, while providing excellent information on consumption and share ownership, are not a panel. This is problematic since the Euler equation holds only for those owning shares in adjacent periods. To deal with this we present an extension of the synthetic cohort technique which defines groups of individuals with constant membership at adjacent dates on the basis of the estimated probabilities of owning stocks.

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The results for the group of likely shareholders, reported in the first column of Table 4, are remarkably good. The point estimate of the coefficient of the iso-elastic utility function is consistent with concavity. It implies a value of the elasticity of intertemporal substitution of about 0.80, consistent with other estimates of this parameters in the UK reported in the literature.10 Finally, the value of the test of over-identifying restrictions is very low and does not indicate any deviations from the null.

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Our second approach is to estimate versions of the Euler equation given by equation (5) for the real return on shares for the total sample and for the two groups defined on the basis of the conditional probability of share ownership. Results are reported in Table 4. As mentioned in Section 2, in the absence of measurement error, any variable dated t-1 is a valid instrument As we use grouped data, however, small sample variability induces MA(1) errors and therefore one has to lag consumption growth twice to avoid getting inconsistent estimates.17 Furthermore, one needs to correct the standard errors for the presence of such an error structure. Finally, one can improve the efficiency of the estimates relative to a simple IV procedure by using a GMM estimator.

There are several ways in which the IMRS can be estimated or approximated. In the simplest version of the life cycle model, the marginal utility of consumption is a monotonic transformation of consumption. In more complex and possibly realistic versions of the model, the IMRS might depend in a flexible fashion on the composition of the household as well as on labor supply behavior. As a detailed characterization of preferences is not the main focus of this paper, we use a parsimonious specification. We assume that utility is an isoelastic function of non-durable consumption per adult equivalent.

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**A Probit model for share ownership**

We obtain the probabilities of share ownership by estimating a problt model on a pooled sample of data containing more than 80,000 households. On the right hand side we include polynomials in age and time, education dummies and interaction terms in these variables. It is important to stress that the time trends are interacted with the other explanatory variables, to allow for the fact that the effects of factors such as age and education appear to change over time. The results (reported in Table 3) show that the probability of share ownership increases with age, time and higher levels of education -although the positive effects of college education and A levels on share ownership diminishes over time. We have obtained very similar results by estimating a different probit for each year in the sample.

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The Euler equations used in asset pricing relationships are not necessarily a simple function of consumption growth. Typically, they involve the rate of growth of the marginal utility of consumption. As long as the IMRS can be made a linear function of parameters, this is not necessarily a problem. Indeed, the Euler equations we estimate below (and discuss in Section 2) were log-linearized for this reason. However, non-linearities do constitute a problem if one works with expressions for the IMRS such as that in equation (9) used to compute the Hansen-Jagannathan bounds. This expression involves the interaction of consumption at time t and /+/, which we cannot compute. Therefore, we approximate the left-hand side of (9) by the following expression:

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The second issue is that the composition of the group of likely shareholders changes over time, both because the probability of ownership may change over time and because the cut-off point changes. If intertemporal prices were the same across individuals and the utility function depended only on consumption and not on unobserved (or unaccounted for) heterogeneity, this would not be a problem. The measured IMRS would differ from the expected one only because of an expectational error that would average to zero over time. In the presence of unobserved heterogeneity, however, the measured IMRS encompasses both genuine changes in consumption growth and composition effects. This introduces a spurious source of volatility. To make this point clear, suppose that the instantaneous utility function is given by и(с;У;) = (1-гУ'(с’;Г exp(r^), where represents unobserved heterogeneity and we are ignoring the effect of demographic and other observable variables for notational simplicity. Continue reading…