They offer contributions to the study of matching in foster care (Chapters 1 and 2), and to the study of the effect of product market competition on managerial incentives (Chapter 3). The empirical application uses a new dataset of confidential care records from Los Angeles County, California.
INTRODUCTION
In particular, the estimates of the model show that if placements were assigned across all administrative regions of Los Angeles County, (i) the average probability of placement disruption across all placements in the system would be reduced by 4.2 percentage points (equivalent to a reduction of 8% in the expected number of foster homes children go through before leaving foster care), and (ii) the distance between foster homes and children's schools would be reduced by 54%. The model captures several dynamic trade-offs, particularly between children's age and the heterogeneity in the expected duration of placements.
WHO GETS PLACED WHERE AND WHY? AN EMPIRICAL FRAMEWORK FOR FOSTER CARE PLACEMENT
Introduction
Nevertheless, it is quite common for children to move through multiple foster homes while in foster care.1 By understanding how children are assigned to foster homes, one can analyze how the matching mechanism used in the field translates into outcomes via placement characteristics. Slaugh, Akan, Kesten, and Ünver (2016) is the only other article in the literature that applies matching and market design tools to a question related to foster care.
Institutional Background and Data
Administrative management of the foster care system is at the county level in the United States.6 The child welfare agency in Los Angeles County is the Department of Children and Family Services (DCFS).7 Like other child welfare agencies, DCFS is responsible for processing and investigating reports of child abuse, taking cases to court and enforcing court decisions. For example, when evaluating prospective foster homes, they may take into account scheduling and transportation considerations, the family environment of the foster home (eg, the age and gender of the family's biological children), and other idiosyncratic factors such as experiences of foster parents and a child's history in the system.
Model
The observed match and the realized outcomes (Mi,Ti,Ri)ni=1 are the outcome (or endogenous) variables of the model. Therefore, the distribution of flavor variation parameters can be obtained directly from the matched data.
Identification Outcome DistributionOutcome Distribution
Identification of the parameters in the matchmaker utility function (µ,ϕ,ϕ¯) is straightforward when the mixing distribution is identified and ϕem = 0 is set. Finally, I discuss the identification of the covariance matrices of the flavor-term variability, Σε and Ση.
Estimation
I then show how to calculate the simulated log-likelihood of the data, which essentially means integrating outΩi from (1.23). To calculate this integral, I draw a sample of Sυ independent draws of the flavor variation terms εc and ηh.
Estimation Results Empirical SpecificationEmpirical Specification
Placements with older children generally have a shorter duration, regardless of the reason for cancellation. This captures that the valuation of an age-based proxy varies with the reason for termination.
Market Thickness
Conclusion
The model includes key institutional features of foster care placement: (1) children should be placed with relatives whenever possible; (2) social workers must prioritize the location of prospective foster homes relative to children's schools, and (3) social workers have discretion in how to weigh all factors contributing to a successful placement. An empirical exercise uses a new dataset of confidential foster care records from Los Angeles County, California. A key contribution of this chapter is the quantification of the benefits in terms of better placement outcomes arising from denser markets in foster care.
MATCHING IN FOSTER CARE: A DYNAMIC AND CENTRALIZED APPROACH
Introduction
The parameters of the model are such that there is a scarcity of foster parents on the market. I report the expectation of several variables of interest in the steady state for different specifications of the model's parameters. Related literature. – The economic analysis of the foster care system is largely missing from the economic literature.
Model
The fit decidesat = ag,x,yt. g,x,y)∈G×X×Y, wherebyg,x,y indicates the number of matches formed in periodt between a child of age type x, and a parent of. In any given period, the number of children in the system, matched and matched, is bounded since the arrival distribution of children has finite support. The number of children of age g and type x in the system in periodt, matched or mismatched, is bounded above by the maximum possible number of arrivals of type-x children who are g periods old in period t.
Analytic and Computational Exercises
The expected duration of matches in the steady state,l∗, is the expected duration of the expected matches. The first panel of Table 2.1 reports the expected number of available children in the stationary state. Not surprisingly, the expected duration of matches in the system is greater when there is the same type of bias (r = 0.5) and parent-1 bonus (w =2, column 5) or higher survival rate (s =3, column 7).
Data
The biological/primary parents of about 10% of the children in CF have lost their parental rights. The data also include characteristics of each child's primary/biological and foster families. These regressions include only child characteristics as independent variables, so they use almost all observations in the data.
Conclusion and Further Research
Although matching as many children as possible is one of the main goals of the system, the empirical part of this chapter notes that strong sorting patterns exist between important variables, such as race. If the child is still in FC at the end of the financial year, the last removal and placement will relate to the current removal and placement. Note: The dependent variable is the proportional race of the foster parent: (1) African American, (2) Hispanic, (3) White, and the independent variables are characteristics of the children.
EXECUTIVE COMPENSATION AND COMPETITIVE PRESSURE IN THE PRODUCT MARKET: HOW DOES FIRM
ENTRY SHAPE MANAGERIAL INCENTIVES?
Introduction
More intensified product market competition affects each of these two effects through the size of the market and the effective size of the cost reduction. Since the optimal contracting and production decisions of entrants are negatively affected by total current output, the entry of new firms implies an increase in both the size of the market and the effective size of the cost reduction for incumbents. It is worth noting that, even in the absence of the marginal-profitability-of-effort effect, an increasing number of entries strengthens the effect of reducing the cost value.
Related Literature and Our Contribution
This effect points in the same direction as the standard scale effect, which suggests a negative relationship between competition and incentives. The devaluation effect and the liquidation threat effect often do not point in the same direction. To model market competition in the present context, we follow Daughety, 1990, which is a generalization of the standard notion of Stackelberg competition.
Managerial Incentives in Sequential Oligopoly
Note also that the manager's utility, i.e. the manager's net compensation level in each established firm, is given by: From Figure 3.4 it is immediately apparent that qi(c, e, m) decreases in mif and only asa0(m) − θ0(m)c < 0, which turns out to be the case, i.e. the loss to the The fact that incumbent firms with high costs resulting from an increase in the size of the cost savings outweigh the gains resulting from an increase in market size . entrants influence the expected value of cost reduction and the expected marginal profitability of incumbents' efforts, i.e., the two terms on the left side of (FOCi), evaluated at a. Proposition 3 The equilibrium value of incumbents decreases in the number of entrants.
Testable Implications
Total industry welfare consists of three components: (i) consumer surplus (CS), (ii) total producer surplus of existing firms (PSI), and (iii) total producer surplus of inputs (PSJ). Expected consumer surplus in both sequential (Stackelberg) and simultaneous (Cournot) competition, ECS and ECSsim are increasing in number of participants. In particular, while consumer surplus is always increasing in the number of inputs, producer surplus is decreasing.
Extensions
Note: Social welfare (top), consumer surplus (center), and producer surplus (bottom) in simultaneous and sequential oligopolies. a) The symmetric equilibrium managerial effort of the participants is given by eBJ(m, PI) which solves. Proposition 6 establishes that the equilibrium effort of incumbents is decreasing in the number of entries in a price-setting environment. Second, the equilibrium managerial effort induced by incumbent firms is decreasing in the number of firms when both incumbents and entrants set prices at the same time.
Conclusion
By showing that firm entry increases both the market size and the magnitude of cost reduction for incumbents, and by analyzing in turn how these two influence the expected value of cost reduction and the expected marginal profitability of the effort, we see that incumbents find this optimal. to provide stronger management incentives when new companies enter the market. Moreover, we also show that the extent to which incumbents strengthen managerial incentives increases with the number of new entrants; greater competitive pressure provokes a sharper response from incumbents. In the opposite case, where production capacity can be obtained immediately, i.e. new entrants are symmetrical to incumbents and simultaneously establish contracts and production, the association is negative: incumbents find it optimal to provide weaker management incentives as more firms enter the market enter. .
BIBLIOGRAPHY
Heterogeneity in Organizational Form: Why Otherwise Identical Firms Choose Different Incentives for Their Managers.” The RAND Journal of Economics25, p. Conditional Choice Probabilities and the Estimation of Dynamic Models.” The Review of Economic Studies60.3, p. Market Competition, R&D and corporate profits in an asymmetric oligopoly." The Journal of Industrial Economics59, p.
APPENDIX TO CHAPTER 1
Estimation Details
Matching Covariance
Consider a market with three children whose types are given by x,x0,x00 ∈ X and a single house whose type is y ∈ Y . The set of feasible matches in this market contains three matches: M0 = (x,y), M1 = ( x0,y), and M2 = (x00,y), where I abuse notation and define the match over the types of children and houses . Consider a market with three children whose types are given by x,x0,x00 ∈ X and two houses whose types are y,y0 ∈Y.
APPENDIX TO CHAPTER 2
Details on Example
Plots of Observation 4
APPENDIX TO CHAPTER 3
- The Base Model
- Proofs
- Numerical Implementation
- Social Welfare
We focus on the equilibrium in which the cdf FJ is a smooth function, i.e., the distribution has no atoms. In contrast to the quantity game, managerial effort has no value beyond the realization of true cost, i.e., the marginal benefit of effort is worthless in a price setting environment. To calculate the expected producer surplus of an input, one must obtain the expectation of the aggregate output of current operators along the equilibrium path, QI.
