Policy and Complex Systems
attributed to error in linear models may be informative . This finding has implications across the field for the strength of prevailing linear models for child welfare time series .
Overall , the CCM findings indicate that entries into out-of-home care cause exits , and that exits from out-of-home care cause entries . This suggests the existence of a shared manifold structure indicating the presence of an attractor in these coupled time series . The strength of these relationships differs across care types . These findings suggest that there may be some structural component to the out-of-home care system that creates the need of a certain equilibrium between entries and exits . These attractor structures represent resource constraints within the foster care system , and suggest that the dynamics of out-ofhome care populations are driven , in part , by system feedback loops produced by the management of these resources .
Findings further indicate that the conceptualizations of population problems in child welfare systems are suitable for the application of population ecology theory and methods in some cases . Specifically those entry / exit regimes in child welfare do display similar behaviors to birth / death regimes in the study of biological populations . Thus , out-of-home care time series do contain variation that can be explained by population biology models . This opens up a robust literature where system behavior has been studied with incomplete information for centuries . Analogizing ways in which ecologists have solved these problems could create a leap in child welfare methodology .
The primarily limitation of this study is that the method provides no insights into what factors might comprise the attractor around which the time series manifold orbits . The presence of nonlinear causal relationships is of interest in and of themselves , but further study is necessary to understand what factors might influence those relationships and how those factors might operate in nonlinear space distinctly from how they operate in linear space . Additionally , this study only reviews state-level aggregate time series from a single state . Further investigations will be required to see if similar nonlinear behavior is found in the outof-home care systems of other states , and at different levels of spatial aggregation .
Conclusion
Analytic methods focused on different geometries produce different stories . Andersen ( 1980 ) recognized that different analytic paradigms applied to the same data set could lead to different policy conclusions . We argue that this is due , in part , to the policy narratives that we attach to the geometries of the data . The results of this study offer alternative policy narratives , which can grow out of nonlinear causal models .
At the most basic level , the prediction of resource constraints acting as a causal influence contributing to the dynamics of the out-of-home care system as portrayed in entry / exit time series data predicted in Wulczyn ( 1996 ) receives strong empirical support in this analysis . As is the case with other systems operating in a rich ecological context , though we do not directly observe the decision-making processes , the entry / exit signal the system gives off reveals a great deal about the nature of causality within the system . This analysis suggests the influence of resource constraints as operate at a fine-grained time scale : Each day , each week , each month , caseworkers are tasked with making admission and discharge decisions . The cumulative impact of those decisions balances out over the period of interest to determine whether the caseload grows , shrinks , or stays the same . The avail-
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