Lessons in Funder Collaboration: What the Packard Foundation Has Learned about Working with Other Funders

As the Foundation approached its 50th anniversary this year, it asked The Bridgespan Group to assist in taking stock of what Packard can learn from its many collaborations. When it comes to the structure of collaborations, Bridgespan has identified five main models: knowledge exchange, coordination of funding, coinvesting in an existing entity, creating a new entity, and funding the funder. As with all taxonomies, these five categories are meant to serve as signposts along a continuum. Each collaboration differs in a variety of ways, whether it is the flow of funds, decision making, expectations and roles of funding partners, or legal structure. Bridgespan focused on Packard's collaborations that require alignment and more intensive coordination by program staff. Six case studies provide an in-depth look inside examples of all four types of collaboration that venture beyond exchanging knowledge

The Variance Ratio Statistic at large Horizons

We make three contributions to using the variance ratio statistic at large horizons. Allowing for general heteroscedasticity in the data, we obtain the asymptotic distribution of the statistic when the horizon k is increasing with the sample size n but at a slower rate so that k/n¨0. The test is shown to be consistent against a variety of relevant mean reverting alternatives when k/n¨0. This is in contrast to the case when k/n¨ƒÂ>0, where the statistic has been recently shown to be inconsistent against such alternatives. Secondly, we provide and justify a simple power transformation of the statistic which yields almost perfectly normally distributed statistics in finite samples, solving the well known right skewness problem. Thirdly, we provide a more powerful way of pooling information from different horizons to test for mean reverting alternatives. Monte Carlo simulations illustrate the theoretical improvements provided.Mean reversion, frequency domain, power transformations

GMM Estimation for Long Memory Latent Variable Volatility and Duration Models

We study the rate of convergence of moment conditions that have been commonly used in the literature for Generalised Method of Moments (GMM) estimation of short memory latent variable volatility models. We show that when the latent variable possesses long memory, these moment conditions have an n^{1/2-d} rate of convergence where 0GMM, long memory, stochastic volatility and durations

Semiparametric Estimation of Fractional Cointegrating Subspaces

We consider a common components model for multivariate fractional cointegration, in which the s>=1 components have different memory parameters. The cointegrating rank is allowed to exceed 1. The true cointegrating vectors can be decomposed into orthogonal fractional cointegrating subspaces such that vectors from distinct subspaces yield cointegrating errors with distinct memory parameters, denoted by d_k for k=1,...,s. We estimate each cointegrating subsspace separately using appropriate sets of eigenvectors of an averaged periodogram matrix of tapered, differenced observations. The averaging uses the first m Fourier frequencies, with m fixed. We will show that any vector in the k'th estimated coingetraging subspace is, with high probability, close to the k'th true cointegrating subspace, in the sense that the angle between the estimated cointegrating vector and the true cointegrating subspace converges in probability to zero. The angle is O_p(n^{- \alpha_k}), where n is the sample size and \alpha_k is the shortest distance between the memory parameters corresponding to the given and adjacent subspaces. We show that the cointegrating residuals corresponding to an estimated cointegrating vector can be used to obtain a consistent and asymptotically normal estimate of the memory parameter for the given cointegrating subspace, using a univariate Gaussian semiparametric estimator with a bandwidth that tends to \infty more slowly than n. We also show how these memory parameter estimates can be used to test for fractional cointegration and to consistently identify the cointegrating subspaces.Fractional Cointegration; Long Memory; Tapering; Periodogram

Needle-Moving Community Collaboratives: A Promising Approach to Addressing America's Biggest Challenges

Communities face powerful challenges -- a high-school dropout epidemic, youth unemployment, teen pregnancy -- that require powerful solutions. In a climate of increasingly constrained resources, those solutions must help communities to achieve more with less. A new kind of community collaborative -- an approach that aspires to significant community-wide progress by enlisting all sectors to work together toward a common goal -- offers enormous promise to bring about broader, more lasting change across the nation