Fully Modified OLS for Heterogeneous Cointegrated Panels

This chapter uses fully modified OLS principles to develop new methods for estimating and testing hypotheses for cointegrating vectors in dynamic panels in a manner that is consistent with the degree of cross sectional heterogeneity that has been permitted in recent panel unit root and panel cointegration studies. The asymptotic properties of various estimators are compared based on pooling along the ‘within’ and ‘between’ dimensions of the panel. By using Monte Carlo simulations to study the small sample properties, the group mean estimator is shown to behave well even in relatively small samples under a variety of scenarios.

Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors

In this paper we describe a method for testing the null of no cointegration in dynamic panels with multiple regressors and compute approximate critical values for these tests. Methods for non-stationary panels, including panel unit root and panel cointegration tests, have been gaining increased acceptance in recent empirical research. To date, however, tests for the null of no cointegration in heterogeneous panels based on Pedroni (1995, 1997a) have been limited to simple bivariate examples, in large part due to the lack of critical values available for more complex multivariate regressions. The purpose of this paper is to ®ll this gap by describing a method to implement tests for the null of no cointegration for the case with multiple regressors and to provide appropriate critical values for these cases. The tests allow for considerable heterogeneity among individual members of the panel, including heterogeneity in both the long-run cointegrating vectors as well as heterogeneity in the dynamics associated with short-run deviations from these cointegrating vectors.

Panel Cointegration: Asymptotic and Finite Sample Properties of Pooled Time Series Tests with an Application to the PPP Hypothesis

We examine properties of residual-based tests for the null of no cointegration for dynamic panels in which both the short-run dynamics and the long-run slope coefficients are permitted to be heterogeneous across individual members of the panel. The tests also allow for individual heterogeneous fixed effects and trend terms, and we consider both pooled within dimension tests and group mean between dimension tests. We derive limiting distributions for these and show that they are normal and free of nuisance parameters+ We also provide Monte Carlo evidence to demonstrate their small sample size and power performance, and we illustrate their use in testing purchasing power parity for the post–Bretton Woods period.Cointegration, PPP, Time Series

The Effect of Infrastructure on Long Run Economic Growth

We investigate the long run consequences of infrastructure provision on per capita income in a panel of countries over the period 1950-1992. Simple panel based tests are developed which enable us to isolate the sign and direction of the long run effect of infrastructure on income in a manner that is robust to the presence of unknown heterogeneous short run causal relationships. Our results provide clear evidence that in the vast majority of cases infrastructure does induce long run growth effects. But we also find a great deal of variation in the results across individual countries. Taken as a whole, the results demonstrate that telephones, electricity generating capacity and paved roads are provided at close to the growth maximizing level on average, but are under-supplied in some countries and over-supplied in others. These results also help to explain why cross section and time series studies have in the past found contradictory results regarding a causal link between infrastructure provision and long run growth.

Robust Unit Root and Cointegration Rank Tests for Panels and Large Systems

This study develops new tests for unit roots and cointegration rank in heterogeneous time series panels using methods that are robust to the presence of both incidental trends and cross sectional dependency of unknown form. Furthermore, the procedures do not require a choice of lag truncation or bandwidth to accommodate higher order serial correlation. The cointegration rank tests can also be implemented in relatively large dimensioned systems of equations for which conventional VECM based tests become infeasible. Monte Carlo simulations demonstrate that the procedures have high power and good size properties even in panels with relatively small dimensions.Panel Unit Roots, Cointegration Rank Tests, Robust Autocovariance Estimation

Regional Income Divergence in China

Numerous policy studies have argued that conditions have prevailed in China since the open door economic reforms of the late 1970s that have encouraged rapid growth at the expense of regional income inequality across the provinces of China. In this paper we use recently developed nonstationary panel techniques to provide empirical support for the fact that the long run tendency since the reforms has been for provincial level incomes to continue to diverge. More importantly, we show that this divergence cannot be attributed to the presence of separate, regional convergence clubs divided among common geographic subgroupings such as the coastal versus interior provinces. Furthermore, we also show that the divergence cannot be attributed to differences in the degree of preferential open-door policies. Rather, we find that the divergence is pervasive both nationally and within these various regional and political subgroupings. We argue that these results point to other causes for regional income divergence, and they also carry potentially important implications for other regions of the world.China, convergence, nonstationary panels

Social Capital, Barriers to Production, and Capital Shares: Implications for the Importance of Parameter Heterogeneity from a Nonstationary Panel Approach

Recent advances in the growth literature have proposed that difficult to quantify concepts such as social capital may play an important role in explaining the degree of persistent income disparity that is observed among countries. Other recently explored possibilities include institutional mechanisms which generate barriers to aggregate production. An important limitation for empirical work in this area stems from the fact that it is difficult to distinguish sources of heterogeneity when direct observations are not available. In this study, we show how developments in the analysis of nonstationary dynamic panels can aid in this endeavor. In contrast to traditional panel data analysis, this approach focuses explicitly on low frequency behavior. Under relatively mild assumptions, the approach can be used to infer properties of aggregate production which are robust to the presence of large classes of unobserved features. In this framework we are able to estimate and test the implied distribution of production function parameters that would be required in order to generate conditional forecast convergence of per capita incomes even when some of the key factors required to explain growth are unobserved. The results indicate that in order to fully explain the observed persistence in the disparity of per capita incomes, the manner in which unobserved mechanisms influence production must go beyond merely accounting for differences in the trending behavior of aggregate productivity. Specifically, the results demonstrate that if such mechanisms are to be successful empirically, then they must also be able to account for cross country heterogeneity in steady state capital shares. This adds to a growing literature that provides support for models with multiple production regimes.Growth, Convergence, Social Capital, Nonstationary Panels

Nonparametric Rank Tests for Non-stationary Panels

This study develops new rank tests for panels that include panel unit root tests as a special case. The tests are unusual in that they can accommodate very general forms of both serial and cross-sectional dependence, including cross-unit cointegration, without the need to specify the form of dependence or estimate nuisance parameters associated with the dependence. The tests retain high power in small samples, and in contrast to other tests that accommodate cross-sectional dependence, the limiting distributions are valid for panels with finite cross-sectional dimensions.Nonparametric rank tests, unit roots, cointegration, cross-sectional dependence

Comment: Judicial Accountability and Discipline

The judicial disciplinary process and the specter of politically motivated misconduct allegations against state judges poses an important challenge to judicial independence

Conversion of Artificial Recurrent Neural Networks to Spiking Neural Networks for Low-power Neuromorphic Hardware

In recent years the field of neuromorphic low-power systems that consume orders of magnitude less power gained significant momentum. However, their wider use is still hindered by the lack of algorithms that can harness the strengths of such architectures. While neuromorphic adaptations of representation learning algorithms are now emerging, efficient processing of temporal sequences or variable length-inputs remain difficult. Recurrent neural networks (RNN) are widely used in machine learning to solve a variety of sequence learning tasks. In this work we present a train-and-constrain methodology that enables the mapping of machine learned (Elman) RNNs on a substrate of spiking neurons, while being compatible with the capabilities of current and near-future neuromorphic systems. This "train-and-constrain" method consists of first training RNNs using backpropagation through time, then discretizing the weights and finally converting them to spiking RNNs by matching the responses of artificial neurons with those of the spiking neurons. We demonstrate our approach by mapping a natural language processing task (question classification), where we demonstrate the entire mapping process of the recurrent layer of the network on IBM's Neurosynaptic System "TrueNorth", a spike-based digital neuromorphic hardware architecture. TrueNorth imposes specific constraints on connectivity, neural and synaptic parameters. To satisfy these constraints, it was necessary to discretize the synaptic weights and neural activities to 16 levels, and to limit fan-in to 64 inputs. We find that short synaptic delays are sufficient to implement the dynamical (temporal) aspect of the RNN in the question classification task. The hardware-constrained model achieved 74% accuracy in question classification while using less than 0.025% of the cores on one TrueNorth chip, resulting in an estimated power consumption of ~17 uW