Heterogeneous Convergence

We use U.S. county-level data containing 3,058 cross-sectional observations and 41 conditioning variables to study economic growth and explore possible heterogeneity in growth determination across 32 individual states. Using a 3SLS-IV estimation method, we find that all statistically significant convergence rates (for 32 individual states) are above 2 percent, with an average of 8.1 percent. For 7 states the convergence rate can be rejected as identical to at least one other state’s convergence rate with 95 percent confidence. Convergence rates are negatively correlated with initial income. The size of government at all levels of decentralization is either unproductive or negatively correlated with growth. Educational attainment has a non-linear relationship with growth. The size of the finance, insurance and real estate, and entertainment industries are positively correlated with growth, while the size of the education industry is negatively correlated with growth. Heterogeneity in the effects of balanced growth path determinants across individual states is harder to detect than in convergence rates.Economic Growth, Conditional Convergence, County Level Data

Sigma Convergence Versus Beta Convergence: Evidence from U.S. County-Level Data

This note outlines (i) why σ-convergence may not accompany β-convergence; (ii) cites evidence of β-convergence in the U.S.; (iii) demonstrates that σ-convergence does not hold across the U.S., or within most U.S. states; and (iv) demonstrates the robustness of this finding to increases in mean income. The distributions of shocks appear important towards accounting for income disparity.σ-convergence, β-convergence, Solow growth model, speed of convergence

Heterogeneity in Convergence Rates and Income Determination across U.S. States: Evidence from County-Level Data

We utilize county-level data to explore growth determination in the U.S. and possible heterogeneity in growth determination across individual states. The data includes over 3,000 cross-sectional observations and 39 demographic control variables. We use a consistent two stage least squares estimation procedure. (We report OLS estimates as well.) The estimated convergence rate across the U.S. is about 7 percent per year – higher than the 2 percent normally found with OLS in cross-country, U.S. state, and European region samples. Estimated convergence rates for 32 individual states are above 2 percent with an average of 8.1 percent. For 29 states the convergence rate is above 2 percent with 95 percent confidence. For seven states the convergence rate can be rejected as identical to at least one other state’s convergence rate with 95 percent confidence. In examining the determinants of balanced growth path heights, we find that government at all levels of decentralization is negatively correlated with economic growth. Educational attainment of a population has a non-linear relationship with economic growth according to our estimates: growth is positively related to high-school degree attainment, seemingly unrelated to obtaining some college education, and then positively related to four-year degree or more attainment. Also, finance, insurance and real estate industry and entertainment industry are positively correlated with growth, while education industry is negatively correlated with growth. Heterogeneity in the effects of balanced growth path determinants across individual states is much harder to detect (or dismiss) than in convergence rates.Economic Growth, Income Convergence, Solow Growth Model, Balanced Growth Path, Heterogeneity in Convergence, Education and Growth, Size of Government and Growth, Consistent Estimation, County-Level Data

The effects of room design on computer-supported collaborative learning in a multi-touch classroom.

While research indicates that technology can be useful for supporting learning and collaboration, there is still relatively little uptake or widespread implementation of these technologies in classrooms. In this paper, we explore one aspect of the development of a multi-touch classroom, looking at two different designs of the classroom environment to explore how classroom layout may influence group interaction and learning. Three classes of students working in groups of four were taught in the traditional forward-facing room condition, while three classes worked in a centered room condition. Our results indicate that while the outcomes on tasks were similar across conditions, groups engaged in more talk (but not more off-task talk) in a centered room layout, than in a traditional forward-facing room. These results suggest that the use of technology in the classroom may be influenced by the location of the technology, both in terms of the learning outcomes and the interaction behaviors of students. The findings highlight the importance of considering the learning environment when designing technology to support learning, and ensuring that integration of technology into formal learning environments is done with attention to how the technology may disrupt, or contribute to, the classroom interaction practices

Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium

Detonation propagation in a compressible medium wherein the energy release has been made spatially inhomogeneous is examined via numerical simulation. The inhomogeneity is introduced via step functions in the reaction progress variable, with the local value of energy release correspondingly increased so as to maintain the same average energy density in the medium, and thus a constant Chapman Jouguet (CJ) detonation velocity. A one-step Arrhenius rate governs the rate of energy release in the reactive zones. The resulting dynamics of a detonation propagating in such systems with one-dimensional layers and two-dimensional squares are simulated using a Godunov-type finite-volume scheme. The resulting wave dynamics are analyzed by computing the average wave velocity and one-dimensional averaged wave structure. In the case of sufficiently inhomogeneous media wherein the spacing between reactive zones is greater than the inherent reaction zone length, average wave speeds significantly greater than the corresponding CJ speed of the homogenized medium are obtained. If the shock transit time between reactive zones is less than the reaction time scale, then the classical CJ detonation velocity is recovered. The spatio-temporal averaged structure of the waves in these systems is analyzed via a Favre averaging technique, with terms associated with the thermal and mechanical fluctuations being explicitly computed. The analysis of the averaged wave structure identifies the super-CJ detonations as weak detonations owing to the existence of mechanical non-equilibrium at the effective sonic point embedded within the wave structure. The correspondence of the super-CJ behavior identified in this study with real detonation phenomena that may be observed in experiments is discussed