Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation

The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and redistribution. For finding solutions of this equation, it is convenient first to reformulate the Liouville equation by defining a vector corresponding to the elements of the density operator, and determining the corresponding time-evolution matrix. For a system of N energy levels, the size of the evolution matrix is N2xN2. When N is very large, evaluating the elements of these matrices becomes very cumbersome. We describe a novel algorithm that can produce the evolution matrix in an automated fashion for an arbitrary value of N. As a non-trivial example, we apply this algorithm to a fifteen-level atomic system used for producing optically controlled polarization rotation. We also point out how such a code can be extended for use in an atomic system with arbitrary number of energy levels

Labor Laws and Innovation

Can stringent labor laws be e¢ cient? Possibly, if they provide firms with a commitment device to not punish employees' short-run failures and thereby spur the pursuit of value-maximizing innovative activities. In this paper, we provide empirical evidence that strong labor laws indeed appear to have an ex ante positive incentive effect by encouraging the innovative pursuits of firms and their employees. Using patents and citations as proxies for innovation and a time-varying index of labor laws, we find that innovation is fostered by stringent labor laws, especially by laws governing dismissal of employees. We provide this evidence using levels-on-levels, changes-on-changes, and finally difference-in-difference regressions that exploit staggered country-level law changes. We also find that stringent labor laws disproportionately influence innovation in the more innovation-intensive sectors of the economy. Finally, we find that while the overall effect of stringent labor laws is to dampen economic growth, laws that govern dismissal of employees are an exception: stringent laws governing dismissal promote economic growth, consistent with the evidence that they encourage firm-level innovation

Dismissal Laws, Innovation and Economic Growth

I theoretically and empirically show that dismissal laws - laws that impose hurdles on firing of employees - spur innovation and thereby economic growth. Theoretically, dismissal laws make it costly for firms to arbitrarily discharge employees. This enables firms to commit to not punish short-run failures of employees. Because innovation is inherently risky and employment contracts are incomplete, dismissal laws enable such commitment. Specifically, absent such laws, firms cannot contractually commit so ex-ante. The commitment provided by dismissal laws encourages employees to exert greater effort in risky, but path-breaking, projects thereby fostering firm-level innovation. I provide empirical evidence supporting this thesis using the discontinuity provided by the passage of the federal Worker Adjustment and Retraining Notification Act. Using the fact that this Act only applied to firms with 100 or more employees, I undertake difference-in-difference and regression discontinuity tests to provide this evidence. Building on endogenous growth theory, which posits that economic growth stems from innovation, I also show that dismissal laws correlate positively with economic growth. However, other forms of labor laws correlate negatively with economic growth and swamp the positive effect of dismissal laws

Does Strengthening the Property Rights of Employee-Inventors Spur Innovation? Empirical Evidence on Freedom-to-Create Laws Passed by US States

The incompleteness of employment contracts may leave inventors vulnerable to ex post opportunism by their employers, which could curtail their innovative effort. We use passage of freedom-to-create laws by seven US states as a natural experiment to investigate whether laws strengthening the property rights of inventors against employers’ opportunism can foster innovation. We employ a difference-in-differences design that includes a rich set of state, technology, and time fixed effects to compare the quantity and quality of patenting in these seven states vis-à-vis synthetic control states. The laws increased both the number of patents (by 14 percent) and their quality (according to various measures, including citations and the extent of pathbreaking innovation). The increase in innovation was broad, observed for both firm-specific and generic innovation and in firms with and without prior patents

The effectiveness of the Right to Education (RTE) Act in unrecognised schools of Delhi, India

PhD ThesisIn 2009, the Government of India introduced a new Education Act known as the “Right to Education” (RTE). The Act was brought out with all good intentions that would focus on the provision of education to 6 –14 years of age. Focused heavily, on input based indicators the Act intended to improve learning outcomes of children enrolled in private and public schools. The RTE act is being imposed stringently on several low-cost private schools across Delhi, and they have been, threatened with closure in the case of non-compliance to the RTE indicators. This thesis investigates the possible consequences of the Act. The current research using mixed methods attempts to understand the relationship between the various RTE input indicators and the academic outcomes of the children enrolled in the threatened private schools of Delhi. The study used two sets of instruments to measure the learning outcomes of students. First, a test for subject-specific competence was measured through a bespoke exam, known as the ‘diagnostic test’. Second, general intelligence was, measured through Raven’s standard progressive matrices test to control for innate ability. The background of children was also gathered using a questionnaire. Information on school RTE indicators were collected through a school questionnaire. Teacher data related to the RTE were gathered through a semi-structured teacher questionnaire. An in-depth interview was carried out to collect qualitative data and gained narrative accounts from school head teachers and principals to understand more deeply how the RTE indicators were impacting on student outcomes and low-cost private schools in Delhi. These data were analysed using linear regression models, to investigate the impact of the RTE on schools and student outcomes. The study revealed that most RTE infrastructure indicators were not statistically significant regarding student outcomes. Only, two factors were positively significant first, the provision of mid-day meals and second the presence of a library. Teacher qualifications have a positive influence on student outcomes, however other factors mentioned in the RTE including job status of the teacher, the salary range or parent-teacher association meetings, were found not to influence test scores. Finally, regarding the core indicators of the RTE, only two factors affected academic outcomes positively and were found to be significant. First, practising inclusivity and second, allowing ‘hands-on-learning’ for students. Schools that charged a fee on a higher spectrum, as compared to those which charged fees on a lower range, were found to affect student outcomes negatively, at a significant level. Other RTE academic and institutional indicators seemed to have negative or no impact on student learning outcomes, however, they were not significant. ii A major policy implication of this research is to provide feedback to the Government of IndiaA major policy implication of this research is to provide feedback to the Government of India on the gaps that currently exist in the RTE act, that affect student’s learning in low-cost private schools, threatened with closure notices. The study is unique as it gathered data from officially threatened schools, from the districts of New Delhi, that weakly comply with the RTE. The research provides insights generated from data and in-depth discussions with school owners on schooling inputs likely to affect student learning outcomes, teaching and the operation of low-cost private schools to inform future discussions around the RTE

Bank Coordination and Monetary Transmission: Evidence from India

We propose a new channel for the transmission of monetary policy shocks, the coordination channel. We develop a New Keynesian model in which bank lending is strategically complementary. Banks do not observe the distribution of loans but infer it using Gaussian signals. Under this paradigm, expectations of tighter credit conditions reduce banks’ lending response to monetary shocks. As a result, lack of coordination and information about other banks’ actions dampen monetary transmission. We test these predictions by constructing a dataset that links the evolution of interest rates to firms’ bank credit relationships in India. Consistent with our model, we find that the cross-sectional mean and dispersion of lending rates, which capture the expected value and the precision of the signals of credit extended by other banks, are significant predictors of monetary transmission. Our quantitative results suggest that lending complementarities reduce monetary transmission to inflation and output by about a third

Law and Project Finance

We investigate Project Finance as a private response to inefficiencies created by weak legal protection of outside investors. We offer a new illustration that law matters by demonstrating that for large investment projects, Project Finance provides a contractual and organizational substitute for investor protection laws. Project Finance accomplishes this by making cash flows verifiable through two mechanisms: (i) contractual arrangements made possible by structuring the project within a single, discrete entity legally separate from the sponsor; and (ii) private enforcement of these contracts through a network of project accounts that ensures lender control of project cash flows. Comparing bank loans for Project Finance with regular corporate loans for large investments, we show that Project Finance is more likely in countries with weaker laws against insider stealing and weaker creditor rights in bankruptcy. We identify the predicted effects using difference-in-difference and triple-difference tests that exploit exogenous country-level legal changes and inter-industry differences in free cash flow and tangibility of assets

Labor Laws and Innovation

Stringent labor laws can provide firms a commitment device to not punish short-run failures and thereby spur their employees to pursue value-enhancing innovative activities. Using patents and citations as proxies for innovation, we identify this effect by exploiting the time-series variation generated by staggered country-level changes in dismissal laws. We find that within a country, innovation and economic growth are fostered by stringent laws governing dismissal of employees, especially in the more innovation-intensive sectors. Firm-level tests within the United States that exploit a discontinuity generated by the passage of the federal Worker Adjustment and Retraining Notification Act confirm the cross-country evidence.

Labor Laws and Innovation

Can stringent labor laws be e¢ cient? Possibly, if they provide firms with a commitment device to not punish employees' short-run failures and thereby spur the pursuit of value-maximizing innovative activities. In this paper, we provide empirical evidence that strong labor laws indeed appear to have an ex ante positive incentive effect by encouraging the innovative pursuits of firms and their employees. Using patents and citations as proxies for innovation and a time-varying index of labor laws, we find that innovation is fostered by stringent labor laws, especially by laws governing dismissal of employees. We provide this evidence using levels-on-levels, changes-on-changes, and finally difference-in-difference regressions that exploit staggered country-level law changes. We also find that stringent labor laws disproportionately influence innovation in the more innovation-intensive sectors of the economy. Finally, we find that while the overall effect of stringent labor laws is to dampen economic growth, laws that govern dismissal of employees are an exception: stringent laws governing dismissal promote economic growth, consistent with the evidence that they encourage firm-level innovation