Exogeneity, weak identification and instrument selection in econometrics

La dernière décennie a connu un intérêt croissant pour les problèmes posés par les variables instrumentales faibles dans la littérature économétrique, c’est-à-dire les situations où les variables instrumentales sont faiblement corrélées avec la variable à instrumenter. En effet, il est bien connu que lorsque les instruments sont faibles, les distributions des statistiques de Student, de Wald, du ratio de vraisemblance et du multiplicateur de Lagrange ne sont plus standard et dépendent souvent de paramètres de nuisance. Plusieurs études empiriques portant notamment sur les modèles de rendements à l’éducation [Angrist et Krueger (1991, 1995), Angrist et al. (1999), Bound et al. (1995), Dufour et Taamouti (2007)] et d’évaluation des actifs financiers (C-CAPM) [Hansen et Singleton (1982,1983), Stock et Wright (2000)], où les variables instrumentales sont faiblement corrélées avec la variable à instrumenter, ont montré que l’utilisation de ces statistiques conduit souvent à des résultats peu fiables. Un remède à ce problème est l’utilisation de tests robustes à l’identification [Anderson et Rubin (1949), Moreira (2002), Kleibergen (2003), Dufour et Taamouti (2007)]. Cependant, il n’existe aucune littérature économétrique sur la qualité des procédures robustes à l’identification lorsque les instruments disponibles sont endogènes ou à la fois endogènes et faibles. Cela soulève la question de savoir ce qui arrive aux procédures d’inférence robustes à l’identification lorsque certaines variables instrumentales supposées exogènes ne le sont pas effectivement. Plus précisément, qu’arrive-t-il si une variable instrumentale invalide est ajoutée à un ensemble d’instruments valides? Ces procédures se comportent-elles différemment? Et si l’endogénéité des variables instrumentales pose des difficultés majeures à l’inférence statistique, peut-on proposer des procédures de tests qui sélectionnent les instruments lorsqu’ils sont à la fois forts et valides? Est-il possible de proposer les proédures de sélection d’instruments qui demeurent valides même en présence d’identification faible? Cette thèse se focalise sur les modèles structurels (modèles à équations simultanées) et apporte des réponses à ces questions à travers quatre essais. Le premier essai est publié dans Journal of Statistical Planning and Inference 138 (2008) 2649 – 2661. Dans cet essai, nous analysons les effets de l’endogénéité des instruments sur deux statistiques de test robustes à l’identification: la statistique d’Anderson et Rubin (AR, 1949) et la statistique de Kleibergen (K, 2003), avec ou sans instruments faibles. D’abord, lorsque le paramètre qui contrôle l’endogénéité des instruments est fixe (ne dépend pas de la taille de l’échantillon), nous montrons que toutes ces procédures sont en général convergentes contre la présence d’instruments invalides (c’est-à-dire détectent la présence d’instruments invalides) indépendamment de leur qualité (forts ou faibles). Nous décrivons aussi des cas où cette convergence peut ne pas tenir, mais la distribution asymptotique est modifiée d’une manière qui pourrait conduire à des distorsions de niveau même pour de grands échantillons. Ceci inclut, en particulier, les cas où l’estimateur des double moindres carrés demeure convergent, mais les tests sont asymptotiquement invalides. Ensuite, lorsque les instruments sont localement exogènes (c’est-à-dire le paramètre d’endogénéité converge vers zéro lorsque la taille de l’échantillon augmente), nous montrons que ces tests convergent vers des distributions chi-carré non centrées, que les instruments soient forts ou faibles. Nous caractérisons aussi les situations où le paramètre de non centralité est nul et la distribution asymptotique des statistiques demeure la même que dans le cas des instruments valides (malgré la présence des instruments invalides). Le deuxième essai étudie l’impact des instruments faibles sur les tests de spécification du type Durbin-Wu-Hausman (DWH) ainsi que le test de Revankar et Hartley (1973). Nous proposons une analyse en petit et grand échantillon de la distribution de ces tests sous l’hypothèse nulle (niveau) et l’alternative (puissance), incluant les cas où l’identification est déficiente ou faible (instruments faibles). Notre analyse en petit échantillon founit plusieurs perspectives ainsi que des extensions des précédentes procédures. En effet, la caractérisation de la distribution de ces statistiques en petit échantillon permet la construction des tests de Monte Carlo exacts pour l’exogénéité même avec les erreurs non Gaussiens. Nous montrons que ces tests sont typiquement robustes aux intruments faibles (le niveau est contrôlé). De plus, nous fournissons une caractérisation de la puissance des tests, qui exhibe clairement les facteurs qui déterminent la puissance. Nous montrons que les tests n’ont pas de puissance lorsque tous les instruments sont faibles [similaire à Guggenberger(2008)]. Cependant, la puissance existe tant qu’au moins un seul instruments est fort. La conclusion de Guggenberger (2008) concerne le cas où tous les instruments sont faibles (un cas d’intérêt mineur en pratique). Notre théorie asymptotique sous les hypothèses affaiblies confirme la théorie en échantillon fini. Par ailleurs, nous présentons une analyse de Monte Carlo indiquant que: (1) l’estimateur des moindres carrés ordinaires est plus efficace que celui des doubles moindres carrés lorsque les instruments sont faibles et l’endogenéité modérée [conclusion similaire à celle de Kiviet and Niemczyk (2007)]; (2) les estimateurs pré-test basés sur les tests d’exogenété ont une excellente performance par rapport aux doubles moindres carrés. Ceci suggère que la méthode des variables instrumentales ne devrait être appliquée que si l’on a la certitude d’avoir des instruments forts. Donc, les conclusions de Guggenberger (2008) sont mitigées et pourraient être trompeuses. Nous illustrons nos résultats théoriques à travers des expériences de simulation et deux applications empiriques: la relation entre le taux d’ouverture et la croissance économique et le problème bien connu du rendement à l’éducation. Le troisième essai étend le test d’exogénéité du type Wald proposé par Dufour (1987) aux cas où les erreurs de la régression ont une distribution non-normale. Nous proposons une nouvelle version du précédent test qui est valide même en présence d’erreurs non-Gaussiens. Contrairement aux procédures de test d’exogénéité usuelles (tests de Durbin-Wu-Hausman et de Rvankar- Hartley), le test de Wald permet de résoudre un problème courant dans les travaux empiriques qui consiste à tester l’exogénéité partielle d’un sous ensemble de variables. Nous proposons deux nouveaux estimateurs pré-test basés sur le test de Wald qui performent mieux (en terme d’erreur quadratique moyenne) que l’estimateur IV usuel lorsque les variables instrumentales sont faibles et l’endogénéité modérée. Nous montrons également que ce test peut servir de procédure de sélection de variables instrumentales. Nous illustrons les résultats théoriques par deux applications empiriques: le modèle bien connu d’équation du salaire [Angist et Krueger (1991, 1999)] et les rendements d’échelle [Nerlove (1963)]. Nos résultats suggèrent que l’éducation de la mère expliquerait le décrochage de son fils, que l’output est une variable endogène dans l’estimation du coût de la firme et que le prix du fuel en est un instrument valide pour l’output. Le quatrième essai résout deux problèmes très importants dans la littérature économétrique. D’abord, bien que le test de Wald initial ou étendu permette de construire les régions de confiance et de tester les restrictions linéaires sur les covariances, il suppose que les paramètres du modèle sont identifiés. Lorsque l’identification est faible (instruments faiblement corrélés avec la variable à instrumenter), ce test n’est en général plus valide. Cet essai développe une procédure d’inférence robuste à l’identification (instruments faibles) qui permet de construire des régions de confiance pour la matrices de covariances entre les erreurs de la régression et les variables explicatives (possiblement endogènes). Nous fournissons les expressions analytiques des régions de confiance et caractérisons les conditions nécessaires et suffisantes sous lesquelles ils sont bornés. La procédure proposée demeure valide même pour de petits échantillons et elle est aussi asymptotiquement robuste à l’hétéroscédasticité et l’autocorrélation des erreurs. Ensuite, les résultats sont utilisés pour développer les tests d’exogénéité partielle robustes à l’identification. Les simulations Monte Carlo indiquent que ces tests contrôlent le niveau et ont de la puissance même si les instruments sont faibles. Ceci nous permet de proposer une procédure valide de sélection de variables instrumentales même s’il y a un problème d’identification. La procédure de sélection des instruments est basée sur deux nouveaux estimateurs pré-test qui combinent l’estimateur IV usuel et les estimateurs IV partiels. Nos simulations montrent que: (1) tout comme l’estimateur des moindres carrés ordinaires, les estimateurs IV partiels sont plus efficaces que l’estimateur IV usuel lorsque les instruments sont faibles et l’endogénéité modérée; (2) les estimateurs pré-test ont globalement une excellente performance comparés à l’estimateur IV usuel. Nous illustrons nos résultats théoriques par deux applications empiriques: la relation entre le taux d’ouverture et la croissance économique et le modèle de rendements à l’éducation. Dans la première application, les études antérieures ont conclu que les instruments n’étaient pas trop faibles [Dufour et Taamouti (2007)] alors qu’ils le sont fortement dans la seconde [Bound (1995), Doko et Dufour (2009)]. Conformément à nos résultats théoriques, nous trouvons les régions de confiance non bornées pour la covariance dans le cas où les instruments sont assez faibles.

SIMULATIONS OF WINDS OF WEAK-LINED T TAURI STARS. II. THE EFFECTS OF A TILTED MAGNETOSPHERE AND PLANETARY INTERACTIONS

Based on our previous work, we investigate here the effects on the wind and magnetospheric structures of weak-lined T Tauri stars due to a misalignment between the axis of rotation of the star and its magnetic dipole moment vector. In such a configuration, the system loses the axisymmetry presented in the aligned case, requiring a fully three-dimensional (3D) approach. We perform 3D numerical magnetohydrodynamic simulations of stellar winds and study the effects caused by different model parameters, namely the misalignment angle theta(t), the stellar period of rotation, the plasma-beta, and the heating index.. Our simulations take into account the interplay between the wind and the stellar magnetic field during the time evolution. The system reaches a periodic behavior with the same rotational period of the star. We show that the magnetic field lines present an oscillatory pattern. Furthermore, we obtain that by increasing theta(t), the wind velocity increases, especially in the case of strong magnetic field and relatively rapid stellar rotation. Our 3D, time-dependent wind models allow us to study the interaction of a magnetized wind with a magnetized extrasolar planet. Such interaction gives rise to reconnection, generating electrons that propagate along the planet`s magnetic field lines and produce electron cyclotron radiation at radio wavelengths. The power released in the interaction depends on the planet`s magnetic field intensity, its orbital radius, and on the stellar wind local characteristics. We find that a close-in Jupiter-like planet orbiting at 0.05 AU presents a radio power that is similar to 5 orders of magnitude larger than the one observed in Jupiter, which suggests that the stellar wind from a young star has the potential to generate strong planetary radio emission that could be detected in the near future with LOFAR. This radio power varies according to the phase of rotation of the star. For three selected simulations, we find a variation of the radio power of a factor 1.3-3.7, depending on theta(t). Moreover, we extend the investigation done in Vidotto et al. and analyze whether winds from misaligned stellar magnetospheres could cause a significant effect on planetary migration. Compared to the aligned case, we show that the timescale tau(w) for an appreciable radial motion of the planet is shorter for larger misalignment angles. While for the aligned case tau(w) similar or equal to 100 Myr, for a stellar magnetosphere tilted by theta(t) = 30 degrees, tau(w) ranges from similar to 40 to 70 Myr for a planet located at a radius of 0.05 AU. Further reduction on tau(w) might occur for even larger misalignment angles and/or different wind parameters.

Alternative diagnostic diagrams and the `forgotten` population of weak line galaxies in the SDSS

A numerous population of weak line galaxies (WLGs) is often left out of statistical studies on emission-line galaxies (ELGs) due to the absence of an adequate classification scheme, since classical diagnostic diagrams, such as [O iii]/H beta versus [N ii]/H alpha (the BPT diagram), require the measurement of at least four emission lines. This paper aims to remedy this situation by transposing the usual divisory lines between star-forming (SF) galaxies and active galactic nuclei (AGN) hosts and between Seyferts and LINERs to diagrams that are more economical in terms of line quality requirements. By doing this, we rescue from the classification limbo a substantial number of sources and modify the global census of ELGs. More specifically, (1) we use the Sloan Digital Sky Survey Data Release 7 to constitute a suitable sample of 280 000 ELGs, one-third of which are WLGs. (2) Galaxies with strong emission lines are classified using the widely applied criteria of Kewley et al., Kauffmann et al. and Stasinska et al. to distinguish SF galaxies and AGN hosts and Kewley et al. to distinguish Seyferts from LINERs. (3) We transpose these classification schemes to alternative diagrams keeping [N ii]/H alpha as a horizontal axis, but replacing H beta by a stronger line (H alpha or [O ii]), or substituting the ionization-level sensitive [O iii]/H beta ratio with the equivalent width of H alpha (W(H alpha)). Optimized equations for the transposed divisory lines are provided. (4) We show that nothing significant is lost in the translation, but that the new diagrams allow one to classify up to 50 per cent more ELGs. (5) Introducing WLGs in the census of galaxies in the local Universe increases the proportion of metal-rich SF galaxies and especially LINERs. In the course of this analysis, we were led to make the following points. (i) The Kewley et al. BPT line for galaxy classification is generally ill-used. (ii) Replacing [O iii]/H beta by W(H alpha) in the classification introduces a change in the philosophy of the distinction between LINERs and Seyferts, but not in its results. Because the W(H alpha) versus [N ii]/H alpha diagram can be applied to the largest sample of ELGs without loss of discriminating power between Seyferts and LINERs, we recommend its use in further studies. (iii) The dichotomy between Seyferts and LINERs is washed out by WLGs in the BPT plane, but it subsists in other diagnostic diagrams. This suggests that the right wing in the BPT diagram is indeed populated by at least two classes, tentatively identified with bona fide AGN and `retired` galaxies that have stopped forming stars and are ionized by their old stellar populations.

Travel Report from the first field trip within the SIDA supported project "Mini-grids supplied by renewable energy - improving technical and social feasibility : Including visits to Ihushi Development Center, Tweyambe Secondary School and Mavuno Project in Tanzania. Conducted in April 2011

This report describes the outcome of the first visit to Tanzania, within the project "Mini-grids supplied by renewable energy - improving technical and social feasibility". The trip included visits to three different organizations; Ihushi Development Center (IDC) near Mwanza, TIDESO near Bukoba, and Mavuno Project in Karagwe. At IDC, a brief evaluation of the current power system was done and measuring equipment for long term measurements were installed. At all three locations investigations regarding the current and future electricity demand were conducted and connections to people relevant to the study were established. The report is including as well some technical specifications as some observations regarding organization and management of the technical systems. The trip was including only short visits and therefore only brief introductions to the different organizations, based on observations done by the author. The report is hence describing the author’s understanding of the technical system and social structures after only short visits to each of the organizations, and may differ from observations done at another point in time, over a different time period, or by some other person.This report describes the outcome of the first visit to Tanzania, within the project "Mini-grids supplied by renewable energy - improving technical and social feasibility". The trip included visits to three different organizations; Ihushi Development Center (IDC) near Mwanza, TIDESO near Bukoba, and Mavuno Project in Karagwe. At IDC, a brief evaluation of the current power system was done and measuring equipment for long term measurements were installed. At all three locations investigations regarding the current and future electricity demand were conducted and connections to people relevant to the study were established. The report is including as well some technical specifications as some observations regarding organization and management of the technical systems. The trip was including only short visits and therefore only brief introductions to the different organizations, based on observations done by the author. The report is hence describing the author’s understanding of the technical system and social structures after only short visits to each of the organizations, and may differ from observations done at another point in time, over a different time period, or by some other person.

Wald tests for IV regression with weak instruments

This dissertation deals with the problem of making inference when there is weak identification in models of instrumental variables regression. More specifically we are interested in one-sided hypothesis testing for the coefficient of the endogenous variable when the instruments are weak. The focus is on the conditional tests based on likelihood ratio, score and Wald statistics. Theoretical and numerical work shows that the conditional t-test based on the two-stage least square (2SLS) estimator performs well even when instruments are weakly correlated with the endogenous variable. The conditional approach correct uniformly its size and when the population F-statistic is as small as two, its power is near the power envelopes for similar and non-similar tests. This finding is surprising considering the bad performance of the two-sided conditional t-tests found in Andrews, Moreira and Stock (2007). Given this counter intuitive result, we propose novel two-sided t-tests which are approximately unbiased and can perform as well as the conditional likelihood ratio (CLR) test of Moreira (2003).

A Semi-Tethered Test for Power Assessment in Running

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Accountability in Smart Microgrids Based on Conservative Power Theory

Smart microgrids offer a new challenging domain for power theories and metering techniques because they include a variety of intermittent power sources which positively impact on power flow and distribution losses but may cause voltage asymmetry and frequency variation. In smart microgrids, the voltage distortion and asymmetry in presence of poly-phase nonlinear loads can be also greater than in usual distribution lines fed by the utility, thus affecting measurement accuracy and possibly causing tripping of protections. In such a context, a reconsideration of power theories is required since they form the basis for supply and load characterization. A revision of revenue metering techniques is also suggested to ensure a correct penalization of the loads for their responsibility in generating reactive power, voltage asymmetry, and distortion. This paper shows that the conservative power theory provides a suitable background to cope with smart grids characterization and metering needs. Simulation and experimental results show the properties of the proposed approach.

Accountability and revenue metering in smart micro-grids

Smart micro-grids offer a new challenging domain for power theories and metering techniques, because they include a variety of intermittent power sources which positively impact on power flow and distribution losses, but may cause voltage asymmetry and frequency variation. Due to the limited power capability of smart micro-grids, the voltage distortion can also get worse (in case of supplying non-linear loads), affecting measurement accuracy and possibly causing tripping of protections. In such a context, a reconsideration of power theories is required, since they form the basis for supply and load characterization. A revision of revenue metering techniques is also needed, to ensure a correct penalization of the loads for their responsibility in generating reactive power, voltage unbalance and distortion. This paper shows that the Conservative Power Theory (CPT) provides a suitable background to cope with smart grids characterization and metering needs. Experimental results validate the proposed approach. © 2010 IEEE.

A combinatorial approach for transmission expansion & reactive power planning

A metaheuristic technique for solving the short-term transmission network expansion and reactive power planning problems, at the same time, in regulated power systems using the AC model is presented. The problem is solved using a real genetic algorithm (RGA). For each topology proposed by RGA an indicator is employed to identify the weak buses for new reactive power sources allocation. The fitness function is calculated using the cost of each configuration as well as constraints deviation of an AC optimal power flow (OPF) in which the minimum reactive generation of new reactive sources and the active power losses are objectives. With allocation of reactive power sources at load buses, the circuit capacity increases and the cost of installation could be decreased. The method is tested in a well known test system, presenting good results when compared with other approaches. © 2011 IEEE.

An application of CHA to concurrent short-term transmission expansion & reactive power planning

In this paper a heuristic technique for solving simultaneous short-term transmission network expansion and reactive power planning problem (TEPRPP) via an AC model is presented. A constructive heuristic algorithm (CHA) aimed to obtaining a significant quality solution for such problem is employed. An interior point method (IPM) is applied to solve TEPRPP as a nonlinear programming (NLP) during the solution steps of the algorithm. For each proposed network topology, an indicator is deployed to identify the weak buses for reactive power sources placement. The objective function of NLP includes the costs of new transmission lines, real power losses as well as reactive power sources. By allocating reactive power sources at load buses, the circuit capacity may increase while the cost of new lines can be decreased. The proposed methodology is tested on Garver's system and the obtained results shows its capability and the viability of using AC model for solving such non-convex optimization problem. © 2011 IEEE.

Reference generator for voltage controlled power conditioners

Voltage reference generation is an important issue on electronic power conditioners or voltage compensators connected to the electric grid. Several equipments, such as Dynamic Voltage Restorers (DVR), Uninterruptable Power Supplies (UPS) and Unified Power Quality Conditioners (UPQC) need a proper voltage reference to be able to compensate electric network disturbances. This work presents a new reference generator's algorithm, based on vector algebra and digital filtering techniques. It is particularly suited for the development of voltage compensators with energy storage, which would be able to mitigate steady state disturbances, such as waveform distortions and unbalances, and also transient disturbances, like voltage sags and swells. Simulation and experimental results are presented for the validation of the proposed algorithm. © 2011 IEEE.

The low predictive power of simple Phillips curves in Chile

This study uses some backward-looking versions of Phillips curves, estimated from both revised and real-time data, to explore the existence, robustness and size of the contribution that a variety of activity measures may make to the task of predicting inflation in Chile. The main results confirm the findings of the recent international literature: the predictive power of the activity measures considered here is episodic, unstable and of moderate size. This weak predictive contribution is robust to the use of final and real-time data.

Power quality, smart meters and additional information from different power terms

This paper shows how the detailed examination of active and nonactive power components may produce new information for modern smart meters. For this purpose, a prototype of electronic power meter has been implemented and applied to the evaluation of the Conservative Power Theory (CPT). Considering five sorts of loads, under four different operating conditions, the experimental results indicate that the CPT is able to provide a good methodology for load characterization, which could possibly benefits consumers and power utilities in several different ways. The results also show that depending on the situation, the analysis of nonactive power terms may be more important than the observation of traditional power quality indices, such as total harmonic distortion, unbalance factors or the fundamental positive sequence power factor.

Nano-Power Integrated Circuits for Energy Harvesting

The energy harvesting research field has grown considerably in the last decade due to increasing interests in energy autonomous sensing systems, which require smart and efficient interfaces for extracting power from energy source and power management (PM) circuits. This thesis investigates the design trade-offs for minimizing the intrinsic power of PM circuits, in order to allow operation with very weak energy sources. For validation purposes, three different integrated power converter and PM circuits for energy harvesting applications are presented. They have been designed for nano-power operations and single-source converters can operate with input power lower than 1 μW. The first IC is a buck-boost converter for piezoelectric transducers (PZ) implementing Synchronous Electrical Charge Extraction (SECE), a non-linear energy extraction technique. Moreover, Residual Charge Inversion technique is exploited for extracting energy from PZ with weak and irregular excitations (i.e. lower voltage), and the implemented PM policy, named Two-Way Energy Storage, considerably reduces the start-up time of the converter, improving the overall conversion efficiency. The second proposed IC is a general-purpose buck-boost converter for low-voltage DC energy sources, up to 2.5 V. An ultra-low-power MPPT circuit has been designed in order to track variations of source power. Furthermore, a capacitive boost circuit has been included, allowing the converter start-up from a source voltage VDC0 = 223 mV. A nano-power programmable linear regulator is also included in order to provide a stable voltage to the load. The third IC implements an heterogeneous multisource buck-boost converter. It provides up to 9 independent input channels, of which 5 are specific for PZ (with SECE) and 4 for DC energy sources with MPPT. The inductor is shared among channels and an arbiter, designed with asynchronous logic to reduce the energy consumption, avoids simultaneous access to the buck-boost core, with a dynamic schedule based on source priority.

Enhancement of inductive power transfer with flat spiral resonators

The aim of this thesis is to develop a depth analysis of the inductive power transfer (or wireless power transfer, WPT) along a metamaterial composed of cells arranged in a planar configuration, in order to deliver power to a receiver sliding on them. In this way, the problem of the efficiency strongly affected by the weak coupling between emitter and receiver can be obviated, and the distance of transmission can significantly be increased. This study is made using a circuital approach and the magnetoinductive wave (MIW) theory, in order to simply explain the behavior of the transmission coefficient and efficiency from the circuital and experimental point of view. Moreover, flat spiral resonators are used as metamaterial cells, particularly indicated in literature for WPT metamaterials operating at MHz frequencies (5-30 MHz). Finally, this thesis presents a complete electrical characterization of multilayer and multiturn flat spiral resonators and, in particular, it proposes a new approach for the resistance calculation through finite element simulations, in order to consider all the high frequency parasitic effects. Multilayer and multiturn flat spiral resonators are studied in order to decrease the operating frequency down to kHz, maintaining small external dimensions and allowing the metamaterials to be supplied by electronic power converters (resonant inverters).