Assessing bias in the estimation of causal effects: Rosenbaum bounds on matching estimators and instrumental variables estimation with imperfect instruments

Propensity score matching provides an estimate of the effect of a treatment variable on an outcome variable that is largely free of bias arising from an association between treatment status and observable variables. However, matching methods are not robust against hidden bias arising from unobserved variables that simultaneously affect assignment to treatment and the outcome variable. One strategy for addressing this problem is the Rosenbaum bounds approach, which allows the analyst to determine how strongly an unmeasured confounding variable must affect selection into treatment in order to undermine the conclusions about causal effects from a matching analysis. Instrumental variables (IV) estimation provides an alternative strategy for the estimation of causal effects, but the method typically reduces the precision of the estimate and has an additional source of uncertainty that derives from the untestable nature of the assumptions of the IV approach. A method of assessing this additional uncertainty is proposed so that the total uncertainty of the IV approach can be compared with the Rosenbaum bounds approach to uncertainty using matching methods. Because the approaches rely on different information and different assumptions, they provide complementary information about causal relationships. The approach is illustrated via an analysis of the impact of unemployment insurance on the timing of reemployment, the postunemployment wage, and the probability of relocation, using data from several panels of the Survey of Income and Program Participation (SIPP). -- Propensity score matching ermöglicht die verzerrungsfreie Abschätzung der Kausalwirkung einer treatment-Variable auf eine Ergebnisvariable sofern Verzerrungen allein aus dem Zusammenhang zwischen Kausalfaktor und beobachteten Kovariaten resultieren. Matchingverfahren sind allerdings anfällig für Schätzverzerrungen aufgrund von hidden bias durch unbeobachtete Variablen, die sowohl die Zuweisung des Kausalfaktors als auch die Ergebnisvariable bestimmen. Im letzteren Fall besteht eine mögliche Strategie darin, mit Hilfe der Methode der sogenannten Rosenbaumschranken abzuschätzen, wie stark der Einfluss unbeobachteter Kovariaten auf die Zuweisung des Kausalstatus sein müsste, um die beabsichtigten Schlussfolgerungen im Hinblick auf den interessierenden kausalen Effekt qualitativ zu verändern. Instrumentalvariablenschätzer (IV) wären ein zweites Verfahren, um in dieser Situation kausale Effekte abschätzen zu können, allerdings führt das Verfahren in der Regel zu wenig präzisen Schätzungen und beinhaltet in der Anwendung zusätzliche Unsicherheiten aufgrund der empirisch nicht testbaren Annahmen des IV-Ansatzes. In diesem Aufsatz wird eine Methode zur Abschätzung dieser Unsicherheiten vorgeschlagen, wodurch die potentiellen Verzerrungen innerhalb einer IV-Schätzung mit den durch die Rosenbaumschranken abgeschätzten Verzerrungen innerhalb eines entsprechenden Matchingansatzes verglichen werden können. Da diesen Verfahren jeweils unterschiedliche Informationsgrundlage sowie unterschiedliche Annahmen zugrunde liegen, erbringen sie komplementäre Informationen über den Gehalt kausaler Beziehungen. Wir illustrieren die vorgeschlagene Vorgehensweise anhand einer Analyse des kausalen Effekts der Arbeitslosenversicherung auf die Dauer der Arbeitslosigkeit, den Lohn bei Wiederbeschäftigung sowie der Wahrscheinlichkeit geographischer Mobilität auf der Basis von Daten des amerikanischen Survey of Income and Program Participation (SIPP).

Assessing bias in the estimation of causal effects: Rosenbaum bounds on matching estimators and instrumental variables estimation with imperfect instruments

"Propensity score matching provides an estimate of the effect of a 'treatment' variable on an outcome variable that is largely free of bias arising from an association between treatment status and observable variables. However, matching methods are not robust against 'hidden bias' arising from unobserved variables that simultaneously affect assignment to treatment and the outcome variable. One strategy for addressing this problem is the Rosenbaum bounds approach, which allows the analyst to determine how strongly an unmeasured confounding variable must affect selection into treatment in order to undermine the conclusions about causal effects from a matching analysis. Instrumental variables (IV) estimation provides an alternative strategy for the estimation of causal effects, but the method typically reduces the precision of the estimate and has an additional source of uncertainty that derives from the untestable nature of the assumptions of the IV approach. A method of assessing this additional uncertainty is proposed so that the total uncertainty of the IV approach can be compared with the Rosenbaum bounds approach to uncertainty using matching methods. Because the approaches rely on different information and different assumptions, they provide complementary information about causal relationships. The approach is illustrated via an analysis of the impact of unemployment insurance on the timing of reemployment, the postunemployment wage, and the probability of relocation, using data from several panels of the Survey of Income and Program Participation (SIPP)." (author's abstract)"Propensity score matching ermöglicht die verzerrungsfreie Abschätzung der Kausalwirkung einer "treatment"-Variable auf eine Ergebnisvariable sofern Verzerrungen allein aus dem Zusammenhang zwischen Kausalfaktor und beobachteten Kovariaten resultieren. Matchingverfahren sind allerdings anfällig für Schätzverzerrungen aufgrund von "hidden bias" durch unbeobachtete Variablen, die sowohl die Zuweisung des Kausalfaktors als auch die Ergebnisvariable bestimmen. Im letzteren Fall besteht eine mögliche Strategie darin, mit Hilfe der Methode der sogenannten Rosenbaumschranken abzuschätzen, wie stark der Einfluss unbeobachteter Kovariaten auf die Zuweisung des Kausalstatus sein müsste, um die beabsichtigten Schlussfolgerungen im Hinblick auf den interessierenden kausalen Effekt qualitativ zu verändern. Instrumentalvariablenschätzer (IV) wären ein zweites Verfahren, um in dieser Situation kausale Effekte abschätzen zu können, allerdings führt das Verfahren in der Regel zu wenig präzisen Schätzungen und beinhaltet in der Anwendung zusätzliche Unsicherheiten aufgrund der empirisch nicht testbaren Annahmen des IV-Ansatzes. In diesem Aufsatz wird eine Methode zur Abschätzung dieser Unsicherheiten vorgeschlagen, wodurch die potentiellen Verzerrungen innerhalb einer IV-Schätzung mit den durch die Rosenbaumschranken abgeschätzten Verzerrungen innerhalb eines entsprechenden Matchingansatzes verglichen werden können. Da diesen Verfahren jeweils unterschiedliche Informationsgrundlage sowie unterschiedliche Annahmen zugrunde liegen, erbringen sie komplementäre Informationen über den Gehalt kausaler Beziehungen. Wir illustrieren die vorgeschlagene Vorgehensweise anhand einer Analyse des kausalen Effekts der Arbeitslosenversicherung auf die Dauer der Arbeitslosigkeit, den Lohn bei Wiederbeschäftigung sowie der Wahrscheinlichkeit geographischer Mobilität auf der Basis von Daten des amerikanischen Survey of Income and Program Participation (SIPP)." (Autorenreferat

Kausalanalyse durch Matchingverfahren

Having close linkages with the counterfactual concept of causality, nonparametric matching estimators have recently gained in popularity in the statistical and econometric literature on causal analysis. Introducing key concepts of the Rubin causal model (RCM), the paper discusses the implementation of counterfactual analyses by propensity score matching methods. We emphasize the suitability of the counterfactual framework for sociological questions as well as the assumptions underlying matching methods relative to standard regression analysis. We then illustrate the application of matching estimators in an analysis of the causal effect of unemployment on workers' subsequent careers.Matching; Causality; Nonparametric estimators; Observational data; Rubin causal model; Counterfactual analysis

Scaling properties of cavity-enhanced atom cooling

We extend an earlier semiclassical model to describe the dissipative motion of N atoms coupled to M modes inside a coherently driven high-finesse cavity. The description includes momentum diffusion via spontaneous emission and cavity decay. Simple analytical formulas for the steady-state temperature and the cooling time for a single atom are derived and show surprisingly good agreement with direct stochastic simulations of the semiclassical equations for N atoms with properly scaled parameters. A thorough comparison with standard free-space Doppler cooling is performed and yields a lower temperature and a cooling time enhancement by a factor of M times the square of the ratio of the atom-field coupling constant to the cavity decay rate. Finally it is shown that laser cooling with negligible spontaneous emission should indeed be possible, especially for relatively light particles in a strongly coupled field configuration.Comment: 7 pages, 5 figure

Semiclassical theory of cavity-assisted atom cooling

We present a systematic semiclassical model for the simulation of the dynamics of a single two-level atom strongly coupled to a driven high-finesse optical cavity. From the Fokker-Planck equation of the combined atom-field Wigner function we derive stochastic differential equations for the atomic motion and the cavity field. The corresponding noise sources exhibit strong correlations between the atomic momentum fluctuations and the noise in the phase quadrature of the cavity field. The model provides an effective tool to investigate localisation effects as well as cooling and trapping times. In addition, we can continuously study the transition from a few photon quantum field to the classical limit of a large coherent field amplitude.Comment: 10 pages, 8 figure

Cold atoms in a high-Q ring-cavity

We report the confinement of large clouds of ultra-cold 85-Rb atoms in a standing-wave dipole trap formed by the two counter-propagating modes of a high-Q ring-cavity. Studying the properties of this trap we demonstrate loading of higher-order transverse cavity modes and excite recoil-induced resonances.Comment: 4 pages, 4 figure

Collective Sideband Cooling in an Optical Ring Cavity

We propose a cavity based laser cooling and trapping scheme, providing tight confinement and cooling to very low temperatures, without degradation at high particle densities. A bidirectionally pumped ring cavity builds up a resonantly enhanced optical standing wave which acts to confine polarizable particles in deep potential wells. The particle localization yields a coupling of the degenerate travelling wave modes via coherent photon redistribution. This induces a splitting of the cavity resonances with a high frequency component, that is tuned to the anti-Stokes Raman sideband of the particles oscillating in the potential wells, yielding cooling due to excess anti-Stokes scattering. Tight confinement in the optical lattice together with the prediction, that more than 50% of the trapped particles can be cooled into the motional ground state, promise high phase space densities.Comment: 4 pages, 1 figur

Cavity Assisted Nondestructive Laser Cooling of Atomic Qubits

We analyze two configurations for laser cooling of neutral atoms whose internal states store qubits. The atoms are trapped in an optical lattice which is placed inside a cavity. We show that the coupling of the atoms to the damped cavity mode can provide a mechanism which leads to cooling of the motion without destroying the quantum information.Comment: 12 page

Observation of Collective-Emission-Induced Cooling inside an Optical Cavity

We report the observation of collective-emission-induced, velocity-dependent light forces. One third of a falling sample containing 3 x 10^6 cesium atoms illuminated by a horizontal standing wave is stopped by cooperatively emitting light into a vertically oriented confocal resonator. We observe decelerations up to 1500 m/s^2 and cooling to temperatures as low as 7 uK, well below the free space Doppler limit. The measured forces substantially exceed those predicted for a single two-level atom.Comment: 10 pages, 5 figure