Scaling Metric Measurement Invariance Models

This paper aims at clarifying the questions regarding the effects of the scaling method on the discrepancy function of the metric measurement invariance model. We provide examples and a formal account showing that neither the choice of the scaling method in general nor the choice of a particular referent indicator affects the value of the discrepancy function. Thus, the test statistic is not affected by the scaling method, either. The results rely on an appropriate application of the scaling restrictions, which can be phrased as a simple rule: "Apply the scaling restriction in one group only!" We develop formulas to calculate the degrees of freedom of χ²-difference tests comparing metric models to the corresponding configural model. Our findings show that it is impossible to test the invariance of the estimated loading of exactly one indicator, because metric MI models aimed at doing so are actually equivalent to the configural model

A Theory of Merge-and-Shrink for Stochastic Shortest Path Problems

The merge-and-shrink framework is a powerful tool to construct state space abstractions based on factored representations. One of its core applications in classical planning is the construction of admissible abstraction heuristics. In this paper, we develop a compositional theory of merge-and-shrink in the context of probabilistic planning, focusing on stochastic shortest path problems (SSPs). As the basis for this development, we contribute a novel factored state space model for SSPs. We show how general transformations, including abstractions, can be formulated on this model to derive admissible and/or perfect heuristics. To formalize the merge-and-shrink framework for SSPs, we transfer the fundamental merge-and-shrink transformations from the classical setting: shrinking, merging, and label reduction. We analyze the formal properties of these transformations in detail and show how the conditions under which shrinking and label reduction lead to perfect heuristics can be extended to the SSP setting

Cost Partitioning Heuristics for Stochastic Shortest Path Problems

In classical planning, cost partitioning is a powerful method which allows to combine multiple admissible heuristics while retaining an admissible bound. In this paper, we extend the theory of cost partitioning to probabilistic planning by generalizing from deterministic transition systems to stochastic shortest path problems (SSPs). We show that fundamental results related to cost partitioning still hold in our extended theory. We also investigate how to optimally partition costs for a large class of abstraction heuristics for SSPs. Lastly, we analyze occupation measure heuristics for SSPs as well as the theory of approximate linear programming for reward-oriented Markov decision processes. All of these fit our framework and can be seen as cost-partitioned heuristics

Synthesizing Cash for Clunkers: Stabilizing the Car Market, Hurting the Environment?

We examine the impact of the EUR 5 billion German Cash-for-Clunkers program on vehicle registrations and respective CO2 emissions. To construct proper counterfactuals, we develop the multivariate synthetic control method using time series of economic predictors (MSCMT) and show (asymptotic) unbiasedness of the corresponding effect estimator under quite general conditions. Using cross-validation for determining an optimal specification of predictors, we do not find significant effects for CO2 emissions, while the stimulus’ impact on vehicle sales is strongly positive. Modeling different buyer subgroups, we disentangle this effect: 530,000 purchases were simply windfall gains; 550,000 were pulled forward; and 850,000 vehicles would not have been purchased in absence of the subsidy, worth EUR 17 billion

Cross-Validating Synthetic Controls

While the literature on synthetic control methods mostly abstracts from out-of-sample measures, Abadie et al. (2015) have recently introduced a cross-validation approach. This technique, however, is not well-defined since it hinges on predictor weights which are not uniquely defined. We fix this issue, proposing a new, well-defined cross-validation technique, which we apply to the original Abadie et al. (2015) data. Additionally, we discuss how this new technique can be used for comparing different specifications based on out-of-sample measures, avoiding the danger of cherry-picking

Synthetic Control Methods: Never Use All Pre-Intervention Outcomes Together With Covariates

It is becoming increasingly popular in applications of synthetic control methods to include the entire pre-treatment path of the outcome variable as economic predictors. We demonstrate both theoretically and empirically that using all outcome lags as separate predictors renders all other covariates irrelevant. This finding holds irrespective of how important these covariates are for accurately predicting post-treatment values of the outcome, potentially threatening the estimator's unbiasedness. We show that estimation results and corresponding policy conclusions can change considerably when the usage of outcome lags as predictors is restricted, resulting in other covariates obtaining positive weights

Synthetic Control Methods: Never Use All Pre-Intervention Outcomes Together With Covariates

It is becoming increasingly popular in applications of synthetic control methods to include the entire pre-treatment path of the outcome variable as economic predictors. We demonstrate both theoretically and empirically that using all outcome lags as separate predictors renders all other covariates irrelevant. This finding holds irrespective of how important these covariates are for accurately predicting post-treatment values of the outcome, potentially threatening the estimator's unbiasedness. We show that estimation results and corresponding policy conclusions can change considerably when the usage of outcome lags as predictors is restricted, resulting in other covariates obtaining positive weights

Monetary policy uncertainty spillovers in time and frequency domains

We use the recently created monthly Interest Rate Uncertainty measure, to investigate monetary policy uncertainty across the US, Germany, France, Italy, Spain, UK, Japan, Canada, and Sweden in both the time and frequency domains. We find that the largest spillover indices are from innovations in the country itself; however, there are some instances where spillover indices between countries are large. These relationships change over time and we observe large variances in pairwise spillovers during the global financial crisis. We find that most of the volatility is confined to the crisis period. Policy makers should consider accounting for the spillovers from the US, Germany, France and Spain, as we found that they are the most consistent net transmitters of monetary policy uncertainty

The directional volatility connectedness between crude oil and equity markets: New evidence from implied volatility indexes

In this paper, we use a set of newly introduced implied volatility indexes to investigate the directional connectedness between oil and equities in eleven major stock exchanges around the globe from 2008 to 2015. The inference on the oil–equity implied volatility relationships depends on Diebold and Yilmaz (2012, 2014, 2015) who proposed a set of directional measures that enable the dynamic and directional characterization of the relationships among financial variables. We find uniform results across the sample countries indicating that the connectedness between oil and equity is established by the bi-directional information spillovers between the two markets. However, we find that the bulk of association is largely dominated by the transmissions from the oil market to equity markets and not the other way around. The pattern of transmissions is varying over the sample period; however most of the linkages between oil and equities are established from the mid of 2009 to the mid of 2012 which is a period that witnessed the start of global recovery