Alessio Moneta

Social research, from economics to demography and epidemiology, makes extensive use of statistical models in order to establish causal relations. The question arises as to what guarantees the causal interpretation of such models. In this paper we focus on econometrics and advance the view that causal models are ‘augmented’ statistical models that incorporate important causal information which contributes to their causal interpretation. The primary objective of this paper is to argue that causal claims are established on the basis of a plurality of evidence. We discuss the consequences of ‘evidential pluralism’ in the context of econometric modelling.

Graphical models are a powerful tool for causal model specification. Besides allowing for a hierarchical representation of variable interactions, they do not require any a priori specification of the functional dependence between variables. The construction of such graphs hence often relies on the mere testing of whether or not model variables are marginally or conditionally independent. The identification of causal relationships then solely requires some general assumptions on the relation between stochastic and causal independence, such as the Causal Markov Condition and the Faithfulness Condition (Spirtes et al. 2000; Pearl 2000). However, a procedure would require further assumptions to hold. Namely those the independence tests themselves are based on. In continuous settings, Spirtes et al. (2000) suggest causal inference based on a very restrictive formulation of independence, that is, vanishing partial correlations. Such a measure does, however, limit the applicability of causal inference to linear systems. This constitutes a serious drawback especially for the social sciences where an a priori specification of the functional form proves difficult or at odds with linearity. In short: graphical models theoretically reduce specification uncertainty regarding functional dependence, but their implementation in practice deprives them of this virtue. In this paper we investigate how causal structures in continuous settings can be identified when both functional forms and probability distributions of the variables remain unspecified. We focus on tests exploiting the fact that if X and Y are conditionally independent given a set of variables Z, the two conditional densities f (X|Y, Z) and f (X|Z) must coincide. We start by estimating the conditional densities f(X|Y, Z) and f(X|Z) via nonparametric techniques (kernel methods). We proceed by testing if some metric expressing the distance between these very conditional densities is sufficiently close to zero. Out of several metrics available in the literature to express such distance we choose two, the Euclidean, and the Hellinger distance. We investigate in a Monte Carlo study how different tests involving either measure are able to detect statistical independence, conditioned on a small set of variables. One limitation may result from nonparametric density estimation being subject to the curse of dimensionality. As the number of variables increases, the estimated empirical density converges at a slower rate to its population value. To compensate this drawback we use a local bootstrap procedure which consists of resampling the data for each test. While local bootstrap strongly increases the computational time of the test, it succeeds in counterbalancing the curse of dimensionality.

Since Economics survey by Windrum et al., research on empirical validation of agent-based Agent-based model in Economics has made substantial advances, thanks to a constant flow of high-quality contributions. This Chapter attempts to take stock of such recent literature to offer an updated critical review of the existing validation techniques. We sketch a simple theoretical framework that conceptualizes existing validation approaches, which we examine along three different dimensions: Comparison between artificial and real-world Data; Calibration and estimation of model parameters; and parameter space Exploration. Finally, we discuss open issues in the field of ABM validation and Estimation. In particular, we argue that more research efforts should be devoted toward advancing HypothesisTesting in ABM, with specific emphasis on model stationarity and ergodicity.