Graphical Models for Structural Vector Autoregressions

In this paper a method to identify the causal structure associated with a VAR model is proposed. The structure is described by means of a graph, which provides a rigorous language to analyze the statistical and logical properties of causal relations. Under some general assumptions, causal relations are associated with a set of vanishing partial correlations among the variables that constitute them. In order to infer the causal structure among the contemporaneous variable, tests on vanishing partial correlations among the estimated residuals of a VAR are used, jointly with background knowledge. This method is applied to an updated version of the King et al. (1991) dataset and it allows to obtain an orthogonalization of the residuals coherent with the causal structure among the contemporaneous variables and alternative to the standard one, which is based on the Choleski factorization of the covariance matrix of the residuals. The impulse response functions calculated, with the method proposed here, for the King et al. (1991) model confirm their results about the fact that US macroeconomic data do not support the hypothesis that real permanent shocks are the dominant source of business-cycle fluctuations.Causality, Directed Acyclic Graphs, Identification Problem, Residuals Orthogonalization, Impulse Response Functions.

Graph-Based Search Procedure for Vector Autoregressive Models

Vector Autoregressions (VARs) are a class of time series models commonly used in econometrics to study the dynamic effect of exogenous shocks to the economy. While the estimation of a VAR is straightforward, there is a problem of finding the transformation of the estimated model consistent with the causal relations among the contemporaneous variables. Such problem, which is a version of what is called in econometrics “the problem of identification,” is faced in this paper using a semi-automated search procedure. The unobserved causal relations of the structural form, to be identified, are represented by a directed graph. Discovery algorithms are developed to infer features of the causal graph from tests on vanishing partial correlations among the VAR residuals. Such tests cannot be based on the usual tests of conditional independence, because of sampling problems due to the time series nature of the data. This paper proposes consistent tests on vanishing partial correlations based on the asymptotic distribution of the estimated VAR residuals. Two different types of search algorithm are considered. A first algorithm restricts the analysis to direct causation among the contemporaneous variables, a second algorithm allows the possibility of cycles (feedback loops) and common shocks among contemporaneous variables. Recovering the causal structure allows a reliable transformation of the estimated vector autoregressive model which is very useful for macroeconomic empirical investigations, such as comparing the effects of different shocks (real vs. nominal) on the economy and finding a measure of the monetary policy shock.VARs, Problem of Identification, Causal Graphs, Structural Shocks

Comparing shapes of engel curves

We measure how different the shapes of Engel curves are across 59 commodity groups. The same analysis is carried out for their derivatives and variances. While Engel curves possess a relatively homogeneous shape, significantly more heterogeneity is present in derivatives and when particular sub-classes of income are considered.Consumption, Kernel smoothing, Rank correlation, Curve shape

More or Better ? Measuring Quality versus Quantity in Food Consumption

As people become richer they get the opportunity of consuming more but also qualitatively better goods. This holds for a basic commodity like food as well. We investigate food consumption in Russia, taking into account both expenditure and nutrition value in terms of calories. We analyze how food consumption patterns change with increasing income by estimating both "quantity Engel curves" and "quality Engel curves". The former describe the functional dependence of calories consumed on total expenditure. The latter trace out the dependence of price per calorie as a proxy for quality on total expenditure. We compare income elasticities of quantity with income elasticities of quality. In these Russian data for years 2000-2002 the reaction of quality to changes in income is significantly stronger than the reaction of quantity to income changes suggesting that Russian households tend to choose higher quality food items as income rises.Food consumption patterns, calorie intake, income elasticity decomposition, Engel curves, method of average derivatives

Exporting and productivity as part of the growth process: causal evidence from a data-driven structural VAR

This paper introduces a little known category of estimators - Linear Non-Gaussian vector autoregression models that are acyclic or cyclic - imported from the machine learning literature, to revisit a well-known debate. Does exporting increase firm productivity? Or is it only more productive firms that remain in the export market? We focus on a relatively well-studied country (Chile) and on already-exporting firms (i.e. the intensive margin of exporting). We explicitly look at the co-evolution of productivity and growth, and attempt to ascertain both contemporaneous and lagged causal relationships. Our findings suggest that exporting does not have any causal influence on the other variables. Instead, export seems to be determined by other dimensions of firm growth. With respect to learning by exporting (LBE), we find no evidence that export growth causes productivity growth within the period and very little evidence that exporting growth has a causal effect on subsequent TFP growth

Empirical Validation of Agent Based Models: A Critical Survey

This paper addresses the problem of finding the appropriate method for conducting empirical validation in agent-based (AB) models, which is often regarded as the Achilles’ heel of the AB approach to economic modelling. The paper has two objectives. First, to identify key issues facing AB economists engaged in empirical validation. Second, to critically appraise the extent to which alternative approaches deal with these issues. We identify a first set of issues that are common to both AB and neoclassical modellers and a second set of issues which are specific to AB modellers. This second set of issues is captured in a novel taxonomy, which takes into consideration the nature of the object under study, the goal of the analysis, the nature of the modelling assumptions, and the methodology of the analysis. Having identified the nature and causes of heterogeneity in empirical validation, we examine three important approaches to validation that have been developed in AB economics: indirect calibration, the Werker-Brenner approach, and the history-friendly approach. We also discuss a set of open questions within empirical validation. These include the trade-off between empirical support and tractability of findings, the issue of over-parameterisation, unconditional objects, counterfactuals, and the non-neutrality of data.Empirical validation, agent-based models, calibration, history-friendly modelling

Satiation, escaping satiation, and structural change: Some evidence from the evolution of Engel curves

Certain properties of Engel curves have been linked to the occurrence of structural change in the economy (Pasinetti 1981, Metcalfe et al. 2006, Saviotti 2001). From an empirical perspective, however, very little has been done to examine (i) whether indeed satiation is a general property of Engel curves; (ii) whether the rate at which Engel curves converge to satiation may significantly change over time; and (iii) how stable Engel curves are across time such that it may be appropriate to use them to make predictions about structural change. Using data from the UK Family Expenditure Survey, this paper examines these three issues

Graph-based search procedure for vector autoregressive models

In this paper we present a semi-automated search procedure to deal with the problem of the identification of the causal structure related to a vector autoregressive model. The structural form of the model is described by a directed graph and from the analysis of the partial correlations of the residuals the set of acceptable causal structures is derived