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Exogenous variables play a crucial role in econometrics, yet ‘exogeneity’ is often imprecise. Exogenous connotes ‘being determined outside of (the model under analysis)’, so it cannot be a property of variables per se. Rather, exogeneity is a step in model reduction, concerning when inferences about parameters of interest based on a complete analysis of the joint density function of all the observable variables coincide with inferences based on only the conditional density of one sub‐set of variables given another sub‐set. If there is no loss of information from only analysing the conditional sub‐model, then the conditioning variables are weakly exogenous for its parameters of interest, and the marginal process is irrelevant. To forecast conditionally more than one period ahead also requires Granger non‐causality, leading to the concept of strong exogeneity. To justify conditional policy analyses, which change the marginal model, parameter invariance is required in the conditional model, leading to super exogeneity.

Individuals’ socioeconomic status (SES) is positively correlated with their health status. While the existence of this gradient may be uncontroversial, the same cannot be said about its explanation. In this paper, we extend the approach of testing for the absence of causal channels developed by Adams et al. (2003), which in a Granger causality sense promises insights on the causal structure of the health-SES nexus. We introduce some methodological refinements and integrate retrospective survey data on early childhood circumstances into this framework. We confirm that childhood health has lasting predictive power for adult health. We also uncover strong gender differences in the intertemporal transmission of SES and health: While the link between SES and functional as well as mental health among men appears to be established rather late in life, the gradient among women seems to originate from childhood circumstances.

What is the relationship between trade, domestic investment, and GDP in Indonesia, Malaysia, and Thailand (IMT)? Trade fundamentalists argue that GDP and domestic investment in IMT were led by openness to trade. Others argue that the development project in IMT has been about building a domestic capitalist class that is incited to invest. If this argument is correct, primary causality between GDP, trade, and investment should run from investment to trade to GDP. Granger causality tests, panel regressions, and standard times series tests are used to test the trade-led and investment-led growth hypotheses. While some evidence is found to support both hypotheses, the preponderance of the evidence supports investment-led growth. At one level, this finding is not particularly surprising. A long and venerable tradition in economics has amply demonstrated that capital accumulation and the technical change attending it account for a large share of growth in most economies.

Chapter Six explains time series analysis with one or more independent variables. The dependent variable is the monthly violent crime rates and the independent variables are unemployment rates and inflation. This chapter discusses several topics related to the robustness of estimated models, such as how to prewhiten a time series, how to deal with trends and seasonal components, how to deal with autoregressive residuals, and how to discern changes of the dependent variable caused by independent variables from its simple continuity. This chapter also discusses the concepts of co-integration and long-memory effect and related topics such as error correction models and autoregressive distributive lags models.

Functional imaging is primarily a correlational technique. Although there are methods for analyzing the causal structure of systems, proof of causation requires methods that intervene in the workings of the system. If area A influences area B, preventing activity in A should diminish activity in B. The interference with activity in area A can be permanent, as after a brain lesion, or temporary, as with the application of transcranial magnetic stimulation. However, to understand the workings of the system we need to know not only that area A influences area B, but also how it does so. This involves the synchronization of activity in the two areas. To study this one needs methods such as electro-encephalography and magneto-encephalography that provide evidence of synchronized and dynamic oscillations at different frequencies.

This chapter illustrates vector autoregressive VAR models, with a particular focus on estimation and hypothesis testing. It discusses estimation of parameters, deterministic components, VAR order selection, Granger causality, forecasting with multivariate models, and multivariate spectral density. Exercises are provided at the end of the chapter.