24.3 Structural modeling and Causal Inference
Structural modeling and causal inference are both valuable tools in economics and social sciences. In a nutshell, both methods try to understand relationships between variables; however, the objectives and methodologies can differ.
Causal inference focuses on the identification and estimation of causal relationships from observational data. It employs strategies like randomized controlled trials, natural experiments, matching, instrumental variables, difference-in-differences, regression discontinuity, etc., to estimate the causal effect of a treatment on an outcome, while trying to control for confounding.
On the other hand, structural modeling refers to the practice of using economic theory to guide the specification of statistical models. Structural models explicitly model the decision-making process of agents (consumers, firms, etc.), often taking into account optimization behavior and equilibrium conditions.
While causal inference mainly focuses on “reduced-form” relationships (i.e., direct associations between variables, without necessarily modeling the underlying process), structural modeling aims to uncover the “deep parameters” of the underlying process that generates the data, which represent preferences, technologies, or strategic interactions.
As such, structural models have more demanding data requirements and often require stronger assumptions. However, they can be more flexible in extrapolating beyond the observed data (i.e., for policy analysis or prediction), because they’re designed to model the underlying process that generates the data. In other words, while causal inference asks “what is the effect of X on Y?”, structural modeling often asks “how does the system work?”
To transition from causal inference to structural modeling, it might be helpful to focus on these aspects:
Learning more about optimization theory and game theory: These are the foundations of a lot of structural models.
Understanding how to estimate structural models: This usually involves techniques like maximum likelihood estimation or generalized method of moments, which are more complex than the regression-based methods often used in causal inference.
Studying some of the seminal papers in structural modeling (like the ones listed above), to see how they specify and estimate their models.
Practicing with simple structural models, such as the linear demand and supply model, before moving on to more complex models.
Understanding the strengths and weaknesses of structural modeling as compared to causal inference. For example, structural models often require stronger assumptions, but they allow for counterfactual analysis and policy simulations.
It’s also worth noting that the two methods can be complementary. For instance, results from causal inference can be used to test or validate a structural model, and a structural model can be used to guide the search for causal relationships. So, having a background in causal inference can be a big advantage as you’re learning about structural modeling.
Simple Models (Linear Demand and Supply):
A basic model of linear demand and supply involves modeling how quantity demanded and supplied depend on price. For instance, the demand function might be Qd = a - bP, where Qd is the quantity demanded, P is the price, and a and b are parameters to be estimated. Similarly, the supply function might be Qs = c + dP, where Qs is the quantity supplied, and c and d are parameters to be estimated. By solving these two equations, we can find the equilibrium price and quantity. This model is simple, but it forms the basis for more complex structural models.
Strong Assumptions in Structural Models:
Structural models often involve assumptions about:
The functional form of relationships between variables. For example, is demand linear or non-linear in price?
The decision-making process of agents. For instance, do consumers always buy the product that gives them the highest utility?
The information available to agents. Do consumers know everything about all products when making a choice, or do they face uncertainty?
Equilibrium conditions. For example, in a market model, we might assume that the market always clears (demand equals supply).
These assumptions are often necessary to make the model tractable and to allow for estimation, but they can also be a source of bias if they’re incorrect.
Counterfactual Analysis and Policy Simulations:
Counterfactual analysis involves asking “what if” questions about scenarios that did not actually occur. For example, “what would have happened to sales if we had set a different price?” Policy simulations involve asking similar questions about potential future policies. For example, “how would a change in our pricing strategy affect future sales?”
An example: (Gowrisankaran and Rysman 2020)
Complementarity of Causal Inference and Structural Modeling:
While causal inference focuses on estimating the effect of a particular treatment, structural modeling aims to understand the underlying process that generates the data. Therefore, the results from a causal analysis can provide useful information for specifying or validating a structural model. For example, a causal analysis might reveal that price has a negative effect on demand, which could be used to specify the demand function in a structural model.
Conversely, a structural model can help guide causal analysis. For example, it can help identify potential sources of endogeneity or omitted variable bias, and suggest instrumental variables or other strategies for causal identification.
An example is (C. T. Conlon and Mortimer 2013). The authors use structural modeling to address endogeneity in product availability, and use these structural estimates to perform a counterfactual analysis.