Notes for Cameron and Trivedi, Microeconometrics: Methods and Applications. [@Cameron2005]
Macro-econometrics deals with modeling market and aggregate data collected by government agencies. Micro-econometrics emerged in the 1950s and deals with data on individuals, households, and firms. The Nobel Prize in Economics first recognized micro-econometrics in 2000, awarding James Heckman (selective samples) and Daniel McFadden (discrete choice).
The distinguishing feature of econometrics from statistics is the emphasis on causal modeling.
Topics and methods:
The essential components of micro-econometric analysis:
Characteristics of micro-econometric problems, in contrast to macro-econometrics which models market and aggregate data:
Highly parametric models are sufficiently detailed to capture the complexities of data, but these models can be challenging to estimate. Alternatively, statistical inference can be based on standard errors that are “robust” to complications such as heteroskedasticity and clustering.
Handling unobserved heterogeneity:
A **model** is the specification of the probability distribution for a set of observations. A **structure** is the specification of the parameters of that distribution. Therefore, a structure is a model in which all the parameters are assigned numerical values. [@Sargan1988]
Structural models capture causal/behavioral relations, while reduced form models only uncover correlations and associations. Structural models are based on specification of economic behavior, and separate variables into causes/exogenous (externally determined) and effects/endogenous (explained within the model).
In general, a structural model of variables $W = [Y, Z]$ is a known implicit function: $$g(y, z, u|θ) = 0$$ Here, $θ$ is the structural parameters. Assume the structural model has a unique solution for the endogenous variables, then the reduced form of the structural model is: $$y = f(z, u|π)$$ The reduced form parameters $π$ is a function of structural parameters $θ$. If $f$ is additively separable such that $y = h(z|π) + u$, then the regression function (conditional expectation function) of $y$ on $z$ is a natural predictor.
Types of structural models:
If the structural approach is implemented with aggregated data, it will yield estimates of the fundamental parameters only under very stringent (and possibly unrealistic) conditions.
Reduced form analysis does not always take into account all causal interdependencies, and reduced form parameters may not be interpretable without some information about the structural parameters.
Identifiability of causal economic relations.
Three main types of data:
Data source: government agencies, firms.