Notes for @Cameron2005, *Microeconometrics: Methods and Applications*.

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.

- GMM estimation,
- nonparametric regression,
- simulation-based estimation,
- bootstrap methods,
- Bayesian methods [@Geweke2005; @Koop2007],
- stratified and clustered samples,

Topics and methods:

- NONLINEAR MODELING
- nonlinear models

- inference under minimal DISTRIBUTIONAL ASSUMPTIONS
- robust inference

- identifying and measuring CAUSATION rather than mere association
- simultaneous equations
- panel data fixed effects
- treatment evaluation
- differences-in-differences
- instrumental variables

- correcting problems of complex SURVEY methodology
- departures from simple random sampling
- sample selection
- measurement errors
- incomplete and/or missing data

The essential components of micro-econometric analysis:

- an economic specification,
- a statistical model,
- a data set.

Characteristics of micro-econometric problems, in contrast to macro-econometrics which models market and aggregate data:

- Disaggregation
- at individual, household or firm level

- Nonlinear relationships
- Limited dependent variables: censored, truncated, and discrete variable

- Heterogeneity (of individuals, firms, and organizations)

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:

- Assume that unobserved heterogeneity is uncorrelated with observed heterogeneity, and the outcome being studied has no inter-temporal dependence.
- fixed effect, i.e. an individual specific constant
- random effects
- one or more regression parameters varies randomly across the cross section.
- individual specific random component.

```
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:

- Single-equation models;
- Linear simultaneous equations models (SEM);
- Potential outcome model [@Neyman1923, @Rubin1974];

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:

- observational data
- cross-section and longitudinal survey and census data
- electronic records

- data from social experiments
- data from natural experiments

Data source: government agencies, firms.

Important chapters:

- key methods chapter (Chapter 5)
- GMM estimation (Chapter 6)