Introduction
These notes are taken from YouTube video lectures by Matt Woerman.
What is Structural Econometrics?
Definition
 Structural econometrics is defined as combining explicit economic theories with statistical models to identify parameters of economic models based on individual choices or aggregate relations.
 Structural econometrics is a branch of economics that combines economic theory, statistical methods, and empirical analysis to model and understand the underlying structures of economic systems. It aims to uncover the relationships between different economic variables by developing and estimating models based on economic theory.
Contrast with Nonstructural (reduced form) Econometrics
Reduced form econometrics emphasises on:
 Less direct incorporation of economic theory.
 More focus on datadriven, empirical findings without a strong theoretical foundation.
Why Add Structure to an Econometric Model?
Purposes
 Estimation of Unobservable Parameters:
 Examples include marginal utility, marginal cost, risk preferences, discount rates, etc.
 Counterfactual Simulations:
 Assessing what would happen under different economic scenarios.
 Comparing Economic Theories:
 Testing competing theories by modeling their implications.
Balance and Credibility
 The choice between structural and nonstructural approaches depends on research context and questions.
 Structural models can sometimes add credibility, especially in policy analysis or forecasting.
Constructing a Structural Econometric Model
Steps
 Start with Economic Theory:
 Define economic setting, list primitives (preferences, technologies), and equilibrium concepts.
 Transform into Econometric Model:
 Incorporate statistical elements like unobservables and errors.
 Estimation:
 Define functional forms, distributional assumptions, and select estimation methods.
A Simple Example of a Structural Model
This example demonstrates the estimation of output elasticities of capital and labor for a firm using a structural econometric model.
Observations
 Output $(Y_t)$
 Capital $(K_t)$
 Labor $(L_t)$
Steps
1. Start with a CobbDouglas Production Function
The initial economic model is based on the CobbDouglas production function, which is a common representation in economics to describe the relationship between outputs and inputs.

Functional Form: $Y_t = A K_t^\alpha L_t^\beta$

Rewritten as a LogLinear Model: To facilitate estimation and interpretation, this production function is transformed into a loglinear form.
$\ln(Y_t) = \gamma + \alpha \ln(K_t) + \beta \ln(L_t)$
2. Incorporate an Error Term
An error term $(\varepsilon_t)$ is added to the model to account for measurement error and other unobserved factors.
 Assumptions on Error Term:
 The error term is assumed to follow a normal distribution with mean zero and variance $\sigma^2: \varepsilon_t \sim N(0, \sigma^2)$.
 It is assumed that the expectation of the error term, given capital and labor, is zero: $E(\varepsilon_t  K_t, L_t) = 0$.
3. Estimation Using Ordinary Least Squares (OLS)
The final step involves estimating the output elasticities $\alpha$ and $\beta$ using OLS, a standard method in econometrics for estimating the parameters of a linear regression model.

OLS Estimation Model:
$\ln(Y_t) = \gamma + \alpha \ln(K_t) + \beta \ln(L_t) + \varepsilon_t$
A More Complex Example of a Structural Model
This example demonstrates a more complex structural model involving procurement auctions with riskneutral bidders and the goal of estimating the underlying common distribution of costs known to all bidders.
Observations
 Winning Bid $(w_t)$: Observed in T procurement auctions with $(N_t)$ riskneutral bidders.
Steps
1. Economic Theory and Expected Profit Maximization
 Each firm is assumed to maximize its expected profit.
 The expected profit for firm $(i)$ with bid $(b_i)$ and cost $(c_i)$ is given by:
2. FirstOrder Condition for the Bid Function
 Differentiating the expected profit with respect to the bid gives the firstorder condition, leading to the bid function:
3. Distribution of the Winning Bid
 The distribution of the winning bid is derived from the bid function.
Miller and Weinberg (2017) Case Study: Analysis of the MillerCoors Merger
Research Setting and Question
 Industry: US beer industry, dominated by three major firms: Miller, Coors, and ABI.
 Event: Miller and Coors merged their US operations in a new joint venture.
 Regulatory Review: Approved by the US DOJ in June 2008 amidst concerns about potential consumer harm vs. cost efficiencies.
 Research Question: Did the MillerCoors merger lead to new coordinated pricing between MillerCoors and ABI?
Data
 Retail Scanner Data: Weekly revenue and unit sales by UPC code, week, and store (2001–2011 across 39 geographic regions, covering 13 flagship brands). Data aggregated to regionmonth or regionquarter levels.
 American Community Survey: Household demographics (income) from a subsample of US households.
 Geographic Data: Locations of regions and breweries, including driving distance from the nearest brewery to market.
 Fuel Prices: Diesel fuel prices from US EIA and US DOE to account for transportation costs.
Descriptive Evidence of Price Effects
 Observations PostMerger: Prices of Miller Lite, Coors Light, and Bud Light increased by 8%, stopping a downward trend.
 Comparative Analysis: No change in price levels or trends for Corona Extra and Heineken.
 Preliminary Conclusion: Descriptive evidence suggests possible coordinated pricing by MillerCoors and ABI, but also consistent with other explanations like unilateral pricing effects, retail practices, or macroeconomic conditions.
Regression Evidence of TimeSeries and CrossSectional Price Effects
 TimeSeries Analysis: Differenceindifferences regression design to quantify timeseries price effects and analyze more brands. Results show MillerCoors prices increased 5–10% relative to import brands, with ABI prices increasing similarly.
 CrossSectional Analysis: Reducedform regression to examine marketlevel factors (industry concentration, transportation costs). Findings show price increases largely unexplained by these factors, suggesting that unilateral effects may not fully account for observed price increases.
Additional Analyses and Structural Estimation
 Event Studies: Ashenfelter, Hosken, and Weinberg (2015) conducted further analyses to characterize factors explaining unilateral price effects.
 Demand and Supply Models: Structural econometric models used to estimate consumer demand and supplyside parameters, including marginal costs and pricing conduct.
 Results: Increased markups for MillerCoors and ABI beers postmerger, but not for imports. Estimated demand elasticities and supply model parameters suggest substantial coordinated pricing effects.
Counterfactual Simulations and Welfare Calculations
 Simulation: Price trajectories simulated under various market assumptions.
 Findings: ABI price increases largely due to coordinated pricing.
 Welfare Effects: Calculated for different scenarios, indicating that the merger could improve total surplus under certain conditions, depending on cost efficiencies and pricing coordination