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 data-driven, empirical findings without a strong theoretical foundation.

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Why Add Structure to an Econometric Model?

Purposes

1. Estimation of Unobservable Parameters:
   • Examples include marginal utility, marginal cost, risk preferences, discount rates, etc.
2. Counterfactual Simulations:
   • Assessing what would happen under different economic scenarios.
3. 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.

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Constructing a Structural Econometric Model

Steps

1. Start with Economic Theory:
   • Define economic setting, list primitives (preferences, technologies), and equilibrium concepts.
2. Transform into Econometric Model:
   • Incorporate statistical elements like unobservables and errors.
3. Estimation:
   • Define functional forms, distributional assumptions, and select estimation methods.

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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 Cobb-Douglas Production Function

The initial economic model is based on the Cobb-Douglas 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 Log-Linear Model: To facilitate estimation and interpretation, this production function is transformed into a log-linear 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:

  $\ln(Y_t) = \gamma + \alpha \ln(K_t) + \beta \ln(L_t) + \varepsilon_t$

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A More Complex Example of a Structural Model

This example demonstrates a more complex structural model involving procurement auctions with risk-neutral 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 $(N_t)$ risk-neutral 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:

$$E[\pi_i(b_1, ..., b_N)] = (b_i - c_i) . Pr(b_i < b_j , \forall j \neq i | c_i)$$

2. First-Order Condition for the Bid Function

• Differentiating the expected profit with respect to the bid gives the first-order condition, leading to the bid function:

$$b_i = \beta(c_i) = c_i + \frac{\int_{c_i}^{\infty} [1 - F(\tau)]^{N-1} . d\tau ]}{ [1- F(c_i)]^{N-1}}$$

3. Distribution of the Winning Bid

• The distribution of the winning bid is derived from the bid function.

$$h(w) = \frac{N[1 - F(\beta^{-1}(w))]^{N-1} f(\beta^{-1}(w))}{\beta'(\beta^{-1}(w))}$$

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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 region-month or region-quarter 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 Post-Merger: 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 Time-Series and Cross-Sectional Price Effects

• Time-Series Analysis: Difference-in-differences regression design to quantify time-series price effects and analyze more brands. Results show MillerCoors prices increased 5–10% relative to import brands, with ABI prices increasing similarly.
• Cross-Sectional Analysis: Reduced-form regression to examine market-level 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 supply-side parameters, including marginal costs and pricing conduct.
• Results: Increased markups for MillerCoors and ABI beers post-merger, 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