34  Structural Models

A structural model is an empirical model whose parameters are the primitives of an economic theory: the preferences of consumers, the technologies and costs of firms, the information agents hold, and the rules of the game they play. Rather than fit a flexible function from covariates to an outcome, the analyst writes down how agents decide—typically as the solution to an optimization problem under an equilibrium concept—and then estimates the deep parameters that rationalize the observed data. The payoff is that those parameters are, by construction, invariant to the policies the analyst wants to study, so the model can answer questions about worlds that were never observed: a price never charged, a product never launched, a compensation plan never offered.

This is a different ambition from prediction or even from causal inference. A reduced-form analysis asks what is the effect of X on Y? and answers it, ideally, with a research design that isolates exogenous variation. A structural analysis asks how does the system work?—and, having recovered the mechanism, can simulate the effect of any intervention the mechanism admits, including ones for which no experiment or natural experiment exists. The cost of that generality is steep: structural models impose strong assumptions (functional forms, equilibrium, the information environment), and when those assumptions are wrong the conclusions are wrong in ways that are hard to detect. Much of the craft lies in choosing assumptions that buy identification without buying bias, and in being honest about which results lean on which assumptions.

This chapter develops the structural approach for a reader who already understands regression and causal inference and wants to see what changes when economic theory is moved from the discussion section into the likelihood. We proceed from intuition to formalism: first the anatomy of a structural model and its relationship to causal inference (Section 34.1); then a worked supply-and-demand example that exposes the endogeneity problem at the heart of the field (Section 34.2); then the two workhorse estimators—maximum likelihood and the generalized method of moments—and the discrete-choice and dynamic models that dominate marketing applications (Section 34.3 through Section 34.5); and finally the identification threats that decide whether any of it can be believed (Section 34.6). Throughout, the running theme is the one stated above: structural parameters are valuable precisely to the extent that they are policy invariant, and they are policy invariant only to the extent that the model is correct.

34.1 What Makes a Model “Structural”

The defining feature of a structural model is that its parameters have an interpretation outside the data-generating environment in which they were estimated. Chintagunta et al. (2006), in a field review, characterize structural modeling as the practice of using economic theory to discipline the specification of an empirical model so that the estimated coefficients correspond to taste, technology, or strategic primitives rather than to environment-specific correlations. The distinction matters most when the goal is counterfactual: a demand elasticity estimated as a structural taste parameter can be carried into a pricing simulation, whereas a regression slope estimated in one price regime carries no guarantee of stability when the regime changes.

It is useful to state the contrast formally. Suppose an outcome \(y\) is generated by agents who choose actions to maximize an objective indexed by a structural parameter vector \(\boldsymbol{\theta}\) (e.g., utility weights, marginal costs) given a state \(\mathbf{s}\) and a policy \(\mathbf{p}\) (prices, assortment, incentives): \[ y = m(\mathbf{s}, \mathbf{p}; \boldsymbol{\theta}) + \varepsilon , \tag{34.1}\] where \(m(\cdot)\) is the decision rule—the mapping from states and policy to behavior implied by the agent’s optimization and the market equilibrium. A reduced-form analysis estimates a projection of \(y\) on \((\mathbf{s},\mathbf{p})\) that is valid only on the support and policy regime observed. A structural analysis estimates \(\boldsymbol{\theta}\), then re-solves Equation 34.1 under a new policy \(\mathbf{p}'\) to predict \(y' = m(\mathbf{s}, \mathbf{p}'; \boldsymbol{\theta})\). The structural object is reusable; the reduced-form object, strictly, is not.

Causal inference estimates the effect of a treatment that occurred; structural modeling estimates the mechanism that would produce the effect of a treatment that did not. The first is a statement about a realized intervention, the second a statement about a class of interventions the model can simulate.

The two traditions are complements rather than rivals, and the modern literature treats them as such. Credible causal estimates discipline structural models—a quasi-experimental demand elasticity is a moment a structural demand system should reproduce—and structural reasoning, in turn, tells the causal analyst where the endogeneity is and what would constitute a valid instrument. Conlon and Mortimer (2013) illustrate the round trip: they build a structural demand model to handle endogenous product availability (stockouts that are correlated with demand shocks) and then use the structural estimates to run counterfactuals that no reduced-form design could deliver. The remainder of this section makes the three pillars of any structural exercise—behavioral assumptions, equilibrium, and counterfactuals—precise before we turn to estimation.

Figure 34.1 summarizes the workflow that distinguishes the structural pipeline from a reduced-form one.

flowchart TD
    A[Economic theory:<br/>preferences, costs,<br/>information, game] --> B[Agent optimization<br/>+ equilibrium concept]
    B --> C["Decision rule<br/>m(s, p; θ)"]
    C --> D[Estimation:<br/>MLE / GMM<br/>recover θ]
    D --> E[Re-solve under<br/>new policy p′]
    E --> F[Counterfactual /<br/>policy simulation]
    G[(Observed data)] -.->|reduced form| H[Environment-specific<br/>association]
    G --> D

Figure 34.1: The structural modeling pipeline. Economic theory specifies agents’ objectives; optimization and an equilibrium concept yield a decision rule whose deep parameters are estimated by MLE or GMM; the estimated rule is then re-solved under new policies for counterfactual analysis. The dashed path is the reduced-form alternative, which stops at an environment-specific association.

34.1.1 Behavioral and Equilibrium Assumptions

Structural models earn their counterfactual power by committing to assumptions of four kinds, and the credibility of any application rests on how defensible those commitments are.

The first is functional form: the shape of utility, demand, or cost. Is demand linear in price, or constant-elasticity? Is utility linear in attributes, or does it exhibit diminishing marginal utility? These choices are not innocuous, because the counterfactual extrapolates along the assumed curvature.

The second is the decision protocol: the rule by which agents map information to actions. The canonical assumption is utility maximization—each consumer chooses the alternative delivering the highest utility—but the model must also say whether agents are myopic or forward looking, risk neutral or risk averse, and whether they learn.

The third is the information environment. Do consumers know all product attributes when choosing, or do they face uncertainty and update beliefs? Erdem, Keane, and Sun (2008), for instance, build a model in which advertising influences price sensitivity precisely because consumers are uncertain about quality in experience- good markets and advertising conveys information; the substantive conclusion is inseparable from the informational assumption.

The fourth is the equilibrium concept. In a market model the analyst must say how agents’ choices are mutually consistent: that the market clears, or that firms play a Nash equilibrium in prices, or that a dynamic game is in Markov-perfect equilibrium. Kadiyali, Sudhir, and Rao (2001) review how equilibrium assumptions let the analyst infer unobserved competitive conduct—whether firms behave more collusively or more competitively than Bertrand—from the comovement of prices and quantities, an inference impossible without the equilibrium restriction.

These assumptions are what make the model tractable and estimable, and they are simultaneously the model’s principal vulnerability: a misspecified information environment or an incorrect conduct assumption biases the deep parameters and, with them, every counterfactual. The discipline of the field is to state each assumption explicitly, to test those that are testable, and to flag the counterfactuals that hinge on the rest.

34.1.2 Counterfactuals: the Reason to Pay the Price

The justification for the structural apparatus is the counterfactual. Once \(\boldsymbol{\theta}\) is in hand, the analyst re-solves the model under a policy that was never implemented and reads off the predicted outcome—what would sales have been at a price we never charged? or what compensation plan maximizes profit? Gowrisankaran and Rysman (2020) provide a framework for exactly this kind of policy evaluation, and the counterfactual logic is what separates a structural paper from a descriptive one. The validity of a counterfactual is conditional on two things: the parameters are policy invariant (the Lucas-critique requirement), and the new policy lies within the class the model can represent. A model estimated under linear pricing cannot credibly simulate nonlinear tariffs; a static model cannot simulate a policy whose whole point is to change dynamic incentives. Stating the admissible counterfactual class is therefore part of specifying the model, not an afterthought.

34.2 A First Structural Model: Demand and Supply

The simplest model that exhibits the structural way of thinking is linear simultaneous supply and demand. It is worth working through in full because it already contains the central econometric problem of the entire field—the endogeneity of price—and the standard solution.

Let quantity demanded and supplied at price \(p\) be \[ Q^{d} = \alpha_0 - \alpha_1 p + u^{d}, \qquad Q^{s} = \beta_0 + \beta_1 p + u^{s}, \tag{34.2}\] with \(\alpha_1, \beta_1 > 0\) and structural shocks \(u^{d}, u^{s}\) (a demand shifter such as a taste shock; a supply shifter such as an input-cost shock). The structural parameters are the slopes \(\alpha_1\) (how strongly quantity responds to price along the demand curve) and \(\beta_1\) (the analogous supply response); these are the policy-invariant objects a manager would want for pricing. Market clearing, \(Q^{d} = Q^{s}\), is the equilibrium condition, and it determines the observed price \[ p^{\star} = \frac{\alpha_0 - \beta_0 + u^{d} - u^{s}}{\alpha_1 + \beta_1}. \tag{34.3}\]

Equation 34.3 is the crux. Because equilibrium price depends on the demand shock \(u^{d}\), price is endogenous: \(\mathrm{Cov}(p^{\star}, u^{d}) \neq 0\). A naive regression of observed quantity on observed price does not recover \(\alpha_1\); it recovers a hybrid of the demand and supply slopes—the textbook simultaneity bias. Intuitively, the observed price–quantity pairs are intersections of shifting demand and supply curves, so the scatter traces out neither curve. This single fact—that prices are set by agents who observe demand conditions the econometrician does not—motivates the instrumental-variable and control-function machinery that pervades structural demand estimation.

Identification comes from exclusion restrictions: a variable that shifts supply but not demand traces out the demand curve, and vice versa. A cost shifter \(z\) entering supply but excluded from demand instruments for price in the demand equation. Montgomery and Rossi (1999) exploit precisely this logic to estimate price elasticities at the store and household level, recovering structural demand slopes that a single-equation regression would contaminate. The simulation below makes the bias concrete and shows that an instrument recovers the truth.

set.seed(29)
n  <- 5000
a0 <- 10; a1 <- 1.5      # demand intercept, slope (truth)
b0 <- 2;  b1 <- 1.0      # supply intercept, slope (truth)

z  <- runif(n, 0, 4)     # cost shifter: enters supply, excluded from demand
ud <- rnorm(n)           # demand shock
us <- rnorm(n)           # supply shock

# Equilibrium price and quantity (solve Qd = Qs with a cost shifter in supply)
# Qd = a0 - a1 p + ud ;  Qs = b0 + b1 p + g*z + us
g  <- 1.2
p  <- (a0 - b0 - g * z + ud - us) / (a1 + b1)
q  <- a0 - a1 * p + ud

# (1) Naive OLS of quantity on price: biased for the demand slope -a1
ols  <- coef(lm(q ~ p))["p"]

# (2) Two-stage least squares using the cost shifter z as an instrument
phat <- fitted(lm(p ~ z))
iv   <- coef(lm(q ~ phat))["phat"]

cat("True demand slope (-a1):      ", -a1, "\n")
#> True demand slope (-a1):       -1.5
cat("OLS estimate (biased):        ", round(ols, 3), "\n")
#> OLS estimate (biased):         -0.892
cat("IV / 2SLS estimate (consistent):", round(iv, 3), "\n")
#> IV / 2SLS estimate (consistent): -1.513

The OLS slope is attenuated and unstable; the instrumented slope recovers \(-\alpha_1\). This linear example scales, conceptually, all the way to modern differentiated- products demand systems, where the same endogeneity reappears (price correlates with unobserved product quality) and is handled with the same idea—cost or competitor- based instruments—inside a far richer choice model, to which we now turn.

34.3 Estimation: Maximum Likelihood and GMM

Structural parameters are rarely obtained by ordinary least squares. The two dominant estimators are maximum likelihood (ML) and the generalized method of moments (GMM); the standard graduate references develop both in depth (Greene 2003; Cameron and Trivedi 2005; Hensher, Rose, and Greene 2005), and the Handbook of Econometrics chapters on the econometric evaluation of policy collect the identification theory (Heckman and Vytlacil 2007a, 2007b; Abbring and Heckman 2007). The choice between ML and GMM is chiefly a choice about how much of the data-generating process one is willing to specify.

Maximum likelihood specifies the full conditional distribution of the data. If the model implies a density \(f(y_i \mid \mathbf{x}_i; \boldsymbol{\theta})\), the estimator maximizes the log-likelihood, \[ \hat{\boldsymbol{\theta}}_{\mathrm{ML}} = \arg\max_{\boldsymbol{\theta}} \sum_{i=1}^{n} \log f(y_i \mid \mathbf{x}_i; \boldsymbol{\theta}), \tag{34.4}\] which is efficient when the distributional assumption is correct but inconsistent when it is not. ML is the natural estimator for discrete-choice models, where the choice probabilities are the likelihood contributions.

The generalized method of moments specifies only a set of population moment conditions implied by the theory—typically that the structural error is orthogonal to a vector of instruments \(\mathbf{z}_i\), \[ \mathbb{E}\!\left[\, \mathbf{z}_i \, g(y_i, \mathbf{x}_i; \boldsymbol{\theta}) \,\right] = \mathbf{0}, \tag{34.5}\] where \(g(\cdot)\) is the structural residual. GMM minimizes the empirical analog of these moments in a quadratic form, \[ \hat{\boldsymbol{\theta}}_{\mathrm{GMM}} = \arg\min_{\boldsymbol{\theta}} \bar{g}_n(\boldsymbol{\theta})^{\top}\, \mathbf{W}\, \bar{g}_n(\boldsymbol{\theta}), \qquad \bar{g}_n(\boldsymbol{\theta}) = \frac{1}{n}\sum_{i=1}^{n} \mathbf{z}_i\, g(y_i, \mathbf{x}_i; \boldsymbol{\theta}), \tag{34.6}\] with weighting matrix \(\mathbf{W}\); the efficient choice sets \(\mathbf{W}\) to the inverse of the moment covariance. GMM is the estimator of choice when the analyst trusts a few orthogonality conditions (a cost instrument, an equilibrium first-order condition) but does not wish to commit to a full likelihood—exactly the situation in differentiated-products demand, where the famous contraction-mapping estimator inverts market shares to demand shocks and stacks them against instruments in Equation 34.6. Table 34.1 contrasts the two.

Table 34.1: Maximum likelihood versus GMM for structural estimation.

Dimension	Maximum likelihood	Generalized method of moments
Specifies	Full conditional density of the data	A set of moment/orthogonality conditions
Efficiency	Efficient if the distribution is correct	Efficient given the chosen moments; generally less than full ML
Robustness	Inconsistent under distributional misspecification	Consistent under far weaker assumptions
Endogeneity	Handled via control functions or joint likelihood	Handled natively through instrument moments
Typical use	Discrete choice, dynamic discrete choice	Demand systems, Euler-equation and conduct models
Failure mode	Wrong likelihood \(\Rightarrow\) biased everything	Weak or invalid instruments \(\Rightarrow\) weak identification

34.4 Discrete Choice as the Workhorse

A large share of structural marketing models are built on random-utility discrete choice, because most consumer decisions—which brand, which channel, whether to buy at all—are discrete, and because the framework yields choice probabilities that are both behaviorally founded and computationally convenient. The reviews by Dubé et al. (2002) and Heiss (2002) lay out the family and its estimation; the model below is the canonical entry point.

Consumer \(i\) choosing among alternatives \(j = 1,\dots,J\) derives utility \[ U_{ij} = V_{ij} + \varepsilon_{ij} = \mathbf{x}_{ij}^{\top}\boldsymbol{\beta} - \alpha p_{ij} + \xi_j + \varepsilon_{ij}, \tag{34.7}\] where \(\mathbf{x}_{ij}\) are observed attributes, \(p_{ij}\) is price, \(\xi_j\) is an unobserved (to the analyst) product-quality term, and \(\varepsilon_{ij}\) is an idiosyncratic taste shock. The consumer picks \(j\) if \(U_{ij} \ge U_{ik}\) for all \(k\). When \(\varepsilon_{ij}\) is i.i.d. type-I extreme value, the choice probabilities take the closed-form multinomial logit, \[ P_{ij} = \frac{\exp(V_{ij})}{\sum_{k=1}^{J}\exp(V_{ik})}, \tag{34.8}\] which is the likelihood contribution maximized in Equation 34.4. Two structural warnings travel with Equation 34.8. First, the logit imposes independence of irrelevant alternatives (IIA): the relative odds of two alternatives are unaffected by any third, an implausible substitution pattern that the nested logit of Heiss (2002) relaxes by grouping close substitutes into nests. Second, the quality term \(\xi_j\) is correlated with price (better products are priced higher), so \(\alpha\) is endogenous—the same simultaneity as in Section 34.2, now inside a choice model—and is corrected with cost or competitor-price instruments.

A practical route to estimation, due to Berry, inverts the share equation. With an outside option \(j=0\) whose mean utility is normalized to zero, Equation 34.8 implies the linear relation \[ \ln s_j - \ln s_0 = \mathbf{x}_{j}^{\top}\boldsymbol{\beta} - \alpha p_{j} + \xi_j, \tag{34.9}\] so the left-hand side—an observed function of market shares—equals mean utility, and the demand parameters can be estimated by regressing it on attributes and price. The example below builds one market of many products, computes the inverted shares of Equation 34.9, and contrasts a naive regression (which ignores the correlation between price and \(\xi_j\)) with a two-stage least-squares estimator that instruments price with a cost shifter.

set.seed(29)
J    <- 200; N <- 4e5               # products in one market; consumers sampled
x    <- rnorm(J)                    # observed product attribute
xi   <- rnorm(J)                    # unobserved quality -> source of endogeneity
cost <- runif(J, 0, 2)             # cost shifter -> instrument for price
beta_true <- 1.0; alpha_true <- 1.5

# Price rises in unobserved quality (endogeneity) and in the cost shifter
price <- 1.0 + 0.8 * xi + cost + rnorm(J, 0, 0.3)
delta <- x * beta_true - alpha_true * price + xi   # mean utility of products 1..J

# Logit shares with an outside good (utility 0); add sampling noise via multinomial
num    <- exp(delta)
s      <- num / (1 + sum(num)); s0 <- 1 / (1 + sum(num))
counts <- rmultinom(1, N, c(s0, s))[, 1]
share  <- counts[-1] / N; share0 <- counts[1] / N

y <- log(share) - log(share0)       # Berry inversion: y_j = delta_j

ols  <- coef(lm(y ~ x + price))                 # ignores xi: endogenous, biased
phat <- fitted(lm(price ~ x + cost))            # first stage: cost instruments price
iv   <- coef(lm(y ~ x + phat))                  # 2SLS price coefficient

cat("True price coef (-alpha):", -alpha_true, "\n")
#> True price coef (-alpha): -1.5
cat("Naive logit price coef:  ", round(ols["price"], 3), "\n")
#> Naive logit price coef:   -0.718
cat("IV logit price coef:     ", round(iv["phat"], 3), "\n")
#> IV logit price coef:      -1.433

The naive coefficient is badly attenuated toward zero—the unobserved quality \(\xi_j\) raises both utility and price, masking the true price sensitivity—while the instrumented estimate recovers \(-\alpha\). This is the lesson that recurs across every structural demand paper: the price coefficient is the parameter most contaminated by the unobserved quality term, and a valid instrument is the remedy.

34.5 Dynamics, Learning, and Forward-Looking Agents

Many marketing decisions are intertemporal—when to buy a durable, whether a salesperson exerts effort today for a bonus tomorrow, how a relationship evolves—and a static choice model cannot represent them. Dynamic structural models treat the agent as solving a sequential optimization, and they are the technically hardest but most rewarding members of the family.

The canonical object is a forward-looking agent who, in state \(s_t\), chooses action \(a_t\) to maximize the expected present value of a stream of payoffs, \[ V(s_t) = \max_{a_t}\; \Big\{ u(s_t, a_t; \boldsymbol{\theta}) + \delta\, \mathbb{E}\!\left[\, V(s_{t+1}) \mid s_t, a_t \,\right] \Big\}, \tag{34.10}\] the Bellman equation, where \(\delta\) is the discount factor, \(u(\cdot)\) the per-period payoff, and the expectation runs over the law of motion of the state. Estimation recovers the payoff primitives \(\boldsymbol{\theta}\) from observed state–action sequences, typically by nesting the solution of 1 inside a likelihood. The substantive range is wide. Allenby, Leone, and Jen (1999) model purchase timing in direct marketing as a dynamic decision, recovering when a household will next buy. Gowrisankaran and Rysman (2012) let consumer preferences evolve and apply the machinery to durable-goods markets, where today’s purchase forecloses tomorrow’s. Hitsch (2006) study optimal product launch and exit under demand uncertainty, treating the firm as a forward-looking decision maker learning about an uncertain market. Netzer, Lattin, and Srinivasan (2008) model the dynamics of customer–firm relationships as a hidden Markov process, in which a latent relationship state migrates over time and governs observable purchase behavior—a structural account of relationship “states” rather than a reduced-form churn score.

Forward-looking firms appear on the compensation side of the same coin. Misra and Nair (2011) estimate a structural model of sales-force incentives in which the salesperson chooses unobserved effort given the compensation plan, the firm designs the plan anticipating that response, and the recovered primitives (the cost of effort, the agent’s risk attitude) support counterfactual plans the firm never tried—work that Kim, Sudhir, and Uetake (2022) extend to a multitasking sales force allocating effort across acquisition and retention. On the demand side over the customer lifecycle, Gupta et al. (2006) synthesize structural and other models of customer lifetime value, and Kamakura et al. (2005) embed choice models in customer-relationship strategy. Figure 34.2 organizes the marketing applications cited in this chapter by the decision they model.

flowchart LR
    R[Structural marketing models] --> S[Static]
    R --> D[Dynamic / forward-looking]
    S --> S1[Demand & price elasticity<br/>montgomery1999estimating]
    S --> S2[Discrete choice<br/>dube2002structural · heiss2002structural]
    S --> S3[Competitive conduct<br/>kadiyali2001structural]
    D --> D1[Purchase timing & durables<br/>allenby1999dynamic · gowrisankaran2012dynamics]
    D --> D2[Customer relationships<br/>netzer2008hidden · gupta2006modeling]
    D --> D3[Salesforce incentives<br/>misra2011structural · kim2022structural]
    D --> D4[Product launch & exit<br/>hitsch2006empirical]

Figure 34.2: A taxonomy of structural marketing applications by the decision being modeled. Static discrete-choice and demand models sit on the left; dynamic, forward-looking models on the right. Each leaf names a representative study from this chapter.

The dynamic apparatus also extends to settings where behavior and content co-evolve. Goh, Heng, and Lin (2013) model the co-evolution of user behavior in social media, and Rutz, Trusov, and Bucklin (2011) use a structural model to disentangle the indirect effects of paid search advertising—how a search click today shifts later behavior—an effect invisible to a single-period attribution model. Price promotions, too, have dynamic consequences: Elberg et al. (2019) study how promotions move purchases across time rather than merely expanding the category, a stockpiling response that only a dynamic model represents correctly.

34.6 Identification: What Can and Cannot Be Recovered

A model is identified if distinct parameter values imply distinct distributions of the observable data; without identification, no estimator—however clever—can recover the truth, and a perfectly converged optimizer may report a number that the data do not pin down. Because structural models lean on assumptions for identification, naming the threats is as important as writing the likelihood.

The first and most pervasive threat is endogeneity, already met twice: price is set by agents who observe demand shocks the analyst does not, so the price coefficient is identified only through an exclusion restriction—a cost or competitor instrument that shifts the choice set without entering utility directly. When no valid instrument exists, the elasticity is not identified, full stop.

The second is functional-form dependence. In a static logit the substitution pattern is dictated by the IIA assumption rather than estimated, so a counterfactual that turns on cross-elasticities is identified by assumption, not by data; relaxing to nested or random-coefficient logit buys realism at the cost of additional parameters that themselves require variation to identify.

The third is the discount factor in dynamic models. The forward-looking payoff in 1 and the per-period payoff are notoriously hard to separate: a patient agent with low effort costs can mimic an impatient agent with high effort costs, so \(\delta\) is typically fixed rather than estimated, with the counterfactual’s credibility contingent on that choice.

The fourth is the equilibrium and conduct assumption: inferring competitive conduct from price–quantity comovement (Kadiyali, Sudhir, and Rao 2001) identifies conduct only if the maintained equilibrium concept is correct, and a misspecified conduct parameter contaminates the recovered costs.

The pattern across all four is the same and is worth internalizing as the chapter’s governing principle: structural identification trades data variation for assumptions, and every counterfactual inherits the assumptions that identified the parameters it uses. The honest structural paper, accordingly, reports which results are robust to weakening which assumption—and the practitioner reading one should ask, of every headline number, what assumption is this resting on?

34.7 Getting Started

For readers building toward this literature, the graduate econometrics texts of Greene (2003) and Cameron and Trivedi (2005) supply the estimation foundations; Hensher, Rose, and Greene (2005) is the standard reference for the discrete-choice models that anchor most marketing applications; Diamantopoulos, Fritz, and Hildebrandt (2013) surveys quantitative modeling in marketing more broadly; and the Handbook of Econometrics policy-evaluation chapters (Heckman and Vytlacil 2007a, 2007b; Abbring and Heckman 2007) connect structural estimation to the identification of treatment effects. A productive path is to reproduce a linear demand-and-supply system (Section 34.2), then a logit with endogenous price (Section 34.4), before attempting a dynamic model—each step adds one layer of structure, and the endogeneity intuition learned in the first carries unchanged into the last.

34.8 Key Takeaways

• A model is structural when its parameters are economic primitives—tastes, costs, information, conduct—and are therefore policy invariant; the payoff is counterfactual simulation of policies never observed (Equation 34.1).
• Structural modeling and causal inference are complements: causal estimates discipline structural models, and structural reasoning locates the endogeneity a causal design must address.
• Endogeneity of price is the central econometric problem, visible already in linear supply and demand (Equation 34.3) and recurring inside discrete-choice demand; it is resolved only by a credible exclusion restriction.
• MLE (full likelihood, efficient if correct) and GMM (moment conditions, robust) are the two workhorse estimators; the choice is about how much of the data-generating process one is willing to specify (Table 34.1).
• Dynamic models recover forward-looking primitives via the Bellman equation
  1. but face hard identification of the discount factor.
• Every counterfactual inherits the assumptions that identified its parameters; the credible structural paper reports which conclusions survive weakening which assumption (Section 34.6).

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