Structural Econometric Modeling in Industrial Organization … · 2011-05-16 · Structural Econometric Modeling in Industrial Organization Handout 1 Professor Matthijs Wildenbeest

Structural Econometric Modeling inIndustrial Organization

Handout 1

Professor Matthijs Wildenbeest

16 May 2011

1

Reading

Peter C. Reiss and Frank A. Wolak A.Structural Econometric Modeling: Rationales and Examplesfrom Industrial Organization.Handbook of Econometrics 6A, Chapter 64, Sections 1-4,2007.

2

Background on Empirical IO

• Structural versus nonstructural econometrics

• Constructing structural models

• Framework for structural econometrics models in IO

3

Structural versus Nonstructural Econometrics

Example: auctions

Suppose we observe winning bids, y = {y1, . . . , yT}, in a largenumber of T similar auctions, as well as the number of bidders ineach market, x = {x1, . . . , xT}.

Goal exercise: understand equilibrium relationship between winningbids and the number of firms.

Nonstructural approach:

• regress winning bids on the number of bidders.

• use nonparametric smoothing techniques to estimate theconditional density of winning bids given the observed numberof bidders, i.e., f (y |x).

Does the regression coefficient tell us what happens when we addanother bidder?

Not without further knowledge about the auction under study. Forinstance, information paradigm matters.

4


5


6


Structural approach:

• Use the structure of an auction model to say something aboutwinning bids and the number of firms.

For example, Paarsch (1992, j econometrics) shows that forfirst-price sealed-bid auctions with Pareto-distributed private valuebidders, the conditional density of winning bids given the numberof firms f (y |x) is

f (y |x , θ) =θ2x

yθ2x+1

[θ1θ2(x − 1)

θ2(x − 1)− 1

]θ2x

,

so that the expected value of the winning bid given the number ofbidder is

E (y |x , θ) =

[θ1θ2(x − 1)

θ2(x − 1)− 1

]θ2x

θ2x − 1.

7


Why use economic theory in this example?

Helps us to clarify how institutional and economic conditions affectthe relationship between x and y . Think of type of auction(sealed-bid versus open-outcry or first-price versus second-price),bidder behavior (risk neutral versus risk averse), and informationparadigm (common versus private values).

Three general reasons for specifying and estimating a structuraleconometric model:

1 Estimate unobserved parameters that could not otherwise beinferred from the data (costs, elasticities, valuations).

2 Perform counterfactuals or policy experiments.

3 Compare the predictive performance of two competingtheories.

8


Although using structural econometrics has many advantages, thisdoes not always mean structural models should be favored overnonstructural models. Think of a situation where there little or nouseful economic theory to guide the empirical work.

Levitt (1997, am econ rev): using electoral cycles in police hiringto estimate the effect of police on crime.

Studies the effect of police on reducing crime. Previous studiesfound little evidence, likely due to simultaneity problems.

Levitt proposes a new instrument: timing of elections. Effects thesize of the police force, but does not belong directly to the crime“production function.”

9

Constructing Structural Models

Sources of structure

1 economics

2 statistics

Since economic models are often deterministic we have to addstatistical structure to rationalize why economic theory does notperfectly explain the data.

10


Example

Cross-section data on output, Qi , labor inputs, Li , and capitalinputs Ki . Estimate the regression

ln Qi = θ0 + θ1 ln Li + θ2 ln Ki + εi ,

by ordinary least squares (OLS). Error term εi necessary becauseright hand side variables do not perfectly explain log output.

Interpretation?

• Best Linear Predictor (BLP) of ln Qi given a constant, ln Li

and ln Ki : only statistical structure needed (sample secondmoments converge to their population counterparts).

• Estimation of Cobb-Douglas production function: structureneeded from both economics and statistics.

11


Only structure from economics not enough to estimate(logarithmic transformation) of Cobb-Douglas production function

Qi = ALαi Kβ

i : we have to add an error term as well:

Qi = ALαi Kβ

i exp εi .

Where does the error term come from?

If εi is measurement error distributed independently of the righthand side variables the estimated OLS parameters can beinterpreted as the coefficient of the Cobb-Douglas productionfunction.

Moreover, firms should produce on their production function.

Note that if the error includes unobserved differences inproductivity, OLS fails to deliver consistentestimates of the production function parameters.

12


Linear regression model y = α + xβ + ε. From a statisticalperspective we can always regress y on x (or the other wayaround): the coefficients have statistical interpretations (BestLinear Predictor).

However, we need economic arguments to make a case aboutcausation.

Moreover, without an economic model the OLS regression onlygives (under certain conditions) consistent estimates of a bestlinear predictor function.

13


Usually not possible to “test” a deterministic economic model byrunning a regression.

Many descriptive studies treat the linear regression coefficientestimates as as if they were estimates of the derivative of E (y |x)with respect to x , although β = ∂BLP(y |x)/∂x is usually notequal to ∂E (y |x)/∂x .

14


Nonexperimental data raises significant modeling issues.

Estimating the demand curve

qdt = γ0 + γ1pt + γ2x1t + ε1t

by OLS only gives consistent estimates of the demand curveparameters if price pt and a demand shifter like income x1t areuncorrelated with the error ε1t . If we perform experiments wherewe randomly select prices and observe the quantity demanded thiswill work.

Same for the supply curve

qst = β0 + β1pt + β2x2t + ε2t ,

where x2t is now a supply shifter like input prices.

15


In the experiments the quantity supplied will in general not beequal to the quantity demanded. However, no problem since weobserve the quantity demand and supplied directly for eachrandomly generated price.

Prices around us are nonexperimental. OLS no longer possiblebecause of correlations between explanatory variables and errorterm. But if we use economics and impose the market-clearingequation

qst = qd

t ,

we could apply instrumental variable techniques to get consistentestimates of the simultaneous equation model.

16

Constructing Structural ModelsSimultaneous equations models

When dealing with endogeneity it is important to think about a“complete” simultaneous equations model.

Example

Researcher estimates:

pi = POPiθ1 + COMPiθ2 + εi ,

where pi is the price in market i , POPi is population size, andCOMPi is a dummy for whether the firm faces competition.

Has this equation a structural meaning? Could be: θ2 measureseffect of competition on prices.

17


Problem: COMPi is likely to depend on pi :

COMPi = POPiγ1 + piγ2 + ηi .

Therefore COMPi will be correlated with εi , so OLS will giveinconsistent estimates of θ2.

Possible solution: use average income Yi as instrument forCOMPi , since one can argue Yi is correlated with COMPi but notwith εi . Statistical rationale.

18


To be completely convincing two things need to be done:

1 explain why Yi is not part of pi .

2 make the case that Yi is part of COMPi .

Therefore, specify the complete system:

pi = POPiθ1 + COMPiθ2 + εi ;

COMPi = POPiγ1 + piγ2 + Yiγ3 + ηi .

This requires the researcher to think carefully about the economicmodel underlying the simultaneous system of equations.

19

Framework for Structural Econometrics Models in IO

A structural model has two main components:

1 economic model;

2 stochastic model.

The economic model should have the following components:

• description of economic environment (market, actors,information available);

• list of primitives (technologies, preferences, endowments);

• exogenous variables (variables outside the model);

• decision variables and objective functions (utility/profitmaximization);

• equilibrium concept (nash equilibrium)

20


The stochastic model transforms the (usually) deterministiceconomic model into an econometric model. Main differencebetween the two is inclusion of unobservables.

Major stochastic specifications:

• unobserved heterogeneity

• agent uncertainty

• optimization errors

• measurement error

Different forms can have dramatically different implications foridentification and estimation!

21


Unobserved heterogeneity

Situation where agents’ decisions depend on something theeconomist does not observe.

Agent uncertainty

Situation where agents’ decisions depend on something the agentdoes not (fully) observe.

Note that in both cases the econometrician is ignorant. Still, theycan have different implications.

22


Example

Cross-section data on firms consisting of output Q, total costs TC ,and input prices pK and pL. Goal is to estimate α and β inQi = AiL

αi Kβ

i .

Suppose a regulator chooses a price pri and that firms have

different Ai , the latter being observed by the firm and regulatorbut not by the econometrician. Assume inelastic demand.

Firm chooses inputs to maximize

π(Ki , Li ) = pri AiL

αi Kβ

i − pKiKi − pLiLi .

23

Framework for Structural Econometrics Models in IOFirms produce in a cost minimizing way, so

MPL

MPK=

AiαLα−1i Kβ

i

AiβLαi Kβ−1

i

=α

β

Ki

Li=

pLi

pKi.

This means

Ki =pLi

pKi

β

αLi .

Substituting this into the production function gives

Qi = Ai

[pLi

pKi

β

αLi

]β

Lαi = Ai

[pLi

pKi

β

α

]β

Lα+βi ,

and solving for Li gives

Li = Q1

α+β

i A−1

α+β

i

(pLi

pKi

) −βα+β

(β

α

) −βα+β

24


The total labor cost pLiLi is then given by

pLiLi = CLpγKip

1−γLi Qδ

i A−δi ,

where δ = 1/(α + β), γ = β/(α + β), and CL = (α/β)γ .

Similarly, the total capital cost pKiKi is given by

pKiKi = CKpγKip

1−γLi Qδ

i A−δi ,

where CK = (α/β)γ−1.

The total cost function is therefore

TCi = C0pγKip

1−γLi Qδ

i A−δi ,

where C0 = CL + CK .

25


Transforming this equation using natural logarithms gives

ln TCi = ln C0 + γ ln pKi + (1− γ) ln pLi + δ ln Qi − δ ln Ai ,

which holds exactly. The efficiency differences are assumed to bei.i.d. positive random variables, so subtracting E [ln Ai ] from theerror term and adding it to the constant gives

ln TCi = ln C1 + γ ln pKi + (1− γ) ln pLi + δ ln Qi − δ ln ui ,

where ln C1 = ln C0 + E [ln Ai ] and ln ui = ln Ai − E [ln Ai ].

This equation can finally be taken to the data using OLS.

26


Now suppose the firms (and the regulator) do not know theefficiency parameters Ai either. Firms now choose inputs tomaximize

E [π(Ki , Li )] = pri E [AiL

αi Kβ

i ]− pKiKi − pLiLi .

First-order condition for expected profit maximization imply

Li =

[α

β

pKi

pLi

]Ki .

Observed total costs are

TCi =α + β

βpKiKi =

α + β

αpLiLi ,

and do not depend on Ai .

27


This means Li = αβ+αTCi/pLi and Ki = β

β+αTCi/pKi , so

Qai = D0TCα+β

i p−βKi p−α

Li Ai .

Final output produced Qai does depend on Ai .Taking natural

logarithms gives

ln Qai = ln D0 + (α + β) ln TCi − β ln pKi − α ln pLi + ln Ai ,

which holds exactly. Researcher does not observe Ai , so treat asrandom and move unconditional expectation again to the constant:

ln Qai = D1 + (α + β) ln TCi − β ln pKi − α ln pLi + ηi ,

where ηi = ln Ai − E [ln Ai ] and D1 = ln D0 + E [ln Ai ].

28


Optimization errors

Failure of agents’ decisions to satisfy exactly first-order necessaryconditions for optimal decisions.

Measurement errorsOccurs when the variable the research observes are different fromthose the agents observe. Straightforward way of converting adeterministic model into a statistical model.

29


Steps left

1 selection of functional forms;

2 selection of distributional assumptions;

3 selection of an estimation technique; and

4 selection of specification test.

30

Documents

Structural Econometric Modeling in Industrial Organization … · 2011-05-16 · Structural Econometric Modeling in Industrial Organization Handout 1 Professor Matthijs Wildenbeest