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Empirical Industrial Organization — EFIMM0097

创建日期：2024-05-05 17:22:16

所属分类：数学mathematics

标签： EFIMM0097

Empirical Industrial Organization

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HOME ASSIGNMENT

Empirical Industrial Organization — EFIMM0097
This home assignment is made of several questions, which must all be answered (no optional
questions). The points associated to each question are reported below in square brackets. The
first part of the assignment is a continuation of problem sets 7 and 8 and relates to the methods
discussed in topic 5: the estimation of entry games. Perform all the statistical analyses in this first
part of the assignment using MATLAB. The second part of the assignment asks you to discuss an
article not covered in class but included in the reading list.
In addition to writing your answers to all questions, you must provide a copy of the MATLAB codes
used to produce the results in the same document (only submit one computer-typed document
including both answers and codes). Each step of your MATLAB procedure should be well explained
and your answers should rely on the use of mathematical symbols and derivations (as we have been
doing in the course): whenever it is unclear where your results or conclusions come from, no points
will be assigned. The document with your answers and codes should be typed with the computer
(with Microsoft Word or any TeX editor), including mathematical formulae and tables (no hand
writing or drawing).
You must work entirely on your own. The deadline to return the document with your
answers and the MATLAB codes is Monday 9th of May at 11:00am (Bristol time).
1
1 Estimation and Simulation of Entry Games [80 Points]
In this part, you will first estimate a simplified version of the model by Bresnahan & Reiss (1991b)
[i.e., BR] using MATLAB and, second, simulate a simplified version of the entry model by Berry
(1992) again using MATLAB. The estimation of BR using MATLAB requires you to combine
problem set 7 (estimation of probit model using MATLAB) and problem set 8 (estimation of BR
using Stata). The simulation of the entry model by Berry (1992) using MATLAB instead requires
you to perform novel tasks we only discussed in theory, but still building on the same two problem
sets: the simulation of normally distributed random variables with MATLAB (problem set 7)
starting from the Stata estimates of the full model by BR (problem set 8).
We start with the estimation of a binary version of the entry model by BR (1991b) with MATLAB
using the original data on tire dealers. Load the data “BRdata.csv” (these are the data used in
problem set 8), where all the variables have their original names (check out the details in BR,
1991b). The full data include markets with 0, 1, 2, 3, 4, 5, and more than 5 entrants. Focus on
potentially monopolistic markets with no or one tire dealer, drop those observations with “tire >
1”. Then, as in question A of problem set 8, consider the binary entry model:
Nm =

1 if Π1m = Π1m + εm > 0
0 otherwise
where Π1m is market m tire dealer’s profit, Π1m is market m tire dealer’s expected profit, and
εm ∼ N (0, 1). The specific form of Π1m is assumed to be:
Π1m = S (Y ,λ)V1 (Z, α1,β)− F1 (W,γ) .
S (Y ,λ) is a measure of market size, which is a function of local population demographics Y .
V1 (Z, α1,β) is a measure of per-capita demand, which depends on demand shifters Z. F1 (W,γ)
2
is a measure of fixed costs, which depends on cost shifter W . Assume that these functions depend
linearly on the regressors:
S (Y ,λ) = tpop+ λ1opop+ λ2ngrw+ λ3pgrw+ λ4octy.
V1 (Z, α1,β) = α1 + β1eld+ β2pinc+ β3lnhdd+ β4ffrac.
F1 (W,γ) = γ1 + γLlandv.
Note that these assumptions imply that Pr [Nm = 1|Y ,Z,W ] = Φ
(
Π1m
)
, where Φ (·) is the
standard normal CDF. In other words, the decision of entering in market m as a monopolist is
modeled as a binary probit.
[A, 15 Points] Write down the formulae (using matrix notation) of log-likelihood function,
gradient, and hessian of the above binary probit. Note that, given the above functional form
assumptions, Π1m is not linear in the structural parameters λ, α1, β, and γ. Differently, in
question A of problem set 7, we considered the simpler binary probit Pr [Nm = 1|Xm] = Φ (X ′mθ),
whereX ′mθ is linear in the parameters θ. Bear this in mind and adapt the formulae from question
A.2 of problem set 7 accordingly.
[B, 20 Points]. Adapting the codes from question A of problem set 7, estimate the 11 parameters
λ, α1, β, and γ by MLE. Remember to constrain the parameter λ0 in S (Y ,λ) = λ0tpop+λ1opop+
λ2ngrw + λ3pgrw + λ4octy to be equal to 1. To improve numerical precision and computational
speed, provide to MATLAB the analytical formulae of gradient and hessian as derived above (do
not use numerical approximations for gradient and hessian).
3
[C, 10 Points]. Compute the standard errors and p-values of the MLE and display your esti-
mation results in a table. Interpret your estimation results.
[D, 5 Points]. Compare your estimation results to those obtained from Stata in question A of
problem set 8. Discuss the differences, if any.
We now move on to simulating a simplified version of the entry model by Berry (1992), starting
from the Stata estimates of the full entry model by BR (1991b) from question B, problem set 8.
Re-load the full data “BRdata.csv” in MATLAB. Adapt the notation of the entry model used in
problem set 8 to have firm heterogeneity within each market m:
Πim (n) = Sm · Vm (n)− Fm (n) + εim,
where εim is an error term specific to firm i, and n is the number of firms in market m. Any firm
i is willing to enter if and only if Πim (n) ≥ 0 ⇐⇒ εim ≥ − (Sm · Vm (n)− Fm (n)).
Eliminate from the data all those markets with more than four firms and let N = 4 (i.e., the
number of potential entrants in each market). Assume that the εim’s are i.i.d. across firms and
markets, and that are distributed N (0, 1).
[E, 20 Points]. For each marketm, approximate by simulation the expected number of entrants:
Eεm
[
nm|Xm, θ̂
]
=
∫
· · ·
∫
n?m
(
ε1m, ε2m, ε3m, ε4m|Xm, θ̂
)
φ (ε1m, ε2m, ε3m, ε4m) dεm,
where Xm is the vector of observables for market m, θ̂ is the vector of estimated parameters from
question B of problem set 8 (i.e., the ordered probit estimates from Stata), and φ (·) is the product
of four independent and identical standard normal densities. To guarantee a unique equilibrium
4
in the identity of entrants, assume that in each market m firms make entry decisions sequentially.
In order to proceed with the approximation of Eεm
[
nm|Xm, θ̂
]
, for each market m = 1, . . . ,M :
1. Set the number of simulation draws to S = 1000.
2. For each draw s = 1, . . . , S, generate a vector of four independent standard normal random
variables: (εs1m, εs2m, εs3m, εs4m).
3. For each vector (εs1m, εs2m, εs3m, εs4m), compute the number of firms n?sm
(

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