Empirical Industrial Organization — EFIMM0097
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Empirical Industrial Organization — EFIMM0097
2021-2022
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).
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:
.(.) 1
Nm = .
.(.) 0
,
if Πim = Π im + εm > 0
otherwise
where Πim is market m tire dealer’s profit, Π im is market m tire dealer’s expected profit, and εm ~ X (0, 1). The specific form of Π im is assumed to be:
Π im = S (Y , A) Vi (Z, αi , β) | Fi (W, y) .
S (Y , A) is a measure of market size, which is a function of local population demographics Y . Vi (Z, αi , β) is a measure of per-capita demand, which depends on demand shifters Z . Fi (W, y)
is a measure of fixed costs, which depends on cost shifter W . Assume that these functions depend linearly on the regressors:
S (Y , A) = tpop + λiopop + λ玄ngrw + λ之pgrw + λ4octy. Vi (Z, αi , β) = αi + βield + β玄pinc + β之 lnhdd + β4 ffrac.
Fi (W, y) = γi + γL landv.
Note that these assumptions imply that Pr [Nm = 1| Y , Z, W] = Φ╱Π im、, 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, Π im is not linear in the structural parameters A, αi , β, and y. Differently, in question A of problem set 7, we considered the simpler binary probit Pr [Nm = 1| Xm] = Φ (Xm(/)9), where X m(/)9 is linear in the parameters 9. 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 A, αi , β, and y by MLE. Remember to constrain the parameter λá in S (Y , A) = λá tpop+λiopop+ λ玄ngrw + λ之pgrw + 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).
[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 X (0, 1).
[E, 20 Points]. For each market m, approximate by simulation the expected number of entrants:
E6m ← nm | Xm , … = | | | nm(大) ╱ εim, ε玄m, ε之m, ε4m| Xm , ← φ (εim, ε玄m, ε之m, ε4m) dem ,
where Xm is the vector of observables for market m, 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
in the identity of entrants, assume that in each market m firms make entry decisions sequentially. In order to proceed with the approximation of E6m ← nm | Xm , …, 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: (εi(s)m , ε玄(s)m , ε之(s)m , ε4(s)m ).
3. For each vector (εi(s)m , ε玄(s)m , ε之(s)m , ε4(s)m ), compute the number of firms nm(大s) ╱Xm , ← . As discussed in topic 5, nm(大s) ╱Xm , ← can be computed as:
max『0 冬 n 冬 4 │ii 1 入 εi(s)m ≥ | (Sm | Vm (n) | Fm (n))| Xm , ┌ ≥ n 、.
In computing this, assume an order of entry among the firms. Give a “number” to each firm and then let them make entry decisions sequentially: potential entrant 1 moves first, then given 1’s choice, potential entrant 2 moves; then given the choices by 1 and 2, potential
entrant 3 moves; and finally potential entrant 4 moves after having observed the choices of the other three firms.
4. Compute the average S nm(大s) ╱Xm , ←to approximate E6m ← nm | Xm , … in market m.
To summarize your simulation results, plot a figure comparing the observed number of entrants versus the simulated number of entrants across markets: observed number of entrants on the Y-
axis and simulated number of entrants on the X-axis, where each observation in the figure is a market m. Interpret the simulation results plotted in the figure.
[F, 10 Points]. BR (1991b) assumes symmetry of the potential entrants, with εim = εm for every i in market m, while Berry (1992) relaxes this assumption and allows each potential entrant i in market m to have an idiosyncratic εim εm . Discuss pros and cons of these assumptions.
2 Article Discussion [20 Points]
Discuss the article by Toivanen and Waterson (2005, The RAND Journal of Economics): “Market Structure and Entry: Where’s the Beef?” Your discussion should be at most 2 pages. In your assessment of the paper, try to be critical: what do you think about it? What are the authors actually trying to do? Did they succeed? What are the pros and cons of the article, in your
opinion? How does it relate to the existing literature? What do you think is the main contribution of the paper?
2022-04-27