Empirical Industrial Organization 1 - Advanced Topics in Finance
Graded Assignment
Download from the course website the file "Data.csv". There are 10 variables in the dataset in
the following order: market identifier, product identifier, product market share, product attributes
(3 variables), price, cost shifters (3 variables). Note that this is an unbalanced panel, so different
markets have different numbers of products, and that products have different characteristics in
different markets. Do the whole problem set in Matlab (or any similar programming language you
are familiar with).
1. Estimate a Random Coefficient Logit model based on the following utility function that indi-
vidual i derives from buying product j in market n:
where xjn are product characteristics, pjn is the price, jn are unobserved (to the econometri-
cian) product characteristics,"ijn are Type 1 Extreme Value shocks, and 0i; ki N(0;1) are
simulation draws1. Make sure that you generate the appropriate dependent variable for the
estimation, and that you include a constant term. Let the utility from choosing the outside
good be normalized to ui0n = "i0n. Allow for random coefficients on all variables except the
constant, and use as instruments product characteristics, cost shifters, plus the square of all
product characteristics and the square of all cost shifters. Report your results including esti-
mated coefficients and standard errors.2 The true parameters for the mean utility coefficients
are [3, 3, 0.5, 0.5, -2], whereas for the standard deviation coefficients are [0.8, 0.5, 0.5, 0.5].
2. Estimate the same model using also the supply side. Assume firms are single product firms
in each market, compete Bertrand-Nash on prices, and have the following profit function for
product j in market n:
jn = (pjn mcjn)sjn
wheresjn isthemarketshare,pjn istheprice,andmcjn isthemarginalcost. Calculatethefirst
oder condition with respect to prices and use it to construct the supply side moment, where
you estimate both the parameters of the marginal costs (use the cost shifters and a constant,
use marginal costs linearly, without log transformation) and the i in the markup term, using
prices and market shares from the data. You will need to construct a GMM objective function
withbothdemandandsupplymoments, withthepricecoefficient i enteringinbothmoments
1 200 simulations is enough.
2 You can find the formula for the standard error of a nonlinear instrumental variable GMM estimator in any
advanced econometrics textbook. For example, in the 5th edition of W. Greene’s “Econometric Analysis” it’s at the
end of section 18.3, page 547.
(cross-equation restriction). Report your results including estimated coefficients and standard
errors. The true parameters for the coefficients of the marginal costs are [5, 0.5, 0.5, 0.5], the
first being the constant term.
3. Simulate a merger between the two products with the highest market share in each market.
Based on your estimates of the demand and supply in the previous point, you will now need
to construct a profit function and maximize it with respect to prices in the new counterfactual
scenario. Allow merged firms to still charge separate prices, but also to internalize each others’
profits. Provide descriptive statistics (mean, median, standard deviation) of changes in prices,
market shares, and profits for both merged and un-merged products between the baseline and
counterfactual scenarios. Report also changes in consumers’ surplus and total welfare between
the baseline and counterfactual scenarios.
4. [Optional]: Simulate a dataset and the true parameters and use your estimation code to
recover them. As guidelines, follow these steps:
Set the true parameter values for demand and cost models. Make sure you set the cost
parameters such that costs are always positive.
Generate product characteristics (except prices) and cost shifters from a multivariate
normal distribution, allowing for some correlation between them (i.e. larger cars are
more costly to produce). Generate the structural error terms jn (for demand) and !jn
(for costs) from a standard normal.
Adopt the profit function maximization routine you wrote for the merger simulation to
calculate equilibrium prices, making sure to include the structural error terms in the
demand and cost equations.
Calculate market shares.
Estimate the model.