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About this document

This document was created using Weave.jl. The code is available in on github. The same document generates both static webpages and a jupyter notebook.

Introduction

This assigment will attempt to replicate the results of [@berry1995].

Getting started

Load the package for this assignment from github.

using Pkg
#Pkg.activate(".") # If running on  vse.syzygy.ca, you might need to uncomment this command
try
  using BLPDemand
catch
  Pkg.develop(PackageSpec(url="https://github.com/UBCECON567/BLPDemand.jl"))
  using BLPDemand
end

Problem 1: load and explore the data

The data from [@berry1995] is included in the BLPDemand.jl package.

df = data_blp1999()

# Optionally, if you like being able to view all your data
if (false)
  using TableView
  if (notusingjupyterorjuno) # this will throw an error. Delete it  or the else branch 
    using Blink
    w = Blink.window()
    body!(w, TableView.showtable(df));
  else  # this may work on a local installation of jupyter, but it doesn't on vse.syzygy.ca ...
    TableView.showtable(df);
  end
end

Error: ArgumentError: provide a valid sink argument, like `using DataFrames
; CSV.read(source, DataFrame)`

Create some tables and figures to explore the data. You may want to reproduce table I and/or II from [@berry1995].

# using Plots, DataFramesMeta, StatsPlots # (or whatever)

Problem 2: Logit Demand

Part I

Reproduce table III of [@berry1995]. First you’ll need to create instruments as in section 5.1 of the paper. The following code should do it.

using DataFrames
# Create instruments (see section 5.1)
exog = [:const, :hpwt, :air, :mpd, :space, :mpg, :trend] # not sure that this is correct set of variables
function makeinstruments(df, exog)
  for z ∈ exog
    zown = String(z).*"_own"
    zother = String(z).*"_other"
    own=by(df, [:year, :firm_id], z=>sum)
    rename!(own, Symbol(z, "_sum") => Symbol(z, "_own"))
    all=by(df, [:year], z=>sum)
    rename!(all, Symbol(z, "_sum") => Symbol(z, "_other"))
    df=join(df, own, on = [:year, :firm_id])
    df=join(df,all, on = [:year])
    df[!,Symbol(z,"_other")] .-= df[!,Symbol(z,"_own")]
    df[!,Symbol(z,"_own")] .-= df[!,z]
  end
  return(df)
end
df=makeinstruments(df, exog);
nothing

Error: UndefVarError: df not defined

For the regressions, you should modify the following.

using FixedEffectModels, RegressionTables
col2 = reg(df, @formula(logit_depvar ~ hpwt + (price ~ const_own + const_other + hpwt_own + hpwt_other)))
regtable(col2)

Error: UndefVarError: df not defined

Part II

Calculate the elasticities of demand implied by the logit model. Report how many own price elasticities have absolute value less than one (inelastic). Why are inelastic demand estimates undesirable?

For computing the elastiticities, you could adapt the code from the BLPDemand.jl docs

Problem 3: Demand Side Estimation

Estimate a random coefficients demand model. Report the parameter estimates and standard errors. Use the functions estimateRCIVlogit and varianceRCIVlogit from BLPDemand.jl. Note that the paper has price enter the model as $\log(y-p)$, but we lack data on $y$, so just have price enter linearly or log-linearly with a random coefficient.

# some more data prep. You might want to change
df[!,:loghpwt] = log.(df[!,:hpwt])
df[!,:logmpg] = log.(df[!,:mpg])
df[!,:logspace] = log.(df[!,:space])
S = 20
xvars = [:price, :const, :hpwt, :air, :mpd, :space]
costvars = [:const, :loghpwt, :air, :logmpg, :logspace]
dat = BLPData(df, :year, :firm_id, :share, xvars, costvars,
              [:const], [:const], # we'll recreate instruments anyway
              randn(length(xvars),S ,length(unique(df[!,:year]))) )
dat = makeivblp(dat, includeexp=false)

using LinearAlgebra: diag, I
# now the estimation, you might want to try different options

#out=estimateRCIVlogit(dat, method=:NFXP, verbose=true, W=I)
#v = varianceRCIVlogit(out.β, out.σ, dat, W=I)
#@show [out.β  out.σ]
#@show sqrt.(diag(v.Σ))

# or make a nicer table as in https://ubcecon567.github.io/BLPDemand.jl/dev/simulation/#Estimation-1

Error: UndefVarError: df not defined

Problem 4: Demand and Supply

Estimate the full BLP model. Use the estimateBLP and varianceBLP functions. See the docs for example usage. Note that the paper has price enter the model as $\log(y-p)$, but we lack data on $y$, so just have price enter linearly or log-linearly with a random coefficient.

Problem 5: Elasticities

Compute price elasticities (with standard errors) based on your estimates. You can adapt the code in the docs.

Problem 6: Merger Simulation

This is a more challenging problem with less guidance. Consider it optional.

Use your estimates to simulate a merger between firm 11 (Saab, I think) and firm 19 (GM, I think). You can do this by modifying the simulateBLP function. Report the effect of the merger on prices. Be sure to include standard errors.