Market Power in Homogeneous Goods Markets

Introduction

• Market power is a fundamental question in IO
• Market power is measured in markups
• The challenge is to recover firms’ marginal cost from data containing only prices and quantities
• Current strategies estimate first demand and then, in combination with an oligopoly model, back up marginal costs

Introduction

• Traditional strategies rely on instruments to deal with simultaneity in demand estimation
  • Error term violates independence assumption because prices and quantities are determined simultaneously
  • Non-trivial to find good instruments, Unfeasible to test independence assumption, Functional form restriction

Introduction

• Most recent studies focus on differentiated-products markets, yet homogeneous goods markets are far from irrelevant
  • No methodological improvements since the late 90s (Porter 1983; Genesove and Mullin 1998; Wolfram 1999)
  • Cartels and oligopolies are prevalent in international markets of commodities (Itami 2015), e.g., Crude oil, diamonds, rare earths

Contribution

The model

A set of firms compete in a Cournot game

Firm \(i\) produces \(q_{it}\) of a homogeneous good at time \(t\)

Demand

The aggregate demand \(Q_t\) is a function of the price \(P_t\), demand shifters \(X_t\), unobserved demand shifters \(\varepsilon_t\), and demand shifters \(\nu_t\) unobserved by the econometrician but observed by firms

\[ Q_t=F(P_t,X_t,\nu_t, \varepsilon_t) \qquad(1)\]

Demand

Let \(\varepsilon_{t}+\eta_{it}\) be the realization of the exogenous demand shock that corresponds to \(q_{it}\), such that \(E[\eta_{it}|t]=0\)

Assumptions

Not uncommon in the literature, identification using information sets, e.g., productivity, and control functions

Assumptions

Intuitively, firms observe \(X_t\) and \(\nu_t\) and adjust their output production accordingly. However, practitioners do not observe \(\nu\). \(\varepsilon\) is an unexpected demand shock

Inverse demand

The inverse demand of the good is then \(P_t = F^{-1}(X_t,Q_t,\nu_t,\varepsilon_t)\)

I assume the following semiparametric functional form for my estimation strategy

\[ P_t = P(X_t,Q_t,\nu_t)e^{\varepsilon_t} \qquad(2)\]

Supply

Firm \(i\) has a cost function \(C_{it}=C_i(W_t,q_{it})e^{\omega_{it}}\). \(W_t\) is an observed cost shifter. \(\omega_{it}\) is an unobserved cost shock that is not part of the information set of the firm

\[ E[\omega_{it}|\mathcal{I}_{it}]=E[\omega_{it}|q_{it},W_t]=0 \qquad(3)\]

Supply

For firm \(i\), total produced quantity \(Q_t\) at period \(t\) is a function of its production \(q_{it}\), and the production of the competitors \(q_{-it}\), \(Q_t=Q(q_{it},q_{-it})\)

Firm \(i\) maximizes its profits by choosing \(q_{it}\), given the inverse aggregate demand and its cost function

\[ \max_{q_{it}} \left\{ q_{it}E[P(X_t,Q(q_{it},q_{-it}),\nu_t )e^{\varepsilon_t+\eta_{it}}] - E[C_i(W_t,q_{it})e^{\omega_{it}}] \right\} \]

Identification

\[ \begin{aligned} \ln \left( \frac{P_t}{q_{it}} \right) = & \ln \left( \frac{\mathcal{W} C_{i,q_{it}}(W_t,q_{it})}{q_{it}}- \mathcal{E} P_Q(X_t,Q(q_{it},q_{-it}),F^{-1}(\cdot, Q_t))Q_{q_{it}} \right) \\ & - \ln\mathcal{E} + \varepsilon_t + \eta_{it} \\ = & \ln \left( D^{\mathcal{W}}(W_t,q_{it}) - B^{\mathcal{E}}(X_t,Q_t,q_{it},q_{-it}) \right) - \ln\mathcal{E} + \varepsilon_t + \eta_{it} \end{aligned} \qquad(4)\]

Identification

In addition, it should be the case that,

\[ E[P_t] = E\left[\int B^{\mathcal{E}}(X_t,Q_t,q_{it},q_{-it})\right] \qquad(5)\]

To estimate Equation 4, we can use a random time effects model with a flexible form for \(D^{\mathcal{W }}(\cdot)\) and \(B^{\mathcal{E}}(\cdot)\) and imposing Equation 5

Markup estimates

Then, markup estimates are just the difference between the price and the estimated \(D^{\mathcal{W}}(\cdot)\)

We can estimate the average markup \(m_{it}\) and the Lerner index \(L_{it}\),

\[ \begin{aligned} m_t&\equiv \frac{P_t}{q_{it}}-D^{\mathcal{W}}(W_t,q_{it})\\ L_{it}&\equiv \frac{P_t-D^{\mathcal{W}}(W_t,q_{it})q_{it}}{P_t} \end{aligned} \]

Latent cost function

Finally, the cost function can be recovered up to a constant,

\[ \begin{aligned} \mathcal{C}_{it}&\equiv\int q_{it} D^{\mathcal{W}}(W_t,q_{it}) \\ &=\mathcal{W} \int C_{i,q_{it}}(W_t,q_{it}) \\ &=\mathcal{W}C_i(W_t,q_{it}) + \mathcal{W}K(W_t) \end{aligned} \]

Discussion

Next steps

Summary

I take an alternative approach to traditional markup estimation, recognizing that what is needed is the derivative of the (inverse) demand function

I provide a novel identification strategy that does not depend on instruments

Moreover, the endogenous part of the error term can enter non-linearly into the (inverse) demand function provided it can be separated from the random part of the shock