Market Conduct and Endogenous Lobbying: Evidence from the U.S. Mobile Telecommunications Industry

Abstract

This paper empirically explores the relationship between firms' market behavior and their lobbying activities in a regulated market. In particular, we investigate whether the amount of contributions offered by cellular service providers to fund the campaigns of political parties affected market conduct in the early US mobile telecommunications industry. We structurally estimate market interactions while taking the potential endogeneity of lobbying decisions into account. Our results show that competition was more intense in those states where campaign contributions by the cellular industry have been higher. Furthermore, we reject the hypothesis that lobbying activities can be regarded as exogenous in the study of market conduct.

Appendix A: The log-likelihood function of the endogenous lobbying model

The FIML estimation applied in this study matches the specific data structure: policy and lobbying decisions are made at the state level but each state contains an idiosyncratic number of markets, $M_{s}$.²⁷ Denote the vector of residuals for state $s$ with $\mathbf{\varepsilon }_{s}$, with $\dim (\mathbf{\varepsilon } _{s})=2M_{s}+1$. The residuals are a vector valued function ${\textrm{\bf{f}}}_{s}$ of all endogenous variables ${\textrm{\bf{y}}}_{s}=(P_{1s},\ldots P_{M_{s}s},Q_{1s},\ldots Q_{M_{s}s},L_{s})^{\prime }$ and all exogenous variables ${\textrm{\bf{x}}}_{s}$:

$$\mathbf{\varepsilon }_{s}={\textrm{\bf{f}}}_{s}({\textrm{\bf{y}}}_{s},{\textrm{\bf{x}}}_{s}).$$

The log-likelihood of estimating Eq. 9, $M_{s}$ inverse demand Eq. 4, and $M_{s}$ quantity setting Eq. 6 by nonlinear FIML is

$$l=\textit{const}+\sum\limits_{s}\ln |\det {\textrm{\bf{J}}}_{s}|+\frac{1}{2} \sum\limits_{s}\ln (\det \mathbf{\Sigma }_{s}^{-1})-\frac{1}{2} \sum\limits_{s}{\textrm{\bf{f}}}_{s}^{\,\prime }\mathbf{\Sigma }_{s}^{-1}{\textrm{\bf{f}}} _{s},$$

(14)

where $\mathbf{\Sigma }_{s}$ is the state specific covariance and ${\textrm{\bf{J}} }_{s}=\partial {\textrm{\bf{f}}}_{s}/\partial {\textrm{\bf{y}}}_{s}^{\prime }$. Rewriting $\mathbf{\Sigma }_{s}$ yields

$$\left( \begin{array}{lll} \mathbf{\Sigma }_{P} & \mathbf{\Sigma }_{PQ} & \mathbf{\Sigma }_{PL} \\ \mathbf{\Sigma }_{PQ} & \mathbf{\Sigma }_{Q} & \mathbf{\Sigma }_{QL} \\ \mathbf{\Sigma }_{PL}^{\prime } & \mathbf{\Sigma }_{QL}^{\prime } & \sigma _{L} \end{array} \right) ,$$

where $\mathbf{\Sigma }_{P}$ and $\ \mathbf{\Sigma }_{Q}$ are covariance matrices of the inverse demand and supply equations respectively, while $\sigma _{L}$ denotes the variance of the lobbying equation. The matrices $\mathbf{\Sigma }_{PL}$ and $\ \mathbf{\Sigma }_{QL}$ are the covariances between the market equations and the lobbying equation.

We assume that all markets and all states are independent and that all residuals of a specific type of equation are drawn from the same normal distribution with zero mean and variance $\sigma _{P}$, $\sigma _{Q}$, and $\sigma _{L}$. Thereby $\mathbf{\Sigma }_{P}=\mathbf{1}_{M_{s}}\cdot \sigma _{P}$, $\mathbf{\Sigma }_{Q}=\mathbf{1}_{M_{s}}\cdot \sigma _{Q}$, and $\mathbf{\Sigma }_{PQ}=\mathbf{1}_{M_{s}}\cdot \sigma _{PQ}$, where $\mathbf{1 }_{M_{s}}$ is a $M_{s}$-dimensional identity matrix and $\sigma _{PQ}$ denotes the covariance between the inverse demand equation and the supply equation in the same market. Furthermore, let the covariance between the market equations and the state equation be such that (a) the general “affinity” of the state equation to a specific type of market activity (i.e., demand or supply) within this state is independent of the number of these markets and (b) the covariances between the state equation and all market equations of the same type in this state are equal. Assumption (a) is reflected by $\textit{cov}(\varepsilon _{Ls},\varepsilon _{Ps1}+\cdots +\varepsilon _{PsM_{s}})=\sigma _{PL}$ and $\textit{cov}(\varepsilon _{Ls},\varepsilon _{Qs1}+\cdots +\varepsilon _{QsM_{s}})=\sigma _{QL}$ while assumption (b) leads to $\textit{cov}(\varepsilon _{Ls},\varepsilon _{Ps1})=\cdots =\textit{cov}(\varepsilon _{Ls},\varepsilon _{PsM_{s}})$ and $\textit{cov}(\varepsilon _{Ls},\varepsilon _{Qs1})=\cdots =\textit{cov}(\varepsilon _{Ls},\varepsilon _{QsM_{s}})$. This implies that $\textit{cov}(\varepsilon _{Ls},\varepsilon _{Psm})=1/M_{s}\sigma _{PL}$ and $\textit{cov}(\varepsilon _{Ls},\varepsilon _{Qsm})=1/M_{s}\sigma _{QL}$ for all markets $m=1,\ldots ,M_{s}$. Hence, $\mathbf{\Sigma }_{PL}=\textit{{u}}_{M_{s}}\cdot \sigma _{PL}/M_{s}$ and $\mathbf{\Sigma }_{QL}=\textit{{u}}_{M_{s}}\cdot \sigma _{QL}/M_{s}$, where $\textit{{u}}_{M_{s}}$ is a $M_{s}$-dimensional column vector of ones. With this structure, the correlation between the lobbying equation and the sum of the residuals of the market equations of either type decreases in $M_{s}$.²⁸