### 1. Introduction

### 2. Data

### 2.1 Airline Industry

### 2.2 Common Ownership

*s*is the market share,

*γ*is the control weight, and

*β*is the total number of shares. The subscripts

*i, j*and

*k*index shareholder

*i*, firm

*j*, and firm

*k*, respectively. Azar et al. (2018a) use this measure and analyze the anticompetitive effect of common ownership by regressing airfare prices on it. O’Brien and Waehrer (2017) criticize that the MHHI delta and state that it can bias the coefficient on common ownership because of its dependency on market share and the regression model is not well motivated by theory. Specifically, unobserved price factors can affect both prices and market shares, which results in a change in MHHI delta and accordingly an endogeneity problem.

*j*with respect to firm

*k*as

### 3. Model

### 3.1 Demand

*κ*proportions of type

_{r}*r*consumers. For a product of firm

*j*in market

*t*, the utility of consumer

*h*of type

*r*is given by

*x*is a vector of observed product characteristics,

_{jt}*p*is the price, (

_{jt}*β*,

_{r}*α*) are the type

_{r}*r*consumer-specific taste parameters,

*ξ*are unobserved product characteristics,

_{jt}*v*is a nested logit random taste constant across inside goods,

_{ht}*λ*is the nested logit parameter, and

*ε*is an independently and identically distributed logit error. Two nests exist: one is for air-travel inside goods and the other is for the outside option of not buying any of the inside goods. The nested logit parameter,

_{hjt}*λ*∈[0, 1], governs substitution patterns between the two nests. The mean utility of the outside option is normalized to zero.

*r*consumers who choose to purchase a product from the air-travel nest is known to be

*r*consumers choosing product

*j*in market

*t*is

*j*in market

*t*is

### 3.2 Pricing and Marginal Cost

*N*firms owned by

*M*shareholders. Each firm chooses its price to maximize the portfolio profits of the shareholders weighted by their control power.9) If a voting share guarantees an equal amount of control power, the profit maximization problem of firm

*j*is

*p*is the product price of firm

_{j}*j*,

*γ*is the number of shares of firm

_{ij}*j*with voting power exercised by shareholder

*i*, and

*π*is the portfolio profit of shareholder

^{i}*i*. This can be rewritten as

*β*is the total number of shares of firm

_{ij}*j*accruing to shareholder

*i*, and

*S*and

_{j}(p)*mc*are the market share and marginal cost of firm

_{j}*j*, respectively. The subscript

*k*indexes firm

*k*. The common ownership incentive in (8),

*j*is connected to firm

*k*through common ownership of their voting shareholders, which reflects the intensity of the anti-competitive incentive due to this connection.

*j*in which the “coordination weight” that a firm places upon its competitor is a function of the common ownership incentive:

*c*denotes the common ownership incentive, which is equal to

_{jk}*f*(

*c*) is the coordination weight that firm

_{jk}*j*puts on firm

*k*. The coordination weight determines how much a firm internalizes its price effect on the competitor’s profit because of the overlapping shareholder and therefore captures the effect of the common ownership incentive on the price coordination.

*j*is not only determined by the own-price elasticity of demand but also by the degree of price coordination and the cross-price elasticity of demand. The last term of (11) is the additional markup attainable through coordination with other commonly owned firms. The size of additional markup gets bigger when firms care more about common ownership of voting shareholders in their pricing and the cross-price elasticity of demand with respect to the commonly owned firms is larger. If a firm sells a set of multiple products, the right-hand side of (11) includes another markup term achievable by the internalization of price effects on the other products within the same set.

*w*is a vector of observed cost shifters,

_{jt}*φ*is a vector of cost parameters, and

*ω*is an unobserved cost shock.

_{jt}*b*is the model-implied markup.

_{jt}### 3.3 Estimation

*ξ*using the contraction mapping algorithm introduced in Berry et al. (2006), which is a modified version of Berry et al. (1995). For each candidate of demand parameters

*θ*, we evaluate the following equation until

_{d}*ξ*converges to

^{T}*ξ*and therefore the modelimplied market shares

*S*(

*x, p, ξ*;

*θ*) are equal to the actual observed market shares

_{d}*s*. The iteration is expressed as

*T*denotes the

*T*th iteration. Then, the demand unobservable is a nonlinear function of the product characteristics, prices, observed market shares, and parameters:

*W*is a weighting matrix, and

*G*(

*θ*,

_{d}*θ*) is the stacked set of the sample analogs of the population moments, (

_{s}*g*,

_{d}*g*). The population moments are the orthogonality conditions between structural errors and instruments

_{s}*ϕ*equals to 0, we assume that the effect of common ownership on product market competition does not exist. Whereas, if

*ϕ*is set to 1, we assume that firms take into account the common ownership incentive fully in their price setting as implied in the model under the assumption that one vote has one unit of control power. In the main model specification, we allow

*ϕ*to be flexible between -1 and 1 to consider the intermediate case of no effect and additionally full effect. We also allow

*ϕ*to be negative to include the possibility that firms place a penalty on common ownership. A significantly positive coefficient on common ownership suggests a corporate decision is affected by common ownership of voting shareholders, which may result in price coordination among commonly owned firms and reduce the degree of product market competition.

### 4. Results

*ϕ*= 0, (2)

*ϕ*=1, (3) |

*ϕ*| ≤ 1.

*ϕ*is restricted to 0 and therefore firms are not influenced by common ownership of voting shares when they are choosing prices. The estimates are all in the expected signs and are largely consistent with previous studies of the airline industry (e.g., Berry et al., 2006; Berry and Jia, 2010; Ciliberto and Williams, 2014). We find that the price coefficients are -0.949 for the first type and -0.067 for the second type. The fraction of the first type (κ) is 0.855. From this result, we can infer that the first type is the tourist type who is very sensitive to prices and takes a larger fraction of the total consumers. The second type is, then, the business-traveler type. The median own-price elasticities of demand11) are -5.136 for the tourist type and -0.362 for the business-traveler type, which makes -3.461 in total. As expected, consumers prefer direct flight services and airlines that serve diverse markets from originating airports. The concave relationship in distance flown shows consumers find air travel more attractive for trips with long distance but this effect diminishes gradually as the outside option of no air travel becomes more attractive. The nested logit parameter (

*λ*) is 0.646, thereby suggesting that substitution patterns occur within the air-travel nest. On the supply side, we find that the marginal cost is increasing in distance, and decreasing in the number of connections and availability of hub airports.

*ϕ*equals to 1 and the degree of price coordination is determined exactly by the common ownership incentives. As in Ciliberto and Williams (2014), we find that the demand estimates are similar whereas the supply estimates differ from that in Column 1 of <Table 4> in response to a change in the assumed behavioral model. The differences in the estimated coefficients and assumption on the effect of common ownership lead to slightly different estimates of marginal costs and elasticities.

*ϕ*to be flexible between -1 and 1 to enable firms to reflect common ownership incentives only partially or even negatively in their pricing behavior. We find that the coefficient on common ownership incentives is significantly positive. The result implies that airline companies are controlled by their voting shareholders and internalize their price effect on the profits of commonly owned companies. Therefore, common ownership in the financial market is likely to have facilitated price coordination and raised airfare prices in the U.S. airline industry in the first quarter of 2009. The magnitude of the estimate is 0.970, which suggests the weights that firms put on other firms in the profit maximization problem are almost equal to the size of common ownership incentives. In the presence of this nonzero coefficient on common ownership incentives, most demand and supply estimates except for the type 1 fraction are slightly lower than the ones in Columns 1 and 2 of <Table 4>. The price coefficients are -0.925 for the tourist type and -0.066 for the business-traveler type with the tourist-type ratio of 0.869, which leads to a median marginal cost of $211.7, the median own-price elasticity of -5.002 for the tourist type and -0.358 for the business-traveler type.