pyblp.ProblemResults.compute_diversion_ratios

ProblemResults.compute_diversion_ratios(name='prices')

Estimate matrices of diversion ratios, \(\mathscr{D}\), with respect to a variable, \(x\).

Diversion ratios to the outside good are reported on diagonals. For each market, the value in row \(j\) and column \(k\) is

(1)\[\mathscr{D}_{jk} = -\frac{\partial s_{k(j)}}{\partial x_j} \Big/ \frac{\partial s_j}{\partial x_j},\]

in which \(s_{k(j)}\) is \(s_0 = 1 - \sum_j s_j\) if \(j = k\), and is \(s_k\) otherwise.

Parameters

name (str, optional) – Name of the variable, \(x\). By default, \(x = p\), prices.

Returns

Stacked \(J_t \times J_t\) estimated matrices of diversion ratios, \(\mathscr{D}\), for all markets. Columns for a market are in the same order as products for the market. If a market has fewer products than others, extra columns will contain numpy.nan.

Return type

ndarray

Examples