pyblp.ProblemResults.compute_diversion_ratios

ProblemResults.compute_diversion_ratios(name='prices', market_id=None)

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

In market \(t\), the value in row \(j\) and column \(k \neq j\) is

(1)\[\mathscr{D}_{jk} = -\frac{\partial s_{kt}}{\partial x_{jt}} \Big/ \frac{\partial s_{jt}}{\partial x_{jt}}.\]

Diversion ratios for the outside good are reported on diagonals:

(2)\[\mathscr{D}_{jj} = -\frac{\partial s_{0t}}{\partial x_{jt}} \Big/ \frac{\partial s_{jt}}{\partial x_{jt}}.\]

Unlike ProblemResults.compute_long_run_diversion_ratios(), this gives the marginal treatment effect (MTE) version of the diversion ratio. For more information, see Conlon and Mortimer (2018).

Parameters

  • name (str, optional) – Name of the variable, \(x\). By default, \(x = p\), prices. If this is None, the variable will be \(x = \delta\), the mean utility.

  • market_id (object, optional) – ID of the market in which to compute diversion ratios. By default, diversion ratios are computed in all markets and stacked.

Returns

Estimated \(J_t \times J_t\) matrices of diversion ratios, \(\mathscr{D}\). If market_id was not specified, matrices are estimated in each market \(t\) and stacked. 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