class pyblp.DemographicExpectationMoment(product_id, demographics_index, values, market_ids=None)

Configuration for micro moments that match expectations of demographics for agents who choose certain products.

For example, micro data can sometimes be used to compute the mean of a demographic such as income, \(y_{it}\), for agents who choose product \(j\). With the value \(\mathscr{V}_{mt}\) of this mean, a micro moment \(m\) in market \(t\) can be defined by \(g_{M,mt} = \mathscr{V}_{mt} - v_{mt}\) where

(1)\[v_{mt} = \frac{E[y_{it}s_{ijt}]}{s_{jt}}.\]

Integrals of these micro moments are averaged across a set \(T_m\) of markets, which gives \(\bar{g}_{M,m}\) in (34).

  • product_id (object) – ID of the product \(j\) or None to denote the outside option \(j = 0\). If not None, there must be exactly one of this ID in the product_ids field of product_data in Problem or Simulation for each market over which this micro moment will be averaged.

  • demographics_index (int) – Column index of the demographic \(y_{it}\) (which can be any demographic, not just income) in the matrix of agent demographics, \(d\). This should be between zero and \(D - 1\), inclusive.

  • values (float) – Values \(\mathscr{V}_{mt}\) of the statistic estimated from micro data. If a scalar is specified, then \(\mathscr{V}_{mt} = \mathscr{V}_m\) is assumed to be constant across all markets in which the moment is relevant. Otherwise, this should have as many elements as market_ids, or as the total number of markets if market_ids is None.

  • market_ids (array-like, optional) – Distinct market IDs over which the micro moments will be averaged to get \(\bar{g}_{M,m}\). These are also the only markets in which the moments will be computed. By default, the moments are computed for and averaged across all markets.