# pyblp.DemographicExpectationMoment¶

class pyblp.DemographicExpectationMoment(product_ids, demographics_index, value, observations, market_ids=None, market_weights=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 $$\mathscr{V}_m$$ of a demographic such as income, $$y_{it}$$, for agents who choose products in some set $$J$$. Its simulated analogue $$v_{mt}$$ can be defined by

(1)$v_{mt} = \sum_{i \in I_t} w_{it} \frac{\sum_{j \in J} s_{ijt}}{\sum_{j \in J} s_{jt}} y_{it}.$

These are averaged across a set of markets $$T_m$$ and compared with $$\mathscr{V}_m$$, which gives $$\bar{g}_{M,m}$$ in (34).

Parameters
• product_ids (sequence of object) – IDs of the products $$j \in J$$, which may include None to denote the outside option $$j = 0$$. If there is no None, at least one of these IDs should show up 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.

• value (float) – Value $$\mathscr{V}_m$$ of the statistic estimated from micro data.

• observations (int) – Number of micro data observations $$N_m$$ used to estimate $$\mathscr{V}_m$$, which is used to properly scale micro moment covariances in (35).

• 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.

• market_weights (array-like, optional) – Weights for averaging micro moments over specified market_ids. By default, these are $$1 / T_m$$.

Examples

Methods