# pyblp.DemographicInteractionMoment¶

class pyblp.DemographicInteractionMoment(X2_index, demographics_index, value, observations, market_ids=None, market_weights=None)

Configuration for micro moments that match expectations of interactions between product characteristics and demographics.

For example, micro data can sometimes be used to compute the mean $$\mathscr{V}_m$$ of $$x_{jt} y_{it}$$ where $$x_{jt}$$ is a product characteristic of an agent’s choice $$j$$ and $$y_{it}$$ is a demographic of the agent such as income, amongst those agents who purchase an inside good. Its simulated analogue $$v_{mt}$$ can be defined by

(1)$v_{mt} = \sum_{i \in I_t} w_{it} \frac{1 - s_{i0t}}{1 - s_{0t}} z_{it} y_{it}$

where conditional on choosing an inside good, the expected value of $$x_{jt}$$ for agent $$i$$ is

(2)$z_{it} = \sum_{j \in J_t} x_{jt} s_{ij(-0)t}$

where $$s_{ij(-0)t} = s_{ijt} / (1 - s_{i0t})$$ is the probability of $$i$$ choosing $$j$$ when the outside option is removed from the choice set.

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
• X2_index (int) – Column index of $$x_{jt}$$ in the matrix of demand-side nonlinear product characteristics, $$X_2$$. This should be between zero and $$K_2 - 1$$, inclusive.

• 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