pyblp.DemographicCovarianceMoment¶

class
pyblp.
DemographicCovarianceMoment
(X2_index, demographics_index, values, market_ids=None)¶ Configuration for micro moments that match covariances between product characteristics and demographics.
For example, micro data can sometimes be used to compute the sample covariance between a product characteristic \(x_{jt}\) of an agent’s choice \(j\), and a demographic such as income, \(y_{it}\), amongst those agents who purchase an inside good. With the value \(\mathscr{V}_{mt}\) of this sample covariance, a micro moment \(m\) in market \(t\) can be defined by \(g_{M,mt} = \mathscr{V}_{mt}  v_{mt}\) where
(1)¶\[v_{mt} = \text{Cov}(y_{it}, z_{it})\]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.
Integrals of these micro moments are averaged across a set \(T_m\) of markets, which gives \(\bar{g}_{M,m}\) in (34).
 Parameters
X2_index (int) – Column index of \(x_{jt}\) in the matrix of demandside 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.
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 ifmarket_ids
isNone
.market_ids (arraylike, 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.
Examples
Methods