pyblp.build_ownership¶

pyblp.
build_ownership
(product_data, kappa_specification=None)¶ Build ownership matrices, \(O\).
Ownership or product holding matrices are defined by their cooperation matrix counterparts, \(\kappa\). For each market \(t\), \(\mathscr{H}_{jk} = \kappa_{fg}\) where \(j \in J_{ft}\), the set of products produced by firm \(f\) in the market, and similarly, \(g \in J_{gt}\).
 Parameters
product_data (structured arraylike) –
Each row corresponds to a product. Markets can have differing numbers of products. The following fields are required (except for
firm_ids
whenkappa_specification
is one of the special cases):market_ids : (object)  IDs that associate products with markets.
firm_ids : (object)  IDs that associate products with firms. This field is ignored if
kappa_specification
is one of the special cases and not a function.
kappa_specification (str or callable, optional) –
Specification for each market’s cooperation matrix, \(\kappa\), which can either be a general function or a string that implements a special case. The general function is is of the following form:
kappa(f, g) > value
where
value
is \(\mathscr{H}_{jk}\) and bothf
andg
are firm IDs from thefirm_ids
field ofproduct_data
.The default specification,
lambda: f, g: int(f == g)
, constructs traditional ownership matrices. That is, \(\kappa = I\), the identify matrix, implies that \(\mathscr{H}_{jk}\) is \(1\) if the same firm produces products \(j\) and \(k\), and is \(0\) otherwise.If
firm_ids
happen to be indices for an actual \(\kappa\) matrix,lambda f, g: kappa[f, g]
will build ownership matrices according to the matrixkappa
.When one of the special cases is specified,
firm_ids
inproduct_data
are not required and if specified will be ignored:'monopoly'
 Monopoly ownership matrices are all ones: \(\mathscr{H}_{jk} = 1\) for all \(j\) and \(k\).'single'
 Single product firm ownership matrices are identity matrices: \(\mathscr{H}_{jk} = 1\) if \(j = k\) and \(0\) otherwise.
 Returns
Stacked \(J_t \times J_t\) ownership matrices, \(\mathscr{H}\), for each market \(t\). If a market has fewer products than others, extra columns will contain
numpy.nan
. Return type
ndarray
Examples