# pyblp.build_blp_instruments¶

pyblp.build_blp_instruments(formulation, product_data)

Construct “sums of characteristics” excluded BLP instruments.

Traditional “sums of characteristics” BLP instruments are

(1)$Z^\textit{BLP}(X) = [Z^\textit{BLP,Other}(X), Z^\textit{BLP,Rival}(X)],$

in which $$X$$ is a matrix of product characteristics, $$Z^\textit{BLP,Other}(X)$$ is a second matrix that consists of sums over characteristics of non-rival goods, and $$Z^\textit{BLP,Rival}(X)$$ is a third matrix that consists of sums over rival goods. All three matrices have the same dimensions.

Note

To construct simpler, firm-agnostic instruments that are sums over characteristics of other goods, specify a constant column of firm IDs and keep only the first half of the instrument columns.

Let $$x_{jt}$$ be the vector of characteristics in $$X$$ for product $$j$$ in market $$t$$, which is produced by firm $$f$$. That is, $$j \in \mathscr{J}_{ft}$$. Then,

(2)$\begin{split}Z_{jt}^\textit{BLP,Other}(X) = \sum_{k \in \mathscr{J}_{ft} \setminus \{j\}} x_{kt}, \\ Z_{jt}^\textit{BLP,Rival}(X) = \sum_{k \notin \mathscr{J}_{ft}} x_{kt}.\end{split}$

Note

Usually, any supply or demand shifters are added to these excluded instruments, depending on whether they are meant to be used for demand- or supply-side estimation.

Parameters
• formulation (Formulation) – Formulation configuration for $$X$$, the matrix of product characteristics used to build excluded instruments. Variable names should correspond to fields in product_data.

• product_data (structured array-like) –

Each row corresponds to a product. Markets can have differing numbers of products. The following fields are required:

• market_ids : (object) - IDs that associate products with markets.

• firm_ids : (object) - IDs that associate products with firms.

Along with market_ids and firm_ids, the names of any additional fields can be used as variables in formulation.

Returns

Traditional “sums of characteristics” BLP instruments, $$Z^\textit{BLP}(X)$$.

Return type

ndarray

Examples