guide-inequalities

Compute Test Statistic and Critical Value

Compute Test Statistic and Critical Value

g_restriction(
  theta,
  w_data,
  a_matrix,
  j0_vector,
  v_bar,
  alpha,
  grid0 = "all",
  iv_matrix = NULL,
  test0 = "CCK",
  cvalue = "SN",
  account_uncertainty = FALSE,
  bootstrap_replications = NULL,
  rng_seed = NULL,
  bootstrap_indices = NULL,
  an_vec = NULL,
  hat_r_inf = NULL,
  dist_data = NULL
)

Arguments

theta

a vector containing the parameters of interest.

w_data

an n x k matrix of product portfolio data.

a_matrix

an n x (J0 + 1) matrix of estimated revenue differentials.

j0_vector

a J0 x 2 matrix of ownership by the two firms.

v_bar

a tuning parameter as in Assumption 4.2.

alpha

the significance level.

grid0

optional vector of length J0 containing the indices of the products in the market.

iv_matrix

optional n x d_iv matrix of instruments.

test0

optional test statistic to use. Either “CCK” or “RC-CCK”.

cvalue

optional critical value to use. Either “SPUR1”, “SN”, “SN2S”, or “EB2S”.

account_uncertainty

Whether to account for additional uncertainty (as in Equations 49 and 50). If TRUE, the last two elements of theta are assumed to be mu.

bootstrap_replications

the number of bootstrap replications. Required if bootstrap_indices is not specified.

rng_seed

the seed for replication purposes. If not specified, the seed is not set.

bootstrap_indices

an integer vector of indices to use for the bootstrap. If this is specified, bootstrap_replications and rng_seed will be ignored. If this is not specified, bootstrap_replications is required.

an_vec

if using SPUR1, an n-dimensional vector of An values.

hat_r_inf

if using RC-CCK, the lower value of the test statistic.

dist_data

an n x (J + 1) matrix of distances from the product factories to the cities.

Value

a vector containing the test statistic and critical value.