reg_ss.fit {ShiftShareSE}

Inference in a shift-share regression

Description

Basic computing engine to calculate confidence intervals and p-values in shift-share designs using different inference methods, as specified by method.

Usage

reg_ss.fit(
  y,
  X,
  W,
  Z,
  w = NULL,
  method = c("akm", "akm0"),
  beta0 = 0,
  alpha = 0.05,
  region_cvar = NULL,
  sector_cvar = NULL
)

Arguments

y

Outcome variable, vector of length N, with each row corresponding to a region.

X

Shift-share vector with length N of sectoral shocks, aggregated to regional level using the share matrix W. That is, each element of X corresponds to a region.

W

A matrix of sector shares, so that W[i, s] corresponds to share of sector s in region i. The ordering of the regions must coincide with that in the other inputs, such as X. The ordering of the sectors in the columns of W is irrelevant but the identity of the sectors in must coincide with those used to construct X.

Z

Matrix of regional controls, matrix with N rows corresponding to regions.

w

vector of weights (length N) to be used in the fitting process. If not NULL, weighted least squares is used with weights w, i.e., sum(w * residuals^2) is minimized.

method

Vector specifying which inference methods to use. The vector elements have to be one or more of the following strings:

"homosk"

Assume i.i.d. homoskedastic errors

"ehw"

Eicker-Huber-White standard errors

"region_cluster"

Standard errors clustered at regional level

"akm"

Adão-Kolesár-Morales

"akm0"

Adão-Kolesár-Morales with null imposed. Note the reported standard error for this method corresponds to the normalized standard error, given by the length of the confidence interval divided by 2z_{1-\alpha/2}

"all"

All of the methods above

beta0

null that is tested (only affects reported p-values)

alpha

Determines confidence level of reported confidence intervals, which will have coverage 1-alpha.

region_cvar

A vector with length N of cluster variables, for method "cluster_region". If the vector 1:N is used, clustering is effectively equivalent to ehw

sector_cvar

A vector with length S of cluster variables, if sectors are to be clustered, for methods "akm" and "akm0". If the vector 1:S is used, this is equivalent to not clustering.

Value

Returns an object of class "SSResults" containing the estimation and inference results. The print function can be used to print a summary of the results. The object is a list with at least the following components:

beta

Point estimate of the effect of interest \beta

se, p

A vector of standard errors and a vector of p-values of the null H_{0}\colon \beta = \beta_{0} for the inference methods in method, with \beta_{0} specified by the argument beta0. For the method "akm0", the standard error corresponds to the effective standard error (length of the confidence interval divided by 2*stats::qnorm(1-alpha/2))

ci.l, ci.r

Upper and lower endpoints of the confidence interval for the effect of interest \beta, for each of the methods in method