ivreg_ss {ShiftShareSE}

Inference in an IV regression with a shift-share instrument

Description

Computes confidence intervals and p-values in an instrumental variables regression in which the instrument has a shift-share structure, as in Bartik (1991). Several different inference methods can computed, as specified by method.

Usage

ivreg_ss(
  formula,
  X,
  data,
  W,
  subset,
  weights,
  method,
  beta0 = 0,
  alpha = 0.05,
  region_cvar = NULL,
  sector_cvar = NULL
)

Arguments

formula

An object of class "formula" (or one that can be coerced to that class) of the form outcome ~ controls | endogenous_regressor. For a regression with no controls (only an intercept), it takes the form outcome ~ 1 | endogenous_regressor

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.

data

An optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the outcome and running variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which the function is called. Each row in the data frame 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.

subset

An optional vector specifying a subset of observations to be used in the fitting process.

weights

An optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector, with each row corresponding to a region. If non-NULL, for computing the first stage and the reduced form, weighted least squares is used with weights weights (that is, we minimize sum(weights*residuals^2)); otherwise ordinary least squares is used.

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

Note

subset is evaluated in the same way as variables in formula, that is first in data and then in the environment of formula.

References

Bartik, Timothy J., Who Benefits from State and Local Economic Development Policies?, Kalamazoo, MI: W.E. Upjohn Institute for Employment Research, 1991.

Adão, Rodrigo, Kolesár, Michal, and Morales, Eduardo, "Shift-Share Designs: Theory and Inference", Quarterly Journal of Economics 2019, 134 (4), 1949-2010. doi: 10.1093/qje/qjz025.

Examples

## Use ADH data from Autor, Dorn, and Hanson (2013)
ivreg_ss(d_sh_empl ~ 1 | shock, X=IV, data=ADH$reg, W=ADH$W,
         method=c("ehw", "akm", "akm0"))