Bootstrap Standard Error Estimates and Inference

Asymptotic justification of the bootstrap often takes the form of weak convergence of the bootstrap distribution to some limit distribution. Theoretical literature recognized that the weak convergence does not imply consistency of the bootstrap second moment or the bootstrap variance as an estimator of the asymptotic variance, but such concern is not always reflected in the applied practice. We bridge the gap between the theory and practice by showing that such common bootstrap based standard error in fact leads to a potentially conservative inference.

Intergenerational Mobility in Africa

We examine intergenerational mobility (IM) in educational attainment in Africa since independence using census data. First, we map IM across 27 countries and more than 2800 regions, documenting wide cross‐country and especially within‐country heterogeneity. Inertia looms large as differences in the literacy of the old generation explain about half of the observed spatial disparities in IM. The rural‐urban divide is substantial. Though conspicuous in some countries, there is no evidence of systematic gender gaps in IM. Second, we characterize the geography of IM, finding that colonial investments in railroads and Christian missions, as well as proximity to capitals and the coastline are the strongest correlates. Third, we ask whether the regional differences in mobility reflect spatial sorting or their independent role. To isolate the two, we focus on children whose families moved when they were young. Comparing siblings, looking at moves triggered by displacement shocks, and using historical migrations to predict moving‐families' destinations, we establish that, while selection is considerable, regional exposure effects are at play. An extra year spent in a high‐mobility region before the age of 12 (and after 5) significantly raises the likelihood for children of uneducated parents to complete primary school. Overall, the evidence suggests that geographic and historical factors laid the seeds for spatial disparities in IM that are cemented by sorting and the independent impact of regions.

Salvaging Falsified Instrumental Variable Models

What should researchers do when their baseline model is falsified? We recommend reporting the set of parameters that are consistent with minimally nonfalsified models. We call this the falsification adaptive set (FAS). This set generalizes the standard baseline estimand to account for possible falsification. Importantly, it does not require the researcher to select or calibrate sensitivity parameters. In the classical linear IV model with multiple instruments, we show that the FAS has a simple closed‐form expression that only depends on a few 2SLS coefficients. We apply our results to an empirical study of roads and trade. We show how the FAS complements traditional overidentification tests by summarizing the variation in estimates obtained from alternative nonfalsified models.

Media Capture Through Favor Exchange

We use data from Hungary to establish two results about the relationship between the government and the media. (i) We document large advertising favors from the government to connected media, and large corruption coverage favors from connected media to the government. Our empirical strategy exploits sharp reallocations around changes in media ownership and other events to rule out market‐based explanations. (ii) Under the assumptions of a structural model, we distinguish between owner ideology and favor exchange as the mechanism driving favors. We estimate our model exploiting within‐owner changes in coverage for identification and find that both mechanisms are important. These results imply that targeted government advertising can meaningfully influence content. Counterfactuals show that targeted advertising can also influence owner ideology, by making media ownership more profitable to pro‐government connected investors. Our results are consistent with qualitative evidence from many democracies and suggest that government advertising affects media content worldwide.

Inferring Inequality With Home Production

We revisit the causes, welfare consequences, and policy implications of the dispersion in households' labor market outcomes using a model with uninsurable risk, incomplete asset markets, and home production. Allowing households to be heterogeneous in both their disutility of home work and their home production efficiency, we find that home production amplifies welfare‐based differences, meaning that inequality in standards of living is larger than we thought. We infer significant home production efficiency differences across households because hours working at home do not covary with consumption and wages in the cross section of households. Heterogeneity in home production efficiency is essential for inequality, as home production would not amplify inequality if differences at home only reflected heterogeneity in disutility of work.

A New Parametrization of Correlation Matrices

We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisher's Z‐transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n × n correlation matrix from any vector in R n ( n − 1 ) / 2 is provided, and we derive its numerical complexity.