Directed acyclic graphs (DAGs) provide a transparent framework for encoding causal structures and identifying causal effects. This paper demonstrates how DAGs help specify local projections (LPs) for estimating causal impulse responses. Examples illustrate how graphical rules can be used to...

Many instrumental variables applications specify a single Bernoulli treatment. But instruments may change outcomes through multiple pathways or by varying treatment intensity. Lottery instruments that boost charter school enrollment, for instance, may affect outcomes by lengthening time enrolled...

In structural vector autoregressive analysis it has become quite popular to identify some structural shocks of interest by external instruments or proxies. This study points out a range of areas where such proxies have been used and sketches the way the proxies have been constructed. It reviews...

This paper estimates the returns to education in Arkansas-one of the last states to extend compulsory schooling-using ACS 2023 data and the 1987 Compulsory Schooling Law (CSL) reform as an instrument. OLS estimates imply returns of 9.5-10.4 percent per year of schooling. The CSL reform increased...

This paper estimates the returns to education in Arkansas - one of the last states to extend compulsory schooling - using ACS 2023 data and the 1987 Compulsory Schooling Law (CSL) reform as an instrument. OLS estimates imply returns of 9.5-10.4 percent per year of schooling. The CSL reform...

We approximate the finite-sample distribution of impulse response function (IRF) estimators that are just-identified with a weak instrument using the conventional local-to-zero asymptotic framework. Since the distribution lacks a mean, we assess bias using the mode and conclude that researchers...

We extend the heteroskedasticity IV estimator of Rigobon and Sack (2004) from one to multiple monetary policy shocks by imposing recursive zero restrictions on the impact matrix. Unlike high-frequency identification, the approach requires neither intraday tick data nor precise announcement...

How should researchers adjust for covariates? We show that if the propensity score is estimated using a specific covariate balancing approach, inverse probability weighting (IPW), augmented inverse probability weighting (AIPW), and inverse probability weighted regression adjustment (IPWRA)...

This paper studies the limiting behavior of the test for instrument exogeneity in linear models when there is uncertainty about the strength of the identification signal. We consider the test for conditional moment restrictions with an expanding set of constructed instruments. We establish the...

We estimate the causal effect of schooling on log earnings using instrumental variables (IV), addressing the endogeneity of schooling by using father's education as an instrument. The IV estimate implies a return of approximately 7.7 percent per additional year of schooling. First-stage and...

How should researchers adjust for covariates? We show that if the propensity score is estimated using a specific covariate balancing approach, inverse probability weighting (IPW), augmented inverse probability weighting (AIPW), and inverse probability weighted regression adjustment (IPWRA)...

We study the estimation of causal treatment effects on demand when treatment is randomly assigned but prices adjust in response to treatment. We show that regressions of demand on treatment or on treatment and price lead to biased estimates of the direct treatment effect. The bias in both cases...

Textbook theory predicts that t-ratios decline towards zero in regressions when there is increasing collinearity between two independent variables. This article shows that this rarely happens if the two variables are endogenous, and coefficients increase greatly with more collinearity. The...

This study examines the relationship between the number of children and dementia risk among parents, addressing longstanding questions about how parenthood shapes cognitive health in later life. Using comprehensive administrative data on all parents born in Sweden between 1920 and 1950, along...

Accurate macroeconomic forecasts are essential for effective policy decisions, yet their precision depends on the accuracy of the underlying assumptions. This paper examines the extent to which assumption errors affect forecast accuracy, introducing the average squared assumption error (ASAE) as...

This paper examines the effect of macroprudential policies on private domestic investment using a panel of 87 developing countries from 2000 to 2017. Our instrumental variables strategy exploits the geographic diffusion of macroprudential policies across countries, with the idea that reforms in...

We argue that measurement error in historical price data has led researchers to erroneously believe that there was little persistence of inflation during the 19th century. Using a statistical technique that accounts for these errors, we estimate the persistence of (a) US inflation and (b)...

A unified theory of estimation and inference is developed for an autoregressive process with root in (-∞, ∞) that includes the stationary, local-to-unity, explosive and all intermediate regions. The discontinuity of the limit distribution of the t-statistic outside the stationary region and...

Recent technological advances and policy initiatives present Africa with enormous growth potential from participating in global value chains (GVCs). However, the widening income inequality is raising questions as to whether participation in GVCs plays any role in this observed phenomenon....