Instrumental variable (IV) methods are widely used to address endogeneity concerns. Yet, a specific kind of endogeneity – spatial interdependence – is regularly ignored. We show that ignoring spatial interdependence in the outcome results in asymptotically biased estimates even when instruments are randomly assigned. The extent of this bias increases when the instrument is also spatially clustered, as is the case for many widely used instruments: rainfall, natural disasters, economic shocks, and regionally- or globally-weighted averages. Because the biases due to spatial interdependence and predictor endogeneity can offset, addressing only one can increase the bias relative to ordinary least squares. We demonstrate the extent of these biases both analytically and via Monte Carlo simulation. Finally, we discuss a general estimation strategy – S-2SLS – that accounts for both outcome interdependence and predictor endogeneity, thereby recovering consistent estimates of predictor effects.

We identify a form of gender-based governmental discrimination that directly affects billions of women on a daily basis: the setting of import tariffs for gendered goods. These tax rates, which can differ across otherwise identical gender-specific products, often impose direct penalties on women as consumers. Comparing nearly 200,000 paired tariff rates on men’s and women’s apparel products in 167 countries between 1995 and 2015, we find that women suffer a tax penalty that varies systematically across countries. We demonstrate that in democracies, women’s presence in the legislature is associated with decreased import tax penalties on women’s goods. This finding is buttressed by a comparison of democracies and non-democracies and analyses of the implementation of legislative gender quotas. Our work highlights a previously unacknowledged government policy that penalizes women and also provides powerful evidence that descriptive representation can have a substantial, direct impact on discriminatory policies.

Instruments based on realizations of the endogenous variable in other units -for instance, regional or global weighted averages -are commonly used in political science. Such spatial instruments have proved attractive: they are convenient to obtain, typically have power, and are plausibly exogenous. We argue that the assumptions underlying spatial instruments remain poorly understood and challenge whether spatial instruments can satisfy the conditions required for valid instruments. First, when cross-unit dependence exists in the endogenous predictor, other cross-unit relationships -e.g., spillovers and interdependence -likely exist as well and risk violations of the exclusion restriction. Second, spatial instruments produce simultaneity in the first-stage equation, as left-hand side outcomes are included as right-hand side predictors. Because the instrument and the endogenous variable are simultaneously determined, the exclusion restriction is, necessarily and by construction, violated. Taken together, these concerns lead us to conclude that spatial instruments are rarely, if ever, valid. * Thanks to Vincent Arel-Bundock and Michael Ward for their helpful comments. All remaining errors are ours alone. Authors are listed in alphabetical order, equal authorship is implied.

How do firms protect themselves against infringements of their property rights by their own government? The authors develop a theory based on international law and joint asset ownership with foreign firms. Investment agreements protect the assets of foreign firms but are not available to domestic firms. This segmentation of the property rights environment creates a rationale for international financial relationships between firms. By forming financial relationships with foreign firms, domestic firms gain indirect coverage from the property rights available to foreign firms under investment agreements. If a government is less likely to violate the property rights of covered foreign firms, it is also less likely to violate property rights for assets held jointly by domestic and foreign firms. This article presents systematic evidence from data on the activities of firms in countries that have investment agreements with the United States. International financial relationships between firms, through mergers and acquisitions as well as through bond and equity issues, are more common where property rights are weak. The theory suggests a political logic to the fragmentation of firm-ownership stakes across jurisdictions, offers an institutional explanation of international financial flows, and identifies new distributional consequences of international law.

Instruments based on realizations of the endogenous variable in other units—for instance, regional or global weighted averages—are commonly used in political science. Such spatial instruments have proved attractive: they are convenient to obtain, typically have power, and are plausibly exogenous. We argue that the assumptions underlying spatial instruments remain poorly understood and challenge whether spatial instruments can satisfy the conditions required for valid instruments. First, when cross-unit dependence exists in the endogenous predictor, other cross-unit relationships—spillovers and interdependence—likely exist as well and risk violations of the exclusion restriction. Second, spatial instruments produce simultaneity in the first-stage equation, as left-hand side outcomes are included as right-hand side predictors. Because the instrument and the endogenous variable are simultaneously determined, the exclusion restriction is, necessarily and by construction, violated. Taken together, these concerns lead us to conclude that spatial instruments are rarely, if ever, valid.