We propose a way to formalize the relationship between descriptive analysis and structural estimation. A researcher reports an estimate ĉ of a structural quantity of interest c that is exactly or asymptotically unbiased under some base model. The researcher also reports descriptive statistics<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mover accent="true"><a:mi>γ</a:mi><a:mo>ˆ</a:mo></a:mover></a:math>that estimate features γ of the distribution of the data that are related to c under the base model. A reader entertains a less restrictive model that is local to the base model, under which the estimate ĉ may be biased. We study the reduction in worst‐case bias from a restriction that requires the reader's model to respect the relationship between c and γ specified by the base model. Our main result shows that the proportional reduction in worst‐case bias depends only on a quantity we call the informativeness of<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mover accent="true"><d:mi>γ</d:mi><d:mo>ˆ</d:mo></d:mover></d:math>for ĉ . Informativeness can be easily estimated even for complex models. We recommend that researchers report estimated informativeness alongside their descriptive analyses, and we illustrate with applications to three recent papers

Giglio, Maggiori, and Stroebel (2016) show that there is no significant price difference between freeholds and ultra‐long leaseholds in the UK housing market. They claim that this finding precludes the presence of large rational bubbles, as these can only attach to the price of freeholds. But the conclusion presumes that leaseholders cannot acquire bubbles through enfranchisement at favorable prices. We find that the presumption is violated. Enfranchisement rights are comprehensive and cheap to exercise. We also dispute the counter‐argument that cheap enfranchisement proves that market participants, if they have rational expectations, must have explicitly concluded that freehold prices are bubbleless.

We study how aggregate economic conditions affect the timing of marriage, and particularly child marriage, in Sub‐Saharan Africa and in India. In both regions, substantial monetary or in‐kind transfers occur with marriage: bride price across Sub‐Saharan Africa and dowry in India. In a simple equilibrium model of the marriage market in which parents choose when their children marry, income shocks affect the age of marriage because marriage payments are a source of consumption smoothing, particularly for a woman's family. As predicted by our model, we show that droughts, which reduce annual crop yields by 10 to 15% and aggregate income by 4 to 5%, have opposite effects on the marriage behavior of a sample of 400,000 women in the two regions: in Sub‐Saharan Africa they increase the annual hazard into child marriage by 3%, while in India droughts reduce such a hazard by 4%. Changes in the age of marriage due to droughts are associated with changes in fertility, especially in Sub‐Saharan Africa, and with declines in observed marriage payments. Our results indicate that the age of marriage responds to short‐term changes in aggregate economic conditions and that marriage payments determine the sign of this response. This suggests that, in order to design successful policies to combat child marriage and improve investments in daughters' human capital, it is crucial to understand the economic role of marriage market institutions.

We measure the impact of increasing integration between rural villages and outside labor markets. Seasonal flash floods cause exogenous and unpredictable loss of market access. We study the impact of new bridges that eliminate this risk. Identification exploits variation in riverbank characteristics that preclude bridge construction in some villages, despite similar need. We collect detailed annual household surveys over three years, and weekly telephone followups to study contemporaneous effects of flooding. Floods decrease labor market income by 18 percent when no bridge is present. Bridges eliminate this effect. The indirect effects on labor market choice, farm investment, and savings are quantitatively important and consistent with the predictions of a general equilibrium model in which farm investment is risky, and households manage labor market risk and agricultural risk simultaneously. In the calibrated model, the increase in consumption‐equivalent welfare is substantially larger than the increase in income due to the ability to mitigate risk.