Class Size and Sorting in Market Equilibrium: Theory and Evidence

This paper examines how schools choose class size and how households sort in response to those choices. Focusing on the highly liberalized Chilean education market, we develop a model in which schools are heterogeneous in an underlying productivity parameter, class size is a component of school quality, households are heterogeneous in income and hence willingness to pay for school quality, and schools are subject to a class-size cap. The model offers an explanation for two distinct empirical patterns observed among private schools that accept government vouchers: (i) There is an inverted-U relationship between class size and household income in equilibrium, which will tend to bias cross-sectional estimates of the effect of class size on student performance. (ii) Some schools at the class size cap adjust prices (or enrollments) to avoid adding another classroom, which produces stacking at enrollments that are multiples of the class size cap. This generates discontinuities in the relationship between enrollment and household characteristics at those points, violating the assumptions underlying regression-discontinuity (RD) research designs. This result suggests that caution is warranted in applying the RD approach in settings in which parents have substantial school choice and schools are free to set prices and influence their enrollments.

The Quality-Complementarity Hypothesis: Theory and Evidence from Colombia

This paper presents a tractable formalization and an empirical investigation of the quality-complementarity hypothesis, the hypothesis that input quality and plant productivity are complementary in generating output quality. We embed this complementarity in a general-equilibrium trade model with heterogeneous, monopolistically competitive firms, extending Melitz (2003), and show that it generates distinctive implications for two simple, observable within-sector correlations − between output prices and plant size and between input prices and plant size − and for how those correlations vary across sectors. Using uniquely rich and representative data on the unit values of outputs and inputs of Colombian manufacturing plants, we then document three facts: (1) output prices are positively correlated with plant size within industries on average; (2) input prices are positively correlated with plant size within industries on average; and (3) both correlations are more positive in industries with more scope for quality differentiation, as measured by the advertising and R&D intensity of U.S. industries. The predicted and observed correlations between export status and input and output prices are similar to those for plant size. We present additional evidence that market power of either final-good producers or input suppliers does not fully explain the empirical patterns we observe. These findings are consistent with the predictions of our model and difficult to reconcile with alternative models that impose symmetry or homogeneity of either inputs or outputs. We interpret the results as broadly supportive of the quality-complementarity hypothesis.product quality, heterogeneous firms, international trade, plant size

Growth through exports: should governments intervene?

“A thriving export sector is, as the Commission on Growth and Development states, “a critical ingredient of high growth, especially in the early stages.” [1] There is microeconomic evidence to support this claim: recent research suggests that increases in exports lead firms to produce higher-quality products, pay higher wages, and adopt more advanced technologies.[2] There is also evidence that the sophistication of a country’s exports, where the sophistication of a product is measured by the average income of countries that produce the product, is positively correlated with countries’ future growth rates.[3] It appears that growth is closely associated with moving up the quality ladder within industries, and exporting more technology-intensive and capital-intensive, higher-value-added products

Essays on External Conditions and Wage-Setting Within Firms: Dissertation Summary

This dissertation presents two essays investigating the influence of conditions external to firms on wage-setting within them. Chapter 2, “Trade, Quality Upgrading and Wage Inequality in the Mexican Manufacturing Sector,” examines the response of plants in the Mexican manufacturing sector to the shock to product market conditions generated by the peso crisis of late 1994, and the differential consequences for wages of blue-collar and white-collar workers. Chapter 3, “Fairness and Freight-Handlers,” examines changes in the fairness perceptions and performance of employees in the freight-handling terminals of a U.S. trucking firm in response to changes in unemployment rates and the wages of similar workers in the local labor markets surrounding each terminal

Product quality at the plant level: Plant size, exports, output prices and input prices in Colombia

This paper uses uniquely rich and representative data on the unit values of "outputs" (products) and inputs of Colombian manufacturing plants to draw inferences about the extent of quality differentiation at the plant level. We extend the Melitz (2003) framework to include heterogeneity of inputs and a complementarity between plant productivity and input quality in producing output quality and we show that the resulting model carries distinctive implications for two simple reduced-form correlations - between output prices and plant size and between input prices and plant size - and for how those correlations vary across sectors. We then document three plant level facts: (1) output prices are positively correlated with plant size within industries, on average; (2) input prices are positively correlated with plant size within industries, on average; and (3) both correlations are more positive in industries with more scope for quality differentiation, as measured by the advertising and R&D intensity of U.S. firms. The correlations between export status and input and output prices are similar to those for plant size. These facts are consistent with our model of quality differentiation of both outputs and inputs, and difficult to reconcile with models that assume homogeneity or symmetry of either set of goods. Beyond recommending an amendment of the Melitz (2003) model, the results highlight shortcomings of standard methods of productivity estimation, generalize and provide an explanation for the well-known employer size-wage effect, and suggest new channels through which liberalization of trade in output markets may affect input markets and vice-versa

The Quality-Complementarity Hypothesis: Theory and Evidence from Colombia

This paper presents a tractable formalization and an empirical investigation of the quality-complementarity hypothesis, the hypothesis that input quality and plant productivity are complementary in generating output quality. We embed this complementarity in a general-equilibrium trade model with heterogeneous, monopolistically competitive firms, extending Melitz (2003), and show that it generates distinctive implications for two simple, observable within-sector correlations -- between output prices and plant size and between input prices and plant size -- and for how those correlations vary across sectors. Using uniquely rich and representative data on the unit values of outputs and inputs of Colombian manufacturing plants, we then document three facts: (1) output prices are positively correlated with plant size within industries on average; (2) input prices are positively correlated with plant size within industries on average; and (3) both correlations are more positive in industries with more scope for quality differentiation, as measured by the advertising and R&D intensity of U.S. industries. The predicted and observed correlations between export status and input and output prices are similar to those for plant size. We present additional evidence that market power of either final-good producers or input suppliers does not fully explain the empirical patterns we observe. These findings are consistent with the predictions of our model and difficult to reconcile with alternative models that impose symmetry or homogeneity of either inputs or outputs. We interpret the results as broadly supportive of the quality-complementarity hypothesis.

Plants and Imported Inputs: New Facts and an Interpretation

Beginning with Wilfred J. Ethier (1979, 1982), an important current of research has emphasized gains to trade from the greater availability of intermediate inputs, as opposed to the greater availability of consumption goods emphasized by Paul R. Krugman (1979) and others. It has been standard in this literature to model input varieties as symmetric, differentiated horizontally but not vertically. In contrast, anecdotal accounts, especially from developing countries, often stress the importance of gaining access to high-quality inputs on the import market. In theoretical discussions, the need to distinguish between the number of inputs and the quality of those inputs can be avoided by treating different qualities of a good as distinct varieties (see, e.g., Paul Romer 1994) or by redefining units of measurement. But in empirical work, one inherits the product categories and units in the data, and typically one must specify whether the availability-of-inputs mechanism is expected to operate through an increase in the number of input categories or through an increase in the quality of inputs within categories. Because of data constraints—in particular because of a lack of information on input and output prices in standard plant-level datasets—it has been difficult to investigate the role of input-quality differences, and recent empirical work, notably by Christian Broda, Joshua Greenfield, and David Weinstein (2006) and Pinelopi K. Goldberg et al. (2008), has tended to focus more on changes in the number of input categories than on quality differences within those categories. In this short paper, we draw on rich product level information from the Colombian manufacturing census to present a new set of facts about importing plants and input prices. The dataset is unique in that it contains detailed, representative, consistently measured information on the unit values of all inputs and outputs of plants. For the 1982–1988 period, the dataset also contains unit values separately for domestic and imported purchases of each input. As we discuss in more detail below, we interpret the new facts as suggesting that Colombian plants purchase higher-quality inputs on the import market than on the domestic market, within narrow product categories. Our empirical work has been guided in part by a theoretical framework from a related paper, Kugler and Verhoogen (2008). In that paper, we hypothesize a complementarity between input quality and plant productivity in generating output quality, and extend the model of Marc J. Melitz (2003) to accommodate it. The model predicts that, in equilibrium, more-productive plants are larger, use higher-quality inputs, produce higher-quality outputs, and are more likely to enter the export market than less-productive plants in the same industry. Using the Colombian plant census, we show that the cross-sectional correlations between a number of observable variables—output prices, input prices, plant size, and export status—as well as differences in those correlations across sectors,—are consistent with our theoretical framework and difficult to reconcile with alternative models that impose symmetry of either inputs or outputs. The distinctive aspect of the current paper is the focus on the distinction between imported and domestic inputs

Geo-Neutrinos: a short review

Geo-neutrino detection will determine the amount of long lived radioactive elements within our planet and fix the debated radiogenic contribution to the terrestrial heat. In addition, it will provide a direct test of the Bulk Silicate Earth model, a fundamental cosmochemical paradigm about the origin of the Earth. Unorthodox models of Earth's core (including the presence of potassium or the possibility of a giant reactor) can also be checked. This short review presents status and prospects of the field.Comment: 7 pages, 2 figures, presented at Neutrino 2004 in Pari

Neutrinos and Energetics of the Earth

We estimate terrestrial antineutrino and neutrino fluxes according to different models of Earth composition. We find large variations, corresponding to uncertainties on the estimated $U$, $Th$ and $K$ abundances in the mantle. Information on the mantle composition can be derived from antineutrino flux measurements after subtracting the crust contribution. This requires a good description of the crust composition in the region of the detector site. Measurements of terrestrial antineutrinos will provide a direct insight on the main sources of Earth's heat flow.Comment: 11 pages, RevTeX file. To appear on Phys. Lett. B. Addendum contains comparison with KamLAND result

Class-Size Caps, Sorting, and the Regression-Discontinuity Design

This paper examines how schools’ choices of class size and households’ choices of schools affect regression-discontinuity-based estimates of the effect of class size on student outcomes. We build a model in which schools are subject to a class-size cap and an integer constraint on the number of classrooms, and higher-income households sort into higher-quality schools. The key prediction, borne out in data from Chile’s liberalized education market, is that schools at the class-size cap adjust prices (or enrollments) to avoid adding an additional classroom, which generates discontinuities in the relationship between enrollment and household characteristics, violating the assumptions underlying regression-discontinuity research designs