Cowles Foundation Discussion Papers

Between 1880 and 1920, more than 20 million immigrants settled in the United States. We study how this migration wave affected innovation and growth. Using a newly constructed dataset linking individual census records to historical immigration records and the universe of US patents, we highlight a new channel through which immigrants contributed to growth: they disproportionately settled in urban innovation hubs. To quantify the aggregate and regional effects of this mass migration episode, we develop a new spatial growth model in which skilled workers have a comparative advantage in innovation and sort endogenously across space. We find that international arrivals after 1880 raised US income per capita by 8.2% by 1940. Removing the subsequent immigration restrictions of the 1920s would have raised income per capita by a further 1.7% by 2000. Immigrants’ skill composition and their concentration in urban hubs are key drivers of these effects.

We analyze consumer surplus when a monopolist can adjust both prices and prod-uct qualities across segments, engaging in second- and third-degree price discrimination simultaneously. We characterize the consumer-optimal segmentation and show that it has a striking structure: consumers with the same value receive the same quality in every segment, though prices differ. Under mild conditions, any segmentation harms consumers if and only if demand is sufficiently more elastic than supply. Hence, po-tential benefits for consumers depend critically on demand and supply elasticities. These findings have implications for regulatory policy regarding price discrimination and market segmentation.

The AI boom has driven the Nasdaq and the Magnificent Seven tech stocks to record highs. But how much do these new records reflect underlying value, how much is speculation, and how vulnerable are these stocks and the wider market to a major downturn? Our evidence and analyses show clear signs of bubble exuberance in most of these stocks, concentrated in a few names like Nvidia, leading to latent risks for investors who assume their index funds are safely diversified and supported by wider economic fundamentals.

To meet voluntary climate targets, firms often complement internal decarbonization efforts by purchasing carbon credits in the voluntary carbon market (VCM), which finance projects that reduce emissions elsewhere. However, these emissions reductions are difficult to verify, and growing evidence of overcrediting has cast doubt on the VCM's potential to genuinely offset emissions. We investigate how the VCM's defining features shape its climate effectiveness. Our model captures three central elements: adverse selection, as high-quality projects that truly reduce emissions are costlier yet difficult to distinguish from low-quality ones; imperfect third-party certification, as projects are screened based on a noisy signal of quality; and buyer preferences for non-carbon attributes, as some firms value credits that generate observable social or economic co-benefits beyond reducing emissions. We show that the market fails to sustain trade if certification is sufficiently noisy, as quality uncertainty erodes buyer confidence and triggers a market-for-lemons collapse. However, demand for co-benefits can sustain markets that would otherwise collapse. Yet in such cases, the market remains active but yields limited carbon abatement, as most traded credits are low-quality. We then examine policy and market design interventions reflecting recent developments in practice, such as penalizing buyers for greenwashing and offering credit portfolios. We show that these measures can be counterproductive for carbon mitigation if certification remains inaccurate. Accordingly, we demonstrate that the certifier’s incentives for accuracy can be strengthened by modifying its fee structure so that its revenue is tied to the market value rather than the volume of credits.

This paper develops and applies new asymptotic theory for estimation and inference in parametric autoregression with function valued cross section curve time series. The study provides a new approach to dynamic panel regression with high dimensional dependent cross section data. Here we deal with the stationary case and provide a full set of results extending those of standard Euclidean space autoregression, showing how function space curve cross section data raises efficiency and reduces bias in estimation and shortens confidence intervals in inference. Methods are developed for high-dimensional covariance kernel estimation that are useful for inference. The findings reveal that function space models with wide-domain and narrow-domain cross section dependence provide insights on the effects of various forms of cross section dependence in discrete dynamic panel models with fixed and interactive fixed effects. The methodology is applicable to panels of high dimensional wide datasets that are now available in many longitudinal studies. An empirical illustration is provided that sheds light on household Engel curves among ageing seniors in Singapore using the Singapore life panel longitudinal dataset.

This paper proposes a semi-endogenous growth theory that incorporates technology vintages and the endogenous evolution of multiple technological paradigms through innovation. It provides a characterization of both balanced growth equilibrium and transitional dynamics in an environment where new technologies continuously emerge. From a positive perspective, the model rationalizes two distinct empirical patterns. Using two centuries of US patent data, I first document that the age profile of patents has a pronounced hump shape: most contemporary patents build upon technologies that are between 50 and 100 years old. Second, this age profile has remained stable throughout the past century. From a normative standpoint, the theory underscores a misallocation of research effort induced by the tendency among profit-maximizing firms to overinvest in further developing mature technologies. This yields a suboptimally slow development of emerging technologies. According to a calibrated version of the model, correcting such misallocation could generate welfare gains of 7%.