Commonly used frequentist estimation methods for linear factor models of asset returns are invalidated by weak and spurious factors. The problem is amplified by omitted variables and model misspecification, and often calls for specialized non-standard estimation techniques. Conversely, the Bayesian analogue of the popular Fama and MacBeth (1973) two-pass regressions method provides reliable risk premia estimates for both tradable and nontradable factors, detects those weakly identified, delivers valid credible intervals for all objects of interest, and is intuitive, fast and simple to implement. In other words, weak and spurious factors are not a problem for the Bayesian estimation of Fama-MacBeth regressions.

The Bayesian Fama-MacBeth (OLS) estimator is available as part of the Bayesian Factor Zoo package

A Python package implementing the method in full generality (OLS, GLS and with omitted variables) is independently maintained by Gustavo Amarante

We provide a novel priced Wold representation theorem that sharply identifies shocks common to financial markets and the macroeconomy, their propagation, and the term structure of macro risk premia. Our identification leverages the fact that, in equilibrium models, asset prices are jump variables that reveal priced risks in large cross-sections of returns (N → ∞). We find that macro factors’ risk premia are strongly time-varying and countercyclical, with sharply increasing unconditional term structures. This pattern is driven by the slow propagation of a priced common shock, distinct from TFP, that captures most of the persistence in macroeconomic variables. Macro risk premia are negligible in the short run, yet grow to match equity risk premia at the business cycle horizon. This finding is not a mechanical byproduct of persistence: while GDP, consumption, industrial production, and employment exhibit upward-sloping term structures, other similarly persistent factors—e.g., VIX or intermediary-based variables—display downward-sloping or flat ones.

Using an equilibrium network model and a large international panel of cross-border trade, we analyse empirically the drivers of foreign currency invoicing. First, we find strong evidence of strategic complementarity in currency invoicing across countries: Exporting countries tend to invoice more in a given currency when their main trade partners invoice in that same currency. This in turn leads to an amplification of domestic shocks through the trade network. Second, key players for a given currency are not only countries that invoice most of their exports in that foreign currency (e.g., China, South Korea, and Russia), but also countries that are central in the international trade network (e.g., Japan, Germany, and Canada). Third, at the country-level, we find evidence of strategic complementarity, or natural hedging, between the choices of export and import currencies. Fourth, in counterfactual analysis we find that, due to the large network externalities that we identify, the position of the USD as dominant trade currency is inherently fragile with respect to the currency invoicing choices of EU and BRICS countries.

We develop a generalization of the Glosten and Milgrom (1985) sequential trading model that delivers a fully endogenous, multi-time-scale, agent-based equilibrium theory of price dynamics, volatility, liquidity, and trading activity. Starting from an axiomatization of the Glosten-Milgrom model, we characterize the tick-by-tick equilibrium in closed form and establish its scaling limits as traders’ arrival or trading rates increase.
The resulting lower-frequencies price and trade processes are obtained through a novel probabilistic machinery: (i) a continuous (in the Skorokhod topology) mapping from the shadow-valuation process—a branching Brownian motion—to all equilibrium quantities; (ii) a new probabilistic result on the most recent common ancestor; (iii) a mixingale convergence theorem for equilibrium price functionals defined through state-dependent hitting times; and (iv) a central limit theorem for irregularly spaced renewal-reward sequences, which yields the low- and ultra-low-frequency diffusion limits.
These results show that stochastic volatility arises endogenously as a linear functional of the equilibrium number-of-trades process. Our closed-form solutions rationalize a large body of empirical evidence and provide a natural laboratory for analyzing the equilibrium effects of a financial transaction tax.

We consider an economy in which some agents do not continuously hedge their position in derivative assets using the underlying assets market – i.e. we study the effects of an imbalanced derivate market. We show that, even in the presence of complete markets, the imbalance significantly alters the equilibrium price process of the underlying assets: risk premia and volatility become stochastically time varying, hence option implied volatility is characterized by smile and smirk patterns, momentum-like price dynamics arise as well as price spillovers across underlying assets. Moreover, the derivative imbalance generates self-fulfilling equilibria, e.g. if the imbalance takes the form of a bet on an increase in asset volatility, then the equilibrium volatility does increase. Finally, since our formulation is extremely general, our results also apply to segmented markets where some investments are achievable only via financial intermediation.

This paper shows that social networks have significant effects on loan repayments. In the loan records of a peer-to-peer lending platform, we proxy social networks based on the contact persons that borrowers provide at loan applications. We estimate the effect of the propensity to pay of a borrower on the propensity to pay of their contact persons using a Spatial Autoregressive Probit model. If the probability to repay of a borrower’s contact persons increases by 10%, the repayment probability of the linked borrower increases by 0.8%, which increases the lender’s profit on average by 360 RMB (i.e. $52). In contrast, a borrower’s propensity to pay does not significantly affect the propensity to pay of other borrowers from the same home or work address. We interpret the results as evidence that social networks affect loan repayment decisions beyond common borrower characteristics and financial situations.

We study the implications of human capital hedging for international portfolio diversification. First, we show that given the degree of international economic integration observed in the data, very small domestic redistributive shocks can lead to home country bias in portfolio holdings. Second, we find that the seminal empirical result of Baxter and Jermann (1997) – that the international diversification puzzle is worsened if we consider the human capital hedging motive – is driven by an econometric misspecification that restricts the countries considered in their study to be economically not integrated. Moreover, once this misspecification is corrected, considering the human capital risk does not unequivocally worsen the puzzle, and in some cases helps explaining it. Third, we document that the substantial statistical uncertainty on measuring returns to the aggregate capital stock can rationalize the disagreements in the previous literature. Fourth, we find sharp evidence that if the set of assets that can be used to hedge aggregate human capital is restricted to publicly traded stocks, the human capital hedging motive has a negligible impact on optimal portfolio choice. This last finding is driven by the extremely small correlation between stock market returns and returns to human capital.

This paper shows that in a non-representative agent model in which households face short selling constraints and labor income risk, in the form of both uninsurable shocks and a common aggregate component, small differences in the correlation between aggregate labor income shocks and domestic and foreign stock market returns lead to a very large home bias in asset holdings. Calibrating this buffer-stock saving model to match both microeconomic and macroeconomic U.S. labor income data, I demonstrate that, consistent with the empirical literature, a) investors that enter the stock market will initially specialize in domestic assets, b) individual portfolios become more internationally diversified, adding foreign stocks one at a time, as the level of asset wealth increases, and c) most importantly, the implied aggregate portfolio of U.S. investors shows a large degree of home bias consistent with observed levels.