Economics: Research Guide

Motivated by the increasingly common technology for collecting data, like cellphones, smartwatches, etc, functional data analysis has been intensively studied in recent decades, and along with it, functional regression models. However, the majority of functional data methods in general and functional regression models, in particular, are based on the fact that the observed datapresent the same domain. When the data have variable domain it needs to be aligned or registered in order to be fitted with the usual modeling techniques adding computational burden. To avoid this, a model that contemplates the variable domain features of the data is needed, but this type of models are scarce and its e..

We study the effect of treatment on an outcome when parallel trends hold conditional on an interactive fixed effects structure. In contrast to the majority of the literature, we propose identification using time-varying covariates. We assume the untreated outcomes and covariates follow a common correlated effects (CCE) model, where the covariates are linear in the same common time effects. We then demonstrate consistent estimation of the treatment effect coefficients by imputing the untreated potential outcomes in post-treatment time periods. Our method accounts for treatment affecting the distribution of the control variables and is valid when the number of pre-treatment time periods is sma..

Dynamic treatment regimes assign personalized treatments to patients sequentially over time based on their baseline information and time-varying covariates. In mobile health applications, these covariates are typically collected at different frequencies over a long time horizon. In this paper, we propose a deep spectral Q-learning algorithm, which integrates principal component analysis (PCA) with deep Q-learning to handle the mixed frequency data. In theory, we prove that the mean return under the estimated optimal policy converges to that under the optimal one and establish its rate of convergence. The usefulness of our proposal is further illustrated via simulations and an application to ..

Network effects, i.e., an agent's utility may depend on other agents' choices, appear in many contracting situations. Empirically assessing them faces two challenges: an endogeneity problem in contract choice and a reflection problem in network effects. This paper proposes a nonparametric approach to tackle both challenges by exploiting restriction conditions from both demand and supply sides. We illustrate our methodology in the yellow pages advertising industry. Using advertising purchases and nonlinear price schedules from seven directories in Toronto, we find positive network effects, which account for a substantial portion of the publisher's profit and businesses' surpluses. We finally ..

This paper develops Mean Group Distributed Lag (MGDL) estimation of impulse responses in large panels with one or two cross-section dimensions. Sufficient conditions for asymptotic consistency and asymptotic normality are derived, and satisfactory small sample performance is documented using Monte Carlo experiments. MGDL estimators are used to estimate the effects of crude oil price increases on U.S. city- and product-level retail prices.

This paper proposes a structural econometric approach to estimating the basic reproduction number (R0) of Covid-19. This approach identifies R0 in a panel regression model by filtering out the effects of mitigating factors on disease diffusion and is easy to implement. We apply the method to data from 48 contiguous U.S. states and a diverse set of countries. Our results reveal a notable concentration of R0 estimates with an average value of 4.5. Through a counterfactual analysis, we highlight a significant underestimation of the R0 when mitigating factors are not appropriately accounted for.

This paper develops a simple approach to overcome the shortcomings of using a standard, single treatment–effect event study to assess the ability of an empirical model to measure heterogeneous treatment effects. Equally as important, we discuss how the standard errors reported in a typical event-study analysis for the posttreatment event-time effects are, without additional information, of limited use for assessing posttreatment variations in the treatment effects. The simple reformulation of the standard event—study approach described and illustrated with artificially constructed data in this paper overcomes the limitations of conventional event-study analyses.

This study focuses on the role of heterogeneity in network peer effects by accounting for network-specific factors and different driving mechanisms of peer behavior. We propose a novel Multivariate Instrumental Variable (MVIV) estimator which is consistent for a large number of networks keeping the individual network size bounded. We apply this approach to estimate peer effects on school achievement exploiting the network structure of friendships within classrooms. The empirical evidence presented is based on a unique network dataset from German upper secondary schools. We show that accounting for heterogeneity is not only crucial from a statistical perspective, but also yields new structura..

Comparing the relative variation of ordinal variates defined on diverse populations is challenging. Pearsons’ Coefficient of Variation or its inverse (the Sharpe Ratio), each used extensively for comparing relative variation or risk tempered location in cardinal paradigms, cannot be employed in ordinal data environments unless cardinal scale is attributed to ordered categories. Unfortunately, due to the scale dependencies of the Coefficient of Variations denominator and numerator, such arbitrary attribution can result in equivocal comparisons. Here, based upon the notion of probabilistic distance, unequivocal, scale independent, Coefficient of Variation and Sharpe Ratio analogues for ..

Recent work on the conditional mean model offers the possibility of addressing misreporting of participation in social programs, which is common and has increased in all major surveys. However, researchers who employ quantile regression continue to encounter challenges in terms of estimation and statistical inference. In this work, we propose a simple two-step estimator for a quantile regression model with endogenous misreporting. The identification of the model uses a parametric first stage and information related to participation and misreporting. We show that the estimator is consistent and asymptotically normal. We also establish that a bootstrap procedure is asymptotically valid for app..

This paper provides a set of tool box measures for flexibly describing distributional changes and empirically implementing several dominance criteria for social welfare comparisons and broad income inequality comparisons. Dominance criteria are expressed in terms of vectors of quantile statistics based on income shares and quantile means. Asymptotic variances and covariances of these sample ordinates are established from a Quantile Function Approach that provides a framework for direct statistical inference on these vectors. And practical empirical criteria are forwarded for using formal statistical inference tests to reach conclusions about ranking social welfare and inequality between dist..

Many key macroeconomic variables such as the NAIRU, potential GDP, and the neutral real rate of interest—which are needed for policy analysis—are latent. Collectively, these latent variables are known as ‘stars’ and are typically estimated using the Kalman filter or smoother from models that can be expressed in State Space form. When these models contain more shocks than observed variables, they are ‘short’, and potentially create issues in recovering the star variable of interest from the observed data. Recovery issues can occur when the model is correctly specified and its parameters are known. In this paper, we summarize the literature on shock reco..

In this paper, we introduce the concept of fractional integration for spatial autoregressive models. We show that the range of the dependence can be spatially extended or diminished by introducing a further fractional integration parameter to spatial autoregressive moving average models (SARMA). This new model is called the spatial autoregressive fractionally integrated moving average model, briefly sp-ARFIMA. We show the relation to time-series ARFIMA models and also to (higher-order) spatial autoregressive models. Moreover, an estimation procedure based on the maximum-likelihood principle is introduced and analysed in a series of simulation studies. Eventually, the use of the model is illu..

We consider instrumental variable estimation of the proportional hazards model of Cox (1972). The instrument and the endogenous variable are discrete but there can be (possibly continuous) exogenous covariables. By making a rank invariance assumption, we can reformulate the proportional hazards model into a semiparametric version of the instrumental variable quantile regression model of Chernozhukov and Hansen (2005). A na\"ive estimation approach based on conditional moment conditions generated by the model would lead to a highly nonconvex and nonsmooth objective function. To overcome this problem, we propose a new presmoothing methodology. First, we estimate the model nonparametrically - a..

Structural breaks in time series forecasting can cause inconsistency in the conventional OLS estimator. Recent research suggests combining pre and post-break estimators for a linear model can yield an optimal estimator for weak breaks. However, this approach is limited to linear models only. In this paper, we propose a weighted local linear estimator for a nonlinear model. This estimator assigns a weight based on both the distance of observations to the predictor covariates and their location in time. We investigate the asymptotic properties of the proposed estimator and choose the optimal tuning parameters using multifold cross-validation to account for the dependence structure in time seri..

Network experiments have been widely used in investigating interference among units. Under the ``approximate neighborhood interference" framework introduced by \cite{Leung2022}, treatments assigned to individuals farther from the focal individual result in a diminished effect on the focal individual's response, while the effect remains potentially nonzero. \cite{Leung2022} establishes the consistency and asymptotic normality of the inverse-probability weighting estimator for estimating causal effects in the presence of interference. We extend these asymptotic results to the Hajek estimator which is numerically identical to the coefficient from the weighted-least-squares fit based on the inve..

This paper proposes a novel local model averaging estimator for divergent-dimensional functional-coefficient regressions, which selects optimal functional combination weights by minimizing a local leave-h-out forward-validation criterion. It is shown that the proposed leave-h-out forward-validation model averaging (FVMA) estimator is asymptotically optimal in the sense of achieving the lowest possible local squared error loss in a class of functional model averaging estimators, which is also extended to the ultra-high dimensional framework. The rate of the FVMA-based varying-weights converging to the optimal weights minimizing the expected local quadratic errors is derived. Besides, when cor..

According to standard econometric theory, Maximum Likelihood estimation (MLE) is the efficient estimation choice, however, it is not always a feasible one. In network diffusion models with unobserved signal propagation, MLE requires integrating out a large number of latent variables, which quickly becomes computationally infeasible even for moderate network sizes and time horizons. Limiting the model time horizon on the other hand entails loss of important information while approximation techniques entail a (small) error that. Searching for a viable alternative is thus potentially highly beneficial. This paper proposes two estimators specifically tailored to the network diffusion model of pa..

This paper contributes to a growing literature on confidence interval construction for impulse response coefficients based on the local projection (LP) approach. We propose an LP-residual bootstrap method to construct confidence intervals for the impulse response coefficients of AR(1) models. The method uses the LP approach and a residual bootstrap procedure to compute critical values. We present two theoretical results. First, we prove the uniform consistency of the LP-residual bootstrap under general conditions, which implies that the proposed confidence intervals are uniformly asymptotically valid. Second, we show that the LP-residual bootstrap can provide asymptotic refinements to the co..

Regularized m-estimators are widely used due to their ability of recovering a low-dimensional model in high-dimensional scenarios. Some recent efforts on this subject focused on creating a unified framework for establishing oracle bounds, and deriving conditions for support recovery. Under this same framework, we propose a new Generalized Information Criteria (GIC) that takes into consideration the sparsity pattern one wishes to recover. We obtain non-asymptotic model selection bounds and sufficient conditions for model selection consistency of the GIC. Furthermore, we show that the GIC can also be used for selecting the regularization parameter within a regularized $m$-estimation framework,..

Even though dyadic regressions are widely used in empirical applications, the (asymptotic) properties of estimation methods only began to be studied recently in the literature. This paper aims to provide in a step-by-step manner how U-statistics tools can be applied to obtain the asymptotic properties of pairwise differences estimators for a two-way fixed effects model of dyadic interactions. More specifically, we first propose an estimator for the model that relies on pairwise differencing such that the fixed effects are differenced out. As a result, the summands of the influence function will not be independent anymore, showing dependence on the individual level and translating to the fact..

Montiel Olea and Pflueger (2013) proposed the effective F-statistic as a test for weak instruments in terms of the Nagar bias of the two-stage least squares (2SLS) estimator relative to a benchmark worst-case bias. We show that their methodology applies to a class of linear generalized method of moments (GMM) estimators with an associated class of generalized effective F-statistics. The standard nonhomoskedasticity robust F-statistic is a member of this class. The associated GMMf estimator, with the extension f for first-stage, is a novel and unusual estimator as the weight matrix is based on the first-stage residuals. As the robust F-statistic can also be used as a test for underidentificat..

The spatial Mundlak model first considered by Debarsy (2012) is an alternative to fixed effects and random effects estimation for spatial panel data models. Mundlak modelled the correlated random individual effects as a linear combination of the averaged regressors over time plus a random time-invariant error. This paper shows that if spatial correlation is present whether spatial lag or spatial error or both, the standard Mundlak result in panel data does not hold and random effects does not reduce to its fixed effects counterpart. However, using maximum likelihood one can still estimate these spatial Mundlak models and test the correlated random effects specification of Mundlak using Likel..

Network diffusion models are applicable to many socioeconomic interactions, yet network interaction is hard to observe or measure. Whenever the diffusion process is unobserved, the number of possible realizations of the latent matrix that captures agents' diffusion statuses grows exponentially with the size of network. Due to interdependencies, the log likelihood function can not be factorized in individual components. As a consequence, exact estimation of latent diffusion models with more than one round of interaction is computationally infeasible. In the present paper, I propose a trimming estimator that enables me to establish and maximize an approximate log likelihood function that almos..

This paper studies semiparametric estimation of monotone index models in a data-rich environment, where the number of covariates ($p$) and sample size ($n$) can both be large. Motivated by the mini-batch gradient descent algorithm (MBGD) that is widely used as a stochastic optimization tool in the machine learning field, this paper proposes a novel subsample- and iteration-based semiparametric estimation procedure. Starting from any initial guess of the parameter, in each round of iteration we draw a random subsample from the data set, and use such subsample to update the parameter based on the gradient of some well-chosen loss function, where the nonparametric component is replaced with its..

This paper proposes the option-implied Fourier-cosine method, iCOS, for non-parametric estimation of risk-neutral densities, option prices, and option sensitivities. The iCOS method leverages the Fourier-based COS technique, proposed by Fang and Oosterlee (2008), by utilizing the option-implied cosine series coefficients. Notably, this procedure does not rely on any model assumptions about the underlying asset price dynamics, it is fully non-parametric, and it does not involve any numerical optimization. These features make it rather general and computationally appealing. Furthermore, we derive the asymptotic properties of the proposed non-parametric estimators and study their finite-sample ..

In lending, where prices are specific to both customers and products, having a well-functioning personalized pricing policy in place is essential to effective business making. Typically, such a policy must be derived from observational data, which introduces several challenges. While the problem of ``endogeneity'' is prominently studied in the established pricing literature, the problem of selection bias (or, more precisely, bid selection bias) is not. We take a step towards understanding the effects of selection bias by posing pricing as a problem of causal inference. Specifically, we consider the reaction of a customer to price a treatment effect. In our experiments, we simulate varying le..

This paper introduces the $\sigma$-Cell, a novel Recurrent Neural Network (RNN) architecture for financial volatility modeling. Bridging traditional econometric approaches like GARCH with deep learning, the $\sigma$-Cell incorporates stochastic layers and time-varying parameters to capture dynamic volatility patterns. Our model serves as a generative network, approximating the conditional distribution of latent variables. We employ a log-likelihood-based loss function and a specialized activation function to enhance performance. Experimental results demonstrate superior forecasting accuracy compared to traditional GARCH and Stochastic Volatility models, making the next step in integrating do..

This paper introduces FourNet, a novel single-layer feed-forward neural network (FFNN) method designed to approximate transition densities for which closed-form expressions of their Fourier transforms, i.e. characteristic functions, are available. A unique feature of FourNet lies in its use of a Gaussian activation function, enabling exact Fourier and inverse Fourier transformations and drawing analogies with the Gaussian mixture model. We mathematically establish FourNet's capacity to approximate transition densities in the $L_2$-sense arbitrarily well with finite number of neurons. The parameters of FourNet are learned by minimizing a loss function derived from the known characteristic fun..

This paper introduces DeepVol, a promising new deep learning volatility model that outperforms traditional econometric models in terms of model generality. DeepVol leverages the power of transfer learning to effectively capture and model the volatility dynamics of all financial assets, including previously unseen ones, using a single universal model. This contrasts to the prevailing practice in econometrics literature, which necessitates training separate models for individual datasets. The introduction of DeepVol opens up new avenues for volatility modeling and forecasting in the finance industry, potentially transforming the way volatility is understood and predicted.