|
on Econometrics |
| By: | Deb, P.;; Norton, E.C.;; Wooldridge, J.M.;; Zabel, J.E.; |
| Abstract: | This paper proposes a method for estimation of effects in difference -in-differences designs in which the start of treatment is staggered over time and treatment effects are heterogeneous by group, time and covariates, and when the data are repeated cross-sections. We show that a linear-in-parameters regression specification with a sufficiently flexible functional form consisting of group-by-time treatment effects, two-way fixed effects, and interaction terms yields consistent estimates of heterogeneous treatment effects under very general conditions. The estimates are efficient and aggregation of treatment effects and inference are straightforward. We illustrate the use of this model with two empirical examples and provide comparisons to other recently derived estimators. |
| Keywords: | difference-in-differences; causal inference; repeated cross-sections; staggered treatment timing; treatment effect heterogeneity; parallel trends; |
| JEL: | C21 C23 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:yor:hectdg:24/17 |
| By: | Langevin, R.; |
| Abstract: | Finite mixtures are often used in econometric analyses to account for unobserved heterogeneity. This paper shows that maximizing the likelihood of a finite mixture of parametric densities leads to inconsistent estimates under weak regularity conditions. The size of the asymptotic bias is positively correlated with the degree of overlap between the densities within the mixture. In contrast, I show that maximizing the max-component likelihood function equipped with a consistent classifier leads to consistency in both estimation and classification as the number of covariates goes to infinity while leaving group membership completely unrestricted. Extending the proposed estimator to a fully nonparametric estimation setting is straightforward. The inconsistency of standard maximum likelihood estimation (MLE) procedures is confirmed via simulations. Simulation results show that the proposed algorithm generally outperforms standard MLE procedures in finite samples when all observations are correctly classified. In an application using latent group panel structures and health administrative data, estimation results show that the proposed strategy leads to a reduction in out-of-sample prediction error of around 17.6% compared to the best results obtained from standard MLE procedures. |
| Keywords: | panel data; Finite mixtures; EM algorithm; CEM algorithm; K-means; healthcare expenditures; unobserved heterogeneity; |
| JEL: | C14 C23 C51 I10 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:yor:hectdg:24/16 |
| By: | Jianqing Fan; Weining Wang; Yue Zhao |
| Abstract: | High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to their representation power. We ask the question whether individual covariates have additional contributions given the latent factors or more generally a set of variables. Our test statistics are based on the estimated partial derivative of the regression function of the candidate variable for screening and a observable proxy for the latent factors. Hence, our test reveals how much predictors contribute additionally to the non-parametric regression after accounting for the latent factors. Our derivative estimator is the convolution of a deep neural network regression estimator and a smoothing kernel. We demonstrate that when the neural network size diverges with the sample size, unlike estimating the regression function itself, it is necessary to smooth the partial derivative of the neural network estimator to recover the desired convergence rate for the derivative. Moreover, our screening test achieves asymptotic normality under the null after finely centering our test statistics that makes the biases negligible, as well as consistency for local alternatives under mild conditions. We demonstrate the performance of our test in a simulation study and two real world applications. |
| Date: | 2024–08–21 |
| URL: | https://d.repec.org/n?u=RePEc:azt:cemmap:17/24 |
| By: | Lloyd, Simon (Bank of England); Manuel, Ed (London School of Economics) |
| Abstract: | A common approach to estimating causal effects in macroeconomics involves constructing orthogonalised ‘shocks’ then integrating them into local projections or vector autoregressions. For a general set of estimators, we show that this two-step ‘shock-first’ approach can be problematic for identification and inference relative to a one-step procedure which simply adds appropriate controls directly in the outcome regression. We show this analytically by comparing one and two-step estimators without assumptions on underlying data-generating processes. In simple ordinary least squares (OLS) settings, the two approaches yield identical coefficients, but two-step inference is unnecessarily conservative. More generally, one and two-step estimates can differ due to omitted-variable bias in the latter when additional controls are included in the second stage or when employing non-OLS estimators. In monetary-policy applications controlling for central-bank information, one-step estimates indicate that the (dis)inflationary consequences of US monetary policy are more robust than previously realised, not subject to a ‘price puzzle’. |
| Keywords: | Identification; instrumental variables; local projections; omitted-variable bias; vector autoregressions |
| JEL: | C22 C26 C32 C36 E50 E60 |
| Date: | 2024–08–06 |
| URL: | https://d.repec.org/n?u=RePEc:boe:boeewp:1079 |
| By: | Federico A. Bugni; Mengsi Gao; Filip Obradovic; Amilcar Velez |
| Abstract: | This paper studies a specific inference problem for a partially-identified parameter of interest with an interval identified set. We consider the favorable situation in which a researcher has two possible estimators to construct the confidence interval proposed in Imbens and Manski (2004) and Stoye (2009), and one is more efficient than the other. While the literature shows that both estimators deliver asymptotically exact confidence intervals for the parameter of interest, their inference in terms of statistical power is not compared. One would expect that using the more efficient estimator would result in more powerful inference. We formally prove this result. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.20386 |
| By: | Jiafeng Chen |
| Abstract: | When do linear regressions estimate causal effects in quasi-experiments? This paper provides a generic diagnostic that assesses whether a given linear regression specification on a given dataset admits a design-based interpretation. To do so, we define a notion of potential weights, which encode counterfactual decisions a given regression makes to unobserved potential outcomes. If the specification does admit such an interpretation, this diagnostic can find a vector of unit-level treatment assignment probabilities -- which we call an implicit design -- under which the regression estimates a causal effect. This diagnostic also finds the implicit causal effect estimand. Knowing the implicit design and estimand adds transparency, leads to further sanity checks, and opens the door to design-based statistical inference. When applied to regression specifications studied in the causal inference literature, our framework recovers and extends existing theoretical results. When applied to widely-used specifications not covered by existing causal inference literature, our framework generates new theoretical insights. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.21119 |
| By: | Shuping Shi (Macquarie University); Jun Yu (University of Macau); Chen Zhang (University of Macau) |
| Abstract: | This paper introduces a novel and easy-to-implement method for accurately approximating the spectral density of discretely sampled fractional Ornstein-Uhlenbeck (fOU) processes. The method offers a substantial reduction in approximation error, particularly within the rough region of the fractional parameter H 2 (0;0:5). This approximate spectral density has the potential to enhance the performance of estimation methods and hypothesis testing that make use of spectral densities. We introduce the approximate Whittle maximum likelihood (AWML) method for discretely sampled fOU processes, utilising the approximate spectral density, and demonstrate that the AWML estimator exhibits properties of consistency and asymptotic normality when H 2 (0;1), akin to the conventional Whittle maximum likelihood method. Through extensive simulation studies, we show that AWML outperforms existing methods in terms of estimation accuracy in finite samples. We then apply the AWML method to the trading volume of 40 financial assets. Our empirical findings reveal that the estimated Hurst parameters for these assets fall within the range of 0:10 to 0:21, indicating a rough dynamic. |
| Keywords: | Fractional Brownian motion; Fractional Ornstein-Uhlenbeck process; Spectral density; Paxson approximation; Whittle maximum likelihood; Realized volatility |
| JEL: | C13 C22 G10 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:boa:wpaper:202416 |
| By: | Ryan Dew; Nicolas Padilla; Anya Shchetkina |
| Abstract: | Recent years have seen a resurgence in interest in marketing mix models (MMMs), which are aggregate-level models of marketing effectiveness. Often these models incorporate nonlinear effects, and either implicitly or explicitly assume that marketing effectiveness varies over time. In this paper, we show that nonlinear and time-varying effects are often not identifiable from standard marketing mix data: while certain data patterns may be suggestive of nonlinear effects, such patterns may also emerge under simpler models that incorporate dynamics in marketing effectiveness. This lack of identification is problematic because nonlinearities and dynamics suggest fundamentally different optimal marketing allocations. We examine this identification issue through theory and simulations, wherein we explore the exact conditions under which conflation between the two types of models is likely to occur. In doing so, we introduce a flexible Bayesian nonparametric model that allows us to both flexibly simulate and estimate different data-generating processes. We show that conflating the two types of effects is especially likely in the presence of autocorrelated marketing variables, which are common in practice, especially given the widespread use of stock variables to capture long-run effects of advertising. We illustrate these ideas through numerous empirical applications to real-world marketing mix data, showing the prevalence of the conflation issue in practice. Finally, we show how marketers can avoid this conflation, by designing experiments that strategically manipulate spending in ways that pin down model form. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.07678 |
| By: | L. Sanna Stephan |
| Abstract: | Dyadic network formation models have wide applicability in economic research, yet are difficult to estimate in the presence of individual specific effects and in the absence of distributional assumptions regarding the model noise component. The availability of (continuously distributed) individual or link characteristics generally facilitates estimation. Yet, while data on social networks has recently become more abundant, the characteristics of the entities involved in the link may not be measured. Adapting the procedure of \citet{KS}, I propose to use network data alone in a semiparametric estimation of the individual fixed effect coefficients, which carry the interpretation of the individual relative popularity. This entails the possibility to anticipate how a new-coming individual will connect in a pre-existing group. The estimator, needed for its fast convergence, fails to implement the monotonicity assumption regarding the model noise component, thereby potentially reversing the order if the fixed effect coefficients. This and other numerical issues can be conveniently tackled by my novel, data-driven way of normalising the fixed effects, which proves to outperform a conventional standardisation in many cases. I demonstrate that the normalised coefficients converge both at the same rate and to the same limiting distribution as if the true error distribution was known. The cost of semiparametric estimation is thus purely computational, while the potential benefits are large whenever the errors have a strongly convex or strongly concave distribution. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.04552 |
| By: | Kim Christensen; Ulrich Hounyo; Zhi Liu |
| Abstract: | The association between log-price increments of exchange-traded equities, as measured by their spot correlation estimated from high-frequency data, exhibits a pronounced upward-sloping and almost piecewise linear relationship at the intraday horizon. There is notably lower-on average less positive-correlation in the morning than in the afternoon. We develop a nonparametric testing procedure to detect such deterministic variation in a correlation process. The test statistic has a known distribution under the null hypothesis, whereas it diverges under the alternative. It is robust against stochastic correlation. We run a Monte Carlo simulation to discover the finite sample properties of the test statistic, which are close to the large sample predictions, even for small sample sizes and realistic levels of diurnal variation. In an application, we implement the test on a monthly basis for a high-frequency dataset covering the stock market over an extended period. The test leads to rejection of the null most of the time. This suggests diurnal variation in the correlation process is a nontrivial effect in practice. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.02757 |
| By: | Ajay Jasra; Mohamed Maama; Aleksandar Mijatovi\'c |
| Abstract: | In this paper we consider the modeling of measurement error for fund returns data. In particular, given access to a time-series of discretely observed log-returns and the associated maximum over the observation period, we develop a stochastic model which models the true log-returns and maximum via a L\'evy process and the data as a measurement error there-of. The main technical difficulty of trying to infer this model, for instance Bayesian parameter estimation, is that the joint transition density of the return and maximum is seldom known, nor can it be simulated exactly. Based upon the novel stick breaking representation of [12] we provide an approximation of the model. We develop a Markov chain Monte Carlo (MCMC) algorithm to sample from the Bayesian posterior of the approximated posterior and then extend this to a multilevel MCMC method which can reduce the computational cost to approximate posterior expectations, relative to ordinary MCMC. We implement our methodology on several applications including for real data. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.07405 |
| By: | Tompsett, D.;; Vansteelandt, S.;; Grieve, R.;; Petersen, I.; Author Name: Gomes, M.; |
| Abstract: | As longitudinal data becomes more available in many settings, policy makers are increasingly interested in the effect of time-varying treatments (e.g. sustained treatment strategies). In settings such as this, the preferred analysis techniques are the g-methods, however these require the untestable assumption of no unmeasured confounding. Instrumental variable analyses can minimise bias through unmeasured confounding. Of these methods, the Two Stage Least Squares technique is one of the most well used in Econometrics, but it has not been fully extended, and evaluated, in full time-varying settings. This paper proposes a robust two stage least squares method for the econometric evaluation of time-varying treatment. Using a simulation study we found that, unlike standard two stage least squares, it performs relatively well across a wide range of circumstances, including model misspecification. It compares well with recent time-varying instrument approaches via g-estimation. We illustrate the methods in an evaluation of treatment intensification for Type-2 Diabetes Mellitus, exploring the exogeneity in prescribing preferences to operationalise a time-varying instrument. |
| Keywords: | instrumental variable; time-varying; two stage least squares; physician preference; diabetes; |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:yor:hectdg:24/19 |
| By: | Shuo Feng; Ishani Ganguli; Youjin Lee; John Poe; Andrew Ryan; Alyssa Bilinski |
| Abstract: | Difference-in-differences (DiD) is the most popular observational causal inference method in health policy, employed to evaluate the real-world impact of policies and programs. To estimate treatment effects, DiD relies on the "parallel trends assumption", that on average treatment and comparison groups would have had parallel trajectories in the absence of an intervention. Historically, DiD has been considered broadly applicable and straightforward to implement, but recent years have seen rapid advancements in DiD methods. This paper reviews and synthesizes these innovations for medical and health policy researchers. We focus on four topics: (1) assessing the parallel trends assumption in health policy contexts; (2) relaxing the parallel trends assumption when appropriate; (3) employing estimators to account for staggered treatment timing; and (4) conducting robust inference for analyses in which normal-based clustered standard errors are inappropriate. For each, we explain challenges and common pitfalls in traditional DiD and modern methods available to address these issues. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.04617 |
| By: | Abdulnasser Hatemi-J |
| Abstract: | Asymmetric causality tests are increasingly gaining popularity in different scientific fields. This approach corresponds better to reality since logical reasons behind asymmetric behavior exist and need to be considered in empirical investigations. Hatemi-J (2012) introduced the asymmetric causality tests via partial cumulative sums for positive and negative components of the variables operating within the vector autoregressive (VAR) model. However, since the the residuals across the equations in the VAR model are not independent, the ordinary least squares method for estimating the parameters is not efficient. Additionally, asymmetric causality tests mean having different causal parameters (i.e., for positive or negative components), thus, it is crucial to assess not only if these causal parameters are individually statistically significant, but also if their difference is statistically significant. Consequently, tests of difference between estimated causal parameters should explicitly be conducted, which are neglected in the existing literature. The purpose of the current paper is to deal with these issues explicitly. An application is provided, and ten different hypotheses pertinent to the asymmetric causal interaction between two largest financial markets worldwide are efficiently tested within a multivariate setting. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.03137 |
| By: | Patrick Kuiper; Ali Hasan; Wenhao Yang; Yuting Ng; Hoda Bidkhori; Jose Blanchet; Vahid Tarokh |
| Abstract: | The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions built from spatial Poisson point processes. While powerful, these models are only asymptotically valid for large samples. However, since extreme data is by definition scarce, the potential for model misspecification error is inherent to these applications, thus DRO estimators are natural. In order to mitigate over-conservative estimates while enhancing out-of-sample performance, we study DRO estimators informed by semi-parametric max-stable constraints in the space of point processes. We study both tractable convex formulations for some problems of interest (e.g. CVaR) and more general neural network based estimators. Both approaches are validated using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques. Additionally, the proposed method is applied to a real data set of financial returns for comparison to a previous analysis. We established the proposed model as a novel formulation in the multivariate EVT domain, and innovative with respect to performance when compared to relevant alternate proposals. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.00131 |
| By: | Achintya Gopal |
| Abstract: | The use of machine learning for statistical modeling (and thus, generative modeling) has grown in popularity with the proliferation of time series models, text-to-image models, and especially large language models. Fundamentally, the goal of classical factor modeling is statistical modeling of stock returns, and in this work, we explore using deep generative modeling to enhance classical factor models. Prior work has explored the use of deep generative models in order to model hundreds of stocks, leading to accurate risk forecasting and alpha portfolio construction; however, that specific model does not allow for easy factor modeling interpretation in that the factor exposures cannot be deduced. In this work, we introduce NeuralFactors, a novel machine-learning based approach to factor analysis where a neural network outputs factor exposures and factor returns, trained using the same methodology as variational autoencoders. We show that this model outperforms prior approaches both in terms of log-likelihood performance and computational efficiency. Further, we show that this method is competitive to prior work in generating realistic synthetic data, covariance estimation, risk analysis (e.g., value at risk, or VaR, of portfolios), and portfolio optimization. Finally, due to the connection to classical factor analysis, we analyze how the factors our model learns cluster together and show that the factor exposures could be used for embedding stocks. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.01499 |
| By: | Eguren-Martin, Fernando (SPX Capital); Kösem, Sevim (Bank of England); Maia, Guido (Centre for Macroeconomics and London School of Economics); Sokol, Andrej (Bloomberg LP) |
| Abstract: | We propose a novel approach to extract factors from large data sets that maximise covariation with the quantiles of a target distribution of interest. From the data underlying the Chicago Fed’s National Financial Conditions Index, we build targeted financial conditions indices for the quantiles of future US GDP growth. We show that our indices yield considerably better out-of-sample density forecasts than competing models, as well as insights on the importance of individual financial series for different quantiles. Notably, leverage indicators appear to co-move more with the median of the predictive distribution, while credit and risk indicators are more informative about downside risks. |
| Keywords: | Quantile regression; factor analysis; financial conditions indices; GDP-at-risk |
| JEL: | C32 C38 C53 C58 E37 E44 |
| Date: | 2024–08–06 |
| URL: | https://d.repec.org/n?u=RePEc:boe:boeewp:1084 |
| By: | Matthew Read (Reserve Bank of Australia) |
| Abstract: | Policymakers are often interested in the degree to which changes in prices are driven by shocks to supply or demand. One way to estimate the contributions of these shocks is with a structural vector autoregression identified using sign restrictions on the slopes of demand and supply curves. The appeal of this approach is that it relies on uncontroversial assumptions. However, sign restrictions only identify decompositions up to a set. I characterise the conditions under which these sets are informative, examining both historical decompositions (contributions to outcomes) and forecast error variance decompositions (contributions to variances). I use this framework to estimate the contributions of supply and demand shocks to inflation in the United States. While the sign restrictions yield sharp conclusions about the drivers of inflation in some expenditure categories, they tend to yield uninformative decompositions of aggregate inflation. A 'bottom-up' decomposition of aggregate inflation is less informative than a decomposition that uses the aggregate data directly. |
| Keywords: | forecast error variance decomposition; historical decomposition; set identification; sign restrictions; structural vector autoregression |
| JEL: | C32 E31 E32 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:rba:rbardp:rdp2024-05 |
| By: | Ramon de Punder; Timo Dimitriadis; Rutger-Jan Lange |
| Abstract: | Score-driven models have been applied in some 400 published articles over the last decade. Much of this literature cites the optimality result in Blasques et al. (2015), which, roughly, states that sufficiently small score-driven updates are unique in locally reducing the Kullback-Leibler (KL) divergence relative to the true density for every observation. This is at odds with other well-known optimality results; the Kalman filter, for example, is optimal in a mean squared error sense, but may move in the wrong direction for atypical observations. We show that score-driven filters are, similarly, not guaranteed to improve the localized KL divergence at every observation. The seemingly stronger result in Blasques et al. (2015) is due to their use of an improper (localized) scoring rule. Even as a guaranteed improvement for every observation is unattainable, we prove that sufficiently small score-driven updates are unique in reducing the KL divergence relative to the true density in expectation. This positive$-$albeit weaker$-$result justifies the continued use of score-driven models and places their information-theoretic properties on solid footing. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.02391 |
| By: | Michael B. Gordy; Alexander J. McNeil |
| Abstract: | In the spectral backtesting framework of Gordy and McNeil (JBF, 2020) a probability measure on the unit interval is used to weight the quantiles of greatest interest in the validation of forecast models using probability-integral transform (PIT) data. We extend this framework to allow general Lebesgue-Stieltjes kernel measures with unbounded distribution functions, which brings powerful new tests based on truncated location-scale families into the spectral class. Moreover, by considering uniform distribution preserving transformations of PIT values the test framework is generalized to allow tests that are focused on both tails of the forecast distribution. |
| Keywords: | Backtesting; Volatility; Risk management |
| JEL: | C52 G21 G32 |
| Date: | 2024–08–02 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:2024-60 |
| By: | Adan L. Martinez Cruz; Yadira Elizabeth Peralta Torres (Division of Economics, CIDE); Valeria Garcia Olivera |
| Abstract: | The travel cost (TC) method models the number of trips to a recreation site as a function of the costs to reach that site. The single site TC equation is particularly vulnerable to endogeneity since travel costs are chosen by the visitor. This paper suggests a control function approach that breaks the correlation between travel costs and the error term by plugging inferred omitted variables into the TC equation. Inference of omitted variables is carried out on an endogenous free, stated preference equation that, arguably, shares omitted variables with the TC equation. By revisiting the TC and contingent valuation (CV) data analyzed by Fixand Loomis (1998), this paper infers the omitted variables from the CV equation via a finite mixture specification -an inference strategy whose justification resembles the use of heteroscedastic errors to construct instruments as suggested by Lewbel (2012). Results show that not controlling for endogeneity in this particular case produces an overestimation of welfare measures. Importantly, this infer and plug-in strategy is pursuable in a number of contexts beyond recreation demand applications. |
| Keywords: | Travel cost method, endogeneity, stated preference responses, control function |
| JEL: | Q26 C26 C29 |
| Date: | 2024–02 |
| URL: | https://d.repec.org/n?u=RePEc:emc:wpaper:dte632 |
| By: | Gregory Yampolsky; Dhruv Desai; Mingshu Li; Stefano Pasquali; Dhagash Mehta |
| Abstract: | The explainability of black-box machine learning algorithms, commonly known as Explainable Artificial Intelligence (XAI), has become crucial for financial and other regulated industrial applications due to regulatory requirements and the need for transparency in business practices. Among the various paradigms of XAI, Explainable Case-Based Reasoning (XCBR) stands out as a pragmatic approach that elucidates the output of a model by referencing actual examples from the data used to train or test the model. Despite its potential, XCBR has been relatively underexplored for many algorithms such as tree-based models until recently. We start by observing that most XCBR methods are defined based on the distance metric learned by the algorithm. By utilizing a recently proposed technique to extract the distance metric learned by Random Forests (RFs), which is both geometry- and accuracy-preserving, we investigate various XCBR methods. These methods amount to identify special points from the training datasets, such as prototypes, critics, counter-factuals, and semi-factuals, to explain the predictions for a given query of the RF. We evaluate these special points using various evaluation metrics to assess their explanatory power and effectiveness. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.06679 |