Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part A: Volume 40A

Many recent chapters have investigated whether data from internet search engines such as Google can help improve nowcasts or short-term forecasts of macroeconomic variables. These chapters construct variables based on Google searches and use them as explanatory variables in regression models. We add to this literature by nowcasting using dynamic model selection (DMS) methods which allow for model switching between time-varying parameter regression models. This is potentially useful in an environment of coefficient instability and over-parameterization which can arise when forecasting with Google variables. We extend the DMS methodology by allowing for the model switching to be controlled by the Google variables through what we call “Google probabilities”: instead of using Google variables as regressors, we allow them to determine which nowcasting model should be used at each point in time. In an empirical exercise involving nine major monthly US macroeconomic variables, we find DMS methods to provide large improvements in nowcasting. Our use of Google model probabilities within DMS often performs better than conventional DMS methods.

This chapter investigates the behavior of Reddit’s news subreddit users and the relationship between their sentiment on exchange rates. Using graphical models and natural language processing, hidden online communities among Reddit users are discovered. The data set used in this project is a mixture of text and categorical data from Reddit’s news subreddit. These data include the titles of the news pages, as well as a few user characteristics, in addition to users’ comments. This data set is an excellent resource to study user reaction to news since their comments are directly linked to the webpage contents. The model considered in this chapter is a hierarchical mixture model which is a generative model that detects overlapping networks using the sentiment from the user generated content. The advantage of this model is that the communities (or groups) are assumed to follow a Chinese restaurant process, and therefore it can automatically detect and cluster the communities. The hidden variables and the hyperparameters for this model are obtained using Gibbs sampling.

Jeliazkov and Poirier (2008) analyze the daily incidence of violence during the Second Intifada in a statistical way using an analytical Bayesian implementation of a second-order discrete Markov process. We tackle the same data and modeling problem from our perspective as cognitive scientists. First, we propose a psychological model of violence, based on a latent psychological construct we call “build up” that controls the retaliatory and repetitive violent behavior by both sides in the conflict. Build up is based on a social memory of recent violence and generates the probability and intensity of current violence. Our psychological model is implemented as a generative probabilistic graphical model, which allows for fully Bayesian inference using computational methods. We show that our model is both descriptively adequate, based on posterior predictive checks, and has good predictive performance. We then present a series of results that show how inferences based on the model can provide insight into the nature of the conflict. These inferences consider the base rates of violence in different periods of the Second Intifada, the nature of the social memory for recent violence, and the way repetitive versus retaliatory violent behavior affects each side in the conflict. Finally, we discuss possible extensions of our model and draw conclusions about the potential theoretical and methodological advantages of treating societal conflict as a cognitive modeling problem.

We develop a Bayesian approach for modeling brain activation and connectivity from functional magnetic resonance image (fMRI) data. Our approach simultaneously estimates local hemodynamic response functions (HRFs) and activation parameters, as well as global effective and functional connectivity parameters. Existing methods assume identical HRFs across brain regions, which may lead to erroneous conclusions in inferring activation and connectivity patterns. Our approach addresses this limitation by estimating region-specific HRFs. Additionally, it enables neuroscientists to compare effective connectivity networks for different experimental conditions. Furthermore, the use of spike and slab priors on the connectivity parameters allows us to directly select significant effective connectivities in a given network.

We include a simulation study that demonstrates that, compared to the standard generalized linear model (GLM) approach, our model generally has higher power and lower type I error and bias than the GLM approach, and it also has the ability to capture condition-specific connectivities. We applied our approach to a dataset from a stroke study and found different effective connectivity patterns for task and rest conditions in certain brain regions of interest (ROIs).

Standard estimation of ARMA models in which the AR and MA roots nearly cancel, so that individual coefficients are only weakly identified, often produces inferential ranges for individual coefficients that give a spurious appearance of accuracy. We remedy this problem with a model that uses a simple mixture prior. The posterior mixing probability is derived using Bayesian methods, but we show that the method works well in both Bayesian and frequentist setups. In particular, we show that our mixture procedure weights standard results heavily when given data from a well-identified ARMA model (which does not exhibit near root cancellation) and weights heavily an uninformative inferential region when given data from a weakly-identified ARMA model (with near root cancellation). When our procedure is applied to a well-identified process the investigator gets the “usual results,” so there is no important statistical cost to using our procedure. On the other hand, when our procedure is applied to a weakly identified process, the investigator learns that the data tell us little about the parameters – and is thus protected against making spurious inferences. We recommend that mixture models be computed routinely when inference about ARMA coefficients is of interest.

Statistical inference (estimation and testing) for the stochastic volatility (SV) model Taylor (1982, 1986) is challenging, especially likelihood-based methods which are difficult to apply due to the presence of latent variables. The existing methods are either computationally costly and/or inefficient. In this paper, we propose computationally simple estimators for the SV model, which are at the same time highly efficient. The proposed class of estimators uses a small number of moment equations derived from an ARMA representation associated with the SV model, along with the possibility of using “winsorization” to improve stability and efficiency. We call these ARMA-SV estimators. Closed-form expressions for ARMA-SV estimators are obtained, and no numerical optimization procedure or choice of initial parameter values is required. The asymptotic distributional theory of the proposed estimators is studied. Due to their computational simplicity, the ARMA-SV estimators allow one to make reliable – even exact – simulation-based inference, through the application of Monte Carlo (MC) test or bootstrap methods. We compare them in a simulation experiment with a wide array of alternative estimation methods, in terms of bias, root mean square error and computation time. In addition to confirming the enormous computational advantage of the proposed estimators, the results show that ARMA-SV estimators match (or exceed) alternative estimators in terms of precision, including the widely used Bayesian estimator. The proposed methods are applied to daily observations on the returns for three major stock prices (Coca-Cola, Walmart, Ford) and the S&P Composite Price Index (2000–2017). The results confirm the presence of stochastic volatility with strong persistence.

Marcet, and Nicolini (2003) and Milani (2014) demonstrate within the adaptive learning framework that a forecast error-based endogenous gain mechanism that switches between constant gain and decreasing gain may be more effective than the former alone in explaining time-varying parameters. In this paper, we propose an alternative endogenous gain scheme, henceforth referred to as CEG, that is based on recent coefficient estimates by the economic agents. We then show within a controlled simulation environment that CEG outperforms both constant gain learning as well as the aforementioned switching gain algorithm in terms of mean squared forecast errors (MSFE). In addition, we demonstrate within the context of a New Keynesian model that forecasts generated under CEG perform better in certain dimensions, particularly for inflation data, compared to constant gain learning. Combined with the fact that the proposed gain scheme ports easily to existing likelihood based inferential techniques used in constant gain learning, it is readily applicable to richer, more dynamic economic models.

Vector autoregressions (VAR) combined with Minnesota-type priors are widely used for macroeconomic forecasting. The fact that strong but sensible priors can substantially improve forecast performance implies VAR forecasts are sensitive to prior hyperparameters. But the nature of this sensitivity is seldom investigated. We develop a general method based on Automatic Differentiation to systematically compute the sensitivities of forecasts – both points and intervals – with respect to any prior hyperparameters. In a forecasting exercise using US data, we find that forecasts are relatively sensitive to the strength of shrinkage for the VAR coefficients, but they are not much affected by the prior mean of the error covariance matrix or the strength of shrinkage for the intercepts.

This chapter examines the asymptotic properties of the Stein-type shrinkage combined (averaging) estimation of panel data models. We introduce a combined estimation when the fixed effects (FE) estimator is inconsistent due to endogeneity arising from the correlated common effects in the regression error and regressors. In this case, the FE estimator and the CCEP estimator of Pesaran (2006) are combined. This can be viewed as the panel data model version of the shrinkage to combine the OLS and 2SLS estimators as the CCEP estimator is a 2SLS or control function estimator that controls for the endogeneity arising from the correlated common effects. The asymptotic theory, Monte Carlo simulation, and empirical applications are presented. According to our calculation of the asymptotic risk, the Stein-like shrinkage estimator is more efficient estimation than the CCEP estimator.

This chapter develops a predictive approach to Granger causality (GC) testing that utilizes k -fold cross-validation and posterior simulation to perform out-of-sample testing. A Monte Carlo study indicates that the cross-validation predictive procedure has improved power in comparison to previously available out-of-sample testing procedures, matching the performance of the in-sample F-test while retaining the credibility of post- sample inference. An empirical application to the Phillips curve is provided evaluating the evidence on GC between inflation and unemployment rates.

This study provides new evidence on the effect of compulsory schooling laws on educational attainment and earnings. First, we re-examine the effect of compulsory schooling laws for cohorts born between 1900 and 1964 (“older cohorts”) using newly available data that match administrative earnings records with the survey data. Second, we provide among the first evidence on cohorts born between 1977 and 1996 (“younger cohorts”). Our findings suggest that compulsory schooling laws increased the educational attainment of older cohorts, but had no economically significant effect on the educational attainment of younger cohorts. We are unable to find consistent evidence that compulsory schooling laws increased the earnings of older cohorts – a finding which adds to growing evidence that compulsory schooling laws are less beneficial than earlier studies suggest.