Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications: Volume 45B

The authors analyze a model for N different measurements of a persistent latent time series when measurement errors are mean-reverting, which implies a common trend among measurements. The authors study the consequences of overdifferencing, finding potentially large biases in maximum likelihood estimators (MLE) of the dynamics parameters and reductions in the precision of smoothed estimates of the latent variable, especially for multiperiod objects such as quinquennial growth rates. The authors also develop an R² measure of common trend observability that determines the severity of misspecification. Finally, the authors apply their framework to US quarterly data on GDE and GDI, obtaining an improved aggregate output measure.

The authors propose novel tests for the detection of Markov switching deviations from forecast rationality. Existing forecast rationality tests either focus on constant deviations from forecast rationality over the full sample or are constructed to detect smooth deviations based on non-parametric techniques. In contrast, the proposed tests are parametric and have an advantage in detecting abrupt departures from unbiasedness and efficiency, which the authors demonstrate with Monte Carlo simulations. Using the proposed tests, the authors investigate whether Blue Chip Financial Forecasts (BCFF) for the Federal Funds Rate (FFR) are unbiased. The tests find evidence of a state-dependent bias: forecasters tend to systematically overpredict interest rates during periods of monetary easing, while the forecasts are unbiased otherwise. The authors show that a similar state-dependent bias is also present in market-based forecasts of interest rates, but not in the forecasts of real GDP growth and GDP deflator-based inflation. The results emphasize the special role played by monetary policy in shaping interest rate expectations above and beyond macroeconomic fundamentals.

Oil market VAR models have become the standard tool for understanding the evolution of the real price of oil and its impact on the macro economy. As this literature has expanded at a rapid pace, it has become increasingly difficult for mainstream economists to understand the differences between alternative oil market models, let alone the basis for the sometimes divergent conclusions reached in the literature. The purpose of this survey is to provide a guide to this literature. Our focus is on the econometric foundations of the analysis of oil market models with special attention to the identifying assumptions and methods of inference.

This chapter studies the dynamic responses of the conditional quantiles and their applications in macroeconomics and finance. The authors build a multi-equation autoregressive conditional quantile model and propose a new construction of quantile impulse response functions (QIRFs). The tool set of QIRFs provides detailed distributional evolution of an outcome variable to economic shocks. The authors show the left tail of economic activity is the most responsive to monetary policy and financial shocks. The impacts of the shocks on Growth-at-Risk (the 5% quantile of economic activity) during the Global Financial Crisis are assessed. The authors also examine how the economy responds to a hypothetical financial distress scenario.

This chapter proposes a nonparametric estimator of the risk neutral density (RND) based on cross-sectional European option prices. The authors recast the arbitrage-free equation for option pricing as a functional linear regression model where the regressor is a curve and the independent variable is a scalar corresponding to the option price. Then, the authors show that the RND can be viewed as the solution of an ill-posed integral equation. To estimate the RND, the authors use an iterative method called Landweber-Fridman (LF). Then, the authors establish the consistency and asymptotic normality of the estimated RND. These results can be used to construct a confidence interval around the curve. Finally, some Monte Carlo simulations and application to the S&P 500 options show that this method performs well compared to alternative methods.

The time series of the federal funds rate has recently been extended back to 1928, now including several episodes during which interest rates remained near the lower bound of zero. This series is analyzed, using the method of indirect inference, by applying recent research on bounded time series to estimate a set of bounded parametric diffusion models. This combination uncouples the specification of the bounds from the law of motion. Although Louis Bachelier was the first to use arithmetic Brownian motion to model financial time series, he has often been criticized for this proposal, since the process can take on negative values. Most researchers favor processes such as geometric Brownian motion (GBM), which remains positive. Under this framework, Bachelier's proposal remains valid when specified with bounds and is shown to compare favorably when modeling the federal funds rate.

Rapid stock market growth without real economic back-up has led to the 2015 Chinese Stock Market Crash with thousands of stocks hitting the down limit simultaneously multiple times. The authors provide a detailed analysis of structural breaks in heavy-tailedness and asymmetry properties of returns in Chinese A-share markets due to the crash using recently proposed robust approaches to tail index inference. The empirical analysis points out to heavy-tailedness properties often implying possibly infinite second moments and also focuses on gain/loss asymmetry in the tails of daily returns on individual stocks. The authors further present an analysis of the main determinants of heavy-tailedness in Chinese financial markets. It points out to liquidity and company size as being the most important factors affecting the returns’ heavy-tailedness properties. At the same time, the authors do not observe statistically significant differences in tail indices of the returns on A-shares and the coefficients on factors affecting them in the pre-crisis and post-crisis periods.

This chapter aims at shedding light upon how transforming or detrending a series can substantially impact predictions of mixed causal-noncausal (MAR) models, namely dynamic processes that depend not only on their lags but also on their leads. MAR models have been successfully implemented on commodity prices as they allow to generate nonlinear features such as locally explosive episodes (denoted here as bubbles) in a strictly stationary setting. The authors consider multiple detrending methods and investigate, using Monte Carlo simulations, to what extent they preserve the bubble patterns observed in the raw data. MAR models relies on the dynamics observed in the series alone and does not require economical background to construct a structural model, which can sometimes be intricate to specify or which may lack parsimony. The authors investigate oil prices and estimate probabilities of crashes before and during the first 2020 wave of the COVID-19 pandemic. The authors consider three different mechanical detrending methods and compare them to a detrending performed using the level of strategic petroleum reserves.

The authors develop a novel forecast combination approach based on the order statistics of individual predictability from panel data forecasts. To this end, the authors define the notion of forecast depth, which provides a ranking among different forecasts based on their normalized forecast errors during the training period. The forecast combination is in the form of a depth-weighted trimmed mean. The authors derive the limiting distribution of the depth-weighted forecast combination, based on which the authors can readily construct prediction intervals. Using this novel forecast combination, the authors predict the national level of new COVID-19 cases in the United States and compare it with other approaches including the ensemble forecast from the Centers for Disease Control and Prevention (CDC). The authors find that the depth-weighted forecast combination yields more accurate and robust predictions compared with other popular forecast combinations and reports much narrower prediction intervals.

The authors discuss the econometric underpinnings of Barro (2006)'s defense of the rare disaster model as a way to bring back an asset pricing model “into the right ballpark for explaining the equity-premium and related asset-market puzzles.” Arbitrarily low-probability economic disasters can restore the validity of model-implied moment conditions only if the amplitude of disasters may be arbitrary large in due proportion. The authors prove an impossibility theorem that in case of potentially unbounded disasters, there is no such thing as a population empirical likelihood (EL)-based model-implied probability distribution. That is, one cannot identify some belief distortions for which the EL-based implied probabilities in sample, as computed by Julliard and Ghosh (2012), could be a consistent estimator. This may lead to consider alternative statistical discrepancy measures to avoid the problem with EL. Indeed, the authors prove that, under sufficient integrability conditions, power divergence Cressie-Read measures with positive power coefficients properly define a unique population model-implied probability measure. However, when this computation is useful because the reference asset pricing model is misspecified, each power divergence will deliver different model-implied beliefs distortion. One way to provide economic underpinnings to the choice of a particular belief distortion is to see it as the endogenous result of investor's choice when optimizing a recursive multiple-priors utility a la Chen and Epstein (2002). Jeong et al. (2015)'s econometric study confirms that this way of accommodating ambiguity aversion may help to address the Equity Premium puzzle.

In this chapter, the authors contribute toward building a better understanding of farmers’ responses to behavioral drivers of land-use decision by establishing an alternative analytical procedure, which can overcome various drawbacks suffered by methods currently used in existing studies. Firstly, our procedure makes use of spatially high-resolution data, so that idiosyncratic effects of physical environment drivers, e.g., soil textures, can be explicitly modeled. Secondly, we address the well-known censored data problem, which often hinders a successful analysis of land-use shares. Thirdly, we incorporate spatial error dependence (SED) and heterogeneity in order to obtain efficiency gain and a more accurate formulation of variances for the parameter estimates. Finally, the authors reduce the computational burden and improve estimation accuracy by introducing an alternative generalized method of moments (GMM)–quasi maximum likelihood (QML) hybrid estimation procedure. The authors apply the newly proposed procedure to spatially high-resolution data in England and found that, by taking these features into consideration, the authors are able to formulate conclusions about causal effects of climatic and physical environment, and environmental policy on land-use shares that differ significantly from those made based on methods that are currently used in the literature. Moreover, the authors show that our method enables derivation of a more effective predictor of the land-use shares, which is utterly useful from the policy-making point of view.

Transient climate sensitivity relates total climate forcings from anthropogenic and other sources to surface temperature. Global transient climate sensitivity is well studied, as are the related concepts of equilibrium climate sensitivity (ECS) and transient climate response (TCR), but spatially disaggregated local climate sensitivity (LCS) is less so. An energy balance model (EBM) and an easily implemented semiparametric statistical approach are proposed to estimate LCS using the historical record and to assess its contribution to global transient climate sensitivity. Results suggest that areas dominated by ocean tend to import energy, they are relatively more sensitive to forcings, but they warm more slowly than areas dominated by land. Economic implications are discussed.

The authors consider the quasi maximum likelihood (MLE) estimation of dynamic panel models with interactive effects based on the Ahn et al. (2001, 2013) quasi-differencing methods to remove the interactive effects. The authors show that the quasi-difference MLE (QDMLE) over time is inconsistent when N→∞ whether T is fixed or goes to infinity. On the other hand, the QDMLE is consistent and asymptotically unbiased if the difference is taken over individuals when T is large whether N is fixed or large. Monte Carlo studies are conducted to compare the performance of the QDMLE using different quasi-difference methods.

We study the informational content of factor structures in discrete triangular systems. Factor structures have been employed in a variety of settings in cross-sectional and panel data models, and in this chapter we formally quantify their identifying power in a bivariate system often employed in the treatment effects literature. Our main findings are that imposing a factor structure yields point-identification of parameters of interest, such as the coefficient associated with the endogenous regressor in the outcome equation, under weaker assumptions than usually required in these models. In particular, we show that a “non-standard” exclusion restriction that requires an explanatory variable in the outcome equation to be excluded from the treatment equation is no longer necessary for identification, even in cases where all of the regressors from the outcome equation are discrete. We also establish identification of the coefficient of the endogenous regressor in models with more general factor structures, in situations where one has access to at least two continuous measurements of the common factor.

Advances in Econometrics is a series of research volumes first published in 1982 by JAI Press. The authors present an update to the history of the Advances in Econometrics series. The initial history, published in 2012 for the 30th Anniversary Volume, describes key events in the history of the series and provides information about key authors and contributors to Advances in Econometrics. The authors update the original history and discuss significant changes that have occurred since 2012. These changes include the addition of five new Senior Co-Editors, seven new AIE Fellows, an expansion of the AIE conferences throughout the United States and abroad, and the increase in the number of citations for the series from 7,473 in 2012 to over 25,000 by 2022.