Sources Of Misspecification Research Articles

A Simple Correction for Misspecification in Trend-Cycle Decompositions with an Application to Estimating r*

We propose a simple correction for misspecification in trend-cycle decompositions when the stochastic trend is assumed to be a random walk process but the estimated trend displays some serial correlation in first differences. Possible sources of misspecification that would otherwise be hard to detect and correct for include a small amount of measurement error, omitted variables, or minor approximation errors in model dynamics when estimating trend. Our proposed correction is conducted via application of a univariate Beveridge-Nelson decomposition to the preliminary estimated trend and we show with Monte Carlo analysis that our approach can work as well as if the original model used to estimate trend were correctly specified. We demonstrate the empirical relevance of the correction in an application to estimating r* as the trend of a risk-free short-term real interest rate. We find that our corrected estimate of r* is considerably smoother than the preliminary estimate from a multivariate Beveridge-Nelson decomposition based on a vector error correction model, consistent with the presence of at least a small amount of measurement error in some of the variables included in the multivariate model.

Boundaries of Differentiated Product Markets and Retailer Pricing

This paper studies the effects of misspecified boundaries of competition on optimal retail pricing using store-level supermarket scanner data. We focus on two types of misspecification: (i) misspecification of the demand estimation problem, which can arise from either defining the product market to be too narrow or specifying an overly restrictive model of demand; (ii) misspecification of the retailer's decision problem, which can arise from the retailer separately optimizing prices in each category but failing to account for, and thus internalize, cross-category effects. Both sources of misspecification are relevant in differentiated product markets where goods are broadly related but in ways that may not be immediately a priori. Quantifying the costs associated with either form of misspecification is challenging because it requires a flexible yet valid demand system. To this end, we take a nonparametric approach to estimating a multi-category demand system that imposes minimal restrictions on the sign/magnitude of cross-price effects and also satisfies key properties required by economic theory. Our first set of empirical results is descriptive. We use data across nine diverse product groups to show that cross-category effects exists and are often nuanced in their sign and magnitude. That is, many categories are neither obvious substitutes' nor obvious We then zoom in on refrigerated juices and estimate demand nonparametrically across five juice categories where we find empirical support for a flexible model that can accommodate both substitutes and complements. We solve for optimal prices under both sources of misspecification and estimate profit losses to be in the 5-15% range.

Optimal Filter Approximations for Latent Long Memory Stochastic Volatility

Estimating volatility is a challenging because it is latent, and proxies may not be efficient. Alternative to using the proxies in the conventional time series, there are attempts to filter the latent variable conditional on the realized observations. This paper extends the work of state space method and Markov switching model to approximate long memory stochastic volatility. This encompasses incorporating Whittle approximation to the procedure of conditionally Gaussian observed Markov switching model (CGOMSM) for parameter estimation. Monte Carlo simulations are used to examine the performances of these approaches in terms of their accuracy in parameter estimation as well as the filter estimates. The robustness of these approaches is tested by including some sources of misspecification in the data generating process. It emerges that even in moderately fat-tailed innovations, CGOMSM is efficient as long as the long-range effect is not too large. Due to the consistency in Whittle approximation, the computation time of CGOMSM is significantly shorter, especially when the time series is contaminated with level shifts.

Flexible cutoff values for fit indices in the evaluation of structural equation models

Researchers often struggle when applying ‘golden rules of thumb’ to evaluate structural equation models. This paper questions the notion of universal thresholds and calls for adjusted orientation points that account for sample size, factor loadings, the number of latent variables and indicators, as well as data (non-)normality. This research explores the need for flexible cutoffs and their accuracy in single- and two-index strategies. Study 1 reveals that many indices are biased; thus, rigid cutoffs can become imprecise. Flexible cutoff values are shown to compensate for the unique distorting patterns and prove to be particularly beneficial for moderate misspecification. Study 2 sheds further light on this ‘gray’ area of misspecification and disentangles the different sources of misspecification. Study 3 finally investigates the performance of flexible cutoffs for non-normal data. Having substantiated higher performance for flexible reference values, this paper provides to managers an easy-to-use tool that facilitates the determination of adequate cutoffs.

Portfolio Liquidation and Ambiguity Aversion

We consider an optimal execution problem where an agent holds a position in an asset which must be liquidated (using limit orders) before a terminal horizon. Beginning with a standard model for the trading dynamics, we analyse how the acknowledgement of model misspecification affects the agent's optimal trading strategy. The three possible sources of misspecification in this context are: (i) the arrival rate of market orders, (ii) the fill probability of limit orders, and (iii) the dynamics of the asset price. We show that ambiguity aversion with respect to each factor of the model has a similar effect on the optimal strategy, but the magnitude of the effect depends on time and inventory position in different ways depending on the source of uncertainty. In addition we allow the agent to employ market orders to further increase the strategy's profitability and show the effect of ambiguity aversion on the shape of the optimal impulse region. In some cases we have a closed-form expression for the optimal trading strategy which significantly enhances the efficiency in which the strategy can be executed in real time.

Automobile Ownership Model That Incorporates Captivity and Proximate Covariance

The modeling effort in this paper is distinguished from previous models of automobile ownership primarily by the use of the dogit ordered generalized extreme value (DOGEV) model rather than the commonly used multinomial logit and ordered probit or logit models. In comparison with other models, the DOGEV model has two distinct features. First, it recognizes the ordinal nature of automobile ownership levels (zero cars, one car, two cars, and three or more cars) by allowing those levels to be correlated in close proximity (i.e., proximate covariance: ownership levels that are close to each other in the ordering have error terms that are correlated). Second, the DOGEV model allows a household’s automobile ownership choice to be captive or constrained to a particular automobile ownership level and, therefore, avoids the potential misspecification of the choice sets for individual households. The modeling approach is based on a behavioral analysis that explains the factors that influence household automobile ownership decisions in the New York City area, a highly urbanized environment. The estimation results uncover the sensitivity of household automobile ownership choices to transit accessibility, urban forms, traffic congestion, parking costs and availability, and the level of access to opportunity sites through nonmotorized transportation. The results also show that New York City data of automobile ownership are well analyzed by the DOGEV model. Particularly, evidence of captivity and ordering (proximate covariance) in the choice set may suggest an additional source of misspecification in the existing automobile ownership literature.

Relaxing Rational Expectations

The assumption of rational expectations is potentially a serious source of misspecification in DSGE models. Many recent theories of expectations formation have relaxed rational expectations and improved the predictive properties of benchmark macroeconomic models. Problematically, the space of possible theoretical deviations from rational expectations is very large, especially since the aggregate consequences of deviations from rational expectations in equilibrium may not be directly measurable using existing surveys of expectations. This paper provides evidence on which small reduced-form state-contingent deviations from rational expectations yield the most improvement in replicating features of macroeconomic time series, and which aspects of model misspecification are and are not ameliorated by these small deviations from rational expectations. The findings: a) The data favor deviations from rational expectations among firms in which they over-estimate the persistence of inflation. b) Relaxing rational expectations in a New Keynesian model partially substitutes for the additional structural mechanisms in the larger Smets Wouters (2007) model. Relaxing rational expectations within the Smets Wouters (2007) model improves that model’s ability to reproduce some of the spectral coherencies between output growth, investment growth, and labor supply. The mechanism is a combination of shocks to beliefs themselves and the role that deviations from rational expectations have in changing the propagation of other shocks.

Do inflation targets anchor inflation expectations?

We suggest a simple test of whether an inflation target anchors private-sector inflation expectations. The test is easy to compute and it is robust to various sources of misspecification. The test may be a useful alternative to dispersion measures commonly studied in research on inflation targeting. Using data for 22 inflation targeting countries, we find for many countries that the forecasters scatter their inflation forecasts away from the inflation target. We account for the endogeneity of inflation targets, we study the variability of our finding across countries and across time, and we study to which extent our results depend on the level and variability of inflation targets.

Diagnosing affine models of options pricing: Evidence from VIX

Affine jump-diffusion models have been the mainstream in options pricing because of their analytical tractability. Popular affine jump-diffusion models, however, are still unsatisfactory in describing the options data and the problem is often attributed to the diffusion term of the unobserved state variables. Using prices of variance-swaps (i.e., squared VIX) implied from options prices, we provide fresh evidence regarding the misspecification of affine jump-diffusion models, as variance-swap prices are affine functions of the state variables in a broader class of models that do not restrict the diffusion term of the state variables. We apply the nonparametric methodology used by Aït-Sahalia (1996b), supplemented with bootstrap tests and other parametric tests, to the S&P 500 index options data from January 1996 to September 2008. We find that, while the affine diffusion term of the state variables may contribute to the misspecification as the literature has suggested, the affine drift of the state variables, jump intensities, and risk premiums are also sources of misspecification.

POOLING VERSUS MODEL SELECTION FOR NOWCASTING GDP WITH MANY PREDICTORS: EMPIRICAL EVIDENCE FOR SIX INDUSTRIALIZED COUNTRIES

SUMMARYThis paper discusses pooling versus model selection for nowcasting with large datasets in the presence of model uncertainty. In practice, nowcasting a low‐frequency variable with a large number of high‐frequency indicators should account for at least two data irregularities: (i) unbalanced data with missing observations at the end of the sample due to publication delays; and (ii) different sampling frequencies of the data. Two model classes suited in this context are factor models based on large datasets and mixed‐data sampling (MIDAS) regressions with few predictors. The specification of these models requires several choices related to, amongst other things, the factor estimation method and the number of factors, lag length and indicator selection. Thus there are many sources of misspecification when selecting a particular model, and an alternative would be pooling over a large set of different model specifications. We evaluate the relative performance of pooling and model selection for nowcasting quarterly GDP for six large industrialized countries. We find that the nowcast performance of single models varies considerably over time, in line with the forecasting literature. Model selection based on sequential application of information criteria can outperform benchmarks. However, the results highly depend on the selection method chosen. In contrast, pooling of nowcast models provides an overall very stable nowcast performance over time. Copyright © 2012 John Wiley & Sons, Ltd.

Over‐education and spatial flexibility: New evidence from Italian survey data

AbstractThis paper addresses the effect of workers' spatial flexibility (commuting and migration) on their probability of being over‐educated. The empirical analysis deals with two possible sources of misspecification: the endogeneity of migration and the omission of relevant job characteristics. It also controls for area and personal characteristics. Results show that commuting is positively correlated with the quality of the education‐job match. However, analysis does not support the conventional wisdom that migration unambiguously reduces over‐education. It seems fair to conclude that the link between migration and over‐education remains unclear and that further research is needed in order to better ground policy prescriptions.

When Long Memory Meets the Kalman Filter: A Comparative Study

The finite sample properties of the state space methods applied to long memory time series are analyzed through Monte Carlo simulations. The state space setup allows to introduce a novel modeling approach in the long memory framework, which directly tackles measurement errors and random level shifts. Missing values and several alternative sources of misspecification are also considered. It emerges that the state space methodology provides a valuable alternative for the estimation of the long memory models, under different data generating processes, which are common in financial and economic series. Two empirical applications highlight the practical usefulness of the proposed state space methods.

Assessing parametric misspecification and heterogeneity in growth regression

A fully nonparametric analysis is applied to address the problems of nonlinearity and heterogeneity in classical growth regression models using original data from seminal contributions in this field. Nonparametric specification tests and in-sample goodness-of-fit measures, as well as cross-validation based out-of-sample measures provide considerable evidence for parametric misspecification and a superior performance of a nonparametric model, despite the small sample size. In contrast to recent contributions identifying heterogeneity as the primal source of misspecification, a formal and graphical analysis does not reveal evidence for heterogeneity in a parametric and nonparametric quantile regression framework.

Confirmatory Factor Analysis of the Long and Short Forms of the Worry Domains Questionnaire

The Worry Domains Questionnaire was proposed as a measure of both pathological and nonpathological worry, and assesses the frequency of worrying about five different domains: relationships, lack of confidence, aimless future, work, and financial. The present study analyzed the factor structure of the long and short forms of the WDQ (WDQ and WDQ-SF, respectively) through confirmatory factor analysis in a sample of 262 students (M age = 21.8; SD = 2.6; 86.3% females). While the goodness-of-fit indices did not provide support for the WDQ, good fit indices were found for the WDQ-SF. Furthermore, no source of misspecification was identified, thus, supporting the factorial validity of the WDQ-SF scale. Significant positive correlations between the WDQ-SF and its subscales with worry (PSWQ), anxiety (STAI-T), and depression (BDI) were found. The internal consistency was good for the total scale and for the subscales. This work provides support for the use of the WDQ-SF, and potential uses for research and clinical purposes are discussed.

Asset Pricing Using Partially Misspecified Models

This paper studies a robust pricing method using a misspecified model. It is particularly suited if the available model is multi-dimensional (which is increasingly popular in economics and finance), and possibly has good quality along some dimensions of the state variable yet poor quality along other dimensions. Application to the pricing of Treasury options shows a pricing error reduction of over 30% relative to either parametric or nonparametric prices (both in sample and out of the sample), and suggests that the cheapest-to-deliver practice is an important source of misspecification.

Robust monetary policy in a small open economy

Abstract We study how a central bank in a small open economy should conduct monetary policy if it fears that its model is misspecified. Using a new-Keynesian model of a small open economy, we solve analytically for the optimal robust policy rule and the equilibrium dynamics, and we separately analyze the consequences of central bank robustness against misspecification concerning the determination of inflation, output, and the exchange rate. We show that an increase in the preference for robustness makes the central bank respond more aggressively or more cautiously to shocks, depending on the type of shock and the source of misspecification.

A Quasi Maximum Likelihood Approach for Large Approximate Dynamic Factor Models

This paper considers quasi-maximum likelihood estimations of a dynamic approximate factor model when the panel of time series is large. Maximum likelihood is analyzed under different sources of misspecification: omitted serial correlation of the observations and cross-sectional correlation of the idiosyncratic components. It is shown that the effects of misspecification on the estimation of the common factors is negligible for large sample size (T) and the cross-sectional dimension (n). The estimator is feasible when n is large and easily implementable using the Kalman smoother and the EM algorithm as in traditional factor analysis. Simulation results illustrate what are the empirical conditions in which we can expect improvement with respect to simple principle components considered by Bai (2003), Bai and Ng (2002), Forni, Hallin, Lippi, and Reichlin (2000, 2005b), Stock and Watson (2002a,b).

Robust Monetary Policy in a Small Open Economy

This paper studies how a central bank's preference for robustness against model misspecification affects the design of monetary policy in a New-Keynesian model of a small open economy. Due to the simple model structure, we are able to solve analytically for the optimal robust policy rule, and we separately analyze the effects of robustness against misspecification concerning the determination of inflation, output and the exchange rate. We show that an increased central bank preference for robustness makes monetary policy respond more aggressively or more cautiously to shocks, depending on the type of shock and the source of misspecification.

Approximations, Proxies, and Conditional Pricing Models

It is common in empirical tests of conditional asset pricing models to approximate conditioning information using linear functions in observable variables. This practice introduces two potential sources of misspecification into model tests: (i) the observable variables are proxies for the true state variables, and (ii) the linear structure of conditioning may ignore economically significant nonlinearities in the underlying model. We examine the extent of misspecification error created by this approach in a simple economy in which the level of the short rate and the Sharpe ratio on a well-diversified portfolio serve as the two (latent) state variables. In this setting, some of the conditional moments and risk premiums are nonlinear -- but this nonlinearity is not extreme. After calibrating the model to the excess returns to size- and book-to-market sorted portfolios, we examine returns simulated from the model. We find that the proxy problem appears to be more severe than the bias induced by the linear approximation to conditioning information.

Avoiding Nash inflation: Bayesian and robust responses to model uncertainty

We examine learning, model misspecification, and robust policy responses to misspecification in a quasi-real-time environment. The laboratory for the analysis is the Sargent [The Conquest of American Inflation, Princeton Univ. Press, Princeton, NJ, 1999] explanation for the origins of inflation in the 1970s and the subsequent disinflation. Three robust policy rules are derived that differ according to the extent that misspecification is taken as a parametric phenomenon. These responses to drifting estimated parameters and apparent misspecification are compared to the certainty-equivalent case studied by Sargent. We find gains from utilizing robust approaches to monetary policy design, but only when the approach to robustness is carefully tailored to the problem at hand. In the least parametric approach, the medicine of robust control turns out to be too potent for the disease of misspecification. In the most parametric approach, the response to misspecification is too weak and too misdirected to be of help. But when the robust approach to policy is narrowly directed in the correct location, it can avoid Nash inflation and improve social welfare. It follows that agnosticism regarding the sources of misspecification has its pitfalls. We also find that Sargent's story for the rise of inflation of the 1970s and its subsequent decline in the 1980s is robust to most ways of relaxing a strong assumption in the original work.