Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model

A simultaneous confidence band provides a variety of inferences on the unknown components of a regression model. There are several recent papers using confidence bands for various inferential purposes; see for example, Sun et al. (1999) , Spurrier (1999) , Al‐Saidy et al. (2003) , Liu et al. (2004) , Bhargava & Spurrier (2004) , Piegorsch et al. (2005) and Liu et al. (2007) . Construction of simultaneous confidence bands for a simple linear regression model has a rich history, going back to the work of Working & Hotelling (1929) . The purpose of this article is to consolidate the disparate modern literature on simultaneous confidence bands in linear regression, and to provide expressions for the construction of exact 1 ?α level simultaneous confidence bands for a simple linear regression model of either one‐sided or two‐sided form. We center attention on the three most recognized shapes: hyperbolic, two‐segment, and three‐segment (which is also referred to as a trapezoidal shape and includes a constant‐width band as a special case). Some of these expressions have already appeared in the statistics literature, and some are newly derived in this article. The derivations typically involve a standard bivariate t random vector and its polar coordinate transformation.     

A note on fourth-order risk aversion

Keenan et al. (J Risk Uncertain 24:264–277, 2002) introduced a measure of downside risk aversion (third-order risk aversion), and in Theorem 1, they showed four equivalent definitions of increased downside risk aversion. This result is thought as a higher-order extension of Theorem 3 in Diamond et al. (J Econ Theory 8:337–360, 1974). We consider fourth-order risk aversion and show four equivalent definitions of increased fourth-order risk aversion. Our result is thought as a higher-order extension of Theorem 1 in Keenan et al. (2002).     

Narrow Replication of ‘A Spatio‐Temporal Model of House Prices in the Usa’ Using R

I narrowly replicate Holly et al.'s (Journal of Econometrics 2010; 158 (1): 160–173) analysis of the housing market in the USA, using the open source R software instead of the original ad hoc GAUSS routines. Their main findings are confirmed and most results are matched exactly. Attention is given to providing a self‐contained and fully reproducible analysis, exclusively using user‐level features available in the public domain. Copyright © 2014 John Wiley & Sons, Ltd.     

Workplace heterogeneity and wage inequality in Denmark

Wage inequality is on the rise in most developed economies, and this phenomenon has fostered a growing body of research on its potential drivers. Using German data over the period 1985–2009, Card et al. (The Quarterly Journal of Economics 2013, 128(3), 967-1015) argue that rising workplace heterogeneity has contributed substantially to the rise in wage inequality. I revisit their findings in two ways. First, because the generalization of their findings remains an open question, I apply their methodological approach to Danish register data and test whether rising workplace heterogeneity explains a significant share of the rise in wage inequality in Denmark. I find that, contrary to Germany, workplace heterogeneity remained practically stable over time, and this pattern contributed slightly negatively to the rise in wage inequality. Second, I complement Card et al.'s (2013) methods with the variance decomposition exercise proposed by Song et al. (2019) to identify more precisely the sources of the rise in wage inequality in Denmark. Although the rise in wage inequality is partly a between-establishment phenomenon, I show that the strengthening of assortative matching patterns and the rising heterogeneity of workers within establishments are the main drivers of growing inequality.     

Income and Democracy: A Smooth Varying Coefficient Redux

Acemoglu et al. (American Economic Review 2008; 98 : 808–842) find no effect of income on democracy when controlling for fixed effects in a dynamic panel model. Work by Moral‐Benito and Bartolucci (Economics Letters 2012; 117 : 844–847) and Cervellati et al. (American Economic Review 2014; 104 : 707–719) suggests that the original model might have been misspecified and proposes alternative specifications instead. We formally test these parametric specifications by implementing Lee's (Journal of Econometrics 2014; 178 : 146–166) dynamic panel test of linear parametric specifications against a general class of nonlinear alternatives robustly and reject all these specifications. However, using a more flexible model proposed by Cai and Li (Econometric Theory 2008; 24 : 1321–1342) we find that the relationship between income and democracy appears to be mediated by education, but results are not statistically significant. Copyright © 2016 John Wiley & Sons, Ltd.     

He who must not be named

Landsberger et al. have studied a sealed bid first price auction with two players in which the ranking of the valuations is known. They argue that such a situation can arise in a sequential auction where only the name of the winner is revealed. In this paper we consider sequential auctions where two identical goods are sold sequentially to N players who are interested in both objects. In sealed bid auctions, no information is a priori revealed by the mechanism, but the seller can in principle reveal whatever he wants. We restrict our attention to the case where only the name of the winner is revealed to be in the context of Landsberger et al. for the second auction. The aim of the paper is to compare such a sequential auction with a simultaneous auction where both goods are sold as a bundle or equivalently with a sequential auction where no information is revealed. We first show that there exists an equilibrium of the sequential game in pure and monotone strategies. Then, the comparison of the seller's expected revenue in the two cases allows us to conclude that contrary to Landsberger et al.'s predictions, the seller can not use the information to increase his revenue. This result is obtained using simulations for a large class of distribution functions. The seller must not reveal the name of the winner between the two auctions and instead sell both goods using a simultaneous auction.Received: 31 July 2001, Accepted: 5 February 2003, JEL Classification: B44I wish to thank Laurent Linnemer, Thomas Ricke, Michael Visser and Shmuel Zamir for helpful comments and suggestions. I am very grateful to the referees and the associated editors in charge of my paper.     

Panel Stationarity Test with Structural Breaks*

In this paper, we extend the heterogeneous panel data stationarity test of Hadri [Econometrics Journal, Vol. 3 (2000) pp. 148–161] to the cases where breaks are taken into account. Four models with different patterns of breaks under the null hypothesis are specified. Two of the models have been already proposed by Carrion‐i‐Silvestre et al. [Econometrics Journal, Vol. 8 (2005) pp. 159–175]. The moments of the statistics corresponding to the four models are derived in closed form via characteristic functions. We also provide the exact moments of a modified statistic that do not asymptotically depend on the location of the break point under the null hypothesis. The cases where the break point is unknown are also considered. For the model with breaks in the level and no time trend and for the model with breaks in the level and in the time trend, Carrion‐i‐Silvestre et al. [Econometrics Journal, Vol. 8 (2005) pp. 159–175] showed that the number of breaks and their positions may be allowed to differ across individuals for cases with known and unknown breaks. Their results can easily be extended to the proposed modified statistic. The asymptotic distributions of all the statistics proposed are derived under the null hypothesis and are shown to be normally distributed. We show by simulations that our suggested tests have in general good performance in finite samples except the modified test. In an empirical application to the consumer prices of 22 OECD countries during the period from 1953 to 2003, we found evidence of stationarity once a structural break and cross‐sectional dependence are accommodated.     

Missing Data: A Unified Taxonomy Guided by Conditional Independence

Recent work (Seaman et al., 2013 ; Mealli & Rubin, 2015 ) attempts to clarify the not always well‐understood difference between realised and everywhere definitions of missing at random (MAR) and missing completely at random. Another branch of the literature (Mohan et al., 2013 ; Pearl & Mohan, 2013 ) exploits always‐observed covariates to give variable‐based definitions of MAR and missing completely at random. In this paper, we develop a unified taxonomy encompassing all approaches. In this taxonomy, the new concept of ‘complementary MAR’ is introduced, and its relationship with the concept of data observed at random is discussed. All relationships among these definitions are analysed and represented graphically. Conditional independence, both at the random variable and at the event level, is the formal language we adopt to connect all these definitions. Our paper covers both the univariate and the multivariate case, where attention is paid to monotone missingness and to the concept of sequential MAR. Specifically, for monotone missingness, we propose a sequential MAR definition that might be more appropriate than both everywhere and variable‐based MAR to model dropout in certain contexts.     

Decision making under risk in Deal or No Deal

We analyse the choices of 399 contestants in the Australian version of the television game show Deal or No Deal. We calculate risk aversion bounds for each contestant, revealing considerable heterogeneity. We then estimate a structural stochastic choice model that captures the dynamic decision problem faced by contestants. To address individual heterogeneity, we nest the dynamic problem within the settings of both a random effects and a random coefficients probit model. Our structural model produces plausible estimates of risk aversion, confirms the role of individual heterogeneity and suggests that a model of stochastic choice is indeed appropriate. We find mixed evidence of greater risk aversion by females. We also examine generalizations to expected utility theory, finding that the rank‐dependent utility model adds non‐negligible explanatory power and indicates optimism in probability weighting. Finally, we test, but are unable to confirm, the existence of an endowment effect for lotteries. Copyright © 2009 John Wiley & Sons, Ltd.     

Income taxation when markets are incomplete

We investigate the welfare effects of proportional income taxation in a standard general equilibrium model with incomplete markets (GEI). Formally, our analysis is on the allocative effects of state-contingent income tax reforms. Tax reforms are restricted to be anonymous, publicly and truthfully announced before markets open, and they are required to result in an ex-post constrained efficient allocation. Our main result is to show that there do typically exist contingent tax reforms that are Pareto improving. These reforms, acting directly on the asset span, modify private risk-sharing opportunities. Thus, unlike most of the GEI literature, the type of policy transmission mechanism considered does not rely on second-order, relative spot price effects. Yet, the key welfare effects of our tax reforms are substantially equivalent to those induced through changes in relative spot prices, as, for example, in Geanakoplos and Polemarchakis (1986), Geanakoplos et al. (1990), or in Citanna et al. (2001). Mathematics Subject Classification (2000): 58E17, 46N10, 93B29 Journal of Economic Literature Classification: D52, H21, H24, H25     

Adjusting for Non‐Response in Population‐Based Case‐Control Studies

In this paper we discuss the analysis of data from population‐based case‐control studies when there is appreciable non‐response. We develop a class of estimating equations that are relatively easy to implement. For some important special cases, we also provide efficient semi‐parametric maximum‐likelihood methods. We compare the methods in a simulation study based on data from the Women's Cardiovascular Health Study discussed in Arbogast et al. (Estimating incidence rates from population‐based case‐control studies in the presence of non‐respondents, Biometrical Journal 44, 227–239, 2002).     

Relative Risk Aversion and Power‐Law Distribution of Macroeconomic Disasters

The coefficient of relative risk aversion is notoriously difficult to estimate. Recently, Barro and Jin (On the size distribution of macroeconomic disasters, Econometrica 2011; 79 (3): 434–455) have come up with a new estimation approach that fits a power‐law model to the tail of distribution of macroeconomic disasters. We show that their results can be successfully replicated using a more refined power‐law fitting methodology and a more comprehensive dataset. Copyright © 2014 John Wiley & Sons, Ltd.     

Risk aversion in RDEU

Various notions of risk aversion can be distinguished for the class of rank-dependent expected utility (RDEU) preferences. We discuss the relationships amongst five of these, and describe simple (testable) characterizations in terms of elementary probability transformations for all but the weakest notion. The paper also provides the first complete characterization of the RDEU orderings that are risk-averse in the sense of Jewitt [Jewitt, I., 1989. Choosing between risky prospects: the characterization of comparative static results and location independent risk. Management Science 35, 60–70]. We also extend Chew et al.’s [Chew, S.H., Karni, E., Safra, Z., 1987. Risk aversion in the theory of utility with rank-dependent probabilities. Journal of Economic Theory 42, 370–381] important characterization of strong risk aversion [Rothschild, M., Stiglitz, J.E., 1970. Increasing risk: I. A definition. Journal of Economic Theory 2, 225–243] by relaxing strict monotonicity and differentiability assumptions, and allowing for discontinuities in the probability transformation function. The important special case of maximin choice falls within this relaxed RDEU class. It is shown that any strongly risk-averse RDEU order is a convex combination of maximin and another RDEU order with concave utility and continuous, concave probability transformation. Our proof of the result on strong risk aversion is also simpler (as well as more general) than that of Chew et al. [Chew, S.H., Karni, E., Safra, Z., 1987. Risk aversion in the theory of utility with rank-dependent probabilities. Journal of Economic Theory 42, 370–381].     

Behavioral Decision Making in the (Q,R) Purchasing Model: An Experimental Study

This paper presents and analyzes the results of a decision‐making experiment in inventory management under uncertainty. The experiment included 81 participants who played the role of a small car importer facing random demand as in the (Q,R) model. The results show strong evidence of learning and convergence, and the average reorder point (R) closely approaches the optimal level for maximizing profits. However, the participants' decisions are still biased by realizations of extreme values of demand and loss of potential sales. We argue that participants are affected by recency, loss aversion, and, possibly, their own risk aversion. Copyright © 2013 John Wiley & Sons, Ltd.     

The Pareto optimality distribution

Pareto optimality (sometimes known as Pareto efficiency) is an important notion in social sciences and related areas, see e.g. Klaus (2006), Chun (2005), Hild (2004), Kibris (2003), Nandeibam (2003), Papai (2001), Peris and Sanchez (2001), Brams and Fishburn (2000), Denicolo (1999), Klaus et al. (1998), Peremans et al. (1997), and Vohra (1992). This notion invariably involves the comparison of the utility of one outcome versus another, i.e. the ratio of two utilities or in general the ratio of two random variables. In this note, we derive the exact distribution of the ratio X/(X + Y) when X and Y are Pareto random variables, Pareto distribution being the first and the most popular distribution used in social sciences and related areas.     

Arab Consumers' Behavior Towards Credit Card Usage

Abstract

Credit card usage by consumers across the oil-rich Arab countries (such as Qatar, Bahrain, and Kuwait) is changing the landscape of consumer behavior, motivating Arab consumers to buy more often, and promoting impulse buying. Our study examines Arab consumers' behavior towards credit card usage from multi-cultural perspective by replicating a western model propounded by Kaynak et al. (1986) and Kaynak et al. (2001)     

Bubbles and crises: Replicating the Anundsen et al. (2016) results

This paper both narrowly and widely replicates the results of Anundsen et al. (Journal of Applied Econometrics, 2016, 31(7), 1291–1311). I am able to reproduce the same results as theirs. Furthermore, I find that allowing for time‐varying parameters of early warning system models can considerably improve the in‐sample model fit and out‐of‐sample forecasting performance based on an expanding window forecasting exercise.     

Optimal investment for executive stockholders with exponential utility

The scope of this paper is to enhance the model for the own-company stockholder (Desmettre et?al. in Math Methods Oper Res 72(3):347?C378, 2010), who can voluntarily performance-link his personal wealth to his management success by acquiring stocks in the own-company whose value he can directly influence via spending work effort. The executive is thereby characterized by a parameter of risk aversion and the two work effectiveness parameters inverse work productivity and disutility stress. We extend the model to a constant absolute risk aversion framework using an exponential utility/disutility setup. A closed-form solution is given for the optimal work effort an executive will apply and we derive the optimal investment strategies of the executive. Furthermore, we determine an up-front fair cash compensation applying an indifference utility rationale. Our study shows to a large extent that the results previously obtained are robust under the choice of the utility/disutility setup.     

Private returns to R&D in the presence of spillovers,revisited

This is both a replication of Eberhardt et al. (Review of Economics and Statistics, 2013, 95(2), 436–448) using different software, and a critical extension and diagnostic reassessment of the original results. The main findings of the paper are confirmed and sometimes reinforced. We point out some inconsistencies, in particular in the calculation of standard errors for the common correlated effects pooled model; we extend the diagnostic checks; lastly, in the spirit of the original contribution, we show how local cross‐sectional dependence diagnostics can be used to provide a first assessment of the direction of spillovers. We provide complete replication code in open source R.     

HEGY Tests in the Presence of Moving Averages*

We analyze the asymptotic distributions associated with the seasonal unit root tests of Hylleberg et al. (1990) for quarterly data when the innovations follow a moving average process. Although both the t‐ and F‐type tests suffer from scale and shift effects compared with the presumed null distributions when a fixed order of autoregressive augmentation is applied, these effects disappear when the order of augmentation is sufficiently large. However, as found by Burridge and Taylor (2001) for the autoregressive case, individual t‐ratio tests at the semi‐annual frequency are not pivotal even with high orders of augmentation, although the corresponding joint F‐type statistic is pivotal. Monte Carlo simulations verify the importance of the order of augmentation for finite samples generated by seasonally integrated moving average processes.