{"title":"Continuous-Time Linear Models","authors":"J. Cochrane","doi":"10.2139/ssrn.2084437","DOIUrl":"https://doi.org/10.2139/ssrn.2084437","url":null,"abstract":"I translate familiar concepts of discrete-time time-series to contnuous-time equivalent. I cover lag operators, ARMA models, the relation between levels and differences, integration and cointegration, and the Hansen-Sargent prediction formulas.","PeriodicalId":219959,"journal":{"name":"ERN: Other Econometrics: Single Equation Models (Topic)","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125455664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Relationship between the PMI and the Italian Index of Industrial Production and the Impact of the Latest Economic Crisis","authors":"Valentina Aprigliano","doi":"10.2139/ssrn.1960900","DOIUrl":"https://doi.org/10.2139/ssrn.1960900","url":null,"abstract":"Survey data attract considerable interest as timely and reliable series for assessing the state of the economy. We investigate the relationship between the manufacturing PMI and the Index of Industrial Production (IPI) for Italy, with a special focus on the effects of the latest crisis. The manufacturing PMI tracks a medium-to-long run component of the IPI quarterly growth rate, which is estimated by a one-sided multivariate Wavelet filter. This filter provides more efficient estimates at the end of the sample than the Baxter and King method. Furthermore, the Wavelet basis allows us to take into account the time-varying oscillations of a series caused by the large negative shocks characterizing the latest global crisis, while the non-parametric framework does not force us to conclude definitely for the occurrence of structural breaks not yet testable rigorously.","PeriodicalId":219959,"journal":{"name":"ERN: Other Econometrics: Single Equation Models (Topic)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132074769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Estimation of Peaked Densities Over the Interval [0,1] Using Two-Sided Power Distribution: Application to Lottery Experiments","authors":"K. Kontek","doi":"10.2139/ssrn.1597203","DOIUrl":"https://doi.org/10.2139/ssrn.1597203","url":null,"abstract":"This paper deals with estimating peaked densities over the interval [0,1] using two-sided power distribution (Kotz, van Dorp, 2004). Such data were encountered in experiments determining certainty equivalents of lotteries (Kontek, 2010). This paper summarizes the basic properties of the two-sided power distribution (TP) and its generalized form (GTP). The GTP maximum likelihood estimator, a result not derived by Kotz and van Dorp, is presented. The TP and GTP are used to estimate certainty equivalent densities in two data sets from lottery experiments. The obtained results show that even a two-parametric TP distribution provides more accurate estimates than the smooth three-parametric generalized beta distribution GBT (Libby, Novick, 1982) in one of the considered data sets. The three-parametric GTP distribution outperforms GBT for these data. The results are, however, the very opposite for the second data set, in which the data are greatly scattered. The paper demonstrates that the TP and GTP distributions may be extremely useful in estimating peaked densities over the interval [0,1] and in studying the relative utility function.","PeriodicalId":219959,"journal":{"name":"ERN: Other Econometrics: Single Equation Models (Topic)","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115748335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Endogeneity and Instrumental Variables in Dynamic Models","authors":"J. Florens, G. Simon","doi":"10.2139/ssrn.1633935","DOIUrl":"https://doi.org/10.2139/ssrn.1633935","url":null,"abstract":"The objective of the paper is to draw the theory of endogeneity in dynamic models in discrete and continuous time, in particular for diffusions and counting processes. We first provide an extension of the separable set-up to a separable dynamic framework given in term of semi-martingale decomposition. Then we define our function of interest as a stopping time for an additional noise process, whose role is played by a Brownian motion for diffusions, and a Poisson process for counting processes.","PeriodicalId":219959,"journal":{"name":"ERN: Other Econometrics: Single Equation Models (Topic)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130005515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Explicit Solutions for the Asymptotically-Optimal Bandwidth in Cross Validation","authors":"K. Abadir, M. Lubrano","doi":"10.2139/ssrn.1984825","DOIUrl":"https://doi.org/10.2139/ssrn.1984825","url":null,"abstract":"Least squares cross-validation (CV) methods are often used for automated bandwidth selection. We show that they share a common structure which has an explicit asymptotic solution. Using the framework of density estimation, we consider unbiased, biased, and smoothed CV methods. We show that, with a Student t(nu) kernel which includes the Gaussian as a special case, the CV criterion becomes asymptotically equivalent to a simple polynomial. This leads to optimal-bandwidth solutions that dominate the usual CV methods, definitely in terms of simplicity and speed of calculation, but also often in terms of integrated squared error because of the robustness of our asymptotic solution. We present simulations to illustrate these features and to give practical guidance on the choice of nu.","PeriodicalId":219959,"journal":{"name":"ERN: Other Econometrics: Single Equation Models (Topic)","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129038315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"L1-Penalized Quantile Regression in High Dimensional Sparse Models","authors":"V. Chernozhukov, A. Belloni","doi":"10.2139/ssrn.1394734","DOIUrl":"https://doi.org/10.2139/ssrn.1394734","url":null,"abstract":"We consider median regression and, more generally, quantile regression in high-dimensional sparse models. In these models the overall number of regressors p is very large, possibly larger than the sample size n, but only s of these regressors have non-zero impact on the conditional quantile of the response variable, where s grows slower than n. Since in this case the ordinary quantile regression is not consistent, we consider quantile regression penalized by the L1-norm of coefficients (L1-QR). First, we show that L1-QR is consistent at the rate of the square root of (s/n) log p, which is close to the oracle rate of the square root of (s/n), achievable when the minimal true model is known. The overall number of regressors p affects the rate only through the log p factor, thus allowing nearly exponential growth in the number of zero-impact regressors. The rate result holds under relatively weak conditions, requiring that s/n converges to zero at a super-logarithmic speed and that regularization parameter satisfies certain theoretical constraints. Second, we propose a pivotal, data-driven choice of the regularization parameter and show that it satisfies these theoretical constraints. Third, we show that L1-QR correctly selects the true minimal model as a valid submodel, when the non-zero coefficients of the true model are well separated from zero. We also show that the number of non-zero coefficients in L1-QR is of same stochastic order as s, the number of non-zero coefficients in the minimal true model. Fourth, we analyze the rate of convergence of a two-step estimator that applies ordinary quantile regression to the selected model. Fifth, we evaluate the performance of L1-QR in a Monte-Carlo experiment, and provide an application to the analysis of the international economic growth.","PeriodicalId":219959,"journal":{"name":"ERN: Other Econometrics: Single Equation Models (Topic)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130422225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Tax-Spend or Fiscal Illusion? Allowing for Asymmetric Revenue Effects in Expenditure Error-Correction Models","authors":"A. Young","doi":"10.2139/ssrn.1126396","DOIUrl":"https://doi.org/10.2139/ssrn.1126396","url":null,"abstract":"The existing empirical literature on the US federal revenue-expenditure nexus has had mixed findings. Amongst those papers presenting evidence in favor of causation running from taxes to expenditures, support for the conventional, Friedman-type tax-spend hypothesis is nearly ubiquitous. Evidence in favor of the competing, fiscal illusion hypothesis (where taxes affect expenditures inversely) is scant. Using quarterly US data from 1959:3 to 2007:4, I argue that allowing for asymmetric revenue effects results in a compelling case for fiscal illusion: revenue increases inversely Granger-cause expenditure changes. This finding is robust to incorporating additional asymmetries in the error-correction process to long-run budgetary disequilibria.","PeriodicalId":219959,"journal":{"name":"ERN: Other Econometrics: Single Equation Models (Topic)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133751822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Testing Joint Hypotheses When One of the Alternatives is One-Sided","authors":"K. Abadir, W. Distaso","doi":"10.2139/ssrn.1985282","DOIUrl":"https://doi.org/10.2139/ssrn.1985282","url":null,"abstract":"We propose a class of statistics where the direction of one of the alternatives is incorporated. It is obtained by modifying a class of multivariate tests with elliptical confidence regions, not necessarily arising from normal-based distribution theory. The resulting statistics are easy to compute, they do not require the re-estimation of models subject to one-sided inequality restrictions, and their distributions do not require bounds-based inference. We derive explicit distribution and power functions, using them to prove some desirable properties of our class of modified tests. We then illustrate the relevance of the method by applying it to devising an improved test of random walks in autoregressive models with deterministic components. In this example, the usual alternative to a unit root is one-sided in the direction of stable roots, while deterministic components are allowed to go either way, and we show that it is beneficial to take the partially one-sided nature of the alternative into account.","PeriodicalId":219959,"journal":{"name":"ERN: Other Econometrics: Single Equation Models (Topic)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133342705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Finite-Mixture Structural Equation Models for Response-Based Segmentation and Unobserved Heterogeneity","authors":"K. Jedidi, Harsharanjeet S. Jagpal, W. DeSarbo","doi":"10.1287/MKSC.16.1.39","DOIUrl":"https://doi.org/10.1287/MKSC.16.1.39","url":null,"abstract":"Two endemic problems face researchers in the social sciences e.g., Marketing, Economics, Psychology, and Finance: unobserved heterogeneity and measurement error in data. Structural equation modeling is a powerful tool for dealing with these difficulties using a simultaneous equation framework with unobserved constructs and manifest indicators which are error-prone. When estimating structural equation models, however, researchers frequently treat the data as if they were collected from a single population Muthen [Muthen, Bengt O. 1989. Latent variable modeling in heterogeneous populations. Psychometrika54 557--585.]. This assumption of homogeneity is often unrealistic. For example, in multidimensional expectancy value models, consumers from different market segments can have different belief structures Bagozzi [Bagozzi, Richard P. 1982. A field investigation of causal relations among cognitions, affect, intentions, and behavior. J. Marketing Res.19 562--584.]. Research in satisfaction suggests that consumer decision processes vary across segments Day [Day, Ralph L. 1977. Extending the concept of consumer satisfaction. W. D. Perreault, ed. Advances in Consumer Research, Vol. 4. Association for Consumer Research, Atlanta, 149--154.]. \u0000 \u0000This paper shows that aggregate analysis which ignores heterogeneity in structural equation models produces misleading results and that traditional fit statistics are not useful for detecting unobserved heterogeneity in the data. Furthermore, sequential analyses that first form groups using cluster analysis and then apply multigroup structural equation modeling are not satisfactory. \u0000 \u0000We develop a general finite mixture structural equation model that simultaneously treats heterogeneity and forms market segments in the context of a specified model structure where all the observed variables are measured with error. The model is considerably more general than cluster analysis, multigroup confirmatory factor analysis, and multigroup structural equation modeling. In particular, the model subsumes several specialized models including finite mixture simultaneous equation models, finite mixture confirmatory factor analysis, and finite mixture second-order factor analysis. \u0000 \u0000The finite mixture structural equation model should be of interest to academics in a wide range of disciplines e.g., Consumer Behavior, Marketing, Economics, Finance, Psychology, and Sociology where unobserved heterogeneity and measurement error are problematic. In addition, the model should be of interest to market researchers and product managers for two reasons. First, the model allows the manager to perform response-based segmentation using a consumer decision process model, while explicitly allowing for both measurement and structural error. Second, the model allows managers to detect unobserved moderating factors which account for heterogeneity. Once managers have identified the moderating factors, they can link segment membership to observable in","PeriodicalId":219959,"journal":{"name":"ERN: Other Econometrics: Single Equation Models (Topic)","volume":"117 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114133535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Linear Factor Models: Theory, Applications and Pitfalls","authors":"A. Meucci","doi":"10.2139/ssrn.1635495","DOIUrl":"https://doi.org/10.2139/ssrn.1635495","url":null,"abstract":"We clarify the rationale and differences between the two main categories of linear factor models, namely dominant-residual and systematic-idiosyncratic. We discuss the five different, yet interconnected areas of quantitative finance where linear factor models play an essential role: multivariate estimation theory, asset pricing theory, systematic strategies, portfolio optimization, and risk attribution. We present a comprehensive list of common pitfalls and misunderstandings on linear factor models. An appendix details all the calculations. Supporting code is available for download.","PeriodicalId":219959,"journal":{"name":"ERN: Other Econometrics: Single Equation Models (Topic)","volume":"80 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120921544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}