This paper extends the analysis of bivariate seemingly unrelated (SUR) Tobit model by modeling its nonlinear dependence structure through copulas. The capability in coupling together the different marginal distributions allows the flexible modeling for the SUR Tobit. The ability in capturing tail dependence is an additionally useful feature of the copulas, especially in modeling the lower tail dependence of the SUR Tobit where some data are censored. We employ the data augmentation technique to generate the censored observations and proceed the model implementation through the Bayesian Markov Chain Monte Carlo approach. The satisfactory results from the simulation and empirical studies indicate the good performance of our proposed model and method where they are applied to model the U.S. out-of-pocket and non-out-of-pocket medical expenses data and the Thai wage earnings income data.
{"title":"Estimation of Bivariate Copula-Based Seemingly Unrelated Tobit Models","authors":"N. Wichitaksorn","doi":"10.2139/ssrn.2122388","DOIUrl":"https://doi.org/10.2139/ssrn.2122388","url":null,"abstract":"This paper extends the analysis of bivariate seemingly unrelated (SUR) Tobit model by modeling its nonlinear dependence structure through copulas. The capability in coupling together the different marginal distributions allows the flexible modeling for the SUR Tobit. The ability in capturing tail dependence is an additionally useful feature of the copulas, especially in modeling the lower tail dependence of the SUR Tobit where some data are censored. We employ the data augmentation technique to generate the censored observations and proceed the model implementation through the Bayesian Markov Chain Monte Carlo approach. The satisfactory results from the simulation and empirical studies indicate the good performance of our proposed model and method where they are applied to model the U.S. out-of-pocket and non-out-of-pocket medical expenses data and the Thai wage earnings income data.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125672439","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}
We propose a model which enables the measurement of term risk in markets which are sensitive to systemic risk. With its origins in the spectralisation of the AR(1) process (using the Wiener-Khintchine theorem, and a P ~ Q transform), a Q jump martingale solution is found which is unique and independent of the wiener process. The model is tested, in differential equation form, on the risk premia generated in the yield curve, the credit spread of risky bonds, and the term risk in the implied volatility skew (forward variance). An excellent agreement, in both graphical and regression forms for the scale and patterns of term risk premia, is displayed. Because these measures also typify systemic risk characteristics (with their traded risk versions seen in the CDS and forward VIX markets), the model also defines a useful connection between systemic (bank distress) risk with the Q jump systematic risk.
{"title":"A New Term Risk Dynamic for Q Jumps for Measuring Systemic Risk","authors":"John Thorp","doi":"10.2139/ssrn.2082497","DOIUrl":"https://doi.org/10.2139/ssrn.2082497","url":null,"abstract":"We propose a model which enables the measurement of term risk in markets which are sensitive to systemic risk. With its origins in the spectralisation of the AR(1) process (using the Wiener-Khintchine theorem, and a P ~ Q transform), a Q jump martingale solution is found which is unique and independent of the wiener process. The model is tested, in differential equation form, on the risk premia generated in the yield curve, the credit spread of risky bonds, and the term risk in the implied volatility skew (forward variance). An excellent agreement, in both graphical and regression forms for the scale and patterns of term risk premia, is displayed. Because these measures also typify systemic risk characteristics (with their traded risk versions seen in the CDS and forward VIX markets), the model also defines a useful connection between systemic (bank distress) risk with the Q jump systematic risk.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"129 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126969526","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}
We propose a general framework for dealing with endogeneity in models in marketing and economics. It consists of a multivariate, hierarchical, mixed discrete/continuous representation of behavioral response variables. Importantly, it includes a non-parametric approximation to unobserved sources of exogenous information. It complements the instrumental variables (IV) approach in that it may but does not need to include, observable instruments. After presenting the theoretical basis of the method, a simulation study reveals that parameters can be estimated consistently even if instruments are not observed. The proposed approach is applied in three case studies in business and economics. They include a case where a standard IV is inadequate in correcting for endogeneity bias, and two cases where IVs are not available. In the examples, the proposed framework corrects for endogeneity bias without recourse to IVs. Resulting policy actions are shown to be different from equivalent models that ignore endogeneity. We conclude that the approach has applications in marketing and economics as a framework for testing for conjectured endogeneity. The development of theoretical arguments motivating the investigation of endogeneity remains crucial, but even after such a rigorous theoretical analysis there will remain instances in which instruments are not available, cannot be found, or where empirically their quality is insufficient, in which case the proposed framework provides a useful alternative.
{"title":"A Statistical Framework for Dealing with Endogeneity","authors":"P. Ebbes, P. Lenk, M. Wedel","doi":"10.2139/ssrn.2460497","DOIUrl":"https://doi.org/10.2139/ssrn.2460497","url":null,"abstract":"We propose a general framework for dealing with endogeneity in models in marketing and economics. It consists of a multivariate, hierarchical, mixed discrete/continuous representation of behavioral response variables. Importantly, it includes a non-parametric approximation to unobserved sources of exogenous information. It complements the instrumental variables (IV) approach in that it may but does not need to include, observable instruments. After presenting the theoretical basis of the method, a simulation study reveals that parameters can be estimated consistently even if instruments are not observed. The proposed approach is applied in three case studies in business and economics. They include a case where a standard IV is inadequate in correcting for endogeneity bias, and two cases where IVs are not available. In the examples, the proposed framework corrects for endogeneity bias without recourse to IVs. Resulting policy actions are shown to be different from equivalent models that ignore endogeneity. We conclude that the approach has applications in marketing and economics as a framework for testing for conjectured endogeneity. The development of theoretical arguments motivating the investigation of endogeneity remains crucial, but even after such a rigorous theoretical analysis there will remain instances in which instruments are not available, cannot be found, or where empirically their quality is insufficient, in which case the proposed framework provides a useful alternative.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129326810","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}
This paper develops a dependence-switching copula model to examine dependence and tail dependence for four different market statuses, namely, rising-stocks/appreciating-currency, falling-stocks/depreciating-currency, rising-stocks/depreciating-currency, and falling-stocks/appreciating-currency. The model is then applied to daily stock returns and exchange rate changes for six major industrial countries over the 1990–2010 period. The dependence and tail dependence among the above four market statuses are asymmetric for most countries in the negative correlation regime, but symmetric in the positive correlation regime. These results enrich the findings in the existing literature and suggest that analyzing cross-market linkages within a time-invariant copula framework may not be appropriate.
{"title":"A Revisit to the Dependence Structure between Stock and Foreign Exchange Markets: A Dependence-Switching Copula Approach","authors":"Yi-Chiuan Wang, Jyh‐Lin Wu, YiHao Lai","doi":"10.2139/ssrn.2039624","DOIUrl":"https://doi.org/10.2139/ssrn.2039624","url":null,"abstract":"This paper develops a dependence-switching copula model to examine dependence and tail dependence for four different market statuses, namely, rising-stocks/appreciating-currency, falling-stocks/depreciating-currency, rising-stocks/depreciating-currency, and falling-stocks/appreciating-currency. The model is then applied to daily stock returns and exchange rate changes for six major industrial countries over the 1990–2010 period. The dependence and tail dependence among the above four market statuses are asymmetric for most countries in the negative correlation regime, but symmetric in the positive correlation regime. These results enrich the findings in the existing literature and suggest that analyzing cross-market linkages within a time-invariant copula framework may not be appropriate.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121165282","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}
We introduce a new efficient importance sampler for nonlinear non-Gaussian state space models. We propose a general and efficient likelihood evaluation method for this class of models via the combination of numerical and Monte Carlo integration methods. Our methodology explores the idea that only a small part of the likelihood evaluation problem requires simulation. We refer to our new method as numerically accelerated importance sampling. The method is computationally and numerically efficient, facilitates parameter estimation for models with high-dimensional state vectors, and overcomes a bias-variance trade-off encountered by other sampling methods. An elaborate simulation study and an empirical application for U.S. stock returns reveal large efficiency gains for a range of models used in financial econometrics.
{"title":"Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models","authors":"S. J. Koopman, A. Lucas, Marcel Scharth","doi":"10.2139/ssrn.1790472","DOIUrl":"https://doi.org/10.2139/ssrn.1790472","url":null,"abstract":"We introduce a new efficient importance sampler for nonlinear non-Gaussian state space models. We propose a general and efficient likelihood evaluation method for this class of models via the combination of numerical and Monte Carlo integration methods. Our methodology explores the idea that only a small part of the likelihood evaluation problem requires simulation. We refer to our new method as numerically accelerated importance sampling. The method is computationally and numerically efficient, facilitates parameter estimation for models with high-dimensional state vectors, and overcomes a bias-variance trade-off encountered by other sampling methods. An elaborate simulation study and an empirical application for U.S. stock returns reveal large efficiency gains for a range of models used in financial econometrics.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114158521","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}
We show how to estimate a Cronbach's alpha reliability coefficient in Stata after running a principal component or factor analysis. Alpha evaluates to what extent items measure the same underlying content when the items are combined into a scale or used for latent variable. Stata allows for testing the reliability coefficient (alpha) of a scale only when all items receive homogenous weights. We present a user-written program that computes reliability coefficients when implementation of principal component or factor analysis shows heterogeneous item loadings. We use data on management practices from Bloom and Van Reenen (2010) to explain how to implement and interpret the adjusted internal consistency measure using afa.
{"title":"Estimating Reliability Coefficients with Heterogeneous Item Weightings Using Stata: A Factor Based Approach","authors":"Martijn Adriaan Boermans, M. Kattenberg","doi":"10.2139/ssrn.2026433","DOIUrl":"https://doi.org/10.2139/ssrn.2026433","url":null,"abstract":"We show how to estimate a Cronbach's alpha reliability coefficient in Stata after running a principal component or factor analysis. Alpha evaluates to what extent items measure the same underlying content when the items are combined into a scale or used for latent variable. Stata allows for testing the reliability coefficient (alpha) of a scale only when all items receive homogenous weights. We present a user-written program that computes reliability coefficients when implementation of principal component or factor analysis shows heterogeneous item loadings. We use data on management practices from Bloom and Van Reenen (2010) to explain how to implement and interpret the adjusted internal consistency measure using afa.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123992840","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}
We evaluate and compare the effects of a monetary policy shock implemented by one certain tool of the people’s bank of China ,say, open market operation, the required reserve ratio and interest rates, through constructing a mixed identification method that combines the pure sign restrictions method with some zero restrictions in a structural VAR model. We find, (i) a shock induced by open market sales or raising the required reserve ratio brings a stronger negative effect on real output, comparing with a shock induced by raising interest rate.(ii) a shock caused by raising interest rate has a bigger probability to bring price a persistent declining course. Our result implies the Chinese authority should give a priority to the instrument of interest rate when trying to tame inflation in the future.
{"title":"A Comparative Analysis of Different Tools of the People’s Bank of China in Effectiveness","authors":"L. Tian","doi":"10.2139/ssrn.2037279","DOIUrl":"https://doi.org/10.2139/ssrn.2037279","url":null,"abstract":"We evaluate and compare the effects of a monetary policy shock implemented by one certain tool of the people’s bank of China ,say, open market operation, the required reserve ratio and interest rates, through constructing a mixed identification method that combines the pure sign restrictions method with some zero restrictions in a structural VAR model. We find, (i) a shock induced by open market sales or raising the required reserve ratio brings a stronger negative effect on real output, comparing with a shock induced by raising interest rate.(ii) a shock caused by raising interest rate has a bigger probability to bring price a persistent declining course. Our result implies the Chinese authority should give a priority to the instrument of interest rate when trying to tame inflation in the future.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"125 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130123548","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}
Opting for structural or reduced form estimation is often hard to justify if one wants to both learn about the structure of the economy and obtain accurate predictions. In this paper, we show that using both structural and reduced form estimates simultaneously can lead to more accurate policy predictions. Our findings are based on using new information criteria whose econometric properties allow us to pick for both methods the impulse responses that are valid and relevant for prediction. We illustrate our findings in the context of analyzing the monetary transmission mechanism for Armenia. Based on picking valid and relevant information from both structural and reduced form matching estimation, our findings suggest that the interest rate targeting and the exchange rate channel are well specified and strongly reinforce each other in promoting the recent double-digit growth Armenia experienced before the crisis.
{"title":"Structural Versus Matching Estimation: Transmission Mechanisms in Armenia","authors":"K. Poghosyan, O. Boldea","doi":"10.2139/ssrn.1932071","DOIUrl":"https://doi.org/10.2139/ssrn.1932071","url":null,"abstract":"Opting for structural or reduced form estimation is often hard to justify if one wants to both learn about the structure of the economy and obtain accurate predictions. In this paper, we show that using both structural and reduced form estimates simultaneously can lead to more accurate policy predictions. Our findings are based on using new information criteria whose econometric properties allow us to pick for both methods the impulse responses that are valid and relevant for prediction. We illustrate our findings in the context of analyzing the monetary transmission mechanism for Armenia. Based on picking valid and relevant information from both structural and reduced form matching estimation, our findings suggest that the interest rate targeting and the exchange rate channel are well specified and strongly reinforce each other in promoting the recent double-digit growth Armenia experienced before the crisis.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114162935","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}
We propose a new approach to the definition of stress scenarios for volatilities and correlations. Correlations and volatilities depend on a common market factor, which is the key to stressing them in a consistent and intuitive way. Our approach is based on a new asset price model where correlations and volatilities depend on the current state of the market, which captures market-wide movements in equity-prices. For sample portfolios we compare correlations and volatilities in a normal market and under stress and explore consequences for value-at-risk.
{"title":"Stressing Correlations and Volatilities – A Consistent Modeling Approach","authors":"Chris Becker, Wolfgang M. Schmidt","doi":"10.2139/ssrn.1928975","DOIUrl":"https://doi.org/10.2139/ssrn.1928975","url":null,"abstract":"We propose a new approach to the definition of stress scenarios for volatilities and correlations. Correlations and volatilities depend on a common market factor, which is the key to stressing them in a consistent and intuitive way. Our approach is based on a new asset price model where correlations and volatilities depend on the current state of the market, which captures market-wide movements in equity-prices. For sample portfolios we compare correlations and volatilities in a normal market and under stress and explore consequences for value-at-risk.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131987018","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}
Following the work by White (1980ab; 1982) it is common in empirical work in economics to report standard errors that are robust against general misspecification. In a regression setting these standard errors are valid for the parameter that in the population minimizes the squared difference between the conditional expectation and the linear approximation, averaged over the population distribution of the covariates. In nonlinear settings a similar interpretation applies. In this note we discuss an alternative parameter that corresponds to the approximation to the conditional expectation based on minimization of the squared difference averaged over the sample, rather than the population, distribution of a subset of the variables. We argue that in some cases this may be a more interesting parameter. We derive the asymptotic variance for this parameter, generally smaller than the White robust variance, and we propose a consistent estimator for the asymptotic variance.
{"title":"Robust Inference for Misspecified Models Conditional on Covariates","authors":"Alberto Abadie, G. Imbens, Fanyin Zheng","doi":"10.3386/W17442","DOIUrl":"https://doi.org/10.3386/W17442","url":null,"abstract":"Following the work by White (1980ab; 1982) it is common in empirical work in economics to report standard errors that are robust against general misspecification. In a regression setting these standard errors are valid for the parameter that in the population minimizes the squared difference between the conditional expectation and the linear approximation, averaged over the population distribution of the covariates. In nonlinear settings a similar interpretation applies. In this note we discuss an alternative parameter that corresponds to the approximation to the conditional expectation based on minimization of the squared difference averaged over the sample, rather than the population, distribution of a subset of the variables. We argue that in some cases this may be a more interesting parameter. We derive the asymptotic variance for this parameter, generally smaller than the White robust variance, and we propose a consistent estimator for the asymptotic variance.","PeriodicalId":273058,"journal":{"name":"ERN: Model Construction & Estimation (Topic)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125420741","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}
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