灵活的非线性时间序列模型及应用研究
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摘要
经济学中各种变量间的关系往往是非线性的而不是线性的,因此传统的线性模型在对经济变量间的关系进行描述时通常存在模型的误设问题。为了更准确的描述经济变量间的关系,大量的非线性模型被提出。这些非线性模型相对经典的线性模型而言考虑到经济变量间关系的结构性变化,因而能对经济变量间的关系进行更为准确的描述。然而这些非线性模型需要对参数发生结构变化的演进机制进行某种人为的设定,这会从另外一个方面造成模型的误设问题。为了改进非线性模型中由人为因素所导致的模型误设问题,因此迫切的需要开发灵活的非线性模型。这类灵活的非线性模型要能最大程度的减轻模型设定的主观随意性,同时又能容纳各种已出现的非线性模型。
本文在状态空间模型的框架下论述了两种灵活的非线性时间序列模型,即单方程灵活的非线性时间序列模型以及灵活的向量自回归模型。这两种灵活的非线性时间序列模型都不需要对参数的演进规律做出任何的人为假设,而是秉承计量经济学“让数据说话的思想”从数据中估计参数的演进规律。这在很大程度上改进了普通的非线性模型中存在的模型误设问题。另外,本文的模型能容纳各种普通的非线性时间序列模型。当模型中的参数取不同的值的时候,它能转换为各种普通的非线性时间序列模型。单方程灵活的非线性时间序列模型是在传统的时变参数模型(TVP)的基础上改进而成的。通过引入距离函数与排序的思想,时变参数模型模型变得具有高度的灵活性从而成为单方程灵活的非线性时间序列模型。灵活的向量自回归模型则是在传统的向量自回归模型的基础上改进而成的。考虑到向量自回归模型中的自回归系数以及随机扰动项协方差矩阵的结构变化,并用混合创新方法(MixedInnovation)对结构变化建模,我们得到灵活的向量自回归模型。单方程灵活的非线性时间序列模型与灵活的向量自回归模型中的参数均是用马尔科夫链蒙特卡罗方法(MCMC)进行估计的。MCMC方法充分利用了现代计算机的高速运算性能,能对模型中的参数可行而且有效的估计。
利用单方程灵活的非线性时间序列模型与灵活的向量自回归模型,我们分别对中国经济的利率敏感度以及货币政策的冲击效应进行了实证分析。对中国经济的利率敏感度的实证分析表明,在不同的经济增长速度下,我国信贷需求的利率敏感度是不一致的。当经济增长率很高或者很低时,信贷需求对利率是不敏感的,当经济增长速度处于中间区域的时候信贷需求对利率较为敏感。对货币政策的冲击效应的实证分析表明,货币政策对实体经济的冲击效应有着明显的时变特征。在早期,货币政策的冲击对经济增长率和通货膨胀率有比较大的短中期影响,而近年来货币政策的冲击对经济增长率和通货膨胀率的影响相对而言大大弱化了。
综上所述,本文的主要贡献和意义体现在以下几个方面：(1)计量模型与估计方法的创新。在国内现有的实证研究中,所采用的模型大多为线性回归模型和某种普通的非线性模型。而本文论述了两种灵活的非线性时间序列模型,这两种模型能有效改进非线性模型中的模型误设问题同时又能容纳各种普通的非线性模型从而能更好的对经济变量间的关系进行刻画。此外与本文模型相对应的估计方法是MCMC方法。MCMC方法充分利用了现代计算机的高速运算性能,有效改善了普通的最小二乘法和极大似然法在估计参数众多的非线性模型时效率低下的问题。因此本文的计量模型和估计方法为国内改进计量模型进行实证研究做出了探索性的工作,具有显著的方法论意义。(2)研究方法和视角的创新。目前国内对我国信贷需求的利率敏感度的研究,在计量方法上大都基于传统的线性回归模型,本文首次使用灵活的非线性模型进行了实证研究。另外在对我国货币政策冲击效应的分析中,目前国内学者使用的计量方法均为传统的向量自回归模型,本文首次使用灵活的向量自回归模型对货币政策对实体经济冲击效应的时变特征进行了研究。(3)本文的研究结论具有丰富的经济学和政策含义。对信贷需求的利率敏感度的实证结果表明,当经济增长率很高或者很低时,信贷需求对利率是不敏感的,当经济增长速度处于中间区域的时候信贷需求对利率较为敏感。这一结论隐含的政策意义为,在我国利用利率工具熨平经济周期的效果仍然是非常有限的。另外对我国货币政策的冲击效应的研究发现在早期,货币政策的冲击对经济增长率和通货膨胀率有比较大的短中期影响,而近年来货币政策的冲击对经济增长率和通货膨胀率的影响相对而言大大弱化了。这意味着为了实现货币政策的目标,我国在目前仍然需要改善货币政策的传导渠道以增强货币政策的有效性。上述发现都是基于灵活的非线性模型所产生的结论,从这个意义上说,本文具有显著的学术和应用意义。
In economics, the relationship between variables is often nonlinear, not linear. Thus, the traditional linear model is not suitable when describing the relationship between economic variables. In order to describe the relationship between economic variables more accurately, many non-linear models have been proposed. Compared with the linear model, these nonlinear models take into account the structural changes of relationship between economic variables. Thus, these models can describe the relationship more accurately. However, when setting these non-linear models, the evolution of structural changes of parameters is required to be set artificially. It will lead to the new problem of model misspecification. In order to reduce model misspecification in nonlinear model caused by the human factor, there is an urgent need to develop a flexible nonlinear model. Such flexible nonlinear models should reduce the subjectivity and arbitrariness to the maximum when setting models and can accommodate a variety of emerging nonlinear models.
In this paper, we describe two flexible nonlinear time series model in the framework of state space model, a single equation flexible nonlinear time series model and a flexible VAR model. The two flexible nonlinear time series model parameters do not need to make any human assumptions on the law of parameters'evolution, but adhering to the econometrics, "Let the data speak', estimate the law of evolution from the data. This reduce the model misspecification existed in the common nonlinear model greatly. On the other hand, our model can accommodate all kinds of common nonlinear time series model. When the model parameters take different values, it can be converted to a variety of common nonlinear time series model. Single equation flexible nonlinear time series model is developed from the traditional time-varying parameter model (TVP). By introducing distance function and sorting, the time-varying parameter model can be converted to a single equation flexible nonlinear time series model. Flexible VAR model is developed from traditional VAR model. Single equation flexible nonlinear time series model and flexible vector autoregressive model are estimated by Markov chain Monte Carlo method (MCMC). MCMC method uses high-speed computing performance of modern computers and can estimate the parameters of the model feasibly and effectively.
The flexible nonlinear model takes a big step from the nonlinear model and has profound developmental value and applied foreground. It has been regarded adequately and developed rapidly in abroad. But in China, the research on flexible nonlinear model is still seldom and just in the period of beginning. We use the flexible nonlinear model to study several problems of the macroeconomic field. The main contribution of our paper can be expressed in the following:(1) the innovation of econometric model and estimation method. Among the empirical researches in China, most of the models are linear model and common nonlinear model. The model in our paper has great flexibility. It can accommodate linear model and all nonlinear models and it is unnecessary to specify the evolutive mechanism. Our estimation method is MCMC method. In the flexible nonlinear model, it is impossible to use OLS and ML method to estimate the parameters. But MCMC method can make full use of the rapid computational character of computer and make feasible and effective estimation. Therefore our econometric model and estimation method make great contribution to improve domestic econometric model and have significant value on econometric method. (2) the innovation of visual angle in research. Among the literature of studying the sensitivity of credit demand on interest, most of the econometric models are linear model. This paper first uses the flexible nonlinear model to study the problem. The result shows that the sensitivity of credit demand on interest is changing companied by the different speed of economic growth. Among the literature of studying the effect of monetary policy, most of them use traditional VAR model. This paper uses flexible VAR model to study the effect of monetary policy. The result shows that the effect of monetary policy on economy has the significant time varying feature. (3) the conclusion of our research has great value for economics and policy. The result shows that when the speed of economic growth is vey high or very low, credit demand is not sensitive to interest. Only when the speed is medium, credit demand is sensitive to interest. It means that the effect of using interest tool to control economic cycle is still very limited. In the analysis of our monetary policy on, it can be found that monetary policy has bigger effect on economic growth rate and inflation rate in the earlier time. However, in recent years, the effect of monetary policy on economic growth and inflation become weaker. It means that we still need to improve the conductive channel of monetary policy to improve the effect of monetary policy. All the above finds are based on the flexible nonlinear model. From this point, this paper has significant value for academic and application.
本文在状态空间模型的框架下论述了两种灵活的非线性时间序列模型,即单方程灵活的非线性时间序列模型以及灵活的向量自回归模型。这两种灵活的非线性时间序列模型都不需要对参数的演进规律做出任何的人为假设,而是秉承计量经济学“让数据说话的思想”从数据中估计参数的演进规律。这在很大程度上改进了普通的非线性模型中存在的模型误设问题。另外,本文的模型能容纳各种普通的非线性时间序列模型。当模型中的参数取不同的值的时候,它能转换为各种普通的非线性时间序列模型。单方程灵活的非线性时间序列模型是在传统的时变参数模型(TVP)的基础上改进而成的。通过引入距离函数与排序的思想,时变参数模型模型变得具有高度的灵活性从而成为单方程灵活的非线性时间序列模型。灵活的向量自回归模型则是在传统的向量自回归模型的基础上改进而成的。考虑到向量自回归模型中的自回归系数以及随机扰动项协方差矩阵的结构变化,并用混合创新方法(MixedInnovation)对结构变化建模,我们得到灵活的向量自回归模型。单方程灵活的非线性时间序列模型与灵活的向量自回归模型中的参数均是用马尔科夫链蒙特卡罗方法(MCMC)进行估计的。MCMC方法充分利用了现代计算机的高速运算性能,能对模型中的参数可行而且有效的估计。
利用单方程灵活的非线性时间序列模型与灵活的向量自回归模型,我们分别对中国经济的利率敏感度以及货币政策的冲击效应进行了实证分析。对中国经济的利率敏感度的实证分析表明,在不同的经济增长速度下,我国信贷需求的利率敏感度是不一致的。当经济增长率很高或者很低时,信贷需求对利率是不敏感的,当经济增长速度处于中间区域的时候信贷需求对利率较为敏感。对货币政策的冲击效应的实证分析表明,货币政策对实体经济的冲击效应有着明显的时变特征。在早期,货币政策的冲击对经济增长率和通货膨胀率有比较大的短中期影响,而近年来货币政策的冲击对经济增长率和通货膨胀率的影响相对而言大大弱化了。
综上所述,本文的主要贡献和意义体现在以下几个方面：(1)计量模型与估计方法的创新。在国内现有的实证研究中,所采用的模型大多为线性回归模型和某种普通的非线性模型。而本文论述了两种灵活的非线性时间序列模型,这两种模型能有效改进非线性模型中的模型误设问题同时又能容纳各种普通的非线性模型从而能更好的对经济变量间的关系进行刻画。此外与本文模型相对应的估计方法是MCMC方法。MCMC方法充分利用了现代计算机的高速运算性能,有效改善了普通的最小二乘法和极大似然法在估计参数众多的非线性模型时效率低下的问题。因此本文的计量模型和估计方法为国内改进计量模型进行实证研究做出了探索性的工作,具有显著的方法论意义。(2)研究方法和视角的创新。目前国内对我国信贷需求的利率敏感度的研究,在计量方法上大都基于传统的线性回归模型,本文首次使用灵活的非线性模型进行了实证研究。另外在对我国货币政策冲击效应的分析中,目前国内学者使用的计量方法均为传统的向量自回归模型,本文首次使用灵活的向量自回归模型对货币政策对实体经济冲击效应的时变特征进行了研究。(3)本文的研究结论具有丰富的经济学和政策含义。对信贷需求的利率敏感度的实证结果表明,当经济增长率很高或者很低时,信贷需求对利率是不敏感的,当经济增长速度处于中间区域的时候信贷需求对利率较为敏感。这一结论隐含的政策意义为,在我国利用利率工具熨平经济周期的效果仍然是非常有限的。另外对我国货币政策的冲击效应的研究发现在早期,货币政策的冲击对经济增长率和通货膨胀率有比较大的短中期影响,而近年来货币政策的冲击对经济增长率和通货膨胀率的影响相对而言大大弱化了。这意味着为了实现货币政策的目标,我国在目前仍然需要改善货币政策的传导渠道以增强货币政策的有效性。上述发现都是基于灵活的非线性模型所产生的结论,从这个意义上说,本文具有显著的学术和应用意义。
In economics, the relationship between variables is often nonlinear, not linear. Thus, the traditional linear model is not suitable when describing the relationship between economic variables. In order to describe the relationship between economic variables more accurately, many non-linear models have been proposed. Compared with the linear model, these nonlinear models take into account the structural changes of relationship between economic variables. Thus, these models can describe the relationship more accurately. However, when setting these non-linear models, the evolution of structural changes of parameters is required to be set artificially. It will lead to the new problem of model misspecification. In order to reduce model misspecification in nonlinear model caused by the human factor, there is an urgent need to develop a flexible nonlinear model. Such flexible nonlinear models should reduce the subjectivity and arbitrariness to the maximum when setting models and can accommodate a variety of emerging nonlinear models.
In this paper, we describe two flexible nonlinear time series model in the framework of state space model, a single equation flexible nonlinear time series model and a flexible VAR model. The two flexible nonlinear time series model parameters do not need to make any human assumptions on the law of parameters'evolution, but adhering to the econometrics, "Let the data speak', estimate the law of evolution from the data. This reduce the model misspecification existed in the common nonlinear model greatly. On the other hand, our model can accommodate all kinds of common nonlinear time series model. When the model parameters take different values, it can be converted to a variety of common nonlinear time series model. Single equation flexible nonlinear time series model is developed from the traditional time-varying parameter model (TVP). By introducing distance function and sorting, the time-varying parameter model can be converted to a single equation flexible nonlinear time series model. Flexible VAR model is developed from traditional VAR model. Single equation flexible nonlinear time series model and flexible vector autoregressive model are estimated by Markov chain Monte Carlo method (MCMC). MCMC method uses high-speed computing performance of modern computers and can estimate the parameters of the model feasibly and effectively.
The flexible nonlinear model takes a big step from the nonlinear model and has profound developmental value and applied foreground. It has been regarded adequately and developed rapidly in abroad. But in China, the research on flexible nonlinear model is still seldom and just in the period of beginning. We use the flexible nonlinear model to study several problems of the macroeconomic field. The main contribution of our paper can be expressed in the following:(1) the innovation of econometric model and estimation method. Among the empirical researches in China, most of the models are linear model and common nonlinear model. The model in our paper has great flexibility. It can accommodate linear model and all nonlinear models and it is unnecessary to specify the evolutive mechanism. Our estimation method is MCMC method. In the flexible nonlinear model, it is impossible to use OLS and ML method to estimate the parameters. But MCMC method can make full use of the rapid computational character of computer and make feasible and effective estimation. Therefore our econometric model and estimation method make great contribution to improve domestic econometric model and have significant value on econometric method. (2) the innovation of visual angle in research. Among the literature of studying the sensitivity of credit demand on interest, most of the econometric models are linear model. This paper first uses the flexible nonlinear model to study the problem. The result shows that the sensitivity of credit demand on interest is changing companied by the different speed of economic growth. Among the literature of studying the effect of monetary policy, most of them use traditional VAR model. This paper uses flexible VAR model to study the effect of monetary policy. The result shows that the effect of monetary policy on economy has the significant time varying feature. (3) the conclusion of our research has great value for economics and policy. The result shows that when the speed of economic growth is vey high or very low, credit demand is not sensitive to interest. Only when the speed is medium, credit demand is sensitive to interest. It means that the effect of using interest tool to control economic cycle is still very limited. In the analysis of our monetary policy on, it can be found that monetary policy has bigger effect on economic growth rate and inflation rate in the earlier time. However, in recent years, the effect of monetary policy on economic growth and inflation become weaker. It means that we still need to improve the conductive channel of monetary policy to improve the effect of monetary policy. All the above finds are based on the flexible nonlinear model. From this point, this paper has significant value for academic and application.
引文
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