An investigation into a non-linear stochastic trend model

The paper explores the empirical properties of a non-linear stochastic trend model which can be viewed as an intermediate case between a linear and a log-linear trend model. I assess the small sample distribution of the ML estimator by Monte Carlo simulations and use it to model some typical macroeconomic time series. The non-linear trend model turns out to be an important tool which warrants further analysis. I also compute impulse response functions and compare them with those obtained from a conventional linear model. First version received: August 1997/final version received: June 1998     

Convergence of per capita sulphur dioxide emissions across US states

This study examines the stochastic conditional convergence of sulphur dioxide (SO₂) emissions using the Residual Augmented Least Squares–Lagrange Multiplier (RALS–LM) unit root test with structural breaks. This procedure allows the data to account for trend breaks and nonnormal errors that have been ignored or deemphasized in previous studies. The study finds that per capita sulphur dioxide emissions exhibits stochastic conditional convergence across US states.     

An extension of the asymmetric causality tests for dealing with deterministic trend components

This article extends the asymmetric causality tests, as developed by Hatemi-J (2012), for dealing with deterministic trend parts. It is shown how integrated variables up to three degrees with deterministic trend parts can be transformed into positive and negative cumulative partial components. These cumulative components can be used for implementing the asymmetric causality tests based on a Wald test statistic that is shown to follow a chi-square distribution asymptotically. Each solution is expressed as a proposition and a mathematic proof is provided for each underlying proposition. This issue is important because most economic or financial variables seem to be characterized by both stochastic as well as deterministic trend parts. An empirical application is provided in order to show how the oil prices and the exchange rates as integrated variables with drift and trend can be transformed into cumulative partial sums of positive and negative components. The conducted causality tests reveal that allowing for asymmetry has important repercussions for the underlying causal inference between these two variables.     

DSGE models,detrending, and the method of moments

One important question in the DSGE literature is whether we should detrend data when estimating the parameters of a DSGE model using the moment method. It has been common in the literature to detrend data in the same way the model is detrended. Doing so works relatively well with linear models, in part because in such cases the information that disappears from the data is usually related to the parameters that also disappear from the detrended model. Unfortunately, in heavy non‐linear DSGE models, parameters rarely disappear from detrended models, but information does disappear from the detrended data. Using a simple real business cycle model, we show that both the moment method estimators of parameters and the estimated responses of endogenous variables to a technological shock can be seriously inaccurate when detrended data are used in the estimation process. Using a dynamic stochastic general equilibrium model and U.S. data, we show that detrending the data before estimating the parameters may result in a seriously misleading response of endogenous variables to monetary shocks. We suggest building the moment conditions using raw data, irrespective of the trend observed in the data.     

The employability of new graduates: a study of differences between UK universities

The non-stationarity tests of Phillips-Perron (1988) (PP tests) suggest that Australian macroeconomic output possesses a stochastic rather than a deterministic log-linear trend. Kwiatkowski et al. (1991) argue that such tests have low power and propose the KPSS test, in which the null is stationary. However, the KPSS test results reinforce the PP findings for Australia. Cochrane (1988) variance ratio (VR) tests further suggest that there may be a very strong random-walk component in the Australian business cycle. Rappoport and Reichlin (1989), however, argue that all such tests are biased in favour of the stochastic trend alternative if there are trend breaks in the data. Following up on this point, the paper finds that, in Australia's case, the stochastic trend alternative is statistically dominated when the data are allowed to be characterized by a probabilistic, regime-switching, segmented trend specification. Therefore, to the extent that real business-cycle theories of the business cycle gain support from stochastic trends in real output, this latter piece of Australian evidence does not strengthen their case.     

Remeasuring and decomposing stochastic trends in business cycles

This paper is motivated by the fact that the standard deviation of cyclical TFP derived from the standard approach under the stochastic trend is not even close to the real-world data. The main part of the paper devotes to developing a new method to apply geometric Brownian motion to characterize TFP in continuous time and converting it to an estimated process of random walk with drift. As a result, the drift estimate together with the lagged TFP in the random walk process are the stochastic trend of TFP and the stochastic error term in the random walk with drift process is the cyclical component of TFP. I then have two findings: the first one is that the standard deviation of cyclical TFP derived from the new approach is much closer to the real-world data; the second one is that stochastic trend of TFP can be decomposed into three parts: an initial value, a deterministic trend, and a term involved with Weiner process. Moreover, this paper argues that, by recalculating the business cycle statistics based on a rational expectations model, if we remeasure the stochastic trend and cyclical component of TFP using the new approach, then the ability of real business cycle model to mimic real-world economic fluctuations will be significantly improved.     

Further on the Nature of the Australian Business Cycle

Strong and Tan (1991) found Australian output variation was well characterized by a stochastic trend implying output shocks have a permanent effect on the level of activity. The paper finds that in Australia the stochastic trend alternative is statistically dominated when the data are allowed to be characterized by a probabilistic segmented trend specification. This finding implies shocks will only have a permanent effect on output when the series' growth path switches from one growth regime into another as a result of the shock.     

Trend-cycle correlation, drift break and the estimation of trend and cycle in Canadian GDP

Abstract.  Univariate correlated trend cycle models are highly sensitive to the specifications of breaks in the data. This paper argues, using Monte Carlo experiments, that a bivariate correlated unobserved components (UC) framework with breaks delivers substantially more accurate results for the trend-cycle parameters than the corresponding univariate frameworks in a finite sample size. The paper estimates stochastic trend and cyclical fluctuations in Canada from a bivariate UC model. Results show a fairly volatile stochastic trend after the drift break and the negative trend-cycle shock correlation are accounted for. The estimated cyclical component is large, persistent, and consistent with ECRI denoted Canadian recessions.     

Unit roots and structural breakpoints in China’s macroeconomic and financial time series

This paper applies unit-root tests to 10 Chinese macroeconomic and financial time series that allow for the possibility of up to two endogenous structural breaks. We found that 6 of the series, i.e., GDP, GDP per capita, employment, bank credit, deposit liabilities and investment, can be more accurately characterized as a segmented trend stationarity process around one or two structural breakpoints as opposed to a stochastic unit root process. Our findings have important implications for policy-makers to formulate long-term growth strategy and short-run stabilization policies, as well as causality analysis among the series. __________ Translated from Economic Research Journal (经济研究), 2006, (1) (in Chinese)     

过剩产能与通货膨胀的关系分析——基于包含随机波动的TVP模型考察

为了更准确的考察目前中国的过剩产能与通货膨胀的关系,本文构造了一个包含随机波动的TVP模型对中国通货膨胀与产出缺口间的关系进行了实证分析,实证结果表明:中国通货膨胀的随机波动程度有不断增强的趋势;产出缺口对通货膨胀的影响力度有不断减弱的趋势;改善经济发展的结构性矛盾、提高供给部门的效率是实现价格稳定下经济快速增长的根本途径.     

Deterministic and stochastic trends in the Lee–Carter mortality model

The Lee and Carter (1992) model assumes that the deterministic and stochastic time series dynamics load with identical weights when describing the development of age-specific mortality rates. Effectively this means that the main characteristics of the model simplify to a random walk model with age-specific drift components. But restricting the adjustment mechanism of the stochastic and linear trend components to be identical may be too strong a simplification. In fact, the presence of a stochastic trend component may itself result from a bias induced by properly fitting the linear trend that characterizes mortality data. We find empirical evidence that this feature of the Lee–Carter model overly restricts the system dynamics and we suggest to separate the deterministic and stochastic time series components at the benefit of improved fit and forecasting performance. In fact, we find that the classical Lee–Carter model will otherwise overestimate the reduction of mortality for the younger age groups and will underestimate the reduction of mortality for the older age groups. In practice, our recommendation means that the Lee–Carter model instead of a one-factor model should be formulated as a two- (or several) factor model where one factor is deterministic and the other factors are stochastic. This feature generalizes to the range of models that extend the Lee–Carter model in various directions.     

Modelling the trend and seasonality in the consumption of alcoholic beverages in the United Kingdom

A univariate time series analysis of the consumption of beer, wine and spirits in the UK over the period 1964–1995 is presented. The analysis shows that the consumption of beer and wine exhibits stochastic seasonality while the consumption of spirits exhibits deterministic seasonality. Moreover, the three series are found to have stochastic trends. Analysis of the out-of-sample forecasting power of the various models reveals that the model with stochastic trend and seasonality is superior to other models. The results cast doubt on the validity and soundness of the practice of modelling the consumption of alcoholic beverages by assuming deterministic trend and seasonality.     

Seasonality and stochastic trends in German consumption and income, 1960.1–1987.4

The quarterly time series of German consumption and income are analyzed with respect to seasonality and stochastic trends. It emerges that both variables can be appropriately described by a periodically integrated autoregression. An implication is that the stochastic trend and the seasonal fluctuations are not independent for each of the univariate series. In order to test for cointegration across the two series, we propose several methods which take account of the relationship between seasons and trends in the univariate series. Some of these methods boil down to extracting the stochastic trend from the univariate series in a first step and to relating these trends using cointegration techniques in a second step. Another method is an extension of the Johansen cointegration testing approach to periodic vector autoregressions. Monte Carlo simulations are used to evaluate the empirical performance of the various methods. The main empirical result is that only in the first quarter there seems to be cointegration between German consumption and income.     

Fitting survey expectations and uncertainty about trend inflation

Many studies document that the inflation rate is governed by persistent trend shifts and time-varying uncertainty about trend inflation. As both these quantities are unobserved, a forecaster has to learn about changes in trend inflation by a signal extraction procedure. I suggest that the forecaster uses a simple IMA(1, 1) model because it is well suited to forecast inflation and it provides an efficient way to solve the signal extraction problem. I test whether this model provides a good fit for expectations from the Survey of Professional Forecasters. The model appears to be well suited to model observed inflation expectations if we allow for stochastic volatility. When I estimate the implied learning rule, results are supportive for the trend learning hypothesis. Moreover, stochastic volatility seems to influence the way agents learn over time. It appears that survey participants systematically adapt their learning behavior when inflation uncertainty changes.     

Shock Persistence and Stochastic Trends in Australian Aggregate Output and Consumption*

The distinction between transitory and permanent shocks is at the centre of the debate on which class of models is best suited to represent economic variables: stationary models around a deterministic trend, or stationary models around a stochastic trend The debate u here focused on the Australian case. It is found that both aggregate output and consumption are characterized by stochastic trends, but without a transitory component This corresponds to a measure of shock persistence equal to one for both variables. For the specific case of aggregate output, this result may be interpreted as indicating the absence of business cycles     

World economic convergence: Does the estimation methodology matter?

An extant empirical literature produces evidence on economic convergence using methods that assume an underlying deterministic trend. Competing approaches that assume a stochastic trend, however, produce only limited evidence of economic convergence. In this paper we address this puzzling feature of the literature by providing a comprehensive analysis of economic convergence using three methodologies that cover all possible underlying assumptions: deterministic, stochastic, and combination trends. We also develop a method for an overall Stochastic Convergence Rate Index, that combines the outcomes of alternative stochastic tests and provides a single measure of the intensity of stochastic convergence. We consider 135 economies over the period 1980–2017. We find that economic convergence occurs at a global level through the formation of convergence clubs, and economic convergence emerges as a deterministic rather than a stochastic process. Tests that ignore deterministic trends tend to understate the evidence for convergence.     

Comparison of Stochastic and Spline Models for Temperature‐based Derivatives in China

In this paper, we propose modelling the seasonal variation of temperature with a stochastic process to achieve normality of residuals. We conduct a heuristic comparison of the new stochastic seasonal variation model with three established empirical temperature and pricing models: the model of Alaton et al., the continuous autoregressive model and the spline model. The test criteria are residual normality, the Akaike information criterion, relative errors, and stability of price behaviour. The objective of the paper is to find the most suitable model for the application of temperature‐based derivatives in China. Therefore, 30 years of daily average temperature data from 12 cities in mainland China are applied. The results show that the stochastic seasonal variation model dominates the other three models by providing a more precise fitting of the temperature process. Furthermore, the spline model displays inconsistencies when it is applied to Chinese temperature data. This model has the smallest relative errors, but the worst results for normality of residuals.     

A test of the expectations hypothesis of the term structure of interest rates for Sri Lanka

This paper tests the expectations hypothesis of the term structure of interest rates for Sri Lanka. The data support the hypothesis that forward and spot rates are cointegrated suggesting a stochastic trend in the structure of interest rates. However, the hypothesis that forward rates are unbiased predictors of future spot rates is rejected.     

90年代西方经济地理学的文化研究趋向评述

９０年代后半期以来西方经济地理研究呈现出一种文化研究趋向,那重视文化因素在经济活动空间格局的形成和演变中的作用,着重从历史和文化的角度把握世界、国家和区域的时空变化,强调经社会文化与政治经济相互作用的动态过程中来认识资源、资本和劳动力等生产要素的空间特征,通过认识具体区域的基本特性来氢气区域发展的本质,从而更准确地认识地方多样性和地理差异,本文在简要回顾现代经济地理的主要理论流派及其阶段性特征的基     

公司特质波动在上升吗?——基于文献的述评

文章针对目前金融经济学的新兴研究领域——公司特质波动,从两个方面进行文献述评:特质波动测度和时间趋势。公司特质波动的测度方法主要依赖于资产定价模型的选择,因此,其误差根据方法的不同而各异;在时间趋势方面,众多学者对在美国及其他发达国家股市存在明显的特质波动上升趋势从各种角度予以解释;由于针对公司特质波动的研究刚刚展开,国内学者的研究成果较少,大部分仅对中国A股市场平均特质波动水平进行相关测度。在文献综述的基础上,文章提出进一步的研究展望,为今后研究提供借鉴和参考之用。