Forecasting stock market volatility: Further international evidence

Abstract

This paper evaluates the out-of-sample forecasting accuracy of eleven models for monthly volatility in fifteen stock markets. Volatility is defined as within-month standard deviation of continuously compounded daily returns on the stock market index of each country for the ten-year period 1988 to 1997. The first half of the sample is retained for the estimation of parameters while the second half is for the forecast period. The following models are employed: a random walk model, a historical mean model, moving average models, weighted moving average models, exponentially weighted moving average models, an exponential smoothing model, a regression model, an ARCH model, a GARCH model, a GJR-GARCH model, and an EGARCH model. First, standard (symmetric) loss functions are used to evaluate the performance of the competing models: mean absolute error, root mean squared error, and mean absolute percentage error. According to all of these standard loss functions, the exponential smoothing model provides superior forecasts of volatility. On the other hand, ARCH-based models generally prove to be the worst forecasting models. Asymmetric loss functions are employed to penalize under-/over-prediction. When under-predictions are penalized more heavily, ARCH-type models provide the best forecasts while the random walk is worst. However, when over-predictions of volatility are penalized more heavily, the exponential smoothing model performs best while the ARCH-type models are now universally found to be inferior forecasters.     

三种菲利普斯曲线同异辨析

菲利普斯曲线是分析现代宏观经济问题和制定宏观经济政策的重要工具。本文主要阐述初始菲利普斯曲线、李普西菲利普斯曲线和萨缪尔森一索洛的菲利普斯曲线的推导演变过程,并对三种传统的菲利普斯曲线进行评述。     

The Most Beautiful Variations on Fair Wages and the Phillips Curve

This paper explores the connection between inflation and unemployment in two different models with fair wages in both the short and the long runs. Under customary assumptions regarding the sign of the parameters of the effort function, more inflation lowers the unemployment rate, albeit to a declining extent. This is because firms respond to inflation—which spurs effort by decreasing the reference wage—by increasing employment, thus maintaining the effort level constant as implied by the Solow condition. A stronger short‐run effect of inflation on unemployment is produced under varying as opposed to fixed capital, given that in the former case the boom produced by a monetary expansion is reinforced by an increase in investment. Therefore, I provide a new theoretical foundation for recent empirical contributions that find negative long‐ and short‐run effects of inflation on unemployment.     

Hyperbolic Discounting and the Phillips Curve

Using a standard dynamic general equilibrium model, we show that the interaction of staggered nominal contracts with hyperbolic discounting leads to inflation having significant long-run effects on real variables.     

Inventory Investment and the Empirical Phillips Curve

In this paper, we study the Calvo pricing models with finished goods inventory investment to demonstrate that the current inflation can be expressed as a function of the marginal cost of sales, not the marginal production cost, and expected future inflation. Under the assumption that the true aggregate marginal costs are not observable in actual data, we make use of equilibrium conditions for aggregate finished goods inventories to measure the time series of marginal costs, thereby leading to the construction of inflation series on the basis of the Phillips curve. Our results indicate the possibility of a successful fit of the empirical New Keynesian Phillips curve without relying on unit labor cost—a conventional measure of marginal production cost in the literature.     

Momentum and contrarian strategies in international stock markets: Further evidence

Previous studies have shown that market participants underestimate earnings growth for past winner stocks, and that growth stocks are more sensitive to earnings surprises. These findings suggest implementing momentum strategies with growth stocks. This study investigates linkages between value versus growth investment styles and momentum strategies in international markets. In addition, we extend Jegadeesh and Titman (2001)-type tests, which attempt to distinguish between competing explanations of the momentum phenomenon, to international market indices. Our full sample results show that momentum profits are concentrated in the growth indices, and that there is evidence of short-term overreaction in these and other indices that is subsequently corrected. Our subsample results are mixed; there is some evidence that the profitability of momentum (but not contrarian) strategies persists in the post-December 1987 period. However, unlike the earlier period, there is no evidence that markets overreact and that these overreactions are subsequently corrected.     

The New Keynesian Phillips Curve: From Sticky Inflation to Sticky Prices

The New Keynesian Phillips Curve (NKPC) model of inflation dynamics based on forward-looking expectations is of great theoretical significance in monetary policy analysis. Empirical studies, however, often find that backward-looking inflation inertia dominates the dynamics of the short-run aggregate supply curve. This inconsistency is examined by investigating multiple structural changes in the NKPC for the U.S. between 1960 and 2005, employing both inflation expectations survey data and a rational expectations approximation. We find that forward-looking behavior plays a smaller role during the high and volatile inflation regime to 1981 than in the subsequent period of moderate inflation, providing empirical support for sticky price models over the last two decades. A break in the intercept of the NKPC is also identified around 2001 and this may be associated with U.S. monetary policy in that period.     

通胀—增长权衡和中国菲利普斯曲线的平坦化

近年来发达经济体出现了菲利普斯曲线平坦化现象,但有关中国的研究尚缺乏共识。本文基于实证和理论分析,系统研究了中国菲利普斯曲线的平坦化问题。首先,结合货币政策冲击和月度SVAR框架,发现通胀的响应程度在2010年后大幅下降。由于证据显示总需求曲线并未平坦化,因此通胀响应弱化可解读为菲利普斯曲线的平坦化。数据显示,菲利普斯曲线平坦化与生产率增长放缓同时发生,因此,本文在标准DSGE模型中引入纵向内生增长渠道,该渠道基于研发投入和知识资本积累,从而使生产率内生于经济周期。研究发现：(1)内生增长渠道放大了需求冲击对产出的影响,但缩小了需求冲击对通胀的影响;(2)内生增长渠道改变通胀和增长之间的替代关系,但不改变边际成本向通胀的传导。分段估计显示,2010年后,通胀和增长的关系弱化是边际成本传导变弱和内生增长渠道变强共同作用的结果。本文认为,由于菲利普斯曲线的平坦化,中央银行应继续坚持稳增长和就业优先战略,关注但不必过于担心由此引发的通胀压力。     

Downward Nominal Wage Rigidities Bend the Phillips Curve

We introduce a model of monetary policy with downward nominal wage rigidities and show that both the slope and curvature of the Phillips curve depend on the level of inflation and the extent of downward nominal wage rigidities. This is true for the both the long‐run and the short‐run Phillips curve. Comparing simulation results from the model with data on U.S. wage patterns, we show that downward nominal wage rigidities likely have played a role in shaping the dynamics of unemployment and wage growth during the last three recessions and subsequent recoveries.     

Deep Habits in the New Keynesian Phillips Curve

We derive and estimate a New Keynesian Phillips Curve (NKPC) in a model with deep habits. Habits are deep in that they apply to individual consumption goods instead of aggregate consumption. This alters the NKPC in a fundamental manner since it introduces consumption growth and future demand terms into the NKPC equation. We construct the driving process in the deep habits NKPC by using the model's optimality conditions to impute time series for unobservable variables. The resulting series is considerably more volatile than unit labor cost. Generalized methods of moments estimation shows an improved fit and a much lower degree of indexation compared to the standard NKPC.     

Estimating the New Keynesian Phillips Curve: A Vertical Production Chain Approach

It has become customary to estimate the New Keynesian Phillips Curve (NKPC) with generalized method of moments using a large instrument set that includes lags of variables that are ad hoc to the firm's price-decision problem. Researchers have also conventionally used real unit labor cost (RULC) as the proxy for real marginal cost even though it is difficult to support its significance. This paper introduces a new proxy for the real marginal cost term as well as a new instrument set, both of which are based on the micro foundations of the vertical chain of production. I find that the new proxy, based on input prices as opposed to wages, provides a more robust and significant fit to the model. Instruments that are based on the vertical chain of production appear to be both more valid and relevant toward the model.     

现代菲利普斯曲线下的货币政策有效性——基于适应性预期和理性预期

货币政策作为重要的宏观调控工具,其最终目标既包括物价稳定、经济增长、充分就业等内部均衡目标,也包括国际收支平衡的外部均衡目标。内外均衡目标之间存在一定的冲突,同时物价稳定与经济增长(充分就业)内部均衡目标也存在一定的矛盾。菲利普斯曲线是刻画物价稳定与经济增长(充分就业)之间关系的重要工具,也是衡量货币政策有效性的重要尺度。研究主要阐述弗里德曼-菲尔普斯附加预期的菲利普斯曲线和新古典宏观经济学的理性预期菲利普斯曲线,并评注两种现代菲利普斯曲线所反映的货币政策有效性,最后强调了通胀预期管理的重要性。     

Costly Information,Planning Complementarities,and the Phillips Curve

Sticky information models capture the sluggish response of aggregate prices to monetary shocks but fail to match the magnitude and frequency of price changes at the microlevel. This paper shows that accounting for the endogenous decision of when to acquire new information about different shocks can help overcome this shortcoming. In the calibrated model, prices change frequently and by large amounts in response to idiosyncratic shocks but sluggishly to monetary shocks. The paper also highlights that many predictions of the sticky information and rational inattention models are the same and thus robust to different specifications of information processing costs.     

基于产出缺口的菲利普斯曲线对我国通胀预测的研究

基于菲利普斯曲线理论中产出缺口与通货膨胀率的关系,应用卡尔曼滤波方法估算我国的潜在产出与产出缺口,通过格兰杰因果关系验证产出缺口与通货膨胀的因果关系,并建立产出缺口的菲利普斯曲线模型进行通货膨胀预测。实证结果表明该模型能够较好地预测我国通货膨胀,从而能为制定相应的货币政策提供良好的参考。     

The Other January Effect: international evidence

This paper investigates the predictive power of stock market returns in January for the subsequent 11 months’ returns across 19 countries, thereby contributing to the literature on stock market seasonalities. Only 2 out of 19 countries’ stock markets exhibit a robust Other January Effect. In the light of this evidence, we conclude that the Other January Effect is not an international phenomenon.     

The turn-of-the-month effect still lives: the international evidence

This paper examines 19 country stock market indices for recent evidence of the turn-of-the-month (TOM) pattern in daily stock returns using both parametric and nonparametric measures to address concerns regarding methodologies applied in prior anomalies studies. We find that the 4-day TOM period accounts for 87% of the monthly return, on average, across countries, in the stock markets of 15 countries where the TOM pattern exists. These countries account for 77% of the foreign market capitalization value. The parametric and nonparametric results provide information regarding the degree to which distributional assumption violations may lead to incorrect conclusions.     

International Evidence on the New Keynesian Phillips Curve Using Aggregate and Disaggregate Data

We present a unique empirical analysis of the properties of the New Keynesian Phillips Curve (NKPC) using an international data set of aggregate and disaggregate sectoral inflation. Our results from panel time‐series estimation clearly indicate that sectoral heterogeneity has important consequences for aggregate inflation behavior. Heterogeneity helps to explain the overestimation of inflation persistence and underestimation of the role of marginal costs in empirical investigations of the NKPC that use aggregate data. We find that combining disaggregate information with heterogeneous‐consistent estimation techniques helps to reconcile, to a large extent, the NKPC with the data.     

The underreaction hypothesis and the new issue puzzle: evidence from Japan

This article investigates the long-term equity performance ofJapanese firms issuing convertible debt and equity. We findthat issuing firms perform poorly (except for equity rightsissues) compared to nonissuing firms even though the stock-pricereaction to convertible debt and equity issues is not negativefor Japanese firms. This underperformance is strongest for firmsissuing public convertible debt. In contrast to the United States,poor performance is not concentrated in smaller firms and infirms with a high market-to-book ratio. Simple behavioral explanationsadvanced for the new issue puzzle in the United States do notseem consistent with the Japanese experience.     

通胀惯性、混合菲利普斯曲线与中国通胀动态特征

本文在Gali & Gertler(2000)的基础上,构建了一个考虑通胀惯性的高阶滞后混合菲利普斯曲线的结构模型框架,并基于GMM模型对高阶滞后混合菲利普斯曲线进行计量检验和实证分析,通过估计其结构参数和深度参数来度量我国通胀惯性的大小及对通胀的影响,刻画我国通胀的动态特征以及我国厂商的定价行为。实证结果表明,我国通胀具有高阶滞后混合菲利普斯曲线的动态特征,滞后阶数为2,通胀同时存在向前看的理性预期和向后看的适应性预期;我国通胀惯性和通胀预期的强度对通胀率指标范畴十分敏感,CPI通胀率的通胀惯性和持续性大于RPI,CPI通胀率的适应性预期特征强于理性预期特征,RPI通胀率的理性预期特征强于适应性预期特征。在我国厂商定价概率方面,CPI通胀率相对于RPI通胀率,产品价格调整时间间隔较长,厂商对经济政策的反应较不敏感;在厂商价格预期行为方面,CPI通胀率相对于RPI通胀率,厂商对适应性预期的依赖程度超过了理性预期。     

Inflation Dynamics and the New Keynesian Phillips Curve in Four Central European Countries

This paper seeks to shed light on the inflation dynamics of four new central European EU members: the Czech Republic, Hungary, Poland, and Slovakia. To this end, the New Keynesian Phillips curve augmented for open economies is estimated and additional statistical tests applied, with the following results: (1) the claim of New Keynesians that the real marginal cost is the main inflation-forcing variable is fragile, (2) inflation seems to be driven by external factors, and (3) although inflation holds a forward-looking component, the backward-looking component is substantial. An intuitive explanation for higher inflation persistence may be adaptive, rather than rational price setting of local firms.