Unbiased Expectations Research Articles

On the Bias of the Unbiased Expectation Theory

The unbiased expectation theory stipulates that long-term interest rates are determined by the market’s expectations of future short-term interest rates. According to this hypothesis, if investors have unbiased expectations about future interest rate movements, the forward interest rates should be good predictors of future spot interest rates. This hypothesis of the term structure of interest rates has long been a subject of debate due to empirical and theoretical challenges. Despite extensive research, a satisfactory explanation for the observed systematic difference between future spot interest rates and forward interest rates has not yet been identified. In this study, we approach this issue from an arbitrage theory perspective, leveraging on the connection between the expectation hypothesis and changes in probability measures. We propose that the observed bias can be explained by two adjustments: a risk premia adjustment, previously considered in the literature, and a stochastic adjustment that has been overlooked until now resulting from two measure changes. We further demonstrate that for specific instances of the Vasicek and Cox, as well as the Ingersoll and Ross, stochastic interest rate models, quantifying these adjustments reveals that the stochastic adjustment plays a significant role in explaining the bias, and ignoring it may lead to an overestimation of the required risk premia/aversion adjustment. Our findings extend beyond the realm of financial economic theory to have tangible implications for interest rate modelling. The capacity to quantify and distinguish between risk and stochastic adjustments empowers modellers to make more informed decisions, leading to a more accurate understanding of interest rate dynamics over time.

Econometric estimation of the cost of implementing the science-intensive projects based on efficient markets data

Subject. The article investigates cost drivers of research and development, analyzes key indicators of R&D costs characterizing the technical and operational perfection of science-intensive products, using the case of civilian and multipurpose helicopters. Objectives. The aim is to develop an econometric model of dependence of R&D costs on basic performance specifications of the helicopter to decide whether R&D should be undertaken. Methods. The study rests on the theory of fundamental value of assets, econometric methods of data analysis, the time value of money, and also on the theory of purchasing power parity, and unbiased expectations theory of interest rates. Results. The paper unveils the main sources of R&D cost growth for new-generation products in the science-intensive industries. Based on the econometric analysis, we highlight the main determinants of R&D costs, i.e. flight and technical characteristics of the helicopter, which determine the operational efficiency of design and technological decisions taken. We constructed a model to obtain the predictive estimate of R&D cost for Russian helicopters costs. Conclusions. The statistics on R&D costs of Russian civil helicopters does not sufficiently reflect their fair (market) value. Efficient markets are sources of more objective data on R&D costs of science-intensive products. When modeling the market value of R&D for Russian helicopters, it is advisable to rely on the Western markets data, with recalculation of development costs according to the economic conditions of the Russian aviation market. The analog method enables to quickly obtain a preliminary estimate of R&D costs.

A class of doubly stochastic shift operators for random graph signals and their boundedness

A class of doubly stochastic graph shift operators (GSO) is proposed, which is shown to exhibit: (i) lower and upper L2-boundedness for locally stationary random graph signals, (ii) L2-isometry for i.i.d. random graph signals with the asymptotic increase in the incoming neighbourhood size of vertices, and (iii) preservation of the mean of any graph signal – all prerequisites for reliable graph neural networks. These properties are obtained through a statistical consistency analysis of the proposed graph shift operator, and by exploiting the dual role of the doubly stochastic GSO as a Markov (diffusion) matrix and as an unbiased expectation operator. For generality, we consider directed graphs which exhibit asymmetric connectivity matrices. The proposed approach is validated through an example on the estimation of a vector field.

Nonlinear parsimonious forest modeling assuming normal distribution of residuals

To avoid the transformation of the dependent variable, which introduces bias when back-transformed, complex nonlinear forest models have the parameters estimated with heuristic techniques, which can supply erroneous values. The solution for accurate nonlinear models provided by Strimbu et al. (Ecosphere 8:e01945, 2017) for 11 functions (i.e., power, trigonometric, and hyperbolic) is not based on heuristics but could contain a Taylor series expansion. Therefore, the objectives of the present study are to present the unbiased estimates for variance following the transformation of the predicted variable and to identify an expansion of the Taylor series that does not induce numerical bias for mean and variance. We proved that the Taylor series expansion present in the unbiased expectation of mean and variance depends on the variance. We illustrated the new modeling approach on two problems, one at the ecosystem level, namely site productivity, and one at individual tree level, namely stem taper. The two models are unbiased, more parsimonious, and more precise than the existing less parsimonious models. This study focuses on research methods, which could be applied in similar studies of other species, ecosystem, as well as in behavioral sciences and econometrics.

Markov-modulated jump-diffusion models for the short rate: Pricing of zero coupon bonds and convexity adjustment

In this article, we consider a Markov-modulated model with jumps for the short rate. Using the main properties of a telegraphic process with jumps we compute the expected short rate. We obtain closed formulas for the zero coupon bond price assuming the Unbiased Expectation Hypothesis for the forward rates. Next, we obtain the coupled system of partial differential equations for the bond price using only no-arbitrage arguments. Numerical solutions are provided for some selected examples. The results obtained from both methods are compared and allow to estimate the magnitude of the convexity-adjustment.

Unbiased Expectations and Hayek’s Business Cycle Theory

Hayek’s business cycle theory does not depend on its traditional assumption of systematic predictive errors. To the contrary, the theory is also consistent with unbiased expectations where some people overestimate and others underestimate the length of an ongoing monetary expansion. The overestimating people tend to expect low real interest rates for an overly long period and invest in overly long production processes. They also tend to realize the error at the same moment—at the end of the monetary expansion, when they also liquidate the unprofitable investment. With the assumption of unbiased expectations, the theory predicts a cluster of observable errors and replicates the important features of Hayek’s canonical version of the theory.

An Analysis of the Effect of Global Financial Crisis on the Expectation Hypothesis of the Term Structure of Interest Rates in the Korean Bond Market

글로벌 금융위기로 세계의 금융시장은 크게 변화하였다. 본 연구는 이자율의 기간별 구조이론을 설명하는 기대가설에 입각하여 글로벌 금융위기 전후로 한국의 채권시장이 어떻게 변하였는지를 분석하였다. 기대가설에 따르면 채권시장의 선도이자율은 미래 단기이자율의 기댓값으로 해석할 수 있다. Fama, Bliss(1987)는 기대가설을 검정하기 위하여 선도이자율이 채권의 초과수익률을 설명할 수 없다는 가정 하에 회귀방정식을 사용하여 기대가설을 검정하였다. 본 연구에서는 Fama, Bliss(1987)의 회귀방정식을 사용하여 글로벌 금융위기 전과 후를 두 기간으로 나누어 기대가설을 검정하였고 글로벌 금융위기 전에는 통계적으로 기대가설을 반증하는 결과가 나타난다. 이러한 기대가설을 반증하는 결과는 금융시장에서 차익거래가 존재한다고 해석할 수 있고 이것을 채권시장의 이상 현상(anomaly)이라고 해석할 수 있다. 글로벌 금융위기 이후는 통계적으로 기대가설을 반증하는 결과가 줄어드는 실증분석 결과를 볼 수 있다. 그러므로 글로벌 금융위기 전후로 기대가설의 검정의 결과가 시간에 따라 변하였다고 할 수 있고 글로벌 금융위기 전후로 회귀계수가 변화되었음을 Chow 검정을 통하여 보여주었다. 따라서 통계적으로 글로벌 금융위기 전후로 한국의 채권시장의 기대가설의 증거는 변하였다고 해석할 수 있고 한국의 채권시장이 글로벌 금융위기 이후 차익거래 기회가 줄어들고 이상 현상이 줄어들어 채권시장이 더욱 투명해지고 효율적으로 변하고 있다고 해석할 수 있다.According to the expectation hypothesis, the forward rate of interest is an unbiased expectation of future spot rates and excess returns cannot be explained by the forward rates. The global financial crisis had changed many things in the financial market. This paper empirically tests whether the expectation hypothesis changes during the global financial crisis. Using the Korean bond data, we apply the Fama-Bliss regression to test whether forward rates predict excess returns before and after the 2008 financial crisis. We find statistically significant evidence against the expectation hypothesis in the pre-period of the financial crisis. But, the expectation hypothesis is not rejected in the post-period. We also show that the Fama-Bliss regression results change significantly before and after the crisis based on the Chow test. The evidence against the expectation hypothesis can be understood as an anomaly. Therefore, our result means that anomalies in the financial market tend to be diminished after the global financial crisis.

Forward Curve Bias and Optimization Errors

We derive optimal hedging ratios for interest rate risk under different assumptions that underpin the relationship between the forward rate and the expected future spot rate. In some instances, full hedging is optimal, and the conditions for the optimality of a partial hedge are identified. Less hedging (more floating debt in our model) is more optimal under the liquidity preference model than under the unbiased expectations hypothesis. This indicates that in times of higher preference for liquidity less hedging is optimal. Higher preference for liquidity correlates with larger term spreads (a steeper yield curve) and periods of monetary easing. Comparison of the analytical results with historical data indicates that partial hedging for interest rate risk is generally preferable over full hedging strategies with some exceptions. Lastly, the paper shows the role of market timing on hedging decisions.

Identification and Estimation of Dynamic Games When Players’ Beliefs Are Not in Equilibrium

This paper deals with the identication and estimation of dynamic games when players 鈂 beliefs about other players 鈂 actions may not be in equilibrium, i.e., they are not unbiased expectations of the actual behavior of other players. For instance, our model applies to dynamic competition in oligopoly industries when rms may have biased beliefs about competitors 鈂 strategies. First, we show that a exclusion restriction, typically used to identify empirical games, provides testable nonparametric restrictions of the null hypothesis of equilibrium beliefs. Second, we prove that an additional assumption, that we call no strategic uncertainty at two 鈂extreme 鈂

Why Do Migrant Workers Rely More Often on Referrals?

Intuitively, one can expect that migrant workers have smaller social networks in the new destination country and by that smaller probability of finding a job through referrals. However, empirical analysis of the SOEP data from 2002 to 2008 show that 41.21% of migrant workers and 31.79% of native workers found their current job through referrals. Estimation results of the panel probit model with random effects show that 7.26% statistically significant difference of the predicted probabilities of using referrals between migrant and native workers is not explained by the characteristics of the individuals and firms. In order to explain this puzzle, this paper presents a search and matching model with heterogeneous worker groups and several search channels. The firm observes the noisy signal of the productivity, the nationality and the search channel of the worker to form unbiased expectations about the true productivity of the worker. The probabilities to be hired for the two worker groups and different search channels are determined using ex-ante union bargained wage and expectations of the firm. Calibration results of the model show that even when migrant workers have smaller size of the social network, they gain more from recommendations, because their employment chances are initially much lower than employment chances of native workers.

A critical re-examination of the Carlson–Parkin method

ABSTRACTThe euro area has been experiencing a long period of inflation well below the targeted 2%. This has once again brought the problem of quantifying inflation expectations into the scientific focus. Within the framework of the Carlson–Parkin (CP) method, previous research has mostly focused on altering the probability distributions. Analysing as much as 2688 versions of the CP method, we prove that the distribution choice provides only minor improvements in the forecasting accuracy. On the other hand, the method assumptions (unbiased expectations and the number of survey response categories) play the pivotal role. We make an attempt to provide an assumptions-free quantification method by recognizing the fact that agents perceive ‘moderate’ inflation through the inflation targeting policy.

The Rationality Of Economic Forecasts: The Cases Of Rubber, Oil Palm, Forestry And Mining Sector

Forecasts of economic variables is very important for planning and policy making purposes. Forecasts is an important input in decision making processes because obtaining reliable forecasts of some relevant macroeconomic variables is necessary for efficient management of funds, time and resources.Business has always recognised the need for a view of the future and has used explicit forecasts in the design and execution of their economic andJor business policies. For example, a firm trying to decide upon its investment programme will have to take into account not only the current known set of circumstances but also the unknown economic and business conditions in the future. The firm has to form a view about the future, such as the likely sales, costs, prices, competitors' reactions, labour requirements, government regulations and so on. These views about the future values of economic variables are frequently referred to as 'expectations', that is, what the firm expects to happen in the future.In recent years the performances of many microeconomics and macroeconomics series have been erratic. For example, rate of inflation, price of crude oil, prices of primary commodities, rate of interest and other pertinent economic variables have been fluctuating widely and have caused concern among the public, politicians, economists and also the businessmen. According to Mayes (l 981), with such non-uniformity of economic variables observed in the last two decades, the role of expectations has become more relevant in the economic agents' decision making process. Mayes (1981) further states that under the present conditions it has become more important to consider what expectations actually are and how they are formed.The value of economic forecasts of certain macroeconomic variables can be derived from several methods. The three main methods for deriving economic forecasts are (i) time series, (ii) econometric models, and (iii) survey of intentions of concerned agents and organizations. Time seriesanalysis and econometric modeling are the two most widely used methods in economic forecasting, but Holden and Peel (1983) had noted their drawbacks. Recently, economists have turned their direction of interest in evaluating the rationality of economic forecasts from surveys of market participants. The empirical literature on the direct tests of the rational expectations hypothesis is vast and growing. Holden et al. (1985), Lovell (1986), Wallis (1989), Maddala (1991) and Pesaran (1991) had reviewed some of these studies. The aim was to determine whether survey data on economic forecasts are accurate in the Muth's (1961) sense, that is, whether participating economic agents used all available information at the time forecasts are made. in other words, the rational expectations hypothesis of the economic forecast was put to test. In general, the empirical studies do not support the rational expectations hypothesis.Most of the studies carried out to evaluate the rationality of business firms' forecasts of economic variables were conducted on developed nations. Madsen (1993) studies the formation of output expectations in manufacturing industry in Japan, Denmark, Finland, France, Germany, Netherlands, Norway, Sweden and the United Kingdom. He found that the rational expectations hypothesis was weakly rejected. Williams (1988) and Chazelas (1988) found investment forecasts biased predictors of the actual investment value for firms in the United Kingdom and France. Meganck et a!. (1988) have concluded that investment forecasts of the manufacturing firm in Belgium were unbiased predictors of the actual values. However. Daub (1982) failed to find any rationality of the Canadian capital investment intention survey data. On the other hand. a study by Leonard (1982) on employment forecasts by the United States services sectors found that the forecasts were biased and the rationality of these employment forecasts rejected.The purpose of this paper is to present some empirical evidence on the rationality of agricultural firm managers' expectations using survey data. This study is important because it adds to the current literature on the testing of rationality of survey data, in particular, it provides empirical evidence from the perspective of a developing country. As for the country under study, the finding of the study could establish whether the forecasts documented by such survey are accurate or not; and if not, ways to produce more accurate forecasts must be found. 'Rationality' in this paper means that managers in agricultural firms have unbiased expectations and efficiently utilised available information at the time the forecasts are made.

Resampling methods for particle filtering: identical distribution, a new method, and comparable study

This paper considers the arbitrary-proportional finite-set-partitioning problem which involves partitioning a finite set into multiple subsets with respect to arbitrary nonnegative proportions. This is the core art of many fundamental problems such as determining quotas for different individuals of different weights or sampling from a discrete-valued weighted sample set to get a new identically distributed but non-weighted sample set (e.g. the resampling needed in the particle filter). The challenge raises as the size of each subset must be an integer while its unbiased expectation is often not. To solve this problem, a metric (cost function) is defined on their discrepancies and correspondingly a solution is proposed to determine the sizes of each subsets, gaining the minimal bias. Theoretical proof and simulation demonstrations are provided to demonstrate the optimality of the scheme in the sense of the proposed metric.

What Explains Deviations in the Unbiased Expectations Hypothesis? Market Irrationality vs. the Peso Problem

What Explains Deviations in the Unbiased Expectations Hypothesis? Market Irrationality vs. the Peso Problem

What explains deviations in the unbiased expectations hypothesis? Market irrationality vs. the peso problem

Evidence from this study suggests that investor sentiment and the peso problem play a significant role in explaining expectation errors, rejecting the unbiased expectation hypothesis (UEH). The deviation of the UEH for long-term rates is mainly attributable to expectation errors, whereas the deviation of short-term rates is tied to the term premium. We decompose expectation errors and find that irrationality is more apparent in crisis periods, and the rational component becomes an influential factor in tranquil periods.

Testing the Foreign Exchange Parity Relations: A Case Analysis of UK Sterling, Japanese Yen and Us Dollar

Since the financial globalization has expanded and developed increasingly fast in recent years, the international parity relationships have been extensively studied due to their importance in international trade and investment. This paper investigates purchasing power parity (PPP), interest rate parity (IRP) and unbiased expectation hypothesis by analyzing three main currencies; UK sterling, Japanese Yen and US dollar during 2008 to 2010. Further, forward premium or discount is calculated and interpret in the study with time series data and ordinary least square (OLS) regression methodologies. It was found that, the unbiased expectation hypothesis and international interest parity holds for Japan-US case but does not hold for Japan-UK case. Finally, the purchasing Power Parity (PPP) holds for both two cases, which is varies with most previous literature.

Efficient calculation of unbiased expectation values in diffusion quantum Monte Carlo

Despite the proven utility of quantum Monte Carlo methods in addressing the quantum many-body problem, many important observables are difficult to calculate due to the presence of large, and sometimes divergent, statistical errors. The present state of the art allows the construction of renormalized estimators which result in finite variances, but which invariably include some systematic bias. We present a simple method for calculating unbiased expectation values of local operators in the diffusion quantum Monte Carlo method which is applicable to both bare and renormalized estimators, allowing the accurate calculation of important properties such as forces.

Discussion on research methods of bacterial resistant mutation mechanisms under selective culture—uncertainty analysis of data from the Luria-Delbrück fluctuation experiment

Whether bacterial drug-resistance is drug-induced or results from rapid propagation of random spontaneous mutations in the flora prior to exposure, remains a long-term key issue concerned and debated in both genetics and medicinal fields. In a pioneering study, Luria and Delbrück exposed E. coli to T1 phage, to investigate whether the number of resistant colonies followed the Poisson distribution. They deduced that the development of resistant colonies is independent of phage presence. Similar results have since been obtained on solid medium containing antibacterial agents. Luria and Delbrück's conclusions were long considered a gold standard for analyzing drug resistance mutations. More recently, the concept of adaptive mutation has triggered controversy over this approach. Microbiological observation shows that, following exposure to drugs of various concentrations, drug-resistant cells emerge and multiply depending on the time course, and show a process function, inconsistent with the definition of Poisson distribution (which assumes not only that resistance is independent of drug quantity but follows no specific time course). At the same time, since cells tend to aggregate after division rather than separating, colonies growing on drug plates arise from the multiplication of resistant bacteria cells of various initial population sizes. Thus, statistical analysis based on equivalence of initial populations will yield erroneous results. In this paper, 310 data from the Luria-Delbrück fluctuation experiment were reanalyzed from this perspective. In most cases, a high-end abnormal value, resulting from the non-synchronous variation of the two above-mentioned time variables, was observed. Therefore, the mean value cannot be regarded as an unbiased expectation estimate. The ratio between mean value and variance was similarly incomparable, because two different sampling methods were used. In fact, the Luria-Delbrück data appear to follow an aggregated, rather than Poisson distribution. In summary, the statistical analysis of Luria and Delbrück is insufficient to describe rules of resistant mutant development and multiplication. Correction of this historical misunderstanding will enable new insight into bacterial resistance mechanisms.

Term structure information and bond strategies

We examine term structure theories by using a novel approach. We form bond investment strategies based on different theories of the term structure in order to determine which strategy performs best. When using a manipulation-proof performance measure, we find that consistent with prior literature, an active strategy that is based on time varying term premiums can indeed form the basis of a successful bond strategy that outperforms an unbiased expectation inspired passive bond buy and hold strategy. This is true, however, for an earlier time period when the literature first made this claim. In a later time period, we find that the passive buy and hold strategy is significantly superior to all active strategies. This result is confirmed by statistical tests and it suggests that once it became known that an active strategy based on time varying term premiums could outperform a passive buy and hold strategy, the markets adjusted and arbitraged away this opportunity. Overall, it appears that the unbiased expectation hypothesis is the most likely explanation of the behaviour of the term structure during more recent times. This is because economically and statistically significant superior performance cannot be achieved if one uses information from the forward curve or the term structure as a guide to adjusting bond portfolios in response to changes in the term premium.

Measuring Inflation Expectations Using Interval‐Coded Data*

AbstractTo quantify qualitative survey data, the Carlson–Parkin method assumes normality, a time‐invariant symmetric indifference interval, and long‐run unbiased expectations. These assumptions are unnecessary for interval‐coded data. In April 2004, the Monthly Consumer Confidence Survey in Japan started to ask households about their price expectations a year ahead in seven categories with partially known boundaries. Thus one can identify up to six parameters including an indifference interval each month. This paper compares normal, skew normal (SN), skew exponential power (SEP), and skew t (St) distributions, and finds that an St distribution fits the data well. The results help us to better understand the dynamics of heterogeneous expectations.