Over Factoranalyse

Summary This paper is an exposition about the model and techniques in factor analysis, a method of studying the covariance matrix of several properties on the basis of a sample co-variance matrix of independent observations on n individuals. The indeterminacy of the basis of the so called factor space and several possibilities of interpretation are discussed. The scale invariant maximum likelihood estimation of the parameters of the assumed normal distribution which also provides a test on the dimension of the factor space is compared with the customary but unjustified attack of the estimation problem by means of component analysis or modifications of it. The prohibitive slowness of convergence of iterative procedures recommended till now can be removed by steepest ascent methods together with Aitken's acceleration method. An estimate of the original observations according to the model assumed, as to be compared with the data, is given.     

Over Factoranalyse

Summary  This paper is an exposition about the model and techniques in factor analysis, a method of studying the covariance matrix of several properties on the basis of a sample co-variance matrix of independent observations on n individuals. The indeterminacy of the basis of the so called factor space and several possibilities of interpretation are discussed. The scale invariant maximum likelihood estimation of the parameters of the assumed normal distribution which also provides a test on the dimension of the factor space is compared with the customary but unjustified attack of the estimation problem by means of component analysis or modifications of it. The prohibitive slowness of convergence of iterative procedures recommended till now can be removed by steepest ascent methods together with Aitken's acceleration method. An estimate of the original observations according to the model assumed, as to be compared with the data, is given.     

Congestible public goods and local indeterminacy: A two-sector endogenous growth model

This paper shows that the congestible public goods can generate local indeterminacy in a two-sector, constant-return human capital enhanced growth model. While the productive public good exerts positive sector-specific externalities, the congestion effect generates negative aggregate externalities. The sector-specific externalities alone arising from productive public goods cannot establish local indeterminacy without the combination of negative externality in a model with social constant return technology. Congestible public good generates local indeterminacy if the degree of productive public good externality and the degree of congestion effect are large enough. The condition for indeterminacy is independent of the factor intensity rankings. The conditions are quantitatively assessed and the required parameter values for the degrees of public good externality and congestion are consistent with the estimated values in existing literature.     

Impatience and equilibrium indeterminacy

This paper extends the neoclassical one-sector optimal growth model by postulating that individual agents’ time preference (impatience) depends on the economy-wide average consumption and average income, which are social factors taken as external by individual agents. The paper shows that with the socially determined individual time preference local equilibrium indeterminacy can arise. Moreover, local indeterminacy can also be associated with global indeterminacy in many cases. The results hold in models with bounded and unbounded growth.     

Impatience, pollution, and indeterminacy

This paper examines an equilibrium growth model in which production activities generate environmental pollution that has a negative welfare effect and in which individual households' subjective discount rate is a function of individual consumption, which is internal to each household, and of total pollution, which is an external factor to the individual agents. It is shown that there may exist multiple steady states and that the dynamic equilibrium may display indeterminacy, depending on the properties of the discount-rate function, the pollution-capital relationship in production technology, and the pollution-consumption relationship in instantaneous utility. The long-run effects of tighter environmental policy are subsequently examined, and the results are also found to be dependent on the above factors.     

Forecasting the US term structure of interest rates using a macroeconomic smooth dynamic factor model

We extend the class of dynamic factor yield curve models in order to include macroeconomic factors. Our work benefits from recent developments in the dynamic factor literature related to the extraction of the common factors from a large panel of macroeconomic series and the estimation of the parameters in the model. We include these factors in a dynamic factor model for the yield curve, in which we model the salient structure of the yield curve by imposing smoothness restrictions on the yield factor loadings via cubic spline functions. We carry out a likelihood-based analysis in which we jointly consider a factor model for the yield curve, a factor model for the macroeconomic series, and their dynamic interactions with the latent dynamic factors. We illustrate the methodology by forecasting the U.S. term structure of interest rates. For this empirical study, we use a monthly time series panel of unsmoothed Fama–Bliss zero yields for treasuries of different maturities between 1970 and 2009, which we combine with a macro panel of 110 series over the same sample period. We show that the relationship between the macroeconomic factors and the yield curve data has an intuitive interpretation, and that there is interdependence between the yield and macroeconomic factors. Finally, we perform an extensive out-of-sample forecasting study. Our main conclusion is that macroeconomic variables can lead to more accurate yield curve forecasts.     

Factor substitution and taxation in a finance constrained economy

In this paper, we examine the effects of constant-rate factor taxation on macroeconomic stability in the Woodford (1986) model. Our focus is on how the degree of factor substitution, as measured by the elasticity of factor substitution (EOS) in production, affects different balanced-budget tax rules. Analytically, we show that indeterminacy can occur under capital income taxation only when the EOS is very low, whereas indeterminacy under labor income taxation is not subject to the EOS restriction. This finding is robust when we tax all of the factor incomes with equal rates. Thus, in terms of macroeconomic stability, taxing capital income is preferred to taxing labor income.     

Trade,redistribution and indeterminacy

In the present paper a tractable two-sector growth model with technological externalities and many countries is considered. It is shown that the occurrence of indeterminacy, a typical side-product of externalities, may appear due to the enlargement of the markets for goods and factors. Various scenarios of progressive levels of integration are considered. In particular, it is found that the integration into a common market on which countries trade the produced good and the inputs may lead to indeterminacy even when the equilibrium under full autarchy is determinate. A similar result holds when integration only affects consumption and capital goods. However, such result does not occur if the inverse of relative risk aversion is a linear or concave function. We conclude that in many usual situations, as the one with CES preferences, indeterminacy and the associated fragility of expectations and financial instability, is not likely to be increased by market integration.     

Capital–labor substitution and equilibrium indeterminacy

This paper examines the quantitative relationship between the elasticity of capital–labor substitution in production and the conditions needed for equilibrium indeterminacy (and belief-driven fluctuations) in a one-sector growth model. With variable capital utilization, the substitution elasticity has little quantitative impact on the minimum degree of increasing returns needed for indeterminacy. However, when capital utilization is constant, a below-unity substitution elasticity sharply raises the minimum degree of increasing returns because it imposes a higher effective adjustment cost on labor hours. Overall, our results show that empirically-plausible departures from the Cobb–Douglas production specification can make indeterminacy more difficult to achieve.     

Determinacy,indeterminacy and dynamic misspecification in linear rational expectations models

This paper proposes a testing strategy for the null hypothesis that a multivariate linear rational expectations (LRE) model may have a unique stable solution (determinacy) against the alternative of multiple stable solutions (indeterminacy). The testing problem is addressed by a misspecification-type approach in which the overidentifying restrictions test obtained from the estimation of the system of Euler equations of the LRE model through the generalized method of moments is combined with a likelihood-based test for the cross-equation restrictions that the model places on its reduced form solution under determinacy. The resulting test has no power against a particular class of indeterminate equilibria, hence the non rejection of the null hypothesis can not be interpreted conclusively as evidence of determinacy. On the other hand, this test (i) circumvents the nonstandard inferential problem generated by the presence of the auxiliary parameters that appear under indeterminacy and that are not identifiable under determinacy, (ii) does not involve inequality parametric restrictions and hence the use of nonstandard inference, (iii) is consistent against the dynamic misspecification of the LRE model, and (iv) is computationally simple. Monte Carlo simulations show that the suggested testing strategy delivers reasonable size coverage and power against dynamic misspecification in finite samples. An empirical illustration focuses on the determinacy/indeterminacy of a New Keynesian monetary business cycle model of the US economy.     

基于灰色关联理论和熵权法的企业人力资源风险评价

根据企业人力资源风险的成因、危害及其所具有的"灰"特性,采用以灰色关联理论和熵权法为基础的组合评价模型,研究了企业人力资源风险定量评价问题。此模型较好地克服了信息的不完全性和不确定性,给出了企业人力资源各风险要素对企业的影响程度排序,以利于企业规避风险,为企业人力资源风险评价提供了一种综合性的易操作的定量风险管理方法。     

Macroeconomic forecasting using structural factor analysis

The use of a small number of underlying factors to summarize the information from a much larger set of information variables is one of the new frontiers in forecasting. In prior work, the estimated factors have not usually had a structural interpretation and the factors have not been chosen on a theoretical basis. In this paper we propose several variants of a general structural factor forecasting model, and use these to forecast certain key macroeconomic variables. We make the choice of factors more structurally meaningful by estimating factors from subsets of information variables, where these variables can be assigned to subsets on the basis of economic theory. We compare the forecasting performance of the structural factor forecasting model with that of a univariate AR model, a standard VAR model, and some non-structural factor forecasting models. The results suggest that our structural factor forecasting model performs significantly better in forecasting real activity variables, especially at short horizons.     

Trend inflation,sticky prices,and expectational stability

Micro evidence indicates that each period a fraction of prices is kept unchanged under a positive trend inflation rate. In a sticky price model based on this evidence, recent research shows that high trend inflation is a serious cause for indeterminacy of rational expectations equilibrium under the Taylor rule. This paper examines implications of trend inflation for expectational stability of the equilibrium. An empirically plausible calibration of the model demonstrates that a fundamental rational expectations equilibrium is likely to be expectationally stable even in cases of indeterminacy induced by high trend inflation.     

Do credit market imperfections justify a central bank׳s response to asset price fluctuations?

Do credit market imperfections justify a central bank׳s response to asset price fluctuations? This study addresses this question from the perspective of equilibrium determinacy. In the model we use, prices are sticky and the working capital of firms is subject to asset values because of a lack of commitment. If credit market imperfections exist to a small degree, the Taylor principle is a necessary and sufficient condition for equilibrium determinacy, and monetary policy response to asset price fluctuations is good from the perspective of equilibrium determinacy. However, if credit market imperfections exist to a large degree such that the collateral constraint is binding, then the Taylor principle no longer guarantees equilibrium determinacy, and monetary policy response to asset price fluctuations becomes a source of equilibrium indeterminacy. We find that the existence of credit market imperfections makes it unsuitable to initiate a monetary policy response to deal with asset price fluctuations. We also find that reductions in credit market imperfections can enlarge the indeterminacy region of the model parameters.     

城市可持续发展的多准则模糊神经评价模型研究

城市的可持续发展受人口、经济、环境、资源和制度的现状变化及未来趋势等多种因素的影响，由于这些因素具有不确定性，且诸因素间相互耦联具有不易量化衡量的特点，因此本文引入多准则模糊神经理论，通过软计算对计算可持续发展的满意度进行综合评价，以便为城市的可持续发展战略决策提供服务。     

Monetary Policy Indeterminacy and Identification Failures in the U.S.: Results from A Robust Test

We propose a novel identification‐robust test for the null hypothesis that an estimated New Keynesian model has a reduced form consistent with the unique stable solution against the alternative of sunspot‐driven multiple equilibria. Our strategy is designed to handle identification failures as well as the misspecification of the relevant propagation mechanisms. We invert a likelihood ratio test for the cross‐equation restrictions (CER) that the New Keynesian system places on its reduced‐form solution under determinacy. If the CER are not rejected, sunspot‐driven expectations can be ruled out from the model equilibrium and we accept the structural model. Otherwise, we move to a second‐step and invert an Anderson and Rubin‐type test for the orthogonality restrictions (OR) implied by the system of structural Euler equations. The hypothesis of indeterminacy and the structural model are accepted if the OR are not rejected. We investigate the finite‐sample performance of the suggested identification‐robust two‐step testing strategy by some Monte Carlo experiments and then apply it to a New Keynesian AD/AS model estimated with actual US data. In spite of some evidence of weak identification as for the ‘Great Moderation’ period, our results offer formal support to the hypothesis of a switch from indeterminacy to a scenario consistent with uniqueness occurring in the late 1970s. Our identification‐robust full‐information confidence set for the structural parameters computed on the ‘Great Moderation’ regime turns out to be more precise than the intervals previously reported in the literature through ‘limited‐information’ methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Goodness-of-fit measures for multiple correspondence analysis

This paper presents three results: (1) It is shown that the explained variance criterion is inappropriate for multiple correspondence analysis (MCA). (2) There are two strategies to interpret a MCA configuration: factor analytical interpretation and cluster analytical interpretation. Goodness-of-fit measures for both interpretations are constructed. (3) These measures give (a) a more adequate picture of the model fit and (b) allow to differentiate whether a factor analytical interpretation or a cluster analytical interpretation is more adequate.     

Robust inflation-forecast-based rules to shield against indeterminacy

This paper provides a first attempt to quantify and at the same time utilize estimated measures of uncertainty for the design of robust interest rate rules. We estimate several variants of a linearized form of a New Keynesian model using quarterly US data. Both our theoretical and numerical results indicate that inflation-forecast-based (IFB) rules are increasingly prone to the problem of indeterminacy as the forward horizon increases. As a consequence the stabilization performance of optimized rules of this type worsens too. Robust IFB rules can be designed to avoid indeterminacy in an uncertain environment, but at an increasing utility loss as rules become more forward-looking.     

Chaos and sector-specific externalities

Benhabib and Farmer [1996. Indeterminacy and sector specific externalities. Journal of Monetary Economics 37, 397–419] explore the possibility of local indeterminacy in a two-sector model with sector-specific externalities. They find that very small sector-specific externalities are sufficient for local indeterminacy. In this case, it is possible to construct sunspot equilibria where extrinsic uncertainty matters. In this paper, I provide a global analysis of their model revealing the existence of Euler equation branching. This branching allows for regime switching equilibria with cycles and chaotic behavior. These equilibria occur whether the “local dynamics” are determinate or indeterminate.     

Multiple equilibria in two-sector monetary economies: An interplay between preferences and the timing for money

In this paper, we study the occurrence of local indeterminacy in two-sector monetary economies. We consider a general MIUF model with two alternative timings in monetary payments: the Cash-In-Advance timing, in which the cash available to buy goods is money in the consumers’ hands after they leave the bond market but before they enter the goods market, and the Cash-After-the-Market timing, in which agents hold money for transactions after leaving the goods market. We consider three standard specifications of preferences: the additively separable formulation, the Greenwood–Hercovitz–Huffman (GHH) (Greenwood et al., 1988) formulation and the King–Plosser–Rebelo (KPR) (King et al., 1988) formulation. First, we show that for all the three types of preferences, local indeterminacy occurs under the CIA timing with a low enough interest rate elasticity of money demand. Second, we show that with the CAM timing, although determinacy always holds under separable preferences, local indeterminacy can occur with GHH and KPR preferences. We thus prove that compared to aggregate models, two-sector models provide new rooms for local indeterminacy when non-separable standard preferences are considered.