Bayesian point estimation of the cointegration space

A neglected aspect of the otherwise fairly well developed Bayesian analysis of cointegration is point estimation of the cointegration space. It is pointed out here that, due to the well known non-identification of the cointegration vectors, the parameter space is not Euclidean and the loss functions underlying the conventional Bayes estimators are therefore questionable. We present a Bayes estimator of the cointegration space which takes the curved geometry of the parameter space into account. This estimate has the interpretation of being the posterior mean cointegration space and is invariant to the order of the time series, a property not shared with many of the Bayes estimators in the cointegration literature. An overall measure of cointegration space uncertainty is also proposed. Australian interest rate data are used for illustration. A small simulation study shows that the new Bayes estimator compares favorably to the maximum likelihood estimator.     

Nowcasting and forecasting global financial sector stress and credit market dislocation

We introduce a new international model for the systematic distress risk of financial institutions from the US, the European Union, and the Asia-Pacific region. Our proposed dynamic factor model can be represented as a nonlinear, non-Gaussian state space model with parameters that we estimate using Monte Carlo maximum likelihood methods. We construct measures of global financial sector risk and of credit market dislocation, where credit market dislocation is defined as a significant and persistent decoupling of the credit risk cycle from macro-financial fundamentals in one or more regions. We show that, in the past, such decoupling has preceded episodes of systemic financial distress. Our new measure provides a risk-based indicator of credit conditions, and as such, complements earlier quantity-based indicators from the literature. In an extensive comparison with such quantity-based systemic risk indicators, we find that the behaviour of the new indicator is competitive with that of the best quantity-based indicators.     

Predicting equity premium using dynamic model averaging. Does the state–space representation matter?

Dynamic model averaging (DMA) has become a very useful tool with regards to dealing with two important aspects of time-series analysis, namely, parameter instability and model uncertainty. An important component of DMA is the Kalman filter. It is used to filter out the latent time-varying regression coefficients of the predictive regression of interest, and produce the model predictive likelihood, which is needed to construct the probability of each model in the model set. To apply the Kalman filter, one must write the model of interest in linear state–space form. In this study, we demonstrate that the state–space representation has implications on out-of-sample prediction performance, and the degree of shrinkage. Using Monte Carlo simulations as well as financial data at different sampling frequencies, we document that the way in which the current literature tends to formulate the candidate time-varying parameter predictive regression in linear state–space form ignores empirical features that are often present in the data at hand, namely, predictor persistence and predictor endogeneity. We suggest a straightforward way to account for these features in the DMA setting. Results using the widely applied Goyal and Welch (2008) dataset document that modifying the DMA framework as we suggest has a bearing on equity premium point prediction performance from a statistical as well as an economic viewpoint.     

Endogenous credit standards and aggregate fluctuations

Widespread empirical evidence shows that credit standards fluctuate over the business cycle. We build a macroeconomic model in which countercyclical lending standards emerge as an equilibrium outcome. In the model, banks compete on lending rates as well as collateral requirements. The presence of lending relationships between firms and banks gives rise to endogenous fluctuations in interest rate margins and collateral requirements. We demonstrate that endogenous credit standards amplify business cycles, driving up output volatility by around 25% when compared to a model without lending relationships. Finally, we show that in order to combat the effects of endogenous credit standards on macroeconomic volatility, a countercyclical loan-to-value ratio is an effective macroprudential policy tool.     

Firm–bank credit network,business cycle and macroprudential policy

We present an agent-based model to study firm–bank credit market interactions in different phases of the business cycle. The business cycle is exogenously set, and it can give rise to various scenarios. Compared to other models in this literature strand, we improve the mechanism according to which the dividends are distributed, including the possibility of stock repurchase by firms. In addition, we locate firms and banks over a space and firms may ask credit to many banks, resulting in a complex spatial network. The model reproduces a long list of stylized facts and their dynamic evolution as described by the cross-correlations among model variables. The model allows us to test the effectiveness of rules designed by the current financial regulation, such as the Basel III countercyclical capital buffer. We find that the effectiveness of this rule changes in different business cycle environments and this should be considered by policy makers.

     

Quality control for structural credit risk models

Over the last four decades, a large number of structural models have been developed to estimate and price credit risk. The focus of the paper is on a neglected issue pertaining to fundamental shifts in the structural parameters governing default. We propose formal quality control procedures that allow risk managers to monitor fundamental shifts in the structural parameters of credit risk models. The procedures are sequential — hence apply in real time. The basic ingredients are the key processes used in credit risk analysis, such as most prominently the Merton distance to default process as well as financial returns. Moreover, while we propose different monitoring processes, we also show that one particular process is optimal in terms of minimal detection time of a break in the drift process and relates to the Radon–Nikodym derivative for a change of measure.     

Analytical quasi maximum likelihood inference in multivariate volatility models

Quasi maximum likelihood estimation and inference in multivariate volatility models remains a challenging computational task if, for example, the dimension of the parameter space is high. One of the reasons is that typically numerical procedures are used to compute the score and the Hessian, and often they are numerically unstable. We provide analytical formulae for the score and the Hessian for a variety of multivariate GARCH models including the Vec and BEKK specifications as well as the recent dynamic conditional correlation model. By means of a Monte Carlo investigation of the BEKK–GARCH model we illustrate that employing analytical derivatives for inference is clearly preferable to numerical methods.     

Statistical Inference under Symmetry

We explore the consequences of adjoining a symmetry group to a statistical model. Group actions are first induced on the sample space, and then on the parameter space. It is argued that the right invariant measure induced by the group on the parameter space is a natural non-informative prior for the parameters of the model. The permissible sub-parameters are introduced, i.e., the subparameters upon which group actions can be defined. Equivariant estimators are similarly defined. Orbits of the group are defined on the sample space and on the parameter space; in particular the group action is called transitive when there is only one orbit. Credibility sets and confidence sets are shown (under right invariant prior and assuming transitivity on the parameter space) to be equal when defined by permissible sub-parameters and constructed from equivariant estimators. The effect of different choices of transformation group is illustrated by examples, and properties of the orbits on the sample space and on the parameter space are discussed. It is argued that model reduction should be constrained to one or several orbits of the group. Using this and other natural criteria and concepts, among them concepts related to design of experiments under symmetry, leads to links towards chemometrical prediction methods and towards the foundation of quantum theory.     

Bayesian analysis of the error correction model

This paper presents a method for estimating the posterior probability density of the cointegrating rank of a multivariate error correction model. A second contribution is the careful elicitation of the prior for the cointegrating vectors derived from a prior on the cointegrating space. This prior obtains naturally from treating the cointegrating space as the parameter of interest in inference and overcomes problems previously encountered in Bayesian cointegration analysis. Using this new prior and Laplace approximation, an estimator for the posterior probability of the rank is given. The approach performs well compared with information criteria in Monte Carlo experiments.     

On Bayesian analysis and computation for functions with monotonicity and curvature restrictions

Our goal is inference for shape-restricted functions. Our functional form consists of finite linear combinations of basis functions. Prior elicitation is difficult due to the irregular shape of the parameter space. We show how to elicit priors that are flexible, theoretically consistent, and proper. We demonstrate that uniform priors over coefficients imply priors over economically relevant quantities that are quite informative and give an example of a non-uniform prior that addresses this issue. We introduce simulation methods that meet challenges posed by the shape of the parameter space. We analyze data from a consumer demand experiment.     

Consumer credit and consumption forecasts

Recent advances in the theory of consumer behavior indicate that consumption may exhibit non-linear dynamics characterized by occasional surges. Building upon them, and taking explicitly into account the forward-looking nature of consumption, this paper argues that rising consumer debt can signal such surges, as well as the consumption underprediction which will occur if they are not taken sufficiently into account in forecasting. This insight is tested with and strongly confirmed by the Organization of Economic Cooperation and Developments forecasts for the USA. The results should be of interest not only to professional forecasters and policy-makers, but also to theoretical economists and econometricians who study non-linear dynamic models.     

The effects of bargaining power on trade credit in a supply network

We develop a multi-tier supply network model, rooted in social network theory, to evaluate the effect of bargaining power on trade credit and to track the effect of buyers' trade credit on suppliers' trade credit. We apply social network analysis to measure companies' bargaining power in the supply network of Hennes & Mauritz AB (H&M, the Swedish clothing retailer). The results show that the buyer's bargaining power significantly affects the choice of trade credit, and that the supplier's “upstreamness” is significantly associated with its trade credit. We find limited evidence to support the notion of a financial bullwhip effect, a result that merits further research, since this study is limited to the network of one company up to its fourth tier of suppliers in one financial year. Our results can be applied by companies seeking to control their cash flow and, therefore, the financial pressure within their supply network. This study contributes to the literature by bringing social network measures into the buyer–supplier financial flow, as well as offering one of the first empirical examinations of the propagation of financial pressure in a multi-tier supply network.     

A billing policy for credit customers

Firms frequently bill customers on a fixed-period basis (such as once a month), or on a fixed-amount basis (whenever the outstanding credit balance reaches a particular amount). We examine here a more flexible procedure, the bill-or-carry policy, which uses a simple decision rule and results in lower costs than either the fixed-period or fixed-amount procedures. The logic and properties of the bill-or-carry policy are compared with those of the fixed-period and fixed-amount procedures.     

Estimating causal effects of credit decisions

In principle, making credit decisions under uncertainty can be approached by estimating the potential future outcomes that will result from the various decision alternatives. In practice, estimation difficulties may arise as a result of selection bias and limited historic testing. We review some theoretical results and practical estimation tools from observation study design and causal modeling, and evaluate their relevance to credit decision problems. Building on these results and tools, we propose a novel approach for estimating potential outcomes for credit decisions with multiple alternatives based on matching on multiple propensity scores. We demonstrate the approach and discuss results for risk-based pricing and credit line increase problems. Among the strengths of our approach are its transparency about data support for the estimates and its ability to incorporate prior knowledge in the extrapolative inference of treatment-response curves.     

Endogenous trading in credit default swaps

We introduce a real options model in order to quantify the moral hazard impact of credit default swap (CDS) positions on the corporate default probabilities. Moral hazard is widely addressed in the insurance literature, where the insured agent may become less cautious about preventing the risk from occurring. Importantly, with CDS the moral hazard problem may be magnified since one can buy multiple protections for the same bond. To illustrate this issue, we consider a firm with the possibility of switching from an investment to another one. An investor can influence the strategic decisions of the firm and can also trade CDS written on the firm. We analyze how the decisions of the investor influence the firm value when he is allowed to trade credit default contracts on the firm’s debt. Our model involves a time-dependent optimal stopping problem, which we study analytically and numerically, using the Longstaff–Schwartz algorithm. We identify the situations where the investor exercises the switching option with a loss, and we measure the impact on the firm’s value and firm’s default probability. Contrary to the common intuition, the investors’ optimal behavior does not systematically consist in buying CDSs and increase the default probabilities. Instead, large indifference zones exist, where no arbitrage profits can be realized. As the number of the CDSs in the position increases to exceed several times the level of a complete insurance, we enter in the zone where arbitrage profits can be made. These are obtained by implementing very aggressive strategies (i.e., increasing substantially the default probability by producing losses to the firm). The profits increase sharply as we exit the indifference zone.     

Bifurcations in regional migration dynamics

The tomahawk bifurcation is used by Fujita et al. [Fujita, M., Krugman P., Venables A.J., 1999, The Spatial Economy: Cities, Regions, and International Trade, MIT Press: Cambridge, MA.] in a model with two regions to explain the formation of a core–periphery urban pattern from an initial uniform distribution. Baldwin et al. [Baldwin, R., Forslid, R., Martin, P., Ottaviano, G.I.P., Robert-Nicoud, F., 2003, Economic Geography and Public Policy, Princeton University Press: Princeton, NJ.] show that the tomahawk bifurcation disappears when the two regions have an uneven population of immobile agricultural workers. Thus, the appearance of this type of bifurcation is the result of assumed exogenous model symmetry. We provide a general analysis in a regional model of the class of bifurcations that have crossing equilibrium loci, including the tomahawk bifurcation, by examining arbitrary smooth parameter paths in a higher dimensional parameter space. We find that, in a parameter space satisfying a mild rank condition, generically in all parameter paths this class of bifurcations does not appear. In other words, conclusions drawn from the use of this bifurcation to generate a core–periphery pattern are not robust.     

Spatial Vector Autoregressions

Abstract

A spatial vector autoregressive model (SpVAR) is defined as a VAR which includes spatial as well as temporal lags among a vector of stationary state variables. SpVARs may contain disturbances that are spatially as well as temporally correlated. Although the structural parameters are not fully identified in SpVARs, contemporaneous spatial lag coefficients may be identified by weakly exogenous state variables. Dynamic spatial panel data econometrics is used to estimate SpVARs. The incidental parameter problem is handled by bias correction rather than more popular alternatives such as generalised methods of moments (GMM). The interaction between temporal and spatial stationarity is discussed. The impulse responses for SpVARs are derived, which naturally depend upon the temporal and spatial dynamics of the model. We provide an empirical illustration using annual spatial panel data for Israel. The estimated SpVAR is used to calculate impulse responses between variables, over time, and across space. Finally, weakly exogenous instrumental variables are used to identify contemporaneous spatial lag coefficients.     

BAYESIAN STATE SPACE MODELS IN MACROECONOMETRICS

State space models play an important role in macroeconometric analysis and the Bayesian approach has been shown to have many advantages. This paper outlines recent developments in state space modelling applied to macroeconomics using Bayesian methods. We outline the directions of recent research, specifically the problems being addressed and the solutions proposed. After presenting a general form for the linear Gaussian model, we discuss the interpretations and virtues of alternative estimation routines and their outputs. This discussion includes the Kalman filter and smoother, and precision-based algorithms. As the advantages of using large models have become better understood, a focus has developed on dimension reduction and computational advances to cope with high-dimensional parameter spaces. We give an overview of a number of recent advances in these directions. Many models suggested by economic theory are either non-linear or non-Gaussian, or both. We discuss work on the particle filtering approach to such models as well as other techniques that use various approximations – to either the time state and measurement equations or to the full posterior for the states – to obtain draws.     

Analyzing credit risk transmission to the nonfinancial sector in Europe: A network approach

We use a factor model and elastic net shrinkage to model a high-dimensional network of European credit default swap (CDS) spreads. Our empirical approach allows us to assess the joint transmission of bank and sovereign risk to the nonfinancial corporate sector. Our findings identify a sectoral clustering in the CDS network, where financial institutions are in the center and nonfinancial entities as well as sovereigns are grouped around the financial center. The network has a geographical component reflected in different patterns of real-sector risk transmission across countries. Our framework also provides dynamic estimates of risk transmission, a useful tool for systemic risk monitoring.     

Multilateral negotiations and formation of coalitions

This paper analyses properties of games modeling multilateral negotiations leading to the formation of coalitions in an environment with widespread externalities. The payoff generated by each coalition is determined by an exogenous partition function (the parameter space). We show that in almost all games, except in a set of measure zero of the parameter space, the Markov perfect equilibrium value of coalitions and the state transition probability that describe the path of coalition formation is locally unique and stable. Therefore, comparative statics analysis are well-defined and can be performed using standard calculus tools. Global uniqueness does not hold in general, but the number of equilibria is finite and odd. In addition, a sufficient condition for global uniqueness is derived, and using this sufficient condition we show that there is a globally unique equilibrium in three-player superadditive games.