Multivariate Unobserved Components Research Articles

Common Business and Housing Market Cycles in the Euro Area from a Multivariate Decomposition

The 2007 sub-prime crisis in the United States, prolonged by a severe economic recession spread over many countries around the world, has led many economic researchers to focus on the recent fluctuations in housing prices and their relationships with macroeconomics and monetary policies. The existence of common housing cycles among the countries of the euro zone could lead the European Central Bank to integrate more specifically the evolution of such asset prices in its assessment. In this paper, we implement a multivariate unobserved component model on housing market variables in order to assess the common euro area housing cycle and to evaluate its relationship with the economic cycle. Among the general class of multivariate unobserved component models, we implement the band-pass filter based on the trend plus cycle decomposition model and we allow the existence of two cycles of different periods. The dataset consists of gross domestic product and real house prices series for four main euro area countries (Germany, France, Italy and Spain). Empirical results show a strong relationship for business cycles in France, Italy and Spain. Moreover, French and Spanish house prices cycles appear to be strongly related, while the German one possesses its own dynamics. Finally, we find that GDP and house prices cycles are related in the medium-term for fluctuations between 4 and 8 years, while the housing market contributes to the long-term economic growth only in Spain and Germany.

A new production function estimate of the euro area output gap

AbstractWe develop a new version of the production function (PF) approach for estimating the output gap of the euro area. Assuming a CES (constant elasticity of substitution) technology, our model does not call for any (often imprecise) measure of the capital stock and improves the estimation of the trend total factor productivity using a multivariate unobserved components model. With real‐time data, we assess this approach by comparing it with the Hodrick–Prescott (HP) filter and with a Cobb–Douglas PF approach with common cycle and implemented with a multivariate unobserved components model. Our new PF estimate appears highly concordant with the reference chronology of turning points and has better real‐time properties than the univariate HP filter for sufficiently long time horizons. Its inflation forecasting power appears, like the other multivariate approach, less favourable than the statistical univariate method. Copyright © 2009 John Wiley & Sons, Ltd.

Modelling demand for crude oil products in Spain

This paper develops an econometric model for the five most important crude oil products demand in Spain. The aim is the estimation of a range of elasticities of such demands that would serve as the basis for an applied general equilibrium model used for forecasting energy demand in a broader framework. The main distinctive features of the system with respect to previous literature are (i) it takes advantage of monthly information coming from very different information sources and (ii) multivariate unobserved components (UC) models are implemented allowing for a separate analysis of long- and short-run relations. UC models decompose time series into a number of unobserved though economic meaningful components mainly trend, seasonal and irregular. A module is added to such structure to take into account the influence of exogenous variables necessary to compute price, cross and income elasticities. Since all models implemented are multivariate in nature, the demand components are allowed to interact among them through the system noises (similar to a seemingly unrelated equations model). The results show unambiguously that the main factor driving demand is real income with prices having little impact on energy consumption.

Aggregate hedge funds’ flows and returns

In this article, a multivariate unobserved components model for returns and net inflows into hedge funds is employed to assess whether the flows of funds into the industry are dynamically related to returns. The econometric model is used to estimate expected flows and expected returns as unobserved components. The results point to strong autocorrelation in both flows and returns and to positive correlation between past returns and future flows, while the evidence concerning the linkage between past flows and future returns is mixed.

A multivariate unobserved component analysis of US housing market

This study explores price dynamics and price relationships in the US housing market with a focus on four regions: Northeast, Midwest, South, and West. It applies a multivariate state-space model to identify the common trends and common cycles in US regional markets. The study finds that the principal source of secular price variability in the Northeast and West markets is due to two common stochastic trends, while a large share of transitional price variability in the Northeast, West and Midwest originates from three common stochastic cycles. The study estimates the relationships between the common unobserved components and economic variables and finds that unemployment, federal funds rate, corporate default risk, economic expansion, unanticipated inflation in the construction market are significant underlying economic phenomena that impact the evolution of the common movements in both the short run and the long run housing dynamics.

Estimating potential output and the output gap for the euro area: a model-based production function approach

This paper provides an analysis of multivariate unobserved components models for the estimation of potential output and the output gap in the euro area. Bivariate models of output and inflation and multivariate model-based implementations of the production function approach are considered; according to the latter potential output is derived from the permanent components of the factors of production consistent with stable inflation, whereas the output gap results from the combination of the transitory components. This approach allows to measure the contribution of the various factors of production to potential output growth, and to assess the reliability of the output gap estimates. Various alternative statistical specifications for the separation of trend and cycle are considered entertaining different economic hypotheses. The paper also provides an assessment of the reliability of the alternative output gap estimates and analyses their predictive validity by means of a rolling forecast exercise that provides an evaluation of the capability to forecast future inflation.

Tests of seasonal integration and cointegration in multivariate unobserved component models

This paper considers tests of seasonal integration and cointegration for multivariate unobserved component models. First, the locally best invariant (LBI) test of the null hypothesis of a deterministic seasonal pattern against the alternative of seasonal integration is derived for a model with Gaussian i.i.d. disturbances and deterministic trend. Then the null hypothesis of seasonal cointegration is considered and a test for common nonstationary components at the seasonal frequencies is proposed. The tests are subsequently generalized to account for stochastic trends, weakly dependent errors and unattended unit roots. Asymptotic representations and critical values of the tests are provided, while the finite sample performance is evaluated by Monte Carlo simulation experiments. Finally, the tests are applied to the series of industrial production of the four largest countries of the European Monetary Union. It is found that Germany does not appear to cointegrate with the other countries at most seasonal frequencies, while there seems to exist a common nonstationary seasonal component between France, Italy and Spain. Copyright © 2006 John Wiley & Sons, Ltd.

The Dynamics of the Permanent and Transitory Components in International Business Cycles

This paper proposes a generalized multivariate framework to measure the significance of common permanent and transitory components in international business cycle fluctuations. I employ a multivariate unobserved components model with Markov regime switching to investigate the nonlinear dynamics of permanent and transitory components that are common across G7 real GDP series. The common components are modeled to exhibit different behavior in the expansion and recession phases of international business cycles. I find that, in contrast to the individual country's business cycles, the international business cycle does not exhibit classical recession and expansion phases. The international permanent component has two phases: a high-growth phase and a low-growth phase, and there is no evidence of a Friedman's pluck type recessionary period in the international transitory component. The switch from a high-growth regime to a low-growth regime occurs in the second quarter of 1973. There are no further switches that occur from one regime to the other. Among the seven developed nations examined, Japan is the most sensitive and Germany is the least sensitive to international permanent shocks.

Using Additional Infomation in Estimating Output Gap in Peru: A Multivariate Unobserved Component Approach

One of the key elements for inflation targeting regime is the right identification of inflationary or disinflationary pressures through the output gap. In this paper we provide an estimation of the Peruvian output gap using a multivariate unobserved component (MUC) model, relying on an explicit short run relation between the output gap and inflation rate (Phillips Curve) and structural restrictions over output dynamics. The results show that the MUC output gap estimate is less sensible to end of sample problems and exhibits closer dynamics with the inflation process than the standard output gap estimates.

Business and default cycles for credit risk

AbstractVarious economic theories are available to explain the existence of credit and default cycles. There remains empirical ambiguity, however, as to whether these cycles coincide. Recent papers suggest by their empirical research set‐up that they do, or at least that defaults and credit spreads tend to co‐move with macroeconomic variables. If true, this is important for credit risk management as well as for regulation and systemic risk management. In this paper, we use 1933–1997 US data on real GDP, credit spreads and business failure rates to shed new light on the empirical evidence. We use a multivariate unobserved components framework to disentangle credit and business cycles. We distinguish two types of cycles in the data, corresponding to periods of around 6 and 11–16 years, respectively. Cyclical co‐movements between GDP and business failures mainly arise at the longer frequency. At the higher frequency of 6 years, co‐cyclicality is less clear‐cut. We also show that spreads reveal a positive and negative co‐cyclicality with failure rates and GDP, respectively. This pattern disappears, however, if we concentrate on the post World War II period. We comment on the implications of our findings for credit risk management. Copyright © 2005 John Wiley & Sons, Ltd.

Searching for the natural rate of interest: a euro area perspective

A time-varying natural rate of interest is estimated for the euro area using a multivariate unobserved components model. The problem of aggregating interest rate data for the pre-EMU period is directly addressed, and a simple method is proposed in order to adjust the risk premia in the interest rate data prior to 1999. We show that, for the pre-EMU period, using risk-unadjusted policy rates leads to periods of high risk premia being erroneously taken as monetary policy replies to the output gap; in contrast, using risk-adjusted policy rates yields an estimate of the reaction of monetary policy to the output gap corresponding approximately to an increase of 40 basis points for a 1%positive deviation of output from potential output. A positive deviation of inflation from its trend of 1%is estimated to have triggered an approximately 1.2%increase in short-term interest rates.

A Multivariate Unobserved Components Model of Cyclical Activity

This paper presents results from the estimation of a multivariate unobserved components model of cyclical activity. The model is motivated by a desire to let the data speak as much as possible, and hence to avoid imposing ad hoc and unjustifiable assumptions about trends and cycles. Estimated over the period 1970:1 to 1999:3 via the Kalman filter and maximum likelihood, the model identifies a common, trend-reverting component to real output, unemployment and capacity utilisation. The structure of the model allows an interesting factor interpretation to be put on the estimate of the output gap. These estimates are consistent with priors, but there is no consistent match to any one simple smoother such as the HP filter.

Business and Default Cycles for Credit Risk

Various economic theories are available to explain the existence of credit and default cycles. There remains empirical ambiguity, however, as to whether or these cycles coincide. Recent papers suggest by their empirical research set-up that they do, or at least that defaults and credit spreads tend to co-move with macroeconomic variables. If true, this is important for credit risk management as well as for regulation and systemic risk management. In this paper, we use 1927-1997 U.S. data on real GDP, credit spreads, and business failure rates to shed new light on the empirical evidence. We use a multivariate unobserved components framework to disentangle credit from business cycles. It turns out that cyclical co-movements arise between default rates, but not real GDP. There is, however, a contemporaneous correlation between real GDP and default rates. Regarding the longer term evolution of the series, credit spreads influence default rates and real GDP, but not vice versa. This corroborates some of the empirical findings in the recent literature on the correlation between macrovariables and default rates. It also suggests the use of credit spreads besides or instead of economic growth rates to forecast the dynamics of future default rates.

Volatility of Interest Rates in the Euro Area: Evidence from High Frequency Data

This paper estimate the factors underlying the volatility of the euro overnight interest rate and its transmission along the euro area money market yield curve. A new multivariate unobserved components model is proposed allowing for both long-memory and stationary cyclical dynamics. Using hourly data the estimates show repetitive intradaily and monthly patterns that can be explained by the microstructure of the money market and the institutional features of the Eurosystem's operational framework for monetary policy implementation. Strong persistence is dedected in all log-volatility processes and two common long-memory factors are extracted. The first factor explains the long-memory dynamics of the shortest maturity. The second factor explains the transmission of volatility along the money market yield curve. We find evidence that most liquidity effects are cyclical, confined to the ned of reserve maintenance periods, and are not transmitted along the money market yield curve. JEL Classification: C32, E43, F30, G10

Stylised Facts From Output GAP Measures

This paper compares three models of the output gap in New Zealand ‐ the Reserve Bank of New Zealand’s incumbent MV filter, estimates from a Structural VAR, and a multivariate unobserved components model ‐ and investigates whether there are features that are consistent across the measures of the gap. Various detrending methods are used for benchmarking the output gap measures, including a linear trend, a fourth difference filter, a band-pass filter, the Hodrick-Prescott filter, an “optimal λ ” procedure, and a nonparametric estimator of permanent trend. The estimates of the gap are examined to see how they compare as to the lengths and amplitudes of cycles, whether they exhibit regular periodicity and regular shapes, whether they are symmetric in phases and severity of swings, and whether they point to the same turning points. The analysis leads to the conclusion that while different filters result in estimates of the output gap with quite different properties, the three models are generally in agreement about the historical profile of the output gap, if not its precise level. Moreover, there are signs that the models are increasingly in agreement about the level of the gap, indicating that the growth cycle is becoming more regular in the 1990s.

The cyclical sensitivity of seasonality in U.S. employment

This paper investigates interactions between seasonal and cyclical movements in U.S. payroll employment. Using a multivariate unobserved components model, we test for such interactions and find that they are statistically significant in a number of industries. Still, most industry-level seasonality appears to be idiosyncratic. The model also identifies an unobserved common cycle that exhibits similar business cycle properties, but smaller seasonal variation, than aggregate payroll employment. The overall industry-level seasonal factors generated by our model do not differ much from univariate X-11 seasonals in sample, but some differences arise in out-of-sample experiments.

Property and Inflation: The Hedging Characteristics of U.K. Commercial Property, 1967–1994

This paper examines the statistical similarities between U.K. commercial property capital and rental values and the price level. Our aim is to determine whether commercial property is an inflation hedge and, if so, what type of inflation it hedges against. To answer these questions, we use both a multivariate unobserved components model and structural vector autoregressions. We find that commercial property is an inflation hedge but only a weak one. More specifically, we find that property offers some form of partial hedge against changes in the underlying inflation rate but not to either temporary or permanent changes to the price level. We also find that capital values offer a stronger hedge than rental values and that industrial and retail property account for most of this hedging capacity. We find no evidence that property responds differently to high or low inflation but we do find capital and rental values respond more to unexpected inflation than anticipated price changes.