Unobserved Components Approach Research Articles

Approximating Botswana's financial cycle: Expanding the macroprudential toolkit

AbstractThis study estimates the financial cycle for Botswana using the Christiano–Fitzgerald band‐pass filter, unobserved components approach and a Markov switching dynamic factor model. Using real credit and equity prices, together with several macroeconomic variables from 2001Q1 to 2021Q4, we find that the domestic financial cycle generally captures movements along the business cycle, with peaks reflecting the cumulative build‐up of risks during the boom that ultimately burst, coinciding with periods of financial distress. These findings shed light on the implications of financial fluctuations on domestic financial stability, hence, inform effective calibration of macroprudential tools, while also providing traction for implementation of the recently approved macroprudential policy framework for Botswana.

Revisiting the hysteresis hypothesis: an ARIMAX approach

The 2008 financial crisis saw a resurgence of interest in the hysteresis hypothesis, which was subsequently reflected in policy responses to the COVID-19 and cost-of-living crises. In this paper, we present new evidence in favour of the hysteresis hypothesis for Germany, France, and the United Kingdom, using a dataset that spans from 1960 to 2019. Our model is based on the popular unobserved components approach to estimating the degree of hysteresis, which is generalised to permit a reduced form Phillips curve that takes the form of an ARIMAX model. Our results are robust to ARCH effects and varying the sample span. They support contemporary warnings of the risk of scarring effects following the COVID-19 crisis, long-standing Post-Keynesian models of hysteresis, and the recent resurgence of mainstream interest in hysteresis.

Modeling COVID-19 Infection Rates by Regime-Switching Unobserved Components Models

The COVID-19 pandemic is characterized by a recurring sequence of peaks and troughs. This article proposes a regime-switching unobserved components (UC) approach to model the trend of COVID-19 infections as a function of this ebb and flow pattern. Estimated regime probabilities indicate the prevalence of either an infection up- or down-turning regime for every day of the observational period. This method provides an intuitive real-time analysis of the state of the pandemic as well as a tool for identifying structural changes ex post. We find that when applied to U.S. data, the model closely tracks regime changes caused by viral mutations, policy interventions, and public behavior.

A time series approach to player churn and conversion in videogames

Players of a free-to-play game are divided into three main groups: non-paying active users, paying active users and inactive users. A State Space time series approach is then used to model the daily conversion rates between the different groups, i.e., the probability of transitioning from one group to another. This allows, not only for predictions on how these rates are to evolve, but also for a deeper understanding of the impact that in-game planning and calendar effects have. It is also used in this work for the detection of marketing and promotion campaigns about which no information is available. In particular, two different State Space formulations are considered and compared: an Autoregressive Integrated Moving Average process and an Unobserved Components approach, in both cases with a linear regression to explanatory variables. Both yield very close estimations for covariate parameters, producing forecasts with similar performances for most transition rates. While the Unobserved Components approach is more robust and needs less human intervention in regards to model definition, it produces significantly worse forecasts for non-paying user abandonment probability. More critically, it also fails to detect a plausible marketing and promotion campaign scenario.

Cyclical convergence in per capita carbon dioxide emission in US states: A dynamic unobserved component approach

In this paper we evaluate whether the US states have been able to achieve convergence in their carbon emission cycles which may be a key factor in taking a leap as regards the development of a US climate change policy. The use of a dynamic unobserved component approach and a time-varying parameter model enable estimation of the short run dynamics of energy convergence over the extended period 1960–2017. To date, this type of analysis has not received enough attention in the literature. The results reveal the existence of cross-state links in the fluctuations of CO2 emissions, although the degree to which a good part of the states are co-moving is weak. We also find that cyclical convergence patterns differ considerably in both the level and trajectories across the US states. The difficulties in increasing synchronization of the US CO2 emissions highlight the importance of the states to lead climate change mitigation actions. The present study presents valuable information of interest regarding the short-run characteristics in carbon dioxide emissions, for better understanding of factors affecting CO2 mitigation policies.

Measuring business cycles: Empirical evidence based on an unobserved component approach

We adopt an unobserved components time series model to track the business cycles in the G7 countries using the Industrial production index over the period from 1:1961 to 8:2017. The advantage of ad...

Adding cycles into the neoclassical growth model

We propose a stochastic Solow growth model where a cyclical component is added to the total factor productivity process. Theoretically, an important feature of the model is that its main equation takes a state space representation where key parameters can be estimated via an unobserved component approach without involving capital stock measures. In addition, the dynamic properties of the model are mostly unaffected by the newly introduced cyclical component. Empirically, our novel framework is consistent with secular U.S. empirical evidence.

Identifying asymmetric effects of labor market reforms

This paper proposes a novel approach to identify structural long-term driving forces of the labor market and their short-run state-dependent effects. Based on search and matching theory, our empirical model extracts these driving forces within an unobserved components approach. We relate changes in the labor market structures to reforms that enhance the flexibility of the labor market in expansion and recession. Results for Germany and Spain show that labor market reforms have substantially weaker beneficial effects in the short run when implemented in recessions. From a policy perspective, these results highlight the costs of introducing reforms in recessions.

Empirical tests on the asset pricing model with liquidity risk: An unobserved components approach

The aim of this paper is to test empirically the conditional liquidity-adjusted capital asset pricing model (L-CAPM) developed by Acharya and Pedersen (2005). Accordingly, we propose to estimate the L-CAPM using unobserved components methodology, which allows us to take into account the main stylized facts characterizing liquidity. Based on a sample of firms listed on the NASDAQ, our empirical analysis reveals several findings. Firstly, we show that liquidity is time-varying and exhibits strong seasonality. Secondly, we highlight the impact of the liquidity level premium on asset prices. Thirdly, we show that the most important liquidity risk is related to the covariance between portfolio illiquidity and market returns. Fourthly, we observe a negative relationship between portfolio returns and market illiquidity. Fifthly, we find that liquidity risk and illiquidity level are not always positively correlated.

Crude oil and equity market comovements among Asia's for little dragons countries. Evidence of unobserved components approach

Abstract: This paper deals with long-and short-run comovements between crude oil price and selected emerging Asian equity markets qualified, Little dragons countries, by employing the ARDL approach to cointegration of Pesaran et al. (2001) and the unobserved components approach employed by Berger and Pozzi (2013) which deals with the country-specific crude oil effect and common crude oil risk. It is shown in the literature that these techniques enable to obtain reliable results and draw sharp conclusions in several application areas. The short and long run empirical results show evidence of decoupling structure between crude oil price and selected stock markets. The equity markets were heavily fallen at the beginning of the global financial crisis and express less volatility with less magnitude after the GFC crisis. Our findings have important implications for international portfolio diversification.

Consumption and Wealth in the Long Run: An Integrated Unobserved Component Approach

The ratio of consumption to total household wealth (i.e., tangible assets plus unobserved human wealth) is commonly calculated from the estimation of a log-linear version of the household intertemporal budget constraint as a cointegrating relationship between consumption, assets and earnings (i.e., the variable cay). The evidence in favor of a stable cointegrating relationship between these variables in the US is weak however. This paper follows an alternative empirical approach using an unobserved component model applied to US data over the period 1951Q4-2016Q4. The regression of consumption on assets and earnings is augmented with an unobserved stochastic trend, i.e., an integrated component. The results strongly support the presence of such an unobserved component in the consumption equation. We provide evidence that this component is related to financial liberalization which, by relaxing liquidity constraints of consumers, has permanently increased the consumption-to-wealth ratio over the sample period. We calculate an alternative cay variable, i.e., the stationary part of the consumption-to-wealth ratio, and find that its predictive ability for future (excess) stock returns is comparable to that of the standard cay variable.

The cyclicality of fiscal policy: New evidence from unobserved components approach

This paper employs the multivariate version of the unobserved components model to reinvestigate the cyclicality of fiscal policy in eleven OECD countries. The novelty of the multivariate approach lies in its superior ability to disentangle the correlations in cycles from the correlations in slopes of the relevant variables while allowing for those correlations in the model. The results suggest that fiscal policy is mildly counter-cyclical in seven of the eleven countries analyzed which resonates with the standard Keynesian models. However, the slope (growth) of government consumption is found to be positively correlated with real GDP in these economies. There is no evidence of procyclical fiscal policies in any of these eleven industrial countries. The results remain robust when we use subsamples and an alternative fiscal policy variable.

Estimating the New Keynesian Phillips Curve for the UK: evidence from the inflation-indexed bonds market

Abstract This paper utilizes the information in the inflation-indexed bonds market to estimate the New Keynesian Phillips Curve for the UK using an unobserved component approach. The main advantage of this approach comes from using the Kalman filter to explicitly estimate the unobserved expected inflation from the observed break-even inflation rates – the yield difference between the inflation-indexed bonds and the nominal bonds. Our results show that the expected inflation estimated from the unobserved component model plays a significant role in explaining the inflation dynamics in the UK. The evidence also suggests that the estimated inflation expectations are better able to capture the evolution of actual inflation process as compared to the break-even inflation rate as a proxy for expected inflation.

The demand for ‘active travel’: An unobserved components approach

This study informs the interface of travel demand analysis and health policy. There is a demand for cycling, walking or taking non-motorized modes together – a demand for ‘active travel’ – a term describing modes of transport which incur significant cardiovascular effort or metabolic costs. It is possible to establish a meaningful and policy relevant view of active travel demand by controlling for partially unobservable (not simply unobserved) generalized cost effects – where generalized cost can be considered the sum of all individual cost-components. Using monthly aggregated data from the UK National Travel Survey it is found that income effects are greater for lower income households and diminish with wealth and that some ‘seasonal substitution’, due to ‘generalized’ cost effects, can be identified. One consequence of this is that policy for active travel needs to be seasonally adaptive to reflect these substitution effects.

Long-term variations in the net inflow record for Lake Malawi

Lake Malawi is the third largest lake in Africa and plays an important role in water supply, hydropower generation, agriculture and fisheries in the region. Lake level observations started in the 1890s and anecdotal evidence of variations dates back to the early 1800s. A chronology of lake level and outflow variations is presented together with updated estimates for the net inflow to the lake. The inflow series and selected rainfall records were also analysed using an unobserved component approach and, although there was little evidence of long-term trends, there was some indication of increasing interannual variability in recent decades. A weak quasi-periodic behaviour was also noted with a period of approximately 4–8 years. The results provide useful insights into the severity of drought and flood events in the region since the 1890s and the potential for seasonal forecasting of lake levels and outflows.

On some remarks about SEATS signal extraction

In seasonal adjustment a time series is considered as a juxtaposition of several components, the trend-cycle, and the seasonal and irregular components. The Bureau of the Census X-11 method, based on moving averages, correction of large errors and trading day adjustments, has long dominated. With the success of ARIMA modelling at the end of the 20th century, methods with better outlier detection and trading day corrections by regression with ARIMA errors have appeared, with the regARIMA module of Census X-12-ARIMA or Bank of Spain TRAMO-SEATS. SEATS consists of extracting the components by an ARIMA-model-based unobserved components approach. This means that models are used for each component such that the sum of the components is compatible with the ARIMA model for the corrected time series. The underlying theory of the SEATS program is studied in many papers but there is no complete and systematic description of its output. Our purpose is to examine SEATS text output and to explain the results in simple words and formulas. This is done on a simple example, a time series with a non-seasonal model so that the computations can be verified step by step. The principles behind SEATS are first described, including the admissible decompositions and the canonical decomposition, and the derivation of the Wiener-Kolmogorov filter. Then the example is introduced: the interest rates of US certificates of deposits. The text output from SEATS is presented in edited form in several tables. Finally, the main results are checked on the example by means of a Microsoft Excel workbook and direct computations. In particular, the forecasts and backcasts are obtained; the admissible and canonical decompositions with two components are discussed; the filters are first derived using autocorrelations of two auxiliary ARMA processes, then applied on the prolonged time series; and the characteristics of the estimates, the revisions and the growth rates are analyzed.

Phillips curve in Brazil: an unobserved components approach

This paper estimates reduced-form Phillips curves for Brazil with a framework of time series with unobserved components, in the spirit of Harvey (2011). However, we allow for expectations to play a key role using data from the Central Bank of Brazil's Focus survey. Besides GDP, we also use industrial capacity utilization rate and IBC-Br index, as measures of economic activity. Our findings support the view that Brazilian inflation targeting has been successful in reducing the variance of both the seasonality and level of the inflation rate, at least until the beginning of the subprime crisis. Furthermore, inflation in Brazil seems to have responded gradually less to measures of economic activity in recent years. This provides some evidence of a flattening of the Phillips curve in Brazil, a trend previously shown by recent studies for other countries.

Improved beta modeling and forecasting: An unobserved component approach with conditional heteroscedastic disturbances

Recent research on time-varying systematic-risk (beta) modeling reveals significant advantages in utilizing daily financial data and unobserved-component models. This research proposes a state-space market model with conditional heteroscedastic errors, thus addressing the leptokurtosis of the unconditional distribution of the disturbances and reducing the influence of outliers in the estimation process. This approach outperforms the conventional models, providing better levels of in-sample goodness of fit and more accurate point- and interval-dynamic assets returns forecasts. The proposed model provides better levels of empirical, conditional, and unconditional coverage and independence of its interval returns forecasts and reaches lower loss-function scores. Therefore, our model allows improving financial strategies, such as stock pricing, determining the companies’ cost-of-equity, evaluating the performance of managed-investment and pension funds, making portfolio-rebalancing processes and computing the value at risk (VAR) of investment portfolios.

Understanding the Irish price–rent ratio: an unobserved component approach

This article examines the movements in the Irish price-to-rent ratio over the period 1976 to 2012. We use the Campbell–Shiller present value formula to decompose the price–rent ratio into the present discounted values of expected future housing market fundamentals, i.e., rent growth, real interest rate and risk premium for investing in housing. Treating the expectations of the fundamentals as unobserved components, we cast the Campbell–Shiller formula into a state–space model and estimate the deep parameters by maximum likelihood method. It is found that that the variations in the price–rent ratio are mostly due to the expected housing premium, while the expected rent growth and real interest rate account for only small fractions of variations in the price–rent ratio. It is also found that, while the individual contributions of the expected market fundamentals sum up much larger variations than in the price–rent ratio itself, the correlations among them considerably dampen fluctuations in the ratio.

CONSUMPTION AND EXPECTED ASSET RETURNS: AN UNOBSERVED-COMPONENT APPROACH

This paper proposes an unobserved-component approach to estimate expected returns on household assets and expected growth rates of excess consumption (consumption in excess of labor income) within a present-value model of consumption. The present-value model of consumption implies that the excess-consumption–assets ratio can be expressed as a function of the present discounted value of expected excess-consumption growth rate and expected asset returns. Because expected returns and expected excess-consumption growth rate are unobserved variables, we use an unobserved-component approach to extract them from the observed history of realized returns and excess-consumption growth rate. Our results suggest that both filtered returns and filtered excess-consumption growth rate are significant and better predictors of realized returns and realized excess-consumption growth rate than the one obtained by the lagged excess-consumption–assets ratio.