Research

Sieve bootstrap inference for linear time-varying coefficient models

M. Friedrich and Y. Lin (2024), Journal of Econometrics, 239(1), 105345 

Abstract. We propose a sieve bootstrap framework to conduct pointwise and simultaneous inference for time-varying coefficient regression models based on a local linear estimator. The asymptotic validity of the sieve bootstrap in the presence of autocorrelation is established. The bootstrap automatically produces a consistent estimate of nuisance parameters, both at the interior and boundary points. In addition, we develop a bootstrap-based test for parameter constancy and examine its asymptotic properties. An extensive simulation study demonstrates a good finite sample performance of our methods. The proposed methods are applied to assess the price development of CO2 certificates in the European Emissions Trading System. We find evidence of time variation in the relationship between allowance prices and their fundamental price drivers. The time variation might offer an explanation for previous contradicting findings using linear regression models with constant coefficients.

Determination and analysis of time series of CFC-11 (CCl3F) from FTIR solar spectra, in situ observations, and model data in the past 20 years above Jungfraujoch (46°N), Lauder (45°S), and Cape Grim (40°S) stations

I. Pardo Cantos, E. Mahieu, M.P. Chipperfield, D. Smale, J.W. Hannigane, M. Friedrich, P. Fraser, P. Krummel, M. Prignon, J. Makkori, C. Servais and J. Robinson (2022), Environmental Science: Atmospheres

Abstract. The atmospheric concentration of CFC-11 (CCl3F) has declined in response to the phase-out of its production by the Montreal Protocol. Nevertheless, this atmospheric concentration decline suffered a slow-down around 2012 due to emissions from non-reported production. Since CFC-11 is one of the most important ozone-depleting chlorofluorocarbons (CFCs), its continuous monitoring is essential. We present the CFC-11 total column time series (2000–2020) retrieved in a consistent way from ground-based high-resolution solar absorption Fourier transform infrared (FTIR) spectra. These observations were recorded at two remote stations of the Network for the Detection of Atmospheric Composition Change (NDACC): the Jungfraujoch station (Northern Hemisphere) and the Lauder station (Southern Hemisphere). These time series are new. They were produced using improved line parameters and merged considering the instrument changes and setup modifications. Afterwards, they were compared with Cape Grim station in situ surface observations conducted within the Advanced Global Atmospheric Gases Experiment (AGAGE) network and with total column datasets calculated by the TOMCAT/SLIMCAT 3-D chemical transport model. Trend analyses were performed, using an advanced statistical tool, in order to identify the timing and magnitude of the trend change in both hemispheres. The observations are consistent with the model results and confirm the slowdown in the CFC-11 atmospheric concentration decay, since ≈2011 in the Northern Hemisphere, and since ≈2014 in the Southern Hemisphere. 

Stratospheric fluorine as a tracer of circulation changes: comparison between infrared remote‐sensing observations and simulations with five modern reanalyses

M. Prignon, S. Chabrillat, M. Friedrich, D. Smale, S.E. Strahan, P.F. Bernath, M.P. Chipperfield, S.S. Dhomse, W. Feng, D. Minganti, C.Servais and E. Mahieu (2021). Journal of Geophysical Research: Atmospheres. 

Abstract. Using multidecadal time-series of ground-based and satellite Fourier transform infrared measurements of inorganic fluorine (i.e., total fluorine resident in stratospheric fluorine reservoirs), we investigate stratospheric circulation changes over the past 20 years. The representation of these changes in five modern reanalyses are further analysed through chemical-transport model (CTM) simulations. From the observations but also from all reanalyses, we show that the inorganic fluorine is accumulating less rapidly in the Southern Hemisphere than in the Northern Hemisphere during the twenty-first century. Comparisons with a study evaluating the age-of-air of these reanalyses using the same CTM allow us to link this hemispheric asymmetry to changes in the Brewer-Dobson circulation (BDC), with the age-of-air of the Southern Hemisphere getting younger relative to that of the Northern Hemisphere. Large differences in simulated total columns and absolute trend values are, nevertheless, depicted between our simulations driven by the five reanalyses. Superimposed on this multidecadal change, we, furthermore, confirm a 5-to-7-year variability of the BDC that was first described in a recent study analysing long-term time series of hydrogen chloride (HCl) and nitric acid (HNO3). It is important to stress that our results, based on observations and meteorological reanalyses, are in contrast with the projections of chemistry-climate models in response to the coupled increase of greenhouse gases and decrease of ozone depleting substances, calling for further investigations and the continuation of long-term observations. 

Autoregressive wild boostrap inference for nonparametric trends

M. Friedrich, S. Smeekes and J.-P. Urbain (2020). Journal of Econometrics, 214, 81-109.

Abstract. In this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend. The bootstrap method is easy to implement and does not require any adjustments in the presence of missing data, which makes it particularly suitable for climatological applications. We establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions, allowing for general patterns of missing data, serial dependence and heteroskedasticity. The finite sample properties of the method are studied in a simulation study. We use the method to study the evolution of trends in daily measurements of atmospheric ethane obtained from a weather station in the Swiss Alps, where the method can easily deal with the many missing observations due to adverse weather conditions.

A statistical analysis of time trends in atmospheric ethane

M. Friedrich, E. Beutner, H. Reuvers, S. Smeekes, J.-P. Urbain, W. Bader, B. Franco, B. Lejeune and E. Mahieu (2020). Climatic Change, 162, 105-125.

Abstract. Understanding the development of trends and identifying trend reversals in decadal time series is becoming more and more important. Many climatological and atmospheric time series are characterized by autocorrelation, heteroskedasticity and seasonal effects. Additionally, missing observations due to instrument failure or unfavorable measurement conditions are common in such series. This is why it is crucial to apply methods which work reliably under these circumstances. The goal of this paper is to provide a toolbox which can be used to determine the presence and form of changes in trend functions using parametric as well as nonparametric techniques. We consider bootstrap inference on broken linear trends and smoothly varying nonlinear trends. In particular, for the broken trend model, we propose a bootstrap method for inference on the break location and the corresponding changes in slope. For the smooth trend model we construct simultaneous confidence bands around the nonparametrically estimated trend. Our autoregressive wild bootstrap approach, combined with a seasonal filter, is able to handle all issues mentioned above. We apply our methods to a set of atmospheric ethane series with a focus on the measurements obtained above the Jungfraujoch in the Swiss Alps. Ethane is the most abundant non-methane hydrocarbon in the Earth's atmosphere, an important precursor of tropospheric ozone and a good indicator of oil and gas production as well as transport. Its monitoring is therefore crucial for the characterization of air quality and of the transport of tropospheric pollution.

Time-varying effects of housing attributes and economic environment on housing prices

M. Friedrich, Y. Lin, P. Ramdaras and B. van der Sluis

Abstract. We propose a flexible framework that allows for the relationship between housing prices and their determinants to vary over time. Our model incorporates housing-specific characteristics and macroeconomic variables, while accounting for a gradual global trend that reflects the unobserved external environment. We estimate the trend and coefficient curves by local linear estimation and propose a bootstrap procedure for conducting inference. By employing monthly data from the Dutch housing market, covering 60 municipalities from 2006 to 2020, the proposed models show the capability to accurately describe the comovements of housing prices. Our results show strong statistical evidence of time variation in the effects of housing attributes and macroeconomic variables on prices throughout the entire sample period, revealing that the unemployment rate plays a crucial role between approximately 2012 and 2017. The extracted latent global trend reveals a significant influence of the economic environment and takes the shape of a leading indicator of the property market index. Moreover, we find that both the housing characteristics and the external environment explain comparably high proportions of the variation in housing prices, which stresses the importance of including both components in empirical analyses.

Bootstrapping trending time-varying coefficient panel models with missing observations

Y. Lin , B. van der Sluis and M. Friedrich

Abstract. We study a class of trending panel regression models with time-varying coefficients that incorporate cross-sectional and serial dependence, as well as heteroskedasticity. Our models also allow for missing observations in the dependent variable. We introduce a local linear dummy variable estimator capable of handling missing observations and derive its asymptotic properties. A key ingredient in our theoretical framework is a generic uniform convergence result for near-epoch processes in kernel estimation for large panels (N,T → ∞). The resulting limiting distribution reflects the pattern of missing values and depends on various nuisance parameters. An autoregressive wild bootstrap (AWB) is proposed to construct confi- dence intervals and bands. The AWB accommodates missing observations and automatically replicates all the nuisance parameters, demonstrating good finite sample performance. We apply our methods to investigate (i) the relationship between PM2.5 and mortality and (ii) common trends in atmospheric ethane emissions in the Northern Hemisphere. Both examples yield statistical evidence for time variation.

High-dimensional Granger causality for climatic attribution

M. Friedrich, L. Margaritella and S. Smeekes

Abstract. In this paper we test for Granger causality in high-dimensional vector autoregressive models (VARs) to disentangle and interpret the complex causal chains linking radiative forcings and global temperatures. By allowing for high dimensionality in the model we can enrich the information set with all relevant natural and anthropogenic forcing variables to obtain reliable causal relations. These variables have mostly been investigated in an aggregated form or in separate models in the previous literature. Additionally, our framework allows to ignore the order of integration of the variables and to directly estimate the VAR in levels, thus avoiding accumulating biases coming from unit-root and cointegration tests. This is of particular appeal for climate time series which are well known to contain stochastic trends as well as yielding long memory. We are thus able to display the causal networks linking radiative forcings to global temperatures but also to causally connect radiative forcings among themselves, therefore allowing for a careful reconstruction of a timeline of causal effects among forcings. The robustness of our proposed procedure makes it an important tool for policy evaluation in tackling global climate change.

The impact of natural hazards on migration in the United States and the effect of spatial dependence 

M.J. Ton, H. de Moel., J.A. de Bruijn, W.J.W. Botzen, H. Karabiyik, M. Friedrich and J.C.J.H. Aerts

Abstract. In this paper, we analyze the effect of natural hazards on migration in the United States (US) and the importance of spatial dependence in such assessments. We use two measures of migration: migration rates and flows. Migration flows are estimated using the gravity model, whereas out- and in-migration rates are analyzed using the spatial Durbin model. Our results indicate there is a major and significant impact of economic damage caused by natural hazards on out-migration rates and outward migration flows. In the spatial Durbin model and in the gravity model, a $1,000 dollar damage per capita is associated with an increase in out-migration of 16.0% and 8.8%, respectively. However, when spatial dependence is not accounted for, the effect of natural hazards on migration is substantially overestimated: The coefficients are 1.5-2 times larger when spatial dependence is not considered.

Rules vs. discretion in cap-and-trade programs: evidence from the EU emission trading system

M. Friedrich, S. Fries, M. Pahle and Ottmar Edenhofer (2020). CESifo Working Paper No. 8637. 

Abstract. Long-term commitment is crucial for the dynamic efficiency of intertemporal cap-and-trade programs. Discretionary interventions in such programs could destabilize the market, and necessitate subsequent corrective interventions that instigate regulatory instability. In this work, we provide evidence for this claim from the EU's cap-and-trade program (EU ETS). We ground our analysis in  the theoretical finance literature, and apply a mixed method approach (time-varying regression, bubble detection, crash-odds modelling). We find that the recent EU ETS reform triggered market participants into speculation, which likely led to an overreaction that destabilized the market.  We discuss how the smokescreen politics behind the reform, which manifested itself in complex rules, was crucial for this outcome. We conclude that rules only ensure long-term commitment when their impact on prices is predictable.

From fundamentals to financial assets: the evolution of understanding price formation in the EU ETS

M. Friedrich, E.-M. Mauer, M. Pahle and O. Tietjen (2019) 

Abstract. Now in its third compliance period, we can look back at more than 12 years of existence of the emissions trading system (ETS) in the European Union. The focus of this paper is to review the empirical literature on price formation in the EU ETS. As a reoccurring concept, we draw on a simple theoretical model of price formation that we subsequently extend to accommodate three different strands of literature. First, we gather evidence based on empirical papers which look at the role of fundamental price drivers. Second, we review the event study literature, where political and regulatory uncertainty is the main topic. Third, we devote a major part to finance literature in this market. In every section, we pay special attention to the challenges that arise when empirically modeling allowance prices in this complex market. We emphasize that there is a need for more evidence and possibly alternative approaches due to the complex interplay of compliance and finance trading motives. As a result, the findings of this review provide important lessons about price formation in the EU ETS.

Post-peak trend of upper stratospheric hydrogen chloride derived from ground-based FTIR solar spectra and model simulations

E. Mahieu, M. Prignon, C. Servais, S. Chabrillat, Q. Errera, M. Friedrich, S. Smeekes, L. Froidevaux, R.J. Salavitch, P. Wales, J. Notholt and M.P. Chipperfield 

Abstract. The post-peak evolution of stratospheric hydrogen chloride (HCl, the main reservoir for stratospheric chlorine) has been characterized by short-term dynamical variability, which was driven by atmospheric circulation changes, affecting mainly the lower stratosphere (Mahieu et al., 2014). This notably led to a temporary increase of HCl over 2007-2011, complicating the determination of precise HCl trends and the accurate verification of the success of the Montreal Protocol for the protection of the stratospheric ozone layer. Since then, studies have shown that other long-lived tracers (e.g., nitrous oxide, N2O) could be used to remove the effects of dynamical variability in the lower stratosphere (Stolarski et al., 2018), while other investigations showed that trends in the upper stratosphere were potentially more appropriate for the long-term characterization of the HCl decrease (Froidevaux et al., 2015; Bernath and Fernando, 2018).

In this contribution, we use HCl column data derived from the long-term FTIR (Fourier Transform InfraRed) monitoring program conducted at the Jungfraujoch station (Swiss Alps, 3580 m a.s.l.), in the framework of the NDACC network. Version 0.9.4.4 of the SFIT-4 retrieval algorithm implementing the Optimal Estimation Method of Rodgers (2000) is employed, providing information on the column abundance of HCl from the tropopause up to about 40 km altitude. Moreover, the vertical resolution is sufficient such as to determine independent partial columns above and below about 23 km.

With the support of model simulations performed with the BASCOE 3D-Chemistry Transport Model, driven by ERA-Interim meteorological reanalyses, we investigate the post-peak trend of HCl in the upper and lower stratosphere, as derived from the observations and the simulations. We also determine the magnitude of the uncertainties affecting the various trends, carefully accounting for the auto-correlation present in our geophysical data sets.