Anders Rygh Swensen

• Swensen, Anders Rygh (2023). Remaining Loads in a PH/M/c Queue with Impatient Customers. Methodology and Computing in Applied Probability. ISSN 1387-5841. 25(1). doi: 10.1007/s11009-023-10019-0. Full text in Research Archive Show summary

  Abstract There are three contributions to the literature in this note. Firstly, we point out that under some weak conditions the result in Swensen (1986) on the remaining loads in a GI/M/ c queue with impatient customers, derived under the assumption that the distribution of inter-arrival times is Coxian, is also valid for the more general phase type distribution. From this result the distributions of the virtual and the actual waiting time can easily be obtained. Secondly, the relation to an alternative expression for the distribution of the virtual waiting time derived by Kawanishi and Takine (2015) is also clarified. Finally, we explain how the results on the remaining loads can be used to find distributions describing particular fixed servers and provide a couple of numerical examples of how this can be done.

• Johansen, Søren & Swensen, Anders Rygh (2023). Adjustment coefficients and exact rational expectations in cointegrated vector autoregressive models. Journal of Time Series Analysis. ISSN 0143-9782. 45(2), p. 248–268. doi: 10.1111/jtsa.12705. Full text in Research Archive Show summary

  In this article, we consider the cointegrated vector autoregressive model with adjustment parameters 𝛼 and cointegration vectors 𝛽.We discuss estimation of the model under the exact linear rational expectations, when we also have linear restrictions on the adjustment parameters 𝛼. In particular we consider the same restriction on all vectors in 𝛼 and the hypothesis that some vectors in 𝛼 are known.

• Swensen, Anders Rygh (2021). On causal and non-causal cointegrated vector autoregressive time series. Journal of Time Series Analysis. ISSN 0143-9782. 43(2), p. 178–196. doi: 10.1111/jtsa.12607. Full text in Research Archive Show summary

  Previous-30 treatments of multivariate non-causal time series have assumed stationarity. In this article, we consider integrated processes in a non-causal setting. We generalize the Johansen–Granger representation for causal vector autoregressive (VAR) models to allow for dependence on future errors and discuss how the parameters can be estimated. The asymptotic distribution of the trace statistic is also considered. Some Monte Carlo simulations are presented.

• Boug, Pål; Cappelen, Ådne; Jansen, Eilev S & Swensen, Anders Rygh (2020). The Consumption Euler Equation or the Keynesian Consumption Function? Oxford Bulletin of Economics and Statistics. ISSN 0305-9049. 83(1), p. 252–272. doi: 10.1111/obes.12394. Full text in Research Archive Show summary

  We formulate a general cointegrated vector autoregressive (CVAR) model that nests both a class of consumption Euler equations and various Keynesian‐type consumption functions. Using likelihood‐based methods and Norwegian data, we find support for cointegration between consumption, income and wealth once a structural break around the time of the financial crisis is allowed for. The fact that consumption cointegrates with both income and wealth and not only with income points to the empirical irrelevance of an Euler equation. Moreover, we find that consumption equilibrium corrects to changes in income and wealth, but not that income equilibrium corrects to changes in consumption, which would follow from an Euler equation. We also find that most of the parameters stemming from the class of Euler equations are not corroborated by the data when conditional expectations of future consumption and income in CVAR models are considered. Only habit formation seems important in explaining Norwegian consumer behaviour. Our estimated conditional Keynesian‐type consumption function implies a first year marginal propensity to consume (MPC) out of income of close to 40%.

• Boug, Pål; Cappelen, Ådne & Swensen, Anders Rygh (2017). Inflation Dynamics in a Small Open Economy. The Scandinavian Journal of Economics. ISSN 0347-0520. 119(4), p. 1010–1039. doi: 10.1111/sjoe.12194. Full text in Research Archive Show summary

  We evaluate the empirical performance of forward-looking models for inflation dynamicsin a small open economy. Using likelihood-based testing procedures, we find that the exactformulation is at odds with Norwegian data. Moreover, some of the parameters in themodel are not well identified. We also find that the inexact formulation is not rejectedstatistically using a test based on a minimum distance method. However, confidence regionsalso reveal an identification problem with this model. Instead, we find a well-specifiedbackward-looking model with imperfect competition underlying the price setting, which isa model that outperforms an alternative forward-looking model in-sample. The backward-looking model also forecasts somewhat better than the alternative forward-looking model,during and after the recent financial crisis. Keywords: Backward-looking; cointegrated vector autoregressive models; equilibrium correc-tion models; forward-looking; likelihood-based methods; minimum distance method

• Swensen, Anders Rygh (2014). Some exact and inexact linear rational expectation models in vector autoregressive models. Economics Letters. ISSN 0165-1765. 123(2), p. 216–219. doi: 10.1016/j.econlet.2014.02.015. Full text in Research Archive
• Nymoen, Ragnar; Swensen, Anders Rygh & Tveter, Eivind (2012). Interpreting the evidence for New Keynesian models of inflation dynamics. Journal of macroeconomics. ISSN 0164-0704. 34(2), p. 253–263. doi: 10.1016/j.jmacro.2012.01.008. Full text in Research Archive
• Johansen, Søren & Swensen, Anders Rygh (2011). On a graphical technique for evaluating some rational expectations models. Journal of Time Series Econometrics. 3(1). doi: 10.2202/1941-1928.1089. Full text in Research Archive
• Swensen, Anders Rygh (2011). A bootstrap algorithm for testing cointegration rank in VAR models in the presence of stationary variables. Journal of Econometrics. ISSN 0304-4076. 165(2), p. 152–162. doi: 10.1016/j.jeconom.2011.07.002. Full text in Research Archive
• Raknerud, Arvid; Skjerpen, Terje & Swensen, Anders Rygh (2010). Forecasting Key Macroeconomic Variables from a Large Number of Predictors: A State Space Approach. Journal of Forecasting. ISSN 0277-6693. 29(4), p. 367–387. doi: 10.1002/for.1131. Full text in Research Archive
• Boug, Pål; Cappelen, Aadne & Swensen, Anders Rygh (2010). The new Keynesian Phillips curve revisited. Journal of Economic Dynamics and Control. ISSN 0165-1889. 34(5), p. 858–874. doi: 10.1016/j.jedc.2010.01.001. Full text in Research Archive
• Johansen, S & Swensen, Anders Rygh (2008). Exact rational expectations, cointegration, and reduced rank regression. Journal of Statistical Planning and Inference. ISSN 0378-3758. 138, p. 2738–2748. doi: 10.1016/j.jspi.2008.03.030. Full text in Research Archive
• Raknerud, Arvid; Skjerpen, Terje & Swensen, Anders Rygh (2007). A linear demand system within a seemingly unrelated time series equations framework. Empirical Economics. ISSN 0377-7332. 32. doi: 10.1007/s00181-006-0074-5. Full text in Research Archive
• Boug, Pål; Cappelen, Ådne & Swensen, Anders Rygh (2006). Expectations and regime robustness in price formation: evidence from vector autoregressive models and recursive methods. Empirical Economics. ISSN 0377-7332. 31, p. 821–845. Full text in Research Archive
• Swensen, Anders Rygh (2006). Bootstrap algorithms for testing and determining the cointegration rank in VAR models. Econometrica. ISSN 0012-9682. 74, p. 1699–1714. Full text in Research Archive
• Johansen, Søren & Swensen, Anders Rygh (2004). More on testing exact rational expectations in cointegrated vector autoregressive models:Restricted constant and linear term. Econometrics Journal. ISSN 1368-4221. 7, p. 389–397. Full text in Research Archive
• Swensen, Anders Rygh (2003). A note on the power of bootstrap unit root tests. Econometric Theory. ISSN 0266-4666. 19(1), p. 32–48. Full text in Research Archive
• Swensen, Anders Rygh (2003). Bootstrapping unit root tests for integrated processes. Journal of Time Series Analysis. ISSN 0143-9782. 24(1), p. 99–126. Full text in Research Archive
• Sexton, Joe & Swensen, Anders Rygh (2000). ECM algorithms that converge at the rate of EM. Biometrika. ISSN 0006-3444. 87(3), p. 651–662. Full text in Research Archive Show summary

  We show that the ECM algorithm can always be constructed to converge at the same or approximately the same rate as the EM algorithm. The construction is based on the well-known conjugate directions algorithm. This result both suggests ways of speeding up the convergence of ECM and provides a simple way of identifying cases where the simplicity and stability of ECM over EM is attained at effectively no loss in convergence speed. Three examples are given.

• Johansen, Soeren & Swensen, Anders Rygh (1999). Testing exact rational expectations in cointegrated vector autoregressive models. Journal of Econometrics. ISSN 0304-4076. 93, p. 73–91. Full text in Research Archive Show summary

  This paper considers the testing of restrictions implied by rational expectations hypotheses in a cointegrated vector autoregressive model for I(1) variables. If the rational expectations involve one-step-ahead observations only and the coefficients are known, an explicit parameterization of the restrictions is found, and the maximum- likelihood estimator is derived by regression and reduced rank regression. An application is given to a present value model.

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• Swensen, Anders Rygh (2007). Spreads, reduced rank VAR-models and rational expectations. Full text in Research Archive
• Swensen, Anders Rygh (2007). Exact rational expectations and reduced rank vector autoregressive (VAR) models. Full text in Research Archive
• Swensen, Anders Rygh (2005). Finite sample properties of a bootstrap procedure for estimation of rank in reduced rank VAR-models. Full text in Research Archive
• Swensen, Anders Rygh (2004). Bootstrap algorithms for testing and determining the cointegration rank in VAR models. Full text in Research Archive
• Swensen, Anders Rygh (2004). Bootstrap algorithms for testing and determining the cointegration rank in VAR models. Full text in Research Archive
• Swensen, Anders Rygh (2002). A bootstrap algorithm for testing cointegration rank in VAR models. Full text in Research Archive Show summary

  A bootstrap algorithm for a reduced rank VAR-model was analyzed

• Swensen, Anders Rygh (2002). More on restricted exact rational expectations in cointegrated vector autoregressive models. Full text in Research Archive
• Boug, Pål; Cappelen, Ådne & Swensen, Anders Rygh (2016). Modelling OPEC behaviour: Theory and evidence. Statistisk sentralbyrå (SSB). Full text in Research Archive Show summary

  We analyse the behaviour of OPEC as a group for the period 1992 to 2015 by formulating a model that encompasses several of the alternatives discussed in the literature. There is no consensus in the literature on how OPEC behaviour affects crude oil prices. Some studies treat the oil market as a standard competitive market where OPEC plays no important role, whereas others argue that OPEC is a dominant producer with a competitive fringe or a cartel that adjusts its production to influence crude oil prices in a way that benefits the member states. We analyse the behaviour of OPEC as a group for the period 1992 to 2015 by formulating a model that encompasses several of the alternatives discussed in the literature. Applying a system-based cointegration analysis, we find support for the imperfect competition hypothesis regarding the output decision of OPEC. We also find, using full information maximum likelihood and recursive methods, that a dynamic equilibrium correction model with imperfect competition is reasonably stable in-sample and has somewhat better fit than an alternative dynamic model with weaker theoretical underpinnings. However, a forecasting exercise reveals that the dynamic equilibrium correction model breaks down following the OPEC meeting in November 2014. At the end of 2015 the model underpredicts the production of OPEC by almost 2.5 million barrels per day. We therefore conclude that the OPEC behaviour has changed significantly, probably to limit the role of competitors like American producers of shale oil.

• Boug, Pål; Cappelen, Ådne & Swensen, Anders Rygh (2011). The new Keynesian Phillips curve: Does it fit Norwegian data? Statistisk sentralbyrå (SSB). Full text in Research Archive Show summary

  We evaluate the empirical performance of the new Keynesian Phillips curve (NKPC) for a small open economy using cointegrated vector autoregressive models, likelihood based methods and general method of moments. Our results indicate that both baseline and hybrid versions of the NKPC as well as exact and inexact formulations of the rational expectation hypothesis are most likely at odds with Norwegian data. By way of contrast, we establish a well-specified dynamic backward-looking imperfect competition model (ICM), a model which encompasses the NKPC in-sample with a major monetary policy regime shift from exchange rate targeting to inflation targeting. We also demonstrate that the ICM model forecasts well both post-sample and during the recent financial crisis. Our findings suggest that taking account of forward-looking behaviour when modelling consumer price inflation is unnecessary to arrive at a well-specified model by econometric criteria. Keywords: The new Keynesian Phillips curve, imperfect competition model, cointegrated vector autoregressive models (CVAR), equilibrium correction models, likelihood based methods and general method of moments (GMM)

• Johansen, Søren & Swensen, Anders Rygh (2007). Exact Rational Expectations, Cointegration, and Reduced Rank Regression. Økonomisk institutt, Københavns Universitet. Full text in Research Archive Show summary

  We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important

• Boug, Pål; Cappelen, Aadne & Swensen, Anders Rygh (2007). The New Keynesian Phillips Curve revisited. Statistisk sentralbyrå (SSB). Full text in Research Archive Show summary

  Abstract: Recently, several authors have questioned the evidence claimed by Galí and Gertler (1999) and Galí, Gertler and López-Salido (2001) that a hybrid version of the New Keynesian Phillips Curve approximates European and US inflation dynamics quite well. We re-examine the evidence using likelihood-based methods. Although including lagged inflation enhances the empirical fit, the improvement is not large enough to yield a model that passes a likelihood ratio test. We also show that the likelihood surface is rather flat, especially in the European case, indicating that the model may be weakly identified as criticised by others using alternative methods. Keywords: European and US inflation, the New Keynesian Phillips Curve, vector autoregressive models and likelihood ratio tests.

• Raknerud, Arvid; Skjerpen, Terje & Swensen, Anders Rygh (2007). Forecasting key macroeconomic variables from a large number of predictors: A state space approach. Statistisk sentralbyrå (SSB). Full text in Research Archive Show summary

  Abstract: We use state space methods to estimate a large dynamic factor model for the Norwegian economy involving 93 variables for 1978Q2–2005Q4. The model is used to obtain forecasts for 22 key variables that can be derived from the original variables by aggregation. To investigate the potential gain in using such a large information set, we compare the forecasting properties of the dynamic factor model with those of univariate benchmark models. We find that there is an overall gain in using the dynamic factor model, but that the gain is notable only for a few of the key variables. Keywords: Dynamic factor model, Forecasting, State space, AR models

• Boug, Pål; Cappelen, Ådne & Swensen, Anders Rygh (2006). The New Keynesian Phillips curve for a small open economy. Statistisk sentralbyrå (SSB). Full text in Research Archive Show summary

  Abstract: The New Keynesian Phillips Curve (NKPC) has become the benchmark model for understanding inflation in modern monetary economics. One reason for the popularity is the microfoundation of the model, which decomposes agents' behaviour into price adjustments and deviations of the price level from its target. The empirical relevance of the NKPC is, however, a matter of debate as recent studies reveal that some supportive evidence depends crucially on the econometric methods applied. We show how to evaluate the features of the model using cointegration techniques and tests based on both single-behavioural equations and cointegrated VAR models. Our results indicate that the forward-looking part of the NKPC is most likely at odds with Norwegian data. By contrast, we establish a well-specified dynamic model interpreted as a standard backward-looking mark-up price equation. We also demonstrate that the dynamic mark-up model forecasts well post-sample and during a major change in the monetary policy regime, which certainly is strong evidence in favour of this model. Consequently, we conclude that taking account of forward-looking behaviour when modelling consumer price inflation in Norway seems unnecessary to arrive at a well-specified model by econometric criteria. Keywords: The New Keynesian Phillips Curve, mark-up pricing, single-equation estimation methods, encompassing tests, cointegrated vector autoregressive models and equilibrium correction models.

• Liu, Gang; Skjerpen, Terje; Swensen, Anders Rygh & Telle, Kjetil Elias (2006). Unit roots, Polynomial transformations and the environmental Kuznets curve. Statistisk sentralbyrå (SSB). Full text in Research Archive Show summary

  Abstract: Time-series regressions including non-linear transformations of an integrated variable are not uncommon in various fields of economics. In particular, within the Environmental Kuznets Curve (EKC) literature, where the effect on the environment of income levels is investigated, it is standard procedure to include a third order polynomial in the income variable. When the income variable is an I(1)-variable and this variable is also included nonlinearly in the regression relation, the properties of the estimators and standard inferential procedures are unknown. Surprisingly, such problems have received rather limited attention in applied work, and appear disregarded in the EKC literature. We investigate the properties of the estimators of long-run parameters using Monte-Carlo simulations. We find that the mean of the ordinary least squares estimates are very similar to the true values and that standard testing procedures based on normality behave rather well. Keywords: Emissions, Environmental Kuznets Curve, Unit Roots, Monte Carlo Simulations

• Swensen, Anders Rygh (2004). Bootstrap algorithms for testing and determining the cointegration rank in VAR models. Universitetet i Oslo. Full text in Research Archive Show summary

  In this paper a bootstrap algorithm for a reduced rank VAR-model with a restricted linear trend is analyzed. For testing the cointegration rank the asymptotic distribution under the hypothesis is the same as for the usual likelihood ratio test. It is furthermore shown that a bootstrap procedure for determining the rank is asymptotically consistent in the sense that the probability of choosing the rank too small converges to zero. An empirical illustration is given.

• Johansen, Søren & Swensen, Anders Rygh (2003). More on testing exact rational expectations in cointegrated vector autoregressive models: Resticted drift terms. Universitetet i Oslo. Full text in Research Archive Show summary

  In this note we consider testing of a type of linear restrictions implied by rational expectations hypotheses in a cointegrated vector autoregressive model for <I>I</I>(1) variables when there in addition is a restriction on the deterministic drift terms.

• Johansen, Søren & Swensen, Anders Rygh (2003). More on testing exact rational expectations in cointegrated vector autoregressive models: Restricted drift terms. Statistisk sentralbyrå (SSB). Full text in Research Archive Show summary

  Abstract: In this note we consider testing of a type of linear restrictions implied by rational expectations hypotheses in a cointegrated vector autoregressive model for I(1) variables when there in addition is a restriction on the deterministic drift term. Keywords: VAR model, cointegration, restricted drift term, rational expectations

• Swensen, Anders Rygh (2003). A linear demand system within a seemingly unrelated time series equation framework. Statistisk sentralbyrå (SSB). Full text in Research Archive Show summary

  Abstract: We consider a Seemingly Unrelated Time Series Equations framework for the linear Almost Ideal Demand system. The framework is applied to a consumer demand system covering nine non-durable commodities. We test for demand homogeneity within a specification where the static linear Almost Ideal Demand system is augmented by three stochastic trends and three stochastic seasonal variables. The homogeneity restriction is rejected for about half of the commodities and in the system as a whole using conventional significance levels. However, when comparing the out-of-sample predictions from a homogeneous and non-homogeneous model, we do not find that the non-homogenous model performs better than the homogeneous one. Moreover, the income and price elasticities calculated under homogeneity restrictions are all of the right sign and have reasonable magnitudes. Keywords: Consumer demand. Linear Almost Ideal Demand system. Seemingly Unrelated Time Series Equations. Prediction.

• Swensen, Anders Rygh (2001). A note on the power of bootstrap unit root test. Universitetet i Oslo. Full text in Research Archive Show summary

  In this note we consider the asymptotic power functions of some bootstrap unit root tests under local alternatives and show that they are in fact the same as for ordinary unit root tests. This is regardless of whether the differences of the observations, i.e. the so-called restricted residuals, or the ordinary least squares residuals are used to construct the resampled observations. We also consider models containing a constant and a linear trend and the DF-GLS tests proposed by Elliot et al.(1996). A small Monte Carlo experiment is included.

• Swensen, Anders Rygh (2000). Bootstrapping unit root tests. Universitetet i Oslo. Full text in Research Archive
• Boug, Pål; Cappelen, Aadne & Swensen, Anders Rygh (2000). Expectations in Export Price Formations Tests using Cointegrated VAR models. Statistisk sentralbyrå (SSB). Full text in Research Archive
• Skjerpen, Terje & Swensen, Anders Rygh (2000). Testing for long-run homogeneity in the Linear Almost Ideal Demand System: An application on Norwegian quarterly data for non-durables. Statistisk sentralbyrå (SSB). Full text in Research Archive Show summary

  Abstract: We consider testing for long-run homogeneity within a dynamic consumer demand system allowing for non-stationarities. The static long-run solution is assumed to follow the Linear Almost Ideal Demand System and we test for long-run homogeneity within this system utilizing a triangular representation. Both long-run homogeneity in single equations and in the entire consumer system are considered. Consistent with the general triangular representation the deduced share equations depend on both current, lagged and leaded differenced explanatory variables (besides level variables and deterministic variables capturing trend and seasonality). Before testing for long-run homogeneity we test whether prices and real total expenditure are Granger-caused by the share variables. In the case with Granger-causality the leaded differenced variables can be omitted from the equation to be estimated. Thus Granger non-causality can be tested by looking at the joint significance of all leaded variables in all share equations simultaneously. The methodological framework is applied on non-durable consumption data from 1966:1 to 1997:4 taken from the unadjusted Norwegian National Accounts. We find that the null of no Granger-causality are clearly rejected and in light of this the differenced variables are retained when testing for long-run homogeneity. When testing for long-run homogeneity we consider different specifications of the deterministic trend and of the lags/leads specification. We find that the homogeneity-tests are substantially influenced by the specification of the deterministic trend. In one of the specifications long-run homogeneity is neither rejected for the single equations nor for the entire system. By imposing long-run homogeneity long-run Engel- and price elasticties can be calculated. Generally, the long-run elasticities seem reasonable.

• Swensen, Anders Rygh (1976). DEFICIENCIES IN LINEAR NORMAL EXPERIMENTS. Universitetet i Oslo. Full text in Research Archive

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