Variable Lag Research Articles

Asymmetric Conjugate Priors for Large Bayesian VARs

Large Bayesian VARs are now widely used in empirical macroeconomics. One popular shrinkage prior in this setting is the natural conjugate prior as it facilitates posterior simulation and leads to a range of useful analytical results. This is, however, at the expense of modelling exibility, as it rules out cross-variable shrinkage – i.e. shrinking coefficients on lags of other variables more aggressively than those on own lags. We develop a prior that has the best of both worlds: it can accommodate cross-variable shrinkage, while maintaining many useful analytical results, such as a closed-form expression of the marginal likelihood. This new prior also leads to fast posterior simulation - for a BVAR with 100 variables and 4 lags, obtaining 10,000 posterior draws takes less than half a minute on a standard desktop. In a forecasting exercise, we show that a data-driven asymmetric prior outperforms two useful benchmarks: a data-driven symmetric prior and a subjective asymmetric prior.

Consumption vs. Investments for stimulating economic growth and employment in the CEE Countries – a panel analysis

The aim of this paper is to find out if the high economic growth rates achieved by the CEE countries are based either on consumption or on investments, considering many exogenous factors that impact on the economic growth and how these factors can contribute to the employment process in the CEE economies to stress if these trends of economic growth and employment are sustainable in the long run. We performed two Panel Least Squares and Pool Least Squares estimations to determine the impact of the exogenous variables on the economic growth (as GDP per capita growth) and on the unemployment rate in the short and long run, depending on the lags of the exogenous variables used in the analysis. We used yearly data series during 2004–2017 for eight selected CEE countries. Our results show that private consumption is positively related with economic growth in the short run, but it doesn’t support the job creation process, in the same way as the savings rate can’t determine positive effects on the employment. Public spending is strongly and negatively correlated with economic growth and positively correlated with the unemployment rate in the CEE region, while the net export is weakly impacting on the economic growth in the CEE region and doesn’t support the employment process in this area. The impact of the domestic investments on the economic growth is weaker in the CEE area than the impact of both private and public spending, but they are positively correlated with the economic growth and negatively correlated with the unemployment rate, while the correlation of the foreign direct investments (FDIs) with both economic growth and unemployment is very weak, as it is the case of net exports. We conclude that the economic growth in the CEE area is mainly based on the private consumption in the short run but the private consumption doesn’t support the job creation process either in the long run or in the short run. The qualitative factors included in the analysis by using global competitiveness index (corruption control, bureaucracy, infrastructure quality, governance effectiveness, political stability, rule of law factors, property rights, markets efficiency, etc.) and corruption perception index are strongly and positively correlated with the economic growth and negatively correlated with the unemployment rate.

Measurement of atmospheric oxides of nitrogen and a preliminary investigation of their source

Abstract Introduction Maintenance of a breathable atmosphere is a core tenet of dived submarine operations, and the responsibility for this falls to the medical department. Nitrogen oxides (NOx) are atmospheric contaminants from a currently unconfirmed source. If not controlled, these contaminants can act as respiratory irritants and asphyxiants which may endanger health and threaten sustained dived operations. Methods Using the issued Dräger Short Term Detection Tubes (STDTs) to sample strategic locations, the relationship between atmospheric contaminants and NOx was investigated in an attempt to determine the source of NOx formation. Interventions were implemented to reduce NOx by reducing leakage of monoethanolamine (MEA) from carbon dioxide (CO2) scrubbing equipment, a known potential source of NOx if oxidised (combusted). Dräger STDTs for NH3 demonstrate cross-reactivity with MEA, these levels being referred to as NH3/MEA. Results A relationship was demonstrated between elevated readings for atmospheric NH3/MEA and elevated readings for NOx, with a variable lag period. Findings suggest that NOx production may be reduced by control of atmospheric NH3/MEA. Of the control measures examined, replacement of resin filter bags was noted to reduce atmospheric NH3/MEA, while replenishment of CO2 scrubber MEA was noted to increase it, with a resultant increase in NOx production. Conclusions Elevated NH3 atmospheric readings may in fact be due to MEA from CO2 scrubbers. This, when catalytically oxidised by CO/H2 burners, produces NOx. Management of MEA egress from CO2 scrubbers (carryover) represents a potential target for NOx control interventions. Specific MEA detection equipment is required to demonstrate whether MEA or NH3 is the progenitor species for NOx. Furthermore, controlled trials are required to prove a definitive relationship between MEA and NOx and to evaluate the best control measures.

Constrained temporal parallel decomposition for EEG-fMRI fusion

Objective. Multimodal neuroimaging has become a common practice in neuroscience research. Simultaneous EEG–fMRI is a popular multimodal recording approach due to the complementary spatiotemporal relationship between the two modalities. Several data fusion techniques have been proposed in the literature for EEG-fMRI fusion, including joint-ICA and parallel-ICA frameworks. Previous EEG–fMRI fusion approaches have used sensor-level EEG features. Recently, we introduced source-space ICA for EEG–MEG source reconstruction and component identification, which was shown to be a superior alternative to sensor-space ICA. Approach. Here, we extend source-space ICA to the fusion of EEG–fMRI data. Additionally, we incorporate the use of a paradigm signal (constrained) and a lag-based signal decomposition approach to accommodate recent findings demonstrating the potentially variable lag structure between electrophysiological and BOLD signals. We evaluated this method on simulated concurrent EEG–fMRI during a boxcar task design, as well as real concurrent EEG–fMRI data from three participants performing an N-Back working memory task. The block diagram of the algorithm and corresponding source codes are provided. Main results. Based on the results of the real working memory task, for all three subjects, one frontal theta component, and one right posterior alpha component had the highest contribution coefficients (~0.5) to the paradigm-related fused component. There were also two more alpha band components with contribution coefficients of 0.3. The highest contributing fMRI component (~0.8) was one known in the literature to be related to the attention network. The second fMRI component was related to the well-known default mode network, with a contribution coefficient of 0.3. Significance. The proposed EEG–fMRI fusion approach, is capable of estimating the brain maps of the EEG and fMRI for the fused components and account for the variable lag structure between electrophysiological and BOLD signals.

An Integrated Investigation of Spatiotemporal Habitat Quality Dynamics and Driving Forces in the Upper Basin of Miyun Reservoir, North China

Understanding changes in habitat quality and the driving forces of these changes at landscape scales is a critical part of effective ecosystem management. The present study investigated spatiotemporal habitat quality dynamics and related driving forces from 2005 to 2015 in the upper basin of Miyun Reservoir in North China by constructing an effective framework integrated InVEST and binary logistic regression models. This framework expanded the driving force analysis into an assessment of changes in habitat quality and intuitively verified the effectiveness of relevant environmental policies. The proposed method of combining the equidistant random sampling method and the method of introducing spatial lag variables in logistic regression equation can effectively solve spatial autocorrelation with a large enough number of sampling points. Overall, habitat quality improved during the study period. Spatially, a concentrated loss of habitat occurred in the southeastern part of the basin between the reservoir and mountainous areas, while other areas gradually recovered. Driving force analysis showed that lower elevation mountain land, gentle slopes, locations near rural land or roads, larger areas of grain cultivation, and areas with little population change had a higher likelihood of having changed in habitat quality in the upper basin of Miyun Reservoir. These results suggested that the present policy of protecting the ecosystem had a positive effect on improving habitat quality. In the future, the human activity management related to habitat quality needs to be strengthened. The present study would provide a reference for land use policy formulation and biodiversity conservation.

Transportation Accessibility Benefit and the Dynamic Pattern of Real Estate Prices: Emerging Literature

Location preference is a repeatedly debated subject in urban land economics. By and large, these deliberations are either empirical or theoretical in nature. A sizeable number of the previous studies tackle the question of most favorable location provisional on a certain set of constrictions. Moreover, other studies are dedicated to elucidating the nature (worth) of a real property at a particular location. Nevertheless, the problem of ascertaining the indicators that influence real property price is general to both sets of studies. The current body of knowledge on the impact of transportation infrastructure on real estate prices is diverse in its outcome and result with particular reference to degree or extent of impact as well as bearing, ranging from a negative to an unimportant or a positive effect. On the literature results, multiple spatial lag variables were found to be statistically significant signifying that a number of features or attributes of adjoining residential accommodations have significant influence on the subject residential property's value. Whereas the largest part of earlier hedonic price empirical studies considered only selected factors (such as, positive as well as negative impacts of single transportation mode or means, positive or else negative impacts of multiple transportation modes) into account, the majority of recent empirical studies, however, considered all these key determinants, factors and indicators into consideration for analyzing joint impacts of transportation facility. Through considerable strategy, policy in addition to planning or forecasting implications underlying the association between transit oriented developments and real estate values and the difference between previous studies’ outcomes and results, there is a strong necessity and requirement for further study and analysis to ascertain an advanced, reliable in addition to dependable level of conclusiveness.

Foreign Body-Related Extremity Trauma in Children: A Single-Center Experience.

The extremity foreign body in a child has propensity of getting missed or mistaken diagnosis. We report our experience of extremity foreign body trauma in order to increase awareness of this disease entity. The retrospective series of 24 retained foreign bodies was based on a 10-year chart review of emergency data (ICD code Z18). Patients with both upper and lower limb affections were included. Patients with ocular, otolaryngeal, tracheobronchial, gastrointestinal, and axial foreign bodies were excluded from the study. Male predominance (M:F = 20:4), young patient age (mean 6.8 years), variable lag period for consultation (range 3 h–8 years), and majority lower limb affection (58%; foot [7; 29%] and knee [5; 20.8%]) were some characteristics of extremity foreign bodies trauma. The foreign bodies reported were metallic needle (7; 29%), rubber band (3; 12.5%), pellets (3; 12.5%), bangle glass (2; 8%), glass pieces (2; 8%) “dhaga,” wooden twig, wooden thorn, ceramic earthen pot pieces, stapler pin, broomstick, and cracker piece in one case each (1; 4%). Postremoval, the wound healing was uneventful in all patients. Foreign body-related extremity trauma in children is a rare event. It has its own set of characteristics and differential diagnosis. Familiarity with the regional practices and customs is must to establish the circumstances/nature of the foreign body injury. The foreign body should preferably be removed in a well-equipped setting.

THE EFFECT OF AUDIT OPINION, PUBLIC ACCOUNTING FIRM’S SIZE, COMPANY SIZE, AND COMPANY PROFITABILITY TO DELAY AUDITS IN REGISTERED MANUFACTURING COMPANIES IN INDONESIA STOCK EXCHANGE IN 2015-2017

This study aims to determine the effect of audit opinion, Public Accounting Firm’s size, company size, and company profitability on audit delay in manufacturing goods in the consumer goods industry sector listed on the Indonesia Stock Exchange in 2015-2017. The sample selection technique used was purposive sampling. There are several criteria that must be met by companies listed in the Indonesia Stock Exchange to be able to be sampled in this study. This research method uses multiple regression analysis which is used to determine the effect of independent variables on the dependent variable together and partially. The t test is used to test the effect of each audit opinion variable, Public Accounting Firm’s, company size, and company profitability on report lag variables. F statistic test aims to examine the effect of audit opinion variables, Public Accounting Firm’s, company size, and corporate profitability together with delay audit variables. R2 test (coefficient of determination) is done to determine how much influence the audit opinion variable, Public Accounting Firm’s, company size, and company profitability on audit delay variables. The populations of this study were 114 companies and the samples used in this study were 63 consumer goods manufacturing industry companies listed on the Indonesia Stock Exchange in 2015-2017. Data collection methods in this study use secondary data in the form of financial reports that have been published. Data is processed using SPSS 21 program. From the results of the t test, it is known that audit opinion, Public Accounting Firm’s partially has no significant effect on audit delay. Variable company size, profitability partially has a significant effect on audit delay variables. From the F test results, it is known that audit opinion, Public Accounting Firm’s, company size and profitability simultaneously have a significant effect on audit delay variables in manufacturing companies listed on the Indonesia Stock Exchange in 2015-2017.
 
 Keywords : audit delay, audit opinion, Public Accounting Firm’s size, company size, company profitability.

Assessment of the Influence of the Extraction of Energy Resources on the Environment

In the paper a proposed model for evaluating the influence of energy resource extraction activities on indicators for assessing the state of the environment is considered. The model was constructed under several different assumptions. The first suggests that there exists an environment in which different processes are taking place, e.g. forests and fresh water stocks are changing along with temperature. These processes are to be assessed by endogenous variables. Moreover, each process has its own prehistory that is also being affected by each endogenous variable. The second assumption states that all the processes taking place in the environment are interrelated. The third assumption supposes that the environment is affected by external factors, primarily human activity. In the current paper the human activity of energy resource extraction was considered. The model comprised four econometric equations, each of which was considered to be an ADL model. The model represented the coefficient calculation methodology with time series stationarity and multicollinearity verification. Identification of endogenous variable lags correlated strongly with the current period variable value and verification of the significance of autocorrelation coefficients. The findings of the study allowed conclusions to be drawn, which offered directions for further investigation.

News-based forecasts of macroeconomic indicators: A semantic path model for interpretable predictions

The macroeconomic climate influences operations with regard to, e.g., raw material prices, financing, supply chain utilization and demand quotas. In order to adapt to the economic environment, decision-makers across the public and private sectors require accurate forecasts of the economic outlook. Existing predictive frameworks base their forecasts primarily on time series analysis, as well as the judgments of experts. As a consequence, current approaches are often biased and prone to error. In order to reduce forecast errors, this paper presents an innovative methodology that extends lag variables with unstructured data in the form of financial news: (1) we apply a variety of models from machine learning to word counts as a high-dimensional input. However, this approach suffers from low interpretability and overfitting, motivating the following remedies. (2) We follow the intuition that the economic climate is driven by general sentiments and suggest a projection of words onto latent semantic structures as a means of feature engineering. (3) We propose a semantic path model, together with estimation technique based on regularization, in order to yield full interpretability of the forecasts. We demonstrate the predictive performance of our approach by utilizing 80,813 ad hoc announcements in order to make long-term forecasts of up to 24 months ahead regarding key macroeconomic indicators. Back-testing reveals a considerable reduction in forecast errors.

Water level management of lakes connected to regulated rivers: An integrated modeling and analytical methodology

Reservoir operations significantly alter the hydrological regime of the downstream river and river-connected lake, which has far-reaching impacts on the lake ecosystem. To facilitate the management of lakes connected to regulated rivers, the following information must be provided: (1) the response of lake water levels to reservoir operation schedules in the near future and (2) the importance of different rivers in terms of affecting the water levels in different lake regions of interest. We develop an integrated modeling and analytical methodology for the water level management of such lakes. The data-driven method is used to model the lake level as it has the potential of producing quick and accurate predictions. A new genetic algorithm-based synchronized search is proposed to optimize input variable time lags and data-driven model parameters simultaneously. The methodology also involves the orthogonal design and range analysis for extracting the influence of an individual river from that of all the rivers. The integrated methodology is applied to the second largest freshwater lake in China, the Dongting Lake. The results show that: (1) the antecedent lake levels are of crucial importance for the current lake level prediction; (2) the selected river discharge time lags reflect the spatial heterogeneity of the rivers’ impacts on lake level changes; (3) the predicted lake levels are in very good agreement with the observed data (RMSE ≤ 0.091 m; R2 ≥ 0.9986). This study demonstrates the practical potential of the integrated methodology, which can provide both the lake level responses to future dam releases and the relative contributions of different rivers to lake level changes.

DOES REVERSE CAUSALITY EXPLAINS THE RELATIONSHIP BETWEEN ECONOMIC PERFORMANCE AND TECHNOLOGICAL DIVERSITY?

Previous studies have highlighted technological innovation as a key instrument for economic development. However, although the relationship between innovation and economic growth has been extensively explored, few studies have investigated the impacts of crucial dimensions of innovation on economic growth. This paper presents one of the first empirical attempts to analyze how the “diversity” aspect of technological progress (or innovation) influences economic performance by considering the possible bidirectional causal effects between these two factors. A series of econometric techniques, including a two-stage-least-squares instrumental variable and dynamic autoregressive distributed lag model, are applied on a dataset of 55 countries. The dataset includes patent data from the United States Patent and Trademark Office and combined macroeconomic data from the World Bank’s development indicators and International Monetary Fund’s economic outlook databases. The results show that generally, technological diversity does not directly affect economic growth. By contrast, a negative effect of diversity on GDP per capita is observed in non-high-income countries. This study contributes to the macroeconomics and innovation management literature by providing an integrated empirical application of various popular firm management theories and a well-known endogenous economic growth theory.

Lag as moderator meta-analysis: A methodological approach for synthesizing longitudinal data

Longitudinal data are common and essential to understanding human development. This paper introduces an approach to synthesizing longitudinal research findings called lag as moderator meta-analysis (LAMMA). This approach capitalizes on between-study variability in time lags studied in order to identify the impact of lag on estimates of stability and longitudinal prediction. The paper introduces linear, nonlinear, and mixed-effects approaches to LAMMA, and presents an illustrative example (with syntax and annotated output available as online Supplementary Materials). Several extensions of the basic LAMMA are considered, including artifact correction, multiple effect sizes from studies, and incorporating age as a predictor. It is hoped that LAMMA provides a framework for synthesizing longitudinal data to promote greater accumulation of knowledge in developmental science.

Hydromechanical Earthquake Nucleation Model Forecasts Onset, Peak, and Falling Rates of Induced Seismicity in Oklahoma and Kansas

AbstractThe earthquake activity in Oklahoma and Kansas that began in 2008 reflects the most widespread instance of induced seismicity observed to date. We develop a reservoir model to calculate the hydrologic conditions associated with the activity of 902 saltwater disposal wells injecting into the Arbuckle aquifer. Estimates of basement fault stressing conditions inform a rate‐and‐state friction earthquake nucleation model to forecast the seismic response to injection. Our model replicates many salient features of the induced earthquake sequence, including the onset of seismicity, the timing of the peak seismicity rate, and the reduction in seismicity following decreased disposal activity. We present evidence for variable time lags between changes in injection and seismicity rates, consistent with the prediction from rate‐and‐state theory that seismicity rate transients occur over timescales inversely proportional to stressing rate. Given the efficacy of the hydromechanical model, as confirmed through a likelihood statistical test, the results of this study support broader integration of earthquake physics within seismic hazard analysis.

Partial dust obscuration in active galactic nuclei as a cause of broad-line profile and lag variability, and apparent accretion disc inhomogeneities

The profiles of the broad emission lines of active galactic nuclei (AGNs) and the time delays in their response to changes in the ionizing continuum ("lags") give information about the structure and kinematics of the inner regions of AGNs. Line profiles are also our main way of estimating the masses of the supermassive black holes (SMBHs). However, the profiles often show ill-understood, asymmetric structure and velocity-dependent lags vary with time. Here we show that partial obscuration of the broad-line region (BLR) by outflowing, compact, dusty clumps produces asymmetries and velocity-dependent lags similar to those observed. Our model explains previously inexplicable changes in the ratios of the hydrogen lines with time and velocity, the lack of correlation of changes in line profiles with variability of the central engine, the velocity dependence of lags, and the change of lags with time. We propose that changes on timescales longer than the light-crossing time do not come from dynamical changes in the BLR, but are a natural result of the effect of outflowing dusty clumps driven by radiation pressure acting on the dust. The motion of these clumps offers an explanation of long-term changes in polarization. The effects of the dust complicate the study of the structure and kinematics of the BLR and the search for sub-parsec SMBH binaries. Partial obscuration of the accretion disc can also provide the local fluctuations in luminosity that can explain sizes deduced from microlensing.

Circatrigintan instead of lunar periodicity of larval release in a brooding coral species

Larval release by brooding corals is often assumed to display lunar periodicity. Here, we show that larval release of individual Stylophora pistillata colonies does not comply with the assumed tight entrainment by the lunar cycle, and can better be classified as a circatrigintan pattern. The colonies exhibited three distinct reproductive patterns, characterized by short intervals, long intervals and no periodicity between reproductive peaks, respectively. Cross correlation between the lunar cycle and larval release of the periodic colonies revealed an approximately 30-day periodicity with a variable lag of 5 to 10 days after full moon. The observed variability indicates that the lunar cycle does not provide a strict zeitgeber. Other factors such as water temperature and solar radiation did not correlate significantly with the larval release. The circatrigintan patterns displayed by S. pistillata supports the plasticity of corals and sheds new light on discussions on the fecundity of brooding coral species.

Multiyear Shallow Conduit Changes Observed With Lava Lake Eruption Seismograms at Erebus Volcano, Antarctica

AbstractWe analyze near‐repeating broadband seismograms from nearly 3,000 eruptions (2003–2011) from the Erebus volcano lava lake to investigate temporal changes in the shallow eruptive dynamics of an open conduit volcano. Cross‐correlation analysis reveals progressive variable time lags between correlation‐aligned short period (SP) and very long period (VLP) seismogram components ranging over approximately ±1 s and evolving over weeks to months. Lava lake eruptions both excite an SP explosion seismic signal and gravitationally unload the conduit. After a delay of several seconds, this unloading excites a posteruptive, minute‐long VLP seismic signal that persist for several minutes until the lava lake is refilled. VLP‐SP lag variations are consistent across multiple seismic stations and are independent of eruption size, spectral characteristics, eruption frequency, and lava lake morphology changes. Lag changes are interpreted in terms of variable communication time between eruptions and the subsequent elastic and gravitational response of a tomographically imaged near‐summit magma storage and VLP source region several hundred meters below the lava lake. Tomographic and VLP moment tensor studies, combined with modeling, suggest that the elastodynamic communication time between the distinct SP and VLP source regions is mediated by conduit‐guided Stoneley waves within the uppermost magma‐filled conduit system that are sensitive to small shallow conduit geometry changes. Conduit geometry changes may be driven by internal or external processes, including conduit wall melting and refreezing, repeated eruptive slug erosion, and deformation from inner crater inflation or collapse.

Hybrid ARIMAX quantile regression method for forecasting short term electricity consumption in east java

The need for energy supply, especially for electricity in Indonesia has been increasing in the last past years. Furthermore, the high electricity usage by people at different times leads to the occurrence of heteroscedasticity issue. Estimate the electricity supply that could fulfilled the community’s need is very important, but the heteroscedasticity issue often made electricity forecasting hard to be done. An accurate forecast of electricity consumptions is one of the key challenges for energy provider to make better resources and service planning and also take control actions in order to balance the electricity supply and demand for community. In this paper, hybrid ARIMAX Quantile Regression (ARIMAX-QR) approach was proposed to predict the short-term electricity consumption in East Java. This method will also be compared to time series regression using RMSE, MAPE, and MdAPE criteria. The data used in this research was the electricity consumption per half-an-hour data during the period of September 2015 to April 2016. The results show that the proposed approach can be a competitive alternative to forecast short-term electricity in East Java. ARIMAX-QR using lag values and dummy variables as predictors yield more accurate prediction in both in-sample and out-sample data. Moreover, both time series regression and ARIMAX-QR methods with addition of lag values as predictor could capture accurately the patterns in the data. Hence, it produces better predictions compared to the models that not use additional lag variables.

Determinants of Sawnwood Consumption in Slovakia

This paper aimed to determine coniferous and non-coniferous sawnwood demand drivers and used historical data on their development as independent variables in the sawnwood demand models. The study presented a general form of ad hoc model that explained sawnwood consumption per capita as a function of a range of socio-economic factors. Based on the theory of demand, the most important factors were identified to enter the regression model including significant price and income variables. In the case of the non-coniferous sawnwood model, time lag variables were applied. The results of the estimated econometric models confirmed the presence of different explanatory variables for both types of sawnwood. While consumption per capita of both coniferous and non-coniferous sawnwood was determined by the activities of the construction sector, and demand appeared to be very elastic in relation to the number of completed dwellings, the price and substitution for other wood materials had a significant impact only on non-coniferous sawnwood.

Inference with Cumulative Relative Risk in Environmental Epidemiology: Part III. Inference from Lag Variables

Background/Aim: A distributed lag model (DLM) including a single lag variable has been widely used in air pollution and temperature studies. Researchers have questioned which is the unbiased model among the variety of candidate models. Causal inference from a lag variable (e.g. lag1) may be doubtful if it is not consistent with a lag time implied in toxicological studies. Based upon reasoning in Part I and Part II, we aimed to prove that a coefficient of interest including a single and a sum (i.e. cumulative) of coefficients should be treated as a lower bound of a true (cumulative) coefficient. Methods: We simulated 5,000 runs of estimation of PM risk on all-cause mortality based upon real data. PM effect scenarios include 1) an effect on the same day, 2) effects upto the previous 2 days, 3) effects with exponential decay over time, 4) full harvesting, 5) limited harvesting with effects in longer lags. We compared candidate models in terms of bias, mean squared error (MSE), nominal coverage and probability of model selection by information criteria. Results: DLM with sufficient lags provided unbiased estimates while MSE tended to be compromised. In this regard, information criteria performed poorly in selecting an unbiased model. In a harvesting scenario, models with limited lags were bound to away-from-the null bias. DLM with sufficient lags only for harvesting yielded an estimate smaller than or equal to a true effect. We call these types of bias as insufficient lag bias. Conclusions: Inference based upon a face value of a lag variable should be disregarded if population dynamics cannot be ruled out. A coefficient/sum of coefficients of interest should be interpreted as a lower bound of a true cumulative coefficient. In epidemiologic studies, prior knowledge is crucial in order to reach an unbiased estimate.