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Integration of the US cannabis market
Abstract
I examine the degree to which markets for cannabis are integrated using semiparametric models of spatial price linkages among US states. US attitudes toward the use of cannabis have evolved and, at the same time, laws restricting its use have been eliminated in many states. Cannabis presents the case of a unique commodity for which any interstate trade is explicitly illegal. A voluminous empirical literature has examined spatial arbitrage, trade, and market integration. Most of these studies utilize linear time series regression models. More recent work has considered increasingly more nonlinear models of market integration. I utilize fully nonlinear semiparametric generalized additive models to evaluate the spatial integration of US cannabis markets. The results confirm important nonlinearities in price relationships. Nonlinear price transmission elasticities are derived from the nonparametric modeling results. The results suggest that California cannabis markets are largely integrated with states across the nation. I find that California, which is a leading cannabis exporter, plays a price leadership role. Production of cannabis in California far exceeds the amount that can be legally grown and sold, and much of this cannabis is exported to other states. Colorado, a second primary cannabis market, generally operates in isolation from cannabis markets in other states. The likely mechanism integrating cannabis markets is the thriving trade in illegal cannabis, which has long preceded recent state‐level legislative actions that have legalized cannabis use.
The 2018 United States Farm Bill has opened the possibility for farmers to increase their profits through hemp cultivation. The literature suggests hemp has the potential to replace soybeans in soybean–wheat double-cropping because hemp shares key attributes of soybeans as a rotation crop (profitability, potential as an energy crop, and maintenance of soil fertility). Nonetheless, due to a short history of hemp cultivation in the USA, it is difficult to predict a time series relationship between hemp, soybean, and wheat through conventional approaches. In this article, we use Bayesian time series models and data from Statistics Canada and the Alberta Agricultural and Rural Development Department to examine a time series relationship between hemp, wheat, and soybean acreage and therefore predict farmers’ decision when hemp is a legal alternative agricultural commodity. Our results show evidence of complementary and substitution relationships for hemp–wheat and hemp–soybean, respectively. In addition, the results indicate a potential of hemp monoculture as a positive response to self-positive shock on hemp acreage that lasts for years.
Background
While cannabis is known to have immunomodulatory properties, the clinical consequences of its use on outcomes in COVID-19 have not been extensively evaluated. We aimed to assess whether cannabis users hospitalized for COVID-19 had improved outcomes compared to non-users.
Methods
We conducted a retrospective analysis of 1831 patients admitted to two medical centers in Southern California with a diagnosis of COVID-19. We evaluated outcomes including NIH COVID-19 Severity Score, need for supplemental oxygen, ICU (intensive care unit) admission, mechanical ventilation, length of hospitalization, and in-hospital death for cannabis users and non-users. Cannabis use was reported in the patient’s social history. Propensity matching was used to account for differences in age, body-mass index, sex, race, tobacco smoking history, and comorbidities known to be risk factors for COVID-19 mortality between cannabis users and non-users.
Results
Of 1831 patients admitted with COVID-19, 69 patients reported active cannabis use (4% of the cohort). Active users were younger (44 years vs. 62 years, p < 0.001), less often diabetic (23.2% vs 37.2%, p < 0.021), and more frequently active tobacco smokers (20.3% vs. 4.1%, p < 0.001) compared to non-users. Notably, active users had lower levels of inflammatory markers upon admission than non-users—CRP (C-reactive protein) (3.7 mg/L vs 7.6 mg/L, p < 0.001), ferritin (282 μg/L vs 622 μg/L, p < 0.001), D-dimer (468 ng/mL vs 1140 ng/mL, p = 0.017), and procalcitonin (0.10 ng/mL vs 0.15 ng/mL, p = 0.001). Based on univariate analysis, cannabis users had significantly better outcomes compared to non-users as reflected in lower NIH scores (5.1 vs 6.0, p < 0.001), shorter hospitalization (4 days vs 6 days, p < 0.001), lower ICU admission rates (12% vs 31%, p < 0.001), and less need for mechanical ventilation (6% vs 17%, p = 0.027). Using propensity matching, differences in overall survival were not statistically significant between cannabis users and non-users, nevertheless ICU admission was 12 percentage points lower ( p = 0.018) and intubation rates were 6 percentage points lower ( p = 0.017) in cannabis users.
Conclusions
This retrospective cohort study suggests that active cannabis users hospitalized with COVID-19 had better clinical outcomes compared with non-users, including decreased need for ICU admission or mechanical ventilation. However, our results need to be interpreted with caution given the limitations of a retrospective analysis. Prospective and observational studies will better elucidate the effects cannabis use in COVID-19 patients.
Objectives
To investigate the impact of cannabis use on the infection and survival outcomes of COVID-19.
Study Design
Cross-sectional study based on the UK Biobank (UKB) dataset.
Methods
We identified 13,099 individuals with cannabis smoking history in the UKB COVID-19 Serology Study. The Charlson-Quan Comorbidity Index was estimated using inpatient ICD-10 records. Multivariable logistic regression characterized features associated with COVID-19 infection. Cox models determined the hazard ratios (HR) for COVID-19-related survival.
Results
Cannabis users were more likely to getting COVID-19 (odds ratio: 1.22, P = 0.001) but multivariable analysis showed that cannabis use was a protective factor of COVID-19 infection (adjusted odds ratio: 0.81, P = 0.001). Regular cannabis users, who smoked more than once per month, had a significantly poorer COVID-19-related survival, after adjusting for known risk factors including age, gender, smoking history, and comorbidity (adjusted hazard ratio: 2.81, P = 0.041).
Conclusions
The frequency of cannabis use could be considered as a candidate predictor for mortality risk of COVID-19.
Traditional sources of retail price information, such as scanner data and government price surveys, are not available for cannabis. To help fill this gap, between October 2016 and July 2018 the UC Agricultural Issues Center collected online retail price ranges for dried cannabis flower and cannabis-oil cartridges at retailers around California. During this 21-month time period, the legal landscape of the California cannabis market underwent three broad regulatory changes: adult-use decriminalization, licensing and regulation and mandatory testing. This article provides unique primary data on legal cannabis prices in California before and after each of these three changes. Our data are imperfect but do provide a glimpse of the patterns of California cannabis prices at different times. For dried cannabis flower, we observe relatively stable retail prices over the 21-month period at both the top and bottom ends of the price range. For cannabis-oil cartridges, we observe relatively stable prices at the bottom end but increasing prices at the top end between November 2017 and July 2018.
On agricultural frontiers, minimal regulation and potential windfall profits drive opportunistic land use that often results in environmental damage. Cannabis, an increasingly decriminalized agricultural commodity in many places throughout the world, may now be creating new agricultural frontiers. We examined how cannabis frontiers have boomed in northern California, one of the United States' leading production areas. From 2012-2016 cannabis farms increased in number by 58%, cannabis plants increased by 183%, and the total area under cultivation increased by 91%. Growth in number of sites (80%), as well as in site size (56% per site) contributed to the observed expansion. Cannabis expansion took place in areas of high environmental sensitivity, including 80%-116% increases in cultivation sites near high-quality habitat for threatened and endangered salmonid fish species. Production increased by 40% on steep slopes, sites more than doubled near public lands, and increased by 44% in remote locations far from paved roads. Cannabis farm abandonment was modest, and driven primarily by farm size, not location within sensitive environments. To address policy and institutions for environmental protection, we examined state budget allocations for cannabis regulatory programs. These increased six-fold between 2012-2016 but remained very low relative to other regulatory programs. Production may expand on frontiers elsewhere in the world, and our results warn that without careful policy and institutional development these frontiers may pose environmental threats, even in locations with otherwise robust environmental laws and regulatory institutions.
Marijuana is the most common illicit drug with vocal advocates for legalization. Among other things, legalization would increase access and remove the stigma of illegality. Our model disentangles the role of access from preferences and shows that selection into access is not random. We find that traditional demand estimates are biased resulting in incorrect policy conclusions. If marijuana were legalized, those under 30 would see modest increases in use of 28 percent, while on average use would increase by 48 percent (to 19.4 percent). Tax policies are effective at curbing use, where Australia could raise AU12 billion).
International economics has overwhelmingly relied on Samuelson's (1954) assumption that trade costs are proportional to value. We develop a quantitative analytical framework that features both additive and multiplicative (iceberg) trade costs, building on a model of international trade with heterogeneous firms and demand heterogeneity. We structurally estimate the magnitude of additive trade costs, for every product and destination available in our firm-level data of Norwegian exporters. Identification is aided by the theoretical finding that the elasticity of demand to producer price is dampened, in absolute value, when prices are low, and this mechanism is magnified when additive trade costs are high. This magnification mechanism becomes useful inthe subsequent econometric analysis. Estimated additive trade costs are substantial. On average, additive costs are 33 percent, expressed relative to the median price. This leads us to reject the pure iceberg cost assumption. We assess the importance of these costs in shaping global trade flows. Our micro estimates of additive trade costs explain most of the geographical variation in aggregate trade. An implication of our work is that inferring trade costs from standard gravity models suffers from specification bias, since these models assume away the role of additive trade costs.
This paper considers the costs of reducing consumption of a good by making its production illegal and punishing apprehended illegal producers. We use illegal drugs as a prominent example. We show that the more inelastic either demand for or supply of a good is, the greater the increase in social cost from further reducing its production by greater enforcement efforts. So optimal public expenditures on apprehension and conviction of illegal suppliers depend not only on the difference between the social and private values from consumption but also on these elasticities. When demand and supply are not too elastic, it does not pay to enforce any prohibition unless the social value is negative. We also show that a monetary tax could cause a greater reduction in output and increase in price than optimal enforcement against the same good would if it were illegal, even though some producers may go underground to avoid a monetary tax. When enforcement is costly, excise taxes and quantity restrictions are not equivalent.
This paper proposes a new testing procedure to detect the presence of a cointegrating relationship that follows a globally stationary smooth transition process. In the context of nonlinear smooth transition error correction models (ECMs) we provide two simple operational versions of the tests. First, we obtain the associated nonlinear ECM-based tests. Second, we derive the nonlinear analogue of the residual-based test for cointegration in linear models. We derive the asymptotic distributions of the proposed tests. Monte Carlo simulation exercises confirm that our proposed tests have much better power than the linear counterparts against the alternative of a globally stationary nonlinear cointegrating process. In an application to the price-dividend relationship, our test is able to find cointegration, whereas the linear-based tests fail to do so.We are grateful to an associate editor, two anonymous referees, Richard Baillie, In Choi, Atanas Christev, Hira Koul, Richard Harris, Cheng Hsiao, Changjin Kim, Joon Park, Peter Schmidt, Yoonjae Whang, Jeff Wooldridge, and seminar participants at University of Edinburgh, Heriot-Watt University, Korea University, University of Leeds, Michigan State University, University of Newcastle, and Sungkunkwan University for their helpful comments. Partial financial support from the ESRC (grant R000223399) is gratefully acknowledged. The usual disclaimer applies.
Existing point estimates of half-life deviations from purchasing power parity (PPP), around 3-5 years, suggest that the speed of convergence is extremely slow. This article assesses the degree of uncertainty around these point estimates by using local-to-unity asymptotic theory to construct confidence intervals that are robust to high persistence in small samples. The empirical evidence suggests that the lower bound of the confidence interval is between four and eight quarters for most currencies, which is not inconsistent with traditional price-stickiness explanations. However, the upper bounds are infinity for all currencies, so we cannot provide conclusive evidence in favor of PPP either.
We define new procedures for estimating generalized additive nonparametric regression models that are more efficient than the O.B. Linton and W. Härdle [Biometrika 83, No. 3, 529-540 (1996; Zbl 0866.62017)] integration-based method and achieve certain oracle bounds. We consider criterion functions based on the linear exponential family, which includes many important special cases. We also consider the extension to multiple parameter models like the gamma distribution and to models for conditional heteroskedasticity.
The spread of SARS-CoV-2 and ongoing COVID-19 pandemic underscores the need for new treatments. Here we report that cannabidiol (CBD) inhibits infection of SARS-CoV-2 in cells and mice. CBD and its metabolite 7-OH-CBD, but not THC or other congeneric cannabinoids tested, potently block SARS-CoV-2 replication in lung epithelial cells. CBD acts after viral entry, inhibiting viral gene expression and reversing many effects of SARS-CoV-2 on host gene transcription. CBD inhibits SARS-CoV-2 replication in part by up-regulating the host IRE1α RNase endoplasmic reticulum (ER) stress response and interferon signaling pathways. In matched groups of human patients from the National COVID Cohort Collaborative, CBD (100 mg/ml oral solution per medical records) had a significant negative association with positive SARS-CoV-2 tests. This study highlights CBD as a potential preventative agent for early-stage SARS-CoV-2 infection and merits future clinical trials. We caution against use of non-medical formulations including edibles, inhalants or topicals as a preventative or treatment therapy at the present time.
We review recent developments in the analysis of price transmission in agricultural markets. Markets may be separated in time, form, and space (as well as in combinations of such factors). Transactions and storage costs as well as production and marketing factors delineate these markets. We show that much of the research on spatial market linkages has reflected methodological advances that have led to increasingly nonlinear time-series models. Advances in the theoretical and empirical literature over the last few decades have demonstrated that price relationships in the food chain are highly context specific. Improvements in marketing, information, and transportation technology have strengthened the links between prices in the food system, but at the same time links in the food chain are increasingly subject to vertical coordination and, thus, less visible to outside observers, including researchers.
Expected final online publication date for the Annual Review of Resource Economics, Volume 13 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
Cannabis legalization is spreading rapidly. In California, as the plant transitions from an illegal drug to agricultural product, regulations have been implemented to manage its production and associated environmental impacts. Yet, at the early stages of this process, many of the state's cannabis farmers continue to operate illicitly. This study examines why some cannabis farmers are engaging in the state's licensing initiative while others are not. Through an anonymous survey of cannabis farmers in California, we analyzed socio-normative and cost-related factors influencing farmers' decisions to participate in legal markets, or not. Approximately one third of the 362 cannabis farmers who completed the survey reported that they had never applied for a license. These non-compliant farmers were likely to be smaller cultivators who grew cannabis as part of a diversified livelihood strategy. Farmers' non-compliance was primarily attributed to an inability to overcome barriers to participation. These included not only financial barriers but also administrative and psychological ones, all of which disproportionately affect farmers with fewer resources. Socio-normative factors, including pressure from neighbors and perspectives on the benefits of environmental regulations, were not found to motivate non-compliance. As a result, policy efforts to mitigate the administrative burdens of compliance, such as streamlining permitting processes, extending agricultural support services, and supporting farmer collectives, warrant further attention to enhance compliance, public safety, environmental outcomes, and rural development in cannabis cultivating communities. Reforms to promote compliance, particularly among smaller farmers, may prevent the kinds of industrial consolidation seen in agricultural and in other governmental efforts to regulate informal resource use and trade.
An extensive line of research has examined linkages among spatially‐distinct markets. We apply semi‐parametric, generalized additive vector autoregressive models to a consideration of basis linkages among North Carolina corn and soybean markets. An extensive suite of linearity tests suggests that basis and price relationships are nonlinear. Marginal effects, transmission elasticities, and generalized impulse responses are utilized to describe patterns of adjustment among markets. The semi‐parametric models are compared to standard threshold vector autoregressive models and are found to reveal more statistical significance and substantially more nonlinearity in basis adjustments. Marginal effects are nonlinear and impulse responses suggest greater adjustments to extreme shocks and asymmetric adjustment patterns. The results provide evidence in favor of efficiently linked markets.
Cannabis agriculture is a multi-billion dollar industry, yet the factors driving the spatial location of cannabis production are not well understood. That knowledge gap is troubling, as there is evidence that outdoor production takes place in ecologically sensitive areas. Policy aimed at mitigating the impacts of current and future cultivation should be based on an understanding of what drives cultivation siting. Using parcel level data and a Heckman sample selection model, we estimate where cannabis cultivation is likely to take place and the number of plants in each site using biophysical, historical, and network variables. We use this model to estimate drivers of greenhouse and outdoor cultivation siting. We find strong implied network effects – parcels are far more likely to have cultivation sites if there are cannabis plants nearby. However, the proximity of other cannabis sites does not impact the size of a parcel's own cultivation. Similarly, a history of timber harvest increases the likelihood of outdoor cultivation, but is linked to cultivation sites with fewer plants. Biophysical properties such as slope, aspect, and distance to water did not statistically impact the likelihood of a parcel to be cultivated. Our results are a first step toward understanding the emergence of an agricultural activity likely to grow in other locales in the future.
Using high-quality data collected in France in 2005 from more than 250 regular cannabis users, we estimate both quantity discount and price elasticity of cannabis net of the effect of perceived quality and real potency. We find evidence of substantial price discount and obtain a short-term price consumption elasticity ranging from −1.7 to −2.1, meaning that the demand for cannabis is elastic. Controlling for potency, either real or perceived, has little effect on the magnitude of the discount effect – even if customers are ready to pay more when their perception of the product quality is high – and no impact on price elasticity.
This article proposes an extension to the Engle-Granger testing strategy by permitting asymmetry in the adjustment toward equilibrium in two different ways. We demonstrate that our test has goad power and size properties over the Engle-Granger test when there are asymmetric departures from equilibrium. We consider an application-namely, whether there exists cointegration among interest rates for instruments with different maturities. This issue has been widely tested with mixed results. We argue that either cautious policy, or possibly opportunistic behavior on the part of the Federal Reserve implies that an equilibrium relationship between short- and long-term interest rates exists but that adjustments from disequilibrium are asymmetric in nature. Empirical tests using U.S. yields confirm the asymmetric nature of error correction among interest rates of different maturities.
The threshold vector error correction model is a popular tool for the analysis of spatial price transmission. In the literature,
the profile likelihood estimator is the preferred choice for estimating this model. Yet, in many settings this estimator performs
poorly. In particular, if the true thresholds are such that one or more regimes contain only a small number of observations,
if unknown model parameters are numerous, or if parameters differ little between regimes, the profile likelihood estimator
displays large bias and variance. Such settings are likely when studying price transmission. We analyze the weaknesses of
the profile likelihood approach and propose an alternative regularized Bayesian estimator, which was developed for simpler
but related threshold models. Simulation results show that the regularized Bayesian estimator outperforms profile likelihood
in the estimation of threshold vector error correction models. Two empirical applications demonstrate the relevance of this
new estimator for spatial price transmission analysis.
The most general form of a nonlinear strictly stationary process is that referred to as a Volterra expansion; this is to a
linear process what a polynomial is to a linear function. Because of this similarity, an analogue of Tukey's one degree of
freedom for non-additivity test is constructed as a test for linearity versus a second-order Volterra expansion.
Recent debates regarding liberalization of marijuana policies often rest on assumptions regarding the extent to which such policy changes would lead to a change in marijuana consumption and by whom. This paper reviews the economics literature assessing the responsiveness of consumption to changes in price and enforcement risk and explicitly considers how this responsiveness varies by different user groups. In doing so, it demonstrates how most of the research has examined responsiveness to prevalence of use, which is a composite of different user groups, rather than level of consumption among regular or heavy users, which represent the largest share of total quantities consumed. Thus, it is not possible to generate reliable estimates of the impact of liberalizing policies on either tax revenues or harms, as these outcomes are most directly influenced by the amounts consumed by regular or heavy users, not prevalence rates.
The threshold autoregressive model is one of the nonlinear time series models available in the literature. It was first proposed by Tong (1978) and discussed in detail by Tong and Lim (1980) and Tong (1983). The major features of this class of models are limit cycles, amplitude dependent frequencies, and jump phenomena. Much of the original motivation of the model is concerned with limit cycles of a cyclical time series, and indeed the model is capable of producing asymmetric limit cycles. The threshold autoregressive model, however, has not received much attention in application. This is due to (a) the lack of a suitable modeling procedure and (b) the inability to identify the threshold variable and estimate the threshold values. The primary goal of this article, therefore, is to suggest a simple yet widely applicable model-building procedure for threshold autoregressive models. Based on some predictive residuals, a simple statistic is proposed to test for threshold nonlinearity and specify the threshold variable. Some supplementary graphic devices are then used to identify the number and locations of the potential thresholds. Finally, these statistics are used to build a threshold model. The test statistic and its properties are derived by simple linear regression. Its performance in the finite-sample case is evaluated by simulation and real-world data analysis. The statistic performs well as compared with an alternative test available in the literature. Further applications of threshold autoregressive models are also suggested, including handling heterogeneous time series and modeling random processes with periodic variances whose periodicity is not fixed. The latter phenomenon is commonly encountered in practice, especially in econometrics and biological sciences.
Conventional tests for food market integration ask, often misleadingly, whether prices in different locations move together.
In this paper an alternative methodology, the parity bounds model (PBM), is developed which uses information on transfer costs
in addition to food prices to assess the efficiency of spatial arbitrage. Monte Carlo experiments using data generated by
a point-space spatial price equilibrium model show the PBM to be statistically reliable. An application to Philippine rice
markets demonstrates that the PBM detects efficient arbitrage when other tests do not.
Price dynamics for North American oriented strand board markets are examined. The role of transactions costs are explored vis-à-vis the law of one price. Nonlinearities induced by unobservable transactions costs are modeled by estimating time-varying smooth transition autoregressions (TV-STARs). Results indicate that nonlinearity and structural change are important features of these markets; price parity relationships implied by economic theory are generally supported by the estimated models. Implications for the efficiency of spatial market linkages and the dynamics associated with price adjustments are also examined. Copyright 2011, Oxford University Press.
This paper rigorously establishes that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available. In this sense, multilayer feedforward networks are a class of universal approximators.
Let be a pair of random variables such that and let f by a function that depends on the joint distribution of A variety of parametric and nonparametric models for f are discussed in relation to flexibility, dimensionality, and interpretability. It is then supposed that each that Y is real valued with mean and finite variance, and that f is the regression function of Y on X. Let of the form be chosen subject to the constraints for to minimize Then is the closest additive approximation to f, and if f itself is additive. Spline estimates of and its derivatives are considered based on a random sample from the distribution of Under a common smoothness assumption on and some mild auxiliary assumptions, these estimates achieve the same (optimal) rate of convergence for general J as they do for
This paper develops and applies a methodology to test for efficiency of interregional commodity arbitrage. Application of
the methodology requires only time-series data on prices for alternative cities, regions, countries, or product forms. Yet,
the approach is capable of generating evidence on a number of market parameters including market integration, arbitrage efficiency,
the magnitude of marketing margins, product substitutability, and competitiveness of markets. Estimation is based on a switching
regression model with three regimes: efficient arbitrage, relative shortage, and relative glut. Results from application of
the model to U.S. celery marketing indicated significant departures from efficient arbitrage for both California and Florida
celery.
I discuss the production of low rank smoothers for "d" ≥ 1 dimensional data, which can be fitted by regression or penalized regression methods. The smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thin plate spline smoothing problem and are optimal in the sense that the truncation is designed to result in the minimum possible perturbation of the thin plate spline smoothing problem given the dimension of the basis used to construct the smoother. By making use of Lanczos iteration the basis change and truncation are computationally efficient. The smoothers allow the use of approximate thin plate spline models with large data sets, avoid the problems that are associated with 'knot placement' that usually complicate modelling with regression splines or penalized regression splines, provide a sensible way of modelling interaction terms in generalized additive models, provide low rank approximations to generalized smoothing spline models, appropriate for use with large data sets, provide a means for incorporating smooth functions of more than one variable into non-linear models and improve the computational efficiency of penalized likelihood models incorporating thin plate splines. Given that the approach produces spline-like models with a sparse basis, it also provides a natural way of incorporating unpenalized spline-like terms in linear and generalized linear models, and these can be treated just like any other model terms from the point of view of model selection, inference and diagnostics. Copyright 2003 Royal Statistical Society.
A large body of research has evaluated price linkages in spatially separate markets. Much recent research has applied models
appropriate for nonstationary data. Such analyses have been criticized for their ignorance of transactions costs, which may
inhibit price adjustments and thus affect tests of integration. This analysis utilizes threshold autoregression and cointegration
models to account for a neutral band representing transactions costs. We evaluate daily price linkages among four corn and
four soybean markets in North Carolina. Nonlinear impulse response functions are used to investigate dynamic patterns of adjustments
to shocks. Our results confirm the presence of thresholds and indicate strong support for market integration, though adjustments
following shocks may take many days to be complete. In every case, the threshold models suggest much faster adjustments in
response to deviations from equilibrium than is the case when threshold behavior is ignored.
The relationship between cointegration and error correction models, first suggested by Granger, is here extended and used to develop estimation procedures, tests, and empirical examples. A vector of time series is said to be cointegrated with cointegrating vector a if each element is stationary only after differencing while linear combinations a8xt are themselves stationary. A representation theorem connects the moving average , autoregressive, and error correction representations for cointegrated systems. A simple but asymptotically efficient two-step estimator is proposed and applied. Tests for cointegration are suggested and examined by Monte Carlo simulation. A series of examples are presented. Copyright 1987 by The Econometric Society.
This paper proposes a residual-based test of the null of cointegration using a structural single equation model. It is shown that the limiting distribution of the test statistic for cointegration can be made free of nuisance parameters when the cointegrating relation is efficiently estimated. The limiting distributions are given in terms of a mixture of a Brownian bridge and vector Brownian motion. It is also shown that this test is consistent. Critical values are given for standard, demeaned, and detrended cases. Combining results from our test for cointegration with results from the Phillips-Ouliaris test for no cointegration, we find that there is evidence of cointegration between real consumption and real disposable income over the postwar period.
We propose that analysis of purchasing power parity (PPP) and the law of one price (LOOP) should explicitly take into account the possibility of commodity points' thresholds delineating a region of no central tendency among relative prices, possibly due to lack of perfect arbitrage in the presence of transaction costs and uncertainty. More than eighty years ago, Heckscher stressed the importance of such incomplete arbitrage in the empirical application of PPP. We devise an econometric method to identify commodity points. Price adjustment is treated as a nonlinear process, and a threshold autoregression (TAR) offers a parsimonious specification within which both thresholds and adjustment speeds are estimated by maximum likelihood methods. Our model performs well using post-1980 data reasonable: adjustment outside the thresholds might imply half-lives of price deviations measured in months rather than years and the thresholds correspond to popular rough estimates as to the order of magnitude of actual transport costs. The estimated commodity points appear to be positively related to objective measures of market segmentation, notably nominal exchange rate volatility.
. Recently, a new linearity test for time series was introduced based on concepts from the theory of neural networks. Lee et al. have already studied the power properties of this test and they are further investigated here. They are compared by simulation with those of a Lagrange multiplier (LM) type test that we derive from the same single-hidden-layer neural network model. The auxiliary regression of our LM type test is a simple cubic ‘dual’ of the Volterra expansion of the original series, and the power of the test appears superior overall to that of the other test.
This article considers the application of two families of nonlinear autoregressive models, the logistic (LSTAR) and exponential (ESTAR) autoregressive models. This includes the specification of the model based on simple statistical tests: linearity testing against smooth transition autoregression, determining the delay parameter and choosing between LSTAR and ESTAR models are discussed. Estimation by nonlinear least squares is considered as well as evaluating the properties of the estimated model. The proposed techniques are illustrated by examples using both simulated and real time series.
The author presents a statistical test of the hypothesis that a given multilayer feedforward network exactly represents some unknown mapping subject to inherent noise against the alternative that the network neglects some nonlinear structure in the mapping, leading to potentially avoidable approximation errors. The tests are based on methods that statistically determine whether or not there is some advantage to be gained by adding hidden units to the network.< >
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