Existence of Singularity Bifurcation in an Euler-Equations Model of the United States Economy: Grandmont was Right

Abstract: Grandmont (1985) found that the parameter space of the most classical dynamic general-equilibrium macroeconomic models are stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with all forms of multiperiodic dynamics between. But Grandmont provided his result with a model in which all policies are Ricardian equivalent, no frictions exist, employment is always full, competition is perfect, and all solutions are Pareto optimal. Hence he was not able to reach conclusions about the policy relevance of his dramatic discovery. As a result, Barnett and He (1999, 2001, 2002) investigated a Keynesian structural model, and found results supporting Grandmont’s conclusions within the parameter space of the Bergstrom-Wymer continuous-time dynamic macroeconometric model of the UK economy. That prototypical Keynesian model was produced from a system of second order differential equations. The model contains frictions through adjustment lags, displays reasonable dynamics fitting the UK economy’s data, and is clearly policy relevant. In addition, results by Barnett and Duzhak (2008,2009) demonstrate the existence of Hopf and flip (period doubling) bifurcation within the parameter space of recent New Keynesian models. Lucas-critique criticism of Keynesian structural models has motivated development of Euler equations models having policy-invariant deep parameters, which are invariant to policy rule changes. Hence, we continue the investigation of policy-relevant bifurcation by searching the parameter space of the best known of the Euler equations general-equilibrium macroeconometric models: the path-breaking Leeper and Sims (1994) model. We find the existence of singularity bifurcation boundaries within the parameter space. Although never before found in an economic model, singularity bifurcation may be a common property of Euler equations models, which often do not have closed form solutions. Our results further confirm Grandmont’s views. Beginning with Grandmont’s findings with a classical model, we continue to follow the path from the Bergstrom-Wymer policy-relevant Keynesian model, to New Keynesian models, and now to Euler equations macroeconomic models having deep parameters.Bifurcation; inference; dynamic general equilibrium; Pareto optimality; Hopf bifurcation; Euler equations; Leeper and Sims model; singularity bifurcation; stability

Developing a Practical Forecasting Screener for Domestic Violence Incidents

In this paper, we report on the development of a short screening tool that deputies in the Los Angeles Sheriff\u27s Department could use in the field to help forecast domestic violence incidents in particular households. The data come from over 500 households to which sheriff\u27s deputies were dispatched in the fall of 2003. Information on potential predictors was collected at the scene. Outcomes were measured during a three month follow-up. The data were analyzed with modern data mining procedures in which true forecasts were evaluated. A screening instrument was then developed based on a small fraction of the information collected. Making the screening instrument more complicated did not improve forecasting skill. Taking the relative costs of false positives and false negatives into account, the instrument correctly forecasted future calls for service about 60% of the time. Future calls involving domestic violence misdemeanors and felonies were correctly forecast about 50% of the time. The 50% figure is especially important because such calls require a law enforcement response and yet are a relatively small fraction of all domestic violence calls for service. A number of broader policy implications follow. It is feasible to construct a quick-response, domestic violence screener that is practical to deploy and that can forecast with useful skill. More informed decisions by police officers in the field can follow. Although the same kinds of predictors are likely to be effective in a wide variety of jurisdictions, the particular indicators selected will vary in response to local demographics and the local costs of forecasting errors. It is also feasible to evaluate such quick-response threat assessment tools for their forecasting accuracy. But, the costs of forecasting errors must be taken into account. Also, when the data used to build the forecasting instrument are also used to evaluate its accuracy, inflated estimates of forecasting skill are likely

Measurement of Ad Libitum Food Intake, Physical Activity, and Sedentary Time in Response to Overfeeding

Given the wide availability of highly palatable foods, overeating is common. Energy intake and metabolic responses to overfeeding may provide insights into weight gain prevention. We hypothesized a down-regulation in subsequent food intake and sedentary time, and up-regulation in non-exercise activity and core temperature in response to overfeeding in order to maintain body weight constant. In a monitored inpatient clinical research unit using a cross over study design, we investigated ad libitum energy intake (EI, using automated vending machines), core body temperature, and physical activity (using accelerometry) following a short term (3-day) weight maintaining (WM) vs overfeeding (OF) diet in healthy volunteers (n = 21, BMI, mean ± SD, 33.2±8.6 kg/m2, 73.6% male). During the ad libitum periods following the WM vs. OF diets, there was no significant difference in mean 3-d EI (4061±1084 vs. 3926±1284 kcal/day, p = 0.41), and there were also no differences either in core body temperature (37.0±0.2°C vs. 37.1±0.2°C, p = 0.75) or sedentary time (70.9±12.9 vs. 72.0±7.4%, p = 0.88). However, during OF (but not WM), sedentary time was positively associated with weight gain (r = 0.49, p = 0.05, adjusted for age, sex, and initial weight). In conclusion, short term overfeeding did not result in a decrease in subsequent ad libitum food intake or overall change in sedentary time although in secondary analysis sedentary time was associated with weight gain during OF. Beyond possible changes in sedentary time, there is minimal attempt to restore energy balance during or following short term overfeeding

Existence of Singularity Bifurcation in an Euler-Equations Model of the United States Economy: Grandmont was Right

Abstract: Grandmont (1985) found that the parameter space of the most classical dynamic general-equilibrium macroeconomic models are stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with all forms of multiperiodic dynamics between. But Grandmont provided his result with a model in which all policies are Ricardian equivalent, no frictions exist, employment is always full, competition is perfect, and all solutions are Pareto optimal. Hence he was not able to reach conclusions about the policy relevance of his dramatic discovery. As a result, Barnett and He (1999, 2001, 2002) investigated a Keynesian structural model, and found results supporting Grandmont’s conclusions within the parameter space of the Bergstrom-Wymer continuous-time dynamic macroeconometric model of the UK economy. That prototypical Keynesian model was produced from a system of second order differential equations. The model contains frictions through adjustment lags, displays reasonable dynamics fitting the UK economy’s data, and is clearly policy relevant. In addition, results by Barnett and Duzhak (2008,2009) demonstrate the existence of Hopf and flip (period doubling) bifurcation within the parameter space of recent New Keynesian models. Lucas-critique criticism of Keynesian structural models has motivated development of Euler equations models having policy-invariant deep parameters, which are invariant to policy rule changes. Hence, we continue the investigation of policy-relevant bifurcation by searching the parameter space of the best known of the Euler equations general-equilibrium macroeconometric models: the path-breaking Leeper and Sims (1994) model. We find the existence of singularity bifurcation boundaries within the parameter space. Although never before found in an economic model, singularity bifurcation may be a common property of Euler equations models, which often do not have closed form solutions. Our results further confirm Grandmont’s views. Beginning with Grandmont’s findings with a classical model, we continue to follow the path from the Bergstrom-Wymer policy-relevant Keynesian model, to New Keynesian models, and now to Euler equations macroeconomic models having deep parameters

Existence of Singularity Bifurcation in an Euler-Equations Model of the United States Economy: Grandmont was Right

Abstract: Grandmont (1985) found that the parameter space of the most classical dynamic general-equilibrium macroeconomic models are stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with all forms of multiperiodic dynamics between. But Grandmont provided his result with a model in which all policies are Ricardian equivalent, no frictions exist, employment is always full, competition is perfect, and all solutions are Pareto optimal. Hence he was not able to reach conclusions about the policy relevance of his dramatic discovery. As a result, Barnett and He (1999, 2001, 2002) investigated a Keynesian structural model, and found results supporting Grandmont’s conclusions within the parameter space of the Bergstrom-Wymer continuous-time dynamic macroeconometric model of the UK economy. That prototypical Keynesian model was produced from a system of second order differential equations. The model contains frictions through adjustment lags, displays reasonable dynamics fitting the UK economy’s data, and is clearly policy relevant. In addition, results by Barnett and Duzhak (2008,2009) demonstrate the existence of Hopf and flip (period doubling) bifurcation within the parameter space of recent New Keynesian models. Lucas-critique criticism of Keynesian structural models has motivated development of Euler equations models having policy-invariant deep parameters, which are invariant to policy rule changes. Hence, we continue the investigation of policy-relevant bifurcation by searching the parameter space of the best known of the Euler equations general-equilibrium macroeconometric models: the path-breaking Leeper and Sims (1994) model. We find the existence of singularity bifurcation boundaries within the parameter space. Although never before found in an economic model, singularity bifurcation may be a common property of Euler equations models, which often do not have closed form solutions. Our results further confirm Grandmont’s views. Beginning with Grandmont’s findings with a classical model, we continue to follow the path from the Bergstrom-Wymer policy-relevant Keynesian model, to New Keynesian models, and now to Euler equations macroeconomic models having deep parameters

Effective population sizes of eastern oyster Crassostrea virginica (Gmelin) populations in Delaware Bay, USA

Effective population size (Ne) is an important concept in population genetics as it dictates the rate of genetic change caused by drift. Ne estimates for many marine populations are small relative to the census population size. Small Ne in a large population may indicate high reproductive variance or sweepstakes reproductive success (SRS). The eastern oyster (Crassostrea virginica) may be prone to SRS due to its high fecundity and high larval mortality. To examine if SRS occurs in the eastern oyster, we studied Ne and genetic variation of oyster populations in Delaware Bay. Adult and spat oysters were collected from five locations in different years and genotyped with seven microsatellite markers. Slight genetic differences were revealed by Fst statistics between the adult populations and spat recruits, while the adult populations are spatially homogeneous and temporally stable. Comparisons of genetic diversity and relatedness among adult and spat samples failed to provide convincing evidence for strong SRS. Ne estimates obtained with five different methods were variable, small and often without upper confidence limits. For single sample collections, Ne estimates for spat (140–440) were consistently smaller than that for adults (589–2,779). Analysis of pooled adult samples across all sites suggests that Ne for the whole bay may be very large, as indicated by the large point estimates and the lack of upper confidence limits. These results suggest that Ne may be small for a given spat fall, but the entire adult population may have large Ne and is temporally stable as it is the accumulation of many spat falls per year over many year