The Stochastics of Threshold Accepting: Analysis of an Application to the Uniform Design Problem

Threshold Accepting (TA) is a powerful optimization heuristic from the class of stochastic local search algorithms. It has been applied successfully to different optimization problems in statistics and econometrics, including the uniform design problem. Using the latter application as example, the stochastic properties of a TA implementation are analyzed. We provide a formal framework for the analysis of optimization heuristics like TA, which can be used to estimate lower bounds and to derive convergence results. It is also helpful for tuning real applications. Based on this framework, empirical results are presented for the uniform design problem. In particular, for two problem instances, the rate of convergence of the algorithm is estimated to be of the order of a power of -0.3 to -0.7 of the number of iterations. --Heuristic optimization,Threshold Accepting,Stochastic analysis of heuristics

Heuristic model selection for leading indicators in Russia and Germany

Business tendency survey indicators are widely recognized as a key instrument for business cycle forecasting. Their leading indicator property is assessed with regard to forecasting industrial production in Russia and Germany. For this purpose, vector autoregressive (VAR) models are specified and estimated to construct forecasts. As the potential number of lags included is large, we compare full–specified VAR models with subset models obtained using a Genetic Algorithm enabling ’holes’ in multivariate lag structures. The problem is complicated by the fact that a structural break and seasonal variation of indicators have to be taken into account. The models allow for a comparison of the dynamic adjustment and the forecasting performance of the leading indicators for both countries revealing marked differences between Russia and Germany.Leading indicators, business cycle forecasts, VAR, model selection, genetic algorithms

The convergence of optimization based estimators : theory and application to a GARCH-model

The convergence of estimators, e.g. maximum likelihood estimators, for increasing sample size is well understood in many cases. However, even when the rate of convergence of the estimator is known, practical application is hampered by the fact, that the estimator cannot always be obtained at tenable computational cost. This paper combines the analysis of convergence of the estimator itself with the analysis of the convergence of stochastic optimization algorithms, e.g. threshold accepting, to the theoretical estimator. We discuss the joint convergence of estimator and algorithm in a formal framework. An application to a GARCH-model demonstrates the approach in practice by estimating actual rates of convergence through a large scale simulation study. Despite of the additional stochastic component introduced by the use of an optimization heuristic, the overall quality of the estimates turns out to be superior compared to conventional approaches. --GARCH,Threshold Accepting,Optimization Heuristics,Convergence

The Economics of Crime: Investigating the Drugs-Crime Channel

The rising trends both in drug addiction and crime rates are of major public concern in Germany. Surprisingly, the economic theory of crime seems to ignore the drugs-crime nexus, whereas the criminological literature considers illicit drug use a main reason of criminal activities. This paper provides an econometric assessment of the drugs-crime channel within a Becker-Ehrlich model of crime supply. We analyse three different channels from drug abuse to crime: system-related, economic-related and pharmacological effects. Estimation with panel data from the German states allows us to take into account further factors that might influence both drug abuse and crime. The results indicate that drug offences have a significant impact, in particular on property crimes. We attribute this to a strong economic-related channel of drug abuse on crime.

Indirect Estimation of the Parameters of Agent Based Models of Financial Markets

Agent based models take into account limited rational behaviour of individuals acting on financial markets. Explicit simulation of this behaviour and the resulting interac-tion of individuals provide a description of aggregate financial market time series. Al-though the outcomes of such simulations often exhibit similarities with real financial market time series, methods for explicit validation are required. This paper proposes validation using simulation based indirect estimation. It uses typical characteristic moments of financial market data to assess the similarity of simulation outcomes. Fur-thermore, the parameters of the agent based models can be estimated by maximizing this similarity. The paper presents details of this estimation approach and first results for the US–$/DM exchange rate.Agent Based Models; Indirect Estimation; Validation

The Stochastics of Threshold Accepting: Analysis of an Application to the Uniform Design Problem

Threshold Accepting (TA) is a powerful optimization heuristic from the class of stochastic local search algorithms. It has been applied successfully to different optimization problems in statistics and econometrics, including the uniform design problem. Using the latter application as example, the stochastic properties of a TA implementation are analyzed. We provide a formal framework for the analysis of optimization heuristics like TA, which can be used to estimate lower bounds and to derive convergence results. It is also helpful for tuning real applications. Based on this framework, empirical results are presented for the uniform design problem. In particular, for two problem instances, the rate of convergence of the algorithm is estimated to be of the order of a power of -0.3 to -0.7 of the number of iterations

Some notes on the computational complexity of optimal aggregation

A combinatorical problem is said to be of high computational complexity, if it can be shown that every efficient algorithm needs a high amount of resources as measured in Computing time or storage capacity. This paper will (1) introduce some basic concepts of mathematical complexity theory; (2) show that the problem of Optimal Aggregation is of high computational complexity; and (3) outline a possible way to obtain results good enough for practical use despite of this high computational complexity

Credit rationing at the firm level: Some microeconometric evidence

Over the last decade credit rationing has been regarded increasingly as the outcome of asymmetric Information. Profit maximization of the banks might lead to interest rates lower than the market equilibrium rate. Administering loans at a higher interest rate to the rationed customers will decrease the expected return due to adverse selection and adverse incentive effects. This paper deals with the effects of age and business relations of firms on the degree of informational asymmetry between banks and firms. The resulting impact on the probability of rationing on the loan market is also studied. The main contribution of this paper is a direct test of the resulting hypotheses with data at the firm level. Both, the influence of the age of firms and a measure of informational asymmetry on the probability of be-ing rationed on the loan market is estimated. The estimation is based on microdata of the IFO Institute for economic research, Munich

Hedonic regression for digital cameras in Germany

Standard measures of consumer price inflation are based on a bundle of representative goods. It is well known that this approach might overstate inflation for new products and products with fast increasing quality. For this reason, hedonic adjustment methods have been proposed and introduced in official statistics for some products like personal computers. In this contribution, we consider the application of a hedonic regression to digital cameras, which have been introduced in the product bundle of the German consumer price index in 2003 – so far without hedonic quality adjustment. We present first results on hedonic price measurement for digital cameras in Germany for the time period 1999 to 2004. The results are based on data sampled from public interest journals and advertisements. --Hedonic regression,hedonic price index,quality adjustment