Stochastic frontier analysis by means of maximum likelihood and the method of moments

The stochastic frontier analysis (Aigner et al., 1977, Meeusen and van de Broeck, 1977) is widely used to estimate individual efficiency scores. The basic idea lies in the introduction of an additive error term consisting of a noise and an inefficiency term. Most often the assumption of a half-normal distributed inefficiency term is applied, but other distributions are also discussed in relevant literature. The natural estimation method seems to be Maximum Likelihood (ML) estimation because of the parametric assumptions. But simulation results obtained for the half normal model indicate that a method of moments approach (MOM) (Olson et al., 1980) is superior for small and medium sized samples in combination with inefficiency not strongly dominating noise (Coelli, 1995). In this paper we provide detailed simulation results comparing the two estimation approaches for both the half-normal and the exponential approach to inefficiency. Based on the simulation results we obtain decision rules for the choice of the superior estimation approach. Both estimation methods, ML and MOM, are applied to a sample of German commercial banks based on the Bankscope database for estimation of cost efficiency scores. --stochastic frontier,Maximum Likelihood,Method of moments,Bank efficiency

Downward wage rigidity in Europe: A new flexible parametric approach and empirical results

We suggest a new parametric approach to estimate the extent of downward nominal wage rigidity in ten European countries between 1994 and 2001. The data base used throughout is the User Data Base (UDB) of the European Community Household Panel (ECHP). The proposed approach is based on the very flexible generalized hyperbolic distribution which allows to model wage change distributions characterized by thick tales, skewness and leptokurtosis. Significant downward nominal wage rigidity is found in all countries under analysis, but the extent varies considerably across countries. Yearly estimates reveal increasing rigidity in Italy, Greece and Portugal, while rigidity is declining in Denmark and Belgium. The results imply that the costs of price stability differ substantially across Europe. --

The success of bank mergers revisited: an assessment based on a matching strategy

The question of whether or not mergers and acquisitions have helped to enhance banks' efficiency and profitability has not yet been conclusively resolved in the literature. We argue that this is partly due to the severe methodological problems involved. In this study, we analyze the effect of German bank mergers in the period 1995-2000 on banks' profitability and cost efficiency. We suggest a new matching strategy to control for the selection effects arising from the fact that predominantly under-performing banks engage in mergers. Our results indicate a neutral effect of mergers on profitability and a positive effect on cost efficiency. Comparing our results with those obtained from a naive performance comparison of merging and non-merging banks indicates a severe negative selection bias with regard to the former. --Bank mergers,performance measurement,propensity score matching

Analysing wage differences between the USA and Germany using proportional hazards models

We analyse differences between the wage distributions in the USA and Germany in 2001 both for women and men. The empirical analysis is based on the decomposition of differences using Cox's marginal (partial) likelihood. The approach based on rank invariant estimators such as Cox's is borrowed from the literature on failure time data. Donald et al. (2000) pioneered this approach. However, they did not use the full power of the semi-parametric approach. Instead, they argued for using a piecewise constant hazard rate model. We improve on their work by showing that the semi-parametric features of Cox's marginal likelihood are as appropriate for the analysis of wage decompositions and as easy to interpret. Moreover, we extend their approach by allowing for nonlinear regression effects. We will show empirically that this formulation will both increase the flexibility of their approach and improve the discriminatory power between wage regimes. --

Diversification and the banks' risk-return-characteristics: evidence from loan portfolios of German banks

Banks face a tradeoff between diversifying and focusing their loan portfolio. In this paper we carry out an empirical study for the German market to shed light on the question whether or not the benefits of risk sharing outweigh those of specialization. We use data from the Bundesbank's quarterly borrowers statistic to determine the degree of diversification in the banks' loan portfolios and combine this data with the banks' balance sheets and audit reports. The unique database comprises data from all German banks during the period from 1993 to 2003. Our main results can be summarized in three statements: i) Specialized banks have a slightly higher return than diversified banks. ii) Specialized banks have lower relative loan loss provisions and lower shares of non-performing loans, iii) However, the standard deviations of the loan loss provision ratio and the non-performing loan ratio are lower for diversified banks. --bank lending,loan portfolio,portfolio theory,diversification,riskreturn analysis

Dynamic Q-investment functions for Germany using panel balance sheet data and a new algorithm for the capital stock at replacement values

The paper explores the investment behaviour of German firms in the context of the Qapproach, which plays a dominant role in empirical investment research. The analysis is based on the Deutsche Bundesbank's corporate balance sheet statistics. The panel data set contains some 2,300 German firms' balance sheet data covering the years 1988-1998. While the Q-theory is mainly applied on the basis of stock market data, which facilitates the exploitation of market expectations and the calculation of average Q, the direct forecasting approach (Chirinko 1993) suggested by Abel and Blanchard (1986) and extended to panel data by Gilchrist and Himmelberg (1995, 1998) enables the Q-theory to be applied to non-quoted firms which are by far the majority in Germany. One of the key variables when using balance sheet data, which has attracted much detailed research, is firms' net capital stock at replacement costs. The challenge is to transform historical cost data, depreciated at non-economic, tax-oriented depreciation rates, into unreported and probably unknown economically meaningful data at actual replacement values. We suggest a complex procedure for calculating reliable replacement values of a firm's capital stock. To calculate Q we follow two different operationalisation strategies. First we estimate average Q based on balance sheet data by forecasting the present value of future profits using a VAR model. Second, we estimate marginal Q following the approach suggested by Gilchrist and Himmelberg. We compare the results from two different estimation techniques for dynamic investment models, GMM and direct bias correction. The results show that marginal as well as average Q influence investment significantly. When classifying the firms by size, we find that smaller firms react more strongly to Q and, to a lesser extent, to lagged investment. -- Die vorliegende Arbeit untersucht das Investitionsverhalten deutscher Unternehmen im Rahmen der Q-Theorie, die eine der dominierenden Investitionstheorien darstellt. Grundlage der geschätzten Investitionsfunktionen ist die Unternehmensbilanzstatistik der Deutschen Bundesbank. Der Paneldatensatz umfasst über 2300 Unternehmen und den Zeitraum 1988 bis 1998. Die übliche Verwendung von Aktienkursen zur Berechnung des durchschnittlichen Q beschränkt die Anwendung der Q-Theorie auf börsennotierten Unternehmen. Die explizite Modellierung eines Prognosemodells (direct forecasting appraoch, Chirinko (1993)) in Anlehnung an Arbeiten von Abel and Blanchard (1986) und Gilchrist and Himmelberg (1995, 1998) ermöglicht die Anwendung auch für nicht börsennotierte Unternehmen, die in Deutschland eindeutig dominieren. Eine zentrale Größe der Analyse des Investitionsverhaltens auf der Grundlage von Unternehmensbilanzdaten ist der Kapitalstock der Unternehmen zu Wiederbeschaffungskosten anstelle des bilanziellen Nettoanlagevermögens zu historischen Anschaffungskosten. In der Arbeit wird ein komplexer Algorithmus zu einer möglichst exakten Schätzung vorgeschlagen. Zur Berechnung von Q werden zwei unterschiedliche Operationalisierungsstrategien verfolgt. Zum einen wird in Anlehnung an Abel und Blanchard das durchschnittliche Q über eine Schätzung des Marktwertes des Eigenkapitals mittels eines Vektor- Autoregressiven-Modells für Paneldaten ermittelt. Zum anderen wird auf dem Ansatz von Gilchrist and Himmelberg beruhend eine Abschätzung des marginalen Q vorgenommen. Die Ergebnisse der Q-Investitionsfunktionen werden für zwei alternative Schätztechniken, GMM und eine direkte Biaskorrektur, verglichen. Es zeigt sich, dass sowohl das durchschnittliche als auch das marginale Q die Investitionen in signifikantem Ausmaß beeinflussen. Die Analyse für Größenklassen zeigt, dass im wesentlichen kleinere Unternehmen in stärkerem Maße auf Q und in geringerem Maße auf zeitlich verzögerte Investitionen reagieren.investment,Q,capital stock,replacement costs,VAR,dynamic panel data

A comparison of dynamic panel data estimators: Monte Carlo evidence and an application to the investment function

In our analysis we discuss several dynamic panel data estimators proposed in the literature and assess their performance in Monte Carlo simulations. It is a well known fact that the natural choice, the least squares dummy variable estimator is biased in the context of dynamic estimation. The estimators taking into account the resulting bias can be grouped broadly into the class of instrumental estimators and the class of direct bias corrected estimators. The simulation results clearly favour the direct bias corrected estimators, especially the estimator proposed by Hansen (2001). The superiority of these estimators decreases with growing numbers of individuals in the simulation. This is the well known fact of large sample properties of the GMM-methods. In the case of endogenous predetermined regressors, the system-estimator proposed by Blundell and Bond is unbiased and most efficient, while direct bias corrected estimators perform similar to the GMM-estimator proposed by Arellano and Bond (1991). Turning to the empirical comparison, we find that the different estimators lead to the same conclusions concerning the investment behaviour of German manufacturing firms based on the Deutsche Bundesbank's Corporate Balance Sheet Statistics. Investment is strongly positive dependent on lagged investment and Q. Nevertheless, in detail the differences of the estimated parameters are not negligible. -- In der vorliegenden Arbeit werden verschiedene in der Literatur vorgeschlagen dynamische Schätzer für Paneldaten diskutiert und im Rahmen einer Monte Carlo-Studie verglichen. Es ist wohlbekannt, dass der Least Squares Dummy Variable-Estimator für den Fall verzögerter endogener erklärender Variablen einen Bias aufweist. Die diskutierten Schätzer lassen sich zwei unterschiedlichen Klassen zuordnen, einer Klasse von Instrumentenschätzern und einer Klasse von biaskorrigierten Schätzern. Den Ergebnissen der Simulationsstudie zufolge sind die biaskorrigierten Schätzer leicht überlegen, insbesondere die von Hansen (2001) vorgeschlagene Biaskorrektur. Die Überlegenheit nimmt jedoch mit wachsender Zahl der beobachteten Einheiten ab. Hier spiegeln sich die bekannt günstigen Eigenschaften von GMM-Schätzern bei großer Beobachtungszahl wider. Im Falle endogener vorherbestimmter Regressoren weist der von Blundell und Bond (1998) vorgeschlagene System-GMM-Schätzer die höchste Effizienz auf. Biaskorrigierte Schätzer führen hier zu vergleichbaren Ergebnissen wie der GMMSchätzer von Arellano und Bond (1991). Bei der empirischen Anwendung zur Schätzung von dynamischen Q-Invstitionsfunktionen für Unternehmen des deutschen Verarbeitenden Gewerbes auf Grundlage der Bilanzstatistik der Deutschen Bundesbank, zeigt sich eine starke positive Abhängigkeit der Investitionen, sowohl von den Vorjahresinvestitionen als auch von Q. Bei gleicher ökonomischer Grundaussage weisen die mittels der verschiedenen diskutierten Methoden geschätzten Parameter jedoch nicht zu vernachlässigende Unterschiede auf.dynamic panel data estimation,GMM,bias correction,investment

Properties of the Histogram Location Approach and the Extent and Change of Downward Nominal Wage Rigidity in the EU

The histogram location approach has been proposed by Kahn (1997) to estimate the fraction of wage cuts prevented by downward nominal wage rigidity. In this paper, we analyze the validity of the approach by means of a simulation study which yielded evidence of unbiasedness but also of potential underestimation of rigidity parameter uncertainty and therefore of potential anticonservative inference. We apply the histogram location approach to estimate the extent of downward nominal wage rigidity across the EU for 1995-2001. Our data base is the User Data Base (UDB) of the European Community Household Panel (ECHP). The results show wide variation in the fraction of wage cuts prevented by nominal wage rigidity across the EU. The lowest rigidity parameters are found for the UK, Spain and Ireland, the largest for Portugal and Italy. Analyzing the change of rigidity between sub periods 1995-1997 and 1999-2001 even shows an widening of the differences in nominal wage rigidity. Due to the finding of large differences across the EU, the results imply that the costs of low inflation policies across the EU differ substantially.Wage rigidity, Inflation, Unemployment

Dynamic Q-investment functions for Germany using panel balance sheet data and a new algorithm for the capital stock at replacement values

The paper explores the investment behaviour of German firms in the context of the Qapproach, which plays a dominant role in empirical investment research. The analysis is based on the Deutsche Bundesbank's corporate balance sheet statistics. The panel data set contains some 2,300 German firms' balance sheet data covering the years 1988-1998. While the Q-theory is mainly applied on the basis of stock market data, which facilitates the exploitation of market expectations and the calculation of average Q, the direct forecasting approach (Chirinko 1993) suggested by Abel and Blanchard (1986) and extended to panel data by Gilchrist and Himmelberg (1995, 1998) enables the Q-theory to be applied to non-quoted firms which are by far the majority in Germany. One of the key variables when using balance sheet data, which has attracted much detailed research, is firms' net capital stock at replacement costs. The challenge is to transform historical cost data, depreciated at non-economic, tax-oriented depreciation rates, into unreported and probably unknown economically meaningful data at actual replacement values. We suggest a complex procedure for calculating reliable replacement values of a firm's capital stock. To calculate Q we follow two different operationalisation strategies. First we estimate average Q based on balance sheet data by forecasting the present value of future profits using a VAR model. Second, we estimate marginal Q following the approach suggested by Gilchrist and Himmelberg. We compare the results from two different estimation techniques for dynamic investment models, GMM and direct bias correction. The results show that marginal as well as average Q influence investment significantly. When classifying the firms by size, we find that smaller firms react more strongly to Q and, to a lesser extent, to lagged investment.Die vorliegende Arbeit untersucht das Investitionsverhalten deutscher Unternehmen im Rahmen der Q-Theorie, die eine der dominierenden Investitionstheorien darstellt. Grundlage der geschätzten Investitionsfunktionen ist die Unternehmensbilanzstatistik der Deutschen Bundesbank. Der Paneldatensatz umfasst über 2300 Unternehmen und den Zeitraum 1988 bis 1998. Die übliche Verwendung von Aktienkursen zur Berechnung des durchschnittlichen Q beschränkt die Anwendung der Q-Theorie auf börsennotierten Unternehmen. Die explizite Modellierung eines Prognosemodells (direct forecasting appraoch, Chirinko (1993)) in Anlehnung an Arbeiten von Abel and Blanchard (1986) und Gilchrist and Himmelberg (1995, 1998) ermöglicht die Anwendung auch für nicht börsennotierte Unternehmen, die in Deutschland eindeutig dominieren. Eine zentrale Größe der Analyse des Investitionsverhaltens auf der Grundlage von Unternehmensbilanzdaten ist der Kapitalstock der Unternehmen zu Wiederbeschaffungskosten anstelle des bilanziellen Nettoanlagevermögens zu historischen Anschaffungskosten. In der Arbeit wird ein komplexer Algorithmus zu einer möglichst exakten Schätzung vorgeschlagen. Zur Berechnung von Q werden zwei unterschiedliche Operationalisierungsstrategien verfolgt. Zum einen wird in Anlehnung an Abel und Blanchard das durchschnittliche Q über eine Schätzung des Marktwertes des Eigenkapitals mittels eines Vektor- Autoregressiven-Modells für Paneldaten ermittelt. Zum anderen wird auf dem Ansatz von Gilchrist and Himmelberg beruhend eine Abschätzung des marginalen Q vorgenommen. Die Ergebnisse der Q-Investitionsfunktionen werden für zwei alternative Schätztechniken, GMM und eine direkte Biaskorrektur, verglichen. Es zeigt sich, dass sowohl das durchschnittliche als auch das marginale Q die Investitionen in signifikantem Ausmaß beeinflussen. Die Analyse für Größenklassen zeigt, dass im wesentlichen kleinere Unternehmen in stärkerem Maße auf Q und in geringerem Maße auf zeitlich verzögerte Investitionen reagieren

Downward wage rigidity in Europe: A new flexible parametric approach and empirical results

We suggest a new parametric approach to estimate the extent of downward nominal wage rigidity in ten European countries between 1994 and 2001. The data base used throughout is the User Data Base (UDB) of the European Community Household Panel (ECHP). The proposed approach is based on the very flexible generalized hyperbolic distribution which allows to model wage change distributions characterized by thick tales, skewness and leptokurtosis. Significant downward nominal wage rigidity is found in all countries under analysis, but the extent varies considerably across countries. Yearly estimates reveal increasing rigidity in Italy, Greece and Portugal, while rigidity is declining in Denmark and Belgium. The results imply that the costs of price stability differ substantially across Europe