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(Nov 22, 2004)
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We examine the properties of automatic model selection, as embodied in PcGets, and evaluate its performance across different (unknown) states of nature. After describing the basic algorithm and some recent changes, we discuss the consistency of its selection procedures, then examine the extent to which model selection is non-distortionary at relevant sample sizes. The problems posed in judging performance on collinear data are noted. The conclusion notes how PcGets can handle more variables than observations, and hence how it can tackle non-linear models.
The objective of this study is to compare alternative computerized model-selection strategies in the context of the vector autoregressive (VAR) modeling framework. The focus is on a comparison of subset modeling strategies with the general-to-specific reduction approach automated by PcGets. Different measures of the possible gains of model selection are considered: (i) the chances of finding the `correct' model, that is, a model which contains all necessary right-hand side variables and is as parsimonious as possible, (ii) the accuracy of the implied impulse-responses and (iii) the forecast performance of the models obtained with different specification algorithms. In the Monte Carlo experiments, the procedures recover the DGP specification from a large VAR with anticipated size and power close to commencing from the DGP itself when evaluated at the empirical size. We find that subset strategies and PcGets are close competitors in many respects, with the forecast comparison indicating a clear advantage of the PcGets algorithm.
By implementing the general-to-specific (Gets) approach to econometric modelling, PcGets automatically selects a an undominated, congruent model even though the precise formulation of the econometric relationship is not known a priori. Starting from a general model which is congruent with the data evidence, statistically-insignificant variables are eliminated, with diagnostic tests checking the validity of reductions, to ensure a congruent final selection. PcGets (see Hendry and Krolzig, 1999a) focuses on linear, dynamic, regression models, so can also be applied to equations within (e.g.) vector autoregressive representations (VARs), or cross-section models. The logic of the PcGets approach is to implement, in the context of model selection, the theory of reduction by which empirical models arise. That theory delineates the steps by which the data-generating process (DGP) has been reduced to deliver the specified model, what the consequential information losses must be, and how they can be evaluated empirically (see Hendry 1995, Ch. 9). For practical implementation, an initial general model -- designed to embed all the relevant information -- is formulated in place of the DGP. However, some variables in this general unrestricted model (GUM) may prove to be unnecessary, so a selection problem results. The GUM must be congruent with the available evidence, since the DGP certainly is: thus, the algorithm first tests the GUM against a range of potential mis-specifications to ensure data coherence. If that condition is satisfied, then the GUM can be simplified by eliminating statistically-irrelevant variables. PcGets checks that each simplification step is acceptable by the user’s criteria, and that none of the diagnostic tests reveals an invalid reduction, so the final choice of model loses no significant information about the desired relationship from the data sample available. Consequently, the final choice parsimoniously encompasses the GUM, and is undominated by any other model.
There are many ways in which a model can be simplified, so PcGets adopts a multi-path search strategy, exploring the consequences of every initially-feasible path, and collecting the ‘terminal’ models resulting from each search. Once all paths have been explored, a set of admissible, congruent models results. If that set has a single member, called the ‘final’ model, the search terminates: a reduction has been found that loses no ‘significant’ information from the GUM, that is congruent, that parsimoniously encompasses the GUM, and such that further reductions will lose information. If many ‘terminal’ models have been found, these are tested for parsimoniously encompassing their union, namely the smallest model that nests all the contenders. Again, if precisely one survives, the search has ended in a ‘final’ model. If several survive, their union is formed to see if further elimination is possible; if not, then the multi-path search re-commences from that latest union. This sequence repeats until either a unique congruent ‘final’ model emerges, or no further elimination is possible. In the second case, model selection is made using an information criterion, since several congruent, mutually encompassing representations have been found. Thus, in each instance, PcGets finds a valid parsimonious simplification of the initial specification.
The properties of automatic model selection are discussed, focusing on PcGets. We explain the background concepts and why automatic methods can perform well. Criticisms of model selection procedures are noted and rebutted. The algorithm is sketched, distinguishing between costs of search and costs of inference: the latter are unavoidable in any statistical science, whereas the costs of searching seem small in comparison. The choice of a ‘search strategy’ and the actual simulation performance of the approach are discussed. We outline a number of developments that will improve the behavior, and generalize the scope, of such programs, and tackle hitherto intractable problems.
When the DGP is nested in the model, PcGets delivers high performance selection across different (unknown) states of nature. One of its steps involves sub-sample post-selection assessment, and here we consider its properties and investigate its practical application. The simulation results show that conditional on retaining a variable, sub-sample information cannot discriminate between sub-stantive and adventitious significance. The Monte Carlo experiments also reveal that the sub-sample selection method suggested by Hoover and Perez (1999) is dominated by procedures selecting only on full-sample evidence, when both approaches are evaluated at a given size. Nevertheless, although the sub-sample procedures do not result in a genuinely beneficial trade-off between size and power, they are particularly successful in controlling the size for selection problems that were previously deemed almost intractable.
After reviewing the simulation performance of general-to-specific automatic regressionmodel selection, as embodied in PcGets, we show how model selection can be nondistortionary: approximately unbiased ‘selection estimates’ are derived, with reported standard errors close to the sampling standard deviations of the estimated DGP parameters, and a near-unbiased goodness-of-fit measure. The handling of theory-based restrictions, non-stationarity, and problems posed by collinear data are considered. Finally, we consider how PcGets can handle three ‘intractable’ problems: more variables than observations in regression analysis; perfectly collinear regressors; and modelling simultaneous equations without a priori restrictions
Structural vector autoregressive (SVAR) models have emerged as a dominant research strategy in empirical macroeconomics, but suffer from the large number of parameters employed and the resulting estimation uncertainty associated with their impulse responses. In this paper we propose general-to-specific model selection procedures to overcome these limitations. After showing that single-equation procedures are efficient for the reduction of the SVAR, but generally not for the reduction of its reduced form, the proposed reduction procedure is computer-automated using PcGets and its small-sample properties are evaluated in a realistic Monte Carlo experiment. The model selection procedure is shown to recover the DGP specification from a large unrestricted SVAR model with controlled size and power. The impulse responses generated by the selected SVAR are compared to those of the unrestricted and reduced VAR and found to be more precise and accurate. The proposed reduction strategy is then applied to the US monetary system considered by Christiano, Eichenbaum and Evans (1996). Although the selection process is hampered by the misspecification of the unrestricted VAR, the results are consistent with the Monte Carlo and question the validity of the impulses responses generated by the full system.
We consider the analytic basis for PcGets, an Ox Package implementing automatic general-to-specific (Gets) modelling for linear, dynamic, regression models. PcGets mimics the theory of reduction -- whereby empirical models arise -- by commencing from a general congruent specification, which is then simplified to a minimal representation consistent with the desired selection criteria and the data evidence. We discuss the properties of PcGets, since results to date suggest that model selection can be relatively non-distortionary, even when the mechanism is unknown, and contrast Gets with possible alternatives.
Vector autoregressive models are widely used in empirical macroeconomics. Unfortunately, they are subjected to the curse of dimensionality. Single-equation general-to-specific reduction procedures using PcGets are proposed to overcome the problem: Starting from the unrestricted VAR, standard testing procedures eliminate statistically-insignificant variables in every equation of the VAR, with diagnostic tests checking the validity of reductions. Weak exogeneity conditions are derived for the efficiency of such single-equation reduction procedures. In Monte Carlo experiments the proposed reduction strategy recovers the DGP from a large unrestricted VAR with size and power close to commencing from the DGP itself.
Unrestricted reduced form vector autoregressive (VAR) models have become a dominant research strategy in empirical macroeconomics since Sims (1980) critique of traditional macroeconometric modeling. They are however subjected to the curse of dimensionality. In this paper we propose general-to-specific reductions of VAR models and consider computer-automated model selection algorithms embodied in PcGets (see Hendry and Krolzig, 2001) for doing so. Starting from the unrestricted VAR, standard testing procedures eliminate statistically-insignificant variables, with diagnostic tests checking the validity of reductions, ensuring a congruent final selection. Since jointly selecting and diagnostic testing eludes theoretical analysis, we evaluate the proposed strategy by simulation. The Monte Carlo experiments show that PcGets recovers the DGP specification from a large unrestricted VAR model with size and power close to commencing from the DGP itself. The application of the proposed reduction strategy to a US monetary system demonstrates the feasibility of PcGets for the analysis of large macroeconomic data sets.
Disputes about econometric methodology partly reflect a lack of evidence on alternative approaches. We reconsider econometric model selection from a computer-automation perspective, focusing on general-to-specific reductions, embodied in PcGets. Starting from a general congruent model, standard testing procedures eliminate statistically-insignificant variables, with diagnostic tests checking the validity of reductions, ensuring a congruent final selection. Since jointly selecting and diagnostic testing has eluded theoretical analysis, we study modelling strategies by simulation. The Monte Carlo experiments show that PcGets recovers the DGP specification from a general model with size and power close to commencing from the DGP itself.
Kevin Hoover and Steven Perez take important steps towards resolving some key issues in econometric methodology. They simulate general-to-specific (Gets) selection for linear, dynamic regression models, and find that their algorithm performs well in re-mining the `Lovell database'. We discuss developments that improve on their results, automated in PcGets. Monte Carlo experiments and re-analyses of empirical studies show that pre-selection F-tests, encompassing tests, and sub-sample reliability checks all help eliminate `spuriously-significant' regressors, without impugning recovery of the correct specification with the same accuracy as if it were known.
Developed jointly with D.F.Hendry, PcGets is an Ox Package implementing automatic general-to-specific (Gets) modelling for linear regression models based on the theory of reduction, as in Hendry (1995, Ch.9). PcGets offers a new computer-automated approach to econometric modelling, ‘outperforming’ even experienced econometricians. Designed for modelling economic data when the precise formulation of the equation under analysis is not certain, PcGets implements a general-to-specific approach to automatically select a congruent and undominated model. The current version is for linear dynamic single-equation models.
- Reviews:
- Bardsen, G. (2001). `Review of PcGets 1 for Windows', Econometrics Journal, 4(2), 311-318.
- Owen, D. (2003). `General-to-Specific Modelling using PcGets', Journal of Economic Surveys, 17(4), 609-628.
- Yaffee, R.A. (2004) `Econometric Data Mining with PcGets', Connect: Information Technology at NYU, }, 14(2), 46-47.
- Links:
This paper proposes a new framework for the impulse-response analysis of business cycle transitions. A cointegrated vector autoregressive Markov-switching model is found to be a congruent representation of post-war US employment and output data. In this model some parameters change according to the phase of the business cycle which effects employment and output simultaneously. The long run dynamics are characterized by a cointegrating vector including employment, output and a trend as a proxy for technological progress and capital accumulation. Short-run and long-run dynamics are jointly estimated in a Markov-switching vector-equilibrium-correction model with three regimes representing recession, growth and high growth. For the analysis of the dynamics of output and employment, a new set of impulse-response exercises is considered.
MSVAR is an Ox package designed for the econometric modelling of univariate and multiple time series subject to shifts in regime. It provides the statistical tools for the maximum likelihood estimation (EM algorithm) and model evaluation of Markov-Switching Vector Autoregressions as discussed in the book of the same name. A variety of model specifications regarding the number of regimes, regime-dependence versus invariance of parameters etc. provides the necessary flexibility for empirical research and will be of use to econometricians intending to construct and use models of dynamic, non-linear, non-stationary or cointegrated systems.
This paper develops a new methodological approach to the statistical analysis of cointegrated linear systems subject to changes in regime. We consider Markov-switching cointegrated vector autoregressive processes and their representation as time-varying vector equilibrium correction models and constant finite vector autoregressive moving-average models. A two-stage maximum likelihood estimation technique is proposed. First, the Johansen cointegration analysis is applied to a finite order VAR approximation. Conditional on the estimated cointegration matrix, an EM algorithm is employed to estimate the remaining parameters. The methodology is illustrated with an investigation of regime shifts in a small macroeconomic model of six OECD countries.
Markov-Switching Vector Autoregressions presents a systematic and operational approach to econometric modelling of time series subject to shifts in regime. The first part of the book gives a comprehensive mathematical and statistical analysis of the Markov-switching vector autoregressive model. It deals with the theoretical properties and the statistical tools for empirical research (including specification strategies, estimation techniques, testing, model evaluation, simulation and forecasting). The discussed theoretical and practical developments will be of use to econometricians intending to construct and use models of dynamic, multivariate, possibly non-stationary systems. The second part of the book includes an intensive study of international business cycles. Particular attention is paid to the case of Germany. It is designed so that it can be used by researchers who are interested in applying the methods without going into too much detail about the underlying econometric theory.
While there has been a great deal of interest in the modelling of non-linearities and regime shifts in economic time series, there is no clear consensus regarding the forecasting abilities of these models. In this paper we develop a general approach to predict multiple time series subject to Markovian shifts in the regime. The feasibility of the proposed forecasting techniques in empirical research is demonstrated and their forecast accuracy is evaluated.
We propose testing for business cycle first-moment asymmetries in Markov-switching autoregressive (MS-AR) models. We derive the parametric restrictions on MS-AR models that rule out types of asymmetries such as deepness, steepness, and sharpness, and set out a testing procedure based on Wald statistics which have standard asymptotics. For a two-regime model, such as that popularised by Hamilton (1989), we show that deepness implies sharpness (and vice versa) while the process is always non-steep. We illustrate with two and three-state MS-AR models of US GNP growth, and models of US investment and consumption growth. Our findings are compared with those obtained from standard non-parametric tests, which are unable to distinguish between first-moment asymmetries and heteroscedasticity.
This paper introduces the concept of common deterministic shifts (CDS). This concept is simple, intuitive and relates to the common structure of shifts or policy interventions. We propose a Reduced Rank technique to investigate the presence of CDS and to estimate the cobreaking vectors. The proposed testing procedure has standard asymptotics and good small-sample properties. We further link the concept of CDS to that of super-exogeneity. It is shown that CDS tests can be constructed which allow to test for super-exogeneity. The Monte Carlo evidence indicates that the CDS test for super-exogeneity dominates testing procedures proposed in the literature.
While there has been a great deal of interest in the modelling of non-linearities in economic time series, there is no clear consensus regarding the forecasting abilities of non-linear time series models. We evaluate the performance of two leading non-linear models in forecasting post-war US GNP, the self-exciting threshold autoregressive model and the Markov-switching autoregressive model. Two methods of analysis are employed: an empirical forecast accuracy comparison of the two models, and a Monte Carlo study. The latter allows us to control for factors that may otherwise undermine the performance of the non-linear models.
MSVAR is an Ox package (see Doornik, 2001) designed for the econometric modelling of univariate and multiple time series subject to shifts in regime. It provides the statistical tools for the maximum likelihood estimation (EM algorithm) and model evaluation of Markov-Switching Vector Autoregressions.
This paper intends to harmonize two different approaches to the analysis of the business cycle and in doing so it retrieves the stylized facts of the business cycle in Europe. We start with the `classical' approach proposed in Burns and Mitchell (1946) of dating and analyzing the business cycle; we then adopt the `modern' alternative: the Markov-switching autoregression. The model's regime probabilities provide an optimal statistical inference of the turning point of the European business cycle. For assessing the capacity of the parametric approach to generate the stylized facts of the classical cycle in Europe, the stylized facts of the original data are compared to those of simulated data. The MS-VAR model is shown to be a good candidate for use as an statistical instrument to improve the understanding of the business cycle.
This paper analyzes regime shifts in the stochastic process of economic growth of six major OECD countries over the last three decades. For the statistical measurement of the underlying global business cycle, we generalize Hamilton's model of the U.S.\ business cycle to a Markov-switching vector autoregressive time series model. Applying the model to six series of quarterly GNP growth rates, the paper provides empirical evidence for the dominance of common shocks as the source of international business cycles. For all countries, business cycles can be identified as regime shifts in the mean growth rate occurring mainly simultaneously across countries. We also find significant evidence for a structural break in the second quarter of 1973 affecting the growth path of the world economy as well as the correlation structure of country-specific shocks.
In this paper we advocate a parametric approach to the construction of turning point chronologies for the euro-zone business cycle. In generalization of Hamilton (1989), the Markov-switching vector autoregressive (MS-VAR) model is utilized for the analysis of the business cycle, providing the mechanism for identifying peaks and troughs of the business cycle. Building upon ideas developed in Krolzig (1997) and Artis, Krolzig and Toro (2003), the approach for the constructing the turning point chronology consists of (i) modelling the euro-zone business cycle as a single common factor generated by a hidden Markov chain, (ii) fitting a congruent statistical model to the data, (iii) deriving the conditional probabilities of the regimes `expansion' and `recession' from the estimated model, (iv) classifying each point in time to the regime with the highest probability, and (v) dating the turning points of the business cycle. The MS-VAR also provides measures of uncertainty associated with the turning point chronology, facilitates real-time detection of business cycle transitions, and offers a well-developed theory for the prediction of the business cycle. Examining the properties of the proposed dating procedure, we show that aggregation and model misspecification can severely hamper the detection of business cycle turning points. In the empirical part, the MS-VAR approach is applied to three multi-country data sets consisting of real GDP and industrial production growth rates of 12 euro-zone countries (in total) over the period from 1973 to 2002. Although the empirical models are found to be sensitive to data quality (with seasonal adjustment, outlier correction and smoothing being all influential), the estimated models were found useful for the assessment of business cycle synchronization among the EMU member states, and for the construction of a turning point chronology of the euro-zone business cycle.
The ability of Markov-switching (MS) autoregressive models to replicate selected classical business-cycle features found in US post-war consumption, investment and output is compared to that of linear models. Univariate MS models appear to offer more dynamically parsimonious representations, but generally are unable to reproduce features missed by linear models. In the multivariate models, some cointegration restrictions were found to have a crucial impact, and the ability of models that imposed cointegration to reproduce business cycle features was enhanced by Markov-switching.
This paper deals with the existence and identification of a common European growth cycle. It has recently been argued that the formation of a monetary union creates in itself a tendency for business cycle symmetry to emerge. If this holds for the European monetary Union and the quasi-union of the Exchange Rate Mechanism of the European Monetary System, then we might expect already to be able to find an emergent ``European cycle'' which will become more dominant in future years. Univariate Markov switching autoregressions (MS-AR) are used for individual countries in order to detect changes in the mean growth rate of industrial production. The smoothed probabilities obtained from these models give support to the possibility of inferring a common European cycle by jointly modelling the industrial production indices of the nine countries under study. An MS-VAR model is then used to identify the common cycle in Europe and the results confirm the existence of such a cycle. The European business cycle is dated on the basis of the regime probabilities. Two further issues are investigated. First we investigate the contribution of the European Business Cycle to the individual country cycles. Second, we undertake an impulse response analysis where we investigate the response of each individual country to European expansions and recessions. We analyze the response of industrial production in each country due to a change in regime. We focus mainly on two types of shocks, the response of industrial production in individual countries due to a European recession, and the effect of an expansionary period in Europe.
There is a wide literature on the dynamic adjustment of employment and its relationship with the business cycle. In this paper we present a statistical model that offers a congruent representation of part of the UK labour market since the mid 1960s. We use a cointegrated vector autoregressive Markov-switching model in which some parameters change according to the phase of the business cycle. Output, employment, labour supply and real earnings are found to have a common cyclical component. The long run dynamics are characterized by one cointegrating vector relating unemployment to trend-adjusted real wages and output. Despite there having been many changes affecting this sector of the UK economy, the Markov-switching vector-equilibrium-correction model with three regimes (representing recession, normal growth, and high growth) provides a good characterization of the sample data, and performs well relative to alternative linear and non-linear models. The results of an impulse-response analysis highlight the dangers of using VARs when the constancy of the estimated coefficients has not been established, and demonstrate the advantages of generating regime dependent responses.
We consider whether oil prices can account for business cycle asymmetries. We test for asymmetries based on the Markov switching autoregressive model popularized by Hamilton (1989), using the tests devised by Clements and Krolzig (1993). We find evidence against the conventional wisdom that recessions are more violent than expansions: while some part of the downturn in economic activity that characterises recessionary periods can be attributed to dramatic changes in the price of oil, post-War US economic growth is characterized by the steepness of expansions.
By generalizing Hamilton's model of the US business cycle to a three-regime Markov-switching vector autoregressive model, this paper analyzes regime shifts in the stochastic process of economic growth in the US, Japan and Europe over the last four decades. Empirical evidence is established for the presence of a structural break in the expansionary GDP growth for the US and Japan based on an output-employment MS vector equilibrium correction model, and a structural break in the context of a common European business cycle. For the United States the long expansions of recent years signify basic changes in the business cycles pattern. In the case of Japan we identify long episodes of rapid economic expansions (existing until the mid 1970s) and long economic recessions (as in the 1990s). In Europe we find after an episode of catching-up in the 1970s, convergence in the business cycle pattern which suggests the notion of a European business cycle. The multi-regime Markov-switching VARs proposed are profoundly checked for their economic content and statistical congruency, and are found to provide a sound statistical framework for a comprehensive analysis of the business cycle.
This paper addresses the issues of identification and dating of the Euro-zone business cycle by using the Markov-switching approach innovated by Hamilton in his analysis of the US business cycle. Regime shifts in the stochastic process of economic growth in the Euro-zone over the last two decades are identified by fitting Markov-switching models to aggregated and single-country Euro-zone real GDP growth data. The models are found to be statistically congruent and economically meaningful. Based of the smoothed regime probabilities from the Markov-switching models the Euro-zone business cycle is dated and recessions from 1980Q1-1981Q1 and 1992Q3-1993Q2 are revealed. A Markov-switching vector autoregression of real GDP growth rates in eight EMU member states shows that while the business cycles in the Euro-zone have not been perfectly synchronized over the last two decades, the overall evidence for the presence of a common Euro-zone cycle is strong.
Exploring index of production data for six major UK manufacturing sectors, this paper investigates the interaction of the UK business cycle with changes in the industrial structure of the UK economy during the last three decades. We propose a Markov-switching vector equilibrium correction model with three regimes representing recession, normal growth and high growth. The regime shifts simultaneously affect the common growth rate and the sectoral equilibrium allocation of industrial production. In contrast to previous investigations, a common cycle can be uncovered which is closely related to traditional datings of the UK\ business cycle.
Mit dem Hamilton-Modell des U.S.-Konjunkturzyklus von 1989 ist die Bedeutung des Markov-Regimewechselmodells als Instrument der Konjunkturanalyse erkannt geworden. Während in den letzten Jahren sowohl die ökonometrisch--theoretische Literatur als auch die Zahl empirischer Anwendung stark angewachsen ist, fehlt für den deutschsprachigen Raum eine systematische Darstellung der formalen Eigenschaften, statistische Behandlung und empirischen Anwendung des Markov--Regimewechselmodells. Eine solche Einführung soll hier präsentiert werden. Darüberhinaus werden die Nutzungsmöglichkeiten des Modells exemplarisch im Rahmen einer Analyse bundesdeutscher Bruttosozialproduktsdaten veranschaulicht.
In this paper we introduce a small Keynesian model of economic growth which is centered around two advanced types of Phillips curves, one for money wages and one for prices, both being augmented by perfect myopic foresight and supplemented by a measure of the medium-term inflationary climate updated in an adaptive fashion. The model contains two potentially destabilizing feedback chains, the so-called Mundell and Rose-effects. We estimate parsimonious and congruent Phillips curves for money wages and prices in the US over the past five decades. Using the parameters of the empirical Phillips curves, we show that the growth path of the private sector of the model economy is likely to be surrounded by centrifugal forces. Convergence to this growth path can be generated in two ways: a Blanchard-Katz-type error-correction mechanism in the money-wage Phillips curve or a modified Taylor rule that is augmented by a term, which transmits increases in the wage share (real unit labor costs) to increases in the nominal rate of interest. Thus the model is characterized by local instability of the wage-price spiral, which however can be tamed by appropriate wage or monetary policies. Our empirical analysis finds the error-correction mechanism being ineffective in both Phillips curves suggesting that the stability of the post-war US macroeconomy originates from the stabilizing role of monetary policy.
Recent theories converge in the idea that international monetary policy cooperation can be counterproductive. This paper reconsiders the role of policy cooperation and credibility in a symmetric two--country model with incomplete information about the type of the coordination mechanism. It is shown that the Rogoff proposition does not hold if the public has incomplete information about the feasibility of policy cooperation. In the perfect Bayesian Nash equilibrium, cooperation of central banks is beneficial even if non-cooperative policymakers are able to signal their type.
This paper examines the effects of fiscal and monetary policies in a two-sectorial endogenous growth model with money in the utility function. By focusing on the linkage between monetary and fiscal policy due to the government budget constraint, our model deviates from the literature. We show that the impacts of monetary policy heavily depend on the allocation of the seignorage. While money is superneutral, long-run economic growth depends on the level of government expenditures in the human-capital production sector. Therefore an increase in the rate of money supply growth has real effects if and only if the resulting seignorage is used for human capital investments.
In this paper we integrate Arrow's notion of learning-by-doing into Lucas' two-sector growth model. In the original Lucas model, endogenous growth arises through general human capital accumulation resulting from intertemporal time-allocation decisions only. The incorporation of the learning-by-doing generalizes Lucas approach by opening a second channel for the accumulation of human capital which has been intensively discussed in the literature: Investment in physical capital exhibits positive externalities which generates specific production-related human capital. Our results suggest that the contribution of external effects arising from physical capital to the process of economic growth is limited: In contrast to the traditional view, positive externalities of investment in physical capital do not necessarily accelerate long-run growth. In the steady-state equilibrium, economic growth depends on the intentional accumulation of human capital resulting from intertemporal time-allocation decisions. An accelerated accumulation of specific production-related human capital due to a more efficient learning-by-doing goes along with a deceleration of general human capital accumulation due to a reduced time for studying. By affecting the time allocation of the agents, shocks to the learning-by-doing parameter leave the total rate of human-capital accumulation on the balanced growth path unchanged.
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