nach oben

Mathematics in Computer Science

Erschienen in:

01.03.2022

Play-Hysteresis in the Joint Dynamics of Employment and Investment

verfasst von: P. R. Mota, P. B. Vasconcelos

Erschienen in: Mathematics in Computer Science | Ausgabe 1/2022

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The slow recovery of many developed economies to the recent financial crisis, and the largest fall in aggregate demand since WWII caused by the COVID-19 Pandemic with its foreseeable negative and persistent effects on the aggregate supply, has generated renewed interest in the subject of hysteresis. The presence of significant hysteresis effects has important theoretical and policy implications. First, there is no unique and predetermined long-run equilibrium level of aggregate employment, as the equilibrium is permanently changed by temporary shocks. Second, as the economic system is not self-adjusting, substantial, timely, and sustained expansionary monetary and fiscal policy should be applied to mitigate the impact of shocks, including the temporary ones. Although it is not possible to quantify hysteresis effects in real time, we can use historical data to shed some light on the possible long-term economic consequences of the COVID-19 pandemic. For that purpose, we use the linear play-hysteresis model in the context of two equation system to analyses the join hysterical dynamics of aggregate employment and investment. We implement the model empirically by means of a new algorithm for the simultaneous equations system applied to Portuguese data that separates the effects of large and small changes in aggregate demand on aggregate employment and investment using an endogenous determined switching parameter as reference.

Vorheriger Artikel Load Bearing Capacity of Light Timber Frame Walls Under Fire

Nächster Artikel Protected Cells in Compositions

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

The difference between these two types of hysteresis if based on the type of remanence and memory of the system (see [2]).

This is a plausible assumption in many industries such agriculture, textiles, consumer electronics, and steel ( [21]).

Examples of non-convex costs of employment adjustment, mainly caused by the institutional characteristics of the labor market are described in [15, 31, 32, 42], and [51]. A firm also usually incurs in sunk cost for the acquisition of physical assets like firm specific equipment or intangible assets (see, e.g., [44, 45, 21, 23], and [25]), and to disinvest (see [19]). Furthermore, to enter new markets, firms often must incur irreversible costs, e.g., for gathering information on the new market revenues, creating distribution and servicing networks, and advertising or establishing a brand name (see, [1]).

Aggregate demand uncertainty interacting with the non-convex adjustment costs have the potential to reinforce the hysteresis effects (see, e.g., [21, 24], and [7]).

\(R_{\alpha _j,\beta _j} (x_t)\) corresponds to the employment demand function of firm j. This simplification does not restrict the application of the model as we can consider a firm disaggregated into single production units, each of them represented by a non-ideal relay (see [7]).

Within the assumptions of the model the trigger values for exiting and entering in the market derived from a profit maximizing problem in discrete time with an infinite plan horizon and a discount factor \(\delta \) are \(\alpha _j=w_j+r_j-\delta F_j\) and \(\beta _j=w_j+r_j+\delta H_j\) respectively (see, e.g., [28], and [39] for a complete description of the model).

See [2, 3].

The Preisach Model, with the improvements of [37, 38] and [36], is one of the most promising phenomenological models used in the description of hysteresis, and is now generally recognized as a fundamental mathematical toolkit in describing a wide range of hysteretic phenomena in quite different areas.

The heterogeneity in the way firms react to aggregate demand shocks arises from specific cost structures including non-convex adjustment costs (that may depend on firms’ age, size, ownership, average work skill level and innovation), and from the way firms deal with uncertainty (see, [43]).

In the Preisach triangle the triggers for upward adjustment, \(\beta _j\), are on the ordinate, and the triggers for downward adjustment, \(\alpha _j\), are on the abscissa.

For a complete explanation of the Preisach model of hysteresis see, e.g., [38], and [39].

Assuming that firms are uniformly distributed in the Preisach triangle, T, the branches of the hysteresis loop are quadratic functions.

The right axis of Fig. 1a is the reference for the \(x_t\) dynamics.

The left axis of Fig. 1a is the reference for the state of the relay \(R_{\alpha _j,\beta _j } (x_t )\).

Changes in \(x_t\) towards a local maximum originates the displacement of an imaginary horizontal line upwards from the position \(\beta _j=\beta _{min}\) to the position corresponding to \(\beta _j=x_{t_1 }\), switching the relays from 0 to 1.

Figures should be read clockwise.

Changes in \(x_t\) towards a local minimum originates the displacement of an imaginary vertical line to the left from the position \(\alpha _j=x_{t_1 }\) to \(\alpha _j=x_{t_2 }\), switching the relays from 1 to 0.

See [52] for a general description of the model.

Here we choose not explain variables like \(X_t\), \(W_t\) and \(R_t\) (as it done in some general equilibrium economic models), keeping the model simple, as we are focusing not on the particular value of the structural parameters but on the hysterical nature of employment and investment and its interaction.

see, e.g., equations 2.22 and 3.1 in [31] pp. 30 and 64).

See, e.g., [30, 35, 49], and [6].

See [9, 39‐41], and [6] for additional details.

Eq.(3) is based on a piecewise linear relationship where the segments (the plays lines and the spurt lines) are connected continuously by knots (for example in Fig. 1d the knots are points b, c, d, e, and f when the input follows the path \(\{x_{t_0}\mapsto x_{t_1} \mapsto x_{t_2} \mapsto x_{t_3}\)). The position of the knots are a priori unknown, because they depend on the width of the play interval, which has to be estimated, and on the position of the play line that is determined by the past path of the aggregate demand shock \(x_t\). Since the adjacent play and spurts segments are joined, the regression is a special case of a switching equation, and similar to a linear spline function (see [47, 48]). In this case, the OLS estimator is asymptotically unbiased (i.e. consistent) and asymptotically normal distributed under the standard regression model assumptions (see [34, 33], and [48].

In the employment equation, although real wages could also be a source of hysteresis, our aim is to test the existence of hysteresis caused by aggregate demand shocks. This is the reason why real wages enters as a non-hysteretic explanatory variable in the employment equation. Likewise, in the investment equation, although the interest rate can have an impact on investment through hysteresis mechanisms (see [19, 29], and [6]), we are focusing on the hysteretic effects caused by aggregate demand shocks. Therefore, \(x_t\) is the common variable in both equations that operates through hysteresis mechanisms.

The model is estimated with the series in logarithms.

Gross fixed capital formation for the industrial sector at quarterly frequency is not available. Besides using the industrial production as a proxy of aggregate demand in an equation for aggregate investment reduces the problem of endogeneity usually present when real GDP is used as the proxy of aggregate demand in \(f_I\).

The 10 year bond spread anchors the relative cost of borrowing face by firms. Besides, it avoids the problem of endogeneity associated to the joint determination of the quantity and the interest rate of credit contracts for investment when this last interest rate is included in \(f_I\).

This method provides an efficient estimation of a system of equations in the case where disturbances of the system are contemporaneously correlated, as it is the case where equations have endogeneity problems, or are serially correlated, and allows the two dependent variables to have different sets of explanatory variables. The SUR method estimates the parameters of the 2 equations simultaneously, implying that the parameters of each individual equation consider the information provided by the other equation. In so being, the regression coefficient estimators are at least asymptotically more efficient than those obtained by an equation-by-equation application of least squares (see [53]: p. 348).

Adamonis, J., Göcke, M.: Modelling economic hysteresis losses caused by sunk adjustment costs. J. Post Keynesian Econ. 42(2), 299–318 (2019)CrossRef

Amable, B., Henry, J., Lordon, F. and Topol, R.: Unit root in the wage-price spiral is not hysteresis in unemployment. Journal of Economic Studies, (1993)

Amable, B., Henry, J., Lordon, F., Topol, R.: Strong hysteresis versus zero-root dynamics. Econ. Lett. 44(1–2), 43–47 (1994)CrossRef

Arestis, P. and Sawyer, M.: Path dependency and demand-supply interactions in macroeconomic analysis. In Path dependency and macroeconomics, (pp. 1–36). Springer, Berlin (2009)

Bassi, F., Lang, D.: Investment hysteresis and potential output: A post-keynesian-kaleckian agent-based approach. Econ. Model. 52, 35–49 (2016)CrossRef

Belke, A., Baudisch, C.F., Göcke, M.: Interest rate bands of inaction and play-hysteresis in domestic investment-evidence for the euro area. J. Econ. Behav. Org. 175, 19–39 (2020)CrossRef

Belke, A., Göcke, M.: A simple model of hysteresis in employment under exchange rate uncertainty. Scottish J. Polit. Econ. 46(3), 260–286 (1999)CrossRef

Belke, A., Göcke, M.: Exchange rate uncertainty and employment: an algorithm describing play. Appl. Stoch. Model. Bus. Ind. 17(2), 181–204 (2001)MathSciNetCrossRef

Belke, A., Göcke, M.: Exchange rate uncertainty and play nonlinearity in aggregate employment. Int. Adv. Econ. Res. 7(1), 38–50 (2001)CrossRef

10.

Belke, A., Göcke, M., Günther, M.: Exchange rate bands of inaction and play-hysteresis in german exports-sectoral evidence for some oecd destinations. Metroeconomica 64(1), 152–179 (2013)CrossRef

11.

Belke, A. H. and Göcke, M.: Interest rate hysteresis in macroeconomic investment under uncertainty. (2019)

12.

Bertola, G.: Job security, employment and wages. Eur. Econ. Rev. 34(4), 851–879 (1990)CrossRef

13.

Blanchard, O., Cerutti, E., Summers, L.: Inflation and activity-two explorations and their monetary policy implications. Technical report, National Bureau of Economic Research (2015)

14.

Brokate, M., Sprekels, J.: Hysteresis and phase transitions, vol. 121. Springer Science & Business Media, Berlin (1996)

15.

Caballero, R. J., Engel, E. M. and Haltiwanger, J. C.: haltiwanger, aggregate employment dynamics: Building from microeconomic evidence. American Economic Review, 87(1), 115–37

16.

Cerra, V., Fatás, A. and Saxena, S.: Hysteresis and business cycles. (2020)

17.

Cross, R.: Unemployment: natural rate epicycles or hysteresis? Eur. J. Econ. Econ. Policies: Intervention 11(2), 136–148 (2014)

18.

Cross, R., Darby, J., Ireland, J. and Piscitelli, L.: Hysteresis and unemployment: a preliminary investigation. (2005)

19.

Dias, J.C., Shackleton, M.B.: Hysteresis effects under cir interest rates. Eur. J. Oper. Res. 211(3), 594–600 (2011)MathSciNetCrossRef

20.

Dixit, A.: Entry and exit decisions under uncertainty. J. Polit. Econ. 97(3), 620–638 (1989)CrossRef

21.

Dixit, A.: Hysteresis, import penetration, and exchange rate pass-through. Q. J. Econ. 104(2), 205–228 (1989)CrossRef

22.

Dixit, A.: Analytical approximations in models of hysteresis. Rev. Econ. Stud. 58(1), 141–151 (1991)CrossRef

23.

Dixit, A.: Investment and hysteresis. J. Econ. Perspect. 6(1), 107–132 (1992)CrossRef

24.

Dixit, A.K., Dixit, R.K., Pindyck, R.S.: Investment under uncertainty. Princeton University Press, NJ (1994)CrossRef

25.

Folta, T.B., Johnson, D.R., O’Brien, J.: Uncertainty, irreversibility, and the likelihood of entry: An empirical assessment of the option to defer. J. Econ. Behav. Org. 61(3), 432–452 (2006)CrossRef

26.

Göcke, M.: An approximation of the hysteresis loop by linear partial functions. econometric modelling and estimation/eine approximation der hysteresis-schleife über lineare teilfunktionen. ökonometrische modellbildung und schätzung. Jahrbücher für Nationalökonomie und Statistik, 213(5):572–596 (1994)

27.

Gocke, M.: A macroeconomic model with hysteresis in foreign trade. Metroeconomica 52(4), 449–473 (2001)MathSciNetCrossRef

28.

Göcke, M.: Various concepts of hysteresis applied in economics. J. Econ. Surv. 16(2), 167–188 (2002)CrossRef

29.

Göckem, M.: Economic hysteresis with multiple inputs–a simplified treatment. Interdisciplinary Description of Complex Systems: INDECS, 17(1-B):98–113, (2019)

30.

Hall, R.E., Jorgenson, D.W.: Tax policy and investment behavior. Am. Econ. Rev. 57(3), 391–414 (1967)

31.

Hamermesh, D. S.: Labor demand and the structure of adjustment costs. The American Economic Review, pp. 674–689, (1989)

32.

Hamermesh, D.S., Pfann, G.A.: Adjustment costs in factor demand. J. Econ. Lit. 34(3), 1264–1292 (1996)

33.

Hinkley, D.V.: Inference about the intersection in two-phase regression. Biometrika 56(3), 495–504 (1969)MathSciNetCrossRef

34.

Hudson, D.J.: Fitting segmented curves whose join points have to be estimated. J. Am. Stat. Assoc. 61(316), 1097–1129 (1966)MathSciNetCrossRef

35.

IMF. World economic outlook. uneven growth. short-and long-term factors, (2015)

36.

Krasnosel’skii, M.A., Pokrovskii, A.V.: Systems with hysteresis. Springer Science & Business Media, Berlin (2012)

37.

Mayergoyz, I.: Mathematical models of hysteresis. IEEE Trans. Magn. 22(5), 603–608 (1986)CrossRef

38.

Mayergoyz, I.D.: Mathematical models of hysteresis and their applications. Academic Press, Cambridge (2003)

39.

Mota, P.R., Varejão, J., Vasconcelos, P.B.: Hysteresis in the dynamics of employment. Metroeconomica 63(4), 661–692 (2012)CrossRef

40.

Mota, P.R., Vasconcelos, P.: The macrodynamics of employment under uncertainty. In: Dynamics Games and Science, pp. 479–497. Springer, Berlin (2015)CrossRef

41.

Mota, P. R. and Vasconcelos, P.: Estimating the employment band of inaction with multiple breaks due to labor market reforms. Mathematics in Computer Science, pp. 1–13, (2020)

42.

Nickell, S.J.: Fixed costs, employment and labour demand over the cycle. Economica 45(180), 329–345 (1978)CrossRef

43.

Pierre, G., Scarpetta, S.: Employment protection: Do firms’ perceptions match with legislation? Econ. Lett. 90(3), 328–334 (2006)CrossRef

44.

Pindyck, R.S.: Irreversible investment, capacity choice, and the value of the firm. Am. Econ. Rev. 78(5), 969–985 (1988)

45.

Pindyck, R.S.: Irreversibility, uncertainty, and investment. J. Econ. Lit. 29(3), 1110–1148 (1991)

46.

Piscitelli, L., Grinfeld, M., Lamba, H., Cross, R.: On entry and exit in response to aggregate shocks. Appl. Econ. Lett. 6(9), 569–572 (1999)CrossRef

47.

Poirier, D.J.: Piecewise regression using cubic splines. J. Am. Stat. Assoc. 68(343), 515–524 (1973)MathSciNet

48.

Poirier, D. J.: Econometrics of structural change, with special emphasis on spline functions. North-Holland Pub. Co., (1976)

49.

Rodriguez Palenzuela, D., Dees, S. et al.: Savings and investment behaviour in the euro area. Number 167. ECB Occasional Paper, (2016)

50.

Setterfield, M.: Path dependency, hysteresis and macrodynamics. In Path dependency and macroeconomics, pp. 37–79. Springer, (2009)

51.

Varejão, J., Portugal, P.: Employment dynamics and the structure of labor adjustment costs. J. Law Econ. 25(1), 137–165 (2007)

52.

Visintin, A.: Differential models of hysteresis, vol. 111. Springer Science & Business Media, Berlin (2013)

53.

Zellner, A.: An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. J. Am. Stat. Assoc. 57(298), 348–368 (1962)MathSciNetCrossRef

Titel: Play-Hysteresis in the Joint Dynamics of Employment and Investment
verfasst von: P. R. Mota
P. B. Vasconcelos
Publikationsdatum: 01.03.2022
Verlag: Springer International Publishing
Erschienen in: Mathematics in Computer Science / Ausgabe 1/2022
Print ISSN: 1661-8270
Elektronische ISSN: 1661-8289
DOI: https://doi.org/10.1007/s11786-022-00523-w

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1/2022

A Time-Splitting Tau Method for PDE’s: A Contribution for the Spectral Tau Toolbox Library

Non-homogeneous Chain of Harmonic Oscillators

Foreword to the Special Focus on Advances in Symbolic and Numeric Computation IV

Symbolic Approach to 2-Orthogonal Polynomial Solutions of a Third Order Differential Equation

Protected Cells in Compositions

Load Bearing Capacity of Light Timber Frame Walls Under Fire

Premium Partner