In this paper we implement an effcient non-parametric statistical method, Random survival forests, for the selection of  the determinants of Central Bank Independence (CBI) among a large data base of political and economic variables for OECD countries.This statistical technique enables us to overcome omitted variables and overftting problems. It turns out that the economic variables
are major determinants compared to the political ones and linear andnonlinear effects of chosen predictors on CBI are found

Cavicchioli, M.

Papana Diagasis, A.

Papana, A.

Pistoresi, B.

In this paper we implement an e cient non-parametric statistical
method, Random survival forests, for the selection of the determinants of
Central Bank Independence (CBI) among a large database of political and
economic variables for OECD countries. This statistical technique enables
us to overcome omitted variables and over tting problems. It turns out that
the economic variables are major determinants compared to the political ones
and linear and nonlinear e ects of chosen predictors on CBI are found

Papana Dagiasis, A.

Archivio istituzionale della ricerca - Università di Modena e Reggio Emilia

English

Determinants of Central Bank Independence: a Random Forest Approach

Determinants of Central Bank Independence:a Random Forest ApproachMaddalena Cavicchiolia, Angeliki Papanab, Ariadni Papana Dagiasiscand Barbara PistoresidAbstract. In this paper we implement an eﬃcient non-parametric statisticalmethod, Random survival forests, for the selection of the determinants ofCentral Bank Independence (CBI) among a large database of political andeconomic variables for OECD countries. This statistical technique enablesus to overcome omitted variables and overﬁtting problems. It turns out thatthe economic variables are major determinants compared to the political onesand linear and nonlinear eﬀects of chosen predictors on CBI are found.Keywords: Central bank independence, Political and economic determinants,Random survival forests.JEL Classiﬁcation: E58, C82.aDepartment of Economics "Marco Biagi", University of Modena and Reggio Emilia,Viale Berengario 51, 41121, Modena (Italy). Oﬃce Phone No: +39 059 2056846. E-mail:<maddalena.cavicchioli@unimore.it>bAristotle University of Thessaloniki (Greece). E-mail: < agpapana@auth.gr>cDepartment of Mathematics, Cleveland State University, 2121 Euclid Avenue, RT1515, Cleveland, Ohio, 44115 (USA). E-mail: <a.papanadagiasis@csuohio.edu>dCorresponding Author: Department of Economics "Marco Biagi" and ReCent, Uni-versity of Modena and Reggio Emilia, Viale Berengario 51, 41121, Modena (Italy). OﬃcePhone No: +39 059 2056881. E-mail: <barbara.pistoresi@unimore.it>11. IntroductionSeveral studies have examined the diﬀerences in inﬂation rates among coun-tries pointing out the key role of the Central Bank Independence (henceforthCBI). It is widely documented, that a higher degree of CBI is associatedwith a lower inﬂation rate in developed countries and that society reducesopposition to inﬂation and public pressure for an independent central bank(Cukierman, 2008, 2013; Alesina and Stella, 2010 for a review). The balancebetween ﬂexibility and credibility in monetary policymaking determines theequilibrium degree of CBI in a country. At the same time, the trade-oﬀ be-tween costs and beneﬁts in delegating the power to manage paper money maydepend on many aspects of the economy and on its institutional framework(Alesina and Grilli, 1995).The recognition of this fact has encouraged the study of the determi-nants that inﬂuence the CBI among the variety of economic, social and in-stitutional variables that cause changes in the degree of commitment of themonetary policy1. A possible limitation in the selection of the relevant groupof variables from a large dataset is the omitted variables issue and overﬁt-ting problems, as recently pointed out by Brumm (2011). Random SurvivalForests (henceforth RSF) (Ishwaran et al., 2008) gives us the ﬂexibility touncover complex data structures such as dealing with nonlinear eﬀects andinteractions among multiple types of variables while allowing for eﬀectivepredictions due to the law of large numbers and its two-step randomizationapproach.The main contribution of the present paper is to analyze the importanceof a large number of economic, political and institutional determinants ofCBI. The selection of the most relevant factors from a complete list of 59explanatory variables is done by RSF, allowing any kind of complexity. Ourresults suggest that the economic variables are major determinants comparedto the political ones and that some of the predictors have a strong nonlineareﬀect on CBI.2. Data and MethodologyData on CBI (legal independence index) are from Polillo and Guillem (2005).Economic variables are taken from IMF (2008) and World Bank (2008). Thepolitical ones are taken from the DPI database (Keefer, 2006) of World Bank.Our ﬁnal sample includes 59 variables, 24 OECD countries and spans from1980 to 20032.1See Fernández-Albertos, 2015, D'Amato, Pistoresi, and Salsano, 2009; Farvaque, 2002,for an overview of the empirical studies on economic and political factors.2Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece,2The economic variables are the following. The world-wide componentin the business cycle (i.e. the correlation between the GDP growth in eachcountry and the world or US GDP growth)3; a dummy EMU taking thevalue one in the 1998-2003 period for the countries that joined the EuropeanMonetary Union after complying with the convergence criteria provided forby the Maastricht Treaty; diﬀerent measures of inﬂation (i.e. current/pastinﬂation and past average inﬂation); various measures of development (i.e.log real GDP total and real GDP growth rate)4.The political factors are: variables relevant to the executive power, vari-ables relevant to the parties that make up the legislative power, variables rel-evant to the electoral rules, variables relevant to the stability of the politicalsystem, variables relevant to the checks and balances system, and variablesrelevant to the state form, for instance whether or not it is a federal state5.To select the determinants of the CBI, we apply RSF which is an exten-sion of Breiman's (2001) method. RSF is a highly accurate ensemble treemethod free of distributional assumptions with a uniﬁed approach for clas-siﬁcation, regression and survival settings. Every tree in the forest is grownfrom a bootstrap sample and a random subset of predictors is selected forsplitting at each node. RSF is data-adaptive, applicable to high dimensionalsettings and it provides a theoretically justiﬁed concept for variable selec-tion, known as minimal depth (Ishwaran et al., 2010). The minimal depthis the average depth of the ﬁrst split for each variable over all trees in theforest and it is used to assess a variable's predictiveness. A built-in thresh-old, which is independent of a priori tuning of parameters, is provided forvariable selection6.3. Empirical ResultsTable 1 reports the ranked minimal depth (depth) of the selected variablesfrom RSF analysis of the CBI dataset. The model size turns out to be 10for depth threshold equal to 6.08. Variable importance (vimp) is also pro-Iceland, Ireland, Italy, Japan, Korea, Luxembourg, Holland, New Zealand, Norway, Por-tugal, Spain, Sweden, Switzerland, UK, US.3For the world GDP growth, we use a weighted average of the growth rates of theeconomies in the sample with weights equal to the GDP levels in each country.4Note that to reduce the endogenity problem, we use average GDP correlation 1960-79to analyze the CBI 1980-91 and average GDP correlation 1980-92 to study the CBI 1992-2003. Moreover, we use past average inﬂation 1960-79 and 1980-92 to analyze the CBI1980-91 and CBI 1992-2003, respectively.5Refer to the DPI database for a deﬁnition of each variable included. Note that we usethe same variable deﬁnitions when we comment the results.6Computations were implemented using the freely available R-software package ran-domForestSRC (RStudio Team, 2015, Ishwaran et al., 2007, 2016).3vided conﬁrming depth ordering. The cumulative contribution of the selectedvariables is computed from the normalized variable importance (vimpnorm)(see Grömping, 2009). The variable emu, which mainly reﬂects a change inthe institutional design of monetary policy, accounts as a major determinant(41% of the total variation in CBI), past average inﬂation, business cyclessynchronization and the degree of development for the 16%, 19% and 4%,respectively, while political variables as a whole for the remaining 20%.Furthermore, the marginal eﬀect of each selected variable on the CBI isexamined in Figure 1 and 2. Here the vertical axis displays the predictedCBI, while each predictor is plotted on the horizontal axis. Results look asfollows. The dummy emu suggests that the participation to the Euro (emuequal to 1 in Figure 1) implies a greater CBI: it encourages the individualcountries to change the institutional design of the monetary policy in viewof greater price stability.Additionally, the predicted smoothed curves in Figure 2 suggest the preva-lent positive or negative behavior of the selected variables towards CBI giventhe mean predictor values of each country (ticks at the bottom). We rec-ognize strong nonlinearity of the variable past average inﬂation (denoted byaverageinﬂ), with a dominant negative relation with the CBI (suggested bythe accumulation of points to the left side of averageinﬂ graph in Figure 2).This fact supports the idea stressed by Cukierman (1992) that inﬂation leadsto the evolution of automatic accommodative mechanisms such as indexationof contracts in the labor and capital markets to the general price level. So-ciety reduces opposition to inﬂation and public pressure for an independentcentral bank.Then, an almost linear and positive behavior can be detected for the twovariables regarding synchronization of business cycles (world cycle and usacycle). In fact, the larger the size of the common component in the businesscycle in the countries, the larger the CBI. To understand this result, considerthat governments expect their economies to be in the same state of the worlds(boom or slumps) as foreign economies. Governments in each country havea strategic incentive to commit monetary policy in order to free ride on thestabilization provided abroad and gain credibility at home. Hence, the largerthe correlation among shocks, the larger the incentives to commitment, i.e.the larger the CBI (see D'Amato and Martina, 2005).From the point of view of the inﬂationary bias approach to monetarypolicy, the impact of per capita GDP is not clear-cut. We ﬁnd that the realGDP per capita (logrealgdp) is linearly and positively linked to CBI. On theone hand, a higher level of per capita income level entails a lower degreeof (real and ﬁnancial) market failures in the economy, a more eﬃcient ﬁs-cal system and therefore a lower incentive to create inﬂation for the central4banker. On the other hand, economic agents in high-income countries mightbe better hedged against inﬂation; hence, their inﬂation aversion may belower (Campillo and Miron, 1997). Opposite eﬀects on the inﬂationary biasin monetary policy entail opposite eﬀects on the incentives to precommitmonetary policy. We consider the real GDP per capita as an indicator of ageneral measure of development. In Romer (1993) a larger per capita GDPhas a negative impact on inﬂation, i.e. lower inﬂationary bias. The reducedinﬂationary bias lowers the incentive to commit with negative impact on thelevel of independence of the central bank. Lane (1997) and Campillo andMiron (1997) obtain a positive sign for the log per capita GDP on averageinﬂation. Hence, our outcome is not consistent with the commitment inter-pretation of the results in Romer (1993), but it is in line with Campillo andMiron's (1997) argument.Also the relationship between political instability and the level of depen-dence is not clear-cut in the commitment literature. On the one hand, thehigh variability of the political environment may imply a lower ability toachieve commitment of monetary policy through delegation to an indepen-dent institution. On the other hand, a larger political instability may increasethe beneﬁts to commitment. From an empirical point of view, the relationbetween political instability and CBI is ambiguous and it mainly dependson the variable used to proxy instability. For example, Cukierman (1992)predicts and empirically veriﬁes that a high level of party political instabilityinduces a larger level of independence, whereas the regime political instabil-ity has a negative eﬀect on CBI7. Broadly speaking, the literature on thepolitical economy approach to CBI suggests that a politically heterogeneouscontext (federal systems, strong systems of checks and balance, coalitionand multiparty governments) pushes for the adoption of independent centralbanks (see Fernández-Albertos, 2015).Among the political variables, we ﬁnd relevant the following: the meandistrict magnitude (mdmh), the number of government and opposition seats(numgov and numopp), the number of seats of the largest government partyand of the largest opposition party (gov1seats and opp1seats).An increase in district magnitude induces a higher CBI, given the accu-mulation of country-points in the ﬁrst bit of the curve. The rationale behindthis outcome is that an increase in district magnitude tends to increase thenumber of parties and party system fragmentation (Rae, 1995); so that thelarger the heterogeneity in policy preferences, the larger the CBI.7A partial list of similar studies, in which diﬀerent measure of political instability andseveral indices of CBI are used, includes De Haan and Van't Hag (1995), Habibi andBagheri (1997) and Farvaque (2002).5Series depth vimp vimpnormemu 1.444 0.028 0.408averageinﬂ 3.012 0.011 0.158world cycle 3.340 0.007 0.100usa cycle 3.623 0.006 0.092mdmh 4.259 0.005 0.069numgov 4.705 0.004 0.051logrealgdp 5.392 0.002 0.035gov1seat 5.482 0.003 0.036numopp 5.554 0.002 0.026opp1seat 6.001 0.002 0.023Table 1: Minimal depth and variable importance (denoted by vimp, vimpnorm whennormalized) obtained from RSF analysis of CBI dataset. The latter includes 59 variablesfor 24 OECD countries and spans from 1980 to 2003, as described in Section 2. Theselection of 10 variables comes from a depth threshold equal to 6.08.In the same direction goes the outcome on government and oppositionparties. The larger the number of government seats, which could imply alarger number of governing parties, makes policy making diﬃcult and inducesa greater incentive to delegate to an independent central bank. A similarargument holds for the number of opposition seats. Moreover, the largerthe ﬁrst government party, the smaller the CBI, while the larger the ﬁrstopposition party, the greater the CBI. This is even more true when takinginto account the relative weight in term of seats' number of these two parties,focusing on the nonlinear behavior in Figure 2. In fact, up to about 100 seatsthe eﬀect on CBI is positive (resp. negative) for gov1seat (resp. opp1seat)while it is negative (resp. positive) for a number larger than 100. Therefore,in general, the larger the fragmentation of government or party system, thelarger the CBI index.4. ConclusionIn this paper we implemented random survival forests to correctly identifythe main economic and political determinants of the CBI index. Some possi-ble limitations of the linear regression framework, which is usually employedto study this problem, have been overcomed using this technique. The anal-ysis shows that the selected economic variables account for the 80% of thevariation in CBI, while the ones reﬂecting party system's fragmentation forthe remaining 20%. Particularly, two-third of the explained variation due6Figure 1: Marginal eﬀect plot of the dummy variable emu on the CBI index.to the economic group is attributed to external constraints, that is, interna-tional business cycle and the participation to EMU. Both of them induce alarger incentive to commit to an independent central bank.Acknowledgments M. Cavicchioli and B. Pistoresi gratefully acknowledge ﬁnancial sup-port from PRIN-MIUR Grant 2010J3LZEN-003 and the research grant FAR 2014 (pro-vided by University of Modena and Reggio E., Italy).References[1] Alesina, A.F., and Stella, A. (2010) The politics of monetary policy,National Bureau of Economic Research (No. w15856).[2] Alesina, A.F., and Grilli, V. (1995) The European Central Bank: re-shaping monetary politics in Europe, in Monetary and Fiscal Policy,Vol. 1: Credibility, edited by Torsten Persson and Guido Tabellini,247-277, The MIT Press, Cambridge MA.[3] Breiman, L. (2001) Random Forests, Machine Learning 45(1), 5.[4] Brumm, H.J. (2011) Inﬂation and central bank independence: Two-waycausality?, Economics Letters 111(3), 220-222.[5] Campillo, M., and Miron, J.A. (1997) Why does inﬂation diﬀer acrosscountries?, in Reducing inﬂation: Motivation and strategy, 335-362,University of Chicago Press.75 10 15 20 25 300.20.40.60.8averageinflPredicted Pollilo−0.2 0.0 0.2 0.4 0.6 0.80.20.40.60.8WORLD.CYCLEPredicted Pollilo−0.2 0.2 0.4 0.6 0.8 1.00.20.40.60.8USA.CYCLEPredicted Pollilo0 50 100 1500.20.40.60.8mdmhPredicted Pollilo0 100 200 300 4000.20.40.60.8numgovPredicted Pollilo24 26 28 300.20.40.60.8log_realgdpPredicted Pollilo0 100 200 300 4000.20.40.60.8gov1seatPredicted Pollilo0 50 150 250 3500.20.40.60.8numoppPredicted Pollilo0 50 100 150 200 2500.20.40.60.8opp1seatPredicted PolliloFigure 2: Marginal eﬀect plots of the predictor variables avergeinﬂ, world cycle, usacycle, logrealgdp, mdmh, numgov, numopp, gov1seat, opp1seat on the predicted CBI indexshown by the curves. Ticks on the horizontal axis correspond to the mean predictor valuesfor each country.8[6] Cukierman, A. (1992) Central Bank Strategy, Credibility, and Indepen-dence: Theory and Evidence, The MIT Press, Cambridge MA.[7] Cukierman, A. (2008) Central Bank Independence and monetary pol-icymaking institutions - past, present and future, European JournalPolitical Economy 24, 722-736.[8] Cukierman, A. (2013) Monetary policy and institutions before, during,and after the global ﬁnancial crisis, Journal of Financial Stability 9(3),373-384.[9] D'Amato, M., and Martina, R. (2005) Credibility and commitment ofmonetary policy in open economies, European Journal of Political Econ-omy 21(4), 872-902.[10] D'Amato, M., Pistoresi, B. and Salsano, F. (2009) On the determinantsof central bank independence in open economies, International Journalof Finance & Economics 14, 107-119.[11] De Haan, J., and Van't Hag, G.J. (1995) Variation in central bankindependence across countries: some provisional empirical evidence,Public Choice 85(3-4), 335-351.[12] Fernández-Albertos, J. (2015) The politics of Central Bank indepen-dence, The Annual Review of Political Science 18, 217-237.[13] Farvaque, E. (2002) Political determinants of Central Bank Indepen-dence, Economics Letters 77, 131-136.[14] Grömping, E. (2009) Variable Importance Assessment in Regression:Linear Regression versus Random Forest, American Statistical Associ-ation 63:4.[15] Habibi, N., and Bagheri, F. M. (1997) Political Institutions and CentralBank Independence: A Cross Country Analysis, No. 9703.[16] IMF (2008), World Economic and Financial Surveys, World EconomicOutlook Database, access march 2009.[17] Ishwaran H., and Kogalur U.B. (2007) Random survival forests for R,R News 7(2), 25-31.[18] Ishwaran, H., Kogalur, U.B., Blackstone, E.H. and Lauer, M.S. (2008)Random Survival Forests, The Annals of Applied Statistics 2(3), 841-860.9[19] Ishwaran, H., and Kogalur, U.B. (2010) High-Dimensional VariableSelection for Survival Data, Journal of the American Statistical Asso-ciation 105(489), 205-217.[20] Ishwaran, H., and Kogalur, U.B. (2016) Random Forests for Survival,Regression and Classiﬁcation (RF-SRC), R package version 2.0.7.[21] Keefer, P. (2006) Database of political institutions (DPI): changes andvariable deﬁnitions, Development Research Group, World Bank.[22] Lane, P. (1997) Inﬂation in Open Economies, Journal of InternationalEconomics 42, 327-347.[23] Polillo, S., and Guillén, M. (2005) Globalization pressures and the State:the worldwide spread of Central Bank independence, American Journalof Sociology 110, 1764-1802.[24] Rae, D.W. (1995) Using district magnitude to regulate political partycompetition, the Journal of Economic Perspectives 9(1), 65-75.[25] Romer, D. (1993) Openness and Inﬂation: Theory and Evidence, Quar-terly Journal of Economics 108, 869-903.[26] RStudio Team (2015) RStudio: Integrated Development for R, RStudio,Inc., Boston, MA. URL: http://www.rstudio.com/.[27] World Bank (2008) World Development Indicators - WDI online. Avail-able at http://databank.worldbank.org/ddp/home.do.10

Determinants of Central Bank independence: a random forest approach

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Determinants of Central Bank independence: a random forest approach

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Archivio istituzionale della ricerca - Università di Modena e Reggio Emilia

Archivio istituzionale della ricerca - Università di Modena e Reggio Emilia