Springer Texts in Business and Economics Maksym Ivanyna Alex Mourmouras Peter Rangazas The Macroeconomics of Corruption Governance and Growth Springer Texts in Business and Economics More information about this series at http://www.springer.com/series/10099 Maksym Ivanyna • Alex Mourmouras Peter Rangazas The Macroeconomics of Corruption Governance and Growth Maksym Ivanyna Joint Vienna Institute Vienna, Austria Alex Mourmouras Washington, DC, USA Peter Rangazas IUPUI Economics, CA 518 Indianapolis, IN, USA The password protected Solutions Manual is available online at http://www.springer.com/us/book/9783319686653 ISSN 2192-4333 ISSN 2192-4341 (electronic) Springer Texts in Business and Economics ISBN 978-3-319-68665-3 ISBN 978-3-319-68666-0 (eBook) https://doi.org/10.1007/978-3-319-68666-0 Library of Congress Control Number: 2017954933 # Springer International Publishing AG 2018 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface This book examines the reasons why governments fail to live up to their responsibilities or worse engage in outright corruption We focus on the quality of governance because of its importance in real-world policy making and because it serves to motivate the development and application of macroeconomic models of political economy The book can be viewed as macroeconomic theory mixed with applied fiscal policy analysis We especially concentrate on the tendencies of the government to burden future generations rather than invest in them and the consequences that this has for long-run economic growth We present the underlying theories in a serious but self-contained fashion, accessible to anyone who has a background in intermediate-level microeconomics A thorough appendix is provided with the necessary technical background to insure that all those who wish to follow the analysis carefully will be able to so Each chapter includes exercises to refine understanding and sharpen modeling skills Solutions to the exercises can be found on the Springer.com page for the book As suggested, the thinking in the book is guided and disciplined by formal economic models Formal models are needed, not only to articulate, explain, and quantify the effects of government corruption and short-sighted policies but also to demonstrate how economics is intertwined with politics For example, we use models to argue that the policies generating the looming fiscal crisis in the developed world are closely connected to other common economic problems: the slowdown in economic growth, the rise in wage inequality, and the exploding costs of medical care and higher education Most of the basic ideas are illustrated using a two-period model that shows the future cost of fiscal policies that favor present consumption and misallocate investment (Chap 2) The more subtle and advanced issues are examined and quantified using the overlapping-generations model of economic growth (Chap 4) These base models, first used to demonstrate the fundamental mechanisms of economic growth, are then extended to incorporate politics and the behavior of public officials (Chaps 3, 5, and 6) The new political economy of macroeconomics can be technically difficult and conceptually challenging.1 We sacrifice full generality to incorporate the relevant thinking from the political economy literature as simply as possible while adding a few new twists along the way The final product offers a unified explanation for the causes and consequences of government failure, the v vi Preface fiscal crisis, growth slowdowns, and rising inequality The needed policy reforms that emerge from the analysis are also discussed in detail (Chap 7) We have used the text with undergraduates by taking a slow pace, making use of the background material in the technical appendix, and assigning easier questions and problems For example, we have based an intermediate macroeconomics course on Chap (Sects 2.1, 2.2, 2.3, 2.4, and 2.10), Chap 4, and Chap In graduate courses, we go through the material in Chaps and more quickly; mix in some political economy from Chaps 3, 5, and 6; and hold the students responsible for the harder problems For researchers, the more original material proposes common causes of the Big Three economic problems facing the developed world (Sects 2.4 and 4.8, and Chap 7), models the cultural connection between tax evasion and corruption (the portion of Chap that summarizes our 2016 Economic Inquiry article), and extends this model to include the interaction between tax evasion, corruption, and public debt (Chap 6) The book has benefited from the comments and assistance of three excellent young scholars: Mark Giblin, John Hanks, and Stephen Rangazas We are grateful that they took an interest in the project and devoted their time to improving the exposition and clarity of the text Vienna, Austria Washington, DC, USA Indianapolis, IN, USA Maksym Ivanyna Alex Mourmouras Peter Rangazas Contents Introduction 1.1 Corruption 1.2 Close Cousins: Kleptocracy, Corruption, and Rent-Seeking 1.3 Modeling the Government 1.3.1 Focus on the National Interest 1.3.2 Efficiency of Resource Use 1.3.3 Limit Economic Disparity 1.3.4 Value Future Generations 1.4 Tax Evasion 1.5 Taxation and Government Debt 1.5.1 Endogenous Tax Rates 1.5.2 Endogenous Government Debt 1.6 Economic Growth 1.7 Modeling the Culture of Corruption 1.8 The Big Three: Growth Slowdown, Wage Inequality, and Fiscal Crisis 1.9 Policy Reforms 1.10 Outline 1.11 Exercises References 8 8 11 14 15 15 18 19 20 22 24 25 27 Two-Period Model of Government Investment 2.1 The Life-Cycle Model of Consumption and Saving 2.1.1 Borrowing Constraints 2.2 Introducing the Government 2.2.1 Taxes and Government Investment 2.2.2 Public Debt and Government Investment 2.3 The Small-Open Economy Model 2.3.1 Private and Public Credit 2.3.2 Only Public Credit 2.4 Human Capital, Inequality, and Public Debt 2.5 Public Capital and Productivity 31 32 34 35 36 37 38 39 41 43 46 vii viii Contents 2.6 2.7 2.8 Pure and Impure Public Capital The Allocation of Public Capital Fiscal Federalism 2.8.1 Tax Financing of Regional Investment 2.8.2 Bond Financing of Regional Investment 2.9 A Note on Migration 2.10 A Dynamic Generational Model 2.10.1 The Growth Model 2.10.2 The Investment Share 2.11 Principles for Tax Collection 2.12 Conclusion 2.12.1 Basic Principles 2.12.2 Regional Issues and Inequality 2.12.3 Identifying the Influence of Politics 2.13 Exercises References 47 49 52 52 54 56 57 58 60 62 62 62 63 63 64 70 Politics and Corruption in the Two-Period Model 3.1 Fiscal Policy with Policy Makers 3.2 The Politics of Investment Allocation 3.3 Fiscal Federalism with Politics 3.3.1 Extending the Fiscal Federalism Model 3.3.2 No Political Influence 3.3.3 Equilibrium with Political Influence 3.3.4 A Note on Decentralization 3.4 Foreign Funding and Regional Inequality 3.4.1 Foreign Funding for the Poor Region 3.4.2 Focusing on Corruption 3.5 Political Polarization 3.5.1 Polarization and Deficit Bias 3.5.2 Public Investment 3.5.3 Fiscal Rules 3.6 Interest Groups and Rent Seeking 3.6.1 Cooperative Solution 3.6.2 Non-cooperative Solution 3.6.3 Foreign Aid 3.7 Determinants of Corruption 3.7.1 Behavior of a Public Official 3.7.2 Equilibrium Corruption 3.7.3 Further Issues to Be Resolved 3.8 Conclusion 3.9 Exercises Appendix References 73 75 77 81 81 83 84 86 87 87 89 89 89 91 93 94 96 96 99 100 101 102 102 103 104 107 108 Contents Overlapping-Generations Model of Economic Growth 4.1 Firms, Production, and the Demand for Capital 4.2 Household Saving and the Supply of Capital 4.2.1 The Supply of Labor and Capital 4.2.2 Household Saving 4.2.3 Supply of Capital per Worker 4.3 Competitive Equilibrium in a Growing Economy 4.3.1 Steady State Growth—Technical Progress 4.4 Quantitative Theory 4.4.1 Calibration 4.4.2 Historical Simulation 4.5 Introducing the Government 4.5.1 The Fiscal Gap 4.5.2 Government Capital and Private Production 4.5.3 Households with Taxes and Transfers 4.5.4 Capital Market Equilibrium and Fiscal Policy 4.6 Fiscal Policy 4.6.1 Government Purchases–Consumption 4.6.2 Government Purchases–Consumption and Investment 4.6.3 Intergenerational Policy 4.6.4 Debt Policy #1 4.6.5 Debt Policy #2 4.6.6 Government Pensions—Fully Funded 4.6.7 Government Pensions—Pay-As-You-Go (PAYG) 4.7 Capital Accumulation in an Open Economy 4.7.1 Open Capital Markets and Growth in Developing Countries 4.8 The Fiscal Crisis 4.8.1 The Fundamentals 4.8.2 The Politics 4.9 Generational Accounting 4.10 Exercises Appendix The Government Intertemporal Budget Constraint Tax Rates References Politics, Corruption, and Economic Growth 5.1 Government: Benevolent Dictator or Kleptocrat? 5.1.1 Firms 5.1.2 Households 5.1.3 Capital Market Equilibrium 5.1.4 Government 5.1.5 Steady State Equilibria and Income Gaps ix 111 112 116 116 117 118 119 122 123 125 127 129 131 131 132 133 133 134 135 136 137 138 138 139 139 140 142 144 145 146 148 155 155 156 157 159 162 162 162 163 163 166 290 Technical Appendix analogous to the one variable case We illustrate the approach in the situation where there are two choice variables In this case, the net benefit function has two arguments, x1 and x2, and is written as ~f ðx1 ; x2 Þ The derivative of ~f ðx1 ; x2 Þ with respect to each choice variable can be taken, one at a time These types of derivatives are called partial derivatives—they give the change in the function due to a change in one of the arguments, holding all other arguments constant One way of reinforcing the notion and the mechanics of taking a partial derivative is to think of a function with a single argument created from ~f ðx1 ; x2 Þ This is done by holding x2 constant When x2 is fixed at a certain value, it simply becomes a constant part of the newly defined function For example,À if weÁthink of x2 as fixed at the value x2 , we can define the new function hðx1 Þ  ~f x1 ; x2 The partial derivative of ~f ðx1 ; x2 Þ with respect to x1 is then defined as ~f x1  h0 ðx1 Þ or, ∂~f using a different notation, as  h0 ðx1 Þ The second notation is a bit clumsy, but ∂x1 it is clearer in dynamic models where subscripts are used to denote time periods Both types of notation are frequently used Of course, the same procedure can be used to define the partial derivative with respect to x2 The partial derivatives are themselves typically functions of x1 and x2 and so they can be differentiated to get the second partial derivatives There is a way of checking for the concavity of ~f ðx1 ; x2 Þ that involves the second partial derivatives This check is a bit complicated, so you need to trust that when we maximization problems in the text, that we are using concave functions However, if you build your own original models, you need to research the different ways of checking for concavity of functions with multiple choice variables If you are sure that ~f ðx1 ; x2 Þ is a strictly concave function of x1 and x2, then you can identify the maximizing choices of x1 and x2 using the first order conditions in a manner perfectly analogous to the case with a function of just one variable The first order conditions simply set the partial derivatives equal to zero, ∂~f ∂~f ¼ and ¼ 0: ∂x1 ∂x2 EXAMPLES FROM THE TEXT In Chap 4, the Cobb-Douglas production function is introduced, Y t ¼ AK tα L1Àα , t where Y denotes output, K denotes the capital stock rented, L denotes the hours of work hired, and where A > and < α < 1are technological parameters The marginal product of an input is the increase in output that results from an increase in the use of an input Formally, it is the partial derivative of the production function with respect to a particular input, holding other inputs constant For a Cobb-Douglas production function, the marginal product of labor and the marginal Technical Appendix 291 ∂Y t ∂Y t ¼ ð1 À ịAK t L ẳ AK L1 (see the rules t and t t ∂Lt ∂K t for differentiating power functions given above) These expressions can be simplified somewhat by using algebra to write them in terms of the capital intensity, kt  Kt/Lt The simplified expressions for the marginal products are, Y t Y t ẳ ịAkt and ¼ αAkαÀ1 (see the algebra rules for manipulating t ∂Lt ∂K t expressions with exponents given above) We assume that markets are perfectly competitive in our production economy As discussed in elementary economics, the notion of competitive markets applies not only to the markets for goods but also to the factor markets for labor and capital The competitive assumption applied to the factor markets means that firms demand inputs to maximize profits taking as given the market prices of the inputs: the wage rate paid to labor (w) and rental rate on physical capital (r) No single firm is large enough to be able to influence market prices when they unilaterally change their production or input levels The price of the economy’s single output good is taken to be one So we can think of output and revenue as being the same Given the competitive assumptions, the profit function can then be written as Yt À wtLt À rtKt Just as in the one-variable case, maximizing profits requires that firms hire capital and labor as long as the marginal benefit (marginal product) exceeds the marginal cost (factor price) Formally, the necessary first order conditions for profit maximization are product of capital are Ak1 ẳ rt t ịAkt ¼ wt : Constrained Maximization with Multiple Choice Variables Let’s extend the discussion from the previous section to the case where f(x1, x2) is a strictly concave function of x1 and x2, but where the choice variables have to satisfy a resource constraints of the general form F(x1, x2) ¼ E, where E is a positive constant When resource constraints are present, there is a very important method that generates the first order conditions for the maximizing values of x1 and x2 It is called the Lagrangian Method , named after its inventor, the mathematician JosephLouis Lagrange He showed that the first order conditions that must be satisfied by the maximizing values of x1 and x2 are ∂f ∂F ∂f F ẳ , ẳ , and Fx1 ; x2 ị ¼ E, ∂x1 ∂x1 ∂x2 ∂x2 where λ is a variable called the Lagrange multiplier 292 Technical Appendix The first order conditions are easy to remember because they can reproduced by maximizing the Lagrangian function, L(x1, x2, λ) ¼ f(x1, x2) ỵ [E F(x1, x2)] with respect to x1, x2, λ In other words, treat L as any other function and find the maximizing values by setting the partial derivatives of L to zero, ∂L ∂L ∂L ¼ 0: ¼ 0, ¼ 0, and ∂x1 ∂x2 ∂λ These three equations, when written out and rearranged algebraically, are exactly the three equations stated above EXAMPLES FROM THE TEXT In Sect 2.3 from Chap 2, households maximize their lifetime utility by choosing the optimal consumption path over their two periods of life subject to their lifetime budget constraint Matching the household’s problem with the general set-up above we have f x1 ; x2 ị  ln c1 ị ỵ ln c2 ị, Fx1 ; x2 ị ẳ c1 ỵ c2 , and E  y1 ỵ r where we have set y2 ¼ g2 ¼ only for simplicity; we could have proceeded just y2 fine by defining E ẳ y1 ỵ 1ỵr g2 , as in the text The Lagrangian function in our application is   c2 Lc1 ; c2 ; ị ẳ ln c1 ị ỵ ln c2 ị ỵ y1 c1 : ỵ r Differentiating and setting the partial derivatives equal to zero, gives us β λ c2 ẳ , ẳ , and c1 ỵ ẳ y1 , c1 c2 ỵ r ỵ r (see the rules above for differentiating the natural log function given above) Solving these three equations for the three unknowns (c1 , c2 , λ), yields the optimal consumption demand functions and a value for the Lagrange multiplier, c1 ¼ A.3 y1 ỵ r ịy1 1ỵ , c2 ẳ , ẳ : y1 1ỵ 1ỵ Nonnegativity Constraints and Corner Solutions The choice variables of economic agents are often restricted to be nonnegative values The optimization approach taken in Sect A.2 does not explicitly acknowledge this type of constraint on the choice variables In many situations this is not a problem because, given the choice variables and the particular functions chosen, the optimal solutions naturally come out to be positive values However, in some Technical Appendix 293 applications it is quite possible that some of the unconstrained optimal choice variables may take on negative values This is not the proper solution if there are economic constraints preventing that possibility Fortunately, the Lagrangian method can be modified to account for nonnegativity constraints The first order conditions with nonnegatvity constraints on x1 and x2 are (i) (ii) ∂L ∂x1 ∂L ∂x2 0, x1 ! 0, 0, x2 ! 0, and (iii) ∂L ∂λ ¼ 0: where in (i) and (ii), at least one of the inequalities must be a strict equality In the situation where the optimal variables of both choices variables is strictly positive, ∂L ∂L then x1 > and x2 > 0, so by the rule just stated ∂x ¼ and ∂x ¼ 0, exactly as in the case where nonngegativity constraints are not accounted for However, if an unconstrained choice of, say x1, turns out to be negative, then the nonnegativity constraint binds and we have ∂L < 0, x1 ¼ 0: ∂x1 This condition can be interpreted intuitively in the following way Begin by ∂L thinking of ∂x as the marginal net benefit of increasing the value of x1 (note that the ∂L Lagranian function incorporates both benefits and costs) If at x1 ¼ 0, ∂x > 0, then the marginal benefit is positive and it is rational to increase x1 above zero However, ∂L < 0, then it is rational to reduce x1 below zero in order to cause the total net if ∂x benefit to rise If this is not permitted, then the best the decision maker can is set x1 ¼ Because x1 ¼ is at the end or at the “corner” of the permissible choices for x1, this is referred as a corner solution EXAMPLES FROM THE TEXT In Sect 2.3 from Chap 2, we consider the possibility of borrowing constraints, which are nonnegativity constraint on asset accumulation We assume that the market for private international loans does not exist and then consider situations where the government may or may not be able to borrow and lend in international markets In this situation the household would like to set s < i.e they would be better off choosing negative saving but are restricted from doing so They are at a corner solution with s ¼ The single-period private budget constraints of the credit-constrained household are, 294 Technical Appendix c1 ¼ ð1 ịy1 ẳ y1 g2 ỵ b2 c2 ẳ ịy2 ẳ y2 ỵ r∗ Þb2 , where we have used the government budget constraints in each period to express the private budget constraints in terms of g2 and b2 The government may be able to relieve the credit constraint if they can borrow in international loan markets, i.e if they are able to choose a positive value of government debt, b2 > To make the government’s problem fit the theory of optimization with nonnegativity constraints, let’s introduce government saving, s2g ¼ Àb2 If the government lends in international markets, then b2 < 0, s2g > g and if they borrow in international markets, then b2 > 0, s2 < The household budget constraints can be rewritten in terms of government saving as g c1 ẳ ịy1 ¼ y1 À g2 À s2 c2 ¼ ð1 À ịy2 ẳ y2 ỵ ỵ r ịs2 : g The À benevolent Á government chooses Á g2 and s2g to maximize À g ∗ g U ¼ ln y1 g2 s2 ỵ ln y2 þ ð1 þ r Þs2 If other countries will accept loans from the government but will not lend to the government, then the government faces the nonnegativity constraint, s2g ! The first order conditions for the government problem are, βμAgμÀ1 À ¼0 c1 c2 β ð1 þ r ∗ Þ À c2 c1 g 0, s2 ! 0: g If b2 < 0, s2 > 0, the government is a lender, and we get the efficient solution given by (13) from the text, ¼ þ r∗ μAgμÀ1 c2 ¼ βð1 þ r ∗ Þ: c1 This would also be the solution if the government could freely borrow and thus doesn’t confront the nonnegativity constraint g If, however, the government would prefer b2 > 0, s2 < 0, but no country or international institution will lend to it, then we have the constrained solution Technical Appendix 295 βμAgμÀ1 À ¼0 c1 c2 ỵ r ị < 0, s2g ¼ 0, c2 c1 which implies μAgμÀ1 > þ r ∗ Government investment is inefficiently low because the marginal product of public capital is greater than the cost of borrowing A.4 Total Differentials and Linear Approximations If y ¼ f(x1, x2) is a differentiable function of x1 and x2, one can define the total differential of f as dy ẳ f f dx1 ỵ dx2 , ∂x1 ∂x2 where dy, dx1, and dx2 are real variables that are interpreted as “changes” in the original variables The concept of the total differential extends naturally to the case where the function has many arguments or independent variables If one imagines that the total differential is taken at a particular point where x1 ¼ x1 and x2 ¼ x2 , then it can be related to the notion of a linear approximation of f(x1, x2), Á ∂f À Á Á À ∂f À y ¼ f x1 ; x2 þ x1 ; x2 dx1 þ x1 ; x2 dx2 , ∂x1 ∂x2 where dx1 and dx2 are interpreted as deviations from the values x1 ¼ x1 and x2 ¼ x2 , and the partial derivatives are evaluated at the point ( x1 , x2) Note that,Àanalogous to Á the interpretations of dx1 and dx2, it is natural to think of dy as y À f x1 ; x2 EXAMPLES FROM THE TEXT In Sect 4.6 from Chap 4, we analyze the nonlinear transition function for private capital accumulation ktỵ1 ẳ t ịwt t ịwt ỵ ztỵ1 =Rt btỵ1 : 1ỵ The transition equation cannot be solved explicitly for kt ỵ because of the nonlinear effect of kt ỵ on Rt However, we can easily a qualitative analysis of how introducing different fiscal policies affect capital accumulation by taking the total differential of the transition equation from an initial position with zt ¼ 0, so that a small change in Rt has no effect on the right-hand-side 296 Technical Appendix Begin by thinking of the transition equation as being a function of the fiscal variables, t , zt ỵ , bt ỵ Now take the total differential with respect to the fiscal variables, dktỵ1 ẳ wt dt wt dt ỵ dztỵ1 =Rt dbtỵ1 , 1ỵ for a given value of wt and where the initial value of zt ỵ is zero The total differential can be used to examine the qualitative effects of small changes in fiscal policy from this particular initial position A.5 L’Hospital’s Rule On occasion one encounters a ratio of functions or expressions that take on an indeterminate form at a point of interest An indeterminate form is one where the ratio becomes 00 or 1 In some cases indeterminate forms actually have a determinate value that is simply not immediately obvious L’Hospital’s Rule indicates when this might be true The rule says that if you have two differentiable expressions, f(x) and h(x), and at a particular value of x, say x ẳ x0, the ratio hf xxịị takes an indeterminate form, then f ð xÞ x!x0 hðxÞ lim f xị h x!x0 xị ẳ lim The result is useful because sometimes the ratio of derivatives has a determinate form EXAMPLES FROM THE TEXT In Sect 2.10 of Chap 2, we introduced a more general lifetime utility function with a single period utility flow from consumption of the form,   1À1=σ ct À1 : ut ¼ ð1 À 1=σ Þ The motivation for needing a more general utility function is provided in the text, but part of the reason for its unusual form is to allow the logarithmic utility function, that we use in most of our models, to appear as a special case Using L’Hospital Rule one can show that ut ¼ ln ct, when σ ¼ To see this, first note that when σ ¼ 1, the utility function has the indeterminate form 00 Second, we need to use the result that the exponential function and the natural log functions are inverses of each other, i.e xa ¼ ea ln x This means we can 1À1=σ write ct as eð1À1=σÞ ln ct Third, the rule for differentiating the exponential function f(x) ¼ eax, is f (x) ¼ aeax Finally, to apply the result, think of the expressions in the numerator and the denominator as functions of σ Now, we can write utility as Technical Appendix 297 À Á eð1À1=σ Þ ln ct À : ut ¼ ð1 À 1=σ Þ Differentiating the numerator and the denominator with respect to σ and then taking the ratio of the two derivatives gives σ2 ln ct eð1À1=σ Þ ln ct ẳ ln ct e11=ị ln ct : At ¼ 1, the ratio is ut ¼ ln ct, because e0 ¼ A.6 Expected Utility In applications where the future is uncertain, economists often take an expected utility approach For concreteness in developing this concept, suppose there are m possible states of nature in the future that affect the level of income and consumption possibilities of our two-period households From the perspective of the current period, period 1, the expected lifetime utility is EU ẳ ln c1 ỵ E ln c2 , where E is the expectation operator that indicates an expected value is being taken over all possible future values of second period consumption To be even more explicit, let π i denote the probability that state i occurs Define c2i as the value of consumption in state i We can then write E ln c2 ¼ m X À Á π i ln c2i : i¼1 Given this definition, the household or government can choose variables in period (e.g household saving, government investment, or government borrowing) knowing that there is also some random variable that affects the resulting value of future consumption (e.g the interest rate on saving or the return to government investment) Essentially the same optimization procedure can be used as in the certainty case, with the complication that the return to the first period choice will vary across the different states of nature EXAMPLES FROM THE TEXT Section 3.5 contains a model where the current government makes transfers of income to two different household types, labeled P and R The government is altruistic in the sense that it values, possibly differently, the utility of the two household types Uncertainty enters because the current government is unsure that it will be re-elected to serve in the future period The uncertainty matters because the government must decide how much to borrow in the current period and 298 Technical Appendix its choice will impact the ability to finance transfers in the future (the more that is borrowed, the more funds that must be used to repay debt in the future) So, the government makes its current period transfers, and the associated debt policy, based on the expected consequences of its actions into the future In the text, we focus on the case where there is complete political polarization One party cares only about the R-households and the other party cares only about the P-households If the party supporting the R-households is currently in power, its expected utility function is ln c1R ỵ E ln c2R , where the expectation is taken over the two political states of nature—the current party is re-elected or not For example, if the probability of being re-elected is ½, we have ln c1R ỵ E ln c2R ẳ ln c1R ỵ β ln c2R : The choices of the R-government in the current period are modeled to maximize this objective function using the same optimization approach as in the certainty case A.7 Game Theory and Nash Equilibrium There are (game theoretic) settings where an individual agent’s (player’s) optimal choice (action) depends on the optimal choice of others in a direct way, rather than simply indirectly through the competitive market price In this case, each agent must form an optimal choice function that is contingent on the choices of others (a best response function) In addition, it is often assumed that there is no cooperation between agents Each agent arrives at his choice without bargaining or colluding with other players (a non-cooperative game) A commonly used equilibrium notion in this type of non-cooperative game is one where (i) each player simultaneously forms a best response based on beliefs about what other players choose and (ii) those beliefs turn out to be correct This type of equilibrium is called a Nash Equilibrium, named after the Nobel Prize winning mathematician, John Nash EXAMPLES FROM THE TEXT Section 3.6 contains a model where different interest groups lobby the government for transfers The groups not coordinate their decisions, i.e each group chooses its rent-seeking activity taking the others’ behavior as given The central government and the different interest groups play a non-cooperative Nash game, where all actions are taken independently and simultaneously The economic problem with this type of uncoordinated equilibrium is that households act under the belief that most of the marginal tax burden of raising Technical Appendix 299 their transfers can be passed off to other groups So, each group acts like the financing of a marginal dollar of transfers is less expensive than it actually is In the end, the tax rate must adjust to reflect all the transfer requests This is known as the common pool (of tax revenue) problem A.8 Quadratic Equations Some equations in the unknown variable x can be written in the following quadratic form ax2 ỵ bx ỵ c ẳ 0, where a 6ẳ Mathematically, there are two solutions for x that satisfy the equation, although one or both may not make sense as solutions to an economic problem The mathematical solution are given by the quadratic formula, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Àb Ỉ b2 À 4ac : x¼ 2a EXAMPLES FROM THE TEXT Section 2.10 derives a transition equation for government capital,   1ị1ị gtỵ1 þ gtþ1 ¼ Γyt ¼ ΓAgtμ , where Γ  (βμ)σ Aσ À In general, there is no explicit solution for gt ỵ One of the situations where an explicit solution is available, is when σ ¼ (2 À μ)/(1 À μ) In this case, the transition ðσÀ1Þð1ÀμÞ equation becomes a quadratic equation in gt ỵ because gtỵ1 ẳ gtỵ1 The transition can then be written in quadratic form as g2tỵ1 ỵ gtỵ1 Agt ẳ 0: The solutions from the quadratic formula are pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ÀΓ ặ ỵ 4Agt , gtỵ1 ẳ but clearly there is only one positive solution that makes sense in the economic application Solving for the only positive root gives us the following transition equation, 300 Technical Appendix gtỵ1 A.9 ẳ q  ỵ 4Agt =Γ À : Infinite Series A sequence is an ordered list of terms, a0 , a1 , a2 , Á , Á , Á , an A special case of a sequence is one where consecutive terms have the same ratio, known as a geometric sequence This is possible when the terms of the sequence have a common base value that is raised to an increasing power as follows: a0 ¼ a0 ¼ , a1 ¼ a1 ¼ a , a2 ¼ a2 , a3 ¼ a3 , Á , Á , Á , an ¼ an So the ratio of consecutive terms is always a Of more direct interest to us is the sum of a geometric sequence known as a geometric series, defined as Sn ¼ n X ẳ ỵ a ỵ ỵ an : iẳ0 Note that Sn aSn ẳ an ỵ 1, so Sn ẳ Finally, note when anỵ1 : 1a a < 1, then if n!1, the infinite geometric series is S1 ¼ : 1Àa EXAMPLES FROM THE TEXT In the solution to Problem 19 from Chap 4, we use the formula for a geometric series twice First, remember that R ẳ ỵ r and because we assume a positive interest 1 rate, < ¼ < In part (a) of Problem 19, we then have R ỵ r   i 1X 1 1 R ¼ and in part (b) of Problem 19 we have ¼ ¼ R i¼0 R R1 À R RR À r À δ 1 X X PDtỵi PD X PD Bt ẳ ẳ PD ị ẳ i ẳ r iỵ1 i Q R R R iẳ0 iẳ0 iẳ0 Rt1ỵj jẳ0 Index A Accounting, 16, 23, 39, 47, 130, 134, 142, 146, 150, 185, 240, 251, 252, 256–260, 268 Afghanistan, Africa, Aging, 16, 22, 23, 25, 144, 147, 227–231, 240–242, 251, 254, 260, 270, 280 Agriculture, 10 Altruism, 8, 63, 76, 82, 85, 86, 163, 195, 198–203, 207, 281 Amakudari, 4, 250 Asia, 236 Austria, 219, 246 Autocracy, 4, 6, 10, 76 B Basic research, 1, 21, 23, 46, 232, 237, 242, 243, 248, 269 Behavioral economics, 243, 271 Bequest-constraint, 42, 200 Brazil, Budget deficit, 44, 93, 129, 149, 231, 239, 274 Budget rules, 255 Budget surplus, 130 C Calibration, 124, 125, 127, 149, 180, 182, 187–189, 191, 208, 210–213, 281 Capital markets imperfections, 33–35, 41–43 open economy, 38–41, 141 CES utility function, 60, 70 China, 21, 143, 232, 236, 237 Cobb-Douglas production function, 112, 122, 131, 203 College costs, Competitive equilibrium capital market, 115 labor market, 119 Congressional Budget Office (CBO), 23, 236, 252, 253, 255 Constrained maximization problems, 34 Consumption government, 40 household, 118, 203 Convergence absence of convergence, 81 absolute convergence, 149 conditional convergence, 149 Corruption effects, 12, 13, 17, 19, 101, 160, 161, 188, 195, 198, 209, 210 examples, modeling, 161 Credit-constraint, 42, 45, 65 Culture, 10–13, 17, 19, 20, 101, 105, 160, 161, 182, 188, 192, 195, 198, 209, 210, 238, 253, 257, 273, 274, 276, 280 Czech Republic, 249 D Deficit bias, 89–91, 93, 145 Democracy, 2–4, 6, 9, 10, 15, 16, 43, 74, 76, 77, 80, 103, 145, 159, 160, 169, 175, 204, 270 Demographic transition, 228 Development economics, 281 Dictatorship, 77, 191, 204, 257 Difference equations first order, 59, 120 transition equations, 59, 120, 210 # Springer International Publishing AG 2018 M Ivanyna et al., The Macroeconomics of Corruption, Springer Texts in Business and Economics, https://doi.org/10.1007/978-3-319-68666-0 301 302 E Economic efficiency investment allocation, 51 Economic growth slowdown, 271 Education, 1, 7, 16, 21, 23, 25, 26, 35, 36, 43–46, 57, 95, 105, 131, 132, 144, 175, 233, 238, 245, 247, 248, 250, 251, 253, 254, 260, 268–270, 275 Egypt, Election campaigns, 273 Elections, 9, 31, 64, 74, 78, 80–82, 84, 91, 93, 104–107, 282 England, 279 Entrepreneurs, 25, 160, 230, 236 Europe, 3, 228 Externalities, 243 F Fiscal consolidation, 197, 211, 239, 247 Fiscal crisis, 7, 20–23, 25, 112, 142–146, 150, 227, 232, 239, 242, 243, 248–251, 254, 259, 260, 270, 271, 282 Fiscal federalism, 52, 81–87, 282 Fiscal gap, 131, 142, 145, 147–150, 195, 236, 240–242, 244, 247, 248, 251–253, 270 Fiscal multipliers, 247 Fiscal policy government investment, 24 government size, 10 modeling the government, 173 taxation, 103, 282 Wagner’s law, 10 Fiscal rules, 23, 24, 89, 93, 94, 105 Foreign aid conditionality, 87–89, 99, 100, 268 failures of, 87–89, 167–169, 256–259 growth effects, 141 international financial institutions, 87–89, 256–259 ownership, 99–100 Foreign investment, 141, 168 France, 246 Fully-funded social security, 231, 242 G Game theory, 197 Generational accounting, 142, 146, 150, 251 Germany, 219, 246 Index Governance principles, 32, 146 Government debt, 14–18, 22, 24, 37, 39, 41, 42, 46, 64, 65, 73, 89, 91, 93, 103, 107, 128, 129, 133, 137, 138, 142, 149, 153, 156, 159, 195–198, 203, 208, 214, 216, 221, 270 failure, 26, 271, 272 investment, 4, 8, 23, 31–70, 74, 76, 81, 91, 92, 96, 103, 129, 134, 135, 149, 167, 185, 195, 202, 205, 206, 210, 211, 221 subsidies, 7, 23, 229–231, 248, 251, 259, 269 transfers, 58, 95, 103, 107, 147, 159, 160, 178 Government Accountability Office (GAO), 252, 259 Government Intertemporal Budget Constraint (GIBC), 130, 131, 149, 153, 155, 156 Greece, 3, 11, 16, 176, 249, 255 H Haiti, Health care costs, 228–231, 240–242, 254, 260 Health insurance, 228, 229, 238, 241–243, 247, 254, 259, 270 Historical growth 20th century, 235 21st century, 235, 236 History lessons from, 273 Human capital as a source of growth, 235–237 health investments, 43–45, 140–145, 228–230 schooling investments, 44, 248, 249 Hungary, 249, 278 I Immigration, 236 Imperfect markets, 33–35, 41–43 Income gaps across countries, 103 across regions/sectors, 56, 106 Indonesia, 5, 26 Infinitely-lived agent model, 281 INFORM Act, 252 Index Infrastructure, 1, 3, 4, 7, 16, 21, 35, 39, 46, 47, 49, 73, 77, 80, 85, 93, 95, 103, 129, 131, 132, 140, 142, 143, 159, 162, 169, 172, 175, 178, 183, 186, 205, 216, 232, 237, 242, 243, 248, 250, 252, 254, 259, 268, 269, 275, 277 Innovation, 142, 236, 241, 248 Institutions, 7, 10, 19, 76, 80, 87, 101, 111, 164, 170, 173, 180, 181, 184, 187, 214, 217, 220, 243, 249, 250, 257, 258, 267, 273, 280 Interest groups, 7, 15, 16, 22, 24, 58, 64, 74, 94–100, 103–105, 145, 159, 160, 163, 168–175, 190, 195, 197, 227, 239, 248, 250, 251, 256, 260, 268, 270–272, 282 Interest rates historical, 127, 128 income and substitution effects on saving, 45 return to capital, 117, 124 Intergenerational income mobility, 43–46, 238, 239 Intergenerational transfers altruism, 8, 43, 63, 203, 204 bequests of financial assets, 44 government, 136, 270 human capital investments in children, 44 International capital flows, 87, 167, 168, 172 International cost of funds, 44 International financial institutions, 87–89, 256–259 International trade, 139, 281 Ireland, 4, 217, 249, 250 Italy, 3, 6, 16, 85, 87, 188, 214, 249, 277 J Japan, 4, 7, 17, 21, 143, 219, 228, 232, 237, 249, 250 L Labor markets, 22, 230, 234, 259, 269 Labor productivity, 122, 123, 126–128, 180, 208, 245, 281 Large landowners, 159, 170, 268 Latin America, 170 Life-cycle model, 32–35, 125, 244 M Mani pulite, 3, 6, 16 Maximization problems, 34, 59, 102, 182, 184, 244 Medicaid, 145, 229, 240–242, 247, 254, 270 303 Medicare, 145, 228–230, 240–242, 247, 250, 254, 270 Middle-skill jobs, 246 Migration domestic, rural to urban, 56, 57, 169–175 restrictions on domestic migration, 56–57 Misallocation of investment, 80 Moral hazard, 80, 243 N Neoclassical production function, 112, 114 Netherlands, 219 Net lifetime taxes, 147 O OECD, 16, 17, 20, 27, 44–46, 93, 142, 175, 180, 196, 217, 227, 231–233, 237, 239, 249, 250 Office of Management and Budget (OMB), 252 Open economy, 38–43, 62, 65, 67, 104, 106, 139–142, 149, 160, 168, 172, 216 Overlapping-generations model, 24, 25, 111–157, 190, 196, 203–208, 221, 281 P Pay-As-You-Go (PAYG) social security, 24, 142, 146, 150, 154, 240, 255 Philippines, Physical capital as a source of growth, 123 capital-labor ratio, 111–121 Pigovian taxes, 23, 243, 248 Polarization, 16, 24, 25, 74, 89–94, 104, 105, 107, 108, 145, 248, 255, 256, 260, 270 Political economy, 25, 170, 227–261, 267, 281, 282 Population growth, 117, 119, 123, 125, 133, 148, 162, 235 Portugal, 249 Preferences government officials, 129, 160, 173, 186, 210 households, 40, 42, 43, 49, 58, 65, 69, 77, 95, 117, 151, 176, 204 Profit maximization, 114, 205 Public capital, 18, 35–37, 39, 40, 42, 46–54, 56, 57, 59, 60, 63, 65, 69, 70, 73, 75–77, 79–82, 91, 93, 100, 101, 103, 105–107, 111, 129, 131, 132, 135, 136, 140, 141, 159, 165–169, 178–180, 185, 187, 189, 190, 192, 193, 196, 205, 208–210, 214, 259, 269, 271 304 Q Quantitative theory calibration, 124 historical simulation, 126 policy analysis, 124 testing theory, 124 R Rate of return college, 237, 247 human capital, 47, 245 physical capital, 47 Regional inequality, 86–89 Rent-seeking, 2–7, 16, 20, 23–25, 31, 62, 74, 80, 95, 97–99, 103, 105, 107, 197, 272, 280 Research and development, 122, 167, 236, 268 Ricardian Equivalence, 204 Rome, 27, 273–278 Russia, 228 S Saving bequest, 200 life cycle, 32–35 Sector differences, 49–54, 77–89, 169–173 government investment, 49–54, 77–89 Serbia, 5, 278 Simulations, 18, 127–129, 149, 152, 211–213 Sin taxes, 243, 248 Slovak Republic, 249 Social security, 24, 57, 129, 133, 139, 142, 145–147, 150, 154, 228, 229, 240–242, 247, 250, 254, 270 Social welfare function, 9, 31, 50, 54, 63, 66 Spain, 249, 277 Stability one sector model, 152 Steady state one sector model, 59, 60, 121, 152 Structural transformation, 63, 86, 159, 160, 169, 175, 190, 268 Sweden, 219, 239 Switzerland, 219, 246 Index T Tax evasion effects, 12, 17, 25 examples, 176 modeling, 11 Technological progress, 21, 131, 133, 143, 149, 152, 172, 205, 229, 231, 232, 235–237, 260, 280 Total factor productivity (TFP), 35, 48, 49, 51, 53, 56, 62, 63, 66, 112, 140, 141, 178, 187, 281 Traditional sector, 170, 171, 173, 174 Transitional dynamics, 123, 212 Transparency, 7, 17, 62, 197, 249–254, 260, 272 Turkey, 3, 16 U Ukraine, United States, 63, 89, 128, 140, 142–144, 147, 228, 229, 232–235, 237–239, 242, 245, 246, 255, 258, 270, 273–276, 279, 280 Utility function, 9, 19, 32, 36, 43, 50, 53, 58, 60, 67, 68, 70, 117, 133, 151, 162, 164, 173, 176, 177, 179, 192, 199, 204, 244, 245 V Value function, 50, 53, 55, 82, 179, 199, 221 Vocational training, 7, 23, 238, 239, 246, 248, 269, 280 W Wages inequality, 1, 7, 20–22, 44, 45, 227, 237–239, 245, 250, 260, 280 Wagner’s Law, 10, 160, 169–175, 184, 191 Welfare effects of government policy, 37, 175 Worker productivity, 5, 36, 46, 49, 66, 76, 77, 91, 122, 126, 128, 132, 143, 148, 149, 152, 154, 155, 157, 161, 166–168, 189–192, 203, 207, 211, 214, 221, 228, 231, 236, 239 World Bank, 5, 22, 217, 218, 220, 258, 261 ... borrow The combination of an expansion in interest groups politics, the tightening budget constraints of the middle class, and the glut of saving around the world created the motivation and the. .. Model of Economic Growth 4.1 Firms, Production, and the Demand for Capital 4.2 Household Saving and the Supply of Capital 4.2.1 The Supply of Labor and Capital... citizens rather than the private interests of politicians and the relatively small groups of their most important supporters The performance of governments in leading their country’s economic growth