3 Underappreciated Indicators to Guide You through a Debt-Saturated Economy Posted on May 5, 2014 by ffwiley If you’re my generation or older, you may remember taking the original Pepsi Challenge – the Coke versus Pepsi taste testing booths that you would find at sporting events, fairs and similar venues. I took the Challenge and stuck with Coke. The majority of people went the other way, as confirmed by even Coke’s private tests. Nowadays, though, I’m guessing the public version of a Challenge booth would bring heckling from the nutrition-conscious folks at the Just Juice stand. The bigger challenges for Coke and Pepsi are health risks linked to their flagship products. Researchers are zeroing in on a handful of ingredients that may be harmful, such as sodium benzoate and phosphoric acid. We have nothing to add to the soda studies, but they somehow seem similar to our research on debt. Like soft drinks, you can think of debt as having different ingredients, some benign and others risky. At the highest level, here are the ingredients that everyone should be aware of (hereafter, we’ll call them funding sources): Funding from outside the U.S. Funding from the Federal Reserve system Funding from private banks Funding from non-money savings Over any period, we can examine the total amount of borrowing and divide it among these sources with only a small residual. Here’s a breakdown for the last 60 years: Now, you may look at this picture and see nothing interesting. If that’s all we have, then there’s no fizz in our soda, right? You already knew that foreigners, the Fed and private banks help to finance our debt. According to mainstream economic thought, that’s a good thing. We don’t think it’s quite that simple. We’ll show that credit financed by lenders outside the U.S., the Fed and private banks is a major source of economic volatility. We’ll also describe three indicators that help to size up the related risks. First, though, we’ll define and comment briefly on each funding category shown in the chart. (If you’re just looking for the bottom line, skip to “ Okay then, what should I be watching? ”) Funding from outside the U.S. Foreigners invest the proceeds of our current account deficits back into U.S. $-denominated investments. Therefore, the money that drains out of our real economy (when we import more than we export) flows back into our financial economy. Large amounts of these flows are unsustainable over the long-term and unstable through the business cycle. Inflows to the financial economy contribute to asset volatility and, in the extreme, bubbles. They also make it easier for politicians to increase public debt. Outflows from the real economy are linked to declining savings rates, which are harmless in the short-term but come back to bite when low-savers inevitably learn they’ve overspent. America’s mix of low personal savings and high public deficits owes much to credit market financing obtained from outside the U.S. Funding from the Fed. Like foreign funding, too much credit from the Fed (primarily debt securities held on its balance sheet) contributes to financial volatility and declining savings rates. These effects are largely intentional. Central bankers who ramp up the supply of credit through, say, quantitative easing, aim to lower interest rates, thereby pushing up asset prices and encouraging more spending and less savings. What you won’t hear from these central bankers (unlike ex-central bankers, who sometimes spill the beans ) is that near-term benefits are invariably followed by an opposite reaction once interest rates, asset prices and savings rates normalize. Funding from private banks. In a fractional reserve system, banks create (“print”) money by conjuring up deposits to deliver loan proceeds. Generally, the extra deposits remain in the banking system for as long as the corresponding loans are retained on bank balance sheets. When loans are either paid down or sold off and removed from bank balance sheets, the extra deposits are extinguished. In other words, bank funding increases when the amount of credit that’s extended and retained on bank balance sheets is greater than the amount that’s paid down and removed from bank balance sheets. (Note that banks also create money through activities that don’t involve loans, but these tend to be either less significant or on the Fed’s behalf.) Because of the link to loan issuance, bank funding typically boosts spending more immediately and certainly than funding supplied by the Fed. Not only that, but loans retained by banks deliver the extra oomph that comes from the fact that deposits are created from thin air. Setting aside potential inflation effects, bank lending essentially turbocharges the economy, creating a “virtuous” feedback loop where more spending leads to more production, which then leads to a higher level of income and reinforces the initial lift in spending. Unfortunately, though, turbocharged lending eventually reaches borrowers who produce things that can’t be profitably sold. Or, it flows to home buyers and consumers who spend more than they can afford. Either way, loans go sour and the virtuous loop gives way to a vicious loop of less lending, spending, production and income. Many economists, although mainly from outside the mainstream such as Austrian business cycle theorists and Chicago Plan advocates, recognize that vicious loops are a natural consequence of balance sheet expansion by banks in a fractional reserve system. While it’s not the only culprit, we’ll demonstrate the link between bank balance sheets and economic volatility in just a moment. Funding from non-money savings. Debt that’s placed directly with domestic, non-bank investors – through either debt security issuance or loans that banks choose to sell and move off their balance sheets – is fundamentally different from other sources of funding. It’s financed by 100% genuine, domestic savings. It excludes the monetary expansion that occurs when banks match a loan on the asset side of the balance sheet with a newly-created deposit on the liability side, thereby lifting the supply of credit without a prior increase in savings. Most of the non-money savings in our economy comes from households, pension funds and insurance companies. You shouldn’t think of these sources of funding as completely risk-free, but they’re the Just Juices of the credit markets. Or, you can think of them as the relatively harmless ingredients in your soda that are mixed with the more dangerous stuff when other funding sources come into play. Uncategorized funding. This is our residual category, which has negligible effects on the analysis. It’s explained in the accompanying “technical notes” post . . . . Okay then, what should I be watching? Now for our three indicators. We start by estimating the percentage of total borrowing that’s funded by the three riskiest sources (the red-shaded areas of the chart above), rather than non-money savings: As noted on the chart, three periods stand out for an unusually high percentage of risky borrowing. The first two coincide with the creeping inflation of the 1960s and Great Inflation of the 1970s. The third overlaps the serial bubbles of the last two decades and leads into the 2008 financial crisis. While some may call this a coincidence, we beg to differ. Problems with either inflation or financial instability are exactly what you should expect when debt funding is tilted heavily towards risky sources. Next, we divide risky borrowing by GDP: This chart can help you gauge how hard the economy might fall after the inevitable cracks appear in credit markets. Not surprisingly, it shows that the three periods with the greatest amounts of risky borrowing were followed by the three hardest falls – severe recessions in 1973-75, 1980-82 and 2008-09. You may have also noticed that virtually every recession follows a drop in risky borrowing. This, too, shouldn’t be surprising. If you agree that large amounts of risky borrowing eventually lead to vicious circles – in which soured loans and a slower borrowing pace drag economic activity lower – then you should expect recessions to occur after risky borrowing peaks. This is exactly what we see. We create a third indicator by measuring the change in risky borrowing. Using two year changes, it looks like this: This isn’t a perfect recession predictor (there’s no such thing), but it helps to narrow down recession probabilities. And while it doesn’t offer ironclad proof that borrowing in excess of non-money savings leads to recessions (once again, there’s no such thing), it fits into the very process described by economists who’ve dared suggest that such borrowing is risky. The bigger picture We recommend including the three indicators in any risk analysis, alongside other factors such as debt ratios and interest rates. Debt ratios show the economy becoming more and more saturated with debt. We’ve seen steady increases in debt-to-GDP, debt-to-income, debt-to-sales, debt-to-assets; name the ratio and we’ll show you an unsustainable upwards trend. (We won’t repeat the charts here, but you can go to our last post and work backwards to others showing data on public and private debt.) These upwards trends are a direct consequence of the risky borrowing shown in the charts above. If borrowing was limited to amounts funded with non-money savings, debt ratios wouldn’t rise. Even a modest margin above non-money savings would leave debt ratios stable. As it is, risky borrowing averaged 8% between 2002 and 2013, a pace that you can call hell-for-leather without much exaggeration. The post-2009 average is only slightly lower at 7% of GDP, thanks to money printing at the Fed and a shift in the debt mix from private borrowers to the U.S. Treasury. Interest rate developments are another important part of the picture. Falling rates may explain why risky borrowing declined sharply in the mid to late 1980s without an especially severe recession. The secular decline in rates continued to provide tailwinds in the 1990s and 2000s, but these tailwinds shouldn’t have much power left, if any, now that we’ve reached the zero lower bound. Conclusions for today’s economy There are two particular messages in the latest indicator readings. First, with risky borrowing on the upswing, we’re still not seeing a recession signal. This is consistent with several other business cycle indicators that remain benign, such as profit margins (still high), bank lending standards (mixed) and the yield curve (still positive). Second, the risky borrowing indicators are troubling, nonetheless. They show that we’ve reverted to old habits of borrowing far more than we can fund with non-money savings. At almost 10% of GDP in 2013, risky borrowing is higher than in all but the early 1970s and middle part of the last decade. This tells us that we’re accumulating risk at a rapid clip, although not for as long as in those earlier episodes. (Yet .) Worse still, policymakers and mainstream economists are unperturbed, failing to acknowledge that some types of financing are riskier than others. It’s as if we’re stuck at a 1970s Pepsi Challenge booth, watching people debate cola tastes with no mention of health risks. With ample evidence of these risks, how can this be? One theory is that the current generation of mainstream economists staked their careers on the soda business, filling resumes with research on topics such as sweetness and carbonation, but nothing on health. It’s just too big a step for them to acknowledge that the old research is unhelpful and the resumes hollow. We can only hope that the unpopular, long-term thinkers who are willing to take that step become more influential over time. In the meantime, keep an eye on the sources of financing and, in particular, the three indicators of risky borrowing discussed above. (Click here for technical notes about this article and a few more charts.)
Journal of Public Economics 66 (1997) 489–504 On the possibility of efficient private provision of public goods through government subsidies Georg Kirchsteiger*, Clemens Puppe Department of Economics, University of Vienna, Hohenstaufengasse 9, A-1010 Vienna, Austria Received 31 March 1996; accepted 21 February 1997 Abstract This paper investigates the possibility of implementing an efficient provision of a public good through distortionary tax-subsidy policies in a simple one-shot game of voluntary contributions. Within the class of all linear tax-subsidy policies two cases are distinguished. The first is where individual taxes only depend on the sum of all other individuals’ contributions. Although such policies may increase total supply of the public good, it is shown that the implementation of an efficient amount is not possible unless the government has complete information about individual characteristics. In the second case, where taxes depend on the distribution of contributions, the equilibrium supply of the public good is no longer unique. For any efficient interior solution there might also exist inefficient boundary solutions. Moreover, unlike the boundary solutions, the efficient interior solution is in general not stable. ó 1997 Elsevier Science S.A. Keywords: Public goods; Tax subsidy; Voluntary contributions JEL classification: H29; H40; H41 1. Introduction Voluntary contributions to a public good typically entail underprovision of that good. Many authors have therefore considered models in which a ‘government’ *Corresponding author. Tel.: 143 1 401032423; fax: 143 1 5321498; e-mail: georg.kirchsteiger@univie.ac.at 0047-2727/97/$17.00 ó 1997 Elsevier Science S.A. All rights reserved. PII S0047-2727(97)00029-7 490 G. Kirchsteiger, C. Puppe / Journal of Public Economics 66 (1997) 489 –504 subsidizes private contributions so as to increase the total supply of the public good. Usually, in these models, government’s subsidy payments are financed by appropriate taxation. While lump-sum transfers typically leave the equilibrium amount of the public good unchanged, distortionary tax-subsidy policies may 1 indeed increase total equilibrium supply of the public good. Given this possibility to influence aggregate supply of a public good, the question arises whether by choosing an appropriately designed tax-subsidy policy a government can implement an efficient amount of the public good. This is the problem addressed by the present paper. The analysis is restricted to the most natural case of linear tax-subsidy policies. Unfortunately, in this case our results are rather negative. Indeed, it is shown that either (i) the government needs to know individual preferences in order to implement an efficient allocation, or (ii) the contribution game admits a multiplicity of equilibria with not all of them corresponding to efficient allocations. Moreover, in the latter case, an efficient equilibrium is in general unstable. The framework for our analysis is the following general tax-subsidy scheme. Each agent’s own contribution is subsidized at some fixed individual subsidy rate. At the same time, each agent faces a tax that is a linear function of all other agents’ contributions to the public good. Subsidy payments and taxes are linked in such a way that the government’s budget is balanced for any possible distribution of individual contributions. In determining the level of her own contribution to the public good, each agent optimizes against all other agents, taking their decisions as given. Aggregate supply of the public good then results from the equilibrium level of individual contributions in this simultaneous one-shot game. Given this general model, two cases have to be distinguished. Firstly, it can be shown that within our framework the model suggested by Andreoni and Bergstrom (1996) corresponds to the case where each agent’s tax only depends on the sum of all other individuals’ contributions (and not on their distribution). In the following, we refer to this case as the case of individually uniform tax rates. In this case, each choice of subsidy rates induces a unique aggregate equilibrium supply of the public good which is increasing with the subsidy rates (see Andreoni and Bergstrom, 1996). Moreover, it is easy to determine subsidy rates that induce an efficient allocation provided that all individual contributions are positive in equilibrium. However, in this paper we prove that given such subsidy rates all individual contributions remain positive in 1Warr (1983) has shown that lump-sum transfers do not alter the equilibrium amount of the public good provided that the set of contributors does not change. Bergstrom et al. (1986) provide a general analysis of income redistributions. Warr’s neutrality result is confirmed in Bernheim (1986) who considers distortionary income taxes. For the possibility to influence aggregate supply of a public good through subsidies to voluntary contributions in a framework with ‘naive’ individuals who ignore the government’s budget constraint, see Roberts (1987), (1992) and Boadway et al. (1989). Non-neutrality of tax financed subsidies with rational individuals who take into account the government budget constraint has been established in the models of Andreoni and Bergstrom (1996) and Falkinger (1996). G. Kirchsteiger, C. Puppe / Journal of Public Economics 66 (1997) 489 –504 491 equilibrium only if the resulting effective prices for the individuals are the Lindahl prices. This implies that in order to implement an efficient allocation the government must have complete information about individual preferences (or at least about the individuals’ demand for the public good). However, if a government does have complete information, there is of course no point in designing a complicated tax-subsidy policy. Indeed, in that case the government has complete control over the state of the economy via much simpler tax policies, e.g. the government could take care of the supply of the public good and impose appropriate lump-sum taxes to cover its expenditures. In order to overcome this difficulty, one has to allow agents’ tax payments to depend on the distribution of the other agents’ contributions to the public good. Indeed, an example of a subsidy policy where the existence of an efficient interior solution is not the exception is the model recently suggested by Falkinger (1996). In this model, the population is divided into subgroups and each agent’s tax only depends on the contributions made by individuals belonging to the same subgroup. If, however, the agents’ tax payments depend on the distribution of the other individuals’ contributions other problems arise. Firstly, in that case the equilibrium amount of the public good is no longer uniquely determined. Specifically, we prove the following result. For any subsidy scheme where tax rates are not individually uniform there exist individual preferences and distributions of incomes such that besides an efficient interior solution there is also a non-efficient boundary solution where at least one individual contributes zero. Moreover, in contrast to the boundary solution the efficient interior solution is not stable in an appropriately defined sense. This result casts some serious doubt on the possibility to implement efficient allocations by linear tax-subsidy policies involving different tax rates for the other agents’ contributions. The plan of the paper is as follows. In Section 2 we present the general framework of our analysis and discuss its relation to the literature. Section 3 is devoted to the case of individually uniform taxation. In Section 4, we consider linear tax rules that are not individually uniform. Concluding remarks are offered in Section 5. 2. The model Consider an economy with n individuals, indexed by i51, . . . , n. Each i individual’s utility is given by a strictly quasi-concave utility function u (c ,G), i where c denotes i’s consumption of a private good and G the consumption of a i purely public good. Throughout, private consumption and the public good are assumed to be strictly normal goods at every level of wealth. Furthermore, we assume that each individual’s utility function is continuously differentiable. Each individual has an initial endowment of m units of the private good. For simplicity, i let the price of the private good be equal to 1. Hence, one may think of m as i 492 G. Kirchsteiger, C. Puppe / Journal of Public Economics 66 (1997) 489 –504 consumer i’s income. The public good is produced from private goods at a cost of one unit private good per unit of public good. The public good is supplied by voluntary contributions of the consumers. For each i, denote by g consumer i’s contribution to the public good. Furthermore, let i G :5o g denote the sum of the contributions of all agents different from i. A 2i j±i j common assumption in a model of private provision of a public good is that each individual takes the activities of all other agents as given for her own decision. Consequently, consumer i’s decision problem is i max u (c ,g 1G ) s.t. c , g i i 2i i i (2.1) c 1g 5m and g $0. i i i i A pair of n-tuples (c*, . . . , c*) and ( g*, . . . , g*) that solves (2.1) for all i is 1 n 1 n hence a Nash equilibrium of the corresponding contribution game played by the n individuals. It is well known that without any intervention an equilibrium of the game described so far entails underprovision of the public good. Many authors have therefore considered extensions of this model allowing for the possibility that a government subsidizes private contributions (see, among others, Andreoni (1988); Andreoni and Bergstrom (1996); Boadway et al. (1989); Brunner and Falkinger (1995); Falkinger (1996) and Roberts (1987), (1992)). In its most general form, such a government intervention may be described as follows. Each individual’s private contribution is subsidized at a rate s , where 0#s ,1. Hence, i i if i contributes g she receives a payment of s g . Government expenditure, in turn, i ii is financed by taxes where each agent’s tax payment depends on all other individuals’ contributions. In the present paper, we confine ourselves to the most natural case where each agent’s tax is a linear function of all other agents’ contributions. Denoting by t $0 agent i’s tax rate with respect to agent j’s ij 2 contribution, consumer i’s budget constraint may thus be written as c 1(12s )g 5m 2Ot g , (2.2) i i i i ij j j±i with the additional constraint that g $0. i Remark: the subsidy scheme described by (2.2) is the most general form of government subsidies through a change of relative prices when taxes are linear. Firstly, observe that there is no rationale to let individual i’s tax depend on other individuals’ private activities, i.e. their private consumption c . Clearly, individual j i’s tax may depend on her own private consumption c . However, any reasonable i form of such a dependence must be linear in c . Since all that matters are relative i prices, such a dependence is already incorporated in the s s. By a similar argument i 2Our analysis is completely general with respect to the distribution of income. Without loss of generality, we therefore neglect lump-sum transfers in our model. G. Kirchsteiger, C. Puppe / Journal of Public Economics 66 (1997) 489 –504 493 one may also assume without loss of generality that agent i’s tax does not depend on her own contribution g to the public good. i Note that if agents optimize against each other according to (2.2) there is a problem of bankruptcy, since some configurations of strategies (i.e. choices of (c , i g )) may entail negative net-income for some consumers. In this case there would i be no well-defined payoff. Consequently, in analyzing the corresponding contribution ‘game’, we will assume throughout that in equilibrium individual contributions ( g*, . . . , g*) satisfy the following condition.3 1 n NB (No bankruptcy). For all i and i i 0,s ,1. Furthermore, for all i and all j, t 5s b, hence consumer i’s total tax i ij i burden is s bG . Rearranging individual i’s budget constraint yields i 2i c 1(12b )g 5m 2s bG. (2.4) i i i i Hence, each consumer’s contribution g is subsidized at a rate of b, and at the i same time the consumer is taxed for a fixed share s of total government i expenditure on subsidies. As a consequence, consumer i’s effective price for the public good is 12b1s b. Clearly, the government’s budget is balanced if and i only if o s 51. Notice that each individual is taxed for each unit of the public i i good provided by any other agent at a constant rate, i.e. each individual’s tax payment only depends on the sum of all other agents’ contributions. Hence, the Andreoni/Bergstrom model belongs to the class of subsidy schemes with individually uniform taxation. In this model, Andreoni and Bergstrom (1996) prove that for each b and any family s , . . . , s with 0,s ,1 and o ]]] is the absolute value of the marginal rate of i i -u (c ,G) /-c i substitution between the public good and private consumption. Summing up over all individuals thus gives n OMRSi 5n2b(n21). i51 Consequently, if all individual contributions are positive in equilibrium — an assumption which will be shown to be extremely restrictive — an efficient provision of the public good would require b51. Indeed, with b51 one obtains i 4 o MRS 51, the condition characterizing efficient allocations. Although also for i b51 there is a unique aggregate equilibrium supply of the public good, individual equilibrium contributions are no longer unique for that particular value of b (see 5 Section 3). Nevertheless, one may ask if by choosing b sufficiently close to 1 one can implement an amount of the public good arbitrarily close to an efficient amount as the result of a unique Nash equilibrium. This question is addressed in Section 3. Another special case of the subsidy scheme described by (2.2) and (2.3) is the model recently proposed by Falkinger (1996). In his model, the population is partitioned into subgroups and each individual is rewarded or penalized on the basis of the average contribution of the subgroup to which the individual belongs (cf. Section 4). Note that, since individual taxes only depend on the contributions made within the same subgroup, taxation is not individually uniform in that model. 3. Efficient allocations with individually uniform tax rates In this section, we investigate existence of efficient allocations for the case of individually uniform tax rates. Hence, assume that in (2.2) each individual i is taxed at a constant rate for each contribution made by another individual, i.e. assume that for all i and all j, t 5t for some t $0. The analysis is substantially ij i i simplified by the observation that any subsidy scheme of the form of (2.2) with that property can be rewritten as in (2.4). Hence, the Andreoni/Bergstrom model described by (2.4) exactly corresponds to the case of individually uniform taxation. Indeed, it can be shown that given the governments budget constraint (2.3) the assumption of individually uniform taxation implies that for all i, j, t 1s 5t 1s . Defining b:5t 1s and s :5t /b, the budget constraint (2.2) then i i j j i i i i 4By strict normality, private consumption and total supply of the public good are always positive in equilibrium. Hence, efficiency in equilibrium is always characterized by the standard Samuelson rule. 5This seems to be the reason why Andreoni and Bergstrom (1996) explicitly exclude the case b51 in their analysis. G. Kirchsteiger, C. Puppe / Journal of Public Economics 66 (1997) 489 –504 495 6 easily transforms into (2.4). Also, it can be checked that o s 51. The case b#1 i i n corresponds to the case where o s #n21. Of course, this is the only case of j51 j interest, since with os .n21 one would obtain ‘overprovision’ of the public j good. Firstly, we analyze the case of interior equilibrium of the contribution game corresponding to (2.4). It has already been observed in the previous section that efficiency in an interior equilibrium requires b51. In order to characterize the equilibrium of contribution game for b51, consider the following closely related problem for individual i. i max u (c ,G) s.t. i ci,G (3.1) c 1s G5m and G$0. i i i The solution G˜ (m , s ) to this problem is individual i’s demand for the public i i i good provided that its price is s and that no other individual contributes to the i public good. Consequently, we refer to G˜ (m , s ) as individual i’s stand-alone i i i contribution. Now, compare (3.1) to individual i’s maximization problem given the subsidy scheme (2.4) for the value b51. i max u (c ,g 1G ) s.t. c , g i i 2i i i (3.2) c 1s G5m and g $0. i i i i Obviously, the only relevant difference to the problem (3.1) is the nonnegativity constraint. Denote by M the set of those individuals with maximal stand-alone contribution, i.e. M:5h j g 2] ( g 1g ),0J, i j k l i 2 j 4 k l where j belongs to the same subgroup, whereas k and l together form the other subgroup. Assuming that all individuals contribute a positive amount, the 9Note that this requires at least three consumers in the economy. Indeed, with only two individuals taxes are automatically individually uniform. G. Kirchsteiger, C. Puppe / Journal of Public Economics 66 (1997) 489 –504 499 following equilibrium contributions can be derived, g*5g*55m /823m /8 and 1 2 I II g*5g*55m /823m /8. Consequently, there is an efficient interior solution if 3 4 II I and only if 3/5,m /m ,5/3. I II However, in addition to the efficient interior equilibrium there is a variety of inefficient boundary solutions. For instance, if 3/5,m /m ,4/3 there are two I II equilibria where exactly one individual from subgroup I contributes zero whereas all other agents make a positive contribution. Similarly, if 3/4,m /m ,5/3 there I II are two equilibria where exactly one individual from subgroup II contributes zero. Hence, whenever an efficient interior solution exists there are also inefficient boundary equilibria. In fact, it can be checked that there are further boundary equilibria in addition to those described. In any of these equilibria the nobankruptcy condition is satisfied, i.e. each agent’s private consumption is positive. Besides the multiplicity of equilibria in this example there is another problem of instability of the interior equilibrium. Indeed, as can be seen from Fig. 2, the reaction curves of two individuals belonging to the same subgroup intersect with Fig. 2. Non-uniqueness and instability of the interior solution. 500 G. Kirchsteiger, C. Puppe / Journal of Public Economics 66 (1997) 489 –504 the ‘wrong’ slope. This implies instability of the interior equilibrium with respect to any dynamics where individuals adjust their contribution in direction of their best responses. The difficulties with non-uniform tax rates are by no means specific to the particular example just discussed. Specifically, one has the following result. Theorem 2: For any linear tax-subsidy scheme with property (4.1) there exist preference and income distributions such that besides the efficient interior equilibrium there is also an inefficient boundary equilibrium for the corresponding contribution game. Before we proceed to the proof of Theorem 2, we need the following preliminary result. Observe first that an efficient interior solution can only exist if subsidy rates satisfy n Os 5n21. (4.2) i i51 Let t˜ denote individual i’s average tax rate, i.e. ˉt :5o t /(n21). i ij±i ij Lemma 4.1: Suppose that subsidy rates satisfy (4.2). Either there exists an individual i whose average tax rate t is larger than her effective price 12s , 0 i 0 i 0 or, for all i, tˉ 512s . i i Proof : Assume by way of contradiction that, for all i, tˉ #12s with strict i i inequality for some i. Summing over i one would obtain n n OOt ,(n21)O(12s ). (4.3) ij i i51j±i i51 However, differentiating the government’s budget constraint (2.3) with respect to g yields s 5o t for all i. Using this and interchanging the order of i i j±i ji n summation in (4.3) one could conclude o s ,n21. However, this is in j51 j contradiction to (4.2). The following proof of Theorem 2 is based upon the case distinction described in Lemma 4.1. Firstly, assume that there is an individual i whose average tax rate 0 is larger than her effective price for the public good. Suppose that the valuation for the public good is sufficiently low for all individuals but i , and consider an 0 income distribution such that there is nevertheless an interior equilibrium in which all individuals contribute the same amount. Since i ’s average tax is higher than 0 her effective price, and since moreover, i ’s valuation for the public good is high 0 compared to the other agents, there is an additional (inefficient) boundary equilibrium in which only i supplies the public good. Next, consider the case 0 where average tax rate equals effective price for all individuals. Then, since taxation is not individually uniform, there must exist two individuals, i and j 0 0 such that i ’s tax rate for j ’s contribution is larger than i ’s effective price for the 0 0 0 public good. From this, the existence of an inefficient boundary equilibrium in G. Kirchsteiger, C. Puppe / Journal of Public Economics 66 (1997) 489 –504 501 addition to the efficient interior equilibrium can be inferred by a similar argument as in the first case. Proof of Theorem 2 : Assume that all individuals are endowed with Cobb- Douglas type preferences ui(c , G)5caiG12ai. In this case, agent i’s (unrestricted) i i reaction function can be calculated as 12a 12a i i g 5]]m 2 ]] O S t 1a D g . (4.4) i 12s i 12s ij i j i j±i i Consider a family of ‘efficient’ subsidy rates s , . . . , s satisfying (4.2). We 1 n distinguish two cases according to Lemma 4.1. Case 1. There exists i such that tˉ .12s . Without loss of generality, 0 i 0 i 0 assume that i 51. Fix a ]m . 1 12s 1 1 On the other hand, since (1, 1, . . . , 1) is a solution one obtains, again by (4.4), 12a1 l t1j ]]m 511(12a ) O]]1a (n21). 12s 1 1 12s 1 1 j±1 1 Since by assumption tˉ .12s , it follows that g**.n. Now consider all 1 1 1 individuals different from 1. Since the vector (1, 1, . . . , 1) is an interior solution, l and since the a converge to 1 one obtains from (4.4) i l 12a i l ]]m ®n if l®`. i 12 s i Hence, since g**.n, agent i’s unrestricted reaction function becomes negative 1 for sufficiently large l provided that all agents j±1,i contribute zero. Conse- quently, i’s best response to g 5g** and g 50 for j±1,i is g**50 for 1 1 j i sufficiently large l. This shows that for large l, ( g**, 0, . . . , 0) is an additional 1 equilibrium. Observe that this equilibrium cannot be efficient. Indeed, at the 1 equilibrium allocation one has MRS 512s . However, all other individuals’ 1 unrestricted reaction function becomes strictly negative in equilibrium. Hence, 502 G. Kirchsteiger, C. Puppe / Journal of Public Economics 66 (1997) 489 –504 j MRS ,12s for j52, . . . , n. Together with (4.2) this immediately implies j inefficiency. Also observe that the no-bankruptcy constraint is satisfied in the boundary equilibrium. Case 2. Suppose now that for all i, tˉ 512s . Since the tax-subsidy scheme i i satisfies (4.1), there must exist i and j ±i such that t .12s . Without loss 0 0 0 i 0 j 0 i 0 of generality, assume that i 51 and j 52. The proof in this case is similar to the 0 0 proof in Case 1. Again, fix a so that in the end the no-bankruptcy condition is 1 satisfied for individual 1, and consider for each i52, . . . , n a strictly increasing l l sequence (a ) converging to 1. For each l, choose the distribution (m , . . . , i l ],1,]], . . . ,]]D is an interior equilibrium. By (4.4) this implies that n21 n21 n21 for all l ]m .2 and ]]m 52. 12s 1 12s 2 1 2 Furthermore, for each i53, . . . , n, l 12ai l ]]m ®2 if l®`. i 12 s i This implies by the same arguments as in Case 1 that, for sufficiently large l, an additional equilibrium is given by 12a1 l ( g**,g**, . . . ,g**)5S]]m ,0, . . . ,0D. 1 2 n 1 12 s1 Again, this equilibrium is inefficient and satisfies the no-bankruptcy constraint if l is large enough. The preferences constructed in the proof of Theorem 2 might seem rather extreme. Note, however, that this is due to the great generality of Theorem 2 since it applies to arbitrary linear tax-subsidy schemes satisfying (4.1). In specific examples — such as the one considered above — much less extreme preference distributions yield similar conclusions. Also note that the instability of the interior equilibrium uncovered in the example is a general phenomenon. Suppose, for instance, that individual preferences are of Cobb-Douglas type. By Lemma 4.1, if a tax-subsidy scheme is not individually uniform, there exist individuals i and j ±i such that t .12s . 0 0 0 i 0 j 0 i 0 If a is sufficiently close to 1 this implies that the reaction curves of individuals i j 0 0 and j intersect qualitatively as shown in Fig. 2. 0 G. Kirchsteiger, C. Puppe / Journal of Public Economics 66 (1997) 489 –504 503 5. Conclusion In this paper, we have argued that linear tax-subsidy policies in a simple one-shot, simultaneous move game of voluntary contributions to a public good are not an appropriate tool for implementing efficient allocations. In designing such a policy, the central planner (the ‘government’) faces a dilemma. Either the government chooses a policy where each individual’s tax only depends on the sum of all other individuals’ contributions, i.e. an individually uniform tax-subsidy scheme, or an incentive scheme where some individuals’ tax depends on the distribution of contributions. In the first case, an efficient interior equilibrium only exists if the government can implement the Lindahl prices through subsidy rates. However, this requires knowledge that the government is assumed not to have. It is worth noting that this problem can be solved in a different framework which has been suggested in the literature. Consider, for instance, the following two-stage game proposed by Danziger and Schnytzer (1991) (see also Althammer and Buchholz (1993); Varian (1994)). In the first stage individuals announce appropriate subsidy rates by which they will subsidize other agents’ contributions to a public good. Given these subsidy rates, individual contributions are then simultaneously determined in a second stage. In this two-stage game, it can be shown that the Lindahl subsidies indeed form the unique subgame perfect equilibrium. Given the difference in the informational structure of the two games, the difference in the results is of course not surprising. In both models, individual preferences are common knowledge to any potential contributor. Consequently, in the Danziger/Schnytzer game all players have complete information. On the other hand, in the model considered in the present paper subsidy rates are set by a central planner who has no information about individual preferences. Clearly, either of the two models implies extremely restrictive informational assumptions on the part of potential contributors. Taking these assumptions for granted, we believe that the model considered here has a priori much more practical appeal, in particular, if the number of agents is large. In the second case, when a subsidy policy is chosen where individuals tax payments depend on the distribution of the other agents’ contributions, it has been shown that uniqueness of the equilibrium is no longer guaranteed. Moreover, even if an efficient interior equilibrium exists, it is in general not stable, and typically there exist additional stable and inefficient boundary equilibria. Our overall conclusion, that linear tax-subsidy policies are not appropriate for implementing efficient allocations, bears some resemblance to negative results obtained in the very different framework of mechanism design models (see e.g. Green and Laffont (1979)). In our context, an interesting open question is whether the multiplicity of equilibria can be avoided by designing suitable non-linear taxation rules. On the other hand, it seems to us that the problem of instability would persist also under more complicated tax policies. 504 G. Kirchsteiger, C. Puppe / Journal of Public Economics 66 (1997) 489 –504 Acknowledgements We are grateful to Josef Falkinger, Konrad Podczeck and two anonymous referees for most valuable comments. References Althammer, W., Buchholz, W., 1993. Lindahl-equilibria as the outcome of a non-cooperative game. European Journal of Political Economy 9, 399–405. Andreoni, J., 1988. Privately provided public goods in a large economy: the limits of altruism. Journal of Public Economics 35, 57–73. Andreoni, J., Bergstrom, T., 1996. Do government subsidies increase the private supply of public goods. Public Choice 88, 295–338. Bernheim, D., 1986. On the voluntary and involuntary provision of public goods. American Economic Review 76, 789–793. Bergstrom, T., Blume, L.,Varian, H., 1986. On the private provision of public goods. Journal of Public Economics 29, 25–49. Boadway, R., Pestieau, P., Wildasin, D., 1989. Tax-transfer policies and the voluntary provision of public goods. Journal of Public Economics 39, 157–176. Brunner, J., Falkinger, J., 1995. Non-neutrality of Taxes and Subsidies for the Private Provision of Public Goods, Working Paper No. 9519. University of Linz. Danziger, L., Schnytzer, A., 1991. Implementing the Lindahl voluntary-exchange mechanism. European Journal of Political Economy 7, 55–64. Falkinger, J., 1996. Efficient private provision of public goods by rewarding deviations from average. Journal of Public Economics 62, 413–422. Green, J., Laffont, J.J., 1979. Incentives in Public Decision Making. North-Holland, Amsterdam. Roberts, R.D., 1987. Financing public goods. Journal of Political Economy 95, 420–437. Roberts, R.D., 1992. Government subsidies to private spending on public goods. Public Choice 74, 133–152. Varian, H., 1994. A solution to the problem of externalities when agents are well-informed. American Economic Review 84, 1278–1293. Warr, P., 1983. The private provision of a public good is independent of the distribution of income. Economics Letters 13, 207–211.
Are We Halfway Through Our Lost Decade? (4 Charts Inside) by JT McGee Tweet Tweet Housing crises tend to create debt crises. And debt crises are generally far more damaging than recessions caused by bloated asset values. I took a quick trip through FRED and Wikipedia only to be shocked at what I found. We’re Broke, But It Sure is Cheap Allow me to introduce you to this chart, the percentage of disposable income used to service the debt of an American household: You’ll notice that consumers seem to be doing very well when it comes to paying their debts. We are very capable of making our monthly obligations. This is why the default rate on credit cards and auto loans is now at a multi-year low. In fact, credit card delinquencies are coming in a sloth-like pace we haven’t seen since 2001 , while only 1/300 people are late on their car payments . Impressive, huh? Most impressively, the debt service costs of the average American continue to drop while the amount of debt consumers finance has only gone up. Observe the change in this chart, a chart of the total amount of household debt relative to disposable income. Notice that in 1980 Americans had debt equal to roughly 70% of their disposable income and debt service payments equal to 11% of their income. In 2012, we spend 11% of our disposable income to finance debt worth as much as 110% of our disposable income. Basically, $11 of debt demands as much from the American consumer budget as $7 of debt did in 1980, adjusting for changes in income. Are the Boom Years Coming Back? Much has been made of a falling debt service ratio. Economists believe that a falling ratio will allow for economic expansion in that borrowers are capable of carrying more debt now than they were before the collapse. I think this is half true. I think consumers are in a position where they can afford to borrow to spend. That’s good, I suppose, from the perspective of economic growth. However, it doesn’t address a critical problem – where will consumers find the money to borrow and spend? That’s the real issue. I want to introduce you to another chart of mortgage equity extraction, or the amount of money that households pulled out of home equity with financed dollars. Here’s a chart: Not pretty. As we know, real estate fueled much of the consumption boom from 2002-2006. In fact, it is believed that 75% of all GDP growth during that period was financed by home equity. Basically, without the real estate boom, the economy would have grown at one-fourth the pace it did from 2002-2006. It would not have grown. It would have just stagnated, kind of like the economy is stagnating right now. This is an important realization. It reminds us that the American economy will go nowhere without housing. Housing is a major source of financial leverage for American balance sheets. Take a look at just how much we inflated our “incomes” with home equity during the boom years: This is why I think we’re still only halfway through our lost decade. While homeowners are deleveraging, building in room in their budgets for debt, they will not be capable of borrowing for major purchases. Homeowners will not be capable of buying homes, or extracting home equity. Borrowers are capable of financing TVs, cars, or washing machines, but these are relatively unimportant when we talk about the grand scheme of things. We still have a long way to go. Yes, interest rates are low. And yes, we are spending significantly less on debt than we have in years gone by. But we are not in a position where we can add significantly more to our personal balance sheets. A credit card here and there and a car loan (secured!) just might fit, but a home equity loan – the source of most American liquidity – is still out of the picture.
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