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This PDF is a selection from a published volume from the National Bureau of Economic Research Volume Title: NBER Macroeconomics Annual 2007, Volume 22 Volume Author/Editor: Daron Acemoglu, Kenneth Rogoff and Michael Woodford, editors Volume Publisher: University of Chicago Press Volume ISBN: 978-0-226-00202-6 Volume URL: http://www.nber.org/books/acem07-1 Conference Date: March 30-31, 2007 Publication Date: June 2008 Chapter Title: Comment on "Aggregate Implications of Credit Market Imperfections" Chapter Author: Nobuhiro Kiyotaki Chapter URL: http://www.nber.org/chapters/c4080 Chapter pages in book: (p. 71 - 77) Comment Nobuhiro 1 Kiyotaki, Princeton and NBER University Introduction What duction are the implications constraint of borrowing for aggregate pro answer has and income distribution? Kiminori Matsuyama's two aspects. First, concerning the behavior of an individual producer, a constraint has the borrowing the invest fairly robust prediction?that ment of each producer in addition to the upon its net worth, depends cost of capital and the expected marginal product of capital. Secondly, the author argues that there is no the aggregate outcomes, concerning and that the borrowing constraint leads to a variety simple prediction, on of aggregate predictions, the environment (in depending underlying to the borrowing addition The constraint may constraint). borrowing generate persistent movement of aggregate quantities, or may cause or may expand during recessions volatility. The inefficient production be aggravated booms. The of the financial during improvement of aggregate before system may first increase the volatility production may it. reducing At one level, this is an impressive piece of work?a toMatsuyama. Like a screwdriver with exchangeable ematically simple framework with borrowing eties of results in business cycles, development, on the attachments. pending world according heads, one math constraint brings in vari and capital At another is complicated level, I find that the model even if it in be terms of mathematics. ory, may simple as as to be critical in to highlight order going possible between the author and me, even though I agree first lay out the key assumptions de in terms of the Hereafter I am the differences to many arguments. Let me flows, of his basic model: of his 72 Kiyotaki are 1. Agents 2. Projects homogeneous. are indivisible and there is no lottery. 3. Agents face borrowing 4. Agents receive 5. Overlapping constraints. credit by the rule of the first-come-first-serve. generations with model each agent living for two pe riods. 6. Agents choose one project (a) Productive versus (b) Pledgeable versus (c) Produce Do we from amenu of projects. unproductive; not-so-pledgeable; capital versus produce consumption goods. really need all six of these assumptions? of (1) ho Assumptions indivisible and credit (4) mogeneous agent, (2) project, rationing are not essential. Here, because the agents are homogeneous, there are neither nor natural lenders borrowers. The only reason for borrowing is that the scale of investment is larger than the saving of an individual no is and there agent lottery. (If there were a lottery so that the winner could get enough funds to finance the project, there would be no need earn returns if they receive credit for borrowing.) Because people higher minimum to finance constraint is binding, the borrowing credit the project when in in is the this needed the role of finance Thus, rationing equilibrium. are in to from those who back the is transfer the power paper purchasing are in to front of the those who queue queue (lucky (unlucky agents) ones). there are many is a complicated theory of credit, because more to it is that the fi think natural consider assumptions.11 This auxiliary nancial system transfers funds from those who have the producers because have investment opportunity, them to those who and consumers are heterogeneous. ismore substantial of (5) overlapping Assumption generations model the overlapping of (1), (2), and (4). But, because than the assumptions to it is model is rich by itself, difficult clearly understand generations genuinely how many of the results the overlapping-generations are due to the borrowing constraint instead of model. an argument similar to the author's, only with the as Can we develop constraint with heterogeneous agents? Here, sumption of (3) borrowing we can use the insight that the overlapping-generations is iso model to some credit-constrained (See, e.g., Woodford economy. morphic Then the and [1989, 1992]). [1986, 1990] genera overlapping Aiyagari 73 Comment be a result of the borrowing tions feature would constraint, not the as sumption. 2 Alternative Model an infinite horizon economy with homogeneous output, are two (even and odd) types of a at and each date.2 There labor capital size of each type of continuum of infinitely lived agents. The population We consider as unity. is normalized agents elastically and has technology Each even-type to invest goods labor in agent supplies in every even number of as: date (1) yt=f(kt)=Akf,0<A,0<a<l. on output at date t and kt is gross investment capital at t -1 is an even number.3 Each odd-type agent supplies in every odd number of date. labor and invests on the same technology where date Both yt is gross t -1, where types have 00 the preference = U( Xr'lncs,0<p<l c$ is consumption storable between periods where as (2) at date s and In c is natural c. Goods are log of < with the gross rate of return B 1/p. = of the agent who is investing (even type if t Let c\ be consumption = of the agent who is even, odd type if t odd) and let chtbe consumption = = even t t if if even, (odd type odd). The resource con harvesting type can be written as: straint of the economy = c\ + ct + kt+i + zt+1 Ak? + Bzt, (3) zt is storage between date t -1 and date t. can see the first best allocation immediately starting from the ini tial capital stock, which is not very different from the steady state level, should satisfy the conditions: where We zt+i kt+1 = = 0, (4) a(3Afc?, = c\ + cht (1 (5) a(3)Afc? (6) (4) implies there should be no storage in the first best alloca Equation the rate of returns is less than the time preference rate. tion, because the rate constant is to and (5) gross saving Equation implies ocp in equal 74 the efficient which allocation, to the model is similar of Brock Kiyotaki and Mir man (1972). In the market in contrast to the first best, each agent faces economy, the borrowing constraint. Following the author, we assume that the bor rower can borrow as as the debt repayment of the next period dt+1 long does not exceed the constant fraction X of returns from the present in vestment kt+1: (7) dt+1<XRt+1kt+1, from Rt+1 is the gross rate of returns on the capital investment t to t + 1. The flow-of-fund constraint of the agent who is investing at date t implies where date = c\ + kt+1 wt + lt + Bzt + -^-. (8) on consumption and investment in Here, his expenditure side (LHS) is financed by the wage income wt, the returns and storage, in addition to the borrowing dt+1/rt (where rt is interest rate) in the right-hand side (RHS). We conjecture agent does not store, which For the agent who is returns on the investment His debt in the RHS is used the harvesting, h?L + Z(+i = Rtkt dr c? + can be verified the left-hand from loan lt, the gross real the investing later. flow-of-fund constraint implies (9) of the previous to finance the period after repaying loan and storage lt+1/rt consumption, in the LHS. The competitive-market equilibrium to the marginal products: equal Rt=f'(kt) wt = = aAkr\ (1 a)Afc?, prices are (11) kt is aggregate capital stock, which is: The credit-market clearing condition is equal to kt in equilibrium. (12) (3), one of the clearing is given by equation not is law. The com by Walras' independent is defined as a set of prices (Rt, wt, rt) and quantities the goods-market conditions market-clearing Although petitive the factor (10) where = lt+1 dt+v implies equilibrium 75 Comment a function (c\, c\, kt+1, zt+1, dt+1, lt+1) as which satisfies the utility maximization clearing conditions. of the state variables of each agent (kt, zt, dt, lt), the market and can show constraint is not tight, that is, X is that, if the borrowing is not binding then the borrowing constraint larger than the threshold, is the first best. and the allocation We constraint is tight (X is small), We can also show that if the borrowing is credit constrained. The credit-constrained then the economy equilib in his paper. rium exhibits many features that the author emphasizes is an increasing (a) Investment function of the net worth of the invest ing agents: wt + *??= lt+ Bzt c\ l-(XRt+1/rt) the numerator ' (13) net saving of the investing agents?the The denominator is the down payment worth minus the consumption. one for the investment of unit?the between the cost of in gap required where is the gross of one unit and the maximum vestment amount of borrowing available. use to the finance the gross saving gap between agents investing cost of investment and the amount of external finance. The function (b) Net worth of the investing agents is an increasing vestment and storage of the previous period in the equilibrium: = wt + lt+ Bzt (1 a + Xa)Ak? + Bzr (c) Inefficient storage is used lower than the time-preference zt = > 0, and rt rate to the savers is rate: B<?. (d) Consumption time: investing c\ and the real interest of in of individual agents is larger at harvesting time than 1 c\+1 PB c\ P 1~ Here, because the aggregate worth (XRt+1/rt) the investing saving is an of the investing agents agents save more function than harvesting agents, of the ratio of the net increasing and that of the harvesting agents. This as 76 Kiyotaki sociation of income distribution overlapping-generations overlapping-generations sume everything). Here, as the author and aggregate to the saving is common even as as it not extreme is the though con which the (in agents harvesting model, model the present distribution af of wealth emphasizes, as seen in (a), and the present fects the present investment investment, as seen (b). This contemporaneous affects the future wealth distribution and interaction between the wealth distribution and the intertemporal investment is the unique feature of the credit-constrained economy. we with the other market and (a) (b) Combining clearing conditions, have: _= (1 - a + Xa)Ak? + Bzt 1 - (XaAk^/B) kt+1 zt+1 = Ak? + Bzt c\ investment (14) kt+1 -c\- c\. This dynamic interaction between ment may generate rich dynamics movement ' (15) the wealth distribution and invest of aggregate economic activities. The is persistent the present because of the aggregate quantities on the net worth depends of the investing The aggregate agents, which is a function of the previous investments. quantities may be more volatile, because the net worth of the investing agents affect the the investment and of the unproduc compositions productive capital tive storage, which changes the total factor productivity (TFP) endoge nously. this alternative model Although this model, with model, infinitely erate exotic nonlinear shares many lived agents, features ismore of the author's difficult to gen than the author's genera overlapping dynamics this is the indivisible project. But I do not consider the income distribution because of the alternative model, shortcoming rate of output during than the growth tends to move more sluggishly the business cycle. tions model 3 with Conclusion an alternative to present it may be a violation of etiquette Perhaps is impor constraint I agree with the author that the borrowing model. ac tant for understanding economic the various features of aggregate tivities. I also consider the liquidity constraint) that the borrowing constraint (ormore broadly, the various features of helps in understanding 77 Comment the monetary economy as the medium is used that the author did not address. Namely, as the means of exchange, of short-term and as the unit of contracts. money saving, on the subject of in other researchers the researchers Therefore, communicate well with liquidity constraints must order to have an impact on the way people understand the economy. include simplicity of theory and how Criteria for good communication the well the simple theory empirically observations. explains Finally, concerning simplicity of theory, it is important to explain the wide phe nomena as clearly as possible with the minimum of auxiliary number as sumptions. Endnotes 1. In remark 3, the author argues that the credit rationing if the initial wealth is not needed and the difference of the investing is converging to zero in the limit. agents are different I still think it artificial that agents who have a penny more in than the average However, less do not invest. If agents have some flexibility in vest, while agents who have a penny choosing ligible the size of project, become as the agents 2. This model 3. Thus follow is based or if there is a lottery, essentially on Woodford then the borrowing would become neg homogeneous. (1990) and Kiyotaki of date kt is capital stock at the beginning the author's notations of capital investment and Moore (2001,2005). is invested at date t,which as closely as possible. t-\. I Here, References Rao. 1989. Equilibrium in an overlapping existence Aiyagari, truistic preferences. Journal of Economic Theory 47:130-52. -. 1992. representative Brock, William, The discounted Co-existence agent and Leonid case. Journal Nobuhiro, Kiyotaki, Review 92 (2): 62-66. -. 2005. of a representative Journal type equilibrium. Mirman. of Economic and John Moore. Financial deepening. agent of Economic type equilibrium Theory 57:230-36. 1972. Optimal economic Theory 4:479-513. 2001. Evil Journal models generations growth is the root of all money. of the European with a non American Economic 3 (2-3): 701-13. Woodford, Journal -. Michael. of Economic 1990. Public 1986. Stationary Theory 40:128-37. debt as private sunspot equilibria liquidity. American in a finance Economic constrained Review al and uncertainty: Association Economic with 80:382-88. economy.