Targeted transfers and the great recession

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1 Targeted transfers and the great recession Hyunseung Oh and Ricardo Reis Columbia University October 2010 Abstract Since 2007, government spending has increased rapidly across the OECD countries. Partly in response, economic research ourished focussing on the impact of government consumption on economic activity. However, about three quarters of the increase in government spending in the United States (and more in other countries) has been in social transfer spending. We document this fact, and show that increased U.S. spending on retirement, disability, and medical care has been higher than all of the increase due to government consumption, investment, and unemployment insurance. We argue that future research should focus on the positive impact of transfers. Towards this, we present a model in which there is no representative agent and Ricardian equivalence does not hold because of uncertainty, imperfect credit markets, and nominal rigidities. Targeted lump-sum transfers are expansionary both because of a neoclassical wealth e ect and a Keynesian aggregate demand e ect. Prepared for the JME-SNB conference: Directions for macroeconomics: what did we learn from the economic crisis? We are grateful to Alan Blinder, Janet Currie and Robert Hall for useful conversations that got us started on this topic, and to Veronica Rappaport, Stephanie Schmitt-Grohe, Martin Uribe, and Michael Woodford for useful comments. Jorge Mejia provided excellent research assistance. Contacts: and 1

2 1 Introduction After many years of neglect, the positive implications of government spending for macroeconomic business-cycle dynamics are again at the center of research. In part there is a pressing real-world motivation behind this interest: all over the developed world, scal spending increased rapidly between 2007 and In the United States, for instance, the ratio of government spending to GDP increased by 4.4%, the largest two-year increase since New theoretical research on the topic has characterized the circumstances under which an increase in government consumption can lead to a signi cant increase in output in standard neoclassical and new Keynesian DSGE models. 1 In empirical work, recent studies have used a variety of econometric techniques and data on many countries to identify the impact of changes in government purchases on output and employment. 2 Many lessons have already come out of this recent work. Economists now understand better the importance of the stance of monetary policy for the e ectiveness of scal expansions, the role of the zero lower bound on nominal interest rates, the importance of identifying exogenous changes in policy, and the crucial role of agents expectations about future policy. However, there is a discomforting disconnect between the real-world motivation behind this interest and the economic research that has sprung from it. While in the world, government spending has increased, the research has been mostly about increases in government consumption or, less often, investment. Government spending is the sum of these two components with two others, one small interest payments and another that is very large transfers. Section 2 starts by discussing the trend increase in the share of social transfers in total U.S. government spending, from 17% of the budget in 1957, to 39% of the budget by In the more recent past, from the end of 2007 until the end of 2009, only one quarter of the large increase in government spending in the United States, is accounted for by government consumption and investment. 3 Three quarters of the increase are due to increases in social 1 Just in the last two years, see Cogan et al. (2010), Christiano et al. (2009), Hall (2009), Woodford (2010), Erceg and Linde (2010) Monacelli and Perotti (2008), Uhlig (2010), and Drautzburg and Uhlig (2010). 2 In the recent past, see Perotti (2008), Mountford and Uhlig (2009), Corsetti et al. (2009), Mertens and Ravn (2010), Barro and Redlick (2009), Ramey (2009), Nekarda and Ramey (2010), Krenn and Gordon (2010), Monacelli et al. (2010). 3 The National Bureau of Economic Reserach declared that December of 2007 was the peak of the business 2

3 transfers. Looking across a sample of 22 countries in the OECD and Europe, the United States does not stand out in this regard. In every country where spending increased, at least 30% of the increase was driven by transfers. The median share of transfers in the increase in spending is 64%. Looking in more detail at the components of this 3.3% of GDP increase in social transfers, 1.8% came solely from increases in retirement spending and medical care. This increase is larger than all of the increase in government consumption, investment and unemployment insurance. From a di erent perspective, a few variables (the fraction of the population over 65, the unemployment rate, and the price of health care) that are likely behind nondiscretionary changes in social transfers can explain about half of the total increase in social transfers during Most macroeconomic models of business cycles are silent about the e ect of social transfers. They typically assume a representative agent, so that lump-sum transfers from one group of agents to another are neutral for aggregate employment and output. Many also assume that the conditions for Ricardian equivalence hold, so that government transfers across time are likewise neutral. We propose a new model where lump-sum transfers, directed from one group in the population to another, can boost employment and output. Under di erent parameter con gurations, our model nests three conventional models: the neoclassical growth model, the Aiyagari incomplete markets model, and a sticky-information new Keynesian model. The two key ingredients of the model are idiosyncratic uninsurable uncertainty about income and health, and nominal rigidities in price setting. Lump-sum directed transfers boost output and employment through two new channels. The rst is a neoclassical channel, whereby the marginal worker is more willing to work to pay for higher transfers to those less fortunate. The second is a Keynesian channel, whereby transfering resources from households with low marginal propensity to consume to those with a high marginal propensity to consume boosts aggregate demand. Section 5 makes a rst attempt at quantitatively evaluating the role of these channels. Shifts in transfers are expansionary, but they are one order of magnitude less e ective at boosting output and employment than are changes in government consumption. In the cycle. 3

4 baseline calibration in this paper, the overall e ect of either form of government spending is small. However, we should note from the start that our simple model ignores many of the ingredients that the recent literature has shown can signi cantly boost spending multipliers, so our quantitative results should be interpreted with caution. A more enduring lesson that we take from our quantitative experiments is that the e ect of transfers is sensitive to who in the population pays and who receives. Transfer programs that are targeted at di erent groups can have very di erent aggregate impacts, and can as easily raise output as they can lower it. Section 6 o ers some brief conclusions. But the main message of the paper can be summarized in one sentence: research on scal spending should be more about research on social transfers. 2 The weight of transfers in the scal expansion Over the last 60 years, scal spending has continuously increased and its share of GDP imn 2009 is about double what it was in Figure 1 shows this increase, as well as the evolution of each component of government spending in the United States as a ratio of GDP, using annual data from 1947 to The compositional change is clear, with transfers steadily rising, starting out as a small share of spending to presently being its largest component. The gure shows that the decisive moment occurred in the mid 1960s, with the Great Society programs of Lyndon Johnson. In the two decades from 1987 to 2007, government spending grew only at the rate of output growth, but transfers kept on rapidly rising, while government consumption steadily declined. Looking more broadly across the OECD, the pattern is quite similar. 5 With the spread of the welfare state, social transfers have steadily been increasing in almost every single country, including in the last 30 years, and even where government spending as whole was 4 Our data comes from NIPA table 3.1, and our categories match those in that table as follows: total spending is the sum of consumption expenditures, gross investment, capital transfers, net purchases of assets minus consumption of xed capital; consumption equals consumption expenditures minus consumption of xed capital; transfers equals government social bene ts plus subsidies plus capital transfers; and investment is the residual. 5 Details are available from the authors. 4

5 constant or falling. These facts are well known in political economy (Drazen (2000)), but less well appreciated among macroeconomists. Little discussed in both groups are the developments of the last two years. 2.1 U.S. scal spending during the great recession, Between the last quarter of 2007 and the last quarter of 2009, U.S. government spending increased by 14.4%, or 4.4% of GDP. This refers to the integrated government spending, including both federal, state and local governments. Looking at the components of spending, government investment accounts for 5.6% of that increase, while government consumption was responsible for 21.1%. Transfers alone account for 75% of the total increase in spending, or 3.3% of GDP. One may wonder whether this increase in transfers just follows the natural trend. As nominal income grows, then spending would be expected to grow. Moreover, the population is aging, increasing those collecting pensions, and the price of health care is increasing, raising medical care expenses. To address this issue, we compute the following statistic: add nominal GDP growth to the trend increase in the years prior to the crisis, using a linear trend t to the data between 1998Q4 and 2006Q4. 6 According to this measure of the normal increase in transfers, taking growth and the usual trend into account, transfers were predicted to increase by 2.8% during the two years. Instead they increased by 27.4%. Another concern is that many tax deductions can be seen as negative transfers (e.g., tax credits for tuition). These tax expenditures, as they are sometimes called, have grown signi cantly in the last two decades but it is di cult to measure their size in the U.S. budget. The 3.3% of GDP increase in transfers calculated above assumed that there are no such tax expenditures. Taking the polar opposite view, that all taxes and social security contributions are negative transfers, then the increase in transfer rises to 6.7% of GDP. In sum, while public works and other consumption plans dominate the debate, in the data, the scal stimulus of has been mostly about increasing social transfers. 6 We chose 8 years from observing gure 1, but starting in 1996 or 2000 does not make a large di erence. 5

6 2.2 International comparison: is the U.S. scal expansion unusual? We obtained quarterly data between 2007Q4 and 2009Q4, for as many countries as we could nd, from two sources, the OECD Economic Outlook and Eurostat. The construction of the series followed the same guidelines as used in NIPA, and we used the U.S. series in the OECD to ensure that the de nitions of the categories of government spending matched. 7 The rst column of Table 1 shows the 22 countries in our sample. The second column has the percentage increase in total government spending. In only one country, Hungary, has government spending fallen, and in the majority of them it has increased above the trend of the past decade. The increase in spending in the United States may be very large compared to its history, but it is only the 6 th largest in the sample. The following two columns have the share of the increase in spending attributed to either a change in transfers, or to consumption plus investment. 8 The two do not add up to one because of the omission of the change in interest payments. The dominance of transfers is true for many countries. In 13 out of the other 20 countries for which spending increase, transfers accounted for a larger share of the increase than consumption plus investment. In no country were transfers responsible for less than 30% of the total increase in spending. The fth column presents the unusual growth in transfers de ned in the previous section: the proportional increase in transfers minus the proportional increase in GDP over the same period, and the 8-quarter predicted increase in total spending from a linear trend t to the years between 1998Q4 and 2006Q4. By this measure, the United States is only beaten by Ireland, Slovakia and Finland. In only two out of the twenty two countries did transfers grow less than what would be expected. Everywhere else transfers grew at an extraordinary rate, often by two percentage digits. All over the developed world, the large scal expansions have also been mostly about increasing social transfers. 7 Using the OECD cateories, now: total spending equals current disbursements plus xed capital formation plus capital transfers minus consumption of xed capital; consumption equals non-wage consumption plus wage consumption minus consumption of xed capital; transfers equals social security bene ts plus subsidies plus capital transfers, and investment is again the residual. 8 The formula for the third column is: (T ransfers 09Q4 T ransfers 07Q4)=(Spending 09Q4 Spending 07Q4) and likewise for the fourth column with government consumption plus investment. 6

7 2.3 Looking at the components: where does the increase in U.S. transfer come from? Using the annual data from Table 3.12 of NIPA, we constructed the following four groups. First are social transfers associated with retirement and disabilities, most prominently through pensions paid by the Social Security system. 9 Second is spending driven by medical reasons, the bulk of which is accounted for by Medicare and Medicaid. 10 Third is unemployment insurance, perhaps the transfer that rst comes to mind as increasing during a recession. The last group includes all other transfers, mostly from income support programs. 11 Figure 2 shows the share of each of these categories in total transfer spending in the thirty years between 1979 to The increase in unemployment insurance in the recessions of , , and 2001 is quite visible, while the share of income assistance and others is at. The most visible trend is the fall on spending in retirement and disability matched by an increase in spending on medical assistance. Tuning then to the period between 2007 and 2009, recall that transfers increased by 3.3% of GDP. The largest share of this increase, 29.5%, is in medical expenses. The second largest share is spending on retirement and disabilities, which accounts for 24.0% of the increase in total transfer spending. Unemployment insurance actually only appears in third place accounting for 23.6% of the increase, almost as much as the others categories which accounts for the remaining 22.8%. From reading the press or following the political debate, one may not have guessed this. But, between 2007 and 2009, government spending in medical care, retirement and disabilities has grown as much as spending on government consumption, investment and unemployment insurance. Because this fact may surprise many, we further break it down by category. 9 Concretely, this category includes the sum of spending on: old-age, survivors, and disability insurance; railroad retirement; pension bene t guaranty; veterans life insurance; veterans bene ts pension and disability; and state and local government s temporary disability insurance. 10 This category includes spending in: hospital and supplementary medical insurance ; workers compensation; military medical insurance; black lung bene ts; state and local government workers compensation; and state and local government s medical care. 11 Half of this is accounted for by three categories: the earned income tax credit, the supplemental nutrition assistance program, and various supplemental security income programs. 7

8 2.3.1 Medical spending The total amount spent on medical care is the product of price times quantity. Using the CPI index for medical care as a measure of the price, of the 12.5% increase in medical transfers between 2007 and 2009, 6.8% were accounted for by higher prices and 5.7% by more quantity. Therefore, the increasing cost of health care in the United States alone can account for 4/9 of the increase in the largest category of spending. In this period, the price of medical care increased by 6.1% even though the consumer price index increased by only 2.8%. To see that this is not extraordinary, gure 3 shows the change in log transfers of medical care, and the decomposition into prices and quantity. The increase in the total amount spent on health care, and the share due to an increase in quantity, is on the high side for the past decade but not out of line in relation to what is usual. Making the same calculations with respect to Medicaid, the provision of health care to the poor, gives very similar results. The percentage increase in Medicaid has been slightly lower than the increase in total health transfers, and the split between price and quantity is similar to what has been typical in the past decade Retirement and disability Between 2007 and 2009, the government transfers under the heading of retirement and disabilities increased by 15.5%. Taking out the population growth rate and in ation (measured using the GDP de ator), the increase in real per capita transfers was 9.8%. To gauge how much of this increase was discretionary, we estimated a linear regression with the log of real spending per capita as the dependent variable and a constant, the share of the total population that is not on the labor force and is more than 65 years old, and the share of the population that is older than 65, as the independent variables. We run the regression in rst di erences to deal with the clear trends in the sample between 1976 and Using the actual values for 2008 and 2009 in this tted equation, the total residual for these two years is 5.6%. That is, almost 2/3 of the total increase in transfers are due to in ation, aging of the population and a larger fraction of those over 65 leaving the labor force. 8

9 2.3.3 Unemployment insurance Total per capita real spending on unemployment insurance, increased by 276% between 2007 and Dividing by the increase in the number of unemployed, the real amount per number of unemployed increased by only 69%. We regressed, in rst di erences on the sample, the log of this variable on a constant and two variables: the unemployment rate to capture systematic increases in the generosity of the system as more people lose their jobs; and the median duration of unemployment to capture the change in bene ts as people remain unemployed for longer. The two residuals in 2008 and 2009 add up to only 12.4%. That is, even though one of the anti-crisis measure was the expansion in the duration of unemployment insurance, this so far seems to have led to a modest increase in government spending on the program. 2.4 Bringing the facts together While not unique in the developed world, the United States has been one of the leading examples of countries with simultaneously large increases in scal spending, and a large share of it accounted for by transfers. It is not unemployment insurance, but medical care, retirement and disability that account for more than half of this increased spending. A handful of simple variables, like population growth, population aging, the price of health care, or the unemployment rate account, almost mechanically, for a large share of this increase. In spite of all the debate and research about large discretionary increases in government consumption in response to the recession, the numbers show instead a mild discretionary response, with a mysteriously large increase of discretionary spending in the quantity of health care provided. 3 Understanding the positive e ects of transfers in theory In a representative-agent economy, lump-sum transfers across agents do not a ect any aggregate quantities. Furthermore, under Ricardian equivalence (Barro (1974)), changes in the time-pattern of government transfers do not a ect private wealth, since any increase in transfers today must be o set by a discounted future change in the opposite amount in 9

10 order for the government to balance its budget. As most models of economic uctuations make these assumptions, they would predict that the massive increase in social transfers in would be neutral with respect to employment and output. The focus would instead be on the e ect of social transfers on inequality and welfare. Away from this dominant benchmark, transfers can have positive e ects if they distort marginal rewards and relative prices. Many transfer programs are not lump-sum but partly progressive, more generous to the poorer or those without a job. While they provide for social insurance, they also typically discourage work e ort, savings, and production. If during a deep recession, transfers are made more progressive, then even though this may be normatively justi ed, it may also lower production and employment. An alternative mechanism through which transfers can have aggregate e ects is by increasing public debt, which raises the supply of assets in the economy that agents can use to self-insure against shocks. Woodford (1990) and Aiyagari and McGrattan (1998) provide two di erent models to capture this e ect and the social bene ts of public debt. In Woodford (1990), increasing transfers raises investment and output by loosening liquidity constraints, whereas in Aiyagari and McGrattan (1998) transfers lower capital and output by reducing the need for precautionary savings. One fact to keep in mind is that, in the United States between 2007 and 2009, public debt increased but private debt fell, so that the total amount of domestic non nancial debt grew at the slowest rate in the past decade. Whether there are more or less assets available for households to smooth shocks is a matter of interpretation. We propose a di erent mechanism through which lump-sum transfers have aggregate e ects: targeting. Transfers across di erent groups of households will raise the consumption and increase labor supply of some, while lowering it for others. If the transfer is welltargeted, the e ect on the former can well exceed the countervailing e ect on the latter, so that aggregate consumption and labor supply increase. The model has two key ingredients: incomplete markets and nominal rigidities. On the household side, people choose how much to consume and whether to work subject to idiosyncratic shocks to both income and their health. The government transfers resources contingent on the two exogenous characteristics of the household, their salary o er and their 10

11 health status. If there are complete insurance markets, then both shocks and transfers have no e ect on the private wealth of these agents, so they do not a ect aggregate output or employment. Without insurance markets, we assume that households can only trade a riskless bond, so they are sensitive to the changes in wealth that lump-sum transfers may bring about. On the rm side, producers only update their information and prices sporadically, following the sticky-information model of nominal rigidities. While rms prices are informationally rigid, they are committed to satisfy the demand for their products. Therefore, if transfers raise aggregate demand, the temporarily low prices lead to an expansion in output and employment. The model merges the work on incomplete markets and on nominal rigidities, recently surveyed in Heathcote et al. (2009) and Mankiw and Reis (forthcoming) respectively. For di erent particular parameter con gurations, it nests three well-known models: the neoclassical growth model with government spending of Baxter and King (1993), the incompletemarkets model of Aiyagari (1994), and the sticky-information model in Mankiw and Reis (2002). Di erently from the literature on scal policy with incomplete markets, our focus is on transfers and on the positive properties of the model in response to shocks rather than on welfare in the steady state. 12 Also new to that literature, we consider health shocks, because the largest component of transfers in the U.S. government budget is medical care. One important simpli cation is that we assume no aggregate uncertainty or, equivalently, that there is perfect foresight with respect to aggregate variables. This greatly simpli es the numerical analysis. We still consider aggregate shocks though, but via perfect-foresight comparative statics: starting from a steady-state that agents expected would persist forever, at date 1 they learn that there has been a change to some exogenous aggregate variables. There are no further changes from then on, and agents can foresee all of the future path for aggregate variables. The experience with the neoclassical growth model is that these perfect-foresight comparative statics are often not too far from the rst-order approximate solutions of stochastic models. 12 Floden (2001) also studies transfers but focuses on welfare at the steady state. 11

12 3.1 The households There is a continuum of households that at each date are characterized by a triplet fk; s; hg where k is their capital, s their individual-speci c salary o er, and h is their health a ecting the relative disutility of working. The problem of each agent is: Z Z V (k; s; h) = max c;n;k 0 ln(c) (1 h)n + V (k 0 ; s 0 ; h 0 )df (s 0 ; h 0 ) n 2 f0; 1g; c 0, and k 0 0. (2) c + k 0 = (1 + r)k + swn + d + T (s; h) + z(k; s; h) (3) ln(s 0 ) = h = 2 2(1 + ) + ln(s) + "0 with " 0 N(0; 2 ) i:i:d: (4) 8 < 1 with probability and i.i.d. (5) : draw from U[0; ] with probability 1 (1) The variables and functions are: V (:) is the value function, c is consumption, n is the choice to work or not, r is the gross interest rate, w is the average wage, d is dividends, are lump-sum taxes, T (:) are non-negative lump-sum transfers, and z(:) are insurance payments. As for the parameters: is the disutility from working with the worst possible health, is the discount factor, is the depreciation rate, and 2 are the persistence and variance of shocks to salary o ers, is the probability that the person is healthy and controls the average utility gap between the healthy and the unhealthy. Throughout the paper, F (:) will denote cumulative density functions, and a prime in a variable denotes its value one period ahead. Going through each equation in turn, equation (1) states that households wish to consume more and su er from working if they are unhealthy. They live forever and face uncertainty on their future health as well as their future salary. There could also be additional terms attributing utility directly from both government spending as well as from health regardless of whether the household works or not. The implicit assumption is not that these terms do not exist, but rather that they enter utility additively. While they would a ect welfare characterizations, they are irrelevant for the positive properties of the model that we will focus on. Our model of health is admittedly stark, so it is useful to stop to understand what we 12

13 are trying to capture and what we are neglecting. Our goal was to capture, in the simplest possible way, the uninsurable health uncertainty that people face, the e ects that its shocks have on people s income, and the large amount of social transfers that are contingent on health status. Our option of not introducing health as a separate good should not be too important: we can see the utility function as the value function derived from optimal choices of health and nal goods consumption. Likewise, we model the transfers as cash payments rather than transfers in kind, but as long as households did not receive more in health transfers than they wanted to consume, or if they can sell part of the transfer, then this would not make too much of a di erence to our model and conclusions. A potentially more problematic assumption would be to allow people to invest in their health, modelled as a stock that the agent can accumulate. Insofar as this investment competes with monetary savings, then it would matter to the e ects that transfers have. We chose not to follow this route because it would require careful modelling of the health-producing sector of the economy, which was not our focus in this paper. The conditions in (2) impose that households can choose whether to work or not, and that they face a borrowing constraint so that they cannot leave a period with negative assets. Equation (3) is the budget constraint stating that consumption plus savings, on the left-hand side, must equal the income from interest on capital, wages from working, dividends from rms, transfers from the government, and insurance payments, minus taxes paid. Importantly, note that transfers are lump-sum: they depend only on the exogenous characteristics of the household. Equations (4) and (5) put strong assumptions on the stochastic processes for the two shocks. These are important to keep the solution of the model simple, but they could be feasibly relaxed at the expense of higher computational burden. The two shocks are independent across agents and independent of each other, so at any date, the cross-sectional distribution of salary o ers is log normal with an average salary equal to E(sw) = w. The cross-sectional distribution of health has point-mass at healthy people with h = 1, and then a uniform distribution over how unhealthy other people are. A restrictive assumption is that health shocks are independent over time. The time period in our model is a year, and the health shocks are not meant to capture disability or old age, but rather temporary 13

14 illness that a ects the ability to work and earn wage. The solution to this problem is a set of functions c (k; s; h), n (k; s; h); and k 0 (k; s; h) that solve the Bellman equation determining how much each household consumes, works and saves. 3.2 The rms There is a representative competitive rm that produces the consumption good by combining capital K and intermediate goods x(j) according to the production function: Z 1 Y = AK X 1 and the aggregator X = x(j) dj 1= : (6) This rm rents capital from households paying r per unit, and buys intermediates at prices p(j). Optimal behavior by the rms together with perfect competition implies the wellknown conditions: K 1 K r = A and p = (1 )A (7) X X p(j) =( 1) Z 1 1 x(j) = X and p = p(j) dj 1=(1 ) (8) p There is also a continuum j 2 [0; 1] of monopolistic intermediate-goods producing rms. They are equally owned by all household, making pro ts d(j); which they immediately 0 0 distribute as dividends. Each rm operates a linear technology: x(j) = l(j); (9) where l(j) is the e ective labor hired by rm j. All of the prices and returns so far have been denominated in real terms, in units of the nal consumption good. Intermediate-goods rms choose instead the nominal price of their product, p(j)q where q is the price of the consumption good. These rms have sticky information: each period, a fraction of the rms learn about the current state of the world, while the remaining 1 have old information. With no aggregate uncertainty, and if there has been no unexpected change, then all rms are fully informed. Following 14

15 an unexpected change at date 1, then at date t there is a group of rms with measure t = P t 1 i=0 (1 )i that know about it, and a second group with measure 1 t that does not and has not changed their price. Their optimal prices are then: p(j) = w if attentive, (10) p(j) = w 0 q 0 =q if inattentive, (11) where w 0 and q 0 are the steady-state wages and prices, which rms that are unaware of the change still expect to be in place. The resulting pro ts are 3.3 The government d(j) = ( 1) wx(j) if attentive, (12) q0 w 0 d(j) = 1 wx(j) if inattentive, (13) qw The monetary authority simply keeps the price of the consumption good q = 1, a strict form of price-level targeting. with monetary policy are left for future work. 13 The focus of this paper is on scal policy, and the interactions The scal authority chooses lump-sum transfers T (:) that are in general di erent according to the exogenous characteristics of households. There is also exogenous government spending G and lump-sum taxes are chosen to balance the budget every period: Z Z G + T (s; h)df (s; h) = : (14) We choose to have lump-sum taxes and a balanced-budget rule to neutralize the two previously studied mechanisms through which transfers can have aggregate e ects. Raising transfers in our model will not lead to an increase in distortionary taxation, nor to an increase in the amount of public debt potentially crowding out or in investment and capital. This way, we can focus on the new mechanisms we propose. 13 We have experimented with two di erent monetary policy rules: nominal-income targeting and a Wicksellian interest-rate rule. The results were quantitatively similar. 15

16 3.4 Aggregates and market clearing As households di er in their history of health and salary o ers, they make di erent decisions about work, consumption and saving, and so enter each period with di erent wealth k. Combining household optimal behavior with the exogenous distribution of household characteristics gives the endogenous distribution F (k; s; h) of households in the economy. Both the capital market, where households rent capital to the nal-goods rm, and the labor market, where they sell labor to the intermediate-goods producers, must clear: Z Z labor market sn (k; s; h)df (k; s; h) = L = l(j)dj; (15) Z capital market k 0 (k; s; h)df (k; s; h) = K 0 : (16) Because the rms are equally held by all households, total dividends paid equal dividends recvied per capita: Z d(j)dj = d: (17) Finally, this is a closed economy, so the insurance payments must add up to zero: Z z(k; s; h)df (k; s; h) = 0 (18) 3.5 Equilibrium and relation to the literature We will focus on three aggregate variables in this model: aggregate output Y, aggregate consumption C = R c (k; s; h)df (k; s; h), and total employment E = R n (k; s; h)df (k; s; h). An equilibrium in these variables is characterized by households and rms behaving optimally and markets clearing, as de ned by equations (1)-(18). There are two key ingredients in the model: imperfect credit markets on the household side and nominal rigidities on the rm s side. There is imperfect insurance as long as the payments z(:) do not reproduce the Pareto optimum allocation of consumption and labor across households, as if the ex ante identical households signed a contract at the beginning of time. There are nominal rigidities as long as < 1 so that following an aggregate shock, some rms will take some time to learn about it, and in the meantime set prices based on 16

17 old plans that do not re ect the news. The following three results are proven in the appendix: Proposition 1 With full insurance, there is a representative household capturing consumer choices, that solves the problem V (K) = max C;L;K 0 ( ln(c) ) [L + (1 )(1 E(s 2 )]2 ) + V (K 0 ) 2 s:t: (19) C + K 0 = (1 + r)k + wl + M (20) taking wages, interest rates, and M; as given. Proposition 2 Without nominal rigidities, there is a representative rm solving: max fy rk (1 + )wlg s.t. Y = AK L 1 (21) taking taxes = 1, wages and interest rates as given. Proposition 3 If there is full insurance and no nominal rigidities, the aggregate equilibrium is the set fy t ; C t ; L t g such that the representative household in proposition 1 behaves optimally, the representative rm in proposition 2 behaves optimally, and in equilibrium: M = wl G: Equilibrium employment is: E = L + [ (1 )(1 )](E(s2 ) 1) E(s 2 ) These three results provide a map between our model and three standard speci cations that it nests. First, with both complete insurance and perfect price exibility, the model reduces to a standard neoclassical growth model with a payroll tax. The aggregate technology is a standard Cobb-Douglas function and the labor income tax captures the ine ciency brought about by markups in the intermediaries sector. The preferences of the representative agent are separable over time and the intertemporal elasticity of substitution is one. As for labor supply, if everyone is healthy, then E = = 1 and all households work all the time, so the model become identical to the textbook Ramsey-Cass-Koopmans model. At 17

18 the other extreme, if = 0 and = 1, then health is uniformly distributed between 0 and 1, and the implied Frisch elasticity of labor supply is exactly 1. Second, if there is full insurance together with nominal rigidities, then the model is similar to the sticky-information model of Mankiw and Reis (2002) with onle two di erences. First, there is capital and investment. Second, the labor market is similar to that in Gali (2010), with the di erence that unemployment is the result not only of bad salary o ers, but also of poor health. As in the bulk of new Keynesian models, aggregate demand policy has real e ects in our model. Third, if prices are exible but there is no private insurance z(:) = 0, then the model is close to the version of the Aiyagari model in Alonso-Ortiz and Rogerson (2010), expanded to have health shocks. Without insurance, transfers move wealth across agents and a ect their willingness to work and consume. 4 The impact of transfers on aggregate activity Total government spending increase between 2007:4 and 2009:4 by 4.4% of GDP, with approximately 3/4 devoted to transfers. What was the impact of this spending on employment and output? 4.1 The neoclassical growth benchmark The neutrality result follows immediately from proposition 3: Corollary 4 With full insurance and exible prices, the choice of T (s; h) is irrelevant for aggregate output and employment. This result is robust to introducing nominal rigidities in price-setting. As long as there is full insurance, so proposition 1 holds, any rearrangement of wealth across households is undone by equivalent insurance payments, so it does not a ect any decisions. In contrast, government consumption lowers private wealth, encouraging the representative consumer to work more. To assess the size of this e ect, we pick the parameter values described in table 1, so that the steady state of the model hits somel calibration 18

19 targets. The rst section of the table has conventional targets and parameter choices for the production technology and household preferences. The second section has the parameters linked to intermediate- rm behavior: the average markup is 25%, while 50% of rms update their information every year. This extent of imperfect competition and nominal rigidities is on the high side, but not out of line with usual values. For the idiosyncratic shocks hitting households, we assume that salary o ers are quite persistent in line with the estimates in Storesletten et al. (2004). The choice of is at the top range of their estimates, because they considered only continuously employed males, whereas in our model, s are salary o ers that may be turned down. For the health shocks, we set to match the share of U.S. households in the labor force without any disability, from Kapteyn et al. (2010). We set so that the Frisch elasticity of labor supply is 0.7, the value suggested by Chetty (2009) in his recent synthesis of micro and macro estimates in the literature. Finally, the calibration of requires some explanation, since we need to take a stand on government consumption over GDP. One approach would be to set G=Y to the historical average in the United States, leading to = 3:00. However, this raises a problem with incomplete markets. Some agents enter a period with little savings and a low salary o er. If G is high, they may be unable to pay their lump-sum taxes even if they consume zero. In other words, the natural debt limit is tighter than zero, since to ensure that in the worst possible circumstances the agents repay their debts, they have to own a strictly positive amount of assets to guarantee that they satisfy their tax obligations. This is unappealing empirically, and speaks to the unrealism of having lump-sum taxes that would make even someone with no assets or income pay taxes to the government. To get around this problem, we calibrate instead to G = 0, leading to a lower = 2:20. The corresponding gures for the alternative calibration are available from the authors: they all lead to larger aggregate impacts of government spending. Figure 4 has the impulse response of employment and output to a shock to G of 4.4% of GDP that lasts for only one period. Employment rises, as the representative consumer works more to compensate for the lost wealth, and this raises output by 0.3%. However, savings fall lowering the capital stock and output from the second period onwards. The 19

20 gure also shows the response if the shocks to government spending is cumulatively of the same size, but now follows an AR(1) with persistence parameter 0.9. The initial impact is smaller but output now converges to its steady state value from above. Importantly, the spending multiplier is small, as in Baxter and King (1993). There are many modi cations of the model that can make it larger. 4.2 Targeted transfers With imperfect insurance, transfers from healthy high-salary households to those with low wealth and low salaries boost employment and output through two channels. First, since the marginal worker pays more in taxes than she receives in transfers, more generous transfers imply she has less wealth and so has a stronger incentive to work. This is the neoclassical channel that is standard in real business cycle models. Second, since the recipients of transfers have on average a higher marginal propensity to consume than the payees, transfers boost aggregate demand, which rms with rigid prices satisfy by hiring more workers and producing more. This is an eminently Keynesian channel. To understand the neoclassical channel, the top left panel of gure 5 plots the threshold ^h(s) = R h (k; s)df (k), where h (k; s) is the optimal threshold function such that people work if and only if h h (k; s). The locus is downward-sloping, and those above it are working, while those below it are not working. Consider then a carefully targeted transfer from the population in the middle box to the population in the corner box, so that total transfers paid amounted to 4.4% of GDP. Crucially, those receiving the transfers were very far from ever working. Therefore, the extra wealth barely changes their work decision. In contrast, those paying the transfer were at the margin between working or not. As their wealth has fallen, they are more willing to take a job, boosting employment. The other panels of gure 5 have the impulse responses to this shock. To isolate the neoclassical channel, we set = 1, so there are no nominal rigidities. In the top right diagram, we see the increase in employment among the marginal workers, and the very slight fall among other groups in the population. The bottom panels show that employment and output increase both by about 0.85%. Turning to the Keynesian channel, panel A of gure 6 plots the marginal propensities 20

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