US trend in‡ation reinterpreted. The role of …scal policies and time-varying nominal rigidities.

Nicola Acocella Sapienza University of Giovanni Di Bartolomeo Sapienza University of Rome Patrizio Tirelli University of Milan Bicocca October 23, 2013

October, 2013

Abstract This paper o¤ers a reinterpretation of the Fed’stime-varying implicit in‡ation target, based on two considerations. The …rst one is that the need to alleviate the burden of distortionary taxation may justify the choice of a positive in‡ation rate. The second one is based on compelling evidence that the degree of price and wage indexation falls with trend in‡ation. In fact, we …nd that a proper characterization of the joint evolution of …scal variables and nominal rigidities has a strong impact on the Ramsey optimal policies, implying optimal in‡ation dynamics which are consistent with the observed evolution of US trend in‡ation. By contrast, tax policies have been too lax, especially at the time of the controversial Bush tax cuts.

Jel codes: E52, E58, J51, E24. Keywords: trend in‡ation, monetary and …scal policy, Ramsey plan.

1 Introduction

The recent years have witnessed increasing interest in the dynamics of US in- ‡ation and output volatility, characterized by a post-1981 “Great Moderation” following the “Great In‡ation”episode of the 1970s. Several explanations have been put forward to the observed gradual reduction in in‡ation and in macro- economic volatility that characterized the US economy up to the 2008 …nancial crisis. Some researchers pointed at a change in the stochastic processes driving structural supply and demand shocks (Stock and Watson, 2003; Primiceri, 2005; Sims and Zha, 2006; Gambetti et al., 2008; Justiniano and Primiceri, 2008). Others emphasized the Fed’s shift to a rule-based approach, including more

1 aggressive interest rate feedback on in‡ation (Carlstrom et al., 2009; Taylor, 2012). A complementary view pinpoints changes in US trend in‡ation as a key factor behind the end of the Great In‡ation and the outset of the Great Moderation (Coibion and Gorodnichenko, 2011). Cogley and Sbordone (2009) document a gradual reduction in the underlying core or trend in‡ation rate. Few macro- would disagree with the statement that trend in‡ation is determined by the long-run target in the ’s policy rule, and the drift in trend in‡ation is usually attributed to shifts in that target. Ireland (2007) estimates a New Keynesian model accounting for an exogenous, time-varying Fed’simplicit in‡ation target. His results suggest that the target gradually rose from slightly above 1 percent at the end of the ’50s to over 8% in the second part of the ’70s; then it gradually fell to about 2% in 2004. Interpreting this result has proved di¢ cult. A number of contributions suggest that the Fed opportunisti- cally transferred supply shocks into persistent in‡ation changes in order to limit output losses in the 70s when shocks were mainly adverse, and to bring down in- ‡ationexpectations in the ’80s and ’90s when shocks were mainly favorable (see Ireland and references cited therein). Another interpretation sees changes in US trend in‡ation as a consequence of policymaker’s mis-perceptions and learning about the true structure of the economy.1 According to evidence provided in Milani (2009) learning accounts for the bulk of observed volatility in US trend in‡ation, and the implicit Fed’sin‡ation target has remained in the 2-3% range throughout the whole post-war sample. Leading macroeconomic models …t uncomfortably with empirical evidence and with these interpretations. According to Schmitt-Grohé and Uribe (2011) theories of monetary non-neutrality (accounting for monetary transaction costs, nominal rigidities, distortionary taxation, the zero lower bound, foreign holdings of domestic currency, the untaxed informal economy) imply that the optimal rate of in‡ation ranges between the Friedman rule and a number insigni…cantly above zero. Similarly, the implied optimal policy responses to shocks require minimal in‡ation volatility and permanent debt adjustment in order to obtain tax-smoothing over the business cycle. In this framework it is clearly impossible to rationalize the “opportunistic view”of the Fed’s responses to shocks, which should have allowed large and persistent variations in in‡ation. Even interpre- tations based on policymakers’mis-perceptions and learning imply a relatively large in‡ation target. This paper o¤ers a reinterpretation of the Fed’stime-varying implicit in‡a- tion target, based on two key factors. The …rst is a recent theoretical …nding that the need to alleviate the burden of distortionary taxation may justify the choice of a positive in‡ation rate (and a substantially larger in‡ation volatility) when total …scal outlays include a substantial amount of transfers in addition to the public consumption expenditures typically considered in macroeconomic models (Di Bartolomeo et al., 2013). The underlying intuition is relatively sim- ple. Coeteris paribus, a permanent change in public consumption causes a fall in private consumption and in real money balances, eroding the in‡ation tax base. By contrast, an equivalent increase in public transfers has no e¤ect on public consumption and real money balances. As a result, the optimal …nancing mix gradually tilts towards stronger reliance on in‡ation when transfers become

1 See Sargent (2001), Cogley and Sargent (2005), Primiceri (2005), Sargent et al. (2006).

2 relatively large. The second factor behind our interpretation is compelling ev- idence of a time-varying pattern in the parameters characterizing the pricing behavior of …rms and wage setters, where the degree of indexation typically falls together with trend in‡ation (Benati, 2008; 2009; Fernández-Villaverde and Rubio-Ramírez, 2008). In fact, we …nd that a proper characterization of the joint evolution of …scal variables and nominal rigidities has a strong impact on the Ramsey optimal policies, implying optimal in‡ation dynamics which are consistent with the observed evolution of US trend in‡ation. In a nutshell, our results are summarized as follows. We see a complementar- ity between our results and previous interpretations of US in‡ation that empha- sized the role of shocks and learning about the true structure of the economy. Up until the mid-60s the optimal in‡ation rate was virtually nil, then the contem- poraneous increase in public transfers and in the degree of in‡ation indexation caused a strong increase in the optimal in‡ation target, 6% by the mid-’70s. Finally, in the last part of the sample the reduction in in‡ation indexation and the stabilization in the level of public transfers cause a fall in the optimal in‡a- tion rate. We also determine the pattern of optimal tax policies. Our predicted …scal revenues track the increase in observed revenues fairly closely up to the end of the 70s, but they are systematically larger during the rest of the sam- ple. This result is consistent with observed debt dynamics, characterized by a reduction until 1980 and a large increase thereafter. This is puzzling in the light of received interpretations of the observed patterns of in‡ation and output volatility. In fact, debt dynamics should have been consistent with the changes in the stochastic processes driving structural shocks. This implies that a debt increase should have been observed in the adverse economic environment of the 1970s, and a contraction should have occurred during the Great Moderation. Our results also contribute to the ongoing debate about the “Great Devi- ation” of US in the years preceding the 2007 …nancial crisis (Taylor, 2010, 2012). In fact our predicted optimal in‡ation rate is very close to observed in‡ation. By contrast tax policies appear considerably lax, exactly at the time when sostituire when con of? the controversial Bush tax cuts. The rest of the paper is structured as follows. The next section introduces our theoretical model. We consider a remarkably simple model, which abstracts from capital accumulation but takes into account monetary transactions costs, monopolistic competition in goods and labor markets, price and wage sticki- ness and in‡ation indexation. Section 3 presents the results. The …nal section concludes.

2 The model

We set up a simple DSGE model characterized by standard nominal and real frictions. The nominal frictions include sluggish price and wage adjustments with indexation to past in‡ation. The real rigidities originate from monopolistic competition in both goods and labor markets. In addition, a transaction tech- nology where money facilitates transactions allows to motivate a money demand function. Exogenous government expenditures (public consumption, transfers and interest payments on debt) are …nanced by a distortionary labor-income tax, money creation (in‡ation tax), and issuance of one-period, nominally risk

3 free bonds.

2.1 Households The economy is populated by a continuum of households of measure 1. House- hold i’spreferences are:

1 t Ui = Et=0 u (Ct;i; lt;i) (1) t=0 X 1  1  where (0; 1) is the discount factor, Ct;i = c (j) dj is a consumption 2 0 t;i bundle, l is a di¤erentiated labor type that is supplied to all …rms. t;i R  The household’s‡ow budget constraint is

Mt;i Bt;i (1  t) Wt;ilt;i Mt 1;i Rt 1Bt 1;i Ct;i (1 + St;i) + + = + + t + Tt + Pt Pt Pt Pt Pt (2) where Wt;i is the nominal wage;  t is the labor income tax rate; Tt denotes real …scal transfers; t are …rms pro…ts; Rt is the gross nominal interest rate, Bt;i is a nominally riskless bond that pays one unit of currency in period t+1. Mt;i de- …nes nominal money holdings to be used in period t+1 in order to facilitate con- sumption purchases. Consumption purchases are subject to a transaction cost, St;i = s(vt;i), where vt;i = Pt;iCt;i=Mt;i is the household’s consumption-based money velocity. The features of s(vt;i) are such that a satiation level of money velocity (v > 0) exists where the transaction cost vanishes and, simultaneously, a …nite demand for money is associated to a zero nominal interest rate. We as- 2 sume that s(vt;i) is twice continuously di¤erentiable and (vt;i v)s0(vt;i) > 0. Households also set wages. We assume that the labor market is character- ized by monopolistic competition and a sluggish wage adjustment. We model nominal wage stickiness as in Rotemberg (1982). Each household maximizes the expected value of (1) subject to the labor demand (described below) facing a quadratic adjustment cost

2 w Wt(i)=Wt 1;(i) 1 (3) w 2 t 1 ! where w > 0 is a measure of wage stickiness and w [0; 1] is the degree of wage indexation to past in‡ation. 2

2.2 Firms Each …rm (j) produces a di¤erentiated good in a monopolistically competitive environment using labor services. The production technology is given by:

yt(j) = ztlt;j; (4)

2 See e.g. Sims (1994), Schmitt-Grohé and Uribe (2004a, 2011), Guerron-Quintana (2009), Altig et al. (2011).

4  1  1  1 3 where zt denotes a shock and lt;j = lt;j(i)  di is a 0 standard labor bundle. Firm (j) demand for labor typeZ (i) is 

 w l (i) = t;i l (5) t;j W t;j  t  1 1 1  1  where Wt = wt;i di is the wage index. We assume a sticky price speci- 0 …cation basedZ on Rotemberg (1982) quadratic cost of nominal price adjustment:

2 p Pt(j)=Pt 1(j) 1 (6) 2 p t 1 ! where p > 0 is a measure of price stickiness and t = Pt=Pt 1 denotes the gross in‡ation rate and p [0; 1] is the degree of price indexation to past in‡ation. 2 2.3 Fiscal sector The consolidated government supplies an exogenous, stochastic and unproduc- 4 tive amount of Gt and implements exogenous transfers Tt. Gov- ernment …nancing is obtained through a labor-income tax, money creation and issuance of one-period, nominally risk free bonds. Its period-by-period budget constraint is

Bt 1 Wt Mt Mt 1 Bt Rt 1 + Gt + Tt =  t lt + + (7) Pt Pt Pt Pt

Gt As in Schmitt-Grohé and Uribe (2004a), ln gt, where gt = , is subject to Yt shocks following an independent AR(1) process.

2.4 Competitive equilibrium The competitive equilibrium is obtained by solving the representative house- hold’sand …rm’sproblems.5 The household’s…rst-order conditions are:

uc (Ct; lt) t = (8) 1 + s(vt) + vts0(vt)  R t = t (9) t+1 t

Rt 1 2 = s0(vt)vt (10) Rt

3 We assume that ln zt follows an AR(1) process. 4 Note that the focus of the paper is the identi…cation of the optimal …nancing mix, where optimality is driven by e¢ ciency considerations. Justifying the existence of government trans- fers as an optimal outcome would require some form of heterogeneity across households. This is beyond the scope of the paper. 5 In the following we assume the symmetrical equilibrium and subindexes i,j are therefore dropped. In addition, we rule out Ponzi schemes.

5 1  1 p (j) c (j) = C t (11) t;i t;i P  t 

Wt w ul (Ct; lt) lt (1  t) w w +  t w + w!tt 1 !tt 1 1 = Pt uc (Ct; lt)  1     t+1 w w = Et w!tt !t+1t 1 (12) t   Condition (8) states that the transaction cost introduces a wedge between the marginal utility of consumption and the marginal utility of wealth that van- ishes only if v = v. Equation (9) is a standard Euler condition. Equation (10) implicitly de…nes the household’s money demand function. Equation (11) de- …nes consumer demand for product j. Correspondingly, the consumption price  1 1    1 index is Pt = 0 pt(i) di . Equation (12) de…nes the wage adjustment w 1 rule, where  =R  ( 1) is the gross wage markup; !t = Wt=Wt 1 is the w  gross wage in‡ation rate;  =  1 de…nes the markup generated by monopo- 1+s(vt)+vts0(vt) listic competition under ‡exible nominal wages; t = de…nes the 1  t policy wedge, which depends on both tax and in‡ation distortions. The …rm’sprice adjustment rule is:

p  lt 1 Wt pt t t+1 pt+1 t+1 p p +   1 = Et   1 (13)  1  Pt p p t p p t 1 t 1 ! t t !   p 1 where  =  de…nes the ‡ex-price markup. Equation (13) is a conventional New Keynesian , which simply states that the presence of price- adjustment costs prevents …rms in the short run from setting their prices so as to equate marginal revenue to marginal cost. Finally, the aggregate resource constraint is 2 2 p t w !t Yt = Ct (1 + St) + Gt + 1 + 1 (14) 2 p 2 w t 1 ! t 1 ! + The competitive equilibrium is thus a set of plans Ct; lt; t; mct; t; vt t=01 + f + g that, given the policies Rt;  t t=01, the exogenous processes zt; gt t=01, and the initial conditions, satis…esf theg above …rst order conditions (8)-(14).f g

2.5 Ramsey solution + The Ramsey solution is a set of plans Rt;  t t=01 that maximizes the expected value of (1) subject to to the competitivef equilibriumg conditions (8)-(14), the government budget constraint (7) and the exogenous stochastic processes driving the …scal and technology shocks.

3 Functional forms and calibration

We assume that the instantaneous utility for the representative household (i) takes the form of a simple log-log function:

u (Ct;i; lt;i) = ln Ct;i +  ln (1 lt;i) (15)

6 and we formalize s(vt;i) as

B  s(vt;i) = Avt;i + 2pAB C (16) v t  t;i  When  = 0, equation (16) is as in Schmitt-Grohé and Uribe (2004a). In this case, as B approaches zero, (16) becomes linear in velocity and the implicit demand for money has the Baumol-Tobin square-root form with respect to the opportunity cost of holding money.6 When 0 <  < 1 monetary transaction costs exhibit decreasing returns to scale and the consumption elasticity of the implicit money demand function is smaller than 1. By combining (10) and (16), we can now derive an explicit money demand function: M C1  t = t (17) Pt B 1 + (Rt 1) A A The solution of the Ramsey planq requires numerical simulations.7 We set the subjective discount factor at 0:96, consistent with a steady-state 4% real interest rate (the time unit is meant to be a year).8 <=VEDI NOTA Following Schmitt-Grohé and Uribe (2004a) transaction cost parameters A and B are set at 0:011 and 0:075, respectively, and the consumption scale parameter  is set at 0. The price markups, p is set at 1:2, as in Schmitt-Grohé and Uribe (2004a). We choose 1:05 for w. The annualized Rotemberg price and 9 nominal wage adjustment costs (p, w) are set at 4:375, in line with Hofmann et al. (2012), who also report that these parameters are rather stable during the post-war period. We allow for time variation in the degree of in‡ation indexation and in the …scal ratios B=Y , G=Y , T=Y (Table 1). The in‡ation indexation parameters are taken from Hofmann et al. (2012), the …scal variables are obtained from the National Accounts (NIPA) data and from the Economic Report of the President.

Table 1 –Time-varying parameters Sample period B=Y G=Y T=Y p w 1960-2005 0:49 0:15 0:095 0:4 0:5 1960-1969 0:48 0:17 0:055 0:3 0:4 1970-1984 0:36 0:16 0:09 0:8 0:9 1985-2005 0:55 0:14 0:10 0:2 0:2 Table 1 re‡ects the dynamics of …scal variables and price and wage index- ation. Public debt as a percentage of GDP fell rapidly in the post-World War II period. It reached a low in 1973 under Nixon Administration. The debt bur- den has then fairly increased since the presidency of Bill Clinton. In the early 2000s, sharp increases in de…cits have implied a new inversion in the debt dy- namics. Government consumption remains fairly constant in all the sample at

6 Moreover, it would be easy to parameterize (16) so as to replicate a Cagan demand function (proof available upon request). 7 These are obtained implementing Schmitt-Grohé and Uribe (2004b) second order approx- imation routines. 8 Results are robust with respect to di¤erent assumptions on the interest rate. A change of 1% in the state steady-state real interest rate has second order quantitative e¤ects on our results. Results are available upon request. 9 This implies that contracts are re-optimized every 9 months on average.

7 about the 15%. During the Kennedy and Johnson years, the budget share going to transfers was constant. During the Nixon10 and successive administrations, transfer payments increases from 5% to 10%. data on index- ation show that, from the late 1960s onwards, the coverage of private sector workers by cost-of-living adjustment clauses steadily increased to levels around 60% in the mid 1980s, after which there was again a decline towards 20% in the mid 1990s, when the reporting of coverage has been discontinued. The es- timation of Hofmann et al. (2012) supports the idea of time variation in price and wage indexation.11 In particular, they show that lagged price in‡ation had a signi…cant impact on wage in‡ation until the early 1980s, but they do not …nd a signi…cant e¤ect afterwards. Theodoridis et al. (2012) …nd a similar path for both price and wage time-varyng indexation by a time-varying parameter VAR in the seven US variables used to estimate the model of Smets and Wouters (2007).

4 Results

R In Table 2 we report the Ramsey optimal in‡ation rate, av, its correspond- ing value obtained when transfers are neglected as in Schmitt-Grohé and Uribe SGU (2004a), av , and observed average-in‡ationvalues, av, for the whole sample period (1960-2005) and for the subsamples 1960-1969, 1970-1984, 1985-2005. In addition, to get more insights on how the dynamic pattern of …scal expen- diture variables a¤ect optimal in‡ation rates, in Figure 1 we plot , R and SGU where the latter two variables are obtained assuming that, in the absence of shocks, the policymaker reacts to the contemporaneous values of public ex- penditures (described in Figure 2 and 3) as if they were at their steady state values.12 This is an admittedly rough-and-ready method for capturing the shift- ing government targets for these variables, but the alternative of …ltering actual public expenditure variables to obtain implicit time-varying targets would not produce substantially di¤erent results. The pattern of SGU is clearly unrelated to observed in‡ation. It is interest- ing to note that during the great in‡ation the relatively large degree of in‡ation indexation induces the policymaker to choose an in‡ation rate that is even closer to the Friedman rule! A theoretical interpretation of this result is provided in Schmitt-Grohé and Uribe (2011), who show that in‡ation indexation tilts the optimal in‡ation rate towards the Friedman rule when the public …nance motive does not matter. By contrast, Di Bartolomeo et al. (2011) show that indexation causes a substantial increase in the optimal in‡ation rate when public transfers are su¢ ciently large. In fact, R is characterized by a strong increase in the ’70s and tracks actual in‡ation fairly closely since the beginning of the 1990s.

10 Between Nixon’s inauguration and his resignation, transfer payments by the national government rose from 24% to 43% of the US budget. 11 Microeconomics data also these results. From the late 1960s onwards, the coverage of private sector workers by cost-of-living adjustment clauses steadily increased to levels around 60% in the mid 1980s, after which there was again a decline towards 20% in the mid 1990s, when the reporting of coverage has been discontinued. 12 Note that public expenditure components include interest payments on previous-period government debt. We also allow for time-varying price and wage indexation parameters, as in Hofmann et al. (2012). More speci…cally, we use averages for the pre-Great In‡ation, Great in‡ation and Great Moderation periods (see Table 1) and smooth the transition between one sample period and the subsequent one by using a four-point linear interpolation.

8 Note that R is very small in the ’60s and its increase follows the surge in the level and persistence in actual in‡ation that we observe since the mid- ’60s.13 In a sense, we see a complementarity between our results and previous interpretations of US in‡ation that emphasized the role of shocks and learning about the true structure of the economy. Up until the mid-’60s the optimal in‡ation rate was virtually nil. Then the contemporaneous increase in public transfers and in the degree of in‡ation indexation caused a strong increase in the optimal in‡ation target, 6% by the mid-’70s. In the last part of the sample the reduction in in‡ation indexation and the stabilization in the level of public transfers cause a fall in the optimal in‡ation rate. To complete our analysis we discuss the dynamics of tax variables. In Figure 4 we plot observed taxes as a ratio of GDP and the predicted tax revenue ratios associated to the  R,  SGU tax rates obtained when computing R, SGU . It is easy to see that …scal revenues under  SGU simply follow the dynamics of public consumption expenditures. Under  R predicted …scal revenues track the increase in actual revenues fairly closely up to the end of the ’70s, but they are systematically larger than actual revenues during the rest of the sample. This result is obviously related to the pattern of debt dynamics reported in Figure 3, where the end of the ’70smarks a clear turning point. In the …rst part of the sample the policy mix allowed a large reduction in the debt-to-GDP ratio. Since then, tax policies caused a complete reversal in debt dynamics, and particularly so between 2000 and 2007. This result is puzzling in the light of received inter- pretations of the observed patterns of in‡ation and output volatility during the Great In‡ation and Great Moderation episodes. In fact, a debt increase should have been observed at a time of adverse shocks and uncertainty – the Great In‡ation episode –and such accumulation should have been reversed during the more favorable Great Moderation period (Schmitt-Grohé and Uribe, 2004; Di Bartolomeo et al., 2013).

Table 2 –Predicted and observed in‡ation R SGU Sample period av av av 1960-2005 4:26 2:08 0:46 1960-1969 2:35 0:61 0:63 1970-1984 7:00 3:15 0:82 1985-2005 3:05 2:03 0:11 13 We found that Granger-causality runs from observed to predicted in‡ation and not vice- versa. Results are available upon request.

9 0.4 Public expenditure/GDP Public consumption/GDP 0.35 Transfers/GDP

0.3

0.25

0.2

0.15

0.1

0.05

0 1960 1970 1980 1990 2000 2007

Figure 1 –Fiscal outlays

0.7 Debt/GDP

0.65

0.6

0.55

0.5

0.45

0.4

0.35

1960 1970 1980 1990 2000 2007

Figure 2 –Real debt dynamics

10 14 Optimal SGU 12 Current inflat ion

10

8

6

4

2

0

•2 1960 1970 1980 1990 2000 2007

Figure 3 –In‡ation dynamics

35 Optimal SGU Act ual t ax 30

25

20

15

10 1960 1970 1980 1990 2000 2007

Figure 4 –Tax dynamics

5 Conclusions

This paper reconsiders the issue of Ramsey-optimal in‡ation and tax policies in the context of the US economy. We are able to rationalize the existence

11 of a positive, time-varying optimal in‡ation rate, whose dynamics are driven by the public …nance motive put forward in Phelps (1973) and by changing degrees of price and nominal wage indexation. Our interpretation is broadly consistent with interpretations that see a combination of learning and changes in the stochastic processes driving structural shocks as the key factors behind the Great In‡ation and the Great Moderation episodes. We uncover a puzzling pattern of tax policies, which, in contrast with theo- retical macro-models, generated the reduction of public debt at a time of great uncertainty and of adverse shocks, and its accumulation later on, when the economic context was relatively favorable. Interpretations of the Great Mod- eration typically overlooked the role of …scal policies. Our contribution calls for further research about the (temporary) e¤ect of these policies in dampening macroeconomic ‡uctuations.

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