The Welfare Effects of Switching from Consumption Taxation to Inflation Taxation in Iran s Economy

Transcription

1 Iranian Journal of Eonoi Studies Vol. 4, No. 2, Fall 2015, 1-15 The Welfare Effets of Swithing fro Consuption Taxation to Inflation Taxation in Iran s Eonoy Hojjat Izadkhasti Faulty of Eonois and Politial Sienes, Shahid Beheshti University Iran h_izadkhasti@sbu.a.ir Rahi Dallali Isfahani Faulty of Adinistrative Sienes and Eonois, University of Isfahan, Iran rateofinterest@yahoo.o Saeed Saadi Faulty of Adinistrative Sienes and Eonois University of Isfahan, Iran saadi_sa@yahoo.o Abstrat The net effets of swithing fro onsuption taxation to inflation taxation on resoure alloation and welfare ruially depend on prodution externalities. With elasti labor supply, raising inflation taxation dereases leisure, but inreases the levels of real onsuption, apital, and output. Moreover, this tax swith has two opposing effets on the level of real oney balanes: A positive effet through the rise in output aused by the faster noinal oney growth and a negative one through the fall in the ratio of real oney balanes to output. In the absene of any prodution, externality the negative effet doinates the positive effet. The real effet of this tax swithing on resoure alloation depends on the behavior of labor supply. If there is not a trade-off between leisure and labor supply, then the real effet of swithing to inflation taxation on real onsuption, apital and output would disappear. With elastiity of labor supply, the welfare effet of this tax swith is onditional on the prodution externality. In the absene of prodution externality, inflation taxation always redues welfare. With a strong enough prodution externality, swithing fro onsuption taxation to inflation taxation ay raise welfare by orreting the under-investent of apital and the under-supply of labor. Keywords: Inflation Taxation, Consuption Taxation, Welfare, Externality, Leisure, Iran. JEL Claifiations: E40, D60. Reeived: 15/2/2014 Aepted: 21/9/2016 * The Corresponding Author

2 Iranian Journal of Eonoi Studies, 4(2), Fall Introdution Governent finanes an expend with noinal oney growth and tax onsuption. Individuals alloate inoe to onsuption and investent in both apital and real oney balanes, and alloate tie to labor and leisure. In this environent, swithing fro onsuption taxation to inflation taxation drives up the ost of holding oney, and thus redues the deand for real oney balanes relative to inoe as is entioned in the literature. Further, the derease in real oney balanes redues the arginal benefits of onsuption and leisure with a non-separable utility funtion onerning these augents, whih tends to redue onsuption and leisure and aordingly labor inrease. The inreased labor in turn raises the arginal produt of apital and stiulates apital auulation, leading to higher output per apita. In the budget balanes of the governent, swithing fro onsuption taxation to inflation taxation, delines onsuption tax, tending to raise onsuption. Given the standard onstant elastiity of inter teporal substitution for of the utility funtion in the literature on eonoi growth, the net effet on the ratio of onsuption to output is zero. Thus, as output rises with the noinal oney growth rate, so does onsuption. The inrease in onsuption tends to raise welfare but the deline in leisure tends to redue the welfare. The net effets of the tax swith on real oney balanes and welfare depend ruially on prodution externalities (Ho et al., 2007). If labor supply were fully inelasti in our odel, then swithing fro onsuption taxation to inflation taxation would have no real effet on real onsuption, apital and prodution in the long-run. Sine the positive effet of the swith to inflation taxation on output takes tie to reah its full potential through prooting apital auulation, the relative strength of the positive welfare effet also depends on the elastiity of inter teporal substitution. More elasti inter teporal substitution aelerates growth and hene strengthens the positive welfare effet. The net welfare effet of swithing fro onsuption taxation to inflation taxation an be positive so long as the externality is strong enough. However, when onsidering the entire equilibriu path in a tratable AK odel with a strong enough

3 3 The Welfare Effets of Swithing fro Consuption Taxation to externality for endogenous growth, a positive net welfare effet of this tax swith also requires the elastiity of inter teporal substitution to be suffiiently high. By reduing the onsuption tax and raising the inflation tax to finane, a given governent fisal oitent an stiulate prodution in the long-run in our odel, as opposed to the long-run neutrality of oney growth in Rebelo and Xie (1999) without a onsuption tax. The paper is organized as follows: Setion 2 reviews the related studies in the field. Setion 3 introdues the odel. Setion 4, Maxiizes welfare funtion in steady state. Epirial results are present in Setion 5 and the last setion onludes. 2. Literature Review When oney enters diretly in to the utility funtion and interats with an elasti labor, oney is generally non-supernatural (Brok, 1974; and Ho et al., 2007). If oney and apital were substitute, higher onetary growth enhanes apital auulation (Tobin, 1965). In the ase, oney is required for purhasing apital goods, higher antiipated inflation dereases steady-state real balanes and apital stok, and hene a reversed Tobin effet eerges (Stokan, 1981; Lu et al., 2011). Soe studies support a rate of oney growth for a positive noinal interest rate by onsidering additional fators suh as prodution externality, elasti labor supply, and distortion of other taxes on labor, output, and onsuption. In Phelps (1973), Braun (1994), and Palivos and Yip (1995), inflation taxation leads to a higher welfare than inoe taxation as a eans of publi finane 1. In Rebelo and Xie (1999), oney does not affet prodution in the steady state, but an alter it during the transition toward the steady state; and the transitional effet be exploited by onetary poliy to iprove welfare, if there are prodution externalities. Ho et al. (2007) offered a oparison of the welfare ost between a seignorage tax and a onsuption tax in the publi finane approah in a odel with real balanes and leisure in utility. They found that without a prodution externality, a seignorage tax always had a higher welfare ost than a onsuption tax in the long- run. With a

4 Iranian Journal of Eonoi Studies, 4(2), Fall prodution externality, a seignorage tax not only had a saller welfare ost than a onsuption tax but ay have a welfare gain. Lu et al. (2010), investigates welfare osts between seignorage and onsuption taxes in a neolaial growth odel with a ash-inadvane onstraint. They opares equilibriu along transitional dynai and steady-state paths and finds that beause of lower onsuption and leisure and thus higher welfare osts of onsuption taxes during early periods, the welfare ost of onsuption taxes is larger than the welfare ost of seignorage taxes. Izadkhasti et al. (2015) fro sensitivity analysis in a steady state found that without externality of prodution, by inreasing inflation tax rate, the ratio of onsuption to GDP reains onstant, but labor, apital stok and prodution will inrease. With derease in the ratio of real oney balanes to GDP and leisure, the level of soial welfare in steady state dereases. Considering prodution externality, apital stok and a rapid prodution inrease, welfare level inreases in steady state. 3. The Basi Model The proble of deterining the optial struture of taxes to finane a given level of expenditures is alled the Rasey proble, after the lai treatent of Rasey (1928). In the representative-agent odels we have been using, the Rasey proble involves setting taxes to axiize the utility of the representative agent, subjet to the governent s revenue requireent Household the eonoy is populated by infinite failies whose wealth is in the for of either oney or apital. Eah household solves the following axiization proble: ax W u(,,l )exp[ t]dt, u, u 0, u, u 0 0 t t t (1) s. t : dat dk t dt w dt dt dt 1 l r k 1 (2) t t t t t t

5 5 The Welfare Effets of Swithing fro Consuption Taxation to Where,, and l t are real onsuption, real oney balanes, and leisure respetively. ρ is the onstant rate of tie preferene. k t is the apital stok, is a rate of inflation tax, and is a rate of onsuption tax. Aue that the rate of population growth is zero. The transversality ondition ruling out the Ponzi gae is given as: ρt lie a 0 (3) t t t 3-2. Firs Firs produed a final good by using apital, and labor, aording to the following tehnology: 1 Y A(1 l ) K K 0 1, 0 1 (4) t t t t Where is the final output, is total fator produtivity, and easures the iportane of apital relative to labor in prodution. Average apital exhibits spillovers of degree. Marginal produt of fators are: w A1 α K (1 l ) r t α α t t t (5) α 1 1α AαK t (1 l t) (6) Where is the real wage rate and is the real interest rate Governent Aue that governent uses a onsuption tax and inflation tax to finane onsuption expenditure and uses others revenue to finane apital expenditure, DenotingGt Go G t a. Aue t that onsuption governent spending is a fixed fration, of final output with. Suppose that the onsuption governent budget is balane at eah point in tie: G βf k,1l,β 0 t t ot t t (7) 4. Maxiizing Welfare Funtion in Steady-State By onsidering the utility funtion by:

6 Iranian Journal of Eonoi Studies, 4(2), Fall t t lt W exp( t) dt (8) 1 0 Where δ, θ, and η easure the iportane of real onsuption, real oney balanes, and leisure, respetively, and is the elastiity of interteporal substitution. The steady-state welfare funtion obtained as follows (Izadkhasti et al., 2015): 1 Ф[F(, )] W 1 (9) Where F, (δθ) δη δ 1α 1αη 1α (ρ ) (1 ) [δ ρ θ ] {η ρ (1 α)[δ ρ θ ]} and 1 Ф { η η [ A(1 ) 1 ( ) ] 1 } 1 0 The steady-state welfare level, is a funtion of the rates of onsuption tax and inflation tax. is a onstant and independent of the onsuption tax and inflation tax. The steady-state welfare level is onotonially inreasing with. We foused on in the welfare analysis with or without the prodution externality. With respet to equation (7), Izadkhasti et al. (2015), obtained onsuption-output ratio and real oney balanes- output ratio in the steady-state: θ (10) 1 θ θ In the absene of any prodution externality ( 0), the steadystate welfare level in equation (8), redues to: δη δ (ρ ) (1 ) F, (11) η ρ (1 α)[δ ρ θ ] In the ase with onsuption taxation only, fro equation (10), we

7 7 The Welfare Effets of Swithing fro Consuption Taxation to have F /1 β, and: θ δ 0 (ρ) (1 β) η (1 α)δ (12) Where the auption θ has been used to siplify the expreion. In the ase with inflation taxation only, fro equation (10), we have δρ / θ 1 β βδ, and: θ δ η θ 0 (ρθ) (1 β) [θ 1β βδ] F (13) η (1 α)δ By oparing the two regies in the steady-state without any prodution externality and with β and β β, shows that using onsuption taxation to finane governent spending obtains a higher welfare level than using pure inflation taxation. Without any prodution externality, we have: F ( ) ( ) (14) F ( ) (1 ) [ 1 ] Obviously, at β we have, and for β we have 1. In the steady-state without any prodution externality and with > 0, if both onsuption taxation and inflation taxation are used to finane governent spending, governent axiizing welfare funtion F (, ) in equation (8), subjet to its budget onstraint (10). Lagrangian funtion is as follows: 1 L F, μ{ β} (15) Where, µ is the ultiplier. The first-order ondition with respet to is: L F, ( ) (1 ) [ ] The first-order ondition with respet to, we get: (16)

8 Iranian Journal of Eonoi Studies, 4(2), Fall L F, [η ( )(1 )] F, ( η) η 1 [ ] (17) 2 (1 ) With any prodution externality, if L 0, it is onvenient to start with onsuption taxation (1 ) and 0. Starting with onsuption taxation we have F, μ (1 β) δ, F, 0. If L 0 at (1 ) and 0, then there should be deflation 0 and aordingly (1 ). Using F, μ (1 β) δ, F, 0 in equation (16) and rearranging ters, we have: L β sign sign 1 0 at and 0 1β (18) In the steady-state without any externality and with, if both onsuption taxation and inflation taxation are used to finane governent spending, their optial ix to axiize welfare, the rate of the inflation tax should be negative and the rate of onsuption tax should be positive. The intuition is as follows: Sine real oney balanes and onsuption enter the utility syetrially, there is a unifor taxation priniple saying that the governent should tax both at the sae rate in order to avoid distorting the argin between onsuption and real oney balanes 2. This onsideration iplies that the rates of onsuption and inflation taxes should be equal. However, real oney balanes are also an aet and ideally, the governent does not want to distort the return on oney relative to the return on apital to avoid distorting the argin between real oney balanes and apital. Sine apital inoe is not taxed in our odel, this onsideration iplies that the inflation tax should be zero. Cobining the onsuption-oney onsideration with the apital-

9 9 The Welfare Effets of Swithing fro Consuption Taxation to oney onsideration suggests that, in the absene of any externality, the onsuption tax should exeed the inflation tax. Moreover, in the spirit of the Friedan rule, beause the soial ost of produing oney is zero, there should be a negative inflation tax suh that the ost of holding oney an be as lose to zero as poible. As a result, the optial inflation tax is negative along with a positive onsuption tax. However, the underlying noinal oney growth rate should exeed the rate that orresponds stritly to the Friedan rule, beause of the distortions of the onsuption tax and the negative inflation tax on leisure and onsuption. In the steady-state with prodution externality and with > 0, if both onsuption taxation and inflation taxation are used to finane governent spending, governent axiizing welfare funtion F (, ) in equation (8), subjet to its budget onstraint (10). Lagrangian funtion is as follows: 1 L F, μ{ β} (19) Differentiating the Lagrangian with respet to, we have: 2 2 L F, (1 η )[η ( )(1 )] F, ( η) (1 ){η 1 } F, ( θ) (1 ) (1 ) (20) Using F, μ (1 β) δ, F, 0in this equation and rearranging ters, we have: L sign sign (1 ) [ (1 )] 1 (1 ) at β and 1β 0 (21) Note that L is inreasing in ψ. If ψ approahes (1 ), then:

10 Iranian Journal of Eonoi Studies, 4(2), Fall L sign sign{ η1 α1 η } 0 (22) In the steady-state with > 0, when onsuption taxation is used to finane governent spending, inflation taxation should also be used together if ψ (0, 1 α) is large enough. If L 0 at (1 ) and 0 then π 0. With a weak prodution externality 0,1, we are able to opare inflation taxation with onsuption taxation. Using onsuption taxation to finane governent spending eans / (1 ) and 0. Substituting these into the definition of F, we have: F ρ (δθ) θ δ 1α (1 β) δ [η 1α δ] 1αη 1α Siilarly, with inflation taxation βδρ / θ1 β 0, we have F ψ(δθ) θ δη θ 1αψ (ρθ) (1 β) [θ 1β βδ] δ [η(1 β) (1 α)δ] ψ(δθ) 1αψ δ (23) βδ and In the steady-state with β, and δ / 1 0,1 (24), if is large enough, then using inflation taxation to finane governent spending obtains a higher welfare level than using onsuption taxation. The ratio of the two welfare levels is defined as: 1αηψ F η θ θ η(1 β) δ(1 α)) 1αψ (1 β) [ ] [ ] H(β) F θ 1β βδ η δ(1 α) (25) Here, it is obvious that, for,θ(1- ) and for a

11 11 The Welfare Effets of Swithing fro Consuption Taxation to large enough we have. When there is a prodution externality, the private rate of return on investent in apital is lower than the soial rate, leading to underinvestent in apital. When the level of apital is below its soially optial level, the private rate of return on labor ust also be lower than the soial rate, leading to a suboptial solution with too little labor and uh leisure. There for, the positive effets of inflation tax on labor and apital auulation an inrease the output. The rise in the inflation tax raises real onsuption in the steady state 3. With a strong enough externality, the rise in the inflation tax ay raise real oney balanes in the steady state, rather than redues it as in without prodution externality ase 4. Thus, the rise in the inflation tax an iprove welfare level in the steady state when the prodution externality is strong enough for the welfare gain fro inreasing onsuption and poibly real oney balanes doinate the welfare lo by dereasing leisure. 5. Epirial Results Using nuerial solution based on the paraeterization,,,,, η and δ in Iran s Eonoy, the quantitative ipliations of the results are illustrated in Tables 1. We first seleted a benhark ase and ade a steady-state welfare oparison with and without prodution externality.

12 With weak externality Without externality Iranian Journal of Eonoi Studies, 4(2), Fall Table 1. Nuerial Results in the Steady State With and Without Prodution Externality ( 0.50) Cases % % l k y W Benhark Soure: Researhers Coputations In the Table 1, we aue that no governent intervention happens in the first ase in the benhark. In the seond ase, either or both of onsuption taxation and inflation taxation be used to finane governent urrent expenditure as 23% of output (β ) 5. When both instruents are used 6, without prodution externality their optial ix is a positive onsuption tax and a negative inflation tax (a deflation transfer at a rate of noinal oney growth -3.0%), iplying higher real oney balanes than in the benhark. Copared to the both instruents are used regarding real alloation and welfare, this optial ix has higher leisure but lower levels of real onsuption, apital, output and welfare in the steady-state than in the benhark. When the onsuption tax is used alone to finane governent spending, there is no real effet on the alloation of tie and output. Sine governent spending is wasted, the onsuption tax redues the welfare. When the inflation tax is used alone in the steady-state, there is a greater lo in the welfare opared to the no intervention ase beause the inflation tax (at a 23.43%) redues onsuption,

13 13 The Welfare Effets of Swithing fro Consuption Taxation to leisure and real oney balanes opared to the no-intervention ase. In this ase, there is a greater lo in the welfare. 6. Conlusion This paper onsidered the effets of swithing fro onsuption taxation to inflation taxation on resoure alloation and welfare. Conerning resoure alloation, we found that swith to inflation taxation dereases leisure and real oney balanes, but inreases the levels of onsuption, apital, and output. The welfare effet of inflation taxation is onditional on the strength of prodution externality and on the elastiity of labor supply. In the absene of prodution externality, swith to inflation taxation always redues the welfare, whether it used alone or with onsuption taxation. In eene, as the rate of inflation taxation rises along with a falling onsuption tax rate, the loes in welfare arising fro the dereases in leisure and real oney balanes doinate the gain fro the inrease in onsuption. With a strong prodution externality, the positive output effet of the inreasing fro swith to inflation taxation ay lead to a positive net effet on the level of real oney balanes. The effets of swithing fro onsuption taxation to inflation taxation ay raise welfare by orreting the under investent of apital and the undersupply of labor. Endnotes 1-Phelps (1973), Braun (1994), and Palivos and Yip (1995), aue that the governent finanes spending by an inoe tax and inflation tax. 2- See Atkinson and Stiglitz (1972) for ore disuions on the unifor taxation priniple. 3- Γ Y Γ Y 4-5- Is aording to entral bank statistis of Iran. 6- However, the underlying inflation tax rate should exeed the rate that orresponds stritly to the Friedan rule, beause of the

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15 15 The Welfare Effets of Swithing fro Consuption Taxation to Wai-Ming Ho & Jinli Zeng & Jie Zhang. (2007). Inflation Taxation and Welfare with Externalities and Leisure. Journal of Money, Credit and Banking, 39 (1),