Factor income taxation, growth, and investment specific technological change

TL;DR: In this paper, the authors construct a tractable endogenous growth model with production externalities in which the public capital stock augments investment speci c technological change and show that there exist several labor and capital tax-subsidy combinations that decentralize the planner's growth rate.

About: This article is published in Economic Modelling.The article was published on 2016-09-01 and is currently open access. It has received 5 citations till now. The article focuses on the topics: Endogenous growth theory & Factor income.

Summary

1 Introduction

• This is reinforced by Figure (2) which plots the di¤erence between the average factor income tax rates for these economies.
• 6The authors setup also allows investment speci c technological change to enhance the accumulation of public capital.
• When there are no production externalities, under a simple parametric restriction; both equal factor income taxes and unequal factor income taxes yield the rst best scal policy.

2 The Model

• Consider an economy that is populated by identical representative agents, who at each period t, derive utility from consumption of the nal good Ct and leisure (1 nt).
• 0; the planner internalizes the e¤ect that n2 has on direct production.
• ItZt thus represents the e¤ective amount of investment driving capital accumulation in time period t+ 1.
• Other papers in the literature - such as Reis (2011) - also assume two types of labor a¤ecting production.

2.1 Investment Speci c Technological Change

• The term Gt Yt 1 represents the externality from public capital in enhancing investment speci c technological change in time period t+1.
• The aggregate capital-output ratio, Kt Yt 1 , is also assumed to exert a positive externality e¤ect on investment speci c technological change.
• 11 10This contrasts with Hu¤man (2008) where = 1 is required for growth rates of Z and output to be along the balanced growth path.
• The authors require 2 (0; 1) for the equilibrium growth rate to adjust to the steady state balanced growth path.

2.2 The Planner s Problem

• The aggregate resource constraint the economy faces in each time period t is given by Ct +.
• It at time period t. Aggregate consumption and investment add up to after-tax levels of output, Yt(1 ), in every time period.
• The planner maximizes life-time utility of a representative agent given by (1) subject to the economy wide resource constraint given by (8), the laws of motion (4) and (5), the equation describing investment speci c technological change (7), the identity for total supply of labor given by (2) and nally, the government budget constraint given by (6).12.
• This yields the rst best scal policy in the model.

2.2.1 First Order Conditions

• I g t = Yt: 13We do not solve for the Ramsey allocations (second best scal policy) in this paper.the authors.
• Equation (11) is an augmented form of the standard Euler equation governing the consumption-savings decision of the household.
• It is easy to see that when = 1; the additional terms in the Euler equation are equal to zero, yielding the standard Euler equation.

2.2.2 Decision Rules

• The authors now derive the closed form decision rules based on the above rst order conditions using the method of undetermined coe¢ cients, as shown the following Lemma (1).
• While decision rules for consumption and investment given by (14) suggest that levels of consumption and investment would fall if the proportional tax rate increases, the share of after tax income spent on consumption given by P increases when rises, and thereby for investment it falls.
• Intuitively, when rises the weight on the ratio of public capital to output, Gt Yt 1 in augmenting investment speci c technological change increases and so the weight on the ratio Kt Yt 1 falls.
• Since the planner solves the optimization problem for the representative agent, the e¤ect of increases in on private investments is therefore expected.
• Hence, while an increase in has an ambiguous e¤ect on n1P ; it reduces n2P and since the latter e¤ect dominates, nP falls.

2.2.3 Balanced Growth Path

• The authors can easily obtain the balanced growth path (BGP) by substituting the above decision rules into the law of motion for investment speci c technological progress, (7).
• The authors therefore have the following Lemma (2).
• First, the growth rate is independent of the technology parameter, A; as in Hu¤man (2008).
• In the steady state, the planner maximizes growth by choosing the proportional tax rate given by = .

2.2.4 Comparative Statics.

• It is important to note that the characterization of optimal growth in the planning problem is identical to Barro (1990) as in Proposition (1):.
• But since public capital a¤ects ISTC, it a¤ects growth through the tax rate.
• For higher values of the contribution from Gt Yt 1 starts dominating and therefore, the growth rates are higher as compared to the growth rates for a lower value of .18.

2.3 The Competitive Decentralized Equilibrium

• The authors now solve the competitive decentralized equilibrium.
• Consider an economy that is populated by a set of homogenous and in nitely lived agents.
• The wage payment wt for both kinds of labor are the same since there is no skill di¤erence assumed between both activities.
• The representative rm produces the nal good based on (3) but takes the externality from n2(given by n2) as given.
• The following is therefore the government budget constraint: Igt = wt(n1t + n2t) n + fYt wt(n1t + n2t)g k: parameter values are borrowed from Hu¤man (2008), except for = 1 which is the externality parameter due to n2P in their framework.

2.3.1 The Firm s Dynamic Pro t Maximization Problem

• Firms solve their dynamic pro t maximization problems which, at time t; have capital stock, Kt; and Zt: Let v(Kt; Zt) denote the value function of the rm at time t.
• The returns to investment in the credit markets are given by rt at time period t:.
• In deriving these factor prices, the authors assume that the externality from n2 in production is assumed to be given.

2.3.2 The Agents Problem

• Agents are allowed to borrow and lend by participating in the credit market.
• As follows at = Kt; 8t 0:.

2.3.3 First Order Conditions

• The following is the Lagrangian for the agent.
• Equations (30) and (31) equate the after tax wage to the MRS between consumption and leisure.

2.3.4 Decision Rules

• Based on the above rst order conditions, the following Lemma (3) states the optimal decision rules for the agents.
• The above decision rules imply that depending upon the parameter values, there exists a feasible range of values that k and n can take such that 0 < A; CE; nCE < 1; are true.
• The relationship between growth rates at the balanced growth path for private capital, public capital, output and investment speci c technological change are identical to that for the planner s version, as given in Lemma (2).

2.4 Decentralizing the Planner s Growth Rate

• The authors would like to ascertain under what conditions the competitive equilibrium allocations yield the planner s growth rate.
• The authors consider two cases: the case in which planner imposes equal factor income taxes on agents, i.e., n = k = ; and the case under which factor income taxes are unequal n 6= k.

2.4.1 Equal factor income taxes:

• No externalities Suppose there are no externalities in the model, i.e., = 1 and as = 0: Further, the government imposes equal factor income taxes on both capital and labor income, such that n = k = :.
• Hence, in this case there is indeterminacy.
• The authors.
• While equal factor income taxation restores the planner s growth rate when there are no externalities, in the presence of externalities, equal factor income taxes may not yield the planner s growth rate.
• As shown in Figure (3), there is no clear ranking between the two level of factor income tax rates.

2.4.2 Unequal factor income taxes

• The authors calibrate the factor income tax gaps in the presence of externalities assuming that the planner taxes factor incomes at di¤erent rates.
• The authors also choose the value of B = 2 although this is just a scaling parameter which can easily be changed.
• The planner therefore sets a higher tax on capital to restore the planning growth rate relative to the case where is low (Case 2).
• Note that Case 1 and Case 2 are directly comparable because the authors are xing and across two arbitrary values of : [Insert Figure 6] Case 3: = 1; = 0:2; = 0:5: As falls, k ! n: And as shown in Figure (7), the externality from aggregate public and private capital is inoperative.
• This is shown in the case with equal factor income taxes.

2.5 Welfare

• The authors compute welfare for agents by substituting the representative agent s optimal decision rules given in Lemma (3) and given by (32), (33), (34), (35), and (36) into the representative agent s discounted life time utility function given by (1).
• Figure (11) shows that the maximum welfare level increases as the externality due to public capital and private capital in Z diminishes.
• Figure (12) replicates the above exercise by assuming as the shifting parameter and as the changing parameter.
• These are available from the authors on request.

2.5.1 Pareto Ranking of Tax Rates: Some Examples

• The authors conduct the following numerical experiment for two extreme values of and .
• 24 This is consistent qualitatively with the experience of a majority of the countries depicted in Figure (2).
• Therefore, both production externalities and endogenous ISTC imply departures from the rst best policy.

3 Conclusion

• This paper constructs a tractable endogenous growth model with production externalities in which the stock of public capital in uences investment speci c technological change.
• The focus of their paper is on endogenous growth.
• In particular, the authors highlight the role that such externalities have in determining the rst best scal policy.
• The authors numerically show that the departure of the welfare maximizing tax rate from the rst best tax policy can be decomposed into 1) the e¤ect because of externalities, and 2) the e¤ect because due to n2:.

Figures

Figure 10: Growth restoring factor income taxes: = 0

Figure 2: Average factor income tax rates for select OECD economies

Figure 8: = 0:7; = 0:4; = 0:6; = 0:5

Figure 9: Growth restoring factor income taxes: = 1

Figure 1: Average growth rates for select OECD economies versus the ratio of tax on capital income to tax on labor income

Figure 6: = 0:4; = 0:2; = 0:5

Figure 7: = 1; = 0:5

Figure 4: Comparative statics - planner s growth rate

Figure 5: = 0:8; = 0:2; = 0:5

Figure 14: Growth versus welfare: = 1

Figure 12: Maximum welfare for changing values of

Figure 13: Growth versus welfare: = 0

Figure 3: Time trend of factor income taxes for G7 economies

Figure 11: Maximum welfare for changing values of

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Factor income taxation, growth, and investment speci c technological change" ?

The authors characterize the rst best scal policy and show that there exist several labor and capital tax-subsidy combinations that decentralize the planner’s growth rate. An earlier version of this paper was titled `` Distortionary Taxes and Public Investment in a Model of Endogenous Investment Speci c Technological Change ''. 

Q2. What future works have the authors mentioned in the paper "Factor income taxation, growth, and investment speci c technological change" ?

In terms of future work, one could formalize the second best Ramsey policy within their environment. 

Q3. What is the role of the public capital stock in lowering the price of capital?

In addition to labor time deployed by the representative rm towards R&D, the public capital stock, G; plays a crucial role in lowering the price of capital accumulation. 

Q4. What is the standard deviation of the average real GDP growth rates?

The standard deviation of the average real GDP growth rates is 0:878 (excluding Ireland, the standard deviation is 0:4756) which indicates low dispersion of growth rates. 

Q5. How can the planner restore the planning growth rate?

as the externality from n2CE falls (and also becomes inoperative), the planner can restore the planning growth rate only by taxing both factor incomes equally. 

Q6. Why does Ott and Turnovsky use the ow of public services to model the public?

Because public capital a¤ects the real price of capital explicitly,8For instance, in Ott and Turnovsky (2006) - who use the ow of public services to model the publicthis means that the public input a¤ects future output through its e¤ect on both future investment speci c technological change, as well as future private capital accumulation. 

Q7. Why do the authors show that the rst tax policy is decomposed into two?

The authors show numerically that the departure of the welfare maximizing tax rate from the rst best tax policy can be decomposed into 1) the e¤ect because of externalities, and 2) the e¤ect because due to n2: