Factor income taxation, growth, and investment specific technological change

Highlights

• Why do economies with different tax arrangements have similar growth rates?

• We build an endogenous growth model with endogenous ISTC to explain this.

• Labor allocated towards ISTC has spillovers on final good production.

• Private and public capitals have spillovers on ISTC.

• Offsetting effects of taxes on labor and capital income explain the growth-tax puzzle.

Abstract

Why do countries with different tax arrangements exhibit the same growth rate? We refer to this as a growth-tax puzzle. To explain the puzzle, we construct a tractable endogenous growth model with endogenous investment specific technological change (ISTC). Public and private capital stock externalities are assumed to augment ISTC. A specialized labor input exerts a positive externality in final good production. Our primary interest is to highlight the role of such externalities in explaining the puzzle. We show that the competitive equilibrium growth rate can be decomposed into a labor factor and a capital factor. Changes in factor income taxes, by affecting these factors, can have opposing effects leading to constancy in growth. Our model builds on the existing endogenous growth literature by providing an alternative, but compatible explanation for the offsetting growth effects of fiscal policy on growth observed in the data.

Introduction

Why do countries with different factor income tax combinations exhibit similar growth rates? In this paper, we develop an endogenous growth model with endogenous investment specific technological change to understand this question.

Fig. 1 plots the average aggregate annual real GDP growth rate from 1990 to 2007 against the factor income tax ratio for several advanced economies.¹ Average growth for all countries (excluding Ireland) falls between 0.875% and 2.462%. The standard deviation of the average real GDP growth rates is low at 0.878 (excluding Ireland, the standard deviation is 0.4756). Fig. 2 plots the range of individual factor income taxes for these countries where the tax on capital and labor income have been averaged over 1990–2007. What is striking is that the range in the ratios of the average capital income tax rate to the average labor income tax rate in these economies is much more pronounced: 0.3951 to 1.725.² Also whereas the difference between factor income taxes is large in some countries, it is quite small in others.³Fig. 1, Fig. 2 suggest that countries with almost similar growth rates are accompanied by totally different factor income tax combinations.

Fig. 3 plots the levels of factor income tax rates across the G7 countries. The incidence of factor income taxation is quite disparate. In the US, UK, Canada, and Japan, the tax on capital income is greater than the tax on labor income. In contrast, for Germany, Italy, and France, the reverse is true.

In other evidence, Jones (1995) also shows in a sample of 15 OECD countries from 1950 to 1987, that changes in investment rates do not have any significant long run growth effects. He shows that shocks to investments – both total and durables and in particular durable equipment – have only a short-run growth effect with no significant effect on long run growth.

Fig. 1, Fig. 2, Fig. 3 and the evidence from Jones (1995) are suggestive of a “growth-tax” puzzle since countries with different factor income tax combinations exhibiting similar growth rates is incompatible with a standard model of endogenous growth.⁴ The standard endogenous (AK) growth model predicts that fiscal policy has a large growth effect through its impact on the economy's investment rate. Taken to the data, these models would predict a high correlation between the investment rate and the growth rate. The above evidence therefore suggests that changes in fiscal policy (or factor income taxes) must have offsetting changes in investments such that growth rates do not change.

The literature has tried to find extensions to the standard endogenous growth model that can explain the apparent absence of growth effects of fiscal policy. McGrattan (1998) develops a theoretical framework where government policy can be incorporated into a standard AK growth model by incorporating two types of capital: structures and equipment capital. She shows that the equilibrium growth rate depends on the investment rate and the capital-output ratio. The reason why fiscal policy has no growth effects is because its effect on the investment rate is offset by the effect of fiscal policy on the capital-output ratio. Because of these offsetting effects, total investment does not change that much. Jaimovich and Rebelo (2012) show that changes in tax rates can have non-linear effects on long-run output growth. To capture this non-linearity, they construct a model where low tax rates have negligible effects on growth but when disincentives to invest are large, larger tax rates have a strong negative effect on output growth. The mechanism in their model is based on a skewed distribution of agents between workers and innovators, which results in a small number of highly productive workers in equilibrium. In a related literature, Glomm and Ravikumar (1998) build a growth model where public education spending, financed by distortionary taxes affect human capital accumulation. Again, they find that despite being distortionary in nature, tax rates have negligible effects on growth rates.

We provide an alternative, but compatible, explanation for the above growth-tax puzzle, i.e., the fact that different combinations of factor income taxes can generate the same growth rate. We construct an endogenous growth model with endogenous investment specific technological change with three types of externalities: (a) an externality from the stock of private capital, (b) an externality from public capital in the process of innovation; and (c) an externality from labor allocated to research in final good production. Investment specific technological change refers to technological change which reduces the real price of capital goods. Specifically, the public capital stock – financed by distortionary taxes – and the private capital stock augment investment specific technological change (ISTC) as a positive externality.⁵ Typically in the literature, the public input is seen as directly affecting final production directly either as a stock or a flow (e.g., see Futagami et al. (1993); Chen (2006); Fisher and Turnovsky, 1997, Fisher and Turnovsky, 1998; and Eicher and Turnovsky (2000)). We show that embedding varying magnitudes of these externalities into a model of endogenous growth with endogenous ISTC leads to offsetting effects of factor income taxes on growth. To the best of our knowledge, we are not aware of any paper in the literature in which public capital affects ISTC.⁶

Our basic model follows Huffman (2008).⁷ There are two sectors in the model: a final goods sector and a research sector. The final good sector produces a final good, using private capital and labor. Labor supply is composite in the sense that one type of labor activity is devoted to final good production, and the other to research which directly reduces the real price of capital goods in the next period. The second sector (the research sector) captures the effect of public capital and private capital stock spillovers and research activity on reducing the real price of capital goods. We assume two types of labor activities: one type is labor allocated for final goods production, or current production, and another type is labor allocated for enhancing investment specific technological change, or future capital accumulation, and therefore future production. While agents supply aggregate labor, firms optimally choose each labor activity. Crucially, in our model, however, firms might not be aware that their allocation of labor towards research also influences productivity of the current period's final goods production. Therefore, although research labor allocation is done from the point of future capital accumulation and hence future output, we assume that firms might be unaware of the spillover it has on current production. This implies that the process of augmenting knowledge – which is designed to influence the price of capital in the future – may affect present output too. Effectively, this means that the process of augmenting knowledge may make routine labor (in the final goods sector) more effective.

The planner maximizes the utility of the representative agent and internalizes the externalities in the research sector and final good sector. In the planner's problem, we assume that public investment is financed by a fixed proportional income tax as in Barro (1990). Given a fixed tax rate, the planner's problem yields the socially efficient allocation. Corresponding to this allocation, we characterize the steady state balanced growth path and show that the growth rate depends on two factors: 1) a labor input devoted to research (the labor factor) and 2) the contribution to growth from public and private capital (the capital factor).

We then ask under what conditions can the planner's allocations be replicated by the competitive decentralized equilibrium with identical and different factor income taxes. We assume that public investment is financed by distortionary factor income taxes on capital and labor income. Our main result is summarized in Proposition 1 which states that under an intuitive sufficient condition, the growth rate corresponding to the efficient allocation can be replicated in the competitive equilibrium by a combination of capital income tax rates and labor income tax rates. In particular, Proposition 1 shows that raising the labor income tax and/or reductions in the capital income tax implement a higher planner's growth rate if the sufficient condition is satisfied. The expressions for the capital and labor factors – which are in closed form – allow us to see how multiple factor income tax combinations – and therefore factor income tax gaps – can implement a given planner's growth rate. In particular, an increase in the capital income tax reduces the capital factor, and reduces growth. However, an increase in the labor income tax exerts both offsetting income and substitution effects. We show that with ISTC, the income effect is stronger than the substitution effect, and so increases in the labor income tax increase labor supply. The increase in labor supply increases the labor factor (which is essentially research-labor input) which increases capital accumulation and growth. We also show that the strength of the income effect becomes stronger the larger the importance of research-labor input on ISTC. Hence, the competitive equilibrium replicates the planner's growth rate, either by an increase in the labor income tax, or a reduction in the capital income tax, or some combination of both. Proposition 1 is therefore consistent with the empirical evidence documented in Fig. 1, Fig. 2, Fig. 3. In a numerical section we show that for a fixed set of parameters a wide range of tax rates imply the same growth rate.⁸

How do the externalities affect the factor income tax gaps that implement the planner's allocations? We first consider the case of a positive spillover from the specialized research labor activity on final good production. In this case, an increase in the spillover increases the planner's allocation towards specialized labor. This is because research labor has a positive effect on final good production over and above its effect on ISTC. This increases the growth rate corresponding to the socially efficient allocation. To implement this higher growth rate, this requires an increase in the labor income tax, which raises the labor factor from the competitive growth rate, or a reduction in the capital income tax, which raises the capital factor. Implementing either leads to a widening of the equilibrium factor income tax gap.⁹

In contrast, when the weight on the positive spillover from the public and private capital stock falls, this leads to a higher weight on the existing stock of ISTC. That is, a lower weight on the stock externalities implies that the weight on the persistence of ISTC is higher since the weights sum to one. More persistent ISTC leads to a higher planner's growth rate. To raise the competitive equilibrium growth rate, as before, a reduction in the tax on capital income that raises the capital factor and/or an increase in the labor income tax that raises the labor factor is required. Such a policy increases the factor income tax gap and implements the planner's growth rate.

Our general result is that to the extent that spillovers from a specialized labor input and the public and private capital stocks exist, an increase in these spillovers from the specialized labor input, and a decrease in the spillover from public and private capital, increases the planner's growth rate, and therefore increases the factor income tax gap required to implement the growth rate corresponding to the efficient allocation. Conversely, for a given level of externalities, maintaining the constancy of growth also requires different combinations of factor income taxes as in McGrattan (1998). We also show that when there are no externalities, equal factor income taxes always yield the optimal growth rate from the planner's problem. Hence, the factor income tax gap is zero.

Finally, we also conduct a simple numerical exercise to show that equilibrium factor income taxes generated by our model are in accordance with Fig. 1, Fig. 2, Fig. 3. As mentioned above, under an intuitive sufficient condition, we are able to analytically characterize replicating the growth rate corresponding to the efficient allocation. We consider two sets of policy experiments: one where the sufficient condition holds and another where the condition is violated. Our main result is to numerically show that for a fixed set of deep parameters, a wide range of tax rates implement the same growth rate when vary the externality parameters,.

With respect to the private capital stock, De Long and Summers (1991) show that investment in machinery is associated with very strong positive externalities, and that increases in investments in equipment implies higher growth. Hamilton and Monteagudo (1998) find that capital is associated with positive external effects in an estimated Solow growth model. Greenwood et al. (1997), show that the real price of capital equipment in the US – since 1950 – has fallen alongside a rise in the investment-GNP ratio. This suggests that the private capital stock exhibits a positive externality in investment specific technological change through the aggregate capital stock. Importantly, Greenwood et al. (1997, p. 342) say: “The negative co-movement between price and quantity…can be interpreted as evidence that there has been significant technological change in the production of new equipment. Technological advances have made equipment less expensive, triggering increases in the accumulation of equipment both in the short and long run.”

With respect to the nexus between public expenditures, R&D, and growth, Griliches (1979) examines how the indirect effects of research and development affect future output through induced changes in factor inputs. In his model, the accumulation of private capital is driven by the aggregate stock of knowledge and current and past stocks of research and development (R&D). Scott (1984) and Levin and Reiss (1984) estimate that the high spillovers from federal research and development spending dominate the crowding-out effect it has on private spending on R&D. The net effect is that public spending has a positive effect on productivity. Finally, David et al. (2000), show that public R&D spending is complementary to private R&D spending.

In the high-tech manufacturing sector, Davidson (2012) documents evidence on the extent to which skills required for advanced manufacturing jobs. He argues that skilled factory workers these days are typically “hybrid-workers”: they are both machinists (engaging in final good production) as well as computer programmers (engaging in research). In the US metal-fabricating sector, workers not only use cutting tools to shape a raw piece of metal, but they also write the computer code that instructs the machine to increase the speed of such operations. Globerman (1975) describes a class of machinists in the manufacturing sector called “tool and die makers”, or also “mold makers” (see Bryce (1997)). The machinist receives on-the-job training which enables him to work with machines and computers, which makes him multi-skilled. Even though on-the-job training is costly, Park (1996) shows, from an empirical study on manufacturing industries in Korea that employing “multi-skilled workers” makes a firm's production more efficient in comparison to employing “single-skilled “or specialized workers to handle each individual activity.¹⁰

Given this, we assume that the specialized labor input which is allocated to augment future output in the research sector exerts a positive externality in the current period's production of the final good. Other examples that support this assumption are outcomes of long-term research projects undertaken by firms – in say the pharmaceutical (drug research) or the IT (software development) sectors – which may only be realized in a future time period. The time allocated towards future research activities however may help improve the productivity of current period's production, although the spillover on current period's production may not be realized by firms.¹¹ In other words, on the job training is undertaken for future benefits but it may also augment the efficiency of standard labor that has been assigned to produce output in the current period. We feel that this link has been ignored by the literature.

The setup of our model is technically similar to Huffman, 2007, Huffman, 2008 who explicitly models the mechanism by which the real price of capital falls when investment specific technological change occurs. Our model however is closer to Huffman (2008) rather than Huffman (2007). Huffman (2008) builds a neoclassical growth model with investment specific technological change. Labor is used in research activities in order to increase investment specific technological change. In particular, the changing relative price of capital is driven by research activity, undertaken by labor effort. Higher research spending in one period lowers the cost of producing the capital good in the next period.¹² Investment specific technological change is thus endogenous in the model, since employment can either be undertaken in a research sector or a production sector. His model includes capital taxes, labor taxes, and investment subsidies that are used to finance a lump-sum transfer. Huffman (2008) finds that a positive capital tax that is larger than a positive investment subsidy along with zero labor tax can replicate the first best allocation. Huffman's models however do not incorporate public capital — a feature we show that is important in explaining the growth-tax puzzle in our paper.

Our paper is also related to the literature on fiscal policy and long run growth in the neoclassical framework. The literature started by Barro (1990) and Futagami et al. (1993) – incorporates a public input – such as public infrastructure – that directly augments production. In Barro (1990), public services are a flow; while in Futagami et al. (1993), public capital accumulates. However, in the large literature on public capital and its impact on growth spawned by these papers, the public input, whether it is modeled as a flow or a stock, doesn't directly influence the real price of capital goods.¹³ Since public capital affects the real price of capital explicitly in our model, this means that the public input affects future output through its effect on both future investment specific technological change, as well as future private capital accumulation.

Finally, in addition to labor time deployed by the representative firm towards R&D, the public capital stock, G, plays a crucial role in lowering the price of capital accumulation. Typically the public input is seen as directly affecting final production — either as a stock or a flow (e.g., see Futagami et al. (1993); Chen (2006); Fisher and Turnovsky, 1997, Fisher and Turnovsky, 1998; Eicher and Turnovsky (2000); and Agénor, 2007, Agénor, 2011). Instead, here we assume that the public input facilitates investment specific technological change. This means that the public input affects future output through future private capital accumulation directly. In the above literature, the public input affects current output directly. This is our point of departure. We therefore formalize the link between fiscal policy and growth through the effect that fiscal policy has on ISTC.