Intangible capital in a real business cycle model

Economic Modelling 39 (2014) 32–48

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Economic Modelling journal homepage: www.elsevier.com/locate/ecmod

Intangible capital in a real business cycle model Kashif Zaheer Malik a, Syed Zahid Ali a, Ahmed M. Khalid b,⁎ a b

Lahore University of Management Sciences, Pakistan Bond University, Australia

a r t i c l e

i n f o

Article history: Accepted 17 February 2014 Available online xxxx JEL classification: E32 E37 Keywords: Intangible capital Real business cycle Productivity shocks

a b s t r a c t Recent empirical studies have shown that intangible capital plays an important role in explaining productivity gains that have occurred during the last two decades. By introducing intangible capital in an otherwise standard theoretical real business cycle model, this paper aims to provide a theoretical foundation of the empirical findings. Our results indicate that investment in intangible capital is pro-cyclical. Both transitory as well as permanent productivity shocks increase investment in intangible capital. However, in case of a permanent technology shock we learn that firms allocate more labor and physical capital to the creation of intangible capital which increases future profits at the cost of current profit. We also find that investment in intangible capital plays an important role in producing endogenous movements in productivity. © 2014 Elsevier B.V. All rights reserved.

1. Introduction A number of existing studies have attempted to identify the drivers of economic growth in knowledge-based economies. Recent studies have closely examined the role of intangible capital. However, most of these studies focus on measuring the size of intangible capital in an economy. For instance, Corrado et al. (2006) suggest that intangible capital is not fully included in the published US data. They argue that the observed pattern of growth in the US economy can be better explained once intangible capital is accurately measured and taken into account. McGrattan and Prescott (2010) suggest that neo-classical growth theory fits well to the post-war US data prior to 1990. However, their prediction shows a decline in US economy during the 1990s contrary to realized upward movement during the same period. This inconsistency disappears once investment in intangible capital is taken into account. This paper utilizes a theoretical model that allows one to examine the role of intangible capital. Specifically, we follow and extend Hou

⁎ Corresponding author at: School of Business, Bond University, University Drive, Gold Coast, Queensland 4229, Australia. Tel.: +61 7 5595 1429; fax: +61 7 5595 1160. E-mail addresses: [email protected] (K.Z. Malik), [email protected] (S.Z. Ali), [email protected] (A.M. Khalid).

http://dx.doi.org/10.1016/j.econmod.2014.02.018 0264-9993/© 2014 Elsevier B.V. All rights reserved.

and Johri's (2009; hereafter HJ) work of using intangible capital into a standard real business cycle (RBC) model.1 Firms expend resources to create intangible capital, which is an additional input in the production process. Within the context of a standard RBC model, firms do not earn abnormal profits as the market structure is assumed to be competitive and production technology exhibits constant returns to scale. A distinctive feature of the model used in this paper is that firms earn abnormal profits despite operating in a perfectly competitive environment. As volatility in corporate profits earned by firms is an important feature of US business cycles, the model used in this paper is more realistic. As stated above, this paper is not only an extension of the HJ model but makes certain improvement in the theoretical literature and focuses on a variety of interesting questions not explored earlier in the

1 Our work is different from HJ in many respects. For instance HJ's main focus was on the direction of causation from volatility in US corporate profits to volatility in the key economic variables such as output in US economy. Their results are based on empirical investigation using US data. In contrast to HJ, we developed an intangible augmented theoretical real business cycle model and performed various simulation exercises such as temporary and permanent technology shocks while using the dynamic version of Christiano's method of undetermined coefficients. Secondly, HJ's main contribution is limited to the behavior of net profits whereas we analyze the movements in key macroeconomic variables such as output, consumption, investment in both physical and intangible capital, hours worked, and profits due to permanent, transitory and preference shocks. Nevertheless, both studies bolster the case for the importance of intangible capital for explaining macroeconomic data.

K.Z. Malik et al. / Economic Modelling 39 (2014) 32–48

literature. For instance we would like to know if the investment in intangible capital is pro-cyclical?2 Do firms prefer investment in intangible over investment in tangible capital? In response to a permanent or transitory productivity shock, do firms accumulate more intangible capital? How do firms behave in response to a preference shock? This paper also examines the efficacy of Gali's (1999) famous result: a decrease in hours worked in response to a permanent technology shock. The analysis presented in this paper suggests that investment in intangible capital is procyclical. We find that in response to a permanent or transitory productivity shock, firms increase their investment in intangible capital. Furthermore permanent technology shock results in higher factor share of labor and capital allocated to create intangible capital which decreases profits in the current period. However, higher investment in intangible capital raises future profits. The model developed in this paper also predicts negative response to hours worked after a permanent technology shock.3 The paper is organized in the following manner. Section 2, which followed the Introduction, provides a brief overview of the literature. Section 3 presents the extended and modified version of the RBC model with intangible capital. It also provides new results on steadystate and dynamic solution, and calibration. Section 4 discusses the results of transitory and permanent and technology shocks. Conclusions and policy implications are presented in Section 5. We have included some discussion on the effect of trend stationary technology shock, impulse responses for normalized variables and the sensitivity analysis for three important parameters in Appendices A, B, and C respectively. 2. Literature review Intangible capital is an important argument of a nation's wealth. World Bank estimates show that approximately 78% of the world's wealth is attributed to intangible capital Hamilton et al. (2005). In developing nations, intangible capital accounts for 59% of the wealth, while in OECD countries this share is approximately 80%. Given this large share of intangible capital it is imperative to analyze its impact on economic growth and a number of empirical studies have attempted to estimate the impact of intangible capital on economic growth. Parente and Prescott (1994) argued that barriers to technology adaption can cause slower economic growth. They conclude that a large unmeasured investment (approximately 40% according to their estimates) exists in the business sector, which can be viewed as technology adoption investment or intangible capital investment. Later, Prescott (1998) suggested that investment in intangible capital is well above the assumed/ implied 32% of the measured output. Recent studies such as Corrado et al. (2006; CHS hereafter) suggest that investment in intangible capital in the US for the period of 1998–2000 was approximately 12% of GDP. Although there is no disagreement concerning the importance of investment in intangible capital, its size within an economy is still not settled mainly due to difference in the way it is defined and measured. Both micro and macro-economist have found evidence to support the presence of investment in intangible capital.4 It is therefore imperative to investigate the precise definition of intangible capital investment. CHS (2006) identifies three important categories — computerized investments, innovative property investments and investment in economic competencies as components of intangible capital.5 Economic competencies by CHS (2006) is defined as “the value of brand names 2

HJ (2009) reported pro-cyclicality of investment in intangible capital. The results of this paper are thus consistent with Gali (1999), Basu et al. (2006), Francis and Ramey (2005) and Gali (2005), who suggest that a permanent technology shock decreases labor hours. 4 See Brynjolfsson et al. (2002) and McGrattan and Prescott (2010) for microeconomics and macroeconomics perspectives respectively. 5 The computerized investment is embedded in computer programs and computerized databases, and innovative property reflects the scientific knowledge embedded in patents, licenses and general know-how (CHS, 2006). 3

33

and other knowledge embedded in firm-specific human and structural resources”. It comprises expenditures on advertising, market research, firm-specific human capital and organizational change. The above definitions suggest that investment in intangible capital stimulates productivity growth through provision of knowledge, increase in sales of a product and development of processes and a productive environment for actual physical production of a good. In other words, due to investment in intangible capital, products and services become more knowledge-intensive.6 In the organizational capital literature, intangible capital is defined as firm's accumulation of unobserved input which can be attributed to learning by doing or learning on the job.7 Cooper and Johri (2002), Johri and Lahiri (2008) and Johri (2009) explored this aspect of intangible capital in a dynamic general equilibrium model in a closed as well as open economy setting. A key difference between those models and the intangible capital model is that firms must expend valuable resources to produce intangible capital while the learning-by-doing process creates organizational capital as a by-product of production. In a recent study HJ applied a standard dynamic general equilibrium model for the U.S. economy (using aggregate data) in which firms expand resources to create intangible capital and hence competitive firms are able to produce positive profits. In their model intangible capital is incorporated as third input for producing final goods. It is argued that if the firm's investment in intangible capital is pro-cyclical then the extra productivity generated by these investments can lead to positive profits. They found that profits are not only more volatile than output but also positively correlated with output. It is generally observed that the neoclassical growth model, for example, failed to account for the booming economy in 1990s. McGrattan and Prescott (2010) overcome this weakness of the model by introducing intangible investment and non-neutral technology change into the standard model. McGrattan and Prescott (2010) emphasize the importance of intangible capital in understanding economic fluctuations. They contended that the post 1990 boom can be explained if intangible capital is added to the model. Corrado et al. (2006) also show the importance of intangible capital in economic growth. Human capital is also a type of intangible capital. Empirical studies such as Mankiw et al. (1992), suggest that an extended version of the neoclassical growth model (i.e., the model that includes human capital) can explain most variation in the cross-country output. Other studies such as Klenow and Rodriguez-Clare (1997), Hall and Jones (1999), Hulten and Isaksson (2007) and Hashmi (2013) argue that one also needs to consider other factors to fully understand disparities across countries. Danthine and Jin (2007) argue that if intangible capital translates into capital stochastically then plausible levels of macroeconomic volatility are compatible with highly variable corporate valuations, price earnings ratios and returns. Jinnai (2009) suggests that intangible capital producing technology is important for medium-frequency business cycle. Perli and Sakellaris (1998) examined the implications of human capital for economic fluctuations. Similarly, Jones et al. (2005) examined the properties of business cycle within the context of an endogenous growth model with human capital accumulation. Comin and Gertler (2006) examined the intellectual antecedents of medium-term business cycles. By including intangible capital in the final good production function, HJ showed that profits are not only more volatile than output but also positively correlated with output. Pyo et al. (2012) examined the rising proportion of intangible capital and economic growth in the US, Japan and Korea. Borgo et al. (2013) measured the contribution of intangible capital to growth from the UK from 2000 to 2008. They found that it contributed to 23% of labor productivity growth. 6 7

job.

Corrado et al. (2009). Lucas (1993), large unmeasured investment in business sector due to learning on the

34

K.Z. Malik et al. / Economic Modelling 39 (2014) 32–48

In summary, a number of empirical studies have examined various aspects of investment in intangible capital. These studies highlight the importance of intangible capital in real economies. In the next section, we utilize a model where intangible capital appears as an additional input into the aggregate production function. The main objective of this paper is to examine the role of investment in intangible capital within the context of a RBC model. For this purpose, the paper extends the standard RBC model to include intangible capital as an additional input in the production process. The intangible capital model used in this paper is different from a number of recent studies explored in the business cycle context using dynamic general equilibrium models. The first set of models study the implications of human capital for economic fluctuations. Early work on these ideas was published in Perli and Sakellaris (1998). They model human capital as being accumulated by workers who supply a joint input of human capital and raw labor to the production technology and get paid a wage commensurate with the return of the composite labor input. Jones et al. (2005) study the business cycle properties of an endogenous growth model with human capital accumulation. The planner can accumulate human capital by allocating consumption goods as investment in physical capital. DeJong and Ingram (2009) estimate a DGE model of skill acquisition using techniques similar to those used here. Unlike the previous study, skill or human capital is acquired purely as a function of time but not of goods. The modeling of human capital also differs in that it enters the production technology with a lag. In contrast with these models where agents expend resources on human capital, Chang et al. (2002) invoke the notion of byproduct learning-by-doing to accumulate human capital, again purely as a function of hours. Kim and Lee (2007) combine both expenditure on human capital and learning by doing into their human capital accumulation equation. As mentioned earlier, intangible capital model focuses on decisions made at the firm level which lead to intangible capital being a state variable in the firms' profit maximization problem hence introducing dynamics in it. The ability of the intangible capital model to explain profits is important as it helps to understand short-term fluctuations and to distinguish itself from a host of other mechanisms which are needed to improve the fit of DGE models for observing output and hours worked and changes in preferences (habit formation in leisure). It also allows us to introduce dynamics in labor supply (learning effects, human capital etc.).8 This paper extends the existing literature with a focus on a number of new and interesting questions. We follow an approach similar to HJ.9 First, we developed an intangible capital augmented theoretical real business cycle model. Then, we performed various simulation exercises such as temporary and permanent technology shocks while using the dynamic version of Christiano method of undetermined coefficients. We also analyze the movements in key macroeconomic variables such as output, consumption, investment in both physical and intangible capital, hours worked, and profits due to permanent and transitory shocks. In contrast to HJ (2009) our paper assumes non-random walk specification of both transitory and permanent shocks. Furthermore we also distinguish between permanent and transitory shocks. Another interesting feature of this paper is to verify Gali's (1999) results of a decrease in hours worked in response to permanent technology shock. Finally, we assess the robustness of our results and perform a detailed sensitivity analysis for various plausible values of three important parameters i.e. ω (current intangible capital contribution in the production of future intangible capital), τ (output elasticity of intangible capital)

and μ and 1 − μ (contribution of labor and capital, respectively towards creation of intangible capital in forthcoming period). 3. The model We use a dynamic general equilibrium model where all agents operate within a competitive market environment comprising two agents, households and firms.10 3.1. Households Consider a representative infinitely lived household who maximizes his/her lifetime utility as follows: max E0

∞ X

t

β U ðC t ; 1−Nt ; Bt Þ

where β is the discount factor, Ct is the consumption in current period, and Nt is the labor supply while Bt is a measure of preferences shock that follows a first-order autoregressive process with an iid error term ln Bt ¼ ρb lnBt−1 þ εbt :

ð2Þ

The utility flow function is given by: U ðct ; Nt Þ ¼ ln ct þ Bηð1−Nt Þ:

ð3Þ

Eq. (3) takes into account labor–leisure trade-off, where leisure in period t is Lt = 1 − Nt. In each period, the representative household supplies labor and physical capital to the firm, given the wage rate wt and the rental rate on capital, rt In addition, as the owner of the firm, the household receives real profits earned by the firm, πt. The budget constraint for the household utility maximization problem is given by C t þ It ¼ wt Nt þ r t K t þ πt

ð4Þ

where It is investment which augments capital stock over as follows: K tþ1 ¼ It þ ð1−δÞK t

ð5Þ

where δ ∈ (0,1) is the rate of depreciation rate of physical capital. Eqs. (4) and (5) can be combined as follows: C t þ K tþ1 ¼ wt Nt þ r t K t þ ð1−δÞK t þ π t :

ð6Þ

Given the initial values, household chooses (Ct,Nt,Kt + 1) to maximize the utility function subject to budget constraint given by Eq. (6). The dynamic programming problem can then be written as: h  i ′ V ðkÞ ¼ max E ln c þ Bηð1−N Þ þ βEV k c;n;k′

s:t: ′ C þ K ¼ wN þ rK þ ð1−δÞK þ π: Solving the above maximization problem, we get the following first order optimality conditions: Uc ¼ λ

ð7Þ

Bη ¼ wλ 1−N

ð8Þ

  ′ βEV k ¼ λ 8 Examples of these include Perli and Sakellaris (1998), Chang et al. (2002), Bouakez and Kano (2006) and Jones et al. (2005). 9 HJ used a simple model of intangible capital for empirical analysis to determine causality from volatility in US corporate profits to volatility in key economic variables.

ð1Þ

t¼0

V k ¼ ðr þ ðð1−δÞÞλ: 10

This model is based on HJ's work.

ð9Þ ð10Þ

K.Z. Malik et al. / Economic Modelling 39 (2014) 32–48

Eqs. (7) to (10) can be reduced to the following equations: w¼

cBη 1−N

1 ¼ βE

ð11Þ

   c ′ : r þ ð 1−δ Þ c′

ð12Þ

3.2. Firms The representative firm operates under conditions of perfect competition. The output is produced using labor, physical capital and intangible capital under constant returns to scale technology: Yt ¼ e

ln θt

ϕ

1−ϕ−τ τ Zt

ðAt stN Nt Þ ðstK K t Þ

ð13Þ

where Nt, Kt and Zt are labor, physical capital and intangible capital, respectively. The presence of the intangible capital distinguishes this model from a typical business cycle model. Intangible capital is produced by means of labor and capital. sN and sK denote respectively the fraction of labor and physical capital, which firm allocates to produce the final good. Hence, the remainder of the labor and physical capital, i.e., (1 − sN) and (1 − sK) are used to produce intangible capital. The permanent technology shock, At, is assumed to follow a non-random walk with persistence parameter ρa and drift process νa11: lnAt ¼ νa þ ρa ln At−1 þ εat

ð14Þ

where εat are iid shocks. The transitory productivity shock is given by a first-order autoregressive process with an iid error term: lnθtþ1 ¼ ρθ ln θt þ εθ;tþ1 :

ð15Þ

state and to compute the decision rules for the representative agent in this economy. Normalization is used for the following reasons: i) variables are normalized such that the transformed system does not exhibit growth, ii) the steady state is computed (i.e. steady state assuming that no shocks occur) in normalized variables and lastly iii) to simulate this deterministic dynamic system in the event of exogenous shocks. The normalized graphs in the Appendix B clearly show all variables in steady state (solid line) with no growth rates. The (potentially) non-linear equations that characterize the solution of the model are linearized around steady state of the model since approximation is valid only around the steady state.13 The normalized system of equations is as follows, where tilde is placed over each of the normalized variables. e þ a′ K e þ rK e þ ð1−δÞK e þπ e ′ ¼ wN e C e e ′ −ð1−δÞK eI ¼ a′ K ( ) e C ′ ′ a ¼ βE r þ ð 1−δ Þ e′ C     e ϕ s K e 1−ϕ−τ Z eτ e ¼ e ln θ s N Y N K  1−ω    e μ ð1−s ÞK e 1−μ e′ a′ ¼ ð1−s ÞN eω : Z Z N K

3.4. Firm optimization In each period, the firm maximizes the present value of its real profits subject to the production function for output and intangible capital; i.e., Eqs. (13) and (16). The firm optimization problem can be written as follows: V ðZ Þ ¼

The stock of intangible capital in period t + 1 depends on labor, physical capital and intangible capital in the current period as follows: h i μ 1−μ 1−ω ω Zt : Z tþ1 ¼ ðAt ð1−stN ÞNt Þ ðð1−stK ÞK t Þ

3.3. Normalization Since the technology shock At is permanent, we need to scale all variables with this shock in order to be able to solve for a constant steady 11 This is different from HJ who assumed a random walk while this paper assumes nonrandom walk of permanent productivity shock. 12 This idea is consistent with the notion of ‘organizational forgetting’ explored in the literature such as in Benkard (2000).

        e K e þ βV Z ′ e ϕ s K e 1−ϕ−τ Z eτ −wN−r Max E U sN N K ′ N;K;sN ;sK ;z  1−ω     e μ ð1−s ÞK e 1−μ e′ a′ : eω −Z ð1−sN ÞN þλ Z K

Which gives the following first order conditions:

ð16Þ

The parameter ω has an interesting interpretation. This captures the idea that knowledge depreciates with time as economic environment passes through various transformations.12 ω ∈ (0,1), which implies that contribution of the past intangible capital decays further back in time it was created. ω = 1 implies that intangible capital is constant over time. While ω = 0 implies that intangible capital present in the current period makes no contribution to the intangible capital in the next period. The productivity shock At appears in the intangible evolution equation to ensure a balanced growth path where increase in labor productivity over time occurs in both the final good and intangible capital good sectors. μ(1 − ω) is the elasticity of labor hours that are used in the current period to create intangible capital with respect to intangible capital in the next period. μ = 1, means physical capital is not used in the creation of intangible capital. When μ = 0, firm allocates labor only to final goods production and no labor is used in the creation of intangible capital.

35

  ′ ′ βE V z ¼ λa

ð17Þ

" # # e e′ μ ð1−ωÞa′ Z Y ϕ þλ e e N N

ð18Þ

" # ′ e′ ð1−μ Þð1−ωÞa Z rU c ¼ U c ð1−ϕ−τ Þ þλ e e N K

ð19Þ

" wU c ¼ U c

" # e Y

Uc

" # " # e e′ ϕY λμ ð1−ωÞa′ Z ¼ 1−sN sN

" # " # ′ e′ e ð1−ϕ−τÞY λð1−μ Þð1−ωÞa Z Uc ¼ : 1−sK sK

ð20Þ

ð21Þ

13 Approximate the non-linear equations in the system around the steady state, using 1st order Taylor approximation.

36

K.Z. Malik et al. / Economic Modelling 39 (2014) 32–48

The envelope condition is as follows: " # # e e′ Y ′Z V z ¼ Uc τ : þ λ ωa e e Z Z

household Euler equation (Eq. (12)) can be solved for optimal value of r as follows:

"

22

r¼

"

"

# " ## e′ e″ Y ′ ″Z ′ þ λ ¼ λa : ωa e′ e′ Z Z

ð23Þ

Since the model includes intangible capital and not all labor and capital is used in the production of the final good, the marginal products of labor and capital do not equal the respective factor prices. In fact within the context of our model, factor prices are higher than the marginal products. In the absence of intangible capital all inputs will be used solely in the production of the final good. Eqs. (18) and (19) suggest that firm allocates capital and labor to the production of intangible capital in a way that marginal decrease in the output of the final good offsets the marginal increase in intangible capital available to the firm. Using Eq. (20) in Eq. (18) and Eq. (21) in Eq. (19) results in the following equations. w¼ϕ

e Y e s N

ð30Þ

Using Eq. (23) we get

Substituting Eq. (22) in Eq. (17) results in

β Uc τ

a −ð1−δÞ: β

ð24Þ

e ¼ βτ λaZ

e UcY : 1−βω

ð31Þ

Whereas, using Eq. (31) in Eqs. (18), (19), (20) and (21) we get the following expressions. w¼

r¼

 e μ ð1−ωÞβτ Y ϕþ e 1−βω N

 e ð1−μ Þð1−ωÞβτ Y ð1−ϕ−τ Þ þ e 1−βω K

ð32Þ

ð33Þ

ð1−sN Þ μβτð1−ωÞ ¼ sN ϕð1−βωÞ

ð34Þ

ð1−sK Þ βτð1−μ Þð1−ωÞ ¼ : sK ð1−ϕ−τÞð1−βωÞ

ð35Þ

N

r ¼ ð1−ϕ−τÞ

e Y e sK K

:

ð25Þ

It is clear from the above equations that factor prices exceed their marginal product in the final good production.14 Eq. (23) represents the marginal value of an extra unit of intangible capital. Investment in intangible capital can be described by Eq. (26) as follows: e ð1−s Þ þ rK e ð1−s Þ: Iez ¼ wN N K

ð26Þ

Iez βτð1−ωÞ : ¼ e 1−βω Y

Using Eqs. (24) and (25), Eq. (26) can be written as follows:   1 1 Iez −1 ϕ þ −1 ð1−ϕ−τÞ: ¼ e sN sK Y

ð27Þ

It is clear from the above relationship that investment in intangible capital is increasing in output and decreasing in shares of factors of labor and capital. The presence of intangible capital leads to profit as follows: e e K: e e ¼ Y−w π N−r

ð28Þ

Using Eqs. (24), (25) and (27) in Eq. (28) leads to the following relationship between profit and intangible investment e Ie : π ¼ τ Y− z

It is interesting to note that the above steady state solutions of the wage, rental on physical capital, income shares of labor and capital are independent of intangible capital. The factor share of labor and capital in the steady state can be easily estimated from Eqs. (34) and (35). Using Eqs. (34) and (35) in Eq. (27), we get the steady state intangible investment to output ratio as

29

The above shows a trade-off between current period profit and investment in intangible capital. 3.5. Steady state In the steady state all variables are constant in different time periods, i.e., C′ = C, Y′ = Y, K″ = K′ = K, Z″ = Z′ = Z, etc. Accordingly,

14 Labor and capital share act as a time varying wedge between factor prices and marginal products.

The ratio of investment in intangible capital to output depends on two important parameters, i.e., τ and ω, where τ is the key parameter. There is a one-to-one correspondence between intangible investment–output ratio and τ. From Eq. (32), labor share of income can be estimated as follows:  e  wN μ ð1−ωÞβτ : ¼ ϕþ e 1−βω Y

ð36Þ

Using Eq. (33), we can solve for capital–output ratio as follows:  e 1 ð1−μ Þð1−ωÞβτ K ð1−ϕ−τÞ þ : ¼ e r 1−βω Y

ð37Þ

The size of parameters μ and τ has a direct bearing on capital to output ratio and labor share of income ratio. As μ increases, the contribution of labor to the creation of intangible capital increases while the contribution of physical capital falls. Since the permanent technology shock is increasing in labor, an increase in μ further increases the ability of the shock to create intangible capital. As τ increases, the share of intangible capital increases in the production of the final good and the share of physical capital decreases. This makes investment in intangible capital more attractive as compared to investment in physical capital, which results in larger investment in intangible capital to investment in physical capital ratio.

K.Z. Malik et al. / Economic Modelling 39 (2014) 32–48

In the steady state intangible capital equation can be written as e¼ Z



e ð1−sN ÞN

μ 

e ð1−sK ÞK

1−μ  1=1−ω a :

3.6. Stochastic model This paper employs Christiano (2002) method of undetermined coefficient to solve the dynamic model.15 The two Euler equations from the household problem can be used to examine the model dynamics. The system of equations that describe the problem of the firm can be reduced by few substitutions. Using Eq. (20) in Eqs. (18), (19), (21) and (23), one can reduce this system of equations to four equations in four unknowns. The four unknowns are capital, intangible capital, income shares of labor and capital. The relationship between the income shares of capital and labor is as follows: ϕð1−μ ÞsK : μ ð1−ϕ−τÞð1−sK Þ þ ϕð1−μ ÞsK

ð39Þ

Eq. (39) shows that the income share of labor depends on the income share of capital. Since sN is known, the output of the final good can be written as Y = f(K,N,sN,sK,Z). Wage can be determined as follows: w¼ϕ

e Y : e s N

ð40Þ

N

The above equation suggests that the output of the final good depends on labor and income share of labor; i.e., w = f(Y,N,sN). The rental rate in the dynamic equilibrium can be determined by using Eq. (41) as follows: r¼

 e ϕð1−μ Þð1−sN Þ Y : ð1−ϕ−τÞ þ e μsN K

ð41Þ

Eq. (41) suggests that the rental rate of physical capital is a function of output, capital and factor share of labor; i.e., r = f(Y,K,sN). Consumption in a dynamic equilibrium can be determined either using budget constraint or goods market clearing condition. Consumption is a function of output and capital only, i.e., C = f(Y,K). ′ e′ e ¼ Y−a e e K þ ð1−δÞK: C

based on the household problem and the other two are based on the firm problem. These equations are as follows:

ð38Þ

e from the production The above equation can be used to eliminate Z function. Since capital–output ratio is already determined, this equation can be used to solve for output of the final good in the steady state. Once output is determined, capital can be calculated. Given the steady state output, wage can be determined using Eq. (36). Similarly consumption can be estimated from the goods market equilibrium condition. Profit in the steady state can be estimated using Eq. (28). Since the steady state values of capital, labor, and income shares of factor of primary inputs are already determined, the stock of intangible capital and investment in intangible capital can be determined using Eqs. (38) and (26) respectively.

sN ¼

37

ð42Þ

The dynamic system consists of four equations that could be solved using the feed-back part of the stochastic model.16 Two equations are

15 Christiano (2002) presented an undetermined coefficients method for obtaining linear approximation to the solution of class of dynamic, rational expectations model. The solution involves two steps. In the first step, feedback part of the solution is solved by finding the zero of a matrix of polynomial. The second step solves a linear system of equations to obtain the feed-forward part of the solution. The solution can be used to compute model's implications for impulse response functions and for second moments. 16 The feed-back part characterizes the impact of the endogenous state variables on the current period endogenous variables. For further reference see Christiano (2002).

e ¼ w

e CBη e 1−N

ð43Þ

(

e C a ¼ βE ′ e C ′

e′ a′ ¼ Z

) ′

r þ ð1−δÞ

 ω    e μ ð1−s ÞK e 1−μ Z eω ð1−sN ÞN K

 3 !2 ′ 1−sN eY e′s μ ð 1−ω Þτ C N 4 5 ¼ 1: β ′ þω ϕ eY e ð1−s Þ s′N C N

ð44Þ

ð45Þ

ð46Þ

Eqs. (43) to (46) are the equilibrium conditions that can be used in our calibration exercise in the next section. 3.7. Model calibration Eleven parameters, namely β,η,δ,ρb,ϕ,τ,μ,ω,ρa,ρθ and νa appear in Eqs. (43) to (46). Some of these parameters also appear in standard RBC models that do not include intangible capital. As a part of the calibration exercise, we set the discount rate at β = 0.99. The depreciation of physical capital is taken as δ = 0.022. The elasticity of labor is assumed to be ϕ = 0.535 whereas the elasticity of capital is assumed to be 0.29. Similar parameter values are used in standard business cycle literature. However, with the inclusion of intangible capital as the third input, we have to use slightly different parameter values. For example, McGrattan and Prescott (2010) assumed income share of capital as 0.26, which is slightly lower. The household intertemporal condition is used to identify the value of utility parameter, i.e., η = 1.85. The drift in the permanent technology shock is assumed to be νa = 0.0034. The persistent parameters of three shocks are: persistence in permanent technology shock, ρa = 0.5, persistence is transitory shock, ρθ = 0.95 and persistence in preference shock, ρb = 0.9767. In the presence of intangible capital three parameters are of special importance17 — i.e., τ,μ and ω. McGrattan and Prescott (2010) use a value of τ which is around 7.6%, which is somewhat lower than those of other studies.18 They assumed that input elasticities for producing both final goods and intangible capital goods are identical. They used information on elasticities along with the information on National Income and Product Accounts' (NIPA) compensation to determine all capital shares. The model presented in the present paper is slightly different from the one suggested by McGrattan and Prescott. Our elasticities are different for final goods production and production of stock of intangible capital in next period. Hashmi (2013) uses a value of 0.13, which is more close to Corrado et al. (2006). Jinnai (2009) chooses a value of 0.27 in an asset pricing intangible capital model. HJ estimated τ = 0.173 by assigning tight priors, because the value of τ is sensitive to steady state ratios. We assume this value to be 17%, which is the average of the values that are used in the existing literature (as cited above). The second important parameter, μ, is generally assumed to have a higher value, which means more labor is allocated to produce intangible capital than physical capital. McGrattan and Prescott (2010) estimated that μ = 0.646. Again, McGrattan and Prescott (2010) assumed that

17 18

For the sensitivity analysis of three important parameters please see Appendix C. McGrattan and Prescott used 1990 levels of U.S. data to obtain estimates.

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Fig. 1. Impulse responses to transitory technology shocks (output, consumption, investment, intangible investment, intangible capital, profits).

the elasticity of labor is same across both production technologies. However, in this paper we use different values for physical and intangible capital. One would expect that the contribution of labor would be higher in producing intangible capital. In the existing literature, the value used

ranges from 0.5 to 0.85. HJ estimated a value close to 0.84. The value of μ is sensitive to the steady state ratios. In this paper, we assumed this parameter to be 0.85, which implies that income share of capital in intangible capital production is much lower than labor. This also implies

Fig. 2. Impulse responses to transitory technology shocks (capital, capital share, capital contribution in production, and capital contribution in production of intangible capital).

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Fig. 3. Impulse responses to transitory technology shocks (hours, labor-share, labor contribution in production, and labor contribution in production of intangible capital).

that more capital is used in the production of the final good, which is likely to be the case. The last important parameter is ω. The existing literature offers very little guidance in this case. HJ estimated the value of ω = 0.592. Their estimated standard deviation on this parameter is 0.075. By analyzing the variation in the mean value, using standard deviation, we use a value which is close to the one that is used by HJ. The steady state ratios are not significantly different from standard model. However, there are some ratios which are of particular importance to our model. Intangible investment to output ratio, and investment in intangible capital to investment in physical capital ratio are two such examples. In the existing literature, a number of different values are used. For example, see McGrattan and Prescott (2010), Corrado et al., 2006 and HJ. We assume intangible investment to output ratio of 0.16. The investment in intangible capital to investment in physical capital ratio is assumed to be 0.68, which is higher than 0.42 assumed by McGrattan and Prescott (2010), but lower than the value assumed by Corrado et al. (2006) and HJ. 4. Results In this section we trace impulse response functions in the event of three types of shocks namely, transitory, permanent, and preference shocks separately while using RBC model with intangible capital.19 4.1. Dynamic responses to a transitory shock In general, the standard RBC predicts that a positive transitory technology shock would result in a simultaneous increase in labor hours worked, capital stock, output, consumption, investment, and labor productivity. A transitory technology shock is believed to be a key driving force of business cycles resulting in strong positive correlation between hours worked and labor productivity. As a result of a

19 Appendix A has a discussion on how the economy responds to a trend stationary transitory shock. The results of preference shocks are provided upon request by the authors.

temporary technology shock, all variables rise above their long-term trends and hence result into a positive deviation. In the standard RBC model, firms are producing in perfectly competitive market, so profits are essentially zero. The distinguishing feature of our model from standard RBC is that it includes intangible capital and positive profits. The impulse responses from a positive transitory technology shock in our model are shown in Figs. 1, 2 and 3. The solid line is the steady state timepath while the dotted line is the respective impulse response. We may note in Figs. 1 and 2 that a transitory technology shock simultaneously increases consumption, investment, capital stock, and output. In Fig. 3 we noticed that the same shock also leads to an increase in hours worked. In Figs. 2 and 3 we may further note that the transitory shock also increases investment in intangible capital and so does the factor shares allocated for the creation of stock of intangible capital. The transitory shock also results in positive profits as shown in Fig. 1. The effect of the shock dissipates slowly over a time since we choose a relatively high persistence level i.e., ρ = 0.95. Since our model is an extension of HJ (2009), it is imperative to provide a comparison of results of this paper to that of HJ (2009). HJ reported a hump-shape and trend reverting path of output in response to transitory shock. Results of this paper are consistent with HJ as well as the standard RBC and Vector Auto-Regressive (VAR) specification models. The results of calibration exercise showing an increase in hours worked in response to transitory shock are also consistent with HJ and standard RBC model. HJ reported decrease in firm's net earnings in response to transitory shock since firms find it more lucrative to invest in intangible capital at the cost of lower current profits. However, the results of our paper suggest that firms find it more profitable to invest in physical capital than in intangible capital. We further note that although investment increases in both physical and intangible capital, investment in the former is found to be higher than the latter and thus leading to higher profits in the current time period. The findings of this paper are consistent with Rebelo (2005) especially when the productivity shock is transitory. Like Rebelo (2005), we found that almost all macroeconomic variables are strongly pro-cyclical, the consumption is less volatile than output, and that

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Fig. 4. Impulse responses to permanent technology shocks (capital, capital share, capital contribution in production, and capital contribution in production of intangible capital).

Fig. 5. Impulse responses to permanent technology shocks (output, consumption, investment, intangible investment, intangible capital, profits).

macroeconomic variables show substantial persistence. However, in the model presented in this paper firms have option to divert factors of production to either production of goods in current time period or to the production of intangible capital in the current time period to produce more output in the future. This decision of the firms induces trade-off between current versus higher future earnings (intertemporal substitution). These results are thus

contrary to the standard RBC model — if we allow firms to earn more than normal profits (it is the case in our model) then RBC standard results may not hold.20

20

Our results for the normalized series are shown in Appendix B below.

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Fig. 6. Impulse responses to permanent technology shocks (hours, labor-share, labor contribution in production, and labor contribution in production of intangible capital).

4.2. Dynamic effects of permanent technology shock The dynamic effects of a permanent technology shock with persistence are presented in Figs. 4, 5 and 6. Our results show that income effect of a productivity shock seems to be dominating the substitution effect. Higher current consumption leads to fall in both investment and capital stock as shown in Figs. 4 and 5. We also note that after an initial decrease, capital stock grows above the balance growth path as depicted in Fig. 5. The same Fig. 5 shows that investment in physical capital decreases after a shock before reverting to a long-run growth path. The readers would note that inclusion of intangible capital produces interesting results. For instance, since firms have incentive to invest in intangible capital it uses more labor and capital in the creation of intangible capital. This raises the investment in intangible capital as shown in Fig. 4. However, the same figure shows that higher investment in intangible capital comes at the cost of lower current profits since there is a trade-off between profits and creation of intangible capital. It is imperative to note here that a higher investment in intangible capital in the present leads to higher profits in the future. As far as the impact on income distribution is concerned as shown in Figs. 5 and 6 we note that the factor share of labor (sN) and factor share of capital (sK ) in production decreases in the event of a shock. This implies that residual labor (1 − sN) and capital (1 − sK ) is allocated to create more intangible capital in the future. The total contribution of labor and capital in output production can be calculated by multiplying their respective factor shares with the size of labor and the size of capital, i.e., (sN × N) for labor, and (sK × K) for capital. Similarly, the contribution of both inputs in the creation of intangible capital can be estimated as follows: ((1 − sN)N) = labor share and ((1 − sK)K) = capital share. The effect of productivity on labor hours worked is the most debated issue in the standard RBC model. Our model predicts that the initial effect of productivity shock results in a decrease in hours worked as shown in Fig. 6. We also find that consumption and investment in intangible capital is increasing while real investment in physical capital is decreasing. Our results also suggest that change in consumption is relatively less than changes in investment which may indicate consumption smoothing preference of consumers.

The results presented here are more plausible since it takes into account the effects of permanent shock along with balanced growth path. The un-normalized impulse response functions (IRFs) show the actual expected changes. We can also notice [from Fig. 6 and Appendix B Fig. B6] a difference between the simulated results of normalized and un-normalized impulse response functions. While normalized IRFs show a drop, the un-normalized IRFs illustrate an increase if the variable in question rises, but not by as much as observed along the balanced growth path (BGP). Since the deviations from the BGP are relatively small, they do not show up as well on the un-normalized IRFs, and that makes the normalized IRFs useful to illustrate the response to the shock. Another interesting result of this paper is that in the event of permanent productivity shock, our model predicts a negative correlation between hours worked and output. This is contrary to HJ who reported a positive and inertial response in hours worked and output. The results of this paper, however, are consistent with Gali (1999) who also found a negative correlation between a permanent technology shock and hours worked for the US economy. The same negative correlation is reported by Basu et al. (2006), Francis and Ramey (2005) and Gali (2005). A similar result has been derived by Ali and Anwar (2012)21. They have discussed two cases in this regard. In Case-I they assume that increase in productivity merely leads to cost savings whereas in Case-II their assumption is that increase in productivity leads to no change in employment but increase in output. In Case-I when firm decides to produce same level of output then they observe a decrease in hours worked since less labor are required to produce the same level of output in the aftermath of increased productivity. In the light of Ali and Anwar (2012) results, Gali results can be justified under the pretext of either sales constraint or a slow growth in demand for goods relative to growth in output. A productivity shock, especially in the presence of intangible capital is more profound, and provides a sufficient cost saving opportunity to the firms. In this case, if growth in demand for goods fall short to growth in supply of goods then firms end-up using less labor despite the overall increase in output. An increase in hours worked would be possible when increase in demand for goods surpass the

21 Ali and Anwar (2012). Macroeconomic Consequences of Increased Productivity in Less Developed Economies. Economic Modelling 29 621–631.

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supply of goods and firms' increase in supply of goods would be inevitable.22 Our model provides more insight to the negative correlation between positive productivity shock and the hours worked. For instance, in the event of enhance labor productivity, as stated above firms need less labor to produce a given level of output. In our model since firm focuses on investment in labor and capital productivity, a decrease in labor hours worked and increase in production at the same time should not be taken as unusual outcome or prediction of the model. Moreover, our results as well as Gali's (1999) prediction are more close to Keynesian view of sales constraint or a sluggish growth in aggregate demand for goods. In such circumstances firms never operate at their full capacity and especially in the event of productivity shocks need less labor to produce a given level of output and thus give rise to negative correlation between productivity shocks and hours worked. Another set of our results are that in the event of permanent technology shock, firms increase investment in intangible capital to capitalize more future productivity. Since firms face a trade-off between current profits and higher earnings in the future, they prefer higher current earnings in response to transitory shock while prefer higher future earnings in response to permanent shock. We argue that in response to transitory shock firms invest more in labor and physical capital and expand current output and invest relatively less in intangible capital. Hence, firms earn higher current profits in response to transitory shock. This result is different from HJ who predicted lower earnings and higher investment in intangible capital in response to both transitory and permanent productivity shocks. The RBC model without intangible capital fails to produce effective mechanism to propagate shocks overtime because output growth is positively auto-correlated in the short-run and weakly auto-correlated in the long-run.23 The RBC model with intangible capital aggravate the shocks since firms respond to an increase in productivity by investing more in intangible capital which causes inertia in the productivity. A better way to examine the consistency of the RBC model with intangible capital is to observe the effect of permanent technology shocks on consumption. The permanent shock does increase consumption, which is consistent with the data as shown in Fig. 4. The important difference between our model and the modified version of the RBC model as suggested by Gali (1999), Basu et al. (2006) and Francis and Ramey (2005) is that our model produces negative hours worked in the event of permanent productivity shock whereas Gali (1999) and Basu et al. (2006) suggested that sticky prices with non-accommodative monetary policy is needed to produce this result. Similarly, Francis and Ramey (2005) suggested the inclusion of real frictions in the model to replicate such results.

5. Conclusion This paper extends a standard RBC model to include intangible capital as an additional input in the production process. Simulation is performed

by choosing suitable parameter values of the model to analyze the impact of technological and preference shocks on key variables of the representative economy. Our model predicts not only a pro-cyclical nature of investment in intangible capital but also exhibits that intangible capital plays a significant role in producing endogenous movements in productivity. The calibration exercise suggests that both transitory and permanent shocks result in an increase in investment in intangible capital. We also observe that although transitory shock results in an increase in investment in both physical and intangible capital the increase in investment in physical capital is relatively larger in magnitude. Another interesting finding of this paper is that in the event of a transitory shock, as compared to investment in intangible capital, firms allocate more labor and capital to the production of the final good. We find that a trend stationary productivity shock also produces the similar results. Contrary to transitory shock, however, it is learned that a permanent productivity shock leads to an increase in investment in intangible capital. As far as profits are concerned we learned that in the event of transitory shock, firms' current profit increases while in case of permanent shock firm's future profits would increase. This result reflects the fact that firms invest in intangible capital at the cost of current period profits. Nevertheless, this investment leads to higher profits in the long-run. Another contrasting result of a permanent versus transitory shock is that employment reduces in the event of permanent shock while it increases in case of transitory shock. We also observed that when permanent shock has a higher level of persistence, it leads to stronger negative effect on employment. Finally, our model predicts that the impact of a permanent shock last longer since firms acquire more intangible capital in response to an increase in productivity, which further raises productivity in the future and thus results in long-term effect. The important policy implication of this paper is to determine the built in stability property of the intangible capital. The model of this paper may be used to calculate the overall loss (for example the variance of output) to the society with or without intangible capital. In case intangible capital serves as a built in stabilizer then it is imperative that we may think of a policy to induce firms (for example through tax/subsidy policies) directly or setup an institution at state level which continuously invest in the creation of intangible capital. Similarly, we may introduce market imperfections (for example sluggish wages and prices adjustment over time) to evaluate sensitivity of the results of this paper (i.e. effects of shocks on the time path of output, investment in physical and intangible capital, profits, etc.). Appendix A Effect of trend stationary transitory shock Suppose that the time series of productivity is described as trend stationary process around the deterministic trend. In this case the productivity shock can take the form of ln At ¼ γa t þ εt εt ¼ ρa εt−1 þ ηt

22

There is a whole set of literature (Gali, 1999; Shea, 1998; Basu et al., 2006; Francis and Ramey, 2005) which used long-run restrictions to identify the permanent and transitory shocks. They argued that real business cycle theory does not hold for the post-war US data since productivity shock is not the main source of business cycle fluctuations. The above conclusion was questioned based on misspecification of VAR model by Christiano et al. (2003) and Chari et al. (2005). The main disagreement is whether hours should enter the VAR model in levels or in the first difference. Christiano et al. (2003) estimated that if hours entered in levels form then productivity shock would cause an increase in hours worked. However, Chari et al. (2005) suggested that alternate space state approaches like business cycle accounting approach are more useful to address issues of misspecification and developing business cycle theory rather than measuring certain variables in level or log forms. 23 Cogley and Nason (1995).

where η ∼ N(0,σ2). We assume that labor market responds to a productivity shock with a lag. In other words, employment does not respond to the shock in the current period. Following the transitory shock, consumption, investment and output all increases above their long-run trend. Firms increase investment both in physical and intangible capital. However, it can be seen that investment in physical capital is relatively higher, which means that more resources are invested in the production. Since there is a trade-off between profit and investment

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Fig. A1. Impulse responses to trend stationary transitory technology shocks (output, consumption, investment, intangible investment, intangible capital, profits).

in intangible capital, profits increase. Fig. A1 shows that due to a trend stationary transitory shock, investment increases relatively larger (in magnitude) as compared to the case of stochastic transitory shock. The response to profits is also found to be relatively higher in case of trend stationary productivity shock as shown in Fig. A1. Fig. A2 shows that as a result of transitory shock, capital stock increases above the long-run trend and revert back slowly overtime. Capital share in output production increases and capital share in intangible capital creation decreases as shown in Fig. A2. Since firms want to

reap benefits of higher productivity in the present time, they invest more in physical capital than in intangible capital. As a result of productivity shock hours worked also increase and firms have more incentive to divert the labor resources towards the production of output than to the production of intangible capital as visible in Fig. A3. Higher productivity increases the current period profits for the firm. The prediction of trend stationary transitory shock is not significantly different from standard RBC model except that capital and labor resources are more diverted towards output production than to intangible capital creation.

Fig. A2. Impulse responses to trend stationary transitory technology shocks (capital, capital contribution in production, and capital contribution in production of intangible capital).

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Fig. A3. Impulse responses to trend stationary transitory technology shocks (hours, labor contribution in production, and labor contribution in production of intangible capital).

Appendix B Normalized impulse response functions The solid line is the balanced growth path while the dotted line represents the movement of the respective variables. It is clearly shown that shock increases initially, but all series revert to the balanced growth path.

Fig. B1. Impulse responses to transitory technology shocks — normalized variables (capital, hours, output, investment, consumption, intangible capital).

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Fig. B2. Impulse responses to transitory technology shocks — normalized variables (intangible investment, profits, labor share, capital share).

Fig. B3. Impulse responses to transitory technology shocks — normalized variables (production labor contribution in production, labor contribution in intangible capital, capital contribution in production, capital contribution in intangible capital).

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Fig. B4. Impulse responses to permanent technology shocks — normalized variables (capital, hours, output, investment, consumption, intangible capital).

Fig. B5. Impulse response to permanent technology shocks — normalized variables (intangible investment, profits, labor share, capital share).

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Fig. B6. Impulse responses to permanent technology shocks — normalized variables (production labor contribution in production, labor contribution in intangible capital, capital contribution in production, capital contribution in intangible capital).

Appendix C Sensitivity analysis Since this model includes intangible capital, three parameters are of special importance i.e. τ, μ and ω. We alter the values of these parameters around the maximum and minimum which are available in the literature to see how it affects the overall performance of the model in general. We also analyze how these changes affect the factor share allocation of labor and capital to the output production and creation of intangible capital. The first parameter is τ. The value of τ used in the paper is 0.173. The minimum value used in the literature is 0.076, which is used by McGrattan and Prescott (2010). This value results in a higher steady state value for both labor and capital shares allocated to production. However, lower value of τ results in investment to output ratio of around 32%, which is very high. The ratio of intangible investment to tangible investment is 23%, which is almost 50% less than what McGrattan and Prescott (2010) reported. We have chosen a 0.33 as the maximum value of τ. The higher value of τ results in lesser labor and capital resources diverted towards output production and more are used to produce intangible capital. A higher value of τ brings the investment to output ratio to less than 14%. This higher value also results in a very high ratio of investment in intangible capital to physical capital and output. The second important parameter is μ. We have used a value which is close to the maximum value available in the literature. We have selected a minimum value of 0.4. A minimum value of μ increases the labor share in production and decreases the capital share as expected. Less of labor but more of capital is used in creation of intangible capital. The minimum value of μ also increases the investment to output ratio to 30%, which is very high in a closed economy model with no government. We have selected a median value of 0.62. A median value results in higher labor share in production. The value of this parameter is very sensitive to the contribution of labor in production and creation of intangible capital. The median value can only increase the investment to output ratio to 28% which is still very high. The intangible investment to physical investment ratio is around 0.60. The last parameter is ω. If the value of ω = 1, means that intangible capital is constant over time and a value of zero means current intangible capital does not contribute to produce intangible capital in the next period. We picked the minimum value of 0.30 and a maximum value of 0.90. A minimum value does not affect too much the capital and labor share allocation. It basically means that current intangible capital is not contributing much for future creation. This number does not alter the steady state ratios, however, the ratio of intangible to tangible capital go up. Although a very high value of ω increases both the allocation share, the increase is not more than 3%. It slightly increases the investment to output ratio. Overall changes in the values of ω are not very sensitive to the steady state ratios. We also performed sensitivity analysis for ρa (in Eq. (14) in the text i.e. ln At = νa + ρa ln At − 1 + εat). Higher and lower values of ρa only bring quantitative changes in terms of magnitude and values do not alter the qualitative results (results are provided on the request). For instance, for higher value of ρa = 0.8, the impulse responses move more closely to the balanced growth path. The literature reports that we do not need much persistence in the permanent shock in growth rates in order to line up the model with the data (the estimated persistence of the permanent technology shock in growth rates to achieve these results is very low, around 0.3–0.4 at the quarterly frequency).24 The persistence parameter value and the results reported in this paper are consistent with the available literature. Since some firms prefer current profits over future profits, it would be interesting to alter the value of discount factor. To test the sensitivity of our result to this belief we performed various simulation exercises by varying the discount factor β. Our simulation exercise reveals that in the event of a shock; when the discount factor takes the value 0.75 or less, firms profit are more in the present than in the future whereas firms profit are less in the present but more in the future when beta takes a value greater than 0.75.25 This value also changes the magnitude of the impulse responses for rest of the variables of the model but it does not change our results qualitatively.26 24 25 26

Linda, Jesper, “The Effects of Permanent Technology Shocks on Labor Productivity and Hours in the RBC model”, Sveriges Riksbank Working Paper Series No. 161 April 2004. Figures can be included in the Appendix of the paper upon reviewers' recommendation. Graphs can be provided upon request.

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