Asset Price Bubbles and Endogenous Growth [PRELIMINARY DRAFT] Abstract

Size: px

Start display at page:

Download "Asset Price Bubbles and Endogenous Growth [PRELIMINARY DRAFT] Abstract"

Silvester Marshall
6 years ago
Views:

1 Asset Price Bubbles and Endogenous Growth [PRELIMINARY DRAFT] Jong Kook Shin 1 Chetan Subramanian 2 Abstract This paper extends a simple Schumpeterian growth model to demonstrate that bubbles can generate economic growth by channelizing excess savings into the R&D sector in nancially constrained economies. Further, we show that while a negative shock to productivity in the R&D sector can potentially result in a bubble fuelled growth, a positive shock could put an end to such an episode. 1 Introduction Recent macroeconomic data indicate that both advanced and emerging economies have been characterized by large uctuations in wealth with GDP growth mirroring movements in wealth. Martin and Ventura (2012) point out that while from wealth to GDP ratio in the US was stable around 3.4; in the run-up to the global nancial crises the number was closer to 6. They also highlight the fact that (1) the behavior of net worth largely followed the pattern exhibited by stock and real estate prices, and (2) the changes in the stock and real estate prices cannot be explained by economic fundamentals. 1 Newcastle University Business School, jong.shin@ncl.ac.uk 2 Corresponding author: Department of Economics and Social Sciences, IIM, Bangalore, Bannergatta Road, India chetan.s@iimb.ernet.in, Phone: (91)

2 The challenge therefore is to square o these stylized facts and explain why bubbly episodes in these asset prices lead to periods of increased economic growth. The traditional view (Samuelson, 1958; Tirole, 1985) held that bubbles diverted savings away from investment and thereby increasing consumption and reducing growth. Saint-Paul (1992), Grossman and Yanagawa (1993), and King and Ferguson (1993) extend the Samuelson- Tirole setup to economies with endogenous growth, and show that bubbles reduce long-run economic growth. This hypothesis is clearly not consistent with recent data. Instead, we introduce nancial constraints into the Schumpeterian growth framework and show explicitly how rational bubbles funnel savings to the R&D sector thereby enhancing growth. Our explanation is motivated by data that indicate periods of stock and real estate price booms have also been followed by increased R&D expenditure (Figure 1). Importantly, we also demonstrate that a positive productivity shock to the R&D sector could potentially eliminate an episode of bubble fuelled growth. We construct a two-period overlapping generation version of the Schumpeterian growth model. Agents are risk neutral and maximize their expected old-age consumption. In period one they work and earn wages. At the beginning of period two, a fraction of them are given an opportunity to become entrepreneurs in the R&D sector. These entrepreneurs nance innovation with their savings as well as borrowings from the non-entrepreneurs. Due to informational frictions their borrowing limit is capped at a fraction of their expected earnings. We then proceed to demonstrate that rational bubbles can emerge in such a nancially 2

3 constrained economy. Intuitively, the suppliers of capital in the economy are the nonentrepreneurs whereas the demand for capital is generated by the entrepreneurs. Due to the presence of borrowing constraints it is conceivable that supply exceeds demand which in turn lowers interest rates. Therefore, bubbles can arise in equilibrium because they increase the demand for capital and solve the excess capital supply problem. This result is similar to Farhi and Tirole (2011) and Basco (2014). Given that innovation is the engine of growth, the transfer of resources from the non-entrepreneurs to the entrepreneurs results in higher growth rates in the economy. Interestingly, we nd that an increase in productivity in the R&D sector has two e ects (1) it increases the probability of innovation, and (2) it increases the value of collateral, thereby relaxing the borrowing constraint. Both these features result in an increase in the demand for savings thereby eliminating the bubble. Conversely a negative productivity shock could nancially constrain the economy thereby opening the door for rational bubbles. This then implies that productivity shocks to the R&D sector could potentially create or eliminate episodes of bubble fuelled growth. Our work is closely linked to Martin and Ventura (2012) who also explain periods of rising growth and bubbles. In their paper nancial markets are segmented and expectation driven bubbles help transfer resources from non-productive investors to productive investors thus facilitating growth. However, the focus in our paper is on endogenous growth with innovation being the engine of growth. The rest of the paper is as follows. In Section 2 we present the basic model. Section 3 3

4 explains rational bubbles and examines the impact of productivity shocks to the R&D sector on bubbles. In Section 4 we conclude. 2 The Model We consider a simple model of Schumpeterian growth (Aghion and Howitt, 2009) with - nancial constraints. People consume one good, called the general good, which is produced by perfectly competitive rms using labor and a continuum of intermediate goods. There are overlapping generations of workers who live for two periods. They are risk neutral and maximize their (expected) old-age consumption. When young, they work in the general good sector and earn wages in competitive labor markets. Growth results from innovations that raise the productivity of the intermediate products. At the start of the second period, a fraction (") of workers are given an opportunity to become entrepreneur-innovators in the intermediate sector. If they succeed, the innovation will create a new version of the intermediate product, which is more productive than the previous versions. In addition to their wage, entrepreneurs can borrow capital from the non-entrepreneurs of their generation to facilitate innovation. Successful innovators return the borrowed amount and interest. At the end of old age, they consume and die. The population (mass) of each generation is normalized to one. 4

5 2.1 The General Sector The economy has one multi-purpose general good. It can be consumed and used for an input to R&D and to production of intermediate goods. The general good is produced by the technology Z " Z t = P 1 A t (i) 1 x t (i) di (1) 0 where 2 (0; 1), P denote labor input, x t (i) is input of the latest generation of intermediate goods at t, and A t (i) is productivity associated with it. The general good is produced in a perfectly competitive market. When we normalize the size of labor P = 1 and take the general good numeraire, the price of intermediate good equates its marginal product p t (i) = 1 At (i) (2) x t (i) 2.2 Intermediate Sectors For each intermediate sector i, one innovator is born each period. An innovator i born at t 1 researches new type of intermediate good i available at t: Let t (i) denote the probability of successful R&D for such an innovator. The productivity of intermediate good i is then, for > 1, 8 >< A t with t (i) A t (i) = >: A t 1 with 1 t (i) (3) 5

6 where A t 1 = R A t 1 (i) di is the average technology level at t 1. Given the homogeneity and the large number of the innovators, the fraction of successful innovators is t = t (i) for any i and the average technology is A t = t A t 1 + (1 t ) A t 1 (4) = ( t + 1 t ) A t 1 The growth rate of average productivity is g t = A t A t 1 A t = t ( 1) (5) The sole input to the intermediate sector is the general good. Using a linear technology, the successful innovator i can convert one unit of general good into one unit of the latest version of intermediate good i: The price of intermediate goods is its marginal product, p it = A t (i) 1 x t (i) 1 The pro t of successful innovator is where = (1 ) t = A t (i) (6) Given the optimal choice of intermediate goods producers, the equilibrium output (1) is Z t = 'A t where ' = 2 1. Therefore GDP grows at the same rate as the technology growth rate gt. 6

7 2.3 The R&D Sector At the start of time t, a fraction " of the generation born in t 1 is given the opportunity to innovate. The innovation technology is given by t = s t N t A t (7) where t denotes the probability of successful innovation, N t is R&D spending required for t, and A t = A t 1 is the target productivity level. The reason why the probability of innovation depends inversely on A is that as technology advances it becomes more di cult to improve upon. Here, t is a R&D productivity parameter. The higher is t, the smaller is the R&D expenses for a given t. It follows that the R&D spending with innovation probability t is given by N t = A t t 2 t (8) Each innovator has access to his wage income w t 1, and must borrow L t = N t w t 1 to invest N t. Suppose that the maximum pledgeable amount for borrowing depends on the expected earnings of innovators due to moral hazard problems (e.g. Farhi and Tirole 2012). Then it can be shown that the innovators are credit constrained with the limit on credit given by N t q t A t (9) 7

8 The parameter q < 1 is commonly referred to as the credit multiplier. The credit multiplier is determined by institutional factors. This constraint determines the maximum R&D investment when the borrowing constraint is binding. The innovators choose R&D spending N t or innovation probability t to maximize their expected pro t max t = t A t R t (N t w t 1 ) (10) A = t A t R t t 2 t w t 1 t subject to the nancial constraint (9) where R t denotes the interest factor Non-binding nancial constraint If the nancial constraint is not binding, we can solve the objective function (10) while ignoring the constraint. The unconstrained innovation probability is therefore given by t = t 2R t (11) Combining (8) and (11), the unconstrained optimum R&D expense is N t = t 2 A t 4R 2 t (12) This result shows that the amount of unconstrained R&D expenses increases in the productivity shock t, target innovation technology A t and innovation margin while it decreases in the interest factor R t. 8

9 2.3.2 Binding constraint If the constraint is binding, the R&D expense is capped by the credit multiplier q, therefore, ^N t = q^ t A t (13) With (7) and (13), the constrained innovation probability is ^ t = q t (14) Comparing (11) and (14), it becomes necessary that q 1 2R t for any feasible values of R t : 2.4 Capital Market Given the OLG structure, the amount available for loans at time t, is equal to the wage of the non-innovator group. The expected return on loans to lenders (non-innovator group) is t R t and the opportunity cost of lending is storage, which o ers gross return of one. Therefore the capital supply curve is 8 >< S t = >: (1 ") w t 1 if R ^ 1 t = 1 q t 0 if R < ^ 1 t = 1 q t (15) 9

10 The aggregate demand for funds by the innovator is D t = " (N t w t 1 ) h = " min nn t ; ^N o t 1 = " t 2 min 4R 2 t w t ; q 2 1 i (1 ) ' A t 1 (16) The min operator re ects the nancial constraint that determines the upperbound of borrowing. The last line is obtained by combining (12) and (13). This means that the capital demand curve is kinked at R t = R ~ = 1. This kink point is decreasing in the credit multiplier 2q q. The dynamics of capital market can be analyzed by the demand and supply curves (15) and (16). Without loss of generality, in a unconstrained economy, the equilibrium interest rate is determined along the decreasing section of the demand curve, i.e. the equilibrium interest rate is set by D t = S t as in Figure 2. In this case, the unconstrained equilibrium interest rate is s Rt " = 2 t 4 (1 ) ' (17) With (5), (11) and (17), the unconstrained growth rate is g t = s (1 ) ' ( 1) 2 t " It follows from (13) and (14) that when the nancial constraint is binding, the investment is ^N t = (q) 2 t A t. In this case there exists excess supply in capital as in Figure 3. The 10

11 prevailing interest rate is the inverse of the innovation probability ^R t = ^ 1 t = 1 q t from the lender s incentive compatibility condition, R 1. The corresponding constrained growth rate is ^g t = q t ( 1) Since is proportional to the amount of R&D investment and g is to, g t > ^g t. 3 Bubbles It is straightforward to see that the unconstrained economy cannot support the rational bubbles. Essentially, this happens because in this case there is no excess supply of capital 3. On the contrary, the constrained economy can bene t from a bubbly episode. Consider a type of bubbles which transfers a tiny fraction of capital from young savers to innovators in a constrained economy. It will shift down the (non-zero part of) supply curve by the amount of bubbles B t = (1 ") (1 ) 'A t 1. If the proceeds from bubbles are equally distributed across innovators, and used for investment in addition to the borrowing, the R&D investment per innovator with bubble is N B t = ^N t + B t " = (q + t) B t A t 1 3 Even in this case, if R < 1+g, it is possible that bubbles can arise because savers can be o ered better return from purchasing bubbles than lending to innovators. Since the marginal return from investment is too low and the growth rate is too high, all generations can increase consumption if they reduced investment and diverted resources from entrepreneurs to savers using bubbles. This ine cient equilibrium has been discussed extensively in Tirole (1985) and the subsequent studies. The empirical support for this equilibrium is rare. Therefore we rule out this case for our discussion. 11

12 where t = 2 q t + q 4 2 q 2 2 t t (1 ") (1 ) '=" =2 2 t > 0 denotes the bubbly investment multiplier. In this case, the innovation probability is B t = (q + t ) t and the bubbly GDP growth rate is g B t = (q + t ) t ( 1) This is clearly higher than ^g because R&D expenditure and the probability of investment are monotonic. The savers are willing to hold this bubbles as long as they believe that the bubble o ers at least a gross return of one. The (expected) return of bubbles can take a continuum of values in this equilibrium as long as it is not to high. However, the maximum return bubble can have is the return on real asset. If bubble return is greater, no one will buy real asset. 3.1 Productivity shocks Consider next the case of a positive productivity shock to the innovation sector. The shock (higher t ) increases the productivity of R&D investment, which shifts out the downward sloping part of the capital demand curve North-East. It also increases the maximum value of pledgeable output, q^ t, by increasing the probability of innovation, which shifts up the horizontal part of the demand curve. It leaves the supply of capital curve unchanged. 12

13 This could lead to potentially interesting implications. On the one hand, the increase in productivity increases the probability of innovation and has a positive impact on growth. On the other hand by relaxing the borrowing constraint the increase in productivity could eliminate existing bubbles. If the nancially constrained economy has relied heavily on bubbles for growth, then the latter e ect may dampen the e ect of a positive productivity shock on growth. Interestingly this is akin to Schumpeter s creative destruction. Even in the absence of obsolescence of existing capital, a positive shock to innovation can eliminate bubbles and bubble nanced growth. Similarly, a negative productivity shock can result in a country becoming nancially constrained, leading to the possibility of to rational bubbles. 4 Conclusion In this paper we develop a framework to understand why recent "bubbly" episodes have been characterized by high economic growth. We demonstrate that in nancially constrained economies bubbles could potentially help transfer savings to the research and development sector thereby promoting innovation and hence growth. Essentially, bubbles help resolve the shortage of assets in a nancially constrained economy. We also show that while an increase in productivity in the R&D sector could potentially increase growth rates by increasing the probability of a successful innovation, it could also lower growth rates by eliminating an existing bubbles. 13

14 References [1] Aghion, P. and PW. Howitt, 2009, The MIT Press, ISBN [2] Basco, S., 2014, Globalization and Financial Development: A Model of the Dot-Com and the Housing Bubbles, Journal of International Economics 92.1, [3] Farhi, E., and J. Tirole, 2011, Bubbly Liquidity, The Review of Economic Studies. [4] King, I. and D. Ferguson, 1993, Dynamic Ine ciency, Endogenous Growth, and Ponzi Games, Journal of Monetary Economics 32, [5] Grossman, G. and N. Yanagawa, 1993, Asset Bubbles and Endogenous Growth, Journal of Monetary Economics 31, [6] Saint Paul, G., 1992, Fiscal Policy in an Endogenous Growth Model, Quarterly Journal of Economics 107, [7] Samuelson, P., 1958, An Exact Consumption-loan Model of Interest with or without the Social Contrivance of Money, Journal of Political Economy 66, [8] Tirole, J., 1985, Asset Bubbles and Overlapping Generations, Econometrica 53 (6), [9] Martin, A., and J. Ventura, 2012, Economic Growth with Bubbles, The American Economic Review, 102.6,

15 Figure 1. R&D Expenditure as % of GDP and Lag of Stock and House Price Indices Developed Countries Developing Countries Sources: MSCI, World Bank (World Development Index), S&P/Case-Shiller, NSO, Kookmin Bank, Oxford Economics Note: All variables are standardized to zero mean and unit standard deviation for plotting.

16 Figure 2. Unconstrained Capital Market S, D ε(λ t π 2 q 2 γ (1 α) φ)a t 1 (1-ε) (1 α) φa t 1 S D R t = επ 2 γλ t 4(1 α)φ R

17 Figure 3. Constrained Capital Market S, D (1-ε) (1 α) φa t 1 S ε(λ t π 2 q 2 γ (1 α) φ)a t 1 D R t = μ t 1 = 1 qπλ t R

Should the Government Protect its Basic Research?

MPRA Munich Personal RePEc Archive Should the Government Protect its Basic Research? Guido Cozzi and Silvia Galli June 2017 Online at https://mpra.ub.uni-muenchen.de/79622/ MPRA Paper No. 79622, posted