Incentives and economic growth

Transcription

1 Econ 307 Lecture 8

2 Incentives and economic growth Up to now we have abstracted away from most of the incentives that agents face in determining economic growth (expect for the determination of technology growth) Specifically, we ve taken the savings rate as given But presumably, savings are affected by the incentives to accumulate

3 More generally The institutional environment operating within a country must have significant implications for growth Property rights Degree of corruption Taxation, regulations All these determine the incentive to save, in either physical or human capital

4 Now to explore incentives and growth First develop a simple model where savings rates are no longer exogenous Can show how various distortions/absence of property rights can affect GDP in economy through savings mechanism Secondly, take a broader perspective, on determinants of incentives (Chapter 7 Jones) Third, look in detail at how corruption affects growth Finally, look at how institutional structures affect growth

5 Model of savings Take the basic model of capital accumulation as before Assume that population growth is zero Abstract from human capital accumulation In order to look at endogenous savings, we need to ask What determines households preferences for consumption today relative to consumption in the future?

6 Household preferences UCt ( ( + )) UCt ( ( + 2 )) UCt ( ( )) ρ (1 + ρ ) A number of underlying assumptions 1. Time is discrete a time period is of length 2. Household s valuation of consumption is separable across periods 3. Household discounts future utility relative to current utility (impatience) 4. U(.) is increasing, but concave (diminishing marginal utility)

7 How are savings determined? Household budget constraint: Ct () + Kt ( + ) Kt ()(1 δ ) = Rt () Kt () + Wt () 1. Flow of consumption plus investment financed by return on capital and wages 2. Depreciation at rate δ per period 3. Capital and labour earn R and W per period

8 Household has a trade-off between consumption now and in the future If it defers consumption now by 1 unit, it can increase its investment and so increase next years capital K(t+ ) by one unit This raises it income next year by R(t+ )+(1 δ ) (the direct return on capital, plus the amount left over after capital has depreciated)

9 If the household is optimizing, at the margin, it should be indifferent between 1 more unit of current consumption, and 1 more unit of capital next period Benefits of one more unit of consumption: U'( C( t)) Benefits of one more unit of capital next period Rt ( + ) + (1 δ ) ρ 1+ U'( C( t+ ))

10 Ct+ ( ) Budget line with slope R(t+ ) +(1 δ ) Indifference curve for U(C(t))+1/(1+δ )U(C(t+ )) Ct ()

11 Implications Higher R(t+ ), higher consumption growth Higher time preference, lower consumption growth So, for given income, savings should increase with a higher interest rate

12 Now let get very small time is continuous (like models in Jones book) C C 1 = R ρ δ σ ( ) Consumption growth is higher, the higher is the interest rate α 1 α C+ K = K A δ K Consumption plus investment equals output

13 To show how to get two conditions on last page (Not required to know this) Optimal consumption condition Rt ( + + ) (1 δ ) U'( C( t)) = U'( C( t+ )) 1+ ρ Now evaluate U (C(t+ ))-U (C(t)) to get: U'( C( t+ )) U'( C( t)) ( ρ+ δ) Rt ( + ) = U'( C( t+ )) 1+ ρ

14 Divide by U'( C( t+ )) U'( C( t)) ( ρ+ δ) Rt ( + ) = U'( C( t+ )) 1+ ρ Take limits, as goes to zero U''( C( t)) C C U'( C( t)) C = ( ρ+ δ) R( t)

15 Where σ is defined as: U''( C( t)) C σ = U'( C( t)) Similar condition gives the aggregate income accounting condition, noting that the sum of capital income plus labour income is equal to output, and output is defined by the production function, which is a function of capital and the technology A, assuming we normalize total labour equal to unity

16 Two conditions give us an economy in which the dynamics of consumption and capital are determined Unlike the previous Solow or other growth models we ve looked at, consumption is not set equal to (1-s) times output, where s is exogenous Now consumption is determined endogenously We want to see what this implies for the economies savings rate how is it determined? The full dynamic analysis of this system is too hard for us at the moment We will focus only on a balanced growth path As before, we assume that A grows at rate g So then we transform the system by dividing by A

17 So divide by A, as before C k α = k ( δ + g) k k α 1 α K A α = sk ( δ + g) k Where s is defined as: C K A i.e. 1 minus the consumption income ratio s α = 1 α 1 α

18 Note from the optimal consumption equation 1 g = R ρ δ σ ( ) This must hold because consumption has to grow at a constant rate in a balance growth path Also, remember our `stylized fact that the return to capital must be constant, along a balanced growth path

19 Question is: what is R? In an economy without any distortions, market failures, taxes, or absence of property rights, then R would just equal the marginal production of capital i.e. R 1 = αk α But we wish to allow for the possibility that there may be taxes, or absence of full property rights, preventing owners of capital from re-couping the full return. So we write R 1 =Ω k α Ω < 1 α

20 Now conditions become 1 σ g ρ αk α + =Ω δ sk α = ( δ + g) k Gives two conditions in s and k

21 First condition This is long run capital market equilibrium The right hand side can be thought of as the supply of capital The left hand side the demand for capital Together, the LHS and RHS determine the equilibrium effective capital stock in the economy

22 That is: Capital Demand Capital supply k

23 Can see that A fall in Ω, representing a rise in capital taxation, or a fall in property rights over capital ownership will Shift back the capital demand locus Lower the long run effective capital stock But from the second condition, this must lower the economy s long run saving rate

24 How is this? We see that the saving rate s is determined by the second condition, which is in algebra equivalent to the balanced growth path of the Solow model but in economic interpretation quite different Equilibrium in the capital market determines k, and from income accounting equilibrium we obtain what s must be

25 Work out equilibrium s s = α δ ( + g) Ω ρ δ σ ( + + g) A rise in capital taxation, or a fall in property rights, will reduce the economy s long run savings rate