# Towards a Structuralist Interpretation of Saving, Investment and Current Account in Turkey

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1 Towards a Structuralist Interpretation of Saving, Investment and Current Account in Turkey MURAT ÜNGÖR Central Bank of the Republic of Turkey April 2012

2 We live in the age of global imbalances... %12 8 China U.S. Current Account Balance (% of GDP) %55 46 China-Saving U.S.-Saving China-Investment U.S.-Investment Saving and Investment (% of GDP) (Source: World Bank Development Indicators Database) 1 / 29

3 Convergence to the Frontier, %28 GDP per Capita: Turkey relative to the U.S (Source: The Conference Board Total Economy Database) 2 / 29

4 Saving, Investment, and Current Account in Turkey, %25 23 Saving and Investment (% of GDP) Investment Saving %2 0 Current Account and Trade Balance (% of GDP) Current Account Trade Balance (Source: T.R. Ministry of Development) 3 / 29

5 Questions for Today To what extent can a growth model be an effective tool in understanding the behavior of the saving/investment rate in Turkey? Do changes in the total factor productivity (TFP) growth rate alone generate most of the changes in the saving/investment rate in Turkey? 4 / 29

6 MODEL 5 / 29

7 Technology The aggregate production function is given by Y t = A t K θ t (H t ) 1 θ (1) Y t is aggregate output A t is TFP K t is aggregate capital H t is aggregate hours θ is capital s share of income 6 / 29

8 Technology TFP factor grows exogenously at the rate γ t : γ t (A t+1 /A t ) 1/(1 θ) (2) The capital stock evolves according to the law of motion: K t+1 = (1 δ)k t + X t (3) X t is aggregate investment and δ is the depreciation rate of capital at time t. 7 / 29

9 Households The stand-in household s utility function is: t=0 ( ) β t N t log c t + αlog(t h t ), (4) The size of the household evolves over time exogenously: η t N t+1 /N t. (5) c t C t /N t is per member consumption T is time endowment per member h t H t /N t is hours worked per member α is the share of leisure in the utility function β is the discount factor, 0 < β < 1. 8 / 29

10 The stand-in household solves subject to max t=0 ( ) β t N t log c t + αlog(t h t ) C t + X t = ω t H t + r t K t τ t (r t δ)k t π t, t = 0, 1, 2,..., given K 0 > 0. ω t is the real wage r t is the rental rate of capital τ t the tax rate on capital income π t is a lump sum tax Households are assumed to own the capital stock, K t, and rent it to businesses. 9 / 29

11 Government There is a government that taxes income from capital (net of depreciation) and uses the proceeds to finance an exogenously given stream of government purchases G t. A lump-sum tax π t is used to ensure that the government budget constraint is satisfied each period: G t = τ t (r t δ)k t + π t. (6) By treating the capital tax income rate τ t as a policy parameter, we are assuming that changes in government purchases are financed by changes in the lump-sum tax π t. Thus, Ricardian Equivalence holds. 10 / 29

12 SOLUTION PROCEDURE 11 / 29

13 Hayashi-Prescott (2002) and Chen-İmrohoroğlu-İmrohoroğlu (2006) 1. We derive the equilibrium conditions of the model, detrend variables to induce stationarity, and then impose these steady-state conditions. 2. We calibrate the model parameters and exogenous variables, and compute a steady-state for Turkish economy. 3. We use a shooting algorithm from given initial conditions toward the steady-state to compute the transition path. 4. We start from a given value of K 0 ; guess a value for C 0 and use the Euler equation and resource constraint to obtain a path for C t, H t and K t+1 towards their steady-state values. 5. If the path does not connect with the steady-state, we iterate on the initial guess for C 0 using this algorithm until convergence to the steady-state is obtained. 6. Equipped with the equilibrium path of C t, H t and K t+1 ; we can then use other equilibrium conditions to construct time paths of all aggregate quantities and prices. 12 / 29

14 Equilibrium Conditions Substituting the production function, the marginal productivity conditions, and the capital accumulation equation into the household s first-order conditions and the resource constraint, we obtain the following equilibrium conditions: C t = (1/α)(T h t )N t (1 θ)a t K θ t (H t ) 1 θ (7) { C t+1 = C [ δ]} t β 1 + (1 τ t+1 ) θa t+1 Kt+1 θ 1 N t+1 N (H t+1) 1 θ (8) t K t+1 = (1 δ)k t + A t K θ t (H t ) 1 θ C t G t (9) These equations together determine the sequence of {C t, K t, H t } given the sequence of {A t, N t, G t } as well as the initial value for K t. 13 / 29

15 We can detrend the model by defining K t k t 1, c t 1, ỹ t 1, 1 θ 1 θ 1 θ At N t At N t At N t ( At+1 ) 1 1 θ γ t, η t N t+1, Ψ t G t. A t N t Y t C t Detrended capital-labor ratio, x t k t h t. Now, three equilibrium conditions become c t = (1/α)(T h t )(1 θ)xt θ, (10) c t+1 = c [ t β 1 + (1 τ t+1 )(θxt+1 ], θ 1 γ δ) (11) t { } k t+1 = 1 [ (1 δ) + (1 Ψ t )xt ] k θ 1 t c t. (12) γ t η t Y t These three equations determine {x t, c t, k t } given {γ t, η t, τ t, Ψ t }. 14 / 29

16 Steady State If {x, c, k} are steady-state values of {x t, c t, k t } when {γ t, η t, τ t, Ψ t } are constant at {γ, η, τ, Ψ}, they satisfy c = (1/α)(T h)(1 θ)x θ, (13) [ ] 1 = (β/γ) 1 + (1 τ)(θx θ 1 δ), (14) {[ k = (1/γη) (1 δ) + (1 Ψ)x θ 1] k } c. (15) These three steady-state equations can be solved for {x, c, k} as x = ( γ β 1 1 τ + δ θ ) 1 θ 1, (16) c = (1/α)(1 θ)(t h)x θ, (17) c k = (1 δ) + (1 Ψ)x θ 1 γη. (18) The steady-state value of detrended output is given by ỹ = kx θ 1 15 / 29

17 Saving Rate Time-varying saving rate, s t, is given by: s t = Y t G t C t δk t Y t δk t (19) The detrended steady-state saving rate, s, is given by: s = (γη 1) k ỹ δ k (20) 16 / 29

18 Calibration Calibration of the Period In my benchmark simulation, I use the actual time series data between 1988 and 2010 for the exogenous variables: TFP growth rate, population growth rate, share of government purchases in output, and capital income tax rate. Calibration of the Steady State For the computation of the steady state, I set the exogenous variables equal to their sample averages. Calibration of 2011 and beyond Between 2011 and the steady state, I assume that all exogenous variables take their steady state values. 17 / 29

19 Benchmark Economy, %18 16 Data Model Saving Rate / 29

20 Counterfactual Experiments In order to isolate the effects of each exogenous variable, I first consider an economy where all the exogenous variables are held constant at their long-run averages throughout the period. Next, I introduce the actual time series path of one exogenous variable at a time. 19 / 29

21 Experiment: Shutting down all the channels % Saving Rate Data Benchmark Constant Path / 29

22 Experiment: The effects of population growth % Saving Rate Data Benchmark Constant Path Population Only / 29

23 Experiment: The effects of tax rate % Saving Rate Data Benchmark 2 Constant Path Population Only Tax Only / 29

24 Experiment: The effects of government share % Saving Rate Data Benchmark Constant Path Population Only Tax Only Government Share Only / 29

25 Experiment: The effects of TFP growth %18 16 Data Benchmark TFP Only Saving Rate / 29

26 Experiment: Main Determinants of the Saving Rate % Saving Rate Data Benchmark TFP Only All Time Series Except TFP / 29

27 Some Forecasts 0.11% for 2011 t, pessimistic TFP Factor Growth Rate = 2.11% for 2011 t, benchmark 4.11% for 2011 t, optimistic % Saving Rate Benchmark Optimistic Pessimistic / 29

28 Concluding Remarks Changes in the TFP growth rate alone can generate most of the secular changes in the Turkish saving/investment rate. A detailed analysis of the factors behind TFP growth would further enhance our understanding of the saving/investment behavior. My quantitative results are obtained in a simple growth model that abstracts from potentially important economic factors. Possible important extensions are left for future research. 27 / 29

29 A Research Agenda: Implications for Current Account Deficits For each country i = {1, 2}, there is a stand-in household with Nt i working-age members at date t. Both capital and labor are immobile across countries. We assume that there is a risk-free bond traded internationally each period. The size of the household evolves over time exogenously. In this framework a representative household maximizes β t Nt(log i ct i + αlog(t ht)) i subject to t=0 ( ) X Bt+1 i + Ct i + Xt i + φkt i i 2 t Kt i ϕ i ( ) Bt i 1 + rt B + wt i Ht i + rt i Kt i τkt i (r t i δ i )Kt i + TRt i πt i K i t+1 = ( 1 δ i) K i t + X i t B i 0, K i 0 given, 28 / 29

30 Saving Rate and Current Account Deficit National account identity is given by:. C i t + I i t + G i t + B i t+1 = Y i t + B i t ( 1 + r B t ). or C i t + I i t + G i t + CA i t = Y i t + B i tr B t One can compute the saving rate using = GNP i t s i t = GNPi t G i t C i t δ i tk i t GNP i t δ i tk i t and one can compute the current account deficit as a percentage of GDP as ca i t = Bi t+1 Bi t Y i t. 29 / 29

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