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 ChinaSaving U.S.Saving ChinaInvestment 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 standin 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 standin 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 lumpsum 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 lumpsum tax π t. Thus, Ricardian Equivalence holds. 10 / 29
12 SOLUTION PROCEDURE 11 / 29
13 HayashiPrescott (2002) and Chenİmrohoroğluİmrohoroğlu (2006) 1. We derive the equilibrium conditions of the model, detrend variables to induce stationarity, and then impose these steadystate conditions. 2. We calibrate the model parameters and exogenous variables, and compute a steadystate for Turkish economy. 3. We use a shooting algorithm from given initial conditions toward the steadystate 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 steadystate values. 5. If the path does not connect with the steadystate, we iterate on the initial guess for C 0 using this algorithm until convergence to the steadystate 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 firstorder 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 capitallabor 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 steadystate 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 steadystate 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 steadystate value of detrended output is given by ỹ = kx θ 1 15 / 29
17 Saving Rate Timevarying saving rate, s t, is given by: s t = Y t G t C t δk t Y t δk t (19) The detrended steadystate 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 longrun 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 standin household with Nt i workingage members at date t. Both capital and labor are immobile across countries. We assume that there is a riskfree 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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