S K K K GDP per capita or worker in our case is GDP L and rate growth in GDP

# S k k k gdp per capita or worker in our case is gdp l

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+ S K _ K K GDP per capita (or worker in our case) is GDP L and rate growth in GDP per capita is d dt Ln ´ GDP L µ = ± GDP GDP ± _ L L Thus, subtract _ L=L from both sides to obtain G _ DP GDP ± _ L L = s 1 _ p 1 p 1 + s 2 _ p 2 p 2 + S L _ A A + _ L L ! + S K _ K K ± _ L L ) G _ DP GDP ± _ L L = s 1 _ p 1 p 1 + s 2 _ p 2 p 2 + ( S L ± 1) _ L L + S L _ A A + S K _ K K Why does labor productivity, G _ DP GDP ± _ L L > 0 ; tend to increase in a recession? 2.5 Contributions to growth The literature often discusses "contributions to growth." What is this? Con- sider G _ DP GDP = s 1 _ p 1 p 1 + s 2 _ p 2 p 2 + S L _ A A + _ L L ! + S K _ K K 16
What is the contribution to G _ DP GDP of each of the right-hand side variables? These are C p 1 = 0 @ s 1 _ p 1 =p 1 ± GDP=GDP 1 A 100 C p 2 = 0 @ s 2 _ p 2 =p 2 ± GDP=GDP 1 A 100 C L = 0 @ S L _ L=L ± GDP=GDP 1 A 100 C K = 0 @ s K _ K=K ± GDP=GDP 1 A 100 C A = 0 @ S L _ A=A ± GDP=GDP 1 A 100 Suppose we have an economic growth model that predicts in the long-run equilibrium, (i.e., the steady state) _ p j =p j = 0 _ L=L = n _ K=K = x + n _ A=A = x 17
Then C ss p 1 = 0 @ s 1 0 ± GDP=GDP 1 A 100 C ss p 2 = 0 @ s 2 0 ± GDP=GDP 1 A 100 C ss L = 0 @ S L n ± GDP=GDP 1 A 100 C ss K = 0 @ s K x + n ± GDP=GDP 1 A 100 C ss A = 0 @ S L x ± GDP=GDP 1 A 100 What does C L ± C ss L C K ± C ss K C A ± C ss A tell us? How far the economy is from long-run equilibrium? Yes And, it provides insight into contributions to growth during "transition" growth. Finally, if we had identi³ed speci³c sectors, (manf., ag., services) we could test the "balanced growth" hypothesis. 3 Measurement of capital stock (see Hall and Jones, and/or Fanjzylber and Lederman Appendix for formula. See also Hulten, p41-51) 3.1 Method I: often used but not desirable Here, we skim the surface of this topic. 18
A common method is to estimate the stock of capital for some initial period, which is referred to as t = 0 : The formula is K (0) = I g + ³ (12) where I = Gross ³xed capital formation in constant LCU g = Rate of growth of GDP in constant LCU ³ = Rate of depreciation Once we have calculated K (0) ; we use the law of motion equation K ( t ) = K (0) (1 ± ³ ) + I (0) ; t = 0 ; 1 ; ² ² ² ; T Does this seem to simple? Yes, it is. 1. Why the formula (12)? In the steady state ..with balanced growth.. we expect the rate of growth in GDP to equal the rate of growth in capital stock, i.e., _ G G = _ K K G ( t ) ± G ( t ± 1) G ( t ± 1) = K ( t ) ± K ( t ± 1) K ( t ± 1) (13) K ( t ) = K ( t ± 1) (1 ± ³ ) + I ( t ± 1) ) K ( t ) ± K ( t ± 1) = ± K ( t ± 1) ³ + I ( t ± 1) ; Now · by K ( t ± 1) ) K ( t ) ± K ( t ± 1) K ( t ± 1) = ± ³ + I ( t ± 1) K ( t ± 1) ) given assumption ( ?? ) G ( t ) ± G ( t ± 1) G ( t ± 1) = ± ³ + I ( t ± 1) K ( t ± 1) Now solve for K ( t ± 1) G ( t ) ± G ( t ± 1) G ( t ± 1) K ( t ± 1) = ± ³K ( t ± 1) + I ( t ± 1) G ( t ) ± G ( t ± 1) G ( t ± 1) K ( t ± 1) + ³K ( t ± 1) = I ( t ± 1) G ( t ) ± G ( t ± 1) G ( t ± 1) + ³ · K ( t ± 1) = I ( t ± 1) 19
to obtain (12) K ( t ± 1) = I ( t ± 1) ² G ( t ) ³ G ( t ³ 1) G ( t ³ 1) + ³ ³ (14) 2. Problems with K (selected) (a) If we are studying economies in the process of economic growth, they are unlikely to be in a steady state, so (13) is unlikely to hold which implies _ G=G < _ K=K in which case (14) over -estimates K (0) :

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• Spring '14
• Roe,TerryLee
• Gdp, TFP, Growth Accounting, GDP Ya GDP, GDP pvs GDP
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