What Is Growth Accounting?

The basic idea of the growth accounting approach is based on the neo-classical growth theory. The contribution of factor inputs in economic growth is eliminated to obtain an estimate of total factor productivity growth. Its essence is an index method. According to the different construction methods of the index, it can be divided into algebraic index method and geometric index method (also known as Solow residual method).

Growth accounting

Right!

The basic idea of the growth accounting approach is based on the neo-classical growth theory. The contribution of factor inputs in economic growth is eliminated to obtain an estimate of total factor productivity growth. Its essence is an index method. According to the different construction methods of the index, it can be divided into algebraic index method and geometric index method (also known as Solow residual method).

Chinese name

Growth accounting

Foreign name

growth accounting approach

Classification

The basic idea of growth accounting approach is based on the neo-classical growth theory. The contribution of factor inputs in economic growth is eliminated to obtain an estimate of total factor productivity growth. Its essence is an index method. According to the different construction methods of the index, it can be divided into

Algebraic exponent method (AIN)
The algebraic index number approach (AIN) was first proposed by Abramvitz (1956). The basic idea is to express total factor productivity as the ratio of the output quantity index to the weighted index of all input factors.
Assuming the price of the commodity is Pt and the quantity is Qt, the total output is PtQt. The capital input in production is Kt, the labor input is Lt, the capital price is the interest rate is rt, and the wage rate is wt, then the total cost is rtKt + wtLt. Under the assumption of perfect competition and constant returns to scale, there is total output equal to total cost, that is:
PtQt = rtKt + wtLt (1)
However, due to the influence of factors such as technological progress, the formula (1) is often untenable, and the formula (1) can be rewritten as:
P0Qt = TFPT [r0Kt + w0Lt] (2)
Where r0, w0

And P0 are base year interest rates, wages, and prices. The parameter TFPt is the total factor productivity, which reflects the influence of factors such as technological progress on output. From (2), we get:
(3) is the algebraic index formula of total factor productivity. Later, economists put forward various algebraic indices of total factor productivity. Although their forms are different, the basic ideas are the same.

The algebraic index method intuitively reflects the connotation of total factor productivity, but its shortcomings are also very obvious, mainly reflected in that although it does not explicitly set the production function, it implies that capital and labor are completely replaceable, and that the marginal productivity is constant. This obviously lacks rationality. Therefore, this method is more of a conceptual approach and is not suitable for specific empirical analysis (Caves, Christensen and Diewart, 1982).
2. Solow residual method (SR)
The Solow residual method was first proposed by Robert M. Solow (1957) .The basic idea is to estimate the total production function and use the residual after subtracting the growth rate of each input factor from the output growth rate to calculate the whole. Factor productivity increases, so it is also called production function method. With constant returns to scale and Hicks neutral technology assumptions, total factor productivity growth is equal to the rate of technological progress. The aggregate production function is:
Yt = (t) F (Xt) (4)
Among them, Yt is output, factor input vector, and xnt is n-th input factor. Assume that (t) is Hicks neutral technology coefficient, which means that technological progress does not affect the marginal substitution rate between input factors. Further, suppose that F (·) is a homogeneous function, that is, returns to scale are constant for all input factors. (4) Both sides of the equation are differentiating time t at the same time and divided by (4).
(5)
Among them, the output share of each input element. From (5):

(6) is the Solow residual formula for total factor productivity growth, which is essentially a geometric index. The output share n of each input factor often needs to be measured by estimating the total production function. In specific estimates, the C-D production function of two factors (capital and labor) is often used: where Yt is the actual output, Lt is the labor input, Kt is the capital stock, and and are the average capital output share and average Labor output share. Take natural logarithms on both sides at the same time:
(7)
As the error term, usually we assume + = 1, that is, the return on scale is unchanged, then there is a regression equation:
(8)
This is a double logarithmic model that can be estimated using OLS. The capital stock needs to be calculated, and the calculation formula is:
Kt = It / Pt + (1 t) Kt 1 (9)

Among them, Kt is the actual capital stock in t years, Kt 1 is the actual capital stock in t-1 years, Pt is the fixed asset investment price index, It is the nominal investment in t years, and t is the depreciation rate of the fixed assets in t years. After determining the initial value of the capital stock and the actual net investment, the actual capital stock of each year can be given by using formula (7). In this way, using the regression equation (8), we can estimate the average capital output share and the average labor output share , and bring it into formula (6) to get the total factor productivity growth rate. The Solow residual method has created a precedent for the analysis of the source of economic growth and is an important contribution of the neoclassical growth theory (Lucas, 1988). But it also has some obvious shortcomings: The Solow residual method is based on the neoclassical assumptions that are perfect competition, constant returns to scale, and Hicks neutral technology.These constraints are strong and often difficult to meet; Because the capital price is difficult to determine accurately, the capital stock is used instead of capital services, and the difference in production efficiency of new and old capital equipment and the impact of capacity realization are ignored. In addition, the Solow residual method uses the so-called "residual" to measure total factor productivity, so it cannot remove the influence of measurement errors. All of these factors inevitably lead to biased estimates of total factor productivity.