Question

How does endogenous growth theories explain that one should not expect growth in
Labor productivity converges towards a common growth rate without the contrary
can expect permanent differences in growth rates between countries?

Answer 1

In terms of the initial neoclassical theory described by Solow (1956) and augmented by others, sustained economic growth occurs through an exogenous factor of production, that is, the passage of time. The neoclassical production function used in this theory relates output to factor inputs, which consist of the stock of accumulated physical capital goods (buildings, machinery, transport equipment, computers, and so on) and labour, which is regarded as only one type. The theory imposes decreasing returns with respect to the use of each (reproducible) factor of production (and constant returns overall). From these assumptions it follows that an increase in the stock of capital goods will result in a less than proportionate increase in output, provided the amount of labour employed stays the same. Eventually more capital stock will produce no more output, resulting in lower profits, and for this reason output growth cease. If new technologies improve the productivity of labour and of capital and so prevent a decrease in the rate of return on investment, the labour force will grow at an exogenous rate. The growth of output is accordingly related to the amount and quality of the stocks of production factors. That part of output growth that cannot be explained by the growth in production factors is often called the Solow residual by economic researchers and/or total factor productivity in applied work. The calculation of total factor productivity assumes perfect competition in labour and capital markets, but also in product and service markets. This assumption allows the calculation of multifactor inputs by weighing labour and capital input increases in terms of their national income shares (remuneration of employees and gross operating surplus respectively).  

This joint factor contribution to output is usually substantially less than the growth in output. This unexplained part of output growth is often called the Solow residual, which he termed the “measure of our ignorance”. This is a rather ambiguous phrase, because it refers to the nebulous knowledge of economists on the matter, but signifies improvement in the knowledge base of the workforce in general. The labour force grows in accordance with population growth and is augmented by technical progress, both exogenously determined. Eventually capital, output and consumption will also grow at this exogenous rate and converge to an equilibrium growth path. Accumulation of capital in exogenous growth theory is a vehicle for ongoing technical development. Neoclassical theory gives no economic explanation for such development, but instead includes a time trend (usually representing technical progress) in the model for the long-run rate of economic growth. The exogenous technical progress assumed in the older versions of growth theory limits the explanation of the growth process. When the standard Solow model is used with real data in order to explain adjustment to balanced growth paths, predictions for the speed of convergence and the capital income share in national income are generally too high.

EXOGENOUS GROWTH

The neoclassical model states that in the long term, the growth rate of output per worker is dependent on the rate of labour-augmenting improvement in technology, which is determined by factor(s) not contained in the model (also known as exogenous factors). The model implies that all economies that use similar technology, which could improve over time, should have converging productivity growth rates . Permanent differences in productivity levels are caused by faster/slower population growth or a higher/lower savings rate. Lower productivity could be due to climate deficiencies or other factors not accounted for in the model The Cobb-Douglas (1928) production function, also called the neoclassical production function, is expressed as follows:  

Y = La

Kb

T where a+b=1 (1)

where:

Y= output

L= labour

K= capital

T= time or the rate of technological progress which changes over time . The weights a and b represent the proportion of Y that accrues to labour (L) and capital (K) respectively. The inclusion of the technology variable freed the neoclassical theory from the doomsaying of Malthus and Ricardo and formulated the ultimate destiny of mature economies in terms of the more acceptable but still rather conservative stationary state, where all real variables grow at a constant, proportional rate. Robert Solow (1970:7) remarked that “the steady state is not a bad place for the theory of growth to start, but may be a dangerous place for it to end”. The simple Solow model depicts the output, Y, of a business, as a function of three variables: capital, K, labour, L, and knowledge or the “effectiveness of labour”, At.  

Y = Ka

(AtL)1-a 0 < a < 1 (2)

Knowledge or technical progress is assumed to be independent of both the capital and labour inputs and to be a nonrival good, which is free for all businesses. It appears multiplicatively with labour in (1), denoting that knowledge contributes by “augmenting” labour and not affecting capital. The exponents a and (1-a) measure the relative contribution of the two inputs of capital and “effective labour”. These exponents add to unity, to comply with the constant-returns-to-scale assumption for production (e.g. doubling of factor inputs resulting in output also increasing by 100 per cent). Equation (1) describes how actual output is determined. The equation is simplified by taking logs, after which the equation indicates output growth so that:  

y = ak + (1-a)(a + l) (3)

Lower-case letters represent the proportional growth rates of their upper-case equivalents. This equation may be rewritten as:  

y - l = ak' + a (4)

where: y - l = the growth of output per worker

k' = the growth of capital per effective worker (K/AL)

To see what the neoclassical growth model predicts, we can simplify matters by assuming that there is no labour force growth (annual entry to the labour market is equal to annual retirement) - a situation not too far removed from the reality in many countries. This means that, in terms of equation (2), y equals the growth of income per worker (i.e. labour productivity).  

This model has three important features which recent growth theories have challenged:  

• If markets are competitive, the contributions of each factor input to output (i.e. a and (1-a)) are equal to their respective shares in the total income (output). For all businesses in an economy taken together, this could be approximated by the national accounts breakdown into wage and non-wage income.  

• If people were to save a constant proportion of their income, capital per effective worker would be constant in the long run, so that k' = 0 in (2)  

and per capita income growth is therefore entirely determined by knowledge growth, a.  

• Increasing the savings (i.e. investment) ratio could raise an economy's income level (permanently) by raising the growth rate of capital (and income) in the short run, but since the ratio of savings to income cannot continue to increase indefinitely, investment cannot cause income to grow permanently. Countries that invest more would be wealthier but would not grow faster since the only source of long-term growth is technical progress (or “knowledge accumulation”), which is assumed to occur at an exogenous rate. According to this model, income growth rates are beyond business and government control. This is a disappointing and dubious outcome because real-life experiences point to the contrary, especially in the case of businesses.

• GROWTH ACCOUNTING  

• Growth accounting is an attempt to allocate growth rates in national output or output per person employed to the determinants of output in order to isolate the causes of growth. The aims are to determine the causes of international differences in output levels and the determinants responsible for differences in growth rates. This is also a method to organise quantitative information conveniently and systematically. Growth accounting stems from an investigation by Denison (1987:572) of the sources of growth in the USA from 1909 to 1958. It has also been used to estimate probable future growth potential (obtained by adding the expected contributions of these sources) and the extent to which the future growth rate could be altered by each of a list of alternate sources. Among the output determinants that were examined were the characteristics of labour that affect its knowledge, skills and energy. This was criticised by Schultz who made the point that “treating a count of (employed persons) as a measure of the quantity of an economic factor is no more meaningful than it would be to count the number of all manner of machines to determine their economic importance either as a stock of capital or as a flow of productive services”. Denison nevertheless found the following to be the most positive sources of growth:  
• • increased employment;
• • improved education of the employed;
• • more and better capital stock;

• growth in the size of markets;

• improved resource allocation;

• advances in the extent of knowledge relevant to production.

The study's most important lesson was that extensive and costly changes would be required if policies were to be adopted to raise the high-employment growth rate (by one per cent) above its normal level. This finding contrasted with the common view that it would be easy to add a whole percentage point to the growth rate. Growth accounting starts by recognising that many different determinants govern the size of a country's output at any given time. It deals in the first instance with:  

• different determinants of output such as the number, hours, demographic composition and education of employed persons;  

• quantities of land and capital;

• the stock of knowledge;

• the size of market;

• the extent to which actual practice departs from lowest-cost practice;

• the extent to which resource allocation departs from the output- maximising allocation;  

• the intensity with which factor inputs are used.

Changes in these determinants caused changes in output – or growth. Sources- of-growth tables are obtained by measuring changes in each determinant and the effect this change had on output. Direct determinants of output are of course influenced by a host of indirect determinants such as tax structure, attitudes to work, inflation, deaths in war or birth control information. Growth accounting studies do not ignore such indirect determinants of output, but measure them indirectly by first judging the extent to which a change in any one (or a difference between two situations, e.g. two tax structures) alters all the direct determinants, and then calculating the effect of these changes on output.

Above table shows the sources of growth for nine Asian industrialized and non Asian industrialized countries.

Endogenous growth with human capital

One way to explain differences in national economic growth rates is to introduce the stock of human capital or alternatively, technology improvement as a causal factor or producible input. Arrow’s point of departure is the neoclassical theory and he does not contradict the “production function as an expression of technological knowledge”. All that has to be added is that “knowledge is growing in time”. He concludes that time as an explanatory variable is intellectually and empirically unsatisfactory and basically a confession of ignorance. Moreover, it contributes nothing in terms of policy variables. He wants to analyse the human knowledge, which underlies the production function, as it accumulates over time.