Lecture 6 - The Solow Model and the Data

We use the Solow model to interpret both:

1. cross-country output differences

2. Economic growth

over time.

Focus on proximate causes of economic growth

Compare national accounts:

-over time: Nominal vs. Real GDP

-across countries: PPP

Development accounting: measuring contribution of factors to

-differences across countries

-method, success & sensitivity to assumptions

-differences across regions

Growth accounting: measuring contribution of factors to growth

Gross Domestic Product is the value of all goods and services produced in an economy in a year (excluding intermediate goods, which are used in the production of final goods)

Transform a nominal series into real terms by using an appropriate price index:

1. Consumer Price Index (CPI)

2. GPD Deflator

Obtain real value from the nominal value by computing:

the GDP price deflator shows how much a change in GDP relies on changes in the price level

How can we compare the GDP of two countries using a different currency

Using the exchange rate, this hinders some problems:

1. Market exchange rates fluctuate daily, often by large amount even without variations in the output produced

2. Comparisons of GDP at market exchange rates systematically understate the relative income of developing countries

   1. The price of goods traded in international markets, relative to goods that are not traded, is higher in poor countries than in rich countries

   2. law of one price: exchange rates tend to be such that the price of traded goods will be the same once converted to a common currency

Prices for tradable goods are relatively equal across countries.

Prices for non-tradable goods vary a lot within and across countries

Example in Slides

Development Accounting: cross-country differences

1. How much does productivity differ among countries?

2. How much of the variation in income per capita among countries is explained by factors of production and how much by productivity differences?

Growth Acconunting: cross-time differences

1. How much does productivity growth differ among countries?

2. How much of the variation in growth rates among countries is explained by variation in productivity growth, and how much by variation in factor accumulation?

Development accounting quantifies the relationship:

Total Factor Productivity (TFP) is the effectiveness with which factors of production are converted into output

Useful tool:

-If factors account for most of the differences: development economics could focus on explaining low rates of factor accumulation

-If productivity differences play a large role: need to explain why some countries extract more output than others from their factors of production

-Consensus in development accounting that productivity plays a large role

What can we infer from the data?

We want to measure how much the inputs in the production function matter for the output per worker difference

Production function (hL = quality adjusted workforce):

Perpetual inventory equation:

Initital capital stock:

Estimating h:

Slopes are estimated from average wages: given our assumptions (production function and perfect competition in factor and good markets) the wage of a worker with s years of education is proportional to his human capital h

Ratio of per capita income can be decomposed into the product of productivity ratio and factors endowments ratio:

so that:

Actual figures:

-Large differences in the productivity level A

-Japan vs. US: Japan better capital endowment and same human capital level, but lower productivity -> Japan is significantly poorer

Among the richest one-fifth of countries, productivity and factor accumulation are similarly important in explaining the gap relative to the U.S.

But for all the other country groups , productivity is slightly more important than factor accumulation (Because the gap is bigger)

A more formal analysis reveals that 47% of the Y/L variation is due to differences in factor accumulation and 53% in productivity differences

How succesful is the factor-only model at explaining cross-country income differences?

2 Measures:

1. Share of variance explained (variance decomposition)

2. Inter-percentile differentials

In sub-samples:

Same intuition: Measure of the dispersion in the factor only model in comparison to dispersion in real data

The smaller the percentiles, the more your measure is influenced by potential outliers

Sensitivity analysis: We check what happens to the results when we modify the assumptions

Question: How much do the conclusions depend on our assumptions or measures?

Question: What is causing two countries to grow differently?

Cobb-Douglas Production Function in per-worker terms:

Taking logs:

Taking the derivative with respect to time and rearranging:

This technique for deriving the growth rate of productivity is called growth accounting