Engel's law

For a poor family, the food expenditure is a big portion of their total budget, while the rich tend to spend more of their money on items such as entertainment and luxury goods.

[4][5] The interaction between Engel's law, technological progress, and the process of structural change is crucial for explaining long-term economic growth as suggested by Leon,[6] and Pasinetti.

The shape of the curve depends on factors such as age, gender, educational level and which type of good it is visualising.

He states: "It is evident that Engel's law, rigidly interpreted is not true for particular families, for particular times, and under certain circumstances" and "The 'Engel' type of standard of living applies to no more than half of the people of the globe."

Based on this research, Houthakker claims that "If no data on the expenditure patterns of a country are available at all, one would not be very far astray by putting the partial elasticity at 0.6 with respect to food.

[2][8] Therefore Engel's law is a commonly accepted economic relationship and often referred to in the introductory sections of academic papers.

References to Engel's law usually involve his tables from his analysis where the correlation between income and food expenditures is highlighted.

The table depicts a series of various annual incomes for families in francs ranging from 200 to 3,000 and the respective share spent on food.

However one issue that is worth raising is how he was able to obtain the 29 observations used as the correlation coefficient between the values is relatively high and Engel never mentioned the method he used to come up with the approximations.

One potential method could have been the least-squares estimation which, after coming up with the regression line and applying the adequate coefficients of interpolation, would fit the equation perfectly.

However, even though it is clearly seen in the paper that the income perceived is rising by 100 francs per sample family, the food expenditure is definitely not decreasing following any fixed arithmetic trend but it could be a geometric rate.

Engel's data could have either been extracted from a variety of news articles and local studies from the English market at the time or from an approximation that he came up with but the soundness of the conclusion derived from the set is very rational.

For that purpose a measure called Engel coefficient is used, which is simply a food budget share at a point in time.

[8] In his paper Pope (2012) illustrates that convergence between food budget shares between rural and urban regions have been used to reflect standards of living.

Hamilton (2001) interprets Engel's law and suggests that movements in the percentage of budget share spent on food may serve as an indicator of changes to the real income.