Rural–urban migration: the Harris–Todaro model

In the 1960s many developing countries had high urban unemployment, and yet migration to the cities was continuing and even growing. The early view was that unemployment would discourage migration. Michael Todaro (1969) argued that migrants respond to expected income, not to the wage actually paid. A rural worker who moves to the city has a good chance of being unemployed for some time, and a smaller chance of a well-paid job. If the urban wage is high enough, the expected income is still above what he earns on the farm. Harris and Todaro (1970) made it a general-equilibrium model with two sectors.

Let N be the labour force. L_r workers are in agriculture and L_u = N − L_r are in the city. Agriculture pays its marginal product, which rises as workers leave: w_r(L_r). The city pays a fixed wage w_u (set by minimum-wage laws, unions or firms) but has only N_u jobs. A person in the urban labour force gets a job with probability N_u/L_u and nothing otherwise, so the expected urban wage is

People move to the city as long as the expected urban wage is above the rural wage, and the more who move, the lower the chance of a job and the higher the rural wage (fewer workers on the farm). Migration stops when

The left side rises with L_u and the right side falls, so they cross once. At the crossing, the urban labour force L_u exceeds the jobs N_u, and the difference U = L_u − N_u is the urban unemployed (or underemployed in informal work, in later versions of the model). The rural wage is well below the urban wage: here, 1.91 against 3.00, with a 64% chance of a job.

Two features are worth remembering. The unemployment is not a failure of the labour market to clear: it is how the market clears, since the unemployed are the cost the migrant accepts for a chance at the high wage. And the equilibrium does not depend on the wage being high for everyone: it is a gamble on the average.

The simulator has 1,000 thousand workers. The rural wage is c/√L_r (a rural productivity c, with diminishing returns); the urban wage is fixed. The blue curve is the expected urban wage as a function of the urban labour force, the green curve the rural wage; where they cross is the equilibrium. The dashed vertical line is the number of urban jobs: everything to its right is unemployment. Use the presets, then try your own: what happens to the urban labour force when you create 100 thousand more jobs, or raise rural productivity?

Raise the number of urban jobs from N_u to N_u + 1. The probability of a job rises, so the expected urban wage rises and migration is above the rural wage again; people move until the two wages are equal once more. In the equilibrium the extra job has attracted dL_u/dN_u new city dwellers. If that is more than one, the city has more unemployed than before. Differentiating the equilibrium condition gives

which is greater than one when w_r(1/N_u − 1/L_u) exceeds |w′_r|: when unemployment is already large and the rural wage does not rise quickly as people leave. In the simulator’s base case the first extra job draws in 1.28 new city dwellers (the last readout), and raising jobs from 200 to 300 thousand raises the urban labour force from 314 to 430 thousand, an average of 1.16 per job, and the unemployed from 114 to 130 thousand. The unemployment rate falls (from 36% to 30%), but the number rises, which is the point of the Harris–Todaro result: urban job creation alone does not solve urban unemployment (the answer to the opening question).

Policies the model supports. Reduce the push: rural development raises w_r and cuts migration at its source (try c = 80 in the simulator: unemployment falls from 114 to 11 thousand). Reduce the pull: narrow the urban–rural wage gap, for instance by not letting the urban wage run ahead of productivity. Create jobs with care: urban jobs help, but together with measures against migration, not as the only policy. Wage subsidies that create jobs without raising the wage of existing workers can help, because they raise N_u without increasing the gap. Restricting migration by decree does not remove the incentive.

Limits. The model assumes that migrants are risk-neutral and that all unemployment is open; in reality many migrants go to the informal sector, which acts as a third option with its own earnings; migrants have networks and information; and wages may vary within the city. Later versions allow for an informal sector and for risk. The model is also about a single period of choice, though the expected wage is partly the expected path of earnings as a migrant settles in.

Questions on the Harris–Todaro model. Questions on the Lewis model and disguised unemployment are in Lesson 3; labour-force measures and informal employment in Lesson 11.