_{1}

This work presents a model aiming to evaluate the impact of rural-urban migration on the aggregate stock of loanable funds and investment by the urban population. Much higher investment costs for immigrants in cities prevent their acquisition of either human or physical capital. That is the reason why immigrants self-select as net lenders and affect urban labor earnings by means of the availability of new loanable funds for investment. This reduces the local interest rates and facilitates urban aggregate investment, especially by the new generations of natives. As a result of that, the aggregate labor income of natives increases unambiguously with the size of new immigration waves.

According to abundant analyses about many less developed countries, rural-urban migration often results in a socioeconomic marginalization of new immigrants in the urban life. Despite the effort often allowing them to become upward movers in response to substantial opportunities for economic betterment, they usually exhibit relatively lower probabilities of economic success. In this sense, a lower economic mobility of rural-urban migrants is both a cause and a consequence of segregated labor markets. In such markets, those immigrants with lower entrepreneurship capacity and human capital are unlikely to associate with highly qualified natives.

Such segregation is also limiting the competition between migrants and the native urbanites with the lowest qualification. More specifically, some recent empirical results uncover an insignificant, and often slightly positive, impact of higher migratory flows on the income and employment of unqualified, native urbanites. This is a standard empirical result, emerging in the context of many different countries, although it is at odds with most of the theoretical predictions. Therefore, “the inconsistency between the theory and the empirical evidences has shaken the basis of the traditional belief that an immigrant influx should lower the wage of competing factors […] and calls for new evidence and new explanations” [

In this respect, our model offers a potential explanation based on a pure capital market complementarity between immigrants and natives. Given that the former turn out to become new, relevant net lenders in the city, it is now easier for the new generations of urbanites to undertake an investment in human capital or an acquisition of entrepreneurial capacity. Our choice of the Chinese case as a plausible illustration for the model is due to “an intriguing empirical confluence” [

To summarize, our Chinese image is useful to illustrate a novel theoretical hypothesis, related to an immigration surplus enlarged by a complementarity in the capital markets. Such hypothesis is clearly different from the traditional complementarity in the labor markets, whose empirical implications were explored and popularized by Borjas [

Our urban economy consists of a population of natives (also called urbanites) whose size is normalized to one. In period t there exists an unexpected migratory shock by which M rural migrants arrive to the city. They will start their urban life during the youth, before undertaking any form of investment. A crucial driving force in our chain of causality is the immigrants’ investment costs being higher than those of natives. Despite this fact, the investment possibilities offered by the urban credit markets are supposed to be absent in their original rural environment. In this sense, we are adopting Lucas’s (2004) [

Our urban economy exhibits a technology combining skilled and unskilled labor to produce a single good. Both labor and product markets are perfectly competitive. It is noticeable that most of the models dealing with an immigration surplus are based on labor market complementarities between unskilled labor and physical capital and/or skilled labor. In these models, the reduction in the remuneration of unskilled labor gives rise to a net gain for the native population, since the capital owners and skilled workers will appropriate a new surplus. Those productive factors will gain, whereas the unskilled workers will be damaged. As Borjas [

In contrast to these explanations, here we will focus on a pure capital market complementarity. In order to sharpen our theoretical point, skilled and unskilled labor will be perfect substitutes and hence their respective salaries will not be affected by immigration. We will then show how the availability of new loanable funds for investment, and the consequent reduction of the equilibrium interest rate, will facilitate the skill upgrading of the new generations. This will give rise to an increase in the aggregate labor income of natives. Our assumption of perfect substitutability is convenient to eliminate any sort of labor market complementarity and emphasize our chain of causality. The value of the unskilled urban wage is equal to one and the skilled wage will be given by

The timing of our model is based on Galor and Zeira [

In the second period of his life, the parent observes his child’s ability. In case he finds the child capable enough, he will facilitate his investment during that particular period. The amount of the bequest will depend on the specific form of the parent’s altruistic preferences. In particular, in this case we will assume the parent derives utility from the child’s gross income, computed at the time the child will consume after his parent’s death. This is a form of income-based altruism à la Becker and Tomes [

This function represents the utility level of an individual born at (t − 1), where c_{t} stands for his own consumption in the second period of his life. W_{t+}_{1} represents the gross income obtained by the following generation, born at period t, which will be used by that child to consume and/or leave another potential bequest at period (t + 1). Finally, β is an indicator of the level of parental altruism towards the next generation.

If a young person born at t decides to invest in that period, he will have to ask immediately for a loan to cover his investment costs. Without loss of generality, let us consider the case of a human capital investment in which the native (immigrant) investor must hire a certain number

When an individual born at t decides whether he should invest or not, he makes the following comparison:

Those individuals who decide to remain unskilled will work in both periods of their life and will save their initial earnings until period (t + 1), when they will be able to both consume and leave a legacy. On the other hand, the individuals born at t willing to become skilled will borrow to cover their investment costs at t; and will repay their debt at (t + 1), once they have received their wage. Therefore, we can compare both expressions above and solve for the lowest ability level necessary to qualify. A native individual born at t will choose to invest if

We will find a similar expression for a young immigrant, just by replacing

Let us assume that every parent observes the realization of the random variable corresponding to his child’s ability. Then he will decide to leave a bequest or not on the basis of such realization. Given that our form of parental altruism assigns utility to the gross future income of the child, the parent will only bequeath the amount being strictly necessary for his child’s investment. This implies that, only if the child is skillful enough to re-

ceive a bequest, according to our expression (2) such legacy will be exactly equal to

The left-hand side of the inequality captures the parental altruistic benefit from the extra income accruing to a child that invests. The right-hand side reflects the cost of the bequest for the parent. Therefore, taking into account (2) and (3), the parent will decide to bequeath if

This cutoff value

biguously,

discourage more people from investing and will increase the necessary ability cutoff required to receive a bequest.

Let us denote now by

In our economy, a competitive equilibrium is characterized by an interest rate and an allocation of native and immigrant workers to the skilled and unskilled occupations, such that the supply of credit is identical in every period to the demand for credit. Such credit will be entirely used by the next generation of qualified workers to invest when young. In other words, we must look for a sequence of equilibrium interest rates that clear the credit market in every particular time period.

In our credit market we can observe two distinct sources of saving at any period t: the young generations who choose not to invest and save their whole unskilled wage to face their adulthood at (t + 1); the adults born at (t − 1) with sufficiently skillful children, who will save at t in order to leave a bequest, according to our Section 2.3.2. On the other hand, the demand for credit to invest comes from the most capable youngsters among the population of natives and immigrants. These young people’s individual demand for credit will be equal to the remuneration of qualified instructors they need to hire at t; that is,

On the left-hand side of the last equation we have the supply of loanable funds by the unskilled young people. On the right-hand side we can observe the aggregate expenditure on investment, equivalent to the remuneration of qualified instructors minus the cost skipped due to the parental bequests. Considering the expressions (2) and (5), the last equation could be simplified as follows:

It is important to notice that, since Equations (5) and (6) depend on the interest rate of a single period (t + 1), our equilibrium interest rate will be always identical. This fact makes our analysis finally static, which facilitates its resolution and interpretation. By rearranging our Equation (6), it is possible to obtain a lemma that specifies sufficient conditions for the existence and uniqueness of the competitive equilibrium.

Lemma: If

The proof of this lemma is examined in the final Appendix. The uniqueness of the competitive equilibrium is ensured by an excess demand function that is strictly decreasing in the credit market. It is crucial to have profitable enough investment opportunities: they will guarantee the existence of an active “demand side” in the market for credit. Those opportunities must be advantageous both from the point of view of the investment benefits (

Now we are ready to derive our main effect of immigration on the availability of loanable funds for investment. As we anticipated above, in this setting the supply of credit comes from the unskilled workers. The most capable youngsters will receive such credit to finance the share of investment costs that is not covered by their parents’ bequests. Consequently, a new immigration wave brings about a higher proportion of unskilled workers providing net lending, due to their very high investment costs. This will be useful to reduce the equilibrium interest rate (

Therefore, for a new migratory influx to provide a higher volume of loanable funds, it is necessary that immigrants face higher investment costs (

Proposition. A higher migratory shock (that is, a rise in the value of M) will reduce

Proof. We can differentiate both sides of Equation (6) with respect to M, computing the total derivative, and obtain

where

If we now insert (8) inside (7), we can finally conclude that

We can check from expression (4) that

tive for sure. Because of that, for (9) to yield a negative value we will clearly need a numerator that is lower than zero, which requires that

Given that the cutoff ability values are increasing in

Finally, we know that in our model all wages are invariant and

Some recent theoretical models, often inspired by the Chinese reality, have considered the possibly beneficial effects of inter-regional migration restrictions from the viewpoint of capital accumulation and/or allocative efficiency. Among them we will mention Fan and Stark [

On the other hand, Vendryes [

The system of geographical registration for Chinese families (hukou) imposes strong restrictions for rural immigrants to access the main urban public services (healthcare, education, pensions, etc.). In the context of our model, this institution establishes higher investment costs in human capital or entrepreneurial activities to the newcomers with rural hukou, limiting their economic mobility in cities. In particular, Heckman [

Such a highly discriminatory character of the Chinese institutions against the floating population is making immigrants exhibit higher net saving rates, in order to cover their future expenses on healthcare, retirement or bequests. Therefore, they are less likely than natives to undertake human capital or entrepreneurial investments. According to Huang’s survey (2010) [

To summarize, we claim that the resilience of the hukou institution, in parallel with the massive recent urbanization, is probably important to understand some recent patterns of accumulation and inequality in China. That Asian image is useful as an illustration for our novel theoretical hypothesis: capital market complementarities, and not only labor market complementarities, may enlarge the immigration surplus as well.

In this work we have presented a novel theoretical mechanism giving rise to an immigration surplus, even in the absence of variations in skilled or unskilled labor remunerations. Immigrants, who are eager to save in the city to guarantee a decent status in old age, or a decent bequest to their children, find it especially difficult to undertake any form of real capital investment. Because of that, there will be a considerable abundance of extra loanable funds in the urban financial system. And it will be the native population who will mostly take advantage of such situation to borrow at lower interest rates given their lower investment costs in human or entrepreneurial capital.

Studying the case of China has been useful as a potential illustration. In 1978 only 18% of the Chinese population used to live in cities. However, by 2003 both the number and the size of its cities had grown so much that the urbanization rate was 41% [

I would like to express my gratitude to Juan Dolado, Michael Manove and especially Dilip Mookherjee for their stimulus and very useful comments. The usual disclaimer applies.

Adolfo CristóbalCampoamor, (2015) A Pure Capital Market Complementarity between Immigrants and Natives. Modern Economy,06,1253-1260. doi: 10.4236/me.2015.612118

We are now ready to prove the existence and uniqueness of a competitive equilibrium in our model. Let us denote by r^{*} our candidate for an equilibrium interest rate. If we multiply both sides of expression (6) by (1 + r) and rearrange, it is possible to characterize in a different way the credit market equilibrium. Let us first define the function Z(r) as follows:

From the Equation (6) it is possible to observe that our equilibrium interest rate must satisfy the condition

That means that

That holds because, for^{*} is such that

It is relatively straightforward to show that

there exists a unique value for r^{*} such that

If, additionally,

and the equilibrium is unique.

Moreover, we also know that