City of Dreams

Correlation between ability and self-confidence.

	Level of education
Age when taking both tests	At most high school	More than high school
15–17	0.017	0.057
18–19	0.156	0.074
20–21	0.194	0.115
22–23	0.242	0.118

	Level of education
Age when taking both tests	At most high school	More than high school
15–17	0.017	0.057
18–19	0.156	0.074
20–21	0.194	0.115
22–23	0.242	0.118

Note: The ability AFQT and the self-confidence Rosenberg test were administered in 1980 to all individuals in our sample.

Table 1.

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Correlation between ability and self-confidence.

	Level of education
Age when taking both tests	At most high school	More than high school
15–17	0.017	0.057
18–19	0.156	0.074
20–21	0.194	0.115
22–23	0.242	0.118

	Level of education
Age when taking both tests	At most high school	More than high school
15–17	0.017	0.057
18–19	0.156	0.074
20–21	0.194	0.115
22–23	0.242	0.118

Note: The ability AFQT and the self-confidence Rosenberg test were administered in 1980 to all individuals in our sample.

To relate empirical results more closely to our model, we define a junior and a senior period for each individual and classify metropolitan areas into two groups that we can directly relate to big and small cities in the model.

Regarding timing, we set the junior period for all respondents at the year after their highest level of education is completed, excluding educational periods that happen after more than 2 years away from education (median age of 20 for individuals without post-secondary education and 24 for the college-educated). To remain close to our model, we set a senior period for all respondents by adding 10 years to their junior period in our initial results.⁷ However, other regression models exploit the full-time dimension of the panel by looking at relocations at any point after the junior period.

Regarding locations, for each respondent, we know the location at the county level at birth, at age 14, and at each interview date since 1979. Based on these counties, we determine whether each respondent lives in a Core Based Statistical Area (CBSA) with a 2010 population above 2 million. If so, we classify them as living in a big city, otherwise, as living in a small city.⁸ This population threshold leads to 40% and 39% of individuals living in big cities during their junior and senior periods, respectively. To construct a standardised occupation variable with consistent codes during the analysis period, we rely on Autor and Dorn (2013).

The initial sample includes all 6,111 individuals in the cross-sectional sample of the NLSY79. We exclude individuals for whom the AFQT or the Rosenberg self-esteem scores are missing, which reduces the sample to 5,671 individuals. We can determine the junior period location of 5,462 of these individuals and, due to sampling attrition, the senior period locations of 5,180 of them. The availability of the demographic controls that we include further reduces our sample to 5,254 individuals in the junior period analysis and 4,985 individuals in the senior period analysis.

4. Observed Location Choices by Self-Confidence and Ability

We first examine how the location choices of individuals vary with self-confidence and ability. To relate these choices to the theoretical predictions depicted in Figure 1, we divide the self-confidence and the ability measures into terciles. Figure 2 plots each of the nine possible combinations of self-confidence (horizontal axis) and ability (vertical axis) terciles in a grid.

Figure 2.

Observed location choices by self-confidence and ability terciles.

Panel (a) illustrates the bivariate distribution of self-confidence and ability by showing the percentage of NLSY79 respondents in each of the nine cells. We see that individuals are far from being concentrated on the three diagonal cells, and those in the middle tercile of ability are spread almost uniformly across self-confidence terciles.

In panel (b), we define a junior period (the year after completing education) and a senior period (10 years later). Using the same labels as in our theoretical Figure 1, we assign each grid cell the most prevalent location trajectory observed in the data for that combination of self-confidence and ability terciles.⁹

The three cells along the diagonal (representing individuals with well-aligned self-confidence and ability) show the assortative matching between cities and workers predicted by our model. Workers with accurate self-assessment tend to locate in small cities if they have low ability (bottom-left and centre–centre cells) and in big cities, if they have high ability (top-right cell).

Turning to individuals whose self-assessment is less accurate, consider individuals in the top tercile of ability but the bottom or middle tercile of self-confidence (top-left and top-centre cells). Their choices are, again, consistent with our theoretical predictions. Once individuals with low self-confidence find they have high ability, they move away from a small city where their underconfidence led them to locate initially. Had their self-assessment been more accurate, they would have been located in a big city from the beginning.

Individuals with intermediate levels of ability and high or low levels of self-confidence also follow the location choices predicted by our model. Those in the top tercile of self-confidence (centre-right cell) start in big cities and remain there. According to our model, they locate in a big city when junior led by their high self-confidence and, hence, acquire valuable experience. They decide to remain in a big city to put that experience to use. Instead, those individuals with lower self-confidence (centre-left cell) but similar intermediate ability tend to locate in a small city and remain there.

Finally, we look at individuals in the bottom tercile of ability who self-assess this inaccurately. Per our theoretical predictions, if their overconfidence is not excessive (bottom-centre cell), they tend to locate in a small city and have no solid reason to move later. The only cell out of nine in Figure 2 that seemingly differs from the theoretical prediction of Figure 1 is the bottom-right cell. The model can still accommodate this empirical finding—the cell with the least frequent values of ability and self-confidence with only 6.1% of the total—if |$\alpha _{BB\succ BS} \equiv \Delta \gamma / (e_B\, \Delta \Omega \, \pi _2)$| is sufficiently low (requiring large values of |$e_B$| and |$\Delta \Omega$|⁠). Then, workers with low ability who are driven to the big city by their overconfidence when junior acquire valuable experience (large |$e_B$|⁠). By remaining there, they take advantage of the much greater opportunities that big cities provide (large |$\Delta \Omega$|⁠).

Panel (b) of Figure 2 only shows the most common location choice in each cell. Panel (c) shows the incidence of all choices in each cell. We now split each of the nine cells into four quadrants corresponding to every possible two-period location trajectory, with darker shades representing a higher frequency of that trajectory compared to the overall population. We mark in white the prevalent location choice.¹⁰ Note how strategy SS becomes less prevalent and BB gradually more prevalent as we move upwards and rightwards.

Overall, the location choices of individuals vary with self-confidence and ability in a way that closely matches our theoretical predictions. Workers with accurate self-assessment tend to locate in small cities if they have low ability and in big cities if they have high ability. Workers with a flawed self-assessment instead make initial location choices that follow their self-confidence rather than their ability. For workers with intermediate ability, any errors in self-assessment are necessarily moderate. Thus, their initial location choices become self-perpetuating even if they do not align with the worker’s ability (per our model, because they affect the value of acquired experience).

Workers with high or low ability can make more substantial errors in self-assessment. These are more likely to be corrected, at least for underconfident high-ability workers who, despite lacking the self-confidence to initially locate in a big city, tend to move to one eventually.

All of these conclusions are so far based on raw data, without taking into account other characteristics and experiences of individuals. The main characteristic is education. We next extend our model to incorporate an education choice. This extension highlights why it is important to control for education to accurately characterise how ability and self-confidence determine location decisions over the life cycle. Taking this into consideration, we then present our main empirical results.

5. An Extended Model with Education

We have solved our model by characterising individual location decisions in the two work periods (junior and senior) depending on the values of ability and self-confidence. However, we have so far remained agnostic about how this self-confidence is formed. We now extend the model to include an education period and a decision to attend college or not, which help shape self-confidence.

We think of overall ability as being the combination of scholastic ability and non-scholastic ability. The latter includes attitudes and values, social and emotional skills, and metacognitive skills. Scholastic ability can be assessed with relative ease while going through the education system as a child or adolescent, while non-scholastic ability includes traits that become more evident after gathering some work experience.

Formally, in the education period, each worker becomes informed about her scholastic ability, |$\kappa$|⁠, during free compulsory education. She can opt to also complete college during the education period at a private cost |$\tau$| and amplify this scholastic ability by a known factor |$c>1$|⁠. A worker’s non-scholastic ability, |$\widetilde{\alpha }$|⁠, is only revealed after the junior work period. Until then, she has an imperfect self-assessment of this non-scholastic ability, |$\widetilde{\sigma }$|⁠. Overall ability is the sum of scholastic ability and non-scholastic ability. Thus, at the beginning of her junior work period, a worker’s self-assessment of her overall ability (which, as before, we call self-confidence) is

$$\begin{eqnarray} \sigma = \left\lbrace \begin{array}{@{}l@{\quad }l@{}}\begin{array}{ll}\kappa c + \widetilde{\sigma } & \text{if college-educated}, \\ \kappa + \widetilde{\sigma } & \text{otherwise}. \\ \end{array} \end{array}\right. \end{eqnarray}$$

(11)

Then, at the end of her junior work period, after her non-scholastic ability is fully revealed, the worker can perfectly assess her overall ability as

$$\begin{eqnarray} \alpha = \left\lbrace \begin{array}{@{}l@{\quad }l@{}}\begin{array}{ll}\kappa c + \widetilde{\alpha } & \text{if college-educated}, \\ \kappa + \widetilde{\alpha } & \text{otherwise}. \\ \end{array} \end{array}\right. \end{eqnarray}$$

(12)

Each worker’s lifetime location trajectory is still fully characterised by Proposition 1, based on |$\sigma$| and |$\alpha$|⁠. However, it is now also important to characterise the worker’s decision to complete college based on her assessment of scholastic ability and evaluation of the impact of college on her working life trajectory. This evaluation is imperfect due to still unascertained non-scholastic ability.

For simplicity, let us focus on parameter values such that |$e_S / \Omega _B \leqslant \Delta e / \Delta \Omega \leqslant e_B / \Omega _S$|⁠. This is the case represented in Figure 1. Following Proposition 1, workers expect to locate in the same city in both periods, and relocations are not planned but driven by an inaccurate self-assessment.¹¹

In Proposition 1, when |$e_S / \Omega _B \leqslant \Delta e / \Delta \Omega \leqslant e_B / \Omega _S$|⁠, low self-confidence is defined as |$\sigma \leqslant \alpha _{BB\succ SS} \equiv 2 \Delta \gamma / [(\Omega _B e_B - \Omega _S e_S)\, \pi _2]$| and high self-confidence as |$\sigma > \alpha _{BB\succ SS}$|⁠. Workers with low self-confidence locate in the small city when junior expecting to remain there, while workers with high self-confidence locate in the big city when junior also expecting to remain there.

Each worker chooses whether to attend college anticipating such location strategies. In particular, if the worker attends college, her self-assessed ability when choosing between a small and a big city is |$\sigma = \kappa c + \tilde{\sigma }$|⁠. Thus, she plans on working in a small city in both periods if |$\kappa c + \tilde{\sigma } \leqslant \alpha _{BB\succ SS}$| and on working in a big city in both periods otherwise. If the worker does not attend college, her self-assessed ability when choosing between a small and a big city is |$\sigma = \kappa + \tilde{\sigma }$|⁠, so she plans on working in a small city in both periods if |$\kappa + \tilde{\sigma } \leqslant \alpha _{BB\succ SS}$| and on working in a big city in both periods otherwise. Since |$\kappa c + \tilde{\sigma } > \kappa + \tilde{\sigma }$|⁠, this leaves us with three possibilities depending on the worker’s scholastic ability and self-assessment of non-scholastic ability.

The first possibility is that |$\kappa c + \tilde{\sigma } \leqslant \alpha _{BB\succ SS}$|⁠. This case arises when a worker’s combination of scholastic ability and self-assessment of non-scholastic ability is low enough that, even with the scholastic boost of college education, her overall self-confidence remains too low to target a big city. The worker will then opt for college if and only if |$U_{SS}(\kappa c + \tilde{\sigma }) - \tau >U_{SS}(\kappa + \tilde{\sigma })$|⁠. Using equation (1) to expand the corresponding utilities, the condition for a worker to go to college becomes

$$\begin{eqnarray} \kappa (c-1) (\pi _1 + \Omega _S e_S \pi _2 ) > \tau . \end{eqnarray}$$

(13)

The left-hand side is the extra return of scholastic ability from attending college if one plans to always work in a small city. The right-hand side is the cost of a college education.

The second possibility is that |$\alpha _{BB\succ SS} < \kappa + \tilde{\sigma }$|⁠. This case arises when a worker’s combination of scholastic ability and self-assessment of non-scholastic ability is high enough that, even without the scholastic lift of college education, her overall self-confidence is high enough to target a big city. The worker will then opt for college if and only if |$U_{BB}(\kappa c + \tilde{\sigma }) - \tau >U_{BB}(\kappa + \tilde{\sigma })$|⁠. Again, using equation (1) to expand these utilities, the condition for a worker to go to college becomes

$$\begin{eqnarray} \kappa (c-1) (\pi _1 + \Omega _B e_B \pi _2 ) > \tau . \end{eqnarray}$$

(14)

The left-hand side is the extra return of scholastic ability from attending college if one plans to always work in a big city, while the right-hand side is the cost of a college education.

The third and final possibility is that |$\kappa + \tilde{\sigma } \leqslant \alpha _{BB\succ SS} < \kappa c + \tilde{\sigma }$|⁠. This case arises when the worker’s combination of scholastic ability and self-assessment of non-scholastic ability is such that it is worthwhile to target a big city only if she has attended college, that is, when the scholastic lift of a college education is enough to push her overall self-confidence above |$\alpha _{BB\succ SS}$|⁠. The worker will then opt for college if and only if |$U_{BB}(\kappa c + \tilde{\sigma }) - \tau >U_{SS}(\kappa + \tilde{\sigma })$|⁠. Following equation (1), the condition for a worker to go to college becomes

$$\begin{eqnarray} \kappa [ (c-1) \pi _1 + (c \Omega _B e_B - \Omega _S e_S ) \pi _2 ] + \tilde{\sigma } (\Omega _B e_B - \Omega _S e_S ) \pi _2 > \tau + 2 \Delta \gamma . \end{eqnarray}$$

(15)

The first term on the left-hand side is the extra return of scholastic ability from attending college and locating in a big city relative to not attending college and locating in a small city. The second term on the left-hand side is the extra return of non-scholastic ability from locating in a big city instead of a small one. The right-hand side is the sum of the cost of college education and the differential urban cost between a big and a small city over the two work periods.

We can draw several conclusions from this extended model. First, although college education tends to provide higher returns in a big city, we expect to see a combination of workers with and without college in both big and small cities. While, as we know from the baseline model, workers with low self-confidence tend to locate in a small city when junior, they may choose to attend college if that low self-confidence arises from a combination of high scholastic ability and a very low self-assessment of non-scholastic ability. Conversely, while workers with high self-confidence tend to locate in a big city when junior, they may choose not to attend college if that high self-confidence results from a low scholastic ability and a high self-assessment of non-scholastic ability.

Second, even some workers with low scholastic ability attend college. They will do so if they are sufficiently self-confident that they expect to succeed in a big city, given that a college education will be particularly beneficial there.

Third, ability and self-confidence matter for location decisions both directly and indirectly through the decision to attend college. For given junior location choice and level of self-confidence, more able individuals are more likely to go to college as they receive a greater expected return from a college education. However, for a given ability level, more self-confident individuals are also more likely to attend college. Indeed, their high self-confidence drives them to a big city when junior, where a college education provides a higher expected benefit. Moreover, for the same reason, those with a college education are more likely to start working in a big city.

All these matters have implications for our empirical analysis. Ability and self-confidence interact with the decisions to attend college and locate in a big city in complex ways. We expect college education to be correlated with both ability and self-confidence as well as with the choice to locate in a big city. Unless we control for college education in our empirical specifications, we may indirectly capture the effect of personality traits on educational choices rather than the role of self-confidence and ability in determining location choices over the life cycle.

6. Determinants of Location in Big and Small Cities

We now test key implications of our model by examining whether self-confidence and ability affect location decisions of individuals across cities of different sizes while controlling for education and other drivers of location and mobility.

Location Trajectories in Junior and Senior Periods

We begin with a specification that remains close to our theoretical framework and its empirical counterpart in Figure 2 but accounts for education and other relevant individual characteristics. This estimation involves a multinomial logit where the choices are all four possible combinations of each individual’s junior and senior period locations. The dependent variable takes value 1 if the individual locates in a small city when junior and a big city when senior (SB), value 2 if the individual locates in a big city when junior and senior (BB), and value 3 if the individual locates in a big city when junior and a small city when senior (BS). The reference category is individuals who locate in a small city when junior and senior (SS). Results are in Table 2, where all columns report exponentiated coefficients (odds ratios), so values above (below) 1 indicate a positive (negative) effect. Standard errors are clustered at the metropolitan area level.

Table 2.

Determinants of individual location trajectories.

	Small city	Big city	Big city
	when junior,	when junior,	when junior,
	big city	big city	small city
	when senior	when senior	when senior
	(SB)	(BB)	(BS)
	(1)	(2)	(3)
Self-confidence percentile	0.9991	1.0048\|$^{***}$\|	1.0014
	(0.0020)	(0.0017)	(0.0024)
Ability percentile	1.0067\|$^{***}$\|	1.0049\|$^{*}$\|	1.0011
	(0.0024)	(0.0025)	(0.0031)
Male	0.8753	0.9611	0.9399
	(0.0884)	(0.1074)	(0.1293)
Hispanic	1.5200	2.8179\|$^{***}$\|	1.0440
	(0.7319)	(0.8985)	(0.3330)
Black	1.0865	1.5951\|$^{*}$\|	0.9648
	(0.3164)	(0.4179)	(0.2543)
High-school graduate	0.9324	1.0187	0.6696\|$^{*}$\|
	(0.1906)	(0.1545)	(0.1486)
Some college	1.6217\|$^{**}$\|	1.0727	0.7161
	(0.3448)	(0.1801)	(0.1785)
College graduate	2.6919\|$^{***}$\|	2.1652\|$^{***}$\|	1.8016\|$^{**}$\|
	(0.6278)	(0.5281)	(0.5042)
Never married	1.0365	1.3994\|$^{**}$\|	0.8282
	(0.2018)	(0.2138)	(0.1781)
One or more children	0.7230\|$^{**}$\|	0.8097\|$^{*}$\|	0.8609
	(0.1012)	(0.1003)	(0.1331)
Full-time working spouse	1.3755\|$^{***}$\|	0.9335	0.8143
	(0.1507)	(0.1253)	(0.1234)
In a small city at age 14	0.2113\|$^{***}$\|	0.0091\|$^{***}$\|	0.0339\|$^{***}$\|
	(0.0509)	(0.0022)	(0.0053)
Observations	4,985
Pseudo \|$R^2$\|	0.3317

	Small city	Big city	Big city
	when junior,	when junior,	when junior,
	big city	big city	small city
	when senior	when senior	when senior
	(SB)	(BB)	(BS)
	(1)	(2)	(3)
Self-confidence percentile	0.9991	1.0048\|$^{***}$\|	1.0014
	(0.0020)	(0.0017)	(0.0024)
Ability percentile	1.0067\|$^{***}$\|	1.0049\|$^{*}$\|	1.0011
	(0.0024)	(0.0025)	(0.0031)
Male	0.8753	0.9611	0.9399
	(0.0884)	(0.1074)	(0.1293)
Hispanic	1.5200	2.8179\|$^{***}$\|	1.0440
	(0.7319)	(0.8985)	(0.3330)
Black	1.0865	1.5951\|$^{*}$\|	0.9648
	(0.3164)	(0.4179)	(0.2543)
High-school graduate	0.9324	1.0187	0.6696\|$^{*}$\|
	(0.1906)	(0.1545)	(0.1486)
Some college	1.6217\|$^{**}$\|	1.0727	0.7161
	(0.3448)	(0.1801)	(0.1785)
College graduate	2.6919\|$^{***}$\|	2.1652\|$^{***}$\|	1.8016\|$^{**}$\|
	(0.6278)	(0.5281)	(0.5042)
Never married	1.0365	1.3994\|$^{**}$\|	0.8282
	(0.2018)	(0.2138)	(0.1781)
One or more children	0.7230\|$^{**}$\|	0.8097\|$^{*}$\|	0.8609
	(0.1012)	(0.1003)	(0.1331)
Full-time working spouse	1.3755\|$^{***}$\|	0.9335	0.8143
	(0.1507)	(0.1253)	(0.1234)
In a small city at age 14	0.2113\|$^{***}$\|	0.0091\|$^{***}$\|	0.0339\|$^{***}$\|
	(0.0509)	(0.0022)	(0.0053)
Observations	4,985
Pseudo \|$R^2$\|	0.3317

Notes: All columns report relative risk ratios (exponentiated coefficients) from a multinomial logit estimation, where coefficients above (below) 1 indicate a positive (negative) effect. The dependent variable takes value 1 if the individual locates in a small city when junior and a big city when senior (SB), value 2 if the individual locates in a big city when junior and senior (BB), and value 3 if the individual locates in a big city when junior and a small city when senior (BS). The reference category is individuals who locate in a small city when junior and senior (SS). A “big city” is a CBSA with a population greater than 2,000,000 in 2010. White, female, ever married, and high-school dropouts are the omitted explanatory categories. All specifications include a constant and birth-year indicator. Standard errors in parentheses are clustered at the metropolitan area level. |$^{*}$|⁠, |$^{**}$|⁠, and |$^{***}$| indicate significance at the 10%, 5%, and 1% levels, respectively.

Table 2.

Determinants of individual location trajectories.

	Small city	Big city	Big city
	when junior,	when junior,	when junior,
	big city	big city	small city
	when senior	when senior	when senior
	(SB)	(BB)	(BS)
	(1)	(2)	(3)
Self-confidence percentile	0.9991	1.0048\|$^{***}$\|	1.0014
	(0.0020)	(0.0017)	(0.0024)
Ability percentile	1.0067\|$^{***}$\|	1.0049\|$^{*}$\|	1.0011
	(0.0024)	(0.0025)	(0.0031)
Male	0.8753	0.9611	0.9399
	(0.0884)	(0.1074)	(0.1293)
Hispanic	1.5200	2.8179\|$^{***}$\|	1.0440
	(0.7319)	(0.8985)	(0.3330)
Black	1.0865	1.5951\|$^{*}$\|	0.9648
	(0.3164)	(0.4179)	(0.2543)
High-school graduate	0.9324	1.0187	0.6696\|$^{*}$\|
	(0.1906)	(0.1545)	(0.1486)
Some college	1.6217\|$^{**}$\|	1.0727	0.7161
	(0.3448)	(0.1801)	(0.1785)
College graduate	2.6919\|$^{***}$\|	2.1652\|$^{***}$\|	1.8016\|$^{**}$\|
	(0.6278)	(0.5281)	(0.5042)
Never married	1.0365	1.3994\|$^{**}$\|	0.8282
	(0.2018)	(0.2138)	(0.1781)
One or more children	0.7230\|$^{**}$\|	0.8097\|$^{*}$\|	0.8609
	(0.1012)	(0.1003)	(0.1331)
Full-time working spouse	1.3755\|$^{***}$\|	0.9335	0.8143
	(0.1507)	(0.1253)	(0.1234)
In a small city at age 14	0.2113\|$^{***}$\|	0.0091\|$^{***}$\|	0.0339\|$^{***}$\|
	(0.0509)	(0.0022)	(0.0053)
Observations	4,985
Pseudo \|$R^2$\|	0.3317

	Small city	Big city	Big city
	when junior,	when junior,	when junior,
	big city	big city	small city
	when senior	when senior	when senior
	(SB)	(BB)	(BS)
	(1)	(2)	(3)
Self-confidence percentile	0.9991	1.0048\|$^{***}$\|	1.0014
	(0.0020)	(0.0017)	(0.0024)
Ability percentile	1.0067\|$^{***}$\|	1.0049\|$^{*}$\|	1.0011
	(0.0024)	(0.0025)	(0.0031)
Male	0.8753	0.9611	0.9399
	(0.0884)	(0.1074)	(0.1293)
Hispanic	1.5200	2.8179\|$^{***}$\|	1.0440
	(0.7319)	(0.8985)	(0.3330)
Black	1.0865	1.5951\|$^{*}$\|	0.9648
	(0.3164)	(0.4179)	(0.2543)
High-school graduate	0.9324	1.0187	0.6696\|$^{*}$\|
	(0.1906)	(0.1545)	(0.1486)
Some college	1.6217\|$^{**}$\|	1.0727	0.7161
	(0.3448)	(0.1801)	(0.1785)
College graduate	2.6919\|$^{***}$\|	2.1652\|$^{***}$\|	1.8016\|$^{**}$\|
	(0.6278)	(0.5281)	(0.5042)
Never married	1.0365	1.3994\|$^{**}$\|	0.8282
	(0.2018)	(0.2138)	(0.1781)
One or more children	0.7230\|$^{**}$\|	0.8097\|$^{*}$\|	0.8609
	(0.1012)	(0.1003)	(0.1331)
Full-time working spouse	1.3755\|$^{***}$\|	0.9335	0.8143
	(0.1507)	(0.1253)	(0.1234)
In a small city at age 14	0.2113\|$^{***}$\|	0.0091\|$^{***}$\|	0.0339\|$^{***}$\|
	(0.0509)	(0.0022)	(0.0053)
Observations	4,985
Pseudo \|$R^2$\|	0.3317

Column (1) examines the trajectory determinants of locating in a small city upon completing education and relocating to a big city (SB) 10 years later. Results show that, relative to the reference category where individuals locate in a small city in both periods (SS), relocating to a big city between the junior and the senior period is more likely if the individual has a higher ability. In particular, an increase of one standard deviation in the ability percentile (28.87 points) raises the probability of an SB trajectory by 19%.¹² In contrast, higher self-confidence does not make SB significantly more likely than SS. This finding matches both our theoretical prediction and our descriptive evidence. In the context of Figure 2, it involves moving upwards, starting from the lower-left corner where SS is the most prevalent location choice, to the upper-left corner where SB becomes the dominant trajectory.

Column (2) analyses the determinants of locating in a big city in both periods (BB). Compared to the reference category (SS), individuals are significantly more likely to locate in a big city in both periods when they have higher self-confidence and higher ability. In this case, an increase of one standard deviation in the self-confidence or ability percentiles raises the probability of a BB trajectory by 14%.¹³ This finding again matches our theoretical prediction and descriptive evidence. In the context of Figure 2, it implies an upward-rightward move starting from the lower-left corner where SS is the most prevalent choice towards the upper right region, where BB becomes the dominant trajectory.

Lastly, column (3) looks at the determinants of locating in a small city upon completing education and relocating to a big city 10 years later (BS). Here, we do not find a significant effect on either self-confidence or ability. According to the baseline model, we expected BS to become the dominant trajectory as we move rightwards from the lower-left corner in Figure 2, where SS is the most prevalent choice. Nevertheless, this was not the case. The education variables hint at a plausible explanation. The positive and significant coefficient on the college graduate indicator tells us that a central distinguishing feature between those who choose BS and SS is that the former are more likely to hold a bachelor’s degree. Following our extended model with education, attending college can make the difference between locating in a small and a big city in the junior period. Then, having incurred the cost of both attending college and living in a big city early on, individuals may rationally become entrenched in that choice even if they grossly miscalculated their overall ability.

When looking at the education variables across columns, we note that college graduates are much more likely to choose a location trajectory that involves spending some time in a big city rather than remaining in a small city in both periods. Regarding other controls, individuals who never marry tend to locate in a big city in both periods. Those with a full-time working spouse have a higher probability (38%) of transitioning from a small city when junior to a big city when senior (likely seeking the advantages of big cities for dual-career couples documented in Costa and Kahn 2000). Having children lowers the probability of working in a big city when senior. Hispanics and Blacks are also more prone to always locate in a big city.

Many people are closely attached to the place where they grew up. One year after completing their education, 71% of individuals in our sample are in the same city as at age 14, and 62% remain there by age 40. Thus, we include as a control an indicator variable for living in a small city at age 14.¹⁴ We see that growing up in a small city decreases notably the probability of living in a big city in either the junior or the senior period.

The specification of Table 2 remains close to our theoretical framework by studying location choices in terms of junior and senior trajectories across two city sizes. However, we must rely on a limited number of observations per trajectory, which constrains our capacity to split the sample further. Moreover, we do not entirely exploit the advantages of our rich panel by focusing on only two periods (junior/senior). For these reasons, we now turn to study location choices upon entering the job market, splitting our sample more finely depending on where people grew up and restricting the analysis to movers. We then study subsequent location choices conditional on that initial location.

Junior Period Location

A central implication of our model is that junior workers sort on self-confidence rather than ability, with more confident workers more likely to locate in big cities upon entry into the labour market. In column (1) of Table 3, we estimate a logit model where the dependent variable takes value 1 if the individual lives in a big city the year after completing education. As before, all columns report exponentiated coefficients (odds ratios), and standard errors are clustered at the metropolitan area level. Results show that individuals with higher levels of self-confidence are more likely to locate in a big city when junior: An increase of one standard deviation in the self-confidence percentile (28.9 points) raises the probability of locating in a big city by 11%. In contrast, conditioning on self-confidence, individuals with higher ability are not more likely to initially locate in a big city.

Table 3.

Determinants of location in big and small cities in junior period.

		Living in a small		Living in a big
		city at age 14,		city at age 14,
	in a	in a	in a	in a	in a
	big	big	bigger	small	smaller
	city	city	city	city	city
	when	when	when	when	when
	junior	junior	junior	junior	junior
	(all)	(all)	(movers)	(all)	(movers)
	(1)	(2)	(3)	(4)	(5)
Self-confidence percentile	1.0037\|$^{**}$\|	1.0049\|$^{**}$\|	1.0043\|$^{**}$\|	0.9974	0.9920\|$^{**}$\|
	(0.0016)	(0.0020)	(0.0022)	(0.0025)	(0.0036)
Ability percentile	1.0011	1.0023	1.0018	1.0013	0.9981
	(0.0024)	(0.0033)	(0.0037)	(0.0039)	(0.0060)
Male	0.9003	0.9721	1.0135	1.2107	0.8044
	(0.0824)	(0.1277)	(0.1427)	(0.1544)	(0.2348)
Hispanic	2.1355\|$^{**}$\|	1.8488	1.7293	0.2583\|$^{***}$\|	0.2622\|$^{**}$\|
	(0.6827)	(0.7655)	(0.6655)	(0.1167)	(0.1419)
Black	1.4228	1.3422	2.4972\|$^{***}$\|	0.6091\|$^{*}$\|	1.9965
	(0.3480)	(0.4745)	(0.7748)	(0.1783)	(1.0082)
High-school graduate	0.9819	0.7778	0.7027	0.6996	1.3362
	(0.1295)	(0.1564)	(0.1695)	(0.1787)	(0.5600)
Some college	1.0351	1.2983	0.9444	1.2576	0.8573
	(0.1738)	(0.3056)	(0.2693)	(0.3194)	(0.3961)
College graduate	2.2374\|$^{***}$\|	3.8153\|$^{***}$\|	1.2911	1.4754	1.0275
	(0.5908)	(1.0282)	(0.4044)	(0.5071)	(0.4788)
Never married	1.3137\|$^{*}$\|	1.1942	1.6201\|$^{**}$\|	0.5945\|$^{*}$\|	0.4775\|$^{*}$\|
	(0.2151)	(0.2354)	(0.3081)	(0.1652)	(0.1946)
One or more children	0.6030\|$^{***}$\|	0.6057\|$^{***}$\|	0.7086\|$^{*}$\|	1.6894\|$^{**}$\|	1.3947
	(0.0793)	(0.1008)	(0.1454)	(0.3790)	(0.7342)
Full-time working spouse	0.9918	0.8281	0.8128	0.8025	2.3426
	(0.1673)	(0.1746)	(0.1663)	(0.2240)	(1.2715)
In a small city at age 14	0.0167\|$^{***}$\|
	(0.0040)
Observations	5,254	3,324	1,129	1,930	406
Pseudo \|$R^2$\|	0.4814	0.0937	0.0596	0.0556	0.0758

		Living in a small		Living in a big
		city at age 14,		city at age 14,
	in a	in a	in a	in a	in a
	big	big	bigger	small	smaller
	city	city	city	city	city
	when	when	when	when	when
	junior	junior	junior	junior	junior
	(all)	(all)	(movers)	(all)	(movers)
	(1)	(2)	(3)	(4)	(5)
Self-confidence percentile	1.0037\|$^{**}$\|	1.0049\|$^{**}$\|	1.0043\|$^{**}$\|	0.9974	0.9920\|$^{**}$\|
	(0.0016)	(0.0020)	(0.0022)	(0.0025)	(0.0036)
Ability percentile	1.0011	1.0023	1.0018	1.0013	0.9981
	(0.0024)	(0.0033)	(0.0037)	(0.0039)	(0.0060)
Male	0.9003	0.9721	1.0135	1.2107	0.8044
	(0.0824)	(0.1277)	(0.1427)	(0.1544)	(0.2348)
Hispanic	2.1355\|$^{**}$\|	1.8488	1.7293	0.2583\|$^{***}$\|	0.2622\|$^{**}$\|
	(0.6827)	(0.7655)	(0.6655)	(0.1167)	(0.1419)
Black	1.4228	1.3422	2.4972\|$^{***}$\|	0.6091\|$^{*}$\|	1.9965
	(0.3480)	(0.4745)	(0.7748)	(0.1783)	(1.0082)
High-school graduate	0.9819	0.7778	0.7027	0.6996	1.3362
	(0.1295)	(0.1564)	(0.1695)	(0.1787)	(0.5600)
Some college	1.0351	1.2983	0.9444	1.2576	0.8573
	(0.1738)	(0.3056)	(0.2693)	(0.3194)	(0.3961)
College graduate	2.2374\|$^{***}$\|	3.8153\|$^{***}$\|	1.2911	1.4754	1.0275
	(0.5908)	(1.0282)	(0.4044)	(0.5071)	(0.4788)
Never married	1.3137\|$^{*}$\|	1.1942	1.6201\|$^{**}$\|	0.5945\|$^{*}$\|	0.4775\|$^{*}$\|
	(0.2151)	(0.2354)	(0.3081)	(0.1652)	(0.1946)
One or more children	0.6030\|$^{***}$\|	0.6057\|$^{***}$\|	0.7086\|$^{*}$\|	1.6894\|$^{**}$\|	1.3947
	(0.0793)	(0.1008)	(0.1454)	(0.3790)	(0.7342)
Full-time working spouse	0.9918	0.8281	0.8128	0.8025	2.3426
	(0.1673)	(0.1746)	(0.1663)	(0.2240)	(1.2715)
In a small city at age 14	0.0167\|$^{***}$\|
	(0.0040)
Observations	5,254	3,324	1,129	1,930	406
Pseudo \|$R^2$\|	0.4814	0.0937	0.0596	0.0556	0.0758

Notes: All columns report odds ratios (exponentiated coefficients) from logit estimations, where coefficients above (below) 1 indicate a positive (negative) effect. The junior period is the year after an individual completes her highest level of continuous education. A “big city” is a CBSA with a population greater than 2,000,000 in 2010. A “bigger city” entails an increase in city size and the city of destination exceeds 1,000,000 in 2010. A “smaller city” entails a drop in city size and the city of destination is below 5,000,000 in 2010. White, female, and ever married are the omitted explanatory categories. All specifications include a constant and birth-year indicator. Standard errors in parentheses are clustered at the metropolitan area level. |$^*$|⁠, |$^{**}$|⁠, and |$^{***}$| indicate significance at the 10%, 5%, and 1% levels, respectively.

Table 3.

Determinants of location in big and small cities in junior period.

		Living in a small		Living in a big
		city at age 14,		city at age 14,
	in a	in a	in a	in a	in a
	big	big	bigger	small	smaller
	city	city	city	city	city
	when	when	when	when	when
	junior	junior	junior	junior	junior
	(all)	(all)	(movers)	(all)	(movers)
	(1)	(2)	(3)	(4)	(5)
Self-confidence percentile	1.0037\|$^{**}$\|	1.0049\|$^{**}$\|	1.0043\|$^{**}$\|	0.9974	0.9920\|$^{**}$\|
	(0.0016)	(0.0020)	(0.0022)	(0.0025)	(0.0036)
Ability percentile	1.0011	1.0023	1.0018	1.0013	0.9981
	(0.0024)	(0.0033)	(0.0037)	(0.0039)	(0.0060)
Male	0.9003	0.9721	1.0135	1.2107	0.8044
	(0.0824)	(0.1277)	(0.1427)	(0.1544)	(0.2348)
Hispanic	2.1355\|$^{**}$\|	1.8488	1.7293	0.2583\|$^{***}$\|	0.2622\|$^{**}$\|
	(0.6827)	(0.7655)	(0.6655)	(0.1167)	(0.1419)
Black	1.4228	1.3422	2.4972\|$^{***}$\|	0.6091\|$^{*}$\|	1.9965
	(0.3480)	(0.4745)	(0.7748)	(0.1783)	(1.0082)
High-school graduate	0.9819	0.7778	0.7027	0.6996	1.3362
	(0.1295)	(0.1564)	(0.1695)	(0.1787)	(0.5600)
Some college	1.0351	1.2983	0.9444	1.2576	0.8573
	(0.1738)	(0.3056)	(0.2693)	(0.3194)	(0.3961)
College graduate	2.2374\|$^{***}$\|	3.8153\|$^{***}$\|	1.2911	1.4754	1.0275
	(0.5908)	(1.0282)	(0.4044)	(0.5071)	(0.4788)
Never married	1.3137\|$^{*}$\|	1.1942	1.6201\|$^{**}$\|	0.5945\|$^{*}$\|	0.4775\|$^{*}$\|
	(0.2151)	(0.2354)	(0.3081)	(0.1652)	(0.1946)
One or more children	0.6030\|$^{***}$\|	0.6057\|$^{***}$\|	0.7086\|$^{*}$\|	1.6894\|$^{**}$\|	1.3947
	(0.0793)	(0.1008)	(0.1454)	(0.3790)	(0.7342)
Full-time working spouse	0.9918	0.8281	0.8128	0.8025	2.3426
	(0.1673)	(0.1746)	(0.1663)	(0.2240)	(1.2715)
In a small city at age 14	0.0167\|$^{***}$\|
	(0.0040)
Observations	5,254	3,324	1,129	1,930	406
Pseudo \|$R^2$\|	0.4814	0.0937	0.0596	0.0556	0.0758

		Living in a small		Living in a big
		city at age 14,		city at age 14,
	in a	in a	in a	in a	in a
	big	big	bigger	small	smaller
	city	city	city	city	city
	when	when	when	when	when
	junior	junior	junior	junior	junior
	(all)	(all)	(movers)	(all)	(movers)
	(1)	(2)	(3)	(4)	(5)
Self-confidence percentile	1.0037\|$^{**}$\|	1.0049\|$^{**}$\|	1.0043\|$^{**}$\|	0.9974	0.9920\|$^{**}$\|
	(0.0016)	(0.0020)	(0.0022)	(0.0025)	(0.0036)
Ability percentile	1.0011	1.0023	1.0018	1.0013	0.9981
	(0.0024)	(0.0033)	(0.0037)	(0.0039)	(0.0060)
Male	0.9003	0.9721	1.0135	1.2107	0.8044
	(0.0824)	(0.1277)	(0.1427)	(0.1544)	(0.2348)
Hispanic	2.1355\|$^{**}$\|	1.8488	1.7293	0.2583\|$^{***}$\|	0.2622\|$^{**}$\|
	(0.6827)	(0.7655)	(0.6655)	(0.1167)	(0.1419)
Black	1.4228	1.3422	2.4972\|$^{***}$\|	0.6091\|$^{*}$\|	1.9965
	(0.3480)	(0.4745)	(0.7748)	(0.1783)	(1.0082)
High-school graduate	0.9819	0.7778	0.7027	0.6996	1.3362
	(0.1295)	(0.1564)	(0.1695)	(0.1787)	(0.5600)
Some college	1.0351	1.2983	0.9444	1.2576	0.8573
	(0.1738)	(0.3056)	(0.2693)	(0.3194)	(0.3961)
College graduate	2.2374\|$^{***}$\|	3.8153\|$^{***}$\|	1.2911	1.4754	1.0275
	(0.5908)	(1.0282)	(0.4044)	(0.5071)	(0.4788)
Never married	1.3137\|$^{*}$\|	1.1942	1.6201\|$^{**}$\|	0.5945\|$^{*}$\|	0.4775\|$^{*}$\|
	(0.2151)	(0.2354)	(0.3081)	(0.1652)	(0.1946)
One or more children	0.6030\|$^{***}$\|	0.6057\|$^{***}$\|	0.7086\|$^{*}$\|	1.6894\|$^{**}$\|	1.3947
	(0.0793)	(0.1008)	(0.1454)	(0.3790)	(0.7342)
Full-time working spouse	0.9918	0.8281	0.8128	0.8025	2.3426
	(0.1673)	(0.1746)	(0.1663)	(0.2240)	(1.2715)
In a small city at age 14	0.0167\|$^{***}$\|
	(0.0040)
Observations	5,254	3,324	1,129	1,930	406
Pseudo \|$R^2$\|	0.4814	0.0937	0.0596	0.0556	0.0758

Consistent with the extended version of the model, ability positively correlates with higher education, and college-educated workers are more likely to locate in a big city. This outcome is partly due to individuals who grow up in a big city having higher college graduation rates and most people starting to work in the same place they grew up (Bosquet and Overman 2019). An individual with a bachelor’s degree has a 124% higher probability of locating in a big city when junior than someone with primary education, other characteristics being equal. However, as outlined in the extended model, there is substantial heterogeneity in ability among workers with the same level of education. Importantly, self-assessment of ability relative to people with the same education is so imperfect that there is virtually no correlation (0.02) between self-confidence and ability among college-educated workers. As a result, controlling for education, a higher ability does not make the initial location in a big city any more likely.

The estimation also includes a set of standard demographic controls. Having children is associated with a drop in the probability of locating in a big city of 40%. Meanwhile, single individuals and Hispanics are 31% and 114% more likely to live in a big city at that point, respectively.

While growing up in a small city notably decreases the probability of entering the job market in a big city, our results regarding the role of ability and self-confidence are similar whether we control for location at age 14 or not. As an alternative to controlling for living in a small city at age 14, we can split the sample between those who lived in a small or big city at age 14 and re-estimate the specification of column (1) separately for each group. Furthermore, since junior period locations may reflect high moving costs rather than a conscious choice for people who began working in the same city where they grew up, we also focus on the subset of individuals who moved between age 14 and when entering the labour market. We present these alternative specifications in columns (2)–(5) of Table 3.

In column (2), we consider all individuals who grew up in a small city, regardless of whether they are still in the same location as at age 14 or not, and examine the determinants of locating in a big city when junior. We find that more self-confident individuals from small cities are more likely to locate in a big city upon entering the labour market. Similarly to column (1), individuals with a bachelor’s degree have a much higher probability of living in a big city when junior. Other individual characteristics also continue to matter for the junior location in similar ways.

In column (3), we repeat the estimation of column (2), but now only for individuals who moved between age 14 and when entering the labour market. Since focusing on movers reduces our sample size substantially, we no longer define the dependent variable based on whether the move between age 14 and the junior period involves moving to a big city but instead to a bigger city more broadly.¹⁵ Results show that conditional on no longer living in the same location as at age 14, more self-confident individuals who grew up in a small city are more likely to have moved to a bigger city by the time they enter the labour market. The estimated effect on the self-confidence percentile resembles those of columns (1) and (2). Instead, individuals with higher ability levels are not more likely to follow this path.

In column (4), we consider all individuals who grew up in a big city, regardless of whether they are still in the same location as at age 14 or not, and examine the determinants of locating in a small city when junior. Here, we do not find evidence that less self-confident individuals from big cities relocate to small cities in their junior period. This outcome may occur because many people do not move. Indeed, when we restrict the estimation to movers between age 14 and the junior period in column (5), moving to a smaller city is significantly associated with lower self-confidence levels for those who grew up in a big city¹⁶ An increase of one standard deviation in the self-confidence percentile decreases the probability of moving to a smaller city by 23%. It is worth noting that a relatively small share of individuals move out of big cities early in their lives—only 406 out of 1,930 individuals (21%) move from a big city in column (5), whereas 1,129 of 3,324 individuals (34%) move from a small city in column (3).

Relocations Over Lifetime Careers

We next study location choices later in life. Our model predicts that ability matters for the location of senior workers but that junior location choices have long-term consequences. In particular, conditional on location upon entering the labour market, higher-ability workers should be more likely to locate in big cities later in their careers. Furthermore, self-confidence should no longer drive location decisions directly in the senior period, mattering only indirectly through early location choices.

To test these implications, we exploit the lifetime careers of workers in the NLSY79 to estimate a competing risks discrete duration model using a multinomial logit. In each period, individuals choose whether to stay in their city, move to a small city, or move to a big city.¹⁷

We show the results regarding relocations after the junior period in Table 4. In columns (1a) and (1b), we focus on individuals living in a small city upon completing education. The dependent variable takes value 1 in the last period prior to migration if the individual relocated to another small city, value 2 if the individual relocated to a big city, and value 0 for all periods if the individual remained in the same city. We report exponentiated coefficients (relative risk ratios), where coefficients above (below) 1 indicate a positive (negative) effect. Results show that self-confidence no longer influences the decision to relocate in any direction. In contrast, the individual’s ability is a crucial relocation driver from small to big cities but not to other small cities. The estimated coefficient on ability in column (1b) implies that a one standard deviation increase in the ability percentile raises the probability of moving from a small to a big city by 22%. Thus, among the set of residents in small cities, the most able move to bigger cities over time.

Table 4.

Determinants of location in big and small cities after junior period.

	In a small city upon		In a big city upon
	completing education,		completing education,
	moved to	moved to	moved to	moved to
	another	a big	a small	another
	small city	city	city	big city
	(1a)	(1b)	(2a)	(2b)
Self-confidence percentile	1.0001	1.0004	0.9996	1.0031\|$^{*}$\|
	(0.0009)	(0.0017)	(0.0011)	(0.0018)
Ability percentile	1.0013	1.0075\|$^{***}$\|	0.9963	1.0019
	(0.0013)	(0.0022)	(0.0026)	(0.0033)
Experience	0.9876	0.9996	0.9694\|$^{*}$\|	0.9894
	(0.0123)	(0.0252)	(0.0158)	(0.0247)
Tenure	0.9186\|$^{***}$\|	0.8888\|$^{***}$\|	0.9518\|$^{***}$\|	0.8957\|$^{***}$\|
	(0.0136)	(0.0268)	(0.0173)	(0.0303)
Unemployed	1.1776\|$^{**}$\|	1.3826\|$^{***}$\|	1.4011\|$^{***}$\|	1.2412\|$^{*}$\|
	(0.0866)	(0.1441)	(0.1818)	(0.1592)
Male	1.1036	0.9650	1.1013	0.9304
	(0.0765)	(0.0955)	(0.0961)	(0.1046)
Hispanic	0.9639	1.5538\|$^{**}$\|	0.4905\|$^{***}$\|	1.0836
	(0.2135)	(0.2900)	(0.1036)	(0.2098)
Black	0.6014\|$^{***}$\|	1.1964	0.5491\|$^{***}$\|	0.8610
	(0.0759)	(0.2088)	(0.0905)	(0.1931)
High-school graduate	0.8695	0.8340	0.9135	1.5520
	(0.0780)	(0.1514)	(0.1301)	(0.4549)
Some college	0.9475	1.4271\|$^{*}$\|	0.9776	2.3240\|$^{**}$\|
	(0.0998)	(0.2614)	(0.1850)	(0.8100)
College graduate	0.9230	1.3632	0.9670	2.7661\|$^{***}$\|
	(0.1166)	(0.3225)	(0.1380)	(0.8174)
Never married	0.8857	0.9020	0.7828\|$^{**}$\|	0.9921
	(0.0839)	(0.1090)	(0.0847)	(0.1841)
One or more children	0.7631\|$^{***}$\|	0.6724\|$^{***}$\|	0.9028	0.8580
	(0.0594)	(0.0937)	(0.0964)	(0.1273)
Full-time working spouse	1.0587	1.3484\|$^{**}$\|	1.1250	1.5968\|$^{***}$\|
	(0.0912)	(0.2034)	(0.1426)	(0.2787)
Same city when junior and age 14	0.3512\|$^{***}$\|	0.4140\|$^{***}$\|	0.4142\|$^{***}$\|	0.3918\|$^{***}$\|
	(0.0243)	(0.0482)	(0.0339)	(0.0560)
Years since junior period indicators	Yes	Yes	Yes	Yes
Observations	34,354		24,926
Pseudo \|$R^2$\|	0.0944		0.0648

	In a small city upon		In a big city upon
	completing education,		completing education,
	moved to	moved to	moved to	moved to
	another	a big	a small	another
	small city	city	city	big city
	(1a)	(1b)	(2a)	(2b)
Self-confidence percentile	1.0001	1.0004	0.9996	1.0031\|$^{*}$\|
	(0.0009)	(0.0017)	(0.0011)	(0.0018)
Ability percentile	1.0013	1.0075\|$^{***}$\|	0.9963	1.0019
	(0.0013)	(0.0022)	(0.0026)	(0.0033)
Experience	0.9876	0.9996	0.9694\|$^{*}$\|	0.9894
	(0.0123)	(0.0252)	(0.0158)	(0.0247)
Tenure	0.9186\|$^{***}$\|	0.8888\|$^{***}$\|	0.9518\|$^{***}$\|	0.8957\|$^{***}$\|
	(0.0136)	(0.0268)	(0.0173)	(0.0303)
Unemployed	1.1776\|$^{**}$\|	1.3826\|$^{***}$\|	1.4011\|$^{***}$\|	1.2412\|$^{*}$\|
	(0.0866)	(0.1441)	(0.1818)	(0.1592)
Male	1.1036	0.9650	1.1013	0.9304
	(0.0765)	(0.0955)	(0.0961)	(0.1046)
Hispanic	0.9639	1.5538\|$^{**}$\|	0.4905\|$^{***}$\|	1.0836
	(0.2135)	(0.2900)	(0.1036)	(0.2098)
Black	0.6014\|$^{***}$\|	1.1964	0.5491\|$^{***}$\|	0.8610
	(0.0759)	(0.2088)	(0.0905)	(0.1931)
High-school graduate	0.8695	0.8340	0.9135	1.5520
	(0.0780)	(0.1514)	(0.1301)	(0.4549)
Some college	0.9475	1.4271\|$^{*}$\|	0.9776	2.3240\|$^{**}$\|
	(0.0998)	(0.2614)	(0.1850)	(0.8100)
College graduate	0.9230	1.3632	0.9670	2.7661\|$^{***}$\|
	(0.1166)	(0.3225)	(0.1380)	(0.8174)
Never married	0.8857	0.9020	0.7828\|$^{**}$\|	0.9921
	(0.0839)	(0.1090)	(0.0847)	(0.1841)
One or more children	0.7631\|$^{***}$\|	0.6724\|$^{***}$\|	0.9028	0.8580
	(0.0594)	(0.0937)	(0.0964)	(0.1273)
Full-time working spouse	1.0587	1.3484\|$^{**}$\|	1.1250	1.5968\|$^{***}$\|
	(0.0912)	(0.2034)	(0.1426)	(0.2787)
Same city when junior and age 14	0.3512\|$^{***}$\|	0.4140\|$^{***}$\|	0.4142\|$^{***}$\|	0.3918\|$^{***}$\|
	(0.0243)	(0.0482)	(0.0339)	(0.0560)
Years since junior period indicators	Yes	Yes	Yes	Yes
Observations	34,354		24,926
Pseudo \|$R^2$\|	0.0944		0.0648

Notes: Columns report odds ratios (exponentiated coefficients) from multinomial logit estimations, where coefficients above (below) 1 indicate a positive (negative) effect. In columns (1a) and (1b), the sample includes individuals who lived in a small city one year after completing education and the dependent variable takes value 1 if the individual moves to another small city and value 2 if she moves to a big city. In columns (2a) and (2b), the sample includes individuals who lived in a big city 1 year after completing education and the dependent variable takes value 1 if the individual moves to a small city and value 2 if she moves to another big city. A “big city” is a CBSA with a population greater than 2,000,000 in 2010. White, female, ever married, and high-school dropouts are the omitted categories. All specifications include a constant and birth-year indicator. Standard errors in parentheses are clustered at the metropolitan area level. |$^*$|⁠, |$^{**}$|⁠, and |$^{***}$| indicate significance at the 10%, 5%, and 1% levels, respectively.

Table 4.

Determinants of location in big and small cities after junior period.

	In a small city upon		In a big city upon
	completing education,		completing education,
	moved to	moved to	moved to	moved to
	another	a big	a small	another
	small city	city	city	big city
	(1a)	(1b)	(2a)	(2b)
Self-confidence percentile	1.0001	1.0004	0.9996	1.0031\|$^{*}$\|
	(0.0009)	(0.0017)	(0.0011)	(0.0018)
Ability percentile	1.0013	1.0075\|$^{***}$\|	0.9963	1.0019
	(0.0013)	(0.0022)	(0.0026)	(0.0033)
Experience	0.9876	0.9996	0.9694\|$^{*}$\|	0.9894
	(0.0123)	(0.0252)	(0.0158)	(0.0247)
Tenure	0.9186\|$^{***}$\|	0.8888\|$^{***}$\|	0.9518\|$^{***}$\|	0.8957\|$^{***}$\|
	(0.0136)	(0.0268)	(0.0173)	(0.0303)
Unemployed	1.1776\|$^{**}$\|	1.3826\|$^{***}$\|	1.4011\|$^{***}$\|	1.2412\|$^{*}$\|
	(0.0866)	(0.1441)	(0.1818)	(0.1592)
Male	1.1036	0.9650	1.1013	0.9304
	(0.0765)	(0.0955)	(0.0961)	(0.1046)
Hispanic	0.9639	1.5538\|$^{**}$\|	0.4905\|$^{***}$\|	1.0836
	(0.2135)	(0.2900)	(0.1036)	(0.2098)
Black	0.6014\|$^{***}$\|	1.1964	0.5491\|$^{***}$\|	0.8610
	(0.0759)	(0.2088)	(0.0905)	(0.1931)
High-school graduate	0.8695	0.8340	0.9135	1.5520
	(0.0780)	(0.1514)	(0.1301)	(0.4549)
Some college	0.9475	1.4271\|$^{*}$\|	0.9776	2.3240\|$^{**}$\|
	(0.0998)	(0.2614)	(0.1850)	(0.8100)
College graduate	0.9230	1.3632	0.9670	2.7661\|$^{***}$\|
	(0.1166)	(0.3225)	(0.1380)	(0.8174)
Never married	0.8857	0.9020	0.7828\|$^{**}$\|	0.9921
	(0.0839)	(0.1090)	(0.0847)	(0.1841)
One or more children	0.7631\|$^{***}$\|	0.6724\|$^{***}$\|	0.9028	0.8580
	(0.0594)	(0.0937)	(0.0964)	(0.1273)
Full-time working spouse	1.0587	1.3484\|$^{**}$\|	1.1250	1.5968\|$^{***}$\|
	(0.0912)	(0.2034)	(0.1426)	(0.2787)
Same city when junior and age 14	0.3512\|$^{***}$\|	0.4140\|$^{***}$\|	0.4142\|$^{***}$\|	0.3918\|$^{***}$\|
	(0.0243)	(0.0482)	(0.0339)	(0.0560)
Years since junior period indicators	Yes	Yes	Yes	Yes
Observations	34,354		24,926
Pseudo \|$R^2$\|	0.0944		0.0648

	In a small city upon		In a big city upon
	completing education,		completing education,
	moved to	moved to	moved to	moved to
	another	a big	a small	another
	small city	city	city	big city
	(1a)	(1b)	(2a)	(2b)
Self-confidence percentile	1.0001	1.0004	0.9996	1.0031\|$^{*}$\|
	(0.0009)	(0.0017)	(0.0011)	(0.0018)
Ability percentile	1.0013	1.0075\|$^{***}$\|	0.9963	1.0019
	(0.0013)	(0.0022)	(0.0026)	(0.0033)
Experience	0.9876	0.9996	0.9694\|$^{*}$\|	0.9894
	(0.0123)	(0.0252)	(0.0158)	(0.0247)
Tenure	0.9186\|$^{***}$\|	0.8888\|$^{***}$\|	0.9518\|$^{***}$\|	0.8957\|$^{***}$\|
	(0.0136)	(0.0268)	(0.0173)	(0.0303)
Unemployed	1.1776\|$^{**}$\|	1.3826\|$^{***}$\|	1.4011\|$^{***}$\|	1.2412\|$^{*}$\|
	(0.0866)	(0.1441)	(0.1818)	(0.1592)
Male	1.1036	0.9650	1.1013	0.9304
	(0.0765)	(0.0955)	(0.0961)	(0.1046)
Hispanic	0.9639	1.5538\|$^{**}$\|	0.4905\|$^{***}$\|	1.0836
	(0.2135)	(0.2900)	(0.1036)	(0.2098)
Black	0.6014\|$^{***}$\|	1.1964	0.5491\|$^{***}$\|	0.8610
	(0.0759)	(0.2088)	(0.0905)	(0.1931)
High-school graduate	0.8695	0.8340	0.9135	1.5520
	(0.0780)	(0.1514)	(0.1301)	(0.4549)
Some college	0.9475	1.4271\|$^{*}$\|	0.9776	2.3240\|$^{**}$\|
	(0.0998)	(0.2614)	(0.1850)	(0.8100)
College graduate	0.9230	1.3632	0.9670	2.7661\|$^{***}$\|
	(0.1166)	(0.3225)	(0.1380)	(0.8174)
Never married	0.8857	0.9020	0.7828\|$^{**}$\|	0.9921
	(0.0839)	(0.1090)	(0.0847)	(0.1841)
One or more children	0.7631\|$^{***}$\|	0.6724\|$^{***}$\|	0.9028	0.8580
	(0.0594)	(0.0937)	(0.0964)	(0.1273)
Full-time working spouse	1.0587	1.3484\|$^{**}$\|	1.1250	1.5968\|$^{***}$\|
	(0.0912)	(0.2034)	(0.1426)	(0.2787)
Same city when junior and age 14	0.3512\|$^{***}$\|	0.4140\|$^{***}$\|	0.4142\|$^{***}$\|	0.3918\|$^{***}$\|
	(0.0243)	(0.0482)	(0.0339)	(0.0560)
Years since junior period indicators	Yes	Yes	Yes	Yes
Observations	34,354		24,926
Pseudo \|$R^2$\|	0.0944		0.0648

Analogously, in columns (2a) and (2b), we focus on individuals living in a big city upon completing their education. The dependent variable takes value 1 in the last period before migration if the individual relocated to a small city, value 2 in the last period before migration if the individual relocated to another big city, and value 0 for all periods if the individual remained in the same city. Results reveal that neither self-confidence nor ability is a key determinant of senior workers’ relocation decisions from big cities in any direction.¹⁸ This finding is consistent with one of our conclusions from Figure 1 when |$e_B$| and |$\Delta \Omega$| are large: If the big-city experience is highly valuable and differences in opportunities between small and big cities are large, then workers who located in a big city upon completing education tend to stay even if their ability is low.

Other findings show that, even conditional on junior period location, having attended college makes locating in a big city later in life more likely. Being partnered with a full-time working spouse increases the odds of moving to a big city, regardless of the worker’s initial location (Costa and Kahn 2000). Having children discourages individuals from leaving small cities. In turn, minorities are less likely to leave a big city. When looking at time-varying labour market variables, a longer job tenure reduces the odds of migrating in any direction. Unemployment is often a major factor that affects the mobility decisions of individuals (Greenwood 1997). We noted above those workers who are initially located in big cities and found good local opportunities to use their previously acquired experience tend to stay put, even if they turn out to have low ability. On the other hand, individuals who find themselves out of work for an extended period in a big city are more likely to move away. Finally, individuals living in the same city upon completing education and at age 14 are much less likely to move anywhere later in life.

Robustness and Alternative Explanations

One source of concern is that the sorting by self-confidence that we observe during the junior period is unrelated to an inaccurate assessment of ability. Instead, it may reflect an additional intrinsic value of self-confidence in big cities. To address this concern, we follow De la Roca and Puga (2017). In column (1) of Table 5, we replicate their results using our US NLSY79 data (their study uses Spanish Social Security data). We regress log earnings on worker fixed effects, job characteristics, measures of overall work experience and work experience acquired in big cities, interactions between these measures of experience and worker fixed effects, and indicator variables for all

individual big cities and groups of similarly sized small cities.¹⁹ The positive and significant coefficient on big-city experience shows that experience acquired in big cities is significantly more valuable than the experience acquired elsewhere, consistent with what we assume in our model.

Table 5.

Relationship between earnings, ability, and self-confidence.

	Log earnings
	(1)	(2)	(3)	(4)
Big-city experience	0.0153***	0.0152***	0.0154***	0.0151***
	(0.0025)	(0.0025)	(0.0025)	(0.0025)
Big-city exp. × experience	−0.0004***	−0.0004***	−0.0004***	−0.0004***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
Big-city exp. × worker fixed-effect	0.0118**	0.0128**
	(0.0052)	(0.0053)
Big-city exp. × ability		0.0068*		0.0078**
		(0.0036)		(0.0036)
Big-city exp. × self-confidence		−0.0041		−0.0051
		(0.0034)		(0.0034)
Experience	0.0289***	0.0271***	0.0290***	0.0273***
	(0.0018)	(0.0018)	(0.0018)	(0.0018)
Experience²	−0.0004***	−0.0003***	−0.0004***	−0.0003***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
Experience × worker fixed-effect	0.0633***		0.0640***
	(0.0079)		(0.0081)
Experience² × worker fixed-effect	−0.0011***		−0.0012***
	(0.0003)		(0.0003)
Experience × ability		0.0314***		0.0309***
		(0.0050)		(0.0050)
Experience² × ability		−0.0005***		−0.0005***
		(0.0002)		(0.0002)
Experience × self-confidence			−0.0026	0.0025
			(0.0048)	(0.0047)
Experience² × self-confidence			0.0001	0.0000
			(0.0002)	(0.0002)
Tenure	0.0287***	0.0289***	0.0287***	0.0288***
	(0.0014)	(0.0014)	(0.0014)	(0.0014)
Tenure²	−0.0010***	−0.0010***	−0.0010***	−0.0010***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
City/city group indicators	Yes	Yes	Yes	Yes
2-digit occupation & sector indicators	Yes	Yes	Yes	Yes
Worker fixed effects	Yes	Yes	Yes	Yes
Observations	46,833	46,833	46,833	46,833
R²	0.2671	0.2583	0.2672	0.2584

	Log earnings
	(1)	(2)	(3)	(4)
Big-city experience	0.0153***	0.0152***	0.0154***	0.0151***
	(0.0025)	(0.0025)	(0.0025)	(0.0025)
Big-city exp. × experience	−0.0004***	−0.0004***	−0.0004***	−0.0004***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
Big-city exp. × worker fixed-effect	0.0118**	0.0128**
	(0.0052)	(0.0053)
Big-city exp. × ability		0.0068*		0.0078**
		(0.0036)		(0.0036)
Big-city exp. × self-confidence		−0.0041		−0.0051
		(0.0034)		(0.0034)
Experience	0.0289***	0.0271***	0.0290***	0.0273***
	(0.0018)	(0.0018)	(0.0018)	(0.0018)
Experience²	−0.0004***	−0.0003***	−0.0004***	−0.0003***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
Experience × worker fixed-effect	0.0633***		0.0640***
	(0.0079)		(0.0081)
Experience² × worker fixed-effect	−0.0011***		−0.0012***
	(0.0003)		(0.0003)
Experience × ability		0.0314***		0.0309***
		(0.0050)		(0.0050)
Experience² × ability		−0.0005***		−0.0005***
		(0.0002)		(0.0002)
Experience × self-confidence			−0.0026	0.0025
			(0.0048)	(0.0047)
Experience² × self-confidence			0.0001	0.0000
			(0.0002)	(0.0002)
Tenure	0.0287***	0.0289***	0.0287***	0.0288***
	(0.0014)	(0.0014)	(0.0014)	(0.0014)
Tenure²	−0.0010***	−0.0010***	−0.0010***	−0.0010***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
City/city group indicators	Yes	Yes	Yes	Yes
2-digit occupation & sector indicators	Yes	Yes	Yes	Yes
Worker fixed effects	Yes	Yes	Yes	Yes
Observations	46,833	46,833	46,833	46,833
R²	0.2671	0.2583	0.2672	0.2584

Notes: A ‘big city’ is a Core Based Statistical Area (CBSA) with a population greater than 2,000,000 in 2010. City/city group indicators include indicator variables for all individual big cities and for groups of similarly-sized small cities. Worker fixed-effect computation follows De la Roca and Puga (2017). All specifications include a constant. Coefficients reported with robust standard errors in parenthesis, which are clustered by worker. ***, **, and * indicate significance at the 1, 5, and 10% levels.

Table 5.

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Relationship between earnings, ability, and self-confidence.

	Log earnings
	(1)	(2)	(3)	(4)
Big-city experience	0.0153***	0.0152***	0.0154***	0.0151***
	(0.0025)	(0.0025)	(0.0025)	(0.0025)
Big-city exp. × experience	−0.0004***	−0.0004***	−0.0004***	−0.0004***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
Big-city exp. × worker fixed-effect	0.0118**	0.0128**
	(0.0052)	(0.0053)
Big-city exp. × ability		0.0068*		0.0078**
		(0.0036)		(0.0036)
Big-city exp. × self-confidence		−0.0041		−0.0051
		(0.0034)		(0.0034)
Experience	0.0289***	0.0271***	0.0290***	0.0273***
	(0.0018)	(0.0018)	(0.0018)	(0.0018)
Experience²	−0.0004***	−0.0003***	−0.0004***	−0.0003***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
Experience × worker fixed-effect	0.0633***		0.0640***
	(0.0079)		(0.0081)
Experience² × worker fixed-effect	−0.0011***		−0.0012***
	(0.0003)		(0.0003)
Experience × ability		0.0314***		0.0309***
		(0.0050)		(0.0050)
Experience² × ability		−0.0005***		−0.0005***
		(0.0002)		(0.0002)
Experience × self-confidence			−0.0026	0.0025
			(0.0048)	(0.0047)
Experience² × self-confidence			0.0001	0.0000
			(0.0002)	(0.0002)
Tenure	0.0287***	0.0289***	0.0287***	0.0288***
	(0.0014)	(0.0014)	(0.0014)	(0.0014)
Tenure²	−0.0010***	−0.0010***	−0.0010***	−0.0010***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
City/city group indicators	Yes	Yes	Yes	Yes
2-digit occupation & sector indicators	Yes	Yes	Yes	Yes
Worker fixed effects	Yes	Yes	Yes	Yes
Observations	46,833	46,833	46,833	46,833
R²	0.2671	0.2583	0.2672	0.2584

	Log earnings
	(1)	(2)	(3)	(4)
Big-city experience	0.0153***	0.0152***	0.0154***	0.0151***
	(0.0025)	(0.0025)	(0.0025)	(0.0025)
Big-city exp. × experience	−0.0004***	−0.0004***	−0.0004***	−0.0004***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
Big-city exp. × worker fixed-effect	0.0118**	0.0128**
	(0.0052)	(0.0053)
Big-city exp. × ability		0.0068*		0.0078**
		(0.0036)		(0.0036)
Big-city exp. × self-confidence		−0.0041		−0.0051
		(0.0034)		(0.0034)
Experience	0.0289***	0.0271***	0.0290***	0.0273***
	(0.0018)	(0.0018)	(0.0018)	(0.0018)
Experience²	−0.0004***	−0.0003***	−0.0004***	−0.0003***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
Experience × worker fixed-effect	0.0633***		0.0640***
	(0.0079)		(0.0081)
Experience² × worker fixed-effect	−0.0011***		−0.0012***
	(0.0003)		(0.0003)
Experience × ability		0.0314***		0.0309***
		(0.0050)		(0.0050)
Experience² × ability		−0.0005***		−0.0005***
		(0.0002)		(0.0002)
Experience × self-confidence			−0.0026	0.0025
			(0.0048)	(0.0047)
Experience² × self-confidence			0.0001	0.0000
			(0.0002)	(0.0002)
Tenure	0.0287***	0.0289***	0.0287***	0.0288***
	(0.0014)	(0.0014)	(0.0014)	(0.0014)
Tenure²	−0.0010***	−0.0010***	−0.0010***	−0.0010***
	(0.0001)	(0.0001)	(0.0001)	(0.0001)
City/city group indicators	Yes	Yes	Yes	Yes
2-digit occupation & sector indicators	Yes	Yes	Yes	Yes
Worker fixed effects	Yes	Yes	Yes	Yes
Observations	46,833	46,833	46,833	46,833
R²	0.2671	0.2583	0.2672	0.2584

Furthermore, the significant interaction between big-city experience and worker fixed effects is evidence of a positive complementarity between ability and the long-term benefits of acquiring work experience in a big city. In column (1), we use worker fixed effects to proxy ability, directly following De la Roca and Puga (2017). Since the NLSY79 includes the AFQT percentile score as a measure of general ability, which we have been using so far, column (2) provides an alternative version of column (1) measuring ability with the AFQT score instead. The same results remain, although they are less salient than when using worker fixed effects.

The critical question is whether self-confidence, like ability, has a higher return in big cities. To answer this, in columns (3) and (4), we add to the specifications of columns (1) and (2), respectively, interactions between both experience types and the self-confidence measure. If anything, the small negative point estimate for the interaction between big-city experience and self-confidence suggests that more overconfident workers (higher self-confidence for given ability) may benefit less from big cities, but the coefficient is not statistically significant.

It is worth noting that these results do not imply that high self-confidence is not an attribute rewarded in the job market. If we re-estimate the specification in column (1) of Table 5 dropping worker fixed effects (and interactions with these) and adding the worker’s self-confidence and ability percentiles, then the estimated coefficients of both attributes are positive and significant. The coefficient on the ability percentile is four times larger than the coefficient on the self-confidence percentile (the corresponding table is available in the Online Appendix). What our results indicate is that self-confidence, unlike ability, is not more rewarded in big cities than in small cities. To allow for immediate, and not just gradual, additional returns to these traits in bigger cities, we have re-estimated column (4) of Table 5 including interactions between self-confidence and a big-city indicator and between ability and a big-city indicator. Neither coefficient is statistically significant.

One may also worry that the empirical relationship between self-confidence and living in a big city upon completing education could be driven by other personality traits correlated with self-confidence.²⁰ Since NLSY79 respondents were not administered a personality test, we turn to a related data set, the NLSY79 Children and Young Adults, which surveys all offspring of NLSY79 female respondents. As part of this survey, young adults were administered the Ten Item Personality Inventory test, measuring the big-five personality traits: extraversion, agreeableness, conscientiousness, neuroticism, and openness to experience. In addition, they were also subjected to the same Rosenberg test measuring self-confidence in our main sample and various ability tests, specifically the Peabody International Achievement Test for math, reading recognition, and reading comprehension. Since this data set follows the offspring of women in our primary sample, respondents are much younger, so we can only examine location determinants upon completing education. When we replicate column (1) of Table 3, with and without the big-five personality traits as controls, we find that the coefficient on the self-confidence percentile remains significant and unchanged after controlling for the big-five personality traits (the corresponding table is available in the Online Appendix). The magnitude of this coefficient is similar to the one in Table 3. The effects of the ability percentile in terms of math and reading comprehension are not significant whether or not we control for the big-five personality traits.

A final related concern is that self-confidence may be capturing attitude towards risk, with more self-confident individuals perhaps more willing to take risks. To the extent that locating in a big city may be seen as a risky investment, that association could be driving in part the relationship between self-confidence and junior location in a big city. The NLSY79 includes a measure of attitude towards risk.²¹ Respondents grade their willingness to take risks on a scale from 0 to 10. We use the individual’s percentile in this scale (with a higher percentile associated with a lower willingness to take risks) as a measure of risk aversion. We re-estimate Table 4 controlling for risk aversion (the corresponding table is available in the Online Appendix). Results show that more risk-averse individuals are less prone to migrate across the board. This finding is consistent with earlier research examining the positive association between willingness to take risks and migration (Jaeger et al. 2010; Bauernschuster et al. 2014). Importantly, the effect of ability on the probability of moving from small to big cities rises. Furthermore, self-confidence and ability do not affect the probability of moving from a big city in any direction.

7. Conclusions

Bigger cities offer more valuable experiences and opportunities in exchange for higher housing costs. While higher-ability workers benefit more from bigger cities, they are not more likely to move to one. Our model of urban sorting by workers with heterogeneous self-confidence and ability suggests flawed self-assessment is partly to blame. Workers who misjudge their ability at an early career stage make location decisions they would not have made had they known their actual ability. By the time they learn enough about their actual ability, those early decisions have had a lasting impact, reducing their incentives to move and affecting their lifetime earnings.

Analysis of NLSY79 data shows that, in line with our model predictions, the location choices of young workers are guided by self-confidence rather than ability. Thus, some overconfident young workers start their career in a big city, while they would have chosen a small city with better self-assessment. That initial misjudged decision then becomes self-validating: Having incurred an excessive cost to gain more valuable experience, they find they might at least take advantage of this by remaining in the big city. Analogously, some underconfident young workers spend their whole lives in a small city, even though a correct initial ability assessment would have made them self-select into a big city instead. Workers who severely underestimate their ability may nevertheless relocate from a small to a big city, once labour market experience provides them better information about their true capabilities. Young workers who are confident enough of their abilities locate in bigger cities to pursue their dreams, but those dreams do not come true for everyone.

Appendix A: Endogenising Urban Structure

In the main text, we have determined individual location choices, taking as given the existence of big and small cities. However, city sizes result from the combination of multiple location choices of individuals, and we must make sure there is consistency between individual choices and city sizes. In other words, we must make sure that the equilibrium we have characterised exists. For this reason, we now endogenise the urban structure and solve for the general equilibrium of the model presented in Section 2. We also show that this equilibrium is unique.

Suppose there are two cities, and each is linear and monocentric.²² Land covered by each city is endogenously determined and can be represented by a segment on the positive real line. All workers in a city perform their job at a single point |$x=0$|⁠, the central business district (CBD).

Workers consume housing and a freely tradable numéraire good. For simplicity, let us assume that all residences have the same size, are built under perfect competition with a constant capital to land ratio, and are owned by absentee landlords.²³ Thus, every individual consumes one unit of floorspace built on one unit of land with a fixed amount of capital. The price of capital is constant throughout the economy, while the price of land varies. Commuting costs increase linearly with distance to the CBD so that a worker living at a distance x incurs a commuting cost |$\tau x$|⁠. The total urban costs for a worker located in a residence at a distance x from the CBD of the city i are the sum of her commuting costs |$\tau x$| and her housing costs |$P_i(x)$|⁠:

$$\begin{eqnarray} \gamma _i(x) = \tau x+P_i(x), \;\; i,j \in \lbrace B, S \rbrace . \end{eqnarray}$$

(A.1)

As a result, any resident in a city is willing to bid |$\tau x$| more for a house that is x closer to the CBD. Equilibrium house prices are then such that the decrease in commuting costs incurred as one relocates towards the CBD is exactly offset by an increase in house prices.

Using |$N_i$| to denote the equilibrium population in city i, house prices in city i can then be expressed as

$$\begin{eqnarray} P_{i}(x)=\tau (N_i-x) + \bar{r}\!,\;\;i,j\in \lbrace B,S\rbrace , \end{eqnarray}$$

(A.2)

where the constant |$\bar{r}$| is the sum of the rental cost of the fixed amount of capital used in every residence and the rental price of land in the best non-urban use (e.g. agriculture). A worker living at the edge of a city has to commute a distance equal to the population of the city, thus incurring a commuting cost |$\tau N_i$|⁠, but only pays |$\bar{r}$| for housing. A worker living at the CBD has no cost of commuting but pays an additional |$\tau N_i$| for her house. Substituting equation (A.2) into (A.1) yields urban cost in city i:

$$\begin{eqnarray} \gamma _i=\tau N_i+\bar{r}. \end{eqnarray}$$

(A.3)

To allow for the coexistence of junior and senior workers in a city, consider overlapping generations of workers. Each generation is made up of a continuum of workers of measure 1 and lives for two periods. Thus, workers coexist when junior with senior workers of the previous generation and coexist when senior with junior workers of the next generation. Since our focus is on the steady state, we avoid using a time subscript for our variables.

The total population of city i, |$N_i$|⁠, is the sum of junior and senior workers in the city. Let us denote by n the difference in population between the big and the small city

$$\begin{eqnarray} n \equiv N_B - N_S. \end{eqnarray}$$

(A.4)

Note that |$0\leqslant n\leqslant 2$| holds since, by definition, the big city has a larger population and since the total population in the economy at any point in time is made up of two living generations with unit population mass each. Combining equations (A.3) and (A.4), we can then express the difference in urban costs between B and S, |$\Delta \gamma \equiv \gamma _B-\gamma _S$|⁠, as

$$\begin{eqnarray} \Delta \gamma = \tau n. \end{eqnarray}$$

(A.5)

Taking n as given, each worker can calculate |$\Delta \gamma$| as per equation (A.5). She can then substitute this into equations (2), (3), (7), (8) and (9) to calculate, respectively, |$\alpha _{BS\succ SS}$|⁠, |$\alpha _{BB\succ BS}$|⁠, |$\alpha _{SB\succ SS}$|⁠, |$\alpha _{BB\succ SB}$| and |$\alpha _{BB\succ SS}$|⁠. Given these thresholds, each worker chooses her optimal location as per Proposition 1. An equilibrium arises when adding up how many workers choose to locate in each city yields a difference in population between the two cities equal to n.

Adding |$N_{B}+N_{S}=2$| to equation (A.4) and solving for |$N_{B}$|⁠, we can express population in B in terms of n:

$$\begin{eqnarray} N_B = 1 + \frac{n}{2}. \end{eqnarray}$$

(A.6)

In equilibrium this must equal the total number of junior and senior workers choosing to reside in B, which we will denote by |$b(n)$|⁠. To obtain an expression for |$b(n)$|⁠, we must refer back to Proposition 1. Let us denote by |$f(\sigma ,\alpha )$| the probability density function for the bivariate distribution of ability and self-confidence for workers in the population. Hence, we can write

$$\begin{eqnarray} b(n) = \left\lbrace \begin{array}{@{}l@{\quad }l@{}}\begin{array}{l} {\displaystyle \int \nolimits _{\alpha _{BB\succ SB}(n)}^{1} \!\! \int \nolimits _{0}^{1} \!\!\! f(\sigma , \alpha ) \mathrm{d}\alpha \mathrm{d}\sigma } + {\displaystyle \int \nolimits _{\alpha _{BB\succ SB}(n)}^{1} \! \int \nolimits _{\alpha _{BB\succ BS}(n)}^{\alpha _{SB\succ SS}(n)} f(\sigma , \alpha ) \mathrm{d}\alpha \mathrm{d}\sigma }\\ \quad + {\displaystyle \int \nolimits _{0}^{1} \int \nolimits _{\alpha _{SB\succ SS}(n)}^{1} f(\sigma , \alpha ) \mathrm{d}\alpha \mathrm{d}\sigma }\quad \text{if}\;\; \frac{\Delta e}{\Delta \Omega } < \frac{e_S}{\Omega _B} \end{array}\\ \begin{array}{l} {\displaystyle \int \nolimits _{\alpha _{BB\succ SS}(n)}^{1} \int \nolimits _{0}^{1} f(\sigma , \alpha ) \mathrm{d}\alpha \mathrm{d}\sigma } + {\displaystyle \int \nolimits _{\alpha _{BB\succ SS}(n)}^{1} \int \nolimits _{\alpha _{BB\succ BS}(n)}^{\alpha _{SB\succ SS}(n)} f(\sigma , \alpha ) \mathrm{d}\alpha \mathrm{d}\sigma } \\ \quad + {\displaystyle \int \nolimits _{0}^{1} \int \nolimits _{\alpha _{SB\succ SS}(n)}^{1} f(\sigma , \alpha ) \mathrm{d}\alpha \mathrm{d}\sigma } \quad\text{if}\;\; \frac{e_S}{\Omega _B} \leqslant \frac{\Delta e}{\Delta \Omega } \leqslant \frac{e_B}{\Omega _S} \end{array}\\ \begin{array}{l} {\displaystyle \int \nolimits _{\alpha _{BS\succ SS}(n)}^{1} \int \nolimits _{0}^{1} f(\sigma , \alpha ) \mathrm{d}\alpha \mathrm{d}\sigma } + {\displaystyle \int \nolimits _{\alpha _{BS\succ SS}(n)}^{1} \int \nolimits _{\alpha _{BB\succ BS}(n)}^{\alpha _{SB\succ SS}(n)} f(\sigma , \alpha ) \mathrm{d}\alpha \mathrm{d}\sigma }\\ \quad + {\displaystyle \int \nolimits _{0}^{1} \int \nolimits _{\alpha _{SB\succ SS}(n)}^{1} f(\sigma , \alpha ) \mathrm{d}\alpha \mathrm{d}\sigma } \quad\text{if}\;\; \frac{e_B}{\Omega _S} < \frac{\Delta e}{\Delta \Omega }. \end{array} \end{array}\right. \end{eqnarray}$$

(A.7)

Equation (A.7) can be readily understood by referring back to Proposition 1. For example, the first case (for |$\Delta e / \Delta \Omega < e_S / \Omega _B$|⁠) has three types of workers choosing to locate in B (each type captured by one of the three double integrals for this first case): junior workers with high self-confidence |$\alpha _{BB\succ SB}<\sigma$|⁠; senior workers with intermediate ability |$\alpha _{BB\succ BS}<\alpha \leqslant \alpha _{SB\succ SS}$| who in their junior period located in B due to high self-confidence |$\alpha _{BB\succ SB}<\sigma$|⁠; and senior workers with high ability |$\alpha _{SB\succ SS}<\alpha$|⁠, regardless of their self-confidence.

We can also interpret equation (A.7) in terms of Figure 1. Given the unit population mass of each generation of workers, the number of junior workers who decide to reside in B is given by the fraction of them with self-confidence and ability in rectangles |$BB$| or |$BS$|⁠. The number of senior workers who decide to reside in B is given by the fraction of them with self-confidence and ability in rectangles |$BB$| or |$SB$|⁠.

Proposition A.1.

There exists a unique equilibrium allocation of the population across cities. In equilibrium, both the big and small cities are populated. The difference n in population between the big and small cities decreases with the common commuting cost per unit of distance |$\tau$|⁠, and increases with the additional opportunities |$\Delta \Omega$| and the additional experience |$\Delta e$| provided by the bigger city.

Proof. Define the auxiliary function

$$\begin{eqnarray} \tilde{b}(n)=1+\frac{n}{2}-b(n). \end{eqnarray}$$

(A.8)

This is the difference between the population of B, |$1+n/2$|⁠, and the number of workers who wish to locate in B given that population, |$b(n)$|⁠. The existence and uniqueness of the urban equilibrium can be proven by showing that |$\tilde{b}(n)$| has a single root in the feasible interval |$0\leqslant n\leqslant 2$|⁠.

We begin by showing that |$b(n)$| is a continuous decreasing function of n over the interval [0,2]. Consider the case where |$\Delta e / \Delta \Omega < e_S / \Omega _B$|⁠. By the fundamental theorem of calculus, |$b(n)$| is a continuous function of |$\alpha _{BB\succ SB}(n)$|⁠, |$\alpha _{BB\succ BS}(n)$|⁠, and |$\alpha _{SB\succ SS}(n)$|⁠, which are in turn continuous functions of n. From equation (A.7), by the fundamental theorem of calculus and the chain rule of derivation, its derivative with respect to n can be written

$$\begin{eqnarray} \displaystyle\begin{array}{ll} \left. b^{{\prime }}(n)\right|_{\frac{\Delta e}{\Delta \Omega } < \frac{e_S}{\Omega _B}} =&\displaystyle -{\alpha _{BB\succ SB}^{\prime }(n) \! \int \nolimits _{0}^{1} \! f(\alpha _{BB\succ SB}(n),\alpha ) \mathrm{d}\alpha } \\ &-{\alpha _{BB\succ SB}^{\prime }(n) \int \nolimits _{\alpha _{BB\succ BS}(n)}^{\alpha _{SB\succ SS}(n)} f(\alpha _{BB\succ SB}(n),\alpha )\mathrm{d}\alpha }\\ &-{\alpha _{BB\succ BS}^{^{\prime }}(n) \int \nolimits _{\alpha _{BB\succ SB}(n)}^{1} f(\sigma ,\alpha _{BB\succ BS}(n))\mathrm{d}\sigma } \\ &-{\alpha _{SB\succ SS}^{\prime }(n) \int \nolimits _{0}^{\alpha _{BB\succ SB}(n)} f(\sigma ,\alpha _{SB\succ SS}(n))\mathrm{d}\sigma }, \end{array} \end{eqnarray}$$

(A.9)

which is negative given that |$\alpha _{BB\succ SB}^{\prime }(n)>0$|⁠, |$\alpha _{BB\succ BS}^{\prime }(n)>0$| and |$\alpha _{SB\succ SS}^{^{\prime }}(n)>0$|⁠. It can be shown analogously that |$b(n)$| is a continuous decreasing function of n over the interval [0,2] when |$e_S / \Omega _B \leqslant \Delta e / \Delta \Omega \leqslant e_B / \Omega _S$| and when |$e_B / \Omega _S < \Delta e / \Delta \Omega$|⁠.

Since |$1+n/2$| is a continuous increasing function of n and |$b(n)$| is a continuous decreasing function of n over the interval [0,2], it follows that |$\tilde{b}(n)=1+n/2-b(n)$| is a continuous increasing function of n over this interval.

By equation (A.5), |$n=0$| implies |$\Delta \gamma =0$|⁠; which in turn, by equations (2), (3), (7), (8), and (9), implies |$\alpha _{BS\succ SS} = \alpha _{BB\succ BS} = \alpha _{SB\succ SS} = \alpha _{BB\succ SB} = \alpha _{BB\succ SS} = 0$|⁠; and substituting these into equation (A.7) yields |$b(0)=2$|⁠; which, by equation (A.8), implies |$\tilde{b}(0)=-1$|⁠. Moreover, since |$1+n/2$| takes value 2 for |$n=2$|⁠, and since |$b(n)$| is decreasing in n over the interval [0,2] starting from the value |$b(0)=2$|⁠, it follows that |$\tilde{b}(2)>0$|⁠.

Since |$\tilde{b}(n)$| is a continuous function of n over the interval [0,2], |$\tilde{b}(0)<0$|⁠, and |$\tilde{b}(2)>0$|⁠, by Bolzano’s theorem, there exists at least one value of |$n\in (0,2)$| such that |$\tilde{b}(n)=0$|⁠. This proofs that an urban equilibrium exists. In addition, both the big and small cities are populated in equilibrium (i.e. the equilibrium value of n satisfies |$0<n<2$| with strict inequality). The urban equilibrium is also unique. Suppose on the contrary that there were two or more values of n in (0,2) such that |$\tilde{b}(n)=0$|⁠. Then, by Rolle’s theorem, there would have to be some n in this interval such that |$\tilde{b}^{\prime }(n)=0$|⁠, which contradicts our previous result that |$\tilde{b}^{\prime }(n)>0$| over the interval [0,2].

Turning to comparative statics, totally differentiating the equilibrium condition |$\tilde{b}(n)=1+n/2-b(n)=0$| and solving for |${\mathrm{d}}n / {\mathrm{d}}\tau$| yields

$$\begin{eqnarray} \frac{{\mathrm{d}}n}{{\mathrm{d}}\tau }=\frac{\frac{{\mathrm{d}}b(n)}{{\mathrm{d}}\tau }}{\tilde{b}^{\prime }(n)}. \end{eqnarray}$$

(A.10)

Since |$\tau$| and n always enter |$b(n)$| together as a product (because |$\Delta \gamma$| enters every threshold level of |$\alpha$| and, by equation (A.5), |$\Delta \gamma =\tau n$|⁠), it follows that |$\mathrm{d}b(n) / \mathrm{d}\tau =b^{\prime }(n)$|⁠, and we have already shown that |$b^{\prime }(n)<0$|⁠. We have also shown that |$\tilde{b}^{\prime }(n)>0$|⁠. Hence, we can sign equation (A.10): |$\mathrm{d}n / \mathrm{d}\tau < 0$|⁠. The comparative statics |$\mathrm{d}n / \mathrm{d}\Delta \Omega > 0$| and |$\mathrm{d}n / \mathrm{d}\Delta e > 0$| can be proven analogously.

When deciding whether to locate in B, junior workers trade off the greater experience they will acquire by locating there against the higher urban costs they need to incur. Senior workers trade off the greater opportunities B provides to use their previously acquired experience against its higher urban costs. In equilibrium, some workers strictly prefer to locate in B and others strictly prefer to locate in S. Individual choices depend on self-confidence and ability, on common parameters capturing the magnitude of the advantages and disadvantages of locating in the big city, and on the choices of all other workers.

In equilibrium, the difference in population n between B and S is such that the difference between the mass of workers who prefer to locate in B and the mass of workers who prefer to locate in S aggregates up to precisely n. Off-equilibrium, the mass of workers who given n prefer B to S may aggregate up to more than n, but then as more workers locate in B and fewer in S commuting and housing costs increase in B relative to S until an equilibrium is restored. And conversely, the reverse adjustment occurs if the mass of workers who given n prefer B to S aggregates up to less than n.

The comparative statics for equilibrium differences in city sizes are fairly intuitive. A higher cost of commuting per unit of distance (⁠|$\tau$|⁠) implies a larger gap in urban costs for any given difference in population between B and S, and so results in a smaller equilibrium difference in population sizes (n). The greater the additional opportunities (⁠|$\Delta \Omega$|⁠) and the additional experience (⁠|$\Delta e$|⁠) provided by B, the more attractive is B relative to S, so a higher difference in population (n) is needed to balance things out in equilibrium.

Appendix B: Alternative Equilibrium Location Choices by Self-Confidence and Ability

Figure 1 in the main text describes location choices under parameter values such that |$e_S / \Omega _{B} \leqslant \Delta e / \Delta \Omega \leqslant e_B / \Omega _{S}$| so that, according to Proposition 1, low self-confidence is defined as |$\sigma \leqslant \alpha _{BB\succ SS}$| and a worker never selects trajectories |$(B,\, S)$| and |$(S,\, B)$| ex ante based on her self-assessed ability, but she might still end up following them ex post if her initial self-assessment turned out to be wrong. Panels (a) and (b) of Figure B.1 describe the only two alternative possibilities.²⁴

Figure B.1.

Alternative equilibrium location choices by self-confidence and ability.

Panel (a) of Figure B.1 describes location choices under parameter values such that |$\Delta e / \Delta \Omega < e_S / \Omega _{B}$|⁠. As before, junior workers locate in S if they have low self-confidence and locate in B if they have high self-confidence, although low self-confidence is now defined by Proposition 1 as |$\sigma \leqslant \alpha _{BB\succ SB}$|⁠. When senior, workers locate in S if either they have low ability or they have intermediate ability and did not locate in the big city during their junior period; they locate in B if either they have high ability or they have intermediate ability and located in the big city during their junior period. The main difference is that some junior workers now choose trajectory |$(S,\, B)$| ex ante. We can see this from the fact that the diagonal (corresponding to perfectly accurate self-assessment |$\sigma =\alpha$|⁠) crosses through the area marked |$SB$|⁠.

Analogously, panel (b) of Figure B.1 depicts the case arising for parameter values |$e_B / \Omega _{S} < \Delta e / \Delta \Omega$|⁠. The same general results of Proposition 1 hold, although low self-confidence is now defined as |$\sigma \leqslant \alpha _{BS\succ SS}$|⁠. The main difference is that some junior workers now choose trajectory |$(B,\, S)$| ex ante. We can see this from the fact that the diagonal crosses through the area marked |$BS$|⁠.

Acknowledgments

We are grateful to Costas Arkolakis, Nathaniel Baum-Snow, Sanghoon Lee, and Jesse Shapiro for very helpful discussions and to Steve Gibbons, Pedro Mira, Theodore Papageorgiou, Frank Pisch, Steve Pischke, Anatoli Segura, Olmo Silva, seminar participants at the LSE, CEMFI, and the NBER Summer Institute, the editor, and two anonymous referees for comments and suggestions. Puga acknowledges funding from the European Research Council under the European Union’s Seventh Research Framework Programme (ERC Advanced Grant agreement 269868—SPYKES) and Horizon 2020 Programme (ERC Advanced Grant agreement 695107—DYNURBAN) and from Spain’s State Research Agency (grants ECO2013-41755-P and ECO2016-80411-P). De la Roca acknowledges funding from Spain’s State Research Agency (MDM-2016-0684) under the María de Maeztu Units of Excellence Programme. Ottaviano is also affiliated with Baffi Carefin, IGIER, CEP, and CEPR and Puga with CEPR. The data (except for the restricted-access NLSY79 geocode data) and replication files for this paper are available at https://diegopuga.org/data/dreams/. The Online Appendix can be found at https://diegopuga.org/research.html#dreams.

Notes

The editor in charge of this paper was Guido Lorenzoni.

Footnotes

An exception is Bacolod, Blum, and Strange (2009). They show that workers with stronger cognitive and people skills (as inferred from occupations and the skills related to them in the Dictionary of Occupational Titles) are more highly rewarded in bigger cities, while those with greater motor skills and physical strength are not.

We arbitrarily break ties between location trajectories in favour of the small city, hence the strong inequality |$U_{BS}(\sigma )>U_{SS}(\sigma )$| and the weak inequality |$U_{BS}(\sigma ) \geqslant U_{BB}(\sigma )$|⁠.

There are only two other possibilities, as per Proposition 1. If |$\Delta e / \Delta \Omega < e_S / \Omega _B$|⁠, then even some workers who assess their ability accurately relocate from S to B when senior. If |$e_B / \Omega _S < \Delta e / \Delta \Omega$|⁠, then even some workers who assess their ability accurately relocate from B to S when senior. We show versions of the figure for such parameter values in Appendix B; the degree of comparative advantage in experience or opportunities for big cities is the only key difference between them. We plot Figure 1 using |$e_B = 0.50$|⁠, |$e_S = 0.24$|⁠, |$\Omega _B = 0.70$|⁠, |$\Omega _S = 0.04$|⁠, |$\pi _2 = 2.75$|⁠, and |$\Delta \gamma = 0.30$|⁠.

The initial NLSY79 sample consisted of a cross-sectional sample of 6,111 respondents selected to represent the non-institutionalised civilian population of the US in 1979 and born between 1 January 1957 and 31 December 1964. The survey included two supplementary samples: one of 5,295 civilian Hispanics, Blacks, and economically disadvantaged non-Black/non-Hispanic respondents of the same ages, and another one of 1,280 individuals selected to represent the population serving in a branch of the US military who were born between 1 January 1957 and 31 December 1961 (Cooksey 2018). Both supplemental samples, in addition to lacking the representativeness of the cross-sectional sample, suffered collective attrition events in 1984 and 1990 due to budget constraints that prevent us from tracking individuals in these samples for a long-enough period. We thus restrict our analysis to the cross-sectional sample.

We are grateful to referee 2 for making this helpful suggestion.

Since the NLSY79 became biennial after 1994, for some individuals there is no interview 10 years after their junior period and we must use the preceding or subsequent year.

Other studies dealing with urban sorting classify cities as big when their population is above a threshold that typically ranges between 1.5 million (Baum-Snow and Pavan 2012) and 2.5 million (Eeckhout, Pinheiro, and Schmidheiny 2014). The effects of self-confidence and ability are virtually identical to those we report in the tables below when we define big cities as those that exceed 1.5 and 2.5 million instead of 2 million in 2010.

When measuring localisation, the relevant benchmark is not a uniform distribution, but the distribution that would arise under random location choices (see e.g. Ellison and Glaeser 1997). Thus, we measure the prevalence of each location trajectory relative to a random-location benchmark where each individual follows each location trajectory with the same probability as the share of that trajectory in the aggregate population regardless of ability and self-confidence.

10.

We are grateful to Jesse Shapiro, our discussant at the NBER Summer Institute, for suggesting this additional panel.

11.

The other two possible parameter ranges are |$\Delta e / \Delta \Omega < e_S / \Omega _B$| and |$e_B / \Omega _S < \Delta e / \Delta \Omega$|⁠, as we saw in Proposition 1. These can be analysed analogously.

12.

We subtract 1 from the estimated coefficient for the ability percentile and multiply the difference by the variable’s standard deviation: |$(1.0067-1)\times 28.87 = 0.193$|⁠.

13.

The calculation is |$(1.0048-1)\times 28.89 = 0.139$| for a one standard deviation increase in self-confidence and |$(1.0049-1)\times 28.87 = 0.141$| for a one standard deviation increase in ability.

14.

Location at age 14 is reasonably exogenous to individuals as it reflects earlier parental location choices. In Table 2, 33.6% of individuals move between both periods, while only 13.4% change city-size class (i.e. SB or BS).

15.

In particular, we let the dependent variable takes value 1 if the individual who grew up in a small city resides in a different city in the junior period, provided this new city has a larger population than where the individual grew up and has at least 1 million people. It takes value 0 when the individual who grew up in a small city resides in an even smaller city or a bigger city with less than 1 million people.

16.

Our dependent variable takes value 1 if the individual who grew up in a big city resides in a different city in the junior period, as long as this new city has a smaller population than where the individual grew up and has at most 5 million people. It takes value 0 when the individual who grew up in a big city resides in an even bigger city or a smaller city that exceeds 5 million people. Nine metropolitan areas exceeded 5 million people in 2010: New York, Los Angeles, Chicago, Dallas, Philadelphia, Houston, Washington DC, Miami, and Atlanta.

17.

The term competing risks derives from the fact that the individual can exit the current location through several alternatives, each involving a move to a different city-size class. See van den Berg (2001) and Bover and Gómez (2004). We focus only on first-time moves, and thus, an individual can move at most once and then drop from the population at risk of migrating for the first time. We can estimate our competing risks (or multiple-exit) discrete duration model using conditional hazard rates or a multinomial logit. In the former, for an individual living in a small city, we would model the probability of moving to a big city at a time t conditional on not having done so before and on not having moved to another small city either. In the latter, we would model the probability of either moving to a small city or moving to a big city at a time t conditional on not having done either before. Bover and Gómez (2004) show that if the transition intensities are multinomial logit, then the conditional exit rates are binary logit with the same parameters. We estimate a multinomial logit by joint maximum likelihood as it is asymptotically more efficient.

18.

The effect of self-confidence is marginally significant for relocations to other big cities. However, in robustness estimations described below, we show the weak effect disappears when controlling for other mobility drivers such as risk aversion, while the effect of ability in column (1b) remains large and highly significant. Moreover, the effect of self-confidence is not robust to alternative thresholds for defining big cities (e.g. 1.5 million or 2.5 million).

19.

We include a separate indicator for every CBSA with a population greater than 2,000,000 in 2010. For CBSAs with smaller populations, we group them in intervals of 100,000 people for population sizes between 1,000,000 and 2,000,000; in intervals of 50,000 people for population sizes between 500,000 and 1,000,000; in intervals of 25,000 people for population sizes between 100,000 and 5,000; and finally, group all with a population below 100,000, and include an indicator for each group.

20.

For example, high self-confidence tends to be positively related to extraversion (Robins et al. 2001) and extravert individuals may be more likely to choose dense locations ((Francis and Rutledge 2004) and (Jones et al., 2013), suggest this pattern based on data for doctors and clergy).

21.

Unfortunately, this risk measure was collected recently in 2010, whereas our measures of ability and self-confidence were collected at the beginning of the survey, when most respondents were teenagers. This is not ideal, since the measure may be affected by the consequences of earlier location choices, and also leads to a large drop in the number of observations. For these reasons, we do not use this as our baseline specification.

22.

We develop a highly simplified version of the monocentric city model (Alonso 1964; Mills 1967; Muth 1969). For more general versions of the monocentric city model, see Brueckner (1987) and Duranton and Puga (2015).

23.

Having instead common ownership of the housing stock by local residents yields essentially the same results. One simply gets |$\gamma _i=\tau N_i / 2$| instead of |$\gamma _i=\tau N_i$| in equation (A.3).

24.

Panel (a) is plotted for |$e_B = 0.40$|⁠, |$e_S = 0.24$|⁠, |$\Omega _B = 0.95$|⁠, |$\Omega _S = 0.21$|⁠, |$\pi _2 = 3.08$|⁠, and |$\Delta \gamma = 0.30$|⁠. Panel (b) is plotted for |$e_B = 0.80$|⁠, |$e_S = 0.70$|⁠, |$\Omega _B = 0.50$|⁠, |$\Omega _S = 0.45$|⁠, |$\pi _2 = 10.80$|⁠, and |$\Delta \gamma = 0.30$|⁠.

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