Abstract
I analyze the intrahousehold allocation of resources among nineteenth-century industrial families. The narrative record and economic theory suggest that we should find allocation differences by gender. Using a large survey of industrial households in the late nineteenth century, I find no evidence of gender bias in household allocations to children, nor can I reject the hypothesis that allocations were efficient. These findings cannot be explained by parental egalitarianism. I find that parents were strategic out of necessity—the future cooperation of children was unknown and highly uncertain, tempering any desire for gender bias in household allocations. Narrative and quantitative evidence supports this conclusion.
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Notes
- 1.
This is not a causal claim—there is an obvious endogeneity between the labor supply of household members and total household income.
- 2.
He reported that “The reason for this pitifully insufficient diet is well expressed by Mrs. Van Vorst in describing
her own experience as a working woman: ‘I am beginning to understand why the meager lunches of preserves, sandwiches, and pickles more than satisfy the girls whom I was prepared to accuse of spending their money on gewgaws rather than on nourishment. It is a fatigue that steals the appetite. I can hardly taste what I put in my mouth; the food sticks in my throat. I do not want wholesome food…’” (Streightoff 1911, p. 91).
- 3.
There is further narrative evidence to support such claims. Glenn (1990) notes that “So important were a daughter’s wages to the family that in some instances her marriage would be postponed until another child could earn enough to replace her…The economic needs and priorities of immigrant families frequently required daughters to drop out of school in order to become wage earners” (Glenn 1990, pp. 84–86).
- 4.
- 5.
One woman described her working conditions as a weaver in the following way: “When I came in 1900, we worked from six in the morning till six at night. I worked solid…Even on the weekends I worked… It wasn’t long till I did see where I was wrong. It was drudgery there; of course, it paid well, but it’s regular drudgery” (Hareven and Langenbach 1978, pp. 44–48).
- 6.
The discussion that follows borrows from Deaton (1997).
- 7.
With prices and public goods, the demand function would be
\( {q}_k={g}_k^i\left[{\theta}^i\left(p,{p}_{\varpi },y,{y}^i,{y}^j\right),{p}^i,\varpi \right]+{g}_k^j\left[\left(y-{\theta}^i\left(p,{p}_{\pi },y,{y}^i,{y}^j\right)-{p}_{\pi}\varpi \right),{p}^j,\varpi \right]. \)
- 8.
- 9.
Equation 11.6 is a direct result of the efficiency assumption. See Browning et al. (1994) for the proof of the existence of the sharing rule. Some researchers have used public goods when performing the test, but Blundell et al. (2005) note that such tests fail to take account of the fact that the model only yields predictions for the allocations to private goods, whose allocation is decided conditional on the public goods allocation.
- 10.
In practice, it is usually easier to argue that some goods are consumed only by parents than only by one adult in the household. Since the grouping here is between parents and children, I leave aside the issue of which of the parents consumes which adult items more than the other.
- 11.
As Deaton (1997) notes, the “transformation of expenditures to budget shares and of total outlay to its logarithm induces an approximate normality in the joint density of the transformed variables, so that the regression function is approximately normal” (p. 231). This joint normality justifies the use of OLS. Horrell and Oxley (1999) use a similar econometric strategy to test for gender discrimination among the British households in the 1888CEX. Since one potential control variable would be skill level, the results are disaggregated for metalworks and textile families.
- 12.
Another important use of this approach is that it fits quite well with the historical era under consideration. In contemporary populations, it is unwise to think of household composition as exogenous. As Behrman (1997) has correctly noted, these types of regressions may fail to reject the hypothesis of gender equality even when there is substantial evidence that women are mistreated in the home. If parents are taking part in activity which eliminates young women from the household (e.g., sex-selective abortion, infanticide, etc.), the failure to find gender differentials in household allocation is not on a firm footing. Historically, there is no evidence of excess infant female mortality in the late nineteenth century—while household size was determined by the family, composition was not similarly constructed through sex-selective practice. Lifetables from the time suggest that the probabilities of dying in the first year of life were equal, and if anything were higher for boys than girls. For more see the Human Mortality Database (http://www.mortality.org)
- 13.
For more on the historical forces shaping the 1888CEX, see US Department of Labor How American Buying Habits Change (1959).
- 14.
The “other income” category provides very little income, on average less than 2.5% of household income.
- 15.
See Smith (1994) for more on the geographic differences by occupation.
- 16.
I also used savings, savings as a share of total income and expenditure, the share of protein in the diet, and the share of protein from animal sources as potential adult goods. As the results for these goods were the same as the most likely adult goods from the data, these results are not reported.
- 17.
The Wald test statistics for metalworks and textile families are based on regressions on the form listed in Table 11.3. Since I use a robust variance-covariance matrix, the F-test for a set of linear restrictions for the regression is not appropriate. Fortunately, the Wald test (which must be used when employing the Eicker-White variance-covariance matrix) reduces to a standard F-test for my hypotheses. Under the null of gender equality, the Wald statistic has a chi-squared distribution with degrees of freedom equal to the number of linear restrictions imposed by the null hypothesis. Since I test each age category separately, each test has one degree of freedom.
- 18.
One would like to include nonlinear forms of the sharing rule such as those exploited by Browning et al. (1994). The issue for the paper is that there are several demographic categories, and one assumes that they have a linear effect on demand. While one would like to use nonlinear forms, I cannot because symmetry of the Slutsky matrix and the additive structure of the specification require a linear model (see Blundell et al. 2003 for a proof).
Chiappori and Browning, since they restrict their sample to two-adult households, do not have the number of demographic categories I use here, and this allows them to try several alternative specifications without regard to this consideration. I am not able to use nonlinear specifications of the sharing rule without the results being suspect and inconsistent with the theoretical model that they are supposed to correspond to.
- 19.
For child income the sharing rule is \( {\theta}_i={\alpha}_i+\phi \ln {\left({y}_{\textrm{child}}\right)}_i+{\beta}_i\ln \left(\frac{x}{n}\right)+{\eta}_i\ln (n)+\sum \limits_{k=1}^{K-1}{\gamma}_{ik}\left(\frac{n_k}{n}\right)+{\varepsilon}_i \). Also, Wald test results for households where no children worked (N = 4826) are qualitatively similar to those where only children worked. See Appendix B.
- 20.
Since prices are fixed in the cross section, we can ignore them here.
- 21.
Note that these demand equations include the sharing rule as a variable. Also, that identification of the sharing rule itself is actually not a requirement for the test—we could similarly test whether the demand-equation parameters were equal to one another (since they all must equal the ratio from the sharing rule, they therefore must be equal to some constant).
- 22.
In only one instance is the hypothesis of efficiency rejected at the α = 0.001 level. There are alternatives to estimating the variance of the quotient for the demand equation. If ∂qj/∂zC = β and ∂qj/∂y = λ, then by the delta method the variance of β/λ is \( V\left(\beta /\lambda \right)=\frac{\sigma_{\beta}^2}{\lambda^2}-2\left[\frac{\beta {\sigma}_{\beta \lambda}}{\lambda^3}\right]+\frac{\beta^2{\sigma}_{\lambda}^2}{\lambda^4} \). Hypothesis tests with estimates of the standard errors from the demand equations based on the delta method led to failure to reject the hypothesis in all instances.
- 23.
We must be mindful, however, to distinguish between altruism and egalitarianism in this context. In models of parental altruism, altruistic parents seek to ensure that children are equally well off, and this is achieved by allocating more resources to the child with the greater marginal utility of consumption. This supposes, then, that parents would allocate resources differentially to children by type insofar as that type signifies differing marginal utilities of consumption. The empirical test, however, does not look at allocations to children directly, only substitution away from adult consumption. While it could certainly be the case that substitution differentials would be highly correlated with allocation differentials, it need not be the case per se.
- 24.
It is important to note that discounting would matter, but the main point hinges on differences between young men and women. As it is unlikely that parents had different discount factor for the earnings of children of different genders, these are suppressed here.
- 25.
Note that both males and females have different intercepts and coefficients on the age terms, so that the two profiles are allowed to be as independent as possible in this specification. Specifications with age minimums of 9, 10, and 11 were also specified, and the income profiles were robust to the age cutoff. There is little narrative evidence that children below the age of 10 worked outside of the household in the USA at the time, and the vast majority who entered the workforce did so around the age of 12 or shortly thereafter.
- 26.
For a full description of the data, see Goldin (1980).
- 27.
The regression coefficient on sex was −0.003 and the standard error was 0.004. This would imply a small (but statistically insignificant) penalty for females in textiles, which is consistent with the wage profiles from the 1888CEX.
- 28.
An important caveat here is that once the wages were realized and the child chose to stay in the home, consumption could increase, and total household welfare could improve. Parents could not guarantee this, however, because of the inability to form contracts and agreements with children (Becker 1991).
- 29.
- 30.
That is, on average, boys could retain 30% more of their earnings than their sisters, assuming daughters gave all of their income to their parents.
- 31.
“It is the general custom for all boys and girls between 14 and 18 to bring pay envelopes to the mother unopened, and she has the entire disbursement of their wages, giving them from $0.25 to $1. a week spending-money, according to the prosperity of the family. After they are 18, the boys usually pay board of $4.−$8. a week, according to their wages…The girls are not usually boarders until they are over 21, and then they pay from $3. to $6 a week to their mothers. In some cases they continue to give all their wages to their mother, who supports them until they are married” (More 1907, p. 87).
- 32.
“Few Jewish daughters considered their wages their own; rather they understood them to be part of the family fund…And Nettie Licht, who began working as a milliner in 1910, faithfully gave her pay envelope to her parents without even bothering to open it…Many other Jewish daughters did the same: as one 1916 report noted, the majority of women in the New York shirtwaist factories gave their “untouched and unopened” pay envelopes to their parents” (Glenn 1990, p. 84).
- 33.
The coefficient on sex in the retained earning regression is −0.029, with a standard error of 0.114.
- 34.
These women are noted as being “adrift.”
- 35.
This was estimated in two ways. First, I regressed the log of the wage on the contributions to family members, age, and experience. For women at home, the coefficient on contributions was 0.47 (0.03), while for women adrift it was 0.147 (0.03). I also regressed the log of contributions to family members on the log of earnings, age, and experience. These can be interpreted as elasticities, which would estimate for every percent increase in income what portion was contributed to the family. For women at home, the coefficient for the log of earnings was 0.924 (0.033), while for women adrift it was 0.492 (0.117). For women away from home, regressions also included education, board payments, and transportation costs—exclusion of these variables results in lower coefficient estimates for women away from home.
- 36.
- 37.
Calculation of the expenditure equivalent ratios is done by \( {\pi}_{jc}=\frac{\left({\eta}_j-{\beta}_j\right)+{\gamma}_{jc}-{\sum}_k{\gamma}_{jk}\left({n}_k/n\right)}{\beta_j+{w}_j} \), where the means of the budget shares and demographic variables are used. See Deaton (1997) for calculation of the standard errors of expenditure equivalent ratios.
- 38.
One could argue that the efficiency result is due to the sharing rule being “unidentified.” There is nothing in the theory, however, which allows us to distinguish “spurious” estimates of the sharing rule with “minimum variance” estimates. The use of the expenditure equivalent ratios here is a partial solution—if the variances of the sharing rule in Table 5 actually reflect variance in the underlying demand with respect to household composition, then the expenditure equivalent ratios will vary as well.
- 39.
Note that these adult good expenditures are (on average) a small percent of the budget—tripling expenditures on tobacco would still imply that tobacco was less than 5% of the household budget.
- 40.
Horrell and Oxley (1999) use age categories of 0–4, 5–14, 15–54, and 55+. Given the focus on the allocations to young children here, the 5-year categories to the age of 25 are used.
- 41.
It is important to note that the regressions used to estimate the expenditure equivalent ratios are done so with an estimate of \( \hat{\theta} \), so the ratio acts as an additional robustness check of gender neutrality with the inclusion of the sharing rule in the demand equation.
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Appendixes
Appendixes
11.1.1 Appendix A: Reflection on Murray
I first met John at meetings of the Economic History Association as an assistant professor. I had heard about him before then because my colleague Rick Steckel had referred to him often as the best student he had ever had. When I met John, I was struck by his intellect and his kindness, and I always looked forward to seeing him at the EHA or Social Science History Association meetings. When I was visiting at the University of Michigan, John invited me down to Toledo to give a seminar. It was at dinner where we discussed the paper in this volume, and John shared insights from his work that were quite important to how I came to think about this project. To this day, it is the longest dinner I have had after a seminar, and it was because of John’s humor and the amazing conversation we had. John’s recollection of data, conceptual frameworks, and models around the issues of household allocation, children as breadwinners, and the role of social norms and gender in parental decisions was powerful. When John moved to Rhodes, I remember filling him in on the great BBQ places that he could enjoy now that he was in the capital of the industry!
11.1.2 Appendix B: Expenditure Equivalent Ratios
The choice of adult goods and the test of efficiency are subject to numerous criticisms. For example, it is unclear if husband’s and wife’s clothing precludes the clothing expenditures of adult children, who could (presumably) fit and wear their parents’ clothing. Similarly, the efficiency test was not particularly powerful, even in its conservative form, because of the large standard errors of the sharing rule derivative quotient. We would like additional information to strengthen the selection of adult goods and the efficiency results. Fortunately, such information exists. We can estimate expenditure equivalent ratios, which measure the percent change in per capita expenditure that would induce the same increase or decrease in expenditure on a particular adult good as an additional child of a certain age and gender. For example, an expenditure equivalent ratio for alcohol for a female aged 0–4 of −0.32 would tell us that per capita expenditure would have to decrease by 32% to induce the same change in alcohol demand as the presence of a girl aged 0–4 does. More precisely, the expenditure equivalent ratio for good j and demographic category c isFootnote 37
The expenditure equivalent ratio serves two purposes. If good j is an adult good consistent with the definition given earlier, then the expenditure equivalent ratio should be the same for all goods since it measures the derivative of the sharing rule (by Eq. 11.8). If gender equality holds, then the ratios will be equal by gender at particular ages. Variation of expenditure equivalent ratios between different goods would tell us if the variances of the sharing rule were spurious or reflected the true variances in the adult expenditure categories. As such, the ratios not only tell us which goods should be considered adult goods, but they serve as a robustness check on the gender neutrality and efficiency results.Footnote 38
Table A1.1 shows the expenditure equivalent ratios for all households and households in metalworks and textiles separately. While the presence of children generally would result in lower per capita expenditures to achieve the same effect as the presence of a child, this is not always the case. Tobacco and alcohol consumption expenditure equivalent ratios suggest that children have the effect of increasing expenditure on these items, some by significant percentages.Footnote 39 As the table shows, there is marked variation of the expenditure equivalent ratios by goods and even for the same good by different samples. We should expect some variation between individual households and also between households employed in different industries, but it is not clear whether this is “too much” variation. This type of variation by adult good is consistent with other estimates of expenditure equivalent ratios, both contemporary and historical (Deaton 1997; Horrell and Oxley 1999).Footnote 40 Given such marked variation, we should expect the standard error to be large for the sharing rule derivative quotient, as it was in the bootstrapping procedure. Consistent with the gender neutrality finding, the expenditure equivalent ratios are very similar for males and females of the same age group.Footnote 41 Overall, the expenditure equivalent ratios confirm the gender neutrality of allocations and the underlying variability of the sharing rule for specific goods.
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Logan, T. (2022). Family Allocation Strategy in the Late Nineteenth Century. In: Gray, P., Hall, J., Wallis Herndon, R., Silvestre, J. (eds) Standard of Living. Studies in Economic History. Springer, Cham. https://doi.org/10.1007/978-3-031-06477-7_11
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