Less Responsive Now?
Labor Supply Behavior of Married
Norwegian Women: 1995-2015
Andreas Haga Raavand
Thesis submitted for the degree of
Master in Economics
30 credits
Department of Economics
UNIVERSITY OF OSLO
Less Responsive Now?
Labor Supply Behavior of Married Norwegian
Women: 1995-2015
c
2017 Andreas Haga Raavand
Less Responsive Now?
http://www.duo.uio.no/
Abstract
I investigate married women’s labor supply in Norway from 1995 to 2015, by adopting the methodological approach of Blau and Kahn (2007). We know that married females have substantially increased their labor supply over this period, but is this followed by smaller wage responsiveness? Do the wage responsiveness of females converge towards that of males? I find that there has been a substantial decrease in the responsiveness of married women’s labor supply with respect to wage over the past two decades: their own wage elasticity fell by between 0.1 and 0.3 percentage points in the period. The labor supply behavior of married women has now moved relatively close to that of men.
Acknowledgements
I would first like to thank my thesis supervisor Thor Olav Thoresen of the Research Department at Statistics Norway. He came up with the main idea of this thesis, and has provided me with relevant literature and data throughout the process. His office was always open whenever I ran into problems or had questions related to my research. He consistently allowed this paper to be my own work, but steered me in the right the direction whenever he thought I needed it.
I would also like to thank a few of Thor Olav Thoresen’s research fellows at Statistics Norway for invaluable help to deal with econometric issues and to overcome obstacles in Stata: Trine Engh Vattø and Zhiyang Jia. Without their input, the empirical analysis would not have been the same. In addition,
John K. Dagsvik and Odd Erik Nyg˚ard deserve to be mentioned for having
attended the mini-seminar on my preliminary findings, providing advice and inspiration for the remainder of my work.
I would also like to acknowledge Oslo Fiscal Studies – Centre for Public Economics at University of Oslo for having granted me a scholarship.
The work with this thesis was 6 months delayed because I got a serious concussion, and I am very grateful for the patience of my supervisor, friends, family and future employer, as well as the kind understanding and very friendly help to deal with the practical implications of the delay provided by the administration at the Economics Department at University of Oslo.
My fellow students, especially at Statistics Norway, should by no means be left unmentioned. Without you, this year would have been a lot less enjoyable. Thank you for the friendliness, the workouts, the economic discussions and for occasionally having laughed at my jokes. You know who you are.
Finally, I must express my very profound gratitude to my family and friends and to my boyfriend for providing me with unfailing support and continuous encouragement throughout my years of study and through the process of researching and writing this thesis. This accomplishment would not have been possible without them. Thank you!
I am alone responsible for any inaccuracies or errors in the thesis. Most of the estimations and preparation of the data has been done in Stata, and the codes can be made available upon request.
Oslo, 11 December 2017
Contents
Abstract i
Acknowledgements iii
1 Introduction 1
2 Theoretical Background 3
2.1 The Standard Textbook Model . . . 3
2.2 Further Definition of the Labor Supply Elasticity . . . 10
3 A Brief Survey of the Labor Supply Literature 13
4 Why May Elasticities Vary Over Time? 19
5 Estimation of Labor Supply Elasticities 23
5.1 Empirical Model . . . 24
5.2 Data and Descriptive Patterns . . . 27
5.3 The Measurement of Wage and Other Econometric Issues . . . 32
5.4 Estimation Results . . . 37
5.5 Sensitivity Checks . . . 40
5.6 Explaining the Changes . . . 45
6 Conclusion 48
References 51
A Appendix A: Estimation Results Using Wage Measure A) 57
B Appendix B: Estimation Results Using Wage Measure B) 65
List of Tables
1 Norway: Labor Supply Elasticites for Married or Coupled females 18
A.1 Wage Regression A) with Heckman Selection Correction (MLE)
- Valid Wage 110 - 2500 NOK . . . 58
A.2 OLS Labor Supply Estimates for Married Women, Using Wage Measure A) (Dependent Variable Is Annual Hours, including
Zeros) . . . 59
A.3 Selected Results for Married Women by Subgroups, Using
Impute Wages for Everyone . . . 60
A.4 Selected Results for Women with Marriage Selection
Correc-tions, Using Imputed Wages for Everyone . . . 61
A.5 Estimation Results for Adjustment along the Extensive and
Intensive Margin . . . 62
A.6 Predicted Changes in Married Women’s Unconditional Annual
Work Hours, 1995-2015 . . . 63
A.7 Equation (2): OLS Labor Supply Estimates for Married Women, Using Wage Measure A) (Dependent Variable Is Annual Hours,
including Zeros) . . . 64
B.1 Wage Regression B) with Heckman Selection Correction (MLE)
- Valid Wage 110 - 2500 NOK . . . 66
B.2 Instrumental Variables Labor Supply Estimates for Married Women, Using Wage Measure B) (Dependent Variable Is
An-nual Hours, including Zeros) . . . 67
B.3 Selected Instrumental Variables Results for Married Women
by Subgroups . . . 68
B.5 Estimation Results for Adjustment along the Extensive and
Intensive Margin . . . 70
B.6 Predicted Changes in Married Women’s Unconditional Annual
Work Hours, 1995-2015 . . . 71
B.7 Equation (2): Instrumental Variables Labor Supply Estimates for Married Women, Using Wage Measure B) (Dependent
Variable Is Annual Hours, including Zeros) . . . 72
C.1 Means for Groups by Work Hours per Week, Married Women
Age 25-54 . . . 74
C.2 Selected Descriptive Statistics for the Full Sample . . . 75
C.3 Mean Values of Selected Explanatory Variables, Estimation
1
Introduction
Wage elasticities are often used to inform about individuals’ responsiveness, which is of key importance for policy analysis, i.e., in the assessment if tax-benefit policy changes. But it is fair to say that estimates of the responsiveness differ widely, both internationally and within the same country. Despite this, there seem to be some regularities. One of them is that married females seem to show falling responsiveness over time. For example, Blau and Kahn (2007) and Heim (2007) both show that in the US the own-wage labor supply elasticities of married women have declined by about 50-60 percent from around 1980 to the turn of the century. At the same time, the corresponding elasticities of married men have remained small and relatively stable, suggesting a convergence of married women’s labor supply behavior towards that of married men.
Do we see a similar movement in Norway? This is the main question I raise in this study. I investigate this by using Labor Force Survey (data) from 1995-2015 for work hours and combine this with register-based income data and use cross-sectional wage variations to estimate labor supply responses for married women over time. Both Heim (2007) and Blau and Kahn (2007) use reduced form labor supply functions to uncover trends in the responsiveness. Blau and Kahn (2007) look at cross-sectional data from the March Current Population Survey (CPS) for 1980, 1990 and 2000. Largely adopting their econometric framework, I estimate the responsiveness for the years 1995, 2000, 2005, 2010 and 2015. My conclusion is that a clear downward trend in the responsiveness of married women is present in Norway too.
There are several challenges in the identification of response. The mea-surement of wage is a prime concern. I, therefore, run all regressions with two different measures of wage, and I argue that the actual labor supply elasticity
lie somewhere in between the two point estimates I obtain, but probably closer to the higher estimate. I find that the own wage elasticity of married women in Norway fell from the range of 0.16 - 0.47 in 1995 to -0.08 - 0.33 in
2015, using the richest model specifications.1 This downward trend seems to
be robust across my sensitivity checks, and separate regressions by subgroups of married women suggest that it is mostly the lower educated and the higher range of the age group that drives this trend. It is not clear to what extent the participation elasticities have changed over the period, but the elasticities conditional on working have converged towards zero.
In Norway, as in most other developed economies, the female labor supply has increased substantially over the past decades. A larger share of women are participating in the labor market, and they tend to work longer hours on average. This is a wanted change, and partly a result of policy reforms aimed at making women work more. These reforms include improved childcare outside of the home at lower cost, which reduces the fixed costs of entering the labor market for women. The pecuniary incentives to work have improved as real wages have increased both for men and women, and as the tax system has changed towards lower marginal rates on labor income. Of course, the preference for work may also have changed. All of these factors would suggest reduced responsiveness and thus give support for my findings.
In section 2, I will present the standard textbook model of labor supply, as the intuition behind it is essential to understand the changes in labor supply behavior and define the labor supply elasticities. Section 3 contains a short literature survey, with a particular focus on response estimates of married females. In section 4, I consider why the labor supply responses might vary
1Using the least rich model specification the corresponding figures are 0.37 - 0.87 and
over time. My estimations have been done in Stata. A presentation of the empirical model and the estimation results are described in detail in section 5. I conclude in section 6.
2
Theoretical Background
The labor market is a key component of the economy. In this paper, the goal is to identify some of the primary forces that drive individuals’ behavior in the labor market, focusing on married women. More specifically, I set out to quantify the relationship between wages and other income and labor supply and to infer what implications this might have in a macroeconomic perspective. In this section, I give a relatively short and simple introduction to a standard textbook theory of labor supply theory. This is a model for individual labor supply decisions, but it can easily be extended to account for labor supply decisions within a family context as well. After that, in section 3, I will give a brief overview of some of the most relevant recent research on female labor supply, to place this study within a context.
2.1
The Standard Textbook Model
A version of the following standard labor supply model can be found in most textbooks on labor economics, such as Pencavel (1986), Killingsworth and Heckman (1986), Atkinson (1993) and Borjas (2016). The model may be seen as rather simple in that agents derive utility from consuming only goods and leisure, assuming that they have the following utility function:
U =f(C, L)
This function transforms consumption and leisure into an index U that
the more satisfied the person. We assume that increasing the amount of either
C, consumption, orL, leisure, or both will increase the agent’s utility. There
is a range of different combinations of C andL that yield the same level of
utility. If depicted in a diagram with the quantity of C andL on each of the
axes, the locus of these points forms indifference curves, with the following properties:
1. Indifference curves are downward sloping.
2. Higher indifference curves indicate higher levels of utility.
3. Indifference curves do not intersect.
4. Indifference curves are convex to the origin.
The absolute value of the slope of the indifference curves will equal the ratio of
marginal utility betweenC andL, also called themarginal rate of substitution
(MRS) in consumption. Property number 4 is equivalent to assuming that
the marginal rate of substitution is diminishing.
The agent’s consumption of goods and leisure is constrained by time and income. We assume that one part of the income is independent of how much
the agent works, and denote this income V. Leth denote the number of hours
the agent will work and let wbe the hourly wage rate. If we ignore any stock
of wealth, the agent’s value of consumption of goods (C) must equal the sum
of labor earnings (wh) and nonwage income (V):
C=wh+V
This is the agent’sbudget constraint. For simplicity, we assume that the wage
rate is constant for any given agent, i. e. we abstract from the fact that the marginal wage rate might vary (most realistically both across jobs and across working hours in the same job). The agent can in each period allocate time to either work or leisure, and the sum of time allocated to these two activities
rearrange terms and express the budget constraint in a full income version:
C = (wT +V)−wL
In a diagram with consumption of goods on the y-axis and leisure on the x-axis, the linear budget constraint now forms a boundary for possible consumption bundles of the two goods. The absolute value of the slope of this line equals the wage rate. Any combination on or under his line forms the agent’s opportunity set.
The agent finds his/her optimal work hours by choosing a particular combination of goods and leisure, given the wage rate and the nonwage income. This combination must of course also be attainable, i. e. within the agent’s opportunity set. The optimal solution to the hours of work decision is therefore at the point where the indifference curve is tangent to the budget constraint, see figure 1. Note that in this point, the MRS (the rate at which the agent is willing to give up leisure hours in exchange for additional consumption) is equal to the wage rate (the rate at which the market allows the agent to substitute one hour of leisure time for consumption). Note also
that the solution described above is an interior solution. However, as we will
see shortly, there might also be cases where it is plausible that the solution
to the work hours decision problem is a corner solution.
Let us first have a quick look at what happens when we alter the com-ponents of the labor-leisure problem. We assume that preferences do not
change. First, observe that if V increases, this shifts the budget constraint
upwards without altering the slope. Given our assumption that leisure is a normal good, hours of work will then decrease, as the agent now can afford a higher consumption of both goods and leisure hours. Second, observe that
if instead the wage rate, w, increases, this will make the budget constraint
Figure 1: Interior Solution to the Labor-Leisure Decision.
All points on or under the budget line form the opportunity set. Point A is attainable but not optimal as there are other points on higher indifference curves which are also attainable. Nor is point Y as it is unattainable. Point P is optimal because the indifference curve here is tangent to the budget line.
Co ns um pt io n Hours of Leisure U' U E wT+V T Hours of Work T 0 0 V Budget Line U'' Y A P
the opportunity set. However, the effect on time allocation for work and leisure is ambiguous. On the one hand, the wage increase increases income, and if leisure is a normal good, the isolated effect is a reduction in work hours.
This is called the income effect. On the other hand, the wage increase also
increases the alternative cost of working, thus making leisure more expensive. This reduces the demand for leisure and increases the hours of work. This is
called the substitution effect. Whether an increase in the wage rate leads to
substitution effect dominates, see figure 2. As we shall see in section 3, most studies find that the substitution effect is largest.
Figure 2: Decomposing the Impact of a Wage Increase into Income and Substitution Effects.
An increase in the wage rate generates both income and substitution effects. The income effect (the move from point P to point Q) reduces hours of work; the substitution effect (the move from Q to R) increases hours of work. Here, the substitution effect dominates.
Co ns um pt io n Hours of Leisure U' U R Q P E D D G F T
This simple framework can also be used to analyze simple tax policies, such as flat tax rates (which will alter the slope of the budget constraint) or
lump sum taxes or transfers (which will shift the level of V). The effects of
taxes and considerations of optimal tax policies are one of the key issues in a lot of labor supply research and more realistic tax regimes require more complicated models of labor supply.
Now, let us return to the cases where there might be corner solutions to the
work hours decision problem. If the nonwage income, V, is sufficiently large,
there will be wage rates that are less steep than the slope of the indifference
curve at the endowment point (T, V), point E in figure 1 and 2. In that
case, the agent is better off not working. The slope of indifference in this
curve is called the reservation wage, as it expresses the minimum wage rate
at which an agent is willing to work. In the labor supply literature there is a distinction between effects on the extensive (working or not working) and the intensive (how many hours to work if working) margin; this refers to the extensive margin. The reservation wage depends on the agent’s preferences over consumption of goods and leisure time, and his/herher nonwage income
V. Note that our assumption implies that if V = 0, then no corner solution
is possible.
The relationship between an agent’s wage rate and hours of work that we now have derived is sufficient to derive this agent’s labor supply curve, which is just a representation of her labor supply for any given wage rate. Assuming that the agent has relatively balanced preferences over consumption of goods and leisure time (prefers bundles of fairly equal quantities of the two), it is given that the labor supply curve will be quite steep for low wage rates (above the reservation wage), as the substitution effect dominates. However, as the wage rate increases, the marginal utility of consumption of goods (indirectly the marginal disutility of working) will decrease as hours of work increases, and decrease the importance of the substitution effect. At some point, the income effect might start dominating, and further increases in the wage rate, above this point, leads to a decrease in the labor supply. In this case, the labor supply curve is said to be backward-bending.
is the assumption of no variation in the marginal wage rate. Not only because part-time and full-time jobs might be paid differently, or because overtime workers receive an overtime premium, but also because most developed economies practice labor tax regimes where the tax rate varies with total income. Assuming that agents are rational, it is the net-after-tax marginal wage rate which should determine at what point she maximizes her utility. I will to some degree address this issue towards the end of my analysis, but even when abstracting from this, it is clear that this theoretic framework can yield some very valuable insights about labor supply behavior. Tax on labor will, as long as the substitution effect dominates, reduce the incentives to work. In the case of varying marginal tax rates (proportional taxes), the budget constraint will no longer be a straight line, but rather a piecewise linear constraint (assuming that the tax rate is the same within certain intervals of labor earnings).
Some economists find this model too simple. The criticism is mainly on this model’s lack of ability to take into account dynamic effects, see for
example Keane (2011)2 or Blundell et al. (2007). Another criticism that has
risen in the surge of behavioral economics’ increased popularity is of a more fundamental character, and is true for most ”pure” microeconomic models: As interdependence between agents is probably important, one should seriously question the ”atomistic” assumption in these models.
Blundell et al. (2007) underline a few points that are of particular interest when it comes to the application of the above mentioned relatively simple theoretical framework, in their contribution to the book ”Labor Supply Models:
Unobserved Heterogeneity, Nonparticipation, and Dynamics”: ”Since many
2Keane notes, following Mincer (1962), that ignoring dynamic effects is a more serious
policy proposals involve the reform of highly nonlinear budget constraints and impact decisions that are discrete and cover the whole life-cycle, we argue that a fully specified dynamic structural model is ideal.[...] However, this ideal has a number of practical and theoretical difficulties. In certain situations, the evaluation of existing reforms can be analyzed using much simpler and more robust techniques” (pp 4671). They also note that the simple, static labor supply model is consistent with intertemporal two-stage budgeting in the absence of liquidity constraints or with liquidity constraints that are
unrelated to labor supply, as long asV =C−wh, and that the model can be
interpreted as more general than the two-good framework we have presented might suggest.
I will go more into detail on the specification of the model I am using in section 5.1.
2.2
Further Definition of the Labor Supply Elasticity
Borjas (2016) notes that ”few topics in applied econometrics have been as thoroughly researched as the empirical relationship between hours of work and wages” (pp 45). One of the most used measures to quantify this relationship is the labor supply elasticity and a lot of published work provides estimates of this. The labor supply elasticity is a measure of the responsiveness of work hours to changes in the wage rate (but it can also be to changes in other income variables). The definition of the labor supply elasticity with respect to the wage rate is:
σ = Percent change in hours of work
Percent change in the wage rate =
∆h
∆w ·
w h
It gives the percentage change in work hours associated with a 1 percent change in the wage rate. Thus, if the labor supply curve is upward sloping,
the labor supply elasticity is positive. The labor supply curve is said to be
inelastic if the absolute value of the elasticity is less than one, and elastic if the absolute value is greater than one. This definition of the elasticity is also
known as the Marshallian or the uncompensated labor supply elasticity with
respect to wage. This is again composed of theHicksianor theuncompensated
elasticity (how much the labor supply changes when the wage rate varies if
holding the utility level constant), and the income effect. The relationship
between the Marshallian and the Hicksian elasticity is given by the Slutsky
equation: ∆h ∆w = ∆h ∆w u +h∆h ∆V
which easily can be manipulated to show that he Marshallian elasticity equals the Hicks elasticity plus the income effect:
w h · ∆h ∆w = w h · ∆h ∆w u + wh V V h · ∆h ∆V
As will be clear in the next subsection, there are large variations in the estimated labor supply elasticities in the literature. This is due to several factors. First of all, the labor supply elasticity depends of course on whether one studies the entire population or just subgroups of it. Secondly, the definition of the wage rate greatly matters. The literature is not always informative on whether the labor supply is measured with respect to the gross wage or the net-after-tax wage. In the literature on the elasticity of taxable income (the ETI), see Saez et al. (2012), the focus is on after-tax-effects, i.e., effects of changes in the net-of-tax rate. In a review of recent research on
labor supply elasticities in the US, McClelland and Mok (2012)3 list four
different types of elasticities:
• The participation elasticity: The percentage change in the share of the
population that is working associated with a 1 percent change in wage rates.
• The hour’s elasticity: The percentage change in hours worked associated with a 1 percent change in wage rates among those already working.
• The substitution elasticity: The percentage change in hours worked
associated with a 1 percent change in the marginal wage rate, holding the utility level of the agent constant (same as the Hicksian or compensated elasticity, see above).
• The income elasticity: The percentage change in hours worked associ-ated with a 1 percent change in total income, holding the wage rate
constant.4
However, this list is not exhaustive. In a more recent review of static own wage labor supply estimates in both Europe and the US, Bargain and Peichl
(2016) report uncompensated wage elasticities (total hours and participation
responses - see the definition above) and income elasticities. In dynamic
models of labor supply, theFrisch elasticity, which describes the rate at which
labor supply is substituted between time periods, is also important. 5
A final remark on labor supply elasticities is that when considering es-timates for cohabiting or married couples, the total effect on labor supply
4The income elasticity equalsS/(1−S) times the income effect, where S is the share of
earned income of total income. See for example Keane (2011), pp 967-968, for more details on this relationship.
5Another distinction of elasticities in the literature is whether it is a so-called average
elasticity (the average of the individual elasticities calculated from formulas for expected hours of work or probability of working given the individual observed characteristics) or an aggregated elasticity (the elasticity of the aggregate/average response, e.g., the elasticity of the population mean hours of work) (Dagsvik and Jia, 2016).
depends on whether one considers a change in the parameters (e.g., the wage rate) for everyone, or not. It is rather common that the partner’s/spouse’s wage rate is included in the individual’s labor supply function. The total effect is then composed of the own wage effect and the cross wage effect. In many scenarios the researcher might be interested in the total labor supply elasticity of wage changes, so that the own and cross wage elasticities are combined, and not reported separately.
The exact definition of the elasticities reported in empirical work is often only implicitly stated but is of crucial importance when comparing findings from different analyses. Following the econometric framework of Blau and Kahn (2007), I will report both uncompensated gross own wage elasticities, as well as uncompensated gross cross wage (spouse wage) elasticities and income elasticities for married women. Since I also include those not working in my sample, these elasticities are unconditional (as opposed to elasticities calculated conditional on working), and unless otherwise specified I report aggregated elasticities.
3
A Brief Survey of the Labor Supply
Literature
Recall that the focus of this study is the responses of married women over time, which seem to have declined over time. In the following I will there-fore in particular focus on evidence on response behavior of this subgroup, emphasizing results obtained on Norwegian data.
There are numerous methodological approaches from which one can obtain labor supply elasticities. From a microdata perspective, there is evidence based on estimations of structural labor supply models, both based on discrete
choice models and the so-called Hausmann approach6. The ETI estimates are also based on microdata, often panel data. Also, evidence based on a macro data perspective is to be found in the literature.
Few, if any, topics in the economic literature have been covered as exten-sively as the labor supply. Even the literature of literature surveys on the topic is vast. Although the estimates of labor supply estimates vary a lot, there is a modest consensus about two things: married women have higher own wage elasticities than married men, and the own wage elasticities of married women have declined over time. Given the limited scope of my paper, I will here sum up some of the key findings on labor supply elasticities as in recent surveys, see Blundell and MaCurdy (1999), Keane (2011), McClelland and Mok (2012) and Bargain and Peichl (2016).
McClelland and Mok (2012) sums up the most recent results from American studies, to define a plausible range of the true value of labor supply elasticities. They note that many studies have shifted from measuring labor input using hours as reported in surveys to using income reported on tax returns (ETI estimates) and that researchers, inspired by Feldstein (1995), have used shifts in taxation regimes to isolate the effects of tax changes on labor supply. Thoresen and Vattø (2015) discuss how these measures can be compared.
McClelland and Mok (2012) conclude that the labor supply elasticities of married women have fallen substantially in the period from 1980 to 2011, but is still higher than for married men and single women. The substitution
6In a strict sense, the Hausman approach uses a continuous labor supply model and
proposes a method explicitly to account for that the entire budget-constraint is generated by a nonproportional tax system, and then estimates labor supply parameters using maximum likelihood techniques (Hausman, 1979; Hausman, 1980; Hausman, 1984; Hausman, 1985). However, the literature seems sometimes to use the term also when referring to structural continuous labor supply models in general.
elasticity is in the range from 0.2 to 0.4 and the income elasticity in the range from -0.1 to zero. Married women appear to be more responsive than single men and women along both the extensive and the intensive margin. The hour’s elasticities range from 0.1 to 0.3 and the participation elasticity from zero to 0.3 (see section 2.2 for a definition of these elasticities).
Another interesting point in McClelland and Mok (2012) is that labor supply estimates relying on macroeconomic data, as in Prescott (2004), Davis and Henrekson (2005) and Prescott (2006), rather than microeconomic data, tend to be substantially higher. Davis and Henrekson (2005) explain this by several factors. Macroeconomic studies tend to focus on the intertemporal substitution of labor (which is captured by the Frisch elasticity). Thus, the responses are derived from more sophisticated models which capture a fuller set of response margins.
In a recent survey by Bargain and Peichl (2016), only literature on static labor supply estimates is surveyed. Here, most of the large variation in the magnitude of labor supply elasticity is explained by two factors: methodology and time effects. Variation across countries seems to be much less important. Bargain and Peichl (2016) separate the elasticity estimates derived from continuous choice labor supply models (of the classical Hausman type) and discrete choice models, where the latter is based on random utility modeling
approach (Soest, 1995). Bargain and Peichl (2016) notes that: ”With the
Hausman approach, the combination of restrictive functional form (linear labor supply) and estimation methods that impose theoretical consistency of the labor supply model everywhere in the sample (global satisfaction of the Slutsky conditions) can lead to biased estimates and possibly an overstatement of work incentives.” (pp 20). The results are also highly dependent on the exact specification of the model and how one controls for different issues (such as
non-random selection into marriage), and on whether one includes fixed costs of working or not. As a result, there are large variations in the elasticities, even for comparable time periods, in the literature relying on the Hausman approach. The estimates relying on discrete-choice models have less variation, although there are differences which most likely stems from differences in the selection criteria. Dagsvik et al. (2014) demonstrates however that the labor supply elasticities derived from ”the standard” discrete choice models depends critically on the labor participation rate in the sample, meaning that two samples of different participation rate can yield very different elasticities even for the same model.
When considering estimates for married women over time, and separated (crudely) by continuous and discrete choice models, there is a clear trend in the literature of declining elasticities, both in Europe and in the US. The decline is, however, steeper for continuous choice models, and post 2000 the surveyed elasticities in Bargain and Peichl (2016) are lower for these than for discrete choice models.
In a literature survey by Keane (2011), no married women estimates from static labor supply models are reported at all (Keane also essentially ignores discrete choice labor supply models in this survey). Following Mincer (1962), Keane argues that life-cycle issues are much harder to ignore for females than for males, as non-participation is more of an issue (which over time also brings in aspects such as human capital depreciation, etc.), and that the choice of when and if to have children is more dominating in the case of females. In general, Keane argues that the dynamics if labor supply decisions are of such importance that static models do not yield reliable results of interest.
However, as demonstrated by both Blau and Kahn (2007) and Heim (2007) static models of the Hausman type, even in reduced form specifications, can
yield some very interesting insights. Despite being vulnerable to criticism about their simplicity, this is exactly what makes them suitable to analyze changes over time, as they are rather computationally manageable, even for large data sets of repeated cross-sections. This allows us to consider, with a consistent method, how the elasticities have evolved, although some would probably dispute the quality of the point estimates. Both of these papers find a substantial decrease in the labor supply elasticities for married women in the US. Blau and Kahn (2007) find that the labor supply elasticities with respect to own wages fell by 50-56 percent, whereas Heim (2007) find a decline of 60 percent.
As already noted, country differences do not seem to be a major cause of the differences in labor supply elasticities in the literature. Still, I will in the following examine what others have found these elasticities to be in Norway over the past two decades. Most of the Norwegian estimates of labor supply elasticities are rooted in the Research Department of Statistics Norway and is derived using discrete choice models with random utility. In the surveyed results presented in table 1, the model used in Bhuller et al. (2016) and Aaberge and Colombino (2012) is a refined version of the one in
Aaberge and Colombino (2006)7. Note however that the elasticities from the
two formers are not directly comparable with the other elasticities, as they combine the total effect of both own and cross wage elasticities for women in couples. Also the model used to derive the elasticities in Thoresen and Vattø (2015), Dagsvik and Jia (2016) and Dagsvik et al. (2008) is more or less an extended version of the one in Dagsvik and Strøm (2006). In this approach, jobs are chosen from a pool of latent jobs. A version of this model is part of a model system that Statistics Norway have made available for Norwegian
policy-makers, see Thoresen et al. (2010).
Table 1: Norway: Labor Supply Elasticites for Married or Coupled females
Own wage elasticities
Authors Year (data) Modela Hours (uncond.) Hours (cond) Participation Aaberge and Colombino (2006)b 1994 DC-RU 0.52 0.31 0.21 Dagsvik and Strøm (2006)c 1994 DC-RU 0.65 0.28 Dagsvik et al. (2008)c 1997 DC-RU 0.612 0.279 0.333 Dagsvik and Jia (2016)c 1997 DC-RU 0.618 0.333 Dagsvik and Jia (2016)c 1997 DC-RU 0.405 0.221 Thoresen and Vattø (2015)c 2004 DC-RU 0.38 0.29 0.09 Bhuller and Aaberge (2012a)d, f 2006 DC-RU -0.1 -0.06 -0.04 Bhuller et al. (2016)e, f 2011 DC-RU 0.13 0.05 0.05
aDC-RU denotes Discrete Choice - Random Utility
b1995 Survey of Level of Living, ages 18-54
cLFS, ages 26-62
dMarried couples/cohabitants, non-immigrants, age 22-62
eRegister based data, ages 26-61
fThese elasticities are the combined elasticitites of both own wage and cross wage elasticitites, and are thus not directly
comparable with the others reported. As the cross wage elasticities normally are negative, the own wage elasticities are thus probably higher.
If we restrict our comparison to the estimates derived from the most similar method (thus only comparing Thoresen and Vattø (2015), Dagsvik and Jia (2016), Dagsvik et al. (2008) and Dagsvik and Strøm (2006)), the own wage elasticity of married women has declined from 0.65 in 1994 to 0.38 in 2004. This downward trend is confirmed in Bhuller and Aaberge (2012b), even though this trend is for the combined effect of the own and cross wage elasticities. Also, unpublished estimates from Statistics Norway (2017) show a decline in married women’s labor supply elasticities. I will not go into details on estimates of married men’s elasticities, but these seem to have remained low and stable over the past decades, implying that there has been a convergence of married women’s responsiveness in the labor market towards that of married men. As noted in another literature survey (Evers et al., 2005)
it could be that the labor supply responsiveness of women on the intensive margin is more elastic than for men, thus questioning whether the relatively low male elasticities will ever be achieved for females.
The elasticities presented here do not take into account differences across income groups. Bhuller et al. (2016) find large variations across income deciles of both men and women, where the low deciles have considerably higher responsiveness than the higher deciles.
On this note, I will now turn to some explanations of why the elasticities of married women may vary over time.
4
Why May Elasticities Vary Over Time?
We have now seen that empirical estimations of labor supply elasticities differ considerably in the literature. Some of this is due to methodological differences, but there seems to also be a time effect. The key question is why responses may vary over time. Regarding the labor supply of married women, we saw in the previous section, that their response estimates are higher than for their male counterparts. A first take on the question raised may, therefore, be that females, in line with their labor supply coming close to the labor supply of males, also adopt the behavior of men, i.e., take up their responsiveness.
I will address these issues more in depth in this section by discussing factors that may influence labor supply responsiveness over time. A fundamental distinction is between preferences and constraints, where by the latter I refer to various institutional factors that are different from preferences. However, empirically, it is hard to distinguish between these concepts clearly.
Since the Labor Force Survey (LFS)8 was first conducted in Norway in 1972, the labor market has undergone some striking changes. The first thing to notice is that the labor force as a share of the population in working
age (15 - 74 years old)9 has increased from 61.4 percent in 1972 to 70.6
percent in 2016, peaking at 73.9 percent in 2008. For the prime age group in the labor force (25-54 years old) the increase has been even more evident; the share has increased from 73.0 percent in 1972 to 86.4 percent in 2016. This change is primarily due to the continued increase of female labor force participation throughout the period. In 1972, 52.3 percent of women aged 25-54 participated in the labor force – a figure that had increased to 83.9 percent in 2016. For women aged 15-74, the corresponding numbers were 44.7 and 67.7 percent.
The increase in the female participation rate has come with a moderate decrease in the participation rate of men. The participation rate for working-aged men decreased from 78.1 percent in 1972 to 73.4 in 2016, and in the prime age group the corresponding figures were 93.2 and 88.9 percent, resulting in the gender gap in labor force participation falling from 33.4 to 5.7 percentage points for everyone in working age and from 40.9 to 5.0 percentage points in the prime age group. That is a decline of 83 and 88 percent, respectively.
This pattern is found in several other developed economies and is the consequence of a cultural and societal transformation, in which men’s positions as breadwinners have been weakened over the years. Over the recent decades, we have witnessed a dramatic change in the division of labor in families, moving the housewives from the home to the labor market. Women’s entry into the formal economy has been a major contributing factor to the economic
8See Bø and H˚aland (2015) for additional details on the LFS.
growth and improved standard of living that most developed countries have experienced since World War II.
The first women to enter the labor force and the formal economy were those who were not married. These women were not in a position to bargain for high wages, as the demand for their labor market services was low. As more and more areas of the labor market were opened up to women, women’s wages rose. For married women, however, the alternative to participating in the labor market was to do work within the family. Some of this work is to some degree necessary, such as taking care of infants, cooking, etc., so if the price of these services is higher than what a woman could make by selling her labor services, the alternative cost of working would be too high. The traditional division of labor within the family, where women can substitute between market labor, home production, and leisure, and men between market labor and leisure, thus explains why women were more sensitive to their own wages than were men (Mincer, 1962). Over the past decades female wages has continued to rise, and at the same time, several measures has been taken to reduce the cost of these necessary services for families (such as non-parental childcare reforms, etc.). Some economists argue that as there seems to be a preference for some of these services to be provided for by members of the family, male and female labor are to some extent substitutes, which helps explain why male labor force participation has decreased. However, other empirical findings suggest that in more recent years, male and female labor supply of married couples is to some extent also complementary, see for example Schirle (2008).
These findings thus suggest that one of the reasons why female labor supply elasticities have declined over time is merely a result of the increased labor supply of females. This is shown in Dagsvik et al. (2014) in terms of a
nonlinear model.
Following the reasoning of Goldin (1990), as women also have taken on career jobs, work represents more than just a means to supplement the family income, and we expect that the substitution effect of own wages should de-crease for women. In addition, their cross wage elasticities should also decline in magnitude. Preference shifts are hard to distinguish from other structural shifts, but one may conjecture stronger preferences for market work have developed. However, it is also possible that it is just other factors that have changed the relative prices of market labor, family production, and leisure. The traditional division of labor has to a large extent broken down. The im-portance of the family as a means to against low income has been dramatically reduced, and the institution of marriage has probably changed considerably. Gender equality has made women much more independent, at the same time as the welfare state, especially in Scandinavia, have expanded. Many policy reforms have been aimed at reducing the entry costs of women into the labor market. Goldin (1990) finds that between 1960 and 1980, most of the increase of female labor force participation in the US can be explained by improving labor market opportunities, and only a smaller part by rightward shifts in women’s labor supply functions. The continued improvement of female labor market opportunities can be thought of as more societal preference shifts.
In Norway, as in most other developed economies, the tax system has changed quite a lot over the recent decades. There has been a move towards lower marginal tax rates on labor. This move will rotate the budget constraint outward (make it steeper) and thus stimulate labor supply as long as the substitution effect dominates (ref. section 2.1). The tax system therefore also helps explain why the gross wage labor supply elasticities have decreased. As taxes become a smaller and smaller proportion of the wages, also the after-tax
wage elasticities and the ETI estimates should decline.
However, shifts in preferences are as already mentioned hard to distinguish from institutional and societal shifts and shifts in parameters in the labor supply function. When the relative price of leisure seems to have gone up, this might be because real wage increases have made the opportunity cost of not working higher, but it could also be because we have developed stronger relative preferences for leisure. What certainly is true, however, is that institutional changes, reforms in tax and transfer regimes and an expansion of the child care opportunities might have played important roles in affecting married women’s labor supply responses in Norway over the past decades.
5
Estimation of Labor Supply Elasticities
In the previous section, we saw how recent research on the labor supply of married women leads us to think that there has been a decline in their responsiveness to wages. Although the evidence may point to a similar development in Norway, this has never been systematically verified within a consistent methodological framework. Following the approaches of Heim (2007) and Blau and Kahn (2007), I will use a reduced form labor supply model with a continuous choice of jobs. With reference to the structural labor supply literature this approach shares similarities with the so-called Hausmann approach (Bargain and Peichl, 2016), but is less complicated. The Hausman model is closer to full optimizing behavior. In the following, I shall begin by specifying the empiric model that I have used, before describing my data and the main econometric issues I have dealt with. I then turn to the results of my estimations and discuss the robustness of my findings. Finally, I discuss the factors behind the response pattern observed. All of
the estimation results are found in the appendices (Appendix A contains the estimation results based on wage measure method A), as discussed in section 5.2, whereas the results based on method B) is found in Appendix B).
5.1
Empirical Model
Inspired by Blau and Kahn (2007) I estimate a semi-log specification of a static labor supply model, where working hours is explained by wage:
h=a0+a1ln(w) +a2ln(ws) +a3V +A0X+u (1)
where for each individuali(suppressing subscripts),his annual hours worked,
w is one own’s hourly wage offer, ws is spouse’s hourly wage offer, V is
family nonwage income (defined as all other income than labor income, and includes income from assets, commercial income and tax-free and taxable
transfers), X is a vector of control variables and u is a disturbance term.
This specification includes a separate term for the spouse’s hourly wage rate, which is thus allowed to have an effect on one’s own labor supply that is different from the effect of the family’s nonlabor income. This allows for considerations of complementarity or substitution between own and spouse’s leisure (Ashenfelter and Heckman, 1974). Such a specification opens up for considerations of family bargaining models (but if this was an issue I wanted to investigate properly, I should have disaggregated the family’s nonlabor
income, V, according to ownership), as opposed to unitary family models in
which it is assumed that all income is pooled.
As a robustness check, I also consider a more traditional specification:
Here, I is family nonwage income, including spouse’s labor income, and eis a
disturbance term. The coefficient b1 is the impact of an uncompensated wage
increase, whereas b2 is the income effect. In contrast, in terms of equation (1)
this is more complicated as the spouse wage enters separately.
The vector of control variables, X, consists of own and spouse age and
age squared, five region of residence dummies, a major city indicator10, a
series of dummies for own and spouse immigration background (EU15 plus Australia, Canada, New Zealand and the US; other EU countries; and other countries) and year dummies (since I pool data from 3 years for each period), which I will describe in more details in section 5.2.
Age is correlated with wages, and we include a square term for age too, to allow for the age-effect on wages to decrease over time. The region dummies are included because there might be differences across these regions when it comes to preferences for work. Perhaps preferences for work in Southern Norway are weaker than in the rest of the country, as this is maybe a more conservative region where ”traditional” family values are expected to be stronger. The major city indicator is included because the cost of living there is higher, thus effectively reducing the real wage. Living in a major city could also be an indicator for preferences for work. Finally, the immigration background dummies are included to control for the demographic composition, assuming that immigration background matters for labor market performance. In line with Blau and Kahn (2007) I estimate four specifications of equation (1): Model 1 has no additional controls, model 2 includes a detailed set of
controls for number of children by age group11, whereas model 3 includes a
set of controls for own and spouse education12. Model 4 controls for both
10A major city is here defined as a municipality with more than 90 000 inhabitants.
11These age groups are 0-1, 2-3, 4-6, 7-11 and 12-16 years old.
children and education, and is thus the richest specification.
Similar to Blau and Kahn (2007) I control for education in some of the models. Education might be an indicator of work orientation and ability. If we do not include education, this might lead to an omitted variable bias. Controlling for it reduces the noise in the estimated coefficient, thus allowing us to place a sharper interpretation on the wage variable. Education might also be an indicator of permanent income or wealth. Then, following the reasoning of Blundell and MaCurdy (1999), the wage coefficient when controlling for education may be an estimate of the intertemporal labor supply elasticity, according to Blau and Kahn (2007). However, the wage variable would refer to a change in wages that also raises lifetime wealth if we exclude controls for education, thus making it reasonable to consider specifications without education. As a robustness check, I also estimate the models separately by education group, as the effect of wage changes may be different for these groups.
The treatment of children is neither straightforward. If we assume that the fertility decision is mainly a question of preferences, then we would expect that women who prefer few or no children will invest more in market-related human capital and work more hours. Not controlling for children could then lead to a spurious positive correlation between wages and labor supply. If we first believe that we should control for children, it makes sense that the effect of children will vary with the age of the children. This is why divide the children controls into age groups. However, it could also be that the fertility decision is a result of an optimizing behavior where women have several time-allocation decisions, including the labor supply decision. Higher wages will then induce women to increase their labor supply and have fewer school, and Higher education.
children. Thus, this highlights that the model is simple; ideally one should model other decisions too, such as the decision of having children.
The model is linear, which implies that it treats the decision to increase labor supply from 0 to 50 hours in the same manner as the decision to increase the hours from 1900 to 1950 hours. Because of this restrictive functional form, I separately investigate the estimates of the extensive and intensive margin in the robustness checks. In addition, there might be issues with truncation of annual hours for women working full-time, as these probably only have limited possibilities to adjust their hours in the case of wage increases. By also estimating median regressions, where the estimates are not sensitive to behavior at the tails of the distribution of annual hours, I allow for such considerations (Blau and Kahn, 2007).
5.2
Data and Descriptive Patterns
As already mentioned, I make use of the Norwegian Labor Force Survey (LFS) to estimate my models. In the LFS, 24 000 respondents aged 15-74 are asked about their attachment to the labor market each quarter. They report how many hours they have worked in a given reference week, as well as how many hours they work in a typical work week.
Following the procedure of Dagsvik and Jia (2016), I measure work hours as the sum of formal work hours in the main and second job (if the individual has a second job). If this information is missing, but the individual is participating in the labor force, I use information on actual working hours in the reference week. My main measure of labor supply is annual hours: this is the product
of work hours per week and number of weeks per year, 5213. Respondents
13Some studies of labor supply based on data from LFS assume 48 weeks instead; a
are defined as belonging to the labor force if they report working at least five hours per week. I exclude individuals with unreasonably high working hours, i.e., more than 80 hours per week. I also exclude individuals with positive working hours who also report having been searching for jobs for more than 1 week, and those with positive work hours reporting having been absent from work for more than 1 week. In order to get as reliable data on absence or job searching as possible during the calendar year, I use LFS data from the 4th quarter, as data from this quarter is richest with respect to information on this.
I restrict my sample to married14 men and women with spouse present
in the sample. To disregard considerations of schooling and retirement, I restrict the sample to age 25-54, as also done by Blau and Kahn (2007). I then merge the LFS data with register based data on income and other family characteristics, using a unique personal identification number.
I adjust all income variables for inflation, by using the Consumer Price
Index. 15 As there are no direct observations of wages in the LFS, I construct
the wage rate as the ratio of annual labor income to annual work hours. It is however evident that survey responses contain measurement errors, which must be taken into account for the observed working hours in my data. I will come back to this in section 5.3. The self-employed and family workers are included in the sample, as well as those with zero work hours, following Blau and Kahn (2007).
Blau and Kahn (2007) estimate their models for 1980, 1990 and 2000, whereas I estimate my models for 1995, 2000, 2005, 2010 and 2015. To expand
14From 1993 to 2008 Norwegian same-sex couples could enter a civil union, which was
a legal parallel to marriage. They are also included here. The practice of same-sex civil unions came to an end in 2008 when Norway legalized same-sex marriage.
the sample, and minimize the effect of selection of end points, Blau and Kahn include the all respondents from the March Current Population Survey in the previous and consecutive year as well. I follow this approach to some degree, in that I include LFS respondents from the previous and consecutive year. However, as opposed to Blau and Kahn (2007) I restrict the number of
times an individual may appear in the sample.16 Thus, I only include those
from the previous and consecutive year, who are not present in the base year. Because income data for 2016 is not yet available, 2015 is expanded by the two previous years. This means that I use five sets of 3 years each: 1994-96 (”1995”), 1999-2001 (”2000”), 2004-2006 (”2005”), 2009-2011 (”2010”) and
2013-2015 (”2015”).
In the period of study, the proportion of women participating in the labor market in my sample has increased from 81 percent in 1995 to 87 percent in 2015, and the average work hours for women have increased from 1340 to 1533. Also the hours conditional on working have increased, from 1646 to 1767. The increase in labor supply, both on the extensive and the intensive margin, have been greater for married women than for unmarried women, suggesting that it is indeed the married women who have driven the aggregated trends in the labor supply of the population. It is also of interest to note that during this period, the unconditional work hours of married women in my sample have surpassed that of unmarried women. This underlines the need of considering changes of self-selection into marriage, following the previous discussion in section 4. For men, there have been a modest decline in the average work hours from 1890 to 1827. A similar decline is found for both married and
16This restriction removes the risk of obtaining biased estimates because of repeated
observations. However, in additional sensitivity analyses (results not reported) I estimated the models without this restriction, and obtained similar results.
Figure 3: Ann ual hours trends for sele cted groups of married w om en. Sample includes those with zero as w ell as p ositiv e w ork hours. 14 1,3 1,0 53 1,2 96 1,6 07 1,2 02 1,2 61 1,3 25 1,3 47 1,3 92 1,1 20 1,3 53 1,5 58 1,3 00 1,3 27 1,3 99 1,4 32 1,4 44 1,0 84 1,3 55 1,6 30 1,3 77 1,3 40 1,4 74 1,4 61 1,5 33 1,1 94 1,4 56 1,7 00 1,5 15 1,4 60 1,5 39 1,5 59 1,5 82 1,2 74 1,4 97 1,7 05 1,5 72 1,4 98 1,6 14 1,5 85 0 20 0 40 0 60 0 80 0 10 00 12 00 14 00 16 00 18 00 Al l Pr im ar y Sc ho ol H ig h Sc ho ol H ig he r E du ca tio n W ith k id s <6 Ag e 25 -3 4 Ag e 35 -4 4 Ag e 45 -5 4 19 95 20 00 20 05 20 10 20 15
unmarried men, see table C.2 for more details.
Figure 3 shows that there has been an increase in the average working hours across for married women in all education groups, across all age groups and for mothers of young children. The increase in hours was, however, of very modest magnitude in all the education groups between 1995 and 2005. The increase between 1995 and 2015 is sharpest for mothers with children under six years old. Women with higher education have relatively high participation in all years.
Table C.3 contains mean values of selected explanatory variables for the sample of married women in the age group 25-54. As we can see, both own and spouse wages have increased in the period. The observations in my sample suggest a real wage increase for women of 46 percent using valid observed wages, 67 percent using the observed or imputed wage and 92 percent using the predicted wage (the corresponding figures for men are 58 percent, 37 percent and 97 percent); definitions and a discussion on these wage measure
follow in section 5.3.17 The nonwage family income has more than doubled
in the period. For women there has been a substantial increase in the share having attained higher education, on expense of the share having high school as highest attained education level: the share having attained higher education has risen from 17 percent in 1995 to 55 percent in 2015. For spouses, this rise has been from 19 percent to 41 percent. The share of both married women and spouses having only primary school has remained almost constant at around 13-14 percent. There has been a small increase in total number of children, from 1.3 to 1.4, but the composition of ages has not changed much.
As the response rate to the LFS has declined (Bø and H˚aland, 2015), and
17The total average real wage increase in Norway between 1995 and 2015 was 65 percent
the share of the sample being married have fallen, it is not surprising that my sample sizes have decreased in the period of study; from 5118 in 1995 to
3524 in 2015.18
5.3
The Measurement of Wage and Other
Econometric Issues
There are several econometric challenges when setting out to empirically estimate labor supply models. These issues are well documented in the literature, see for example Keane (2011). The most pressing challenges are related to the measures of wages. In the following, I will present these challenges and discuss methods to deal with them. As this study follows the approach of Blau and Kahn (2007), the following description is close to their procedure. A main problem is that wage offers are not observed for everyone. Moreover, wage rates are likely measured with error and they are endogenous. Data does not contain a direct measure of the wage rate. I thus construct a wage measure, as mentioned in the previous section. This wage measure is simply annual labor income divided by annual working hours. I will in the
remainder refer to this as the observed or the actual wage rate. I consider
observed wage rates below NOK 110 and above NOK 2500 as invalid. I also experimented with other ranges for the valid range, an issue that I will return to in section 5.5. The wage rate for self-employed and family-workers is treated as unobserved.
The first challenge is that we only observe wages for those being employed. Everyone has a wage offer in the labor market, but this is unobserved for those not working, those with an invalid wage observation and for the self-employed and the family workers. We thus need to assign wage rates to these. As
there may be a positive correlation between the wage offer and the decision to participate in the labor market (effects of self-selection into the labor market), using only the observed wages to model a wage relation for everyone would most likely result in assigning too high wage rates to those not working, as explained by Heckman (1979). This selection-bias can be dealt with in several ways. Blau and Kahn (2007) suggest that because people with a weaker link to the labor market (working less than 20 weeks per year) can be used to determine the wage rate for those not working at all, Thus, inspired by Juhn (1992) and Juhn and Murphy (1997), wage regressions are run separately for those working little or not at all, and for those working more than 20
weeks per year. This method is not appropriate for the Norwegian case.19
Instead, I make use of a Heckman type selection correction, as is done as a sensitivity check by Blau and Kahn (2007). Given that Nawata (1994), finds that a maximum likelihood estimate (MLE) is more efficient than the traditional two-step Heckman correction estimate (Heckman, 1979), I use a
MLE approach.20 See further details below.
Related to the selection problem, wages and other income may be corre-lated with preference for work. It could well be that unobserved characteristics
19In table C.1 it becomes clear that the sample of those not working is not convincingly
similar to the sample of those with a weaker link to the labor market with respect to characteristics that likely determines the wage offer.
20In many analyses this selection bias is ignored for men, as only a small proportion of
men do not work. If it is true that this bias can be ignored for men, then the need to correct for this bias should also diminish for women as their participation rates have increased substantially over the recent decades. I find indeed that the selection problem is present in all years except 2015, see table A.1 and B.1. Heckman selection correction models are,
however, prone to misspecifications, and the negative ρ, the correlation between the error
terms in the participation equation and the wage equation I obtain in 2015, could be an indication of specification problems.
that also affect someone’s wage rate, such as motivation for work or ability, are positively correlated with the labor supply. Thus, a positive correlation between wages and work hours could be due to an omitted variable bias.
Finally, in a seminal article (Borjas, 1980), it is demonstrated that if the observed wage rate is constructed by dividing labor income by working hours, then measurement error in working hours can induce a negative bias on the estimated wage coefficient, the so-called division bias. When the wage rate is a ratio of annual labor income, the measurement error in working hours will be present on both sides of the labor supply equation. If the measurement
error is random, and uncorrelated with the disturbance term, u in equation
(1), it is rather straightforward to show that when dividing the annual labor income by working hours (measured with error), this will lead to a negative bias on the wage coefficient.
Both the omitted variable bias and the measurement error can be dealt with by an instrumental variable (IV) approach. However, finding a suitable instrument that is both relevant and uncorrelated with the disturbance term
uhas proven very hard in practice. I apply two different methods to deal with
the endogeneity problem and the non-observability of wages for nonworkers:
A) The first method is simpler than that of Blau and Kahn (2007).
Here, I first run a wage regression separately for married men and women with a Heckman MLE selection correction based on those with observed wages, and use these regressions to predict a wage rate for everyone. For simplicity, and to avoid issues of collinearity when estimating the labor supply equation (which may arise if the information used to run the wage regression is sufficiently similar to the information used to estimate the labor supply function), I estimate a traditional Mincer type equation, but also include a series of dummy variables indicating the field of education. Predicting the
wage rates in this manner substantially reduces the variation in wage rates. The regressors I use in addition to the set of field of education dummies are potential experience (defined as age less years of schooling less 6), potential experience squared, and years of schooling. The excluded controls for selection correction are children and unearned family income. The full wage regression can be found in table A.1, and is run separately for each gender in each period. The resulting wage rate estimates are unbiased. I will refer to this wage rate
as the predicted wage rate.
This wage measure enters into equation (1) and the labor supply function is estimated by OLS. The underlying reasoning is that the wage prediction method has sufficiently lessened the endogeneity problem.
B) The second method is very similar to that used by Blau and Kahn
(2007), apart from how I correct for the selection bias. In the first step I run a wage regression separately for married men and women with a Heckman MLE selection correction based on observed wages. The regressors used are own and spouse age and age squared, own and spouse immigration background, own and spouse education level, region of residence and the major city indicator. The excluded controls for the selection correction are children and unearned family income. The full wage regression can be found in table B.1. Instead of assigning this wage to everyone, I only assign this estimated wage rate to
those with unobserved wage. I will refer to this as the imputed wage rate.21
Now, everyone in the sample has a wage rate (observed or imputed). However, if we were to use these wage rates directly in equation (1), there would still be potential problems of omitted variables and division bias, which is controlled
21Labeling the estimated wage rate in method A) (predicted) and B) (imputed) in a
different manner is simply an attempt to make it easier to understand which method I am referring to in the remainder of this study, rather than suggesting a semantic or conceptual difference between the two labels.
for by using IV techniques in the estimation of equation (1).
Because measurement error is likely much less frequent in wage deciles than in wage levels, using decile information as instrument can potentially correct for the measurement error (Baker and Benjamin (1997), Juhn and Murphy (1997) and Blau et al. (2003)). A series of dummy variables indicating own and spouse deciles of actual or imputed wage, as well as education, are used as instruments. However, as the LFS does not contain any measure of how many weeks per year the respondents work, the measurement error in working hours may be more severe in my study than in Blau and Kahn (2007).
Another econometric issue is related to marriage. During the period of my study the rate of married women with spouse present in my sample has fallen from 46 percent in 1995 to 36 percent in 2015 (a similar decline is not surprisingly found for men), as shown in table C.2. As Norway has become an increasingly secular society over the past decade, and as the welfare state has improved, the institution of marriage has likely changed. It could be that marriage as an institution to some extent has been replaced by couples cohabiting in more or less formal arrangements, and several studies of female labor supply consider married and coupled women, rather than only married. This raises concern of whether parts of my results are influenced by changes in self-selection into marriage. Married women may become more marriage-prone relative to the average of women, as marriage rates fall. If unobserved marriage-proneness is correlated with motivation to work in the market, comparisons across years may then reflect selection in addition to the actual behavioral changes (Blau and Kahn, 2007). I control for this possibility by also estimating a few approaches with marriage selection corrections (see section 5.5).
5.4
Estimation Results
We now turn to the results of the estimations of the labor supply equations (equation (1) and (2)). I focus on the estimations where spouse log wage is
entered separately (equation (1)).
As Blau and Kahn (2007), I find a reduction in the labor supply respon-siveness over time. The size of the elasticities vary substantially dependent on whether if method A) or B) is used to measure wages, but a clear downward trend is observed across all models, see figure 4. The cross wage elasticities are mostly negative and small in magnitude, and not significant, but if anything they also show a downward trend in magnitude. The income elasticities are small across all specifications, and show no clear trend over the period.
The negative elasticities towards the end of the period of study obtained by method B) could be due to a misspecification of the model, or more likely, method B) may involve some degree of a division bias, which leads to underestimation of the true effect of wage changes, as discussed in section 5.2.
