What Have We Learned from Structural Models?

By RICHARD BLUNDELL∗

At a broad level a structural economic model tural models to improve our understanding of is one where the structure of decision making observed behaviour and to provide reliable pol- is fully incorporated in the specification of the icy counterfactuals. model. By identifying the ‘deep’ parameters The following sections of the paper draw on that describe the preferences and constraints of three related areas: (I) Revealed preference and the decision-making process, structural models unobserved heterogeneity, (II) Discrete choice deliver counterfactual predictions. The abil- models and welfare reform, (III) Dynamic struc- ity to provide policy counterfactuals sets them tural models and human capital investments. apart from reduced-form models.1 But struc- These are areas that have extensive policy ap- tural models require the detailed specification of plications where structural functions and pol- the decision-making problem - the constraints icy counterfactuals are well defined; that ask and the preferences. This will typically place well-formulated questions e.g. ex-ante impact tougher requirements on measurement and rely, of taxes, prices and wages, and optimal design; in part, on stronger assumptions. that analyse static choice and dynamic choice; Structural models aim to identify three dis- and, that use new data, new methods and new tinct, but related, objects: (i) structural ‘deep’ computational developments. Section IV con- parameters: e.g. Frisch and Marshallian elas- cludes. ticities. (ii) underlying mechanisms: e.g. par- tial and self-insurance. (iii) policy counterfac- I. Revealed Preference and Heterogeneity tuals: e.g. ex-ante tax policy evaluations. It is useful, therefore, to distinguish between ‘full- The structure of economic decision-making structural’ dynamic models and quasi- (or semi- models delivers restrictions that can be used ) structural models, the latter identifying a sub- to recover of counterfactuals. For example, set of parameters and/or mechanisms rather than the revealed preference (RP) conditions of con- full counterfactuals. sumer choice theory can be used to place bounds on consumer responses to price and income The focus in this paper is on structural mi- changes, enabling us to examine the impact croeconometric models for policy analysis. Em- counterfactual tax and redistributive policies phasis is given to models that minimize assump- (Blundell et. al., 2008). Recent studies have ex- tions on the structural function of interest and tended these results to models of habits (Craw- on unobserved heterogeneity; and to approaches ford, 2010) and collective family labor supply that align moments from structural and ‘reduced (Cherchye et al, 2011), as well as other devia- form’ approaches. The discussion is limited to tions from simple RP. single agent models omitting, for space reasons, Consider a simple structural demand func- the many important contributions that use equi- tion: y g p I z u that describes demand librium concepts, network interactions and mar- ( , , , ) for good(s)= ‘y’ by consumer z u facing p I . ket structure to help secure identification. The ( , ) ( , ) RP inequalities summarise structural informa- goal throughout is to highlight the use of struc- tion and can be used to bound (set identify) in- dividual demand counterfactuals. An additive ∗ University College London and Institute for Fiscal Studies, [email protected]. Acknowledgements: I am grateful to Lars specification for u is implausible in consumer Hansen for helpful comments and to Orazio Attanasio, Michael models. With nonseparable u and monotonic- Keane, Costas Meghir and Ariel Pakes for helpful discussions. ity, conditional nonparametric quantiles can be This research is part of the ESRC Centre for the Microeconomic shown identify individual structural demands, Analysis of Public Policy at IFS, I would like to thank the ESRC, 2 and the ERC under project MicroConLab, for financial support. see Blundell, Kristensen and Matzkin (2014). 1Hurwicz defines structural models in terms of invariance to the counterfactual experiments they are designed to address. 2With multiple demands invertibility in u is not sufficient for 1 2 PAPERS AND PROCEEDINGS MAY 2017

With multivariate heterogeneity only average Next comes step (ii), the measurement of ef- welfare contrasts are identified, see Hausman fective incentives. An advantage of structural and Newey (2016). The conditional indepen- models is the requirement for a precise state- dence assumption on u may also be relaxed to ment of constraints. For tax and welfare policy allow for endogeneity of prices p, see Blundell, this requires a detailed institutional knowledge Horowtiz and Parey (2015). That study also of overlapping taxes, tax-credits and welfare provides new insights and policy counterfactuals benefits. As the careful studies in Moffitt (2016) for individual gasoline demand, highlighting the show, modern tax and welfare-benefit systems empirical value of RP restrictions, and showing are complex with many overlapping welfare- that demand responses to gasoline price changes benefits and taxes. If we are to accurately re- vary in a key non-monotonic way with income. cover preferences we need to understand not only these overlaps but also the salience of the II. Discrete Choice and Welfare Reform various tax and welfare benefit incentives. This is step (iii) and requires a careful modeling Structural discrete choice models have been of welfare programme participation and stigma the workhorse of the empirical analysis of among eligible families. welfare-benefit reform. The plethora of welfare It is only after having built a clear picture from and tax proposals, and actual reforms, that sur- these first three steps that the rigorous econo- faced in the late 1980s and 1990s gave new im- metric analysis of structure and causality comes petus to their development. Well specified mod- into play. At step (iv) an eclectic mix of re- els incorporate choices not only over part-time duced form and structural approaches is to be and full-time work but also over different wel- preferred. There is a strong complementarity be- fare and tax credit programs, allowing for stigma tween approaches. Quasi-experimental evalua- costs and accounting for the complicated non- tions can provide robust measures of certain pol- linear budget constraints that reflect the impor- icy impacts but are necessarily local and limited tant overlaps of the many welfare programs, tax- in scope. Structural estimation allows counter- credits and personal taxes. factual policy simulations which can then feed This area is ideal for examining the role of into a policy (re-)design analysis in step (v) but structural models in policy analysis. Using the often depend on strong assumptions. Mirrlees Review of tax reform as an example, Structural models have been used extensively Blundell (2012) identifies the following five key to assess the impact of means-tested programs steps in assembling the foundations for empir- and tax-credits and potential reforms to them, ical policy research: (i) Uncovering the mar- see Blundell and Hoynes (2004). These poli- gins of adjustment; (ii) Measuring effective in- cies are directed at relatively poor families with centives; (iii) Understanding the importance of low labor market attachment and low earnings. information and complexity; (iv) Estimating be- Policy counterfactuals are required as these re- havioral responses; and (v) Counterfactual pol- form proposals typically involve non-marginal icy simulation and optimal design. Structural changes to the tax-credit and welfare system.3 models are centre-ground in policy research, en- The key elements of a structural model for low tering directly into steps (iv) and (v), but steps income families (see Keane and Moffitt, 1998) (i) - (iii) are also essential for a well-specified involve a precise definition of the budget con- model and reliable policy advice. straint, with all the tax/tax-credit and benefit in- Step (i) examines the key margins of adjust- teractions. Also the specification of preferences ment. For example, the margins of labor market over different hours and programme options that adjustment for tax and welfare policy analysis. give rise to multinomial choice across discrete Blundell, Bozio and Laroque (2011) show the hours and welfare combinations. Heterogene- importance of a lifetime view of employment ity is essential, reflecting observed differences and hours with key differences between exten- across families through measured demograph- sive and intensive margins that are accentuated at particular ages for different education groups. 3For marginal policy reform, semi-structural models are of- ten sufficient and use robustly estimated local derivatives of identification, see Matzkin (2007). structural functions, as in Chetty (2009) VOL. VOL NO. ISSUE STRUCTURAL MODELS: WHAT HAVE WE LEARNED? 3 ics, and unobservable differences in ‘tastes’ for not be (nonparametrically) identified without ex- work, stigma costs, childcare costs and fixed ternal information on the distribution of unob- costs of work. served preference shocks and the discount rate, There are many examples of where these (see also Arcidiacono and Miller, 2011). models perform well, their ex-ante predictions The upshot is that particular care needs to be matching post-reform behavior, see Blundell taken in specifying, estimating and validating (2012). In the more convincing examples, iden- dynamic structural models. One reaction is to tification is based on sources of plausibly exoge- focus on a subset of structural parameters that nous variation in welfare and tax rules across are more robustly identified. As already noted time and locations. The models have also proven one can view this as a ‘semi’ or ‘quasi’ structural invaluable for counterfactual evaluations of al- approach. For example, one may estimate ‘life- ternative policies and have been used to exam- cycle’ consistent preferences by conditioning on ine optimal design, see Blundell and Shephard consumption (or net saving), see Blundell and (2012). They identify wage and income elastici- Walker (1986). Another example is the partial ties at the extensive and intensive margins across insurance literature, see Blundell, Preston and different demographic groups, proving a secure Pistaferri (2008). Evenso, these quasi-structural basis for targeting earned income tax expansions approaches are not robust to intertemporal non- at low income families. Complexity and over- separability that occurs in models incorporating lapping benefit withdrawal rates are clearly in- human capital decisions. For this we need a efficient and inhibit take-up, providing a clear more fully specified model. motivation for the integration of benefits and tax The ground-breaking work in the develop- credits, see Brewer, Saez and Shephard (2011). ment of structural models of life-cycle labor sup- Recent studies seek to further relax the as- ply choices was carried out by Heckman and sumptions on preferences in structural labor sup- MaCurdy (1980), subsequently developed for ply models and use only the restrictions from re- discrete choice decisions and integrated with vealed preference to identify some key param- human capital choices by Keane and Wolpin eters of interest. For example, Blomquist et (1997) among others. That work uncovered key al (2015) estimate the conditional mean of tax- differences between short-run and longer run re- able income imposing revealed preference re- sponses to wage changes and found that, once strictions and allowing for measurement errors. human capital choices are incorporated, esti- This work aims at a robust measure of the struc- mated labor supply responses from static models tural taxable income function rather than iden- can be quite misleading. tifying the full optimisation problem. Manski The advantage of these structural models is (2014) develops conditions where partial pre- that they identify life-cycle counterfactuals and diction of tax revenue under proposed policies mechanisms e.g. the impact of tax reforms and and partial knowledge of the welfare function the ‘insurance value’ of redistributive policies. for utilitarian policy evaluation is feasible. As a recent example, consider the Blundell et al There remain many areas where these struc- (2016) application to education choices, experi- tural models are in need of further refine- ence capital and female labor supply in the UK. ment. Human capital investment, persistent That study uses panel data and the time series wage shocks, and search frictions add poten- of tax, tax-credit, welfare, and tuition reforms to tially valuable dynamics considerations. identify the structural parameters of human cap- ital and labour supply choices, conditioning on III. Dynamic Structural Models early life-history variables. At the heart of the structural model is a dy- Identification of structural models in ady- namic wage equation estimated jointly with ed- namic optimising environment requires strong ucation and life-cycle labor supply decisions. assumptions on subjective discount rates and the This features a concave work experience term distribution of beliefs. For example, building on on wages and persistent shocks. The structural the original work by Rust (1994), Magnac and model fit is shown to be good. But this isonly Thesmar (2002) show that in discrete choice set- achieved by allowing returns to work experience tings the utility functions in each alternative can- to differ by education level, by conditioning on 4 PAPERS AND PROCEEDINGS MAY 2017 extensive background factors, and by including tributions: they identify ‘deep’ structural param- a part-time work penalty in experience capital. eters; they provide a clear insight into the mech- The results from this structural model de- anisms underlying the observed behaviour; and liver some key new insights: (i) On struc- they provide counterfactuals. In addition, they tural parameters: experience effects display can be used to reconcile earlier results and con- strong dynamic complementarity, with lower sequently help build a knowledge base for policy experience effects for the low educated and for research. those in part-time work; on (ii) On mechanisms: Structural models make explicit the assump- the insurance value of tax-credits is a substan- tions on preferences and constraints being used tial part of welfare gain; and (iii) On counter- to estimate parameters, mechanisms and coun- factuals: lower education women with young terfactuals. These assumptions need to be tested, kids have larger supply responses, implying tax- assessed and relaxed wherever possible. This credits can be an optimal design, although they has been the theme taken here, focusing on the induce little earnings progression. There are also structural analysis of labor supply and consumer found to be significant, but small, effects of tax- behavior. Reliable structural analyses in these credits on education choice, attenuating some of areas acknowledge the importance of aligning the employment gains. moments from structural models with reduced As a by-product the structural model allows form evidence and with minimising the reliance a reconciliation of past results. That is it can on unnecessary assumptions. help explain past (static) structural and quasi- An important recent development has been experimental results. Human capital deprecia- applications which combine structural and ex- tion and the part-time work penalty imply negli- perimental evidence. For example, Todd and gible experience capital wage dynamics for low Wolpin (2006) use experimental data to validate educated women, explaining why static discrete a dynamic structural model of child schooling models that account for detailed tax and benefit and fertility. Attanasio, Meghir and Santiago interactions perform well. (2012) use experimental data to estimate general There are many other important recent con- equilibrium effects. Karlan and Zinman (2009) tributions to the structural modeling of dynamic use a consumer credit experiment to distinguish- life-cycle choices - too many to discuss in de- ing between adverse selection and moral hazard. tail. Key examples include: Cunha, Heckman Duflo, Hanna, and Ryan (2012) design an exper- and Schennach (2010) which provides important iment to identify the impact of monitoring and new results on the identification and estimation financial incentives on teacher absence and on of the ‘household production’ of early years skill learning. formation. French (2005) which shows the key I leave the final words to Frisch (1933) “No role of retirement incentives separate from pref- amount of statistical information, however com- erences at retirement. Meghir, Low and Pistaerri plete and exact, can by itself explain economic (2015) which separates employment risk from phenomena. ... we need the guidance of a pow- wage risk. Low and Pistaferri (2016) which ex- erful theoretical framework. Without this no sig- amines the dynamic incentives in the disability nificant interpretation and coordination of our system. All of these studies provide convincing observations will be possible.” evidence on key structural parameters and coun- terfactuals, helping build our knowledge base on References life-cycle behaviour. Attanasio. P., Orazio, Costas Meghir and Ana Santiago. 2012. “Education Choices in Mexico: IV. Conclusions Using a Structural Model and a Randomized Ex- periment to Evaluate PROGRESA”, Review of Structural models play a key role in un- Economic Studies, 79(1), 37-66. derstanding economic behavior and in policy Peter Arcidiacono, and Robert Miller. 2011. design. They complement reduced form ap- “Conditional Choice Probability Estimation of proaches by explicitly incorporating restrictions Dynamic Discrete Choice Models With Un- from economic decision-making models. By do- observed Heterogeneity”, Econometrica 79(6), ing so they make three related, but distinct, con- 1823-1867 VOL. VOL NO. ISSUE STRUCTURAL MODELS: WHAT HAVE WE LEARNED? 5

Blundell, Richard. 2012. “Tax Policy Re- Cunha., Flavio, James J. Heckman and Su- form: the Role of Empirical Evidence”, Journal sanne M. Schennach, 2010. “Estimating the of European Economics Association, 10, 43-77 Technology of Cognitive and Noncognitive Skill - , Antoine Bozio. and Guy Laroque. 2011. Formation”, Econometrica, 78(3), 883-931. “Extensive and intensive margins of labour sup- Duflo, Esther., Rema Hanna, and Stephen P. ply”. AER Papers and Proceedings, May. Ryan. 2012. “Incentives Work: Getting Teach- - , Martin Browning and Ian Crawford. 2008. ers to Come to School”. American Economic “Best nonparametric bounds on demand re- Review 2012, 102(4): 1241-1278. sponses”, Econometrica, 76:1227-1262. French, Eric. 2005. “The Effects of Health, - and Hilary Hoynes. 2004. “Has In-Work Wealth, and Wages on Labour Supply and Re- Benefit Reform Helped the Labour Market?”, tirement Behaviour”, Review of Economic Stud- in R. Blundell, D. Card and R. Freeman (eds), ies, 72(2): 395-427. Seeking a Premier League Economy, Chicago: Hausman, Jerry A. and Whitney K. Newey, University of Chicago Press. (2016): Individual Heterogeneity and Average -, Dennis Kristensen and Rosa Matzkin, 2014. Welfare, Econometrica, 84(3), May, 1225-1248 “Bounding Quantile Demand Functions using Heckman, J. J. and T. E. MaCurdy (1980). Revealed Preference Inequalities”, Journal of “A Life Cycle Model of Female Labour Supply” Econometrics, 117:112-127. Review of Economic Studies, vol. 47(1): 47-74. -, Monica Costa-Dias, Costas Meghir, and Karlan, D. and Zinman, J. 2009. “Observing Jonathan Shaw. 2016. “Female labor supply, hu- Unobservables: Identifying Information Asym- man capital, and welfare reform”. Econometrica metries With a Consumer Credit Field Experi- 84 (5), 1705-1753. ment” Econometrica, 77: 1993-2008. -, Luigi Pistaferri, and Ian Preston. 2008. Keane, Michael.P. and Robert Moffitt. 1998. “Consumption Inequality and Partial Insurance,” “A structural model of multiple welfare pro- American Economic Review, 98(5): 1887-1921. gram participation and labor supply” Interna- -, and Andrew Shephard. 2012. “Employ- tional Economic Review 39, 553-590. ment, hours of work and the optimal taxation - and Ken. I. Wolpin. (1997). “The Career of low-income families”, Review of Economic Decisions of Young Men”, Journal of Political Studies, 79, 481-510. Economy, 105(3): 473-522. -, and Ian Walker. 1986. “A Life-Cycle Con- Magnac, Thierry and Daniel Thesmar. (2002). sistent Empirical Model of Family Labour Sup- “Dynamic Discrete Choice Processes”, Econo- ply Using Cross-Section Data”, Review of Eco- metrica, 70, 801-816. nomic Studies, 53(4), 539-558. Manski, Charles.F. 2014. “Identification of Blomquist, Soren. Anil Kumar, Che-Yuan income leisure preferences and evaluation of in- Liang and Whitney Newey. 2015. “Individual come tax policy”, Quantitative Economics 5, Heterogeneity, Nonlinear Budget Sets, and Tax- 145-174. able Income”, cemmap WP CWP21/15. Matzkin, Rosa.L. 2007. “Heterogeneous Brewer, Mike., Emmanuel Saez and Andrew Choice,” in Advances in Econometrics, ed. by Shephard. 2011. “Means testing and tax rates on R. Blundell, W. Newey, and T. Persson. Cam- earnings”, in J. Mirrlees et al, (eds), Dimensions bridge University Press. of Tax Design: Oxford University Press. Moffitt, Robert. 2016. “Economics of Means- Cherchye, Laurens, Bram De Rock, Fred- Tested Transfer Programs in the United States”, eric Vermeulen, 2011. “The Revealed Prefer- Volumes I & II. University of Chicago Press. ence Approach to Collective Consumption Be- Rust, John. 1994. “Estimation of dynamic haviour:” Review of Economic Studies, 78(1), structural models, problems and prospects”, in 176-198. C. Sims(ed.) Advances in Econometrics. Cam- Chetty, Raj. 2009. “Sufficient Statistics for bridge University Press. Welfare Analysis: A Bridge Between Structural Todd, P. and K. Wolpin. 2006. “Using Exper- and Reduced-Form Methods”, Annual Review imental Data to Validate a Dynamic Behavioral of Economics Vol. 1: 451-488. Model of Child Schooling and Fertility” Ameri- Crawford, Ian. 2010. “Habits Revealed, Re- can Economic Review, 96(5): 1384-1417 view of Economic Studies”, 77(4), 1382-1402.