Telemaco Lecture 1 April 2015 Microsimulation and Microeconometrics: survey, interpretation and...

Telemaco Lecture 1 April 2015

Microsimulation and Microeconometrics: survey, interpretation and perspectives

Ugo Colombino

Microsimulation and Microeconometrics: survey, interpretation and perspectives

This presentation is in part based on a chapter written by Rolf Aaberge and Ugo Colombino for the Handbook of

Microsimulation Modelling (Ed. C. O’Donoghue), Emerald, 2014.

Outline

• Microsimulation and microeconometrics: marriage, divorce and remarriage

• Modelling strategies: reduced form, structural “marginalist”, random utility-discrete choice

• Can we do without structural models?

• Can we do without utility maximization?

• Policy simulation and identification of optimal policies

What’s Microsimulation?

Guy Orcutt(1917 – 2006)

What’s Microsimulation?• The first proposal for a «microsimulation model» by G. Orcutt

appears in “A new type of socio-economic system”, Review of Economics and Statistics, 39(2), 16-123, 1957.

• More than an academic idea, it’s a proposal addressed to the policy makers.

What’s Microsimulation?• At the time, the models used for policy analysis were macro

models consisting of (mostly accounting) relationships among aggregates, with little and vague micro foundations.

• Orcutt’s critique is focussed on four points: policy relevance, aggregation, micro foundations and representation of behaviour.

What’s Microsimulation?Policy Relevance

“ Existing models of our socio-economic system have proved to be of rather limited predictive usefulness. This is particularly true with respect to predictions about the effects of alternative governmental actions […]


Author(s), TitleConference/Seminar, Month Day, Year

Micro-foundations

[…] “ research efforts in the behavioral sciences have yielded and show promise of yielding very substantial amounts of knowledge about elemental decision-making units. However, existing models of socio-economic systems are neither built in terms of such units nor are they well adapted to making use of knowledge about such units”.

[… ] “The most distinctive feature of this new type of model is the key role played by actual decision making units of the real world such as the individual, the household and the firm”.

What’s Microsimulation?• Aggregation

• “[...] current models of our socio-economic system only predict aggregates and fail to predict distributions of individuals, households, or firms [...]”.

• “Aggregation of relationships about elemental decision-making units is fairly easy if the relationships to be aggregated are linear [...]. However, if nonlinear relationships are present, then stable relationships at the micro level are quite consistent with the absence of stable relationships at the aggregate level”.



• Representation of behaviour

• “This new type of model consists of various sorts of interacting units which receive inputs and generate outputs […] Probability distributions specify the probabilities associated with the possible outputs of the unit.

• “Prediction about aggregates would still be needed but will be obtained by aggregating behavior of elemental units…”


• Policy-relevant models should be based on a disaggregated and explicit representation of the micro-units and of their interactions.

• Micro choices are representes as probabilistic events. • The probabilistic representation of behaviour naturally

suggests simulation as the tool to solve the model: thus, micro-simulation.

What’s Microsimulation?• Early improvements at the end of the 50s in micro data

collection and management and in digital computing made Orcutt confident in the feasibility of the project.

• Realistically, the project was to be articulated in specific bulding blocks or modules.

• Orcutt and associates proceeded to the implementation phase (Wisconsin, Urban Institute, Yale) working in particular on the household sector and on socio-demographic dynamics.

• A summary of early implementations: Orcutt et al. (1961) Microanalysis of socioeconomic systems: A simulation study, New York, Harper & Row. Fantastic book !

Microsimulation and MicroeconomicsConflictual marriage• In principle, Orcutt’s proposal would have represented an ideal match

between policy-relevant modelling and microeconomics (or micro-analytic behavioral theories in general).

• However, the two partners were not ready for that.

• Orcutt – a background in engineering and physics - had probably little confidence in microeconomc theory.

• Orcutt’s project did not receive much interest by microeconomist nor by econometricians. Appropriate empirical specifications of microeconomic models (i.e. microeconometrics) were not available yet.

• As a consequence, the behavioural relationships illustrated for example in Orcutt et al. (1961) are reduced form specifications (ignoring Marshack 1953!).

Microsimulation and MicroeconomicsDivorce

• During the 70s, 80s and 90s, large microsimulation models in various countries (US, Canada, Scandinavian countries, Australia) acquire popularity, also at the policy making level.

• The microsimulation community in this period focusses on the quality of data and the accounting reliability of the predictions.

• Behavioural responses are left outside.

• Arithmetic (aka static or non-behavioural) models are more palatable to policy makers.

• Large part of the research effort is dedicated to tax-benefit simulation models (e.g. EUROMOD).

Microsimulation and MicroeconomicsMeanwhile, however…• The lesson by Marshack 1953 and Hurvicz 1962 – revived by Lucas 1976 – i.e. you need

structural models to make policy simulation, gets eventually fully learnt.

• At the policy level, starting with the mid 60s, there is an increasing interest (war on poverty, tax reforms, welfare reforms etc.) in issues that involve structural changes in the opportunity sets.

• Heckman, Hausman and many others (late 70s – early 80s) develop appropriate models to account for the complexities in the opportunity set.

• Applied microeconomists start using microsimulation techniques to compute responses to policies (Zabalza 1983: possibly the firs one?).

• Discrete choice and random utility models (late 60s) offer a new and more flexible tool to model and simulate choices subject to complicated constraints.

Microsimulation and MicroeconomicsRe-marriage

• The third millennium marks the re-encounter of microsimulation and microecono (-mics)(-metrics).

• The two partners are now ready.

• The policy makers, who in previous decades have learned to appreciate the value of non-behavioural models (a Troy horse?!), now start realizing that a representation of behavioural responses would be important.

• The previous developments in microeconometrics provide the appropriate representations of behavioural responses.

Microsimulation and MicroeconomicsRe-marriage

• Sutherland, Mitton and Weeks (Eds.) Microsimulation Modelling for Policy Analysis: Challenges and Innovations, Cambridge University, 2000 (one paper with behavioural responses: the one by Aaberge, Colombino, Strom and Wennemo!).

• In 2010, ISER (that hosts EUROMOD in Essex) organizes a large workshop on behavioral responses in microsimulation models.

• Compare the program of the IMA conference in Camberra 2003 (most of the papers are arithmetic) to the IMA conference 2013 again in Camberra (most of the papers are behavioural, especially labour supply!).

• The same goes with the last European IMA conference in Maastricht (2014).

Modelling Behaviour

I focus on labour supply choices. Why?

•Most common applications of microsimulation are tax-benefit reforms.

•The main interest is in the effects on incentives to work more or less, with the obvious implications on tax revenue.

•If we introduce a universal basic income, will “poor” households work less?

•If we increase top marginal tax rates, will “rich” households work less?

•What if we introduce a flat tax?

•Etc.

•However, most of what I say carries over to other types of choices: retirement, consumption, savings, child-care, educational choices…

Modelling Behaviour:

• Reduced form• Structural “marginalist”• Random Utility and Discrete Choice

Modelling strategiesReduced form

• It is the common approach up to the early 70s

• It consists of using a (for example) linear approximation such as h = h(w,I), where w = wage rate and I = unearned income.

• This specification might work as an approximation to the observed regime.

• However, your estimates of h(w, I) will also depend on the observed regime.

• When the regime changes (i.e. taxes and benefits induce changes in w and I), you cannot use the previously estimated h(w,I).


• Suppose the data are generated by a Cobb-Douglas utility function

maximized under the budget constraint c = wh + I . This would be the budget if there are no taxes or if taxation is proportional. Then the labour supply function is

The following graph represent the labour supply curve (the heavy black line) and a hypothetical set of observations (the blue circles):

(1- )24 - I

hw

( , ) ln(24 - ) (1- )lnU h c h c

h

w Labour supply function when c = wh + I


• Now suppose you ignore the structural process that generated the data (i.e. the constrained utility maximization) and simply estimate a linear regression h = a + bw that fits the data, as in the following graph:

h

w «Reduced form» labour supply function


• The estimated regression might represent a reasonable approximation to the observations.

• It might also provide reasonable predictions of the effects of w upon h, given the budget constraint c = wh +I.

• However, can you use the estimated regression to predict the effect of w upon h given a different budget constraint?

• The answer in NO. Let’s see why.


• Suppose the budget constraint is c = f(wh + I), where f( ) is a progressive tax rule such as

wh + I

f(wh + I)


• Given the above budget constraint (and Cobb-Douglas preferences), the labour supply function would look like in the following graph (trust me!):

h

w Labour supply function when c = f(wh + I)


• Clearly, the previously estimated regression would be hopeless give this different tax regime:

h

w Labour supply function when c = f(wh + I)


• In turn, if you estimate a regression on the data generated by the progressive tax regime….


• … the estimates would be hopeless if used to make predictions under a linear budget constraint:

h

w

Labour supply function when c = wh + I

«reduced form» estimated when c = f(wh + I)

Modelling strategiesFrom reduced form models to structural models• The point is clarified – in a different application – in a path-

breaking paper by Heckman (1974).

• The policy problem addressed by Heckman (1974) is the evaluation of a child-related welfare policy that introduces significant complications in the budget set.

• The author observes that in order to make such evaluation one has to estimate the preferences as separated from the constraints:

Modelling strategiesFrom reduced form models to structural models

“...the ability to ...(separate preferences and constraints) ... is less important if we are willing to make the conventional assumption that wage rates are independent of hours of work ... but becomes quite important when we acknowledge the existence of progressive taxation, welfare regulations, and time and money costs of work.”

Modelling strategiesStructural “marginalist”

• During the late 70s and the 80s, Heckman, Hausman and many others develop estimation and simulation methods appropriate for non-linear budget constraints (e.g. Hausman 1985).

• Special number of the JHR 1990 with papers that adopt the same (at the time) dominant approach to model labour supply and simulate tax reforms in various countries.

• Those methods use in ingenuous ways the FOCs associated with a constrained utility maximization problem : generalizations of Tobin (1958). The FOCs specify relationships between marginal variations: that’s why I use the term “marginalist”.


0 0

1 1

max ( , )s.t.

0

U h c

c I w hc I w hh

h

c

I0

w0

w1

I1

0 K


The conditions that determines

whether h will be equal to 0

or in the interval (0, K)

or equal to K

or greater than K

depend on the preference parameters.

This allows us to estimate

the preference parameters.h

c

I0

w0

w1

I1

0 K


Let h(w,I) the solution to U(h,c) s.t. c = wh + I, for generic values of w and I. Then it can be verified that the solution to the problem

is (Kuhn-Tucker):

0 0

1 1

max ( , )s.t.

0

U h c

c I w hc I w hh


0 0

0 0 0 0

0 0 1 1

1 1 1 1

0 if ( , ) 0 ( , ) if 0 ( , )

* if ( , ) and ( , )

( , ) if ( , )

h w Ih w I h w I K

hH h w I K h w I Kh w I h w I K

Modelling strategiesStructural “marginalist”: the decline

• The methods proposed by Heckman and (mostly) Hausman work well with convex budget sets and in the two-good case (i.e. leisure and consumption of a single decision maker).

• They tend to become cumbersome and fragile with non-convex budgets, simultaneous household decisions etc.

Modelling strategiesStructural “marginalist”: the decline

h

c

Modelling strategiesA new approach: discrete choice and random utility

• In the labour supply area – as well as in other areas - , a new approach emerges in the early 90s, based on the contributions by McFadden (1974, 1984).

• Oppurtunity set as a set of discrete alternatives.• Random utility.• A very early contribution: Zabalza et al. (1980).

Modelling strategiesFrom this…

h

c

Modelling strategies…to this

h

c

Modelling strategiesDiscrete choice and random utility

• In our survey we distinguish two main types:

• The Random Utility-Fixed Opportunities (RUFO) model (Van Soest 1995 etc.).

• The Random Utility–Random Opportunities (RURO) model (Dagsvk 1994; Aaberge, Dagsvik and Strøm 1995; Aaberge, Colombino and Strøm 1999; etc.).

Modelling strategiesRUFO

There just one opportunity of each type:

h

c

hi

ci

Modelling strategiesRUFO

• Random utility:

• ε is extreme-value distributed

• Choice probability in the RUFO model:

exp ( ,c )

( ,c )exp ( ,c )

i ii i

j jj

v hh

v h

( , ) ( , )U h c v h c

Modelling strategiesRUROThere might be many opportunities of each type:

h

c

Modelling strategiesRURO

• Random utility:

• Random opportunities:

• Choice probability in the RURO model:

exp ( ,c ) ( ,c )

( ,c )exp ( ,c ) ( ,c )

i i i ii i

j j j jj

v h p hh

v h p h

( , ) ( , )U h c v h c

( , ) density of opportunities of type ( , ) k k k kp h c h c

Modelling strategiesRUFO and RURO

• In both versions, it is evident the advantage with respect to the “marginalist” approach:

• however complicated the budget constraint, the model is not affected by those complications.

Can we do without structural models?


• Structural models are necessary for ex-ante policy evaluation.

• We need estimates of parameters that are invariant with respect to policy changes (Marshack 1953, Hurwicz 1962, Heckman 1974, Lucas 1976): i.e. structural parameters…



• Structural models are often criticized for requiring many untestable assumptions. However:

• The ultimate test of reliability of structural estimates is out-of-sample prediction (Keane 2010).

• Not many – but somewhat reassuring exercises (Aaberge & Colombino 2006, Keane & Wolpin 2002, Todd & Wolpin 2006 etc.).

• Structural modelling do not necessarily need strict parametric assumptions (e.g. Blomquist & Newey 2002, Todd & Wolpin 2008, Manski 2012).



• …Moreover:• Structural parameters can also be estimated with experimental or quasi-

experimental data (e.g. Todd & Wolpin 2006, Bargain & Doorley 2013): this might make them more robust.

• Sometimes, policy-invariant parameters can be estimated with minimal parametric assumptions (e.g. the “sufficient statistics” idea of Chetty 2009).

Can we do without utility maximization?


• Behavioural economics (great paper: Chetty 2015).• Agent-Based Modelling: lots of experiments in urban and land use

studies (transportation, traffic, location etc.) using ABM.• Microsimulation platforms seem to provide the ideal environment to try

and introduce these alternative (more general?) representations of choices and interaction among agents.

Identifying Optimal Policies


• Labour supply is central not only in the design and evaluation of specific tax-benefit reforms, but also in the identification of optimal tax-benefit systems (Mirrlees 1971 etc.)

• There have been many exercises that use recent theoretical results by Saez (2001, 2002) in combination with microeconometric estimates (e.g. Blundell et al. 2009).

Identifying Optimal PoliciesSaez (2002):

Identifying Optimal Policies• The above procedure is at risk of being inconsistent, since the

assumptions undelying the theretical results are very different from the assumptions used in the microeconometric estimation.

• A better procedure: directly use the microeconometric model and identify the optimal tax-transfer rule by simulation.

Aaberge & Colombino (2006, 2012, 2013)Blundell & Shephard (2012)

* * * *1 1 1

* *

* *

1

Iterative maximization algorithm

Model micro-simulation

Public budget constraint

max , ,..., ,

s.t.

, argmax , s.t. ( , ; ),

( , ; ) .

N N N

i i i i

N

i i i i i ii

W U h c U h c

h c U h c c f wh I i

w h I f w h I R

Identifying Optimal Policies


• The above procedure has been applied to specific countries (Italy, Norway and UK).

• However, optimal taxation theory produces general results: given the primitives (preferences, productivities etc.) of the economy you get the optimal tax-benefit rule.

• Can we attain a similar level of generality with the microsimulation approach?

Identifying (General) Optimal Policies• Yes:

• Identify the optimal rules for M economies characterized by primitives P1, …, PM.

• Identify the mapping P →

1 ,..., M

.

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