# Methodology of econometrics

The methodology of econometrics is the study of the range of differing approaches to undertaking econometric analysis.[1]

Commonly distinguished differing approaches that have been identified and studied include:

In addition to these more clearly defined approaches, Hoover[6] identifies a range of heterogeneous or textbook approaches that those less, or even un-, concerned with methodology, tend to follow.

## Methods

Econometrics may use standard statistical models to study economic questions, but most often they are with observational data, rather than in controlled experiments.[7] In this, the design of observational studies in econometrics is similar to the design of studies in other observational disciplines, such as astronomy, epidemiology, sociology and political science. Analysis of data from an observational study is guided by the study protocol, although exploratory data analysis may by useful for generating new hypotheses.[8] Economics often analyzes systems of equations and inequalities, such as supply and demand hypothesized to be in equilibrium. Consequently, the field of econometrics has developed methods for identification and estimation of simultaneous-equation models. These methods are analogous to methods used in other areas of science, such as the field of system identification in systems analysis and control theory. Such methods may allow researchers to estimate models and investigate their empirical consequences, without directly manipulating the system.

One of the fundamental statistical methods used by econometricians is regression analysis.[9] Regression methods are important in econometrics because economists typically cannot use controlled experiments. Econometricians often seek illuminating natural experiments in the absence of evidence from controlled experiments. Observational data may be subject to omitted-variable bias and a list of other problems that must be addressed using causal analysis of simultaneous-equation models.[10]

### Experimental economics

In recent decades, econometricians have increasingly turned to use of experiments to evaluate the often-contradictory conclusions of observational studies. Here, controlled and randomized experiments provide statistical inferences that may yield better empirical performance than do purely observational studies.[11]

### Data

Data sets to which econometric analyses are applied can be classified as time-series data, cross-sectional data, panel data, and multidimensional panel data. Time-series data sets contain observations over time; for example, inflation over the course of several years. Cross-sectional data sets contain observations at a single point in time; for example, many individuals' incomes in a given year. Panel data sets contain both time-series and cross-sectional observations. Multi-dimensional panel data sets contain observations across time, cross-sectionally, and across some third dimension. For example, the Survey of Professional Forecasters contains forecasts for many forecasters (cross-sectional observations), at many points in time (time series observations), and at multiple forecast horizons (a third dimension).[12]

### Instrumental variables

In many econometric contexts, the commonly used ordinary least squares method may not recover the theoretical relation desired or may produce estimates with poor statistical properties, because the assumptions for valid use of the method are violated. One widely used remedy is the method of instrumental variables (IV). For an economic model described by more than one equation, simultaneous-equation methods may be used to remedy similar problems, including two IV variants, Two-Stage Least Squares (2SLS), and Three-Stage Least Squares (3SLS).[13]

### Computational methods

Computational concerns are important for evaluating econometric methods and for use in decision making.[14] Such concerns include mathematical well-posedness: the existence, uniqueness, and stability of any solutions to econometric equations. Another concern is the numerical efficiency and accuracy of software.[15] A third concern is also the usability of econometric software.[16]

### Structural econometrics

Structural econometrics extends the ability of researchers to analyze data by using economic models as the lens through which to view the data. The benefit of this approach is that any policy recommendations are not subject to the Lucas critique since counter-factual analyses take an agent's re-optimization into account. Structural econometric analyses begin with an economic model that captures the salient features of the agents under investigation. The researcher then searches for parameters of the model that match the outputs of the model to the data. There are two ways of doing this. The first requires the researcher to completely solve the model and then use maximum likelihood.[17] However, there have been many advances that can bypass the full solution of the model and that estimate models in two stages. Importantly, these methods allow the researcher to consider more complicated models with strategic interactions and multiple equilibria.[18]

A good example of structural econometrics is in the estimation of first price sealed bid auctions with independent private values.[19] The key difficulty with bidding data from these auctions is that bids only partially reveal information on the underlying valuations, bids shade the underlying valuations. One would like to estimate these valuations in order to understand the magnitude of profits each bidder makes. More importantly, it is necessary to have the valuation distribution in hand to engage in mechanism design. In a first price sealed bid auction the expected payoff of a bidder is given by:

${\displaystyle (v-b)\Pr(b\ {\textrm {wins}})}$

where v is the bidder valuation, b is the bid. The optimal bid ${\displaystyle b^{*}}$  solves a first order condition:

${\displaystyle (v-b^{*}){\frac {\partial \Pr(b^{*}\ {\textrm {wins}})}{\partial b}}-\Pr(b^{*}\ {\textrm {wins}})=0}$

which can be re-arranged to yield the following equation for ${\displaystyle v}$

${\displaystyle v=b^{*}+{\frac {\Pr(b^{*}\ {\textrm {wins}})}{\partial \Pr(b^{*}\ {\textrm {wins}})/\partial b}}}$

Notice that the probability that a bid wins an auction can be estimated from a data set of completed auctions, where all bids are observed. This can be done using simple non-parametric estimators. If all bids are observed, it is then possible to use the above relation and the estimated probability function and its derivative to point wise estimate the underlying valuation. This will then allow the investigator to estimate the valuation distribution.

## The realism-antirealism debate

Similarly to the methodology of economics (cf.[20]), the empirical branch of the discipline also was the topic of the debate that dates back to Milton Friedman's[21] famous essay advising an instrumentalist interpretation of the discipline. According to the instrumentalist philosophy of science, models are interpreted as a tool and its truth or falsity is not considered. With the aim to save the viewpoint that econometric models depict (resemble, isolate, idealize, etc.) the realm of economy, various realist interpretations were put forth. Nancy Cartwright[22] interpreted the coefficients of econometric models as probabilistic, causal laws. Kevin Hoover[23] supported the standard scientific-realist interpretation of (econometric) models as isolations of reality. From the position of critical realism, Tony Lawson[24] argued that the lack of robustness of econometric models indicates their falsity, and therefore rejected the scientific-realist interpretation (cf. the criticisms of econometrics). In response to such criticms, Hoover[25] employed perspectival realism to defend the truth of econometric models. Considering that perspectivism is a pragmatically-flavored stance and does not presuppose the ontic commitment, Maziarz[26] employed Uskali Mäki's[27] model of modeling to show that econometric results differ because of their context-specificity, but pairs of contrary models can grasp different aspects of the same economic reality. In other words, purpose, audience, and context, in addition to target, influence the results of econometric modeling.

## References

1. ^ Jennifer Castle and Neil Shephard (Eds) (2009) The Methodology and Practice of Econometrics - A Festschrift in Honour of David F. Hendry ISBN 978-0-19-923719-7
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3. ^ Sims, Christopher (1980) Macroeconomics and Reality, Econometrica, January, pp. 1-48.
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5. ^ Angrist, J. D., & Pischke, J.-S. (2009). Mostly harmless econometrics: An empiricist's companion. Princeton: Princeton University Press.
6. ^ Hoover, Kevin D. (2006). Chapter 2, "The Methodology of Econometrics." in T. C. Mills and K. Patterson, ed., Palgrave Handbook of Econometrics, v. 1, Econometric Theory, pp. 61-87.
7. ^ Wooldridge, Jeffrey (2013). Introductory Econometrics, A modern approach. South-Western, Cengage learning. ISBN 978-1-111-53104-1.
8. ^ Herman O. Wold (1969). "Econometrics as Pioneering in Nonexperimental Model Building," Econometrica, 37(3), pp. 369-381.
9. ^ For an overview of a linear implementation of this framework, see linear regression.
10. ^ Edward E. Leamer (2008). "specification problems in econometrics," The New Palgrave Dictionary of Economics. Abstract.
11. ^ • H. Wold 1954. "Causality and Econometrics," Econometrica, 22(2), p p. 162-177.
• Kevin D. Hoover (2008). "causality in economics and econometrics," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract and galley proof.
12. ^ Davies, A., 2006. A framework for decomposing shocks and measuring volatilities derived from multi-dimensional panel data of survey forecasts. International Journal of Forecasting, 22(2): 373-393.
13. ^ Peter Kennedy (economist) (2003). A Guide to Econometrics, 5th ed. Description Archived 2012-10-11 at the Wayback Machine., preview, and TOC Archived 2012-10-11 at the Wayback Machine., ch. 9, 10, 13, and 18.
14. ^ • Keisuke Hirano (2008). "decision theory in econometrics," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
• James O. Berger (2008). "statistical decision theory," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
15. ^ B. D. McCullough and H. D. Vinod (1999). "The Numerical Reliability of Econometric Software," Journal of Economic Literature, 37(2), pp. 633-665.
16. ^ • Vassilis A. Hajivassiliou (2008). "computational methods in econometrics," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
• Richard E. Quandt (1983). "Computational Problems and Methods," ch. 12, in Handbook of Econometrics, v. 1, pp. 699-764.
• Ray C. Fair (1996). "Computational Methods for Macroeconometric Models," Handbook of Computational Economics, v. 1, pp. [1]-169.
17. ^ Rust, John (1987). "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher". Econometrica. 55 (5): 999–1033. JSTOR 1911259.
18. ^ Hotz, V. Joseph; Miller, Robert A. (1993). "Conditional Choice Probabilities and the Estimation of Dynamic Models". Review of Economic Studies. 60 (3): 497–529. JSTOR 2298122.
19. ^ Guerre, E.; Perrigne, I.; Vuong, Q. (2000). "Optimal Nonparametric Estimation of First Price Auctions". Econometrica. 68 (3): 525–574. doi:10.1111/1468-0262.00123.
20. ^ Mäki, U. (2009). Realistic realism about unrealistic models. The Oxford handbook of philosophy of economics.
21. ^ Friedman, Milton (1953). Essays in Positive Economics. University of Chicago Press. ISBN 9780226264035.
22. ^ Cartwright, Nancy (1994). Nature's Capacities and Their Measurement. Oxford University Press.
23. ^ Hoover, K. D. (2002). Econometrics and reality. Maki, U.(ed.), Economics and Reality. 152-177.
24. ^ Lawson, T. (1997). Economics and reality. Cambridge: Cambridge University Press.
25. ^ Hoover, Kevin. 2012. Pragmatism, perspectival realism, and econometrics. Lahtinen, Aki, Kuorikoski, Jakko, and Ylikoski, Petri (eds.). Economics for real: Uskali Mäki and the place of truth in economics, 223-240.
26. ^ Maziarz, Mariusz (2018-09-08). "'Emerging Contrary Result' Phenomenon and Scientific Realism". Panoeconomicus: 1–20. doi:10.2298/PAN171218024M. ISSN 2217-2386.
27. ^ Mäki, U. (2017). Modelling failure. In Logic, methodology and philosophy of science: Proceedings of the 15th international congress (Helsinki). London: College Publications.

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