The methodology of econometrics is the study of the range of differing approaches to undertaking
econometric analysis
Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships.M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8 ...
.
Commonly distinguished differing approaches that have been identified and studied include:
* the
Cowles Commission
The Cowles Foundation for Research in Economics is an economic research institute at Yale University. It was created as the Cowles Commission for Research in Economics at Colorado Springs in 1932 by businessman and economist Alfred Cowles. In 193 ...
approach
* the
vector autoregression
Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type of stochastic process model. VAR models generalize the single-variable (univariate) autoregres ...
approach
* the
LSE approach to econometrics
The LSE approach to econometrics, named for the London School of Economics, involves viewing econometric models as ''reductions'' from some unknown data generation process (DGP). A complex DGP is typically modelled as the starting point and this co ...
- originated with
Denis Sargan
John Denis Sargan, FBA (23 August 1924 – 13 April 1996) was a British econometrician who specialized in the analysis of economic time-series.
Sargan was born in Doncaster, Yorkshire in 1924, and was educated at Doncaster Grammar School and ...
now associated with
David Hendry (and his general-to-specific modeling). Also associated this approach is the work on integrated and cointegrated systems originating on the work of
Engle and
Granger
Granger may refer to:
People
*Granger (name)
*Hermione Granger, a fictional character in Harry Potter
United States
* Granger, Indiana
* Granger, Iowa
* Granger, Minnesota
* Granger, Missouri
* Granger, New York
* Granger, Ohio
* Granger, Texas ...
and
Johansen
Johansen is a Scandinavian patronymic surname meaning ''"son of Johan (given name), Johan"''. It is most common in Denmark and Norway. The Sweden, Swedish variant is Johansson, while the most common spelling in the US is Johanson. There are still ...
and
Juselius (Juselius 1999)
* the use of calibration -
Finn Kydland
Finn Erling Kydland (born 1 December 1943) is a Norwegian economist known for his contributions to business cycle theory. He is the Henley Professor of Economics at the University of California, Santa Barbara. He also holds the Richard P. Simmons ...
and
Edward Prescott
Edward Christian Prescott (December 26, 1940 – November 6, 2022) was an American economist. He received the Nobel Memorial Prize in Economics in 2004, sharing the award with Finn E. Kydland, "for their contributions to dynamic macroeconomics ...
* the ''
experimentalist
Experimentalism is the philosophical belief that the way to truth is through experiments and empiricism. It is also associated with instrumentalism, the belief that truth should be evaluated based upon its demonstrated usefulness. Experimentalism i ...
'' or
difference in differences
Difference in differences (DID or DD) is a statistical technique used in econometrics and quantitative research in the social sciences that attempts to mimic an experimental research design using observational study data, by studying the differ ...
approach -
Joshua Angrist
Joshua David Angrist (born September 18, 1960) is an Israeli-American economist and Ford Professor of Economics at the Massachusetts Institute of Technology. Angrist, together with Guido Imbens, was awarded the Nobel Memorial Prize in Economics ...
and
Jörn-Steffen Pischke.
In addition to these more clearly defined approaches,
Hoover 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 model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample data (and similar data from a larger Statistical population, population). A statistical model repres ...
s to study economic questions, but most often they are with
observational
Observation is the active acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the perception and recording of data (information), data via the use of scienti ...
data, rather than in
controlled experiments
A scientific control is an experiment or observation designed to minimize the effects of variables other than the independent variable (i.e. confounding variables). This increases the reliability of the results, often through a comparison be ...
.
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
In statistics, exploratory data analysis (EDA) is an approach of analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but pr ...
may by useful for generating new hypotheses. Economics often analyzes systems of equations and inequalities, such as
supply and demand
In microeconomics, supply and demand is an economic model of price determination in a Market (economics), market. It postulates that, Ceteris paribus, holding all else equal, in a perfect competition, competitive market, the unit price for a ...
hypothesized to be in
equilibrium. Consequently, the field of econometrics has developed methods for
identification
Identification or identify may refer to:
*Identity document, any document used to verify a person's identity
Arts, entertainment and media
* ''Identify'' (album) by Got7, 2014
* "Identify" (song), by Natalie Imbruglia, 1999
* Identification ( ...
and
estimation
Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is der ...
of
simultaneous-equation models. These methods are analogous to methods used in other areas of science, such as the field of
system identification
The field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data. System identification also includes the optimal design of experiments for efficiently generating informative data f ...
in
systems analysis
Systems analysis is "the process of studying a procedure or business to identify its goal and purposes and create systems and procedures that will efficiently achieve them". Another view sees system analysis as a problem-solving technique that b ...
and
control theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
. 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
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...
. Regression methods are important in econometrics because economists typically cannot use
controlled experiments
A scientific control is an experiment or observation designed to minimize the effects of variables other than the independent variable (i.e. confounding variables). This increases the reliability of the results, often through a comparison be ...
. Econometricians often seek illuminating
natural experiment
A natural experiment is an empirical study in which individuals (or clusters of individuals) are exposed to the experimental and control conditions that are determined by nature or by other factors outside the control of the investigators. The pro ...
s in the absence of evidence from controlled experiments. Observational data may be subject to
omitted-variable bias
In statistics, omitted-variable bias (OVB) occurs when a statistical model leaves out one or more relevant variables. The bias results in the model attributing the effect of the missing variables to those that were included.
More specifically, OV ...
and a list of other problems that must be addressed using causal analysis of simultaneous-equation models.
Experimental economics
In recent decades, econometricians have increasingly turned to use of
experiments
An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when ...
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.
Data
Data set A data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the ...
s to which econometric analyses are applied can be classified as
time-series data
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Exa ...
,
cross-sectional data
Cross-sectional data, or a cross section of a study population, in statistics and econometrics, is a type of data collected by observing many subjects (such as individuals, firms, countries, or regions) at the one point or period of time. The analy ...
,
panel data
In statistics and econometrics, panel data and longitudinal data are both multi-dimensional data set, data involving measurements over time. Panel data is a subset of longitudinal data where observations are for the same subjects each time.
Time s ...
, and
multidimensional panel data
In econometrics, a multidimensional panel data is data of a phenomenon observed over three or more dimensions. This comes in contrast with panel data, observed over two dimensions (typically, time and cross-sections). An example is a data set cont ...
. 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
The Survey of Professional Forecasters (SPF) is a quarterly survey of macroeconomic forecasts for the economy of the United States issued by the Federal Reserve Bank of Philadelphia. It is the oldest such survey in the United States.
The survey i ...
contains forecasts for many forecasters (cross-sectional observations), at many points in time (time series observations), and at multiple forecast horizons (a third dimension).
Instrumental variables
In many econometric contexts, the commonly used
ordinary least squares
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the prin ...
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 variable
In statistics, econometrics, epidemiology and related disciplines, the method of instrumental variables (IV) is used to estimate causal relationships when controlled experiments are not feasible or when a treatment is not successfully delivered to ...
s (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
In statistics, econometrics, epidemiology and related disciplines, the method of instrumental variables (IV) is used to estimate causal relationships when controlled experiments are not feasible or when a treatment is not successfully delivered to ...
), and Three-Stage Least Squares (
3SLS).
Computational methods
Computational concerns are important for evaluating econometric methods and for use in decision making. Such concerns include
mathematical
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
well-posedness: the
existence
Existence is the ability of an entity to interact with reality. In philosophy, it refers to the ontology, ontological Property (philosophy), property of being.
Etymology
The term ''existence'' comes from Old French ''existence'', from Medieval ...
,
uniqueness
Uniqueness is a state or condition wherein someone or something is unlike anything else in comparison, or is remarkable, or unusual. When used in relation to humans, it is often in relation to a person's personality, or some specific characterist ...
, and
stability
Stability may refer to:
Mathematics
*Stability theory, the study of the stability of solutions to differential equations and dynamical systems
**Asymptotic stability
**Linear stability
**Lyapunov stability
**Orbital stability
**Structural stabilit ...
of any solutions to econometric equations. Another concern is the numerical efficiency and accuracy of software. A third concern is also the usability of
econometric software
The following tables compare general and technical information for a number of statistical analysis packages.
General information
Operating system support
ANOVA
Support for various ANOVA methods
Regression
Support for various regression m ...
.
Structural econometrics
Structural econometrics extends the ability of researchers to analyze data by using
economic model
In economics, a model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework desig ...
s as the lens through which to view the data. The benefit of this approach is that, provided that counter-factual analyses take an agent's re-optimization into account, any policy recommendations will not be subject to the
Lucas critique
The Lucas critique, named for American economist Robert Lucas's work on macroeconomic policymaking, argues that it is naive to try to predict the effects of a change in economic policy entirely on the basis of relationships observed in historic ...
. 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.
One example is
dynamic discrete choice, where there are two common ways of doing this. The first requires the researcher to completely solve the model and then use
maximum likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimation theory, estimating the Statistical parameter, parameters of an assumed probability distribution, given some observed data. This is achieved by Mathematical optimization, ...
. The second bypasses the full solution of the model and estimates models in two stages, allowing the researcher to consider more complicated models with strategic interactions and multiple equilibria.
Another example of structural econometrics is in the estimation of
first-price sealed-bid auction
A first-price sealed-bid auction (FPSBA) is a common type of auction. It is also known as blind auction. In this type of auction, all bidders simultaneously submit sealed bids so that no bidder knows the bid of any other participant. The highest bi ...
s with independent private values.
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
Mechanism design is a field in economics and game theory that takes an objectives-first approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally. Because it starts a ...
. In a first price sealed bid auction the expected payoff of a bidder is given by:
:
where v is the bidder valuation, b is the bid. The optimal bid
solves a first order condition:
:
which can be re-arranged to yield the following equation for
:
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
nonparametric estimators, such as
kernel regression
In statistics, kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation between a pair of random variables ''X'' and ''Y''.
In any nonparametric r ...
. 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.
References
Other sources
*Darnell, Adrian C. and J. Lynne Evans. (1990) ''The Limits of Econometrics''. Aldershot: Edward Elgar.
*Davis, George C. (2000) “A Semantic Conception of Haavelmo’s Structure of Econometrics”, ''Economics and Philosophy'', 16(2), 205–28.
*Davis, George (2005) “Clarifying the ‘Puzzle’ Between Textbook and LSE Approaches to Econometrics: A Comment on Cook’s Kuhnian Perspective on Econometric Modelling”, ''Journal of Economic Methodology''
*Epstein, Roy J. (1987) ''A History of Econometrics''. Amsterdam: North-Holland.
*Fisher, I. (1933) “Statistics in the Service of Economics,” ''
Journal of the American Statistical Association
The ''Journal of the American Statistical Association (JASA)'' is the primary journal published by the American Statistical Association, the main professional body for statisticians in the United States. It is published four times a year in March, ...
'' 28(181), 1-13.
*Gregory, Allan W. and Gregor W. Smith. (1991) “Calibration as Testing: Inference in Simulated Macroeconomic Models,” ''Journal of Business and Economic Statistics'' 9(3), 297-303.
*Haavelmo, Trgyve. (1944) “The Probability Approach in Econometrics,” ''Econometrica'' 12 (supplement), July. 41
*Heckman, James J. (2000) “Causal Parameters and Policy Analysis in Economics: A Twentieth Century Retrospective,” ''Quarterly Journal of Economics'' 115(1), 45-97.
*Hoover, Kevin D. (1995b) “Why Does Methodology Matter for Economics?” Economic Journal 105(430), 715-734.
*Hoover, Kevin D. (ed.) (1995c) ''Macroeconometrics: Developments, Tensions, and Prospects''. Dordrecht: Kluwer.
*Hoover, Kevin D. “The Methodology of Econometrics,” revised 15 February 2005
*Hoover, Kevin D. and Stephen J. Perez. (1999) “Data Mining Reconsidered: Encompassing and the General-to-Specific Approach to Specification Search,” Econometrics Journal 2(2), 167-191. 43
*Juselius, Katarina. (1999) “Models and Relations in Economics and Econometrics,” Journal of Economic Methodology 6(2), 259-290.
*Leamer, Edward E. (1983) “Let’s Take the Con Out of Econometrics,” ''American Economic Review'' 73(1), 31-43.
*Mizon, Grayham E. (1995) “Progressive Modelling of Economic Time Series: The LSE Methodology,” in Hoover (1995c), pp. 107–170.
*{{cite book , last=Morgan , first=Mary S. , author-link=Mary S. Morgan , title=The History of Econometric Ideas , location=New York , publisher=Cambridge University Press , year=1990 , isbn=978-0-521-37398-2 , url=https://books.google.com/books?id=iUpDzJM9lq0C
*Spanos, Aris. (1986) ''Statistical Foundations of Econometric Modelling''. Cambridge: Cambridge University Press.
Econometrics
Economic methodology