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1. Eidgenössische Technische Hochschule ZürichSwiss Federal Institute of Technology Zurich Overview of the Possibilities of Quantitative Methods in Political Science Tobias…

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1. Eidgenössische Technische Hochschule ZürichSwiss Federal Institute of Technology Zurich Overview of the Possibilities of Quantitative Methods in Political Science Tobias Böhmelt ETH Zurich tobias.boehmelt@ir.gess.ethz.chInternational Relations 2. Overview • Introduction • EITM - The Importance of Methods • Choice of Methods • What is Quantitative Methodology? • The Approach of Quantitative Methods in Political Science • Short Overview of Possibilities • Some Problems and Caveats • Conclusion 3. Introduction• What do I hope to accomplish?– Teaching you in-depth knowledge of some quantitative approaches?– Teaching you how to employ quantitative methods?– Making you familiar with statistical software packages? • The answer is simple – no.• Instead:– Clarify the value and challenges of quantitative research.– Help you to get interested in these methods for conducting moreeffective research. 4. EITM – The Importance of Methods: Why Do We Need Methods to Answer Questions in Political Science?EITM – Empirical Implications of Theoretical Models • Prerogative of theory. • Characteristics of theory determine the testing method: scope and generality, parsimony and complexity, prediction and explanation. • Estimating average causal effects or explaining the complexity of a single event? • The “degree of freedom problem:” most theories argue ceteris paribus, other effects have to be controlled for. This is often not possible with one or two cases. • Is it important how much a variable matters or just that it matters? • Case selection: selection bias, self-selection, selection on the dependent variable lack of independence of cases leads to false conclusions. 5. EITM – The Importance of MethodsThe Basic Research Design Problem • N problems = . • For any problem, N theories = . • For any theory, N models = . • For any problem, the number of empirical specifications = . This has implications for the use of methods! 6. EITM – The Importance of Methods• Science contributes to society by simplifying complex phenomena. – Its value increases with the value of the simplification.• Interesting topics per se are insufficient. – You must be able to lead people from where they are to a betterconclusion. 1. The goal is inference. 2. The procedures are public. 3. The conclusions are uncertain. 4. The content is the method. 7. Choice of MethodsFactors Influencing the Research Outcome – A Methods Perspective• The chosen theoretical approach (paradigm) affects the results – approaches oftenpredefine the method to be applied for testing hypotheses.• The method you choose to test propositions impacts the results you get: quantitativevs. qualitative approaches scope and generalizability are crucial!• Case selection: the selection of cases on the basis of the dependent variableimpedes the accumulation of knowledge: this leads to selection bias.• Careful case selection on explanatory variables is crucial in order to obtain reliableand valid results.• Selection criteria should be explicitly stated to ensure replicability and show howselection possibly drives the results. 8. Choice of MethodsDifferent Methods Have Different Comparative Advantages• Deduction: method follows theory:– Test implications of theories against empirical observations.– Hypotheses testing logic of confirmation.• Induction: method used to create or amend theories:– Develop theories: induction, hypothesis formation by studying deviantand outlier cases, historical explanation of individual cases.– Modify theories: adapt theories to outliers. 9. Choice of Methods• Trade off between explanation and prediction.• In general: quantitative methods have a high predictive power andqualitative a high explanatory power.• Theory testing often requires the combination of qualitative andquantitative methods:– qualitative research looks at outliers of a quantitative analysis.– case studies identify important variables and conceptualize variables.– study the crucial case to test the underlying causal mechanism.– study deviant or outlier cases to analyze why these cases do not fit the theory.– study important historical cases. 10. What is Quantitatitve Methodology?Has to do with “numbers”…Simple Example demonstrating the„Usefulness‟ of Statistics:Homer is questioned about his newlyformed vigilante group.Newscaster: “Since your group started up,petty crime is down 20%, but other crimesare up. Such as heavy sack beating, whichis up 800%. So you‟re actually increasingcrime.”Homer: “You can make up statistics toprove anything.” 11. What is Quantitatitve Methodology?Curtis Signorino (1999) “How to Translate a Theory into a StatisticalModel:”1. Specify the theoretical choice model.2. Add a random component (the source of uncertainty).3. Derive the probability model associated with one‟s dependent variable.4. Construct a likelihood equation based on the probability model. 12. What is Quantitatitve Methodology?• Research techniques that are used to gather and analyze quantitativedata, i.e., information dealing with anything that is measurable.• Descriptive statistics: description of central variables by statisticalmeasures such as median, mean, standard deviation and variance.• Inferential statistics: test for a relationship between variables – at leastone explanatory factor and one dependent variable.• Inference is the goal: – is it possible to generalize the regression results for the sample under observation to the universe of cases (the population)? – can you draw conclusions for individuals, countries, and time-points beyond those observations in your data-set? 13. What is Quantitatitve Methodology?• For the application of quantitative data analysis it is crucial that theselected method is appropriate for the data structure:• Dependent Variable: – Dimensionality: spatial and dynamic. – continuous or discrete. – Binary, ordinal categories, count. – Distribution: normal, logistic, poison, negative binomial.• Critical points: – Measurement level of the DV and IV. – Expected and actual distribution of the variables. – Number of observations and variance. 14. What is Quantitatitve Methodology?Definition of Key Concepts:• Variable: a variable is any measured characteristic or attribute that hast thepotential to differ for different subjects.• Independent variables – explanatory variables – exogenous variables –explanans: variables that are causal for a specific outcome (necessaryconditions).• Intervening variables: factors that impact the influence of independentvariables, variables that interact with explanatory variables and alter theoutcome (sufficient conditions).• Dependent variables – endogenous variables – explanandum: outcomevariables, that we want to explain. 15. What is Quantitatitve Methodology?Definition of Key Concepts:• Sample: a specific subset of a population (the universe of cases) – Samples can be random or non-random=selected – For most simple statistical models random samples are a crucial prerequisite• Random sample: drawn from the population in a way that every item in thepopulation has the same opportunity of being drawn – the observations of therandom sample are thus independent of each other.• Sampling error: one sample will usually not be completely representative of thepopulation from which it was drawn – this random variation in the results is known assampling error.• For random samples, mathematical theory is available to assess the sampling error,estimates obtained from random samples can be combined with measures of theuncertainty associated with the estimate, e.g. standard error, confidence intervals. 16. What is Quantitatitve Methodology?Random Samples• Observations are independent of each other.• The random sample mimics the distribution and all characteristics of the underlyingpopulation.• Sampling error is white noise, a random component with no structure, and cantherefore be assessed by mathematical and statistical tools.• Often: not observing a random sample renders statistical results biased andunreliable.Selected Samples• Sample selected on the basis of a specific criterion connected with the dependentvariable.• Sample selection often precludes inference beyond the sample and rendersestimation results biased.• One has to be aware of possible sample selection and account for the possible biasespecially of test statistics. 17. The Approach of Quantitative Political ScienceDatasets• Datasets contain dependent, independent, and intervening variablesfor a specific sample in order to answer a research question/testingspecific theoretical propositions.• All variables in the data have the same dimensionality (observationsfor the same cases, units, and time points).• Variables in a data can have different measurement levels, types, anddistributions. 18. The Approach of Quantitative Political Science 19. The Approach of Quantitative Political Science – Types of DataMicro Data: Individual Data• Survey data: Eurobarometer, National Election Study (US), British Election Study,socio-economic panel (Germany and other countries).Macro Data: Aggregated Data at Different Levels• Economic indicators: Inflation, Unemployment, GDP, growth, population (density)and demographic data, government spending, public debt, tax rates, governmentrevenue, interest rates, exchange rates, income distribution, FDI, foreign aid, trade(exports/ imports), no of employees in different sectors etc.• Political indicators: electoral system (majority, proportional), political system(parliamentary, presidential, federal), political institutions, number of veto players,regime type (democracy, autocracy), union density, labor market regulations, wagenegotiation system (corporatism), human and civil rights, economic and financialopenness, political particularism etc. 20. The Approach of Quantitative Political Science – Types of DataDimensionality of the Data• Cross-sectional data: observations for N units at one point in time.• Time series data: observations for one unit at different points in time.• Panel data: observations for N units at T points in time: N issignificantly larger than T – mostly used for micro data – units areindividuals.• Time series cross section (TSCS) data: panel data, but mostly used formacro data – aggregated (country) data.• Cross section time series (CSTS) data: observations for N units at Tpoints in time: T > N. 21. The Approach of Quantitative Political Science – Data SourcesEconomic Data• OECD: national accounts, government revenue, taxation, main economic indicators(unemployment, inflation, GDP), earnings, labour market, FDI, social expenditure, debt,employment etc.• IMF: economic indictors, direction of trade statistics, international financial statistics (interestrates, exchange rates, capital flows)• World bank: economic indicators• PennWorld tables: macro-economic data• ILO: labour market statistics• WTO: data on preferential trade agreements etc.Political Data• Eurobarometer: regular surveys, microdata European countries• Polity: degree of democracy• Freedom house: human and civil rights• Correlates of War: MID, alliance, membership in IGOs• Event data bases: WEIS (World Event Interaction Survey), IDEA• Cingranelli-Richards (CIRI) Human Rights Database: Political freedom, political rights, civil- andhuman rights. 22. Short Overview of Possibilities 23. Short Overview of Possibilities 24. Short Overview of Possibilities 25. Short Overview of Possibilities 26. Short Overview of Possibilities 27. Short Overview of Possibilities: OLS Regression• A metric variable Y can be determined by a function of X• The specific values of Y therefore depend on the specific values of XY = f(X)• The most straightforward association of such a relationship is linearY = f(X) = a + bX• The „line‟ is hence uniquely determined by two factors:• the constant (a), i.e. the point where the „line‟ crosses the y-axis• and the slope (b), i.e. how does Y change if X is increased by one unit 28. Short Overview of Possibilities: OLS Regression 29. Short Overview of Possibilities: OLS RegressionWe do not have „deterministic‟ relationships, however! Hard – if not impossible - to find in Political Science! 30. Short Overview of Possibilities: OLS Regression• It is impossible to find a linear line on which all points lie jointly.• Nonetheless, you can try to capture all these points straight through aline that describes the underlying relationship in the best way.• And THIS is exactly what regression analysis tries to do.• Which straight line is the best, though? 31. Short Overview of Possibilities: OLS Regression• The method for doing this is called OLS – ordinary least squares.• The function shall plot a straight line through the points so that thesquared distances between the actually observed values (yi) and thevalues as predicted by the function (ŷi) are minimized when summed up.• The straight line – or the parameters of a and b – is chosen thatminimizes the sum of the residuals ei: 32. Short Overview of Possibilities: OLS Regression• The equation for the OLS function is written like this: ŷi = a + bxiyi = a + bxi + ei• The “hat” in the first equation demonstrates that we are just dealingwith estimates ŷi that may differ from the actual values of Y.• Regarding the second equation, the error term ei indicates that not allvalues of our observations may be found on the straight lineautomatically.• It is an approach to capture the underlying relationship as closely aspossible!• It is an estimation! 33. Short Overview of Possibilities: OLS Regression• How to determine the “quality” of a regression line?• Follow the principle of ANOVA: Analysis of Variance. 34. Short Overview of Possibilities: OLS Regression yi = a + bxi + ei conflict=34.94+1.46*water+ eiregression conflict waterSource | SS df MS Number of obs=557-------------+------------------------------F( 1, 555) = 195.62 Model | 16311.805 1 16311.805Prob > F = 0.0000Residual | 46278.3932555 83.3844922 R-squared= 0.2606-------------+------------------------------Adj R-squared= 0.2593 Total | 62590.1981556 112.572299 Root MSE = 9.1315------------------------------------------------------------------------------conflict |Coef. Std. Err.tP>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- water | 1.462844 .104589913.99 0.000 1.2574041.668285 _cons | 34.93685 .647672653.94 0.000 33.6646636.20904------------------------------------------------------------------------------ 35. Short Overview of Possibilities: OLS Regression 36. Problems with Quantiative Research – Stargazing• Begin with a hunch that a particular variable has an unappreciatedassociation with [environmental conflict].• A standard regression is run. The analyst looks for “stars.”• If the stars support the hunch, then the examination stops.• Otherwise, additional regressions are run. No easily stated theoryguides such decisions.• The process stops when the stars align. 37. Problems with Quantiative Research – Misspecification• Claim: “X1, has no effect on Y.”• Evidence: the coefficient of X1 does not achieve a particular level ofstatistical significance. – So, X1 does not have a statistically significant effect within the stated model.• What if the true underlying data generating mechanism is not identicalto the structure of the stated model? 38. Problems with Quantiative Research – Remedies• New estimators.• Replication data.• Greater rigor in relations between theoretical models andthe empirical models used to evaluate them.• Increase transparency and build credibility throughtheoretical development and evaluation.• The importance of transparency and rigor does not stopwhen you have developed an empirical model. 39. Problems with Quantiative Research – RemediesSantiago Ramon y Cajal (1916)“What a wonderful stimulant itwould be for the beginner if hisinstructor, instead of amazing anddismaying him with the sublimityof great past achievements, wouldreveal instead the origin of eachscientificdiscovery… –information that, from a humanperspective, is essential to anaccurate explanation of thediscovery.” 40. Conclusion • EITM - The Importance of Methods • Choice of Methods • What is Quantitative Methodology? • The Approach of Quantitative Political Science • Short Overview of Possibilities • Some Problems and Caveats • Any questions?