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# Econ 3100, Chapter 2 Notes 3100

CU Denver

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This 15 page Class Notes was uploaded by Emily Banks on Friday September 2, 2016. The Class Notes belongs to 3100 at University of Colorado Denver taught by Professor Saul Hoffman in Fall 2016. Since its upload, it has received 3 views. For similar materials see Economics of Race and Gender in Economics at University of Colorado Denver.

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Date Created: 09/02/16

8/11/2016(revised) Ch. 2 – Economics Tools & Thinking – How Economists Do Economics MICROECONOMICS IN 5 REASONABLY EASY STEPS 1. Identify a “problem” – Real World Experience/Observation 2. Set the “problem” up -- Construct a model – role of theory What’s in? What’s out? 3. “Solve” the problem – find rule for best choice 4. Examine Comparative Statics - the most important part 5. Test the model - how? 1 STEP 2: Setting the Problem Up – The Formal Statement WHO? An Economic “Agent” (______________________) WHAT? Chooses something: amount of x to buy, amount of y to sell, # of children, whether to work, etc. Choice is constrained WHY? To maximize something (__________________) that is a function of the choice variable HOW? By following “best choice” rule, usually marginal conditions In equation form: Choose X to MAX V(X) subject to a constraint involving X and other variables (Z). Notation: ▯ X - Endogenous variable (what is being chosen) ▯ V - what is being maximized – Profits, utility, revenue ▯ V(X) - function describing relationship between V and X ▯ Z - Exogenous variable(s) (constraints) Call this structure Constrained Maximization 2 STEP 3: SOLVING THE PROBLEM Solutions come in two “styles” # 1 - Marginal Conditions (FOC) – reveal econ logic Examples: Generic Econ Problem: Benefit/Cost; B=_________; C=________ Choose _______ to Max __________________________ Solution: Specific: π-max Solution: #2 - “Best Choice Function” – rewrite FOC X* = f(Z), where X* is value of X that…. 3 STEP 4: COMPARATIVE STATICS How does X* change when Exogenous Variable changes? ▯ Key: X* changes to re-satisfy the marginal condition Theory should predict sign (or magnitude) of ΔX*/ΔZ ▯ Ex: π-maximization Comp Stat yields testable (refutable) hypothesis – this is core of scientific approach (refutability) 4 An Example–Consumer Demand Theory – ON YOUR OWN Set up as a Choice Problem ▯ Who? _____________ ▯ What? _____________ ▯ Why? ______________ U depends on amounts of goods; Choices are constrained by P & I Formal Version: Solution ▯ Marginal Conditions Best Choice Function ▯ X 1 = D(p1; other prices, income, preferences). What is this function?? Comparative Statics: ∆X*/∆Z Examples: 5 DIGRESSION –USEFUL TOOLS ▯ Functions -- Express relationship between variables; Written as X*=F(Z) or just X*( Z), where Z is ARGUMENT of function ▯ Role of theory – o #1:__________________________ o #2:___________________________ o General relationship: sign, but not numerical value TWO VERY USEFUL FUNCTIONS #1) UTILITY FUNCTION: relationship between amounts of goods consumed and satisfaction (utility) ▯ U = U(X ,1X 2 …, XN); U # on LHS is not a meaningful #. Only ordinal comparisons matter (larger/smaller). ▯ MU (X) ≡ ∆U/∆X (with amts of X ...X constant) = Marginal Utility x 2 N ▯ Almost always, MU (X)x↓ as X ↑--diminishing marginal utility 6 USING UTILITY FUNCTIONS o RATIONAL CHOICE: From utility to choice: If U(A) > U(B) and both are feasible, individual will choose A over B. ▯ REVEALED PREFERENCE (more important): From choice to utility: If A is chosen when B is available and feasible, then must be true that U(A) > U(B). Links observed behavior to underlying unobserved utility. ▯ More later - core of all demand theory #2: PRODUCTION FUNCTION: technological relationship betw amt of inputs & amount of output. ▯ Traditional for a firm, written as: _________________ ▯ Household Production Function: same idea applied to production in non-market sector. G = _______ where G is amount of household goods produced, T is time, Z is other inputs. ▯ Examples: Simple and deep 7 ▯ Important for analysis of women’s issues, b/c much of women’s time was (and is) outside the market. o Marriage, Fertility, and LFP ▯ MP and its Properties ON YOUR OWN ▯ Totals and Marginals (fig 2.1); Supply/ Demand (fig 2.2-2.4) ▯ See me if any problems 8 Step 5: Testing the Model - EMPIRICAL METHODS ▯ Test predictions of theory & provide quantitative estimates of impacts ▯ Analyze via statistical methods – regression analysis Regression Basics – How it Works, What Can Go Wrong, & How to Fix It ▯ Theory: causal relationship b/w some var X & outcome Y: X → Y. ▯ Write as regression equation: Y = α + βi + μ i i o Y is dependent variable, X is independent (causal) variable o i = unit of observation ( ) o μ (“mu”)- all else (unobservable) that affects Y; μ ~ Normal (0, σ ) 2 o α, β are parameters to be estimated from data on X and Y 9 ▯ Interpretation of regression equation: Y i α + βX i μ i o β shows strength and sign of relationship betw Y and X = ΔY/ΔX ˆ Regression finds values for α, β that best fit data& ▯ ▯ o E( ) = β – unbiased estimate. E = expected value = mean estimate if estimated over and over with diff sample. If unbiased, then β is true causal effect of X on Y ˆ o ▯ˆ and ▯ give best prediction of Y, given X (min sqrd error) Example: Fig 2.5—Studying and Grades (Hypothetical, Plausible) 10 Multiple regression: same idea with > 1 independent (causal) variable Yi= α + β 1 i1β X 2 i2X + .3 i3 μ i β 1 ∆Y/∆X , “1olding X and 2 consta3t” or “controlling for” X and X 2 3 Useful Regression Concepts ▯ Reliability: Is ▯ˆ statistically different from 0? -- t- statistic > 1.96 (95% confidence level) ▯ R = % of variance in Y explained by X. Higher better than lower, but be careful… ▯ Independent variables – continuous vs binary (dummy vars) o Measuring Gender or Race in a regression—how? 11 What Can Go Wrong: The Omitted Variables Problem in Regression ▯ True relationship: Y= α i β X + β1 i+ μ,2 it doi’t observe Z (or don’t include for other reasons) Instead estimate Y = a + γ X + 1 ii.ei, Z omitted) ▯ How does ???? ̂1compare toβ ? Is1E(???? ̂1) = β 1 Is it unbiased? ▯ General Answer – NO! (Usually, but not always) ▯ RULE 1: An omitted variable biases estimates of effect of all variables with which it is correlated o Bias = (effect of Z on Y) x (“correlation” between X and Z) =β 2 λ ZX 2 ▯ RULE 2: Omitted variables cause no problem (except low R ) if uncorrelated with included variable, b/c λ =0 ZX ▯ Examples – in the millions: Education and $; Class Size and Achievement; marriage and health. o Esp. likely when variable of interest is “chosen” by persons whose behavior is being examined via regression How big a problem is this? -- Causation vs correlation 12 Solving the omitted variable problem –Experimental Approaches Random Assignment (RCT–Randomized Controlled Trial) ▯ Medical examples ▯ Treatment effect (causal) = difference in mean outcomes (death rates, weight loss, etc) = ???? T ???? .C ▯ As a regression: Y = i + βT + i; T=itreatment indicator (dummy); β is treatment effect = ???? T ???? .C Strengths ▯ Don’t have to measure all other factors - why? ▯ Compare Clinical Trial (RCT) v epidemiological studies ▯ External validity & extrapolation outside experiment are weaknesses In Economics – ▯ Project STAR: Tennessee Student-Teacher Achievement Ratio rd 6,500 students in K-3 grade RA into either std size classes (22-25) or smaller classes (13-17). Tested outcomes all the way through college attendance ▯ Oregon Health Insurance Experiment: Medicaid expansion with lottery; losers of lottery were control group. Examined impact on financial hardship, self-reported health, and access to non- emergency hospital use. ▯ Economic Development: But can’t always do controlled experiments – why? Lead in Flint H O 2 13 NATURAL EXPERIMENTS ▯ When controlled experiments are impossible - look for natural ones! “As if” random or “almost as good” as random. Often policy change or geographic variation. But others… ▯ Key: “treatment” is random (or exogenous). Redefine idea of “Treatment” -- anything that differs across persons Examples– many more to come. We will see them throughout course. ▯ NJ v PA State Minimum Wage Increase ▯ 2009 Federal Minimum Wage Increase ▯ Affordable Care Act - health insurance for young adults < age 25. Compare % insured (I) before and after for 19-25 yr olds (treatment group) with 26-35 yr olds (control). o Result: ΔI – ΔI = +9 % pts – 0 % pts = 9% pts T C ▯ Health Outcomes in States that did and did not expand Medicaid under ACA Stay tuned: ▯ MTVs 16 & Pregnant and teen pregnancy; ▯ Some states provided access to contraceptives to young women sooner than others ▯ Effect of WWII on women’s LFP, via different mobilization rates of men by state ▯ Many, many more 14 How do you do a DID? Easy: If you can subtract…. See Fig 2.6 & Box 2.2 15

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