If you’re on a deadline and one concept is blocking everything else, this page is built for fast scanning. Each “Why” links to a full explanation page, but the one-sentence answers here are designed to help you confirm you’re thinking about the right mechanism.
How to use this hub: Open the section closest to your course/topic. If you notice a gap in a spoke (e.g., you expected to see a topic family but it’s not here), that’s a signal for where we should add more “Why” pages next.
Finance
Corporate Finance & Portfolio Theory
- Why is NPV better than IRR for managerial decisions? — NPV measures dollar value creation using the correct discount rate, while IRR can mis-rank projects and fails with nonstandard cash flows.
- Why does the minimum-variance portfolio not depend on expected returns? — The MVP solves a pure risk minimization problem, so only the covariance matrix matters, not the mean returns.
- Why is the global minimum-variance portfolio unique? — With a positive definite covariance matrix, the quadratic program has a single minimizing weight vector.
- Why does the minimum-variance portfolio not depend on expected returns? — Because its objective is to minimize variance subject to weights constraints, not to optimize a mean-variance tradeoff.
- Why is the global minimum-variance portfolio unique? — Uniqueness follows from strict convexity of variance when the covariance matrix is full rank.
Financial Mathematics
- Why does compounding and discounting convert money across time in PV and FV calculations? — Interest rates define a growth/discount factor that translates cash flows to a common date for apples-to-apples comparison.
- Why do perpetuities have a simple formula but annuities do not? — A perpetuity is an infinite geometric series with a constant ratio, while annuities are finite and require subtracting a tail term.
- Why does the annuity formula look like a perpetuity minus a tail? — You price an infinite stream and subtract the present value of payments that would occur after the annuity ends.
- Why is a bond’s price equal to the present value of its future cash flows? — Arbitrage forces the bond price to equal the discounted value of coupons and principal at market-required yields.
- Why is a bond’s price equal to the present value of its future cash flows? — Yield to maturity is the single discount rate that equates the bond’s market price to discounted promised cash flows.
- Why does modified duration underestimate bond price changes? — Duration is a first-order linear approximation, so it misses curvature (convexity) effects for larger yield moves.
- Why does convexity make bond prices rise more than they fall? — Curvature means the price–yield relationship is nonlinear, so equal yield decreases produce larger price gains than equal yield increases produce losses.
- Why does put–call parity break and what does it mean? — Parity breaks when assumptions (same strike/maturity, frictionless trading, correct carry costs) are violated, creating arbitrage or mispricing signals.
- Why are risk-neutral probabilities not real probabilities in the binomial model? — They’re pricing weights chosen to enforce no-arbitrage, not empirical beliefs about up/down moves.
- Why are the inputs to the Black-Scholes model meaningful? — Each input maps to a specific economic driver of option value (time, volatility, carry, discounting, and moneyness).
Financial & Managerial Accounting
- Why does cost behavior in managerial accounting matter? — Classifying costs as fixed/variable/mixed determines forecasting, break-even analysis, and the profitability impact of volume changes.
- Why does activity-based costing allocate overhead more accurately than a single plant-wide rate? — ABC traces overhead via cost drivers tied to activities, reducing distortion when products consume resources unevenly.
- Why does contribution margin determine the break-even point in managerial accounting? — Contribution margin is the per-unit amount available to cover fixed costs, so break-even occurs when total CM equals fixed costs.
- Why does cost-volume-profit (CVP) analysis determine a firm’s break-even point and profit behavior? — CVP links price, variable cost, fixed cost, and volume to profit through the contribution margin framework.
- Why is contribution margin the foundation of break-even and variable costing? — Variable costing isolates variable costs so contribution margin directly shows how sales volume covers fixed costs and drives profit.
- Why can absorption costing show higher profit even when sales fall? — Fixed manufacturing overhead can be deferred in inventory under absorption costing, inflating current profit when production exceeds sales.
- Why are materials price variance and materials quantity variance separated? — Price variance isolates purchasing performance while quantity variance isolates usage/efficiency, enabling clearer accountability.
- Why does the quick ratio exclude inventory? — Inventory can be less liquid and harder to monetize quickly, so the quick ratio focuses on near-cash assets for short-term solvency.
- Why does vertical analysis use net sales and total assets as the base? — Scaling statements to a common base makes firms and time periods comparable by expressing each line as a percentage.
Management Science
Linear Programming & Optimization
- Why is the Big-M Method in Linear Programming important? — Big-M enforces constraints by penalizing artificial variables so the solver can start from an initial feasible basis.
- Why understand the Two-Phase Simplex Method in Linear Programming? — Two-phase finds feasibility first (Phase I) then optimizes the true objective (Phase II) without relying on huge penalty constants.
- Why do pivot rules matter in the simplex method? — Pivot rules control progress, avoid cycling, and influence numerical stability and speed of convergence.
- Why do basic feasible solutions correspond to corner points in linear programming? — Setting nonbasic variables to zero intersects constraints at extreme points, which are the polytope’s corners.
- Why does every linear programming problem have an optimal solution at a corner point? — A linear objective over a convex polytope attains its optimum at an extreme point (or along an edge of extreme points).
- Why do we identify basic feasible solutions in linear programming before solving? — Simplex moves between BFS corner points, so identifying them clarifies feasibility and the search structure.
- Why can a linear program be unbounded? — If the feasible region allows indefinite movement in an improving direction, the objective can increase (or decrease) without limit.
- Why do multiple optimal solutions occur in linear programming? — When the objective is parallel to a binding edge/face, every point on that edge can achieve the same optimum value.
- Why does degeneracy occur in linear programming? — A BFS can have more binding constraints than needed, creating zero basic variables and potential stalling/cycling.
- Why do shadow prices matter in linear programming? — Shadow prices quantify the marginal value of relaxing a constraint, turning constraints into interpretable economic tradeoffs.
- Why do reduced costs matter in linear programming? — Reduced costs show how much an objective coefficient must improve before a nonbasic variable should enter the solution.
- Why does sensitivity analysis matter in linear programming? — It tells you how robust the solution is to changes in costs, resource limits, and constraints without fully re-solving.
- Why does linear programming use duality? — Duality links primal decisions to resource prices, providing bounds, economic interpretation, and optimality certificates.
- Why does the transportation model matter in linear programming? — It’s a structured LP that models shipping flows efficiently and often solves faster via specialized network methods.
- Why does the max-flow min-cut theorem matter in network optimization? — It equates the best feasible flow with the tightest capacity bottleneck, giving both value and a diagnostic cut.
- Why does the Hungarian Method solve the assignment problem efficiently? — It exploits structure to find a minimum-cost perfect matching in polynomial time using reduced costs and augmenting steps.
- Why do linear, integer, and binary programming models capture real-world optimization problems? — Integer decisions represent yes/no and indivisible choices that linear models can’t express realistically.
- Why do linear, integer, and binary programming models give managers a disciplined way to optimize complex resource decisions? — They convert messy constraints and objectives into a solvable model with transparent tradeoffs and sensitivity outputs.
- Why do linear, integer, and binary programming models help organizations turn complex decisions into optimized, real-world solutions? — They enforce feasibility across many constraints while optimizing a measurable goal, reducing ad-hoc decision making.
- Why does branch and bound solve integer programming efficiently? — It prunes large parts of the search tree using LP relaxations as bounds, focusing only on promising regions.
- Why does the knapsack model capture real-world resource trade-offs? — It formalizes picking a best subset under a capacity limit, mirroring budgeting, selection, and allocation problems.
- Why is Integer Programming so much harder to solve than Linear Programming? — Integrality makes the feasible set nonconvex, turning the problem into combinatorial search rather than convex optimization.
- Why are binary decision variables essential in optimization? — They model on/off choices (open/close, select/reject) and logical constraints that determine real feasibility.
- Why rounding Linear Programming solutions fails in real business decisions — Rounding can violate constraints or destroy optimal structure because feasibility in integer problems is not preserved by rounding.
Inventory & Supply Chain Analytics
- Why does the EOQ model minimize total inventory cost? — EOQ balances ordering cost against holding cost to find the order quantity that minimizes their sum.
- Why does the Newsvendor Model maximize expected profit? — It sets the order quantity where marginal overage cost equals marginal underage cost via the critical fractile.
- Why do EOQ and newsvendor models balance cost tradeoffs in inventory decisions? — Both formalize the cost of too much vs too little inventory using holding/ordering or overage/underage tradeoffs.
- Why do EOQ and newsvendor models optimize inventory decisions? — They convert uncertainty and cost structure into a computable optimal policy rather than intuition-based ordering.
- Why does Little’s Law always work in queueing systems? — In stable systems, average inventory equals arrival rate times average time in system, independent of detailed distributions.
Statistical Process Control (SPC)
- Why do control charts matter in Statistical Process Control? — Control charts separate common-cause variation from special-cause signals so you don’t overreact or miss real problems.
- Why do SPC control charts identify process variation and prevent quality failures? — They detect shifts early so corrective action happens before defects propagate.
- Why does SPC allow managers to detect process problems before defects occur? — Ongoing monitoring flags abnormal patterns before output crosses specification limits.
- Why does SPC allow organizations to detect variation early and prevent quality failures? — Early detection reduces scrap/rework by correcting root causes while variance is still controllable.
- Why does SPC detect process problems before they become failures? — A process can drift while still producing “acceptable” units, and charts catch the drift before it becomes visible failures.
- Why does SPC give managers a real-time system for detecting process variation before it becomes a costly quality problem? — It provides decision rules that trigger investigation when statistical evidence of change appears.
- Why does SPC give organizations an early-warning system for detecting variation and preventing costly quality failures? — SPC creates a standardized alert system that scales across lines/teams without relying on subjective judgment.
Queueing, Capacity, and Service Operations
- Why is Little’s Law essential in operations and queueing? — It links throughput, work-in-process, and flow time so you can infer one from the other in stable systems.
- Why is it important to know the difference between throughput, capacity, and demand in operations? — Confusing them leads to wrong staffing/investment choices because capacity limits output while demand limits sales.
- Why bottleneck is essential in operations and process flow? — The bottleneck sets system throughput and queues, so improving non-bottlenecks rarely increases total output.
- Why is the M/M/1 queue essential in operations and service analytics? — It’s the simplest closed-form model that reveals how utilization drives waiting times nonlinearly.
- Why use the Erlang C formula in the M/M/s queue? — Erlang C estimates delay probability and waiting time in multi-server systems, enabling staffing decisions.
- Why does traffic intensity in the M/M/s queue determine system performance? — As utilization approaches 1, waiting times and queue lengths explode because service can’t keep up with arrivals.
- Why does the M/M/1 queue model matter in operations? — It provides a baseline benchmark for congestion effects when arrivals are random and service times are memoryless.
- Why does the M/M/s queue model improve multi-server staffing decisions? — It captures pooling and congestion effects when multiple agents serve one demand stream.
- Why delays escalate in real service systems? — High utilization amplifies variability, so small demand shocks create disproportionate increases in waiting time.
- Why do queueing models accurately predict congestion and waiting times in real service systems? — They combine arrival variability, service variability, and capacity to predict delay distributions, not just averages.
- Why do queueing models explain waiting times and congestion in service systems? — They show how randomness plus finite capacity creates queues even when average capacity exceeds average demand.
- Why do queueing models help managers diagnose congestion, quantify service levels, and justify staffing decisions? — They translate operational inputs into service metrics (wait, abandonment risk, utilization) for defensible staffing.
- Why do queueing models reveal how congestion builds and why delays explode in service systems? — Because queues grow superlinearly near capacity, models expose tipping points that intuition misses.
Decision Trees, Risk, and Simulation
- Why do decision trees improve managerial decisions? — They structure uncertain choices into comparable strategies with explicit probabilities, payoffs, and rollback logic.
- Why do decision trees, PERT/CPM, and simulation improve complex business decisions? — They model uncertainty and constraints explicitly so decisions are tested against variability rather than averages.
- Why do decision trees, PERT/CPM, and simulation support complex business decisions? — They provide a unified toolkit for sequencing, uncertainty, and tradeoffs when closed-form math is unrealistic.
- Why do managers use EVPI in decision trees? — EVPI quantifies the maximum you should pay for perfect information by comparing uncertainty vs certainty outcomes.
- Why do risk profiles matter more than expected value? — Expected value ignores variability and downside risk, while risk profiles show distributional outcomes decision-makers actually face.
- Why does Monte Carlo simulation beat best-case/worst-case scenarios? — It samples many plausible states to estimate full outcome distributions instead of a few arbitrary extremes.
- Why do managers use simulation instead of simple formulas? — Simulation handles nonlinearities, constraints, and correlated uncertainties that closed-form formulas can’t capture well.
- Why do managers use Excel Solver for optimization? — Solver makes optimization accessible by connecting spreadsheet models to LP/IP algorithms and sensitivity outputs.
- Why My Optimization Model Is Infeasible — Infeasibility typically comes from contradictory constraints, missing bounds, or unit/logic errors that eliminate all feasible solutions.
Project Scheduling (PERT/CPM)
- Why do PERT and CPM improve project scheduling? — They identify critical paths and slack, clarifying which activities control completion time and where delays matter.
Forecasting
- Why do forecasting models improve business planning and decision-making? — Forecasts convert uncertainty into probabilistic expectations that improve capacity, inventory, and budgeting choices.
- Why do forecasting models turn historical data into reliable business predictions? — They extract signal from noise using structured assumptions about trend, seasonality, and error processes.
- Why does exponential smoothing work for business forecasting? — It adaptively weights recent data more while still smoothing noise, performing well under gradual changes.
Statistics
Probability Foundations & Mathematical Statistics
- Why does variance measure the spread of a distribution? — It averages squared deviations from the mean, capturing typical dispersion while penalizing large deviations.
- Why does the standard error measure estimate precision? — SE is the standard deviation of an estimator’s sampling distribution, so smaller SE means tighter repeated estimates.
- Why does covariance measure how two variables move together? — It averages joint deviations from means, indicating whether variables tend to be high/low together.
- Why does correlation measure the strength of linear relationships? — Correlation rescales covariance by standard deviations, giving a unitless measure of linear association.
- Why does the z-score standardize values across different scales? — It converts values to “how many standard deviations from the mean,” enabling cross-scale comparisons.
- Why does the sample variance use n−1 instead of n? — Bessel’s correction offsets bias from estimating the mean, making the variance estimator unbiased under i.i.d. sampling.
- Why is the sample mean an unbiased estimator of the population mean? — The expected value of the sample mean equals the true mean when samples are random and identically distributed.
- Why does the sample mean have the key properties of unbiasedness, efficiency, and sufficiency? — In common exponential-family models, it captures all information about the mean and achieves the Cramér–Rao bound.
- Why do we use the Normal distribution to approximate the Binomial and Poisson distributions? — For large counts, standardized sums of independent variables become approximately normal by the CLT.
- Why do we use the Poisson distribution for counts and the Exponential distribution for waiting times? — In a Poisson process, event counts are Poisson and interarrival times are exponential by construction.
- Why do we use the Poisson distribution instead of the Binomial for modeling rare events? — With small event probability and large trials, Poisson approximates Binomial using a single rate parameter.
- Why does the Central Limit Theorem justify using normal-based confidence intervals in business statistics? — Many estimators are averages/sums, and their sampling distributions become approximately normal as sample size grows.
Statistical Inference
- Why does hypothesis testing guide statistical decision-making? — It formalizes evidence thresholds to control error rates when choosing between competing claims.
- Why does the t-test compare sample means effectively? — It standardizes mean differences by estimated standard error, accounting for sample size and variance.
- Why do we use the t-distribution instead of the normal distribution when σ is unknown? — Estimating σ adds uncertainty, and the t distribution adjusts tails accordingly for finite samples.
- Why do we use Welch’s t-test when population variances are unequal? — Welch adjusts degrees of freedom and standard error to remain valid under heteroskedasticity.
- Why do we use pooled variance in two-sample t-tests when population variances are assumed equal? — Pooling improves precision by combining variance information when equality is a reasonable assumption.
- Why does ANOVA detect differences across multiple group means? — It compares between-group variation to within-group variation using an F statistic grounded in variance decomposition.
- Why do we use ANOVA instead of multiple two-sample t-tests when comparing more than two group means? — ANOVA controls the overall Type I error rate that would inflate under many pairwise tests.
- Why does the chi-square test evaluate categorical relationships? — It compares observed counts to expected counts under independence or a specified distribution model.
- Why Fisher’s Exact Test and the Chi-Square Test useful? — Fisher is exact for small samples while chi-square is an approximation that works well when expected counts are large.
- Why Chi-Square Test of Independence different from Chi-Square Goodness-of-Fit test? — Independence tests association between two categorical variables; goodness-of-fit tests one variable against a target distribution.
- Why use the Likelihood Ratio Chi-Square Test? — The LR chi-square compares log-likelihoods and often aligns naturally with model-based inference and GLM frameworks.
- Why do we use maximum likelihood estimation in business statistics? — MLE provides a systematic way to estimate parameters by choosing values that make observed data most probable under a model.
- Why do we use the Method of Moments, and how does it compare to Maximum Likelihood Estimation? — MoM matches sample moments to theoretical moments for simplicity, while MLE is typically more efficient under correct specification.
- Why is the maximum likelihood estimator the most efficient estimator under regularity conditions? — Under standard conditions, MLE achieves the Cramér–Rao lower bound asymptotically, minimizing variance among unbiased estimators.
Regression, GLM, & Experimental Design
- Why do OLS regression coefficients represent marginal effects holding other variables constant? — OLS isolates partial associations by projecting y onto each regressor net of the others.
- Why do the Gauss-Markov assumptions guarantee OLS is the best linear unbiased estimator? — With exogeneity and homoskedastic errors, OLS has the smallest variance among all linear unbiased estimators.
- Why do t-tests and p-values measure whether a regression coefficient differs from zero? — They compare the estimate to its sampling uncertainty under the null using standardized test statistics.
- Why do we check for heteroskedasticity in regression analysis? — Non-constant error variance breaks standard OLS inference unless corrected with robust methods.
- Why does heteroskedasticity bias standard errors in multiple regression? — Conventional SE formulas assume constant variance, so heteroskedasticity makes them misstate uncertainty.
- Why do we check for multicollinearity in multiple regression? — High collinearity inflates coefficient variance, making estimates unstable and tests weak.
- Why does multicollinearity inflate standard errors in multiple regression? — When regressors move together, the model can’t disentangle their separate effects, increasing estimator variance.
- Why do we check residual plots when evaluating a regression model? — Residual patterns reveal misspecification (nonlinearity, heteroskedasticity, outliers) that summary stats can hide.
- Why do we use adjusted R² instead of regular R² in multiple regression? — Adjusted R² penalizes unnecessary regressors, reducing the “always increases” bias of plain R².
- Why does endogeneity bias OLS estimates in regression analysis? — Correlation between regressors and the error term violates exogeneity, shifting coefficients away from causal effects.
- Why does omitted variable bias distort regression coefficients in multiple regression? — Leaving out a relevant variable that correlates with included regressors pushes coefficients to absorb its effect.
- Why does omitting a relevant variable bias a regression coefficient upward or downward? — The direction depends on the sign of the omitted variable’s effect on y and its correlation with the included regressor.
- Why do we use regression instead of multiple t-tests when analyzing relationships between variables? — Regression models simultaneous controls, reducing omitted-variable confounding and multiple-testing issues.
- Why do we use multiple regression instead of simple regression when analyzing business data? — Business variables move together, so multiple regression isolates partial effects and improves prediction/control.
- Why does endogeneity bias OLS estimates in regression analysis? — Because the error term carries unmodeled influences that become entangled with endogenous regressors.
- Why My Regression Results Don’t Make Sense — When signs/magnitudes look wrong, it’s usually a specification, scaling, multicollinearity, or endogeneity issue rather than “randomness.”
Biostatistics & Survival Analysis
- What is the difference between the hazard function and the survival function? — Survival gives the probability of lasting beyond time t, while hazard is the instantaneous failure rate conditional on surviving to t.
- Why do we use the Kaplan–Meier estimator in survival analysis? — It estimates survival with censoring by multiplying conditional survival probabilities at observed event times.
- Why do we use the Cox Proportional Hazards model in survival analysis? — It models covariate effects on hazard without specifying the baseline hazard shape, balancing flexibility and interpretability.
Student “Stuck” Why Pages
- Why I’m Stuck on My Graduate Statistics Homework — Getting unstuck usually requires identifying whether the blocker is concepts, notation, assumptions, or a workflow/verification gap.
- Why My Assignment Results Don’t Match the Solution — Mismatches typically come from small setup differences (definitions, rounding, constraints, or omitted steps) rather than “wrong math.”
- Why My Exam Practice Problems Keep Going Wrong — Repeated errors often trace to one recurring misread (units, conditioning, hypotheses, or model assumptions) that needs a targeted fix.
- Why My Statistical Model Won’t Converge — Nonconvergence usually indicates identifiability problems, separation, scaling issues, or overly complex model structure for the data.
Economics
Microeconomics
- Why are isoquants convex, and what does diminishing MRTS mean? — Convexity reflects diminishing marginal rates of technical substitution as you substitute one input for another.
- Why does MRTS equal the ratio of marginal products on an isoquant? — Along an isoquant, holding output constant implies the tradeoff between inputs equals MP ratios.
- Why does cost minimization occur where MRTS equals w/r? — At optimum, the marginal rate of technical substitution equals the input price ratio, otherwise you can reallocate inputs to reduce cost.
- Why do firms use the Lagrangian method to find cost-minimizing input demands? — The Lagrangian enforces the output constraint while optimizing cost, yielding conditional factor demand functions.
- Why does optimal consumer choice occur where MRS equals the budget line slope? — At the tangency, the consumer’s marginal willingness to trade matches the market tradeoff given prices.
- Why does Marshallian demand depend on income? — Marshallian demand reflects utility maximization subject to a budget, so the feasible set expands/contracts with income.
- Why does Marshallian demand slope downward? — Price increases reduce real purchasing power and shift substitution incentives, lowering quantity demanded for normal goods.
- Why do Hicksian and Marshallian substitution effects differ when income effects are present? — Hicksian holds utility constant while Marshallian holds income constant, so income effects change the decomposition.
- Why must the Slutsky matrix be symmetric and negative semidefinite? — Symmetry comes from integrability of demand; negative semidefiniteness encodes the law of demand and convex preferences.
- Why is individual optimization not enough for general equilibrium? — GE requires market clearing across all markets, so individual optima must be mutually consistent in aggregate.
- Why is the long-run cost curve the lower envelope of short-run cost curves, revealing economies of scale? — In the long run, firms can choose the best fixed input level, so LR cost is the minimum across all SR options.
Macroeconomics
- Why does macroeconomic equilibrium occur where AD intersects SRAS and LRAS? — Equilibrium requires goods market demand to match output, with SRAS capturing short-run price rigidity and LRAS long-run capacity.
- Why does the IS-LM model determine equilibrium output and interest rates under fiscal and monetary policy? — IS pins goods-market equilibrium and LM pins money-market equilibrium, and their intersection sets (Y, i).
- Why does the IS–LM–FE model determine simultaneous equilibrium in goods, money, and labor markets? — FE adds labor/production-side equilibrium so output is consistent with both demand and factor-market clearing.
- Why does the Solow model converge to a steady state? — Diminishing returns and depreciation create a stable capital level where investment equals break-even investment.
- Why does a higher savings rate raise steady-state capital but not long-run growth in the Solow model? — Saving changes the level of steady-state capital, but long-run per-capita growth depends on exogenous technology growth.
- Why does population growth dilute capital and lower steady-state capital per worker in the Solow model? — More workers spread a given capital stock thinner, raising break-even investment and reducing k*.
- Why is the Golden Rule capital level the point that maximizes consumption? — It balances marginal product of capital against depreciation (and population growth), maximizing steady-state consumption per worker.
- Why does the macro production function have diminishing marginal returns? — With fixed technology and labor, adding capital yields smaller incremental output due to scarcity of complementary inputs.
- Why does the intertemporal Euler equation characterize optimal consumption in graduate macro? — It equalizes discounted marginal utility across time, linking consumption growth to interest rates and preferences.
- Why do technology shocks propagate through capital accumulation and labor supply in the RBC model? — Shocks change productivity, shifting optimal labor and investment, which then affects future capital and output paths.
- Why do the short-run and long-run Phillips curves imply different inflation–unemployment tradeoffs? — In the short run expectations are sticky, but in the long run expectations adjust, eliminating the tradeoff at the natural rate.
Game Theory
- Why do mixed strategy equilibria arise when players are indifferent over the support of their strategies? — Mixing makes opponents indifferent, so no pure deviation yields a higher payoff when probabilities equalize expected payoffs.
- Why does backward induction identify the subgame perfect equilibrium in dynamic games? — Solving from the end enforces optimal play in every subgame, ruling out non-credible threats.
- Why does backward induction reveal the subgame perfect Nash equilibrium? — It selects strategies that are Nash in every subgame, ensuring sequential rationality throughout the game tree.
- Why does Bayesian Nash equilibrium require players to best-respond to beliefs about types? — With private information, optimal actions depend on beliefs, so equilibrium ties strategies to consistent type beliefs.
- Why do pooling equilibria require off-path beliefs to deter deviations? — Because multiple types take the same action, beliefs about unexpected actions must make deviation unattractive.
- Why do separating equilibria require incentive compatibility for both types? — Each type must prefer its intended action over mimicking, otherwise separation collapses into pooling.
Econometrics
- Econometrics: Why fixed effects reduces omitted bias (for econometrics tutoring) — Fixed effects remove time-invariant unobserved heterogeneity that would otherwise correlate with regressors and bias estimates.
Bottom Line
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