Compare models, causal evidence, and value judgments without turning schools of thought into slogans.
By the end: Audit assumptions and calculate a simple difference-in-differences estimate.
Different questions emphasize different mechanisms
Neoclassical analysis often studies constrained choice, marginal tradeoffs, and equilibrium. Keynesian approaches emphasize effective demand, uncertainty, and the possibility of persistent underemployment. Institutional and bargaining approaches emphasize rules, power, and incomplete contracts. These are overlapping research traditions, not mutually exclusive descriptions that every economist follows consistently.
Marxian analysis emphasizes ownership of productive assets, wage dependence, accumulation, and appropriation of surplus labor. Marx's surplus-value concept belongs to a theory of value and class relations; it is not simply the accounting formula for a company's reported profit. Hayek's argument about decentralized knowledge emphasizes how prices can coordinate dispersed information and why central direction faces information problems. Neither argument alone measures all the benefits and costs of an actual institution.
Translate a theoretical explanation into a testable mechanism
Begin an economic explanation by identifying its question, decision-makers, constraints, and outcome. An accounting statement tells us how defined quantities reconcile. A behavioral hypothesis proposes how people or organizations respond when conditions change. An equilibrium combines compatible decisions under stated rules, such as buyers purchasing exactly what sellers offer at a price. A causal estimate tries to recover the difference an intervention makes relative to an unobserved alternative. A normative judgment evaluates outcomes or rights. These statements can appear in one argument, but their support differs. Arithmetic consistency does not validate a behavioral assumption or an ethical conclusion.
Consider a paper example of a workshop with sales of 1,000 during a month. It buys materials for 300, pays workers 400, records depreciation of 100, and pays interest of 50. Under this simplified accounting convention, before tax and any omitted costs, the residual is 150. Subtraction establishes that residual once the classifications and amounts are accepted. It does not tell us whether sales would fall after a price increase, whether workers could obtain better jobs, or whether the owner's claim is justified. Each question needs additional assumptions or evidence rather than a new name for the same residual.
Five entries reconcile the workshop's sales
These five amounts sum to the invented workshop's 1,000 in monthly sales. After materials, wages, depreciation, and interest, the residual is 150 under the stated accounting convention. The bars compare entries, not independent gains. Taxes and omitted costs remain outside the boundary; changing those classifications changes the residual without resolving causal questions or justifying anyone's claim to it.
A neoclassical explanation might ask how the workshop chooses additional output given the price it can obtain and the opportunity cost of another unit. A Keynesian explanation might ask whether weak customer expenditure prevents it from selling available capacity. An institutional or bargaining explanation might ask how incomplete contracts and outside options divide the return between workers and owners. These are distinct mechanisms that can operate together. Their relevance depends on the question and setting. A demand explanation does not prove that costs never matter, and a marginal-cost explanation does not establish that aggregate demand always keeps capacity employed.
Marx's surplus value is part of his account of value production through labor and the purchase of labor power. It cannot be calculated merely by renaming the workshop's 150 accounting residual. Interest, depreciation, prices, and the treatment of labor have different analytical roles in Marx's framework and modern company accounts. To evaluate a Marxian argument, identify the specific claim about ownership, labor dependence, accumulation, or value that it makes. A claim about workplace authority can be investigated without assuming that every element of Marx's value theory has thereby been demonstrated.
Hayek's knowledge argument instead asks how decisions use information dispersed among participants. A price rise may convey scarcity without every buyer knowing its origin. That mechanism does not establish that every price includes pollution costs or reflects equal purchasing power. Ostrom's work examines how particular governance arrangements manage shared resources, rather than assuming either private ownership or central government is always sufficient. These arguments should be compared on their actual claims. Evidence supporting one mechanism gives it support for that question; it does not require assigning every associated theory equal credibility or declaring an entire tradition universally correct.
Two mechanisms, two different claims to test
Information and governance mechanisms
Question
Mechanism
Not established
Price coordination
Dispersed scarcity info
Full pollution costs
Shared-resource use
Rules governing access
One ownership solution
Hayek's price argument concerns dispersed information; Ostrom's governance question concerns rules for shared resources. A scarcity signal does not show that pollution costs enter the price, and successful resource governance does not establish one universally sufficient ownership form. Compare evidence about information use and resource rules rather than treating either argument as a complete institutional ranking.
An outcome before and after is not a counterfactual
Suppose employment in a treated group rises from 100 to 110 after a policy, while a comparison group rises from 100 to 104. The difference-in-differences estimate is 6: subtract the comparison change of 4 from the treated change of 10. The assumption is that, without treatment, the treated group would have followed a comparable trend, not that both groups must have identical levels.
The design can fail if another shock affects only the treated group, people change group membership, treatment spills into the comparison group, or trends would have diverged anyway. Pre-policy trends and institutional evidence help assess plausibility but cannot prove the missing counterfactual. Sampling uncertainty, measurement error, and external validity also matter. The Nobel overview of natural experiments illustrates why research design matters rather than merely collecting more correlations.
Construct the missing outcome before calling a change an effect
A causal effect compares two outcomes for the same unit under different conditions. A city cannot both introduce and not introduce a policy at the same time, so one outcome is missing. A comparison design supplies a justified substitute for that missing outcome. Before-and-after subtraction alone uses the earlier observation as the substitute. That is credible only if other relevant changes would not have altered the outcome. Economic settings rarely stand still. Demand, population, prices, technology, and other policies can change while the intervention occurs, so a time comparison needs an explicit account of those influences.
Use a separate paper case involving training and employment counts, not the lesson's existing numerical example. A treated district has 200 employed participants before a program and 230 afterward. An untreated district has 150 employed people before and 165 afterward. The treated increase is 30 people. The comparison increase is 15. If the untreated district's absolute change is the correct counterfactual trend for the treated district, the latter would have reached 215 without the program. Comparing its observed 230 with that counterfactual gives an estimated effect of 15 employed people.
The key assumption concerns untreated changes, not matching starting levels. But units matter when choosing that assumption. The comparison district grew by 10% because 15 is one tenth of 150. Applying that proportional change to the treated district's starting 200 predicts 220 without treatment. The corresponding estimated effect is 10, not 15. Neither subtraction is inherently fraudulent. They embody different counterfactual models, equal absolute changes or equal proportional changes. Choose a model using institutional knowledge and evidence about the outcome's dynamics, not whichever produces a larger or more convenient policy estimate.
The counterfactual model changes the estimated gap
The invented treated district starts at 200 and ends at 230. Adding the comparison district's absolute gain of 15 predicts 215 without treatment; applying its 10% growth predicts 220. The resulting gaps are 15 or ten people. Both use the same observations. Evidence about untreated dynamics must choose between these assumptions; the larger estimate is not automatically more credible.
Check whether these are counts of a fixed population. If people move into the treated district for the program, employment may rise because the district now contains more people, not because original residents became more likely to work. With 250 original eligible residents, 200 employed means an 80% employment rate. If employment later reaches 230 but the eligible population becomes 300, the rate is about 76.67%. A rising count and falling rate answer different questions. A study of original residents needs a fixed cohort or a method that accounts for changing composition.
Treatment spillovers can contaminate the comparison too. Suppose treated firms hire workers away from untreated firms, reducing comparison employment. Subtracting that depressed comparison trend could exaggerate net employment creation across the region. Conversely, if training raises spending at untreated firms, their employment gains could make a comparison understate the total regional effect. Define whether the target is participant employment, local employment, or net jobs across a wider economy. The same design may answer one target poorly while informing another. Geography and population definitions are part of causal reasoning, not details to append after computing a difference.
Work through the mechanism
Subtract the comparison change
These are changes in the same employment measure. Causal interpretation requires comparable untreated trends and other identifying assumptions.
Group
Before
After
Change
Treated
100
110
+10
Comparison
100
104
+4
Difference in changes
+6
The result is a conditional estimate in invented data. Causal interpretation requires a credible untreated trend and other design assumptions.
Subtract a common change, not a different starting level
This is a separate constructed case from the table, with unequal starting levels. The two bars show changes, not total employment. If the treated group would also have gained nine without treatment, its counterfactual ending level is 129, leaving a treatment estimate of six rather than the raw gain of fifteen. The common-change assumption is imposed for illustration, not demonstrated by these before-and-after figures. A treated-only shock of six could produce the same visible bars even if the policy had no effect.
Stress-test the comparison in the displayed calculation
The displayed formula and table use an invented treated increase of ten and comparison increase of four, producing six in the same employment measure. They are static teaching material. There is no control that changes the groups, generates observations, or verifies parallel trends. Reconstruct the missing counterfactual before looking at the final six. Starting from treated employment of 100, the comparison change predicts 104 without treatment. Observed treated employment is 110. The gap of six is the same arithmetic as subtracting changes, but it makes the unobserved assumption easier to inspect.
Now use paper variants to ask how that result could fail. Suppose a new employer opens only in the treated area during the same period, independently adding five to the employment measure. If the comparison still captures all other untreated changes, the six-unit gap combines five from the employer opening and one from the policy. Attributing all six to the policy would be wrong under these assumptions. The original table cannot detect this event. Employment records, opening dates, and the policy's eligibility rules would help assess whether the proposed confounder actually affected the measured group.
A placebo comparison uses an earlier period when the policy was absent. Suppose an earlier treated observation is 94 and its next pre-policy observation is the displayed 100. The comparison moves from 98 to the displayed 100 over that same earlier interval. Untreated changes before the policy are then six and two, a difference of four. That difference raises concern about assuming equal future untreated changes. It does not prove the policy has no effect. The earlier divergence might be temporary, or it might reflect an ongoing trend. Additional history and substantive knowledge are needed to distinguish those explanations.
An earlier untreated interval already shows divergence
In this invented placebo interval, treated employment rises from 94 to 100 while comparison employment rises from 98 to 100. Their gains differ by four before any policy exists. That divergence challenges equal untreated trends, but does not prove a zero policy effect. More history is needed to distinguish a temporary disturbance from a persistent differential trend.
Sensitivity analysis asks how much the conclusion changes under a specified departure from an assumption. Starting with the displayed six-unit estimate, suppose untreated treated-area employment would have grown two units more than comparison employment even without the policy. The counterfactual is then 106, and the policy estimate becomes four. If that extra untreated growth were six instead, the counterfactual would be 110 and the estimated effect zero. These are not new empirical findings. They show exactly how much unaccounted differential growth would be required to reduce or remove the original estimate.
Measurement uncertainty and causal uncertainty are different. A precise survey can estimate each group's employment well while the comparison remains invalid. A credible comparison can also have wide sampling uncertainty because it contains few independent units. Repeated observations from one workplace do not necessarily provide many independent policy experiments. When reading a reported interval, ask what uncertainty it represents and how the researcher handles correlated outcomes. A confidence interval built around a biased counterfactual does not automatically cover the true causal effect. The arithmetic table teaches subtraction, while research design must justify why the subtraction answers the intended question.
How much untreated divergence removes the estimate?
Starting with the invented six-unit estimate, subtract assumed extra untreated growth in the treated area: zero, two, or six units. The policy gap becomes six, four, or zero. These are sensitivity assumptions, not observations or confidence bounds. They isolate counterfactual bias; more precise measurement would not by itself establish which untreated growth assumption is credible.
Separate descriptive, causal, and normative claims
A descriptive claim reports a pattern. A causal claim says what would change under an intervention relative to an alternative. A normative claim judges outcomes or rights using values. An argument may contain all three, but should not silently move between them. Finding an efficiency gain does not decide who should receive it; preferring equality does not establish that a proposed intervention will achieve it.
Ask an expert which assumptions drive the result, what evidence could reject the mechanism, how uncertainty is represented, and whose outcomes are measured. Do not manufacture equal credibility for incompatible empirical claims merely because each has an ideological label. Equally, do not treat one useful model as a complete description of an economy. The final lesson combines these distinctions in a concrete policy case.
Read effect sizes, scope, and judgments separately
An effect needs a unit, denominator, and horizon. Suppose an intervention raises the employment rate of a fixed eligible population from a counterfactual 70% to an observed 73%. The estimated effect is three percentage points. Relative to the 70% counterfactual rate, that is about a 4.29% increase, found by dividing three by seventy. With 1,000 eligible people, three percentage points corresponds to 30 additional employed people. Calling it a 3% increase would confuse a difference in rates with a proportional change and would give a different implied count.
A budget comparison adds information without settling the whole evaluation. Suppose the intervention costs 300,000 annually and the estimated increase of 30 employed people lasts one year. Dividing cost by the increase gives 10,000 per additional employed person-year. This is not automatically a social cost-benefit ratio. Program expenditure may include transfers rather than resource consumption, new employment may produce output and tax receipts, and participants may face commuting, care, or lost leisure costs. Counting jobs is useful for an employment objective, but it does not value every consequence or establish that any job is better than every alternative.
A rate difference needs a population denominator
For the invented fixed population of 1,000, a 70% counterfactual rate means 700 employed people and an observed 73% means 730. The gap is 30 people, or three percentage points, not a 3% proportional increase. The stated 300,000 annual program budget therefore implies 10,000 per additional employed person-year, conditional on the effect lasting one year, not a complete welfare valuation.
External validity means whether a result applies beyond the people and conditions studied. A program might work for applicants who volunteered, had available transport, and entered during strong demand. Applying its effect to people without transport during a recession adds assumptions about take-up, employer response, and constraints. Scaling can also change the setting. A small program can place participants into existing vacancies; a universal program may encounter limited vacancies, change wages, or shift hiring away from nonparticipants. These are reasons to inspect mechanisms and scale, not reasons to dismiss all limited studies as useless.
Look for predictions that distinguish explanations. If a claim says training improves job-relevant skills, evidence about completion, measured skills, and subsequent job tasks helps test the channel. If a competing claim says employers simply prefer the program's credential, a comparison of similar skills with different credentials could help separate them. Evidence may reject one explanation more strongly than another. Do not preserve equal credibility merely by describing both as perspectives. Equally, a failed prediction should prompt examination of measurement and scope before rejecting every related proposition. The relevant unit of evaluation is the specific claim under specified conditions.
Finally, make the normative step explicit. A positive employment effect does not alone establish fair eligibility rules, adequate job quality, or acceptable obligations imposed on participants. A preferred distribution does not make an unsupported causal estimate true. An expert argument should let the reader reconstruct the numerical claim, identify the counterfactual, inspect the uncertainty, and see the evaluative criterion. You can accept the accounting, question the causal design, and disagree about the judgment without contradiction. That separation makes disagreement more precise because each objection addresses the evidence or value premise that actually supports the conclusion.
Exercises
A different comparison trend
A treated group rises from 80 to 92; a comparison group rises from 60 to 66. What is the difference-in-differences estimate? Does a larger treated starting level invalidate it automatically?
Hint
Compare changes rather than levels.
Worked answer
Group
Before
After
Change
Treated
80
92
12
Comparison
60
66
6
Difference in changes
6
Identical levels are neither necessary nor sufficient for a credible counterfactual trend.
The estimate is 6: the treated change of 12 minus the comparison change of 6. Different starting levels do not automatically invalidate the design. The key question is the plausibility of comparable untreated changes and the absence of relevant confounding.
Label each claim
Classify: rents rose 8%; a subsidy caused the rise; that rise is unfair. What does each require?
Hint
Separate observation, intervention, and evaluation.
Worked answer
Claim
Kind
Additional requirement
Rents rose 8%
Descriptive
Measure, period, and sample
Subsidy caused the rise
Causal
Credible counterfactual
Rise is unfair
Normative
Explicit evaluative criteria
Correct arithmetic does not automatically establish causation or fairness.
The first is descriptive and requires a defined measure and sound data. The second is causal and requires a counterfactual design or justified model. The third is normative and requires explicit criteria about rights, needs, or distribution, informed by facts but not derived from the percentage alone.
Sources and further reading
The lessons and answers stand alone. These optional references identify underlying models, evidence, and perspectives. All numerical examples here are invented unless explicitly attributed; none is a forecast or a personal investment recommendation.
Definitions of capitalism, production, historical change, technology, and institutions. The course is a mechanism-based introduction, not a claim that one institution alone explains growth.
Ownership, organizational authority, incomplete employment contracts, and worker incentives. Our wage-sharing formula is an illustrative bargaining rule, not an estimated wage equation.
Primary exposition of surplus labor and surplus value within Marxian theory. It is presented as a theoretical perspective, not equated with modern accounting profit or treated as an uncontested price theory.
Primary argument about dispersed knowledge and price coordination. Optional further reading; this endpoint blocked automated retrieval during authoring.