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ce of the estimator which measures the dispersion of individual estimates around their mean a common misconception holds that a desirable estimator must simultaneously exhibit both properties this presumption is however fallacious an estimator may be unbiased yet exceedingly imprecise or highly precise yet substantially biased this distinction constitutes the conceptual foundation of one of the most counterintuitive results in modern decision theory stein s paradox the distinction can be illustrated through a familiar heuristic consider a darts player throwing darts at a dartboard if the darts form a tight cluster consistently displaced five centimetres to the upper left of the bullseye the throws are precise low variance but biased nonzero expected loss conversely if the darts are widely scattered across the board yet their centroid coincides with the bullseye the player is unbiased zero mean error but imprecise high variance in statistical terms the first player exhibits low variance but high bias whereas the second exhibits zero bias but high variance both scenarios are undesirable yet they illustrate that unbiasedness and precision address fundamentally different issues unbiasedness concerns the location of the sampling distribution whereas precision concerns its dispersion this divergence acquires theoretical significance when evaluating estimator quality through the lens of mean squared error mse conventionally decomposed as mse θ var θ bias θ 2 this decomposition formalises a fundamental trade off one may reduce variance by tolerating some bias or eliminate bias at the cost of elevated variance critically a slight increment in bias can engender a substantial decrement in variance yielding a net reduction in mse consequently the unbiased estimator is not invariably optimal in finite sample contexts this trade off constitutes the crux of stein s paradox stein demonstrated that when estimating three or more population means simultaneously the ordinary sample mean the canonical unbiased estimator is inadmissible under squared error loss that is there exists an alternative estimator that dominates it uniformly in terms of total mse irrespective of the true parameter values the james stein estimator the most prominent instantiation of this principle shrinks each sample mean towards the grand mean of all groups this shrinkage deliberately introduces bias into each individual estimate systematically attenuating deviations from the centre yet the variance reduction achieved through information pooling more than compensates for the incurred bias producing a lower aggregate mse across all estimates the counterintuitive nature of this result stems from its violation of the intuition that estimation of a given parameter should rely exclusively upon data pertinent to that parameter the james stein estimator however demonstrates that group information can improve estimation quality by stabilising individual estimates analogously a team of darts players might adjust their throws towards a common centre individually each may diverge from the bullseye yet the collective mean squared deviation diminishes because no player throws excessively far astray this principle finds direct application in empirical economics consider the problem of forecasting gdp growth across multiple regions or sectors let the true growth rate for a given period be 2 0 per cent two forecasters lars and milton provide annual predictions lars employs a complex econometric model incorporating numerous noisy indicators over repeated forecasts his mean error converges to zero he is asymptotically unbiased however his year to year predictions are highly volatile ranging from 4 0 to 1 0 per cent thus while lars s estimator is unbiased in expectation its large variance renders it practically unreliable for short term policy formulation milton in contrast adheres to a conservative heuristic he adjusts the previous year s growth rate only slightly producing predictions tightly clustered around 2 2 per cent his forecasts exhibit low variance they are precise in the technical sense yet suppose the true long run average growth is 2 5 per cent and milton persistently underestimates expansions his forecasts are biased downward by 0 3 percentage points on average although stable they are systematically erroneous leading to recurrent underestimation of output growth and consequently excessively contractionary fiscal or monetary policy this comparison illustrates that unbiasedness and precision are not merely mathematically distinct but practically incompatible under certain conditions lars s forecasts are correct in the long run but too erratic to guide policy milton s are stable but consistently misleading in both cases reliance solely on one property proves detrimental the optimal approach as stein s paradox suggests may involve accepting a modest bias to reduce variance these insights have profound implications for macroeconomic forecasting central banks finance ministries and international organisations routinely confront a trade off between forecast accuracy and stability a forecast that is unbiased but excessively volatile is ill suited for budget planning or interest rate decisions a forecast that is precise but biased will accrue systematic errors over time contemporary forecasting practice increasingly adopts regularisation techniques that deliberately introduce bias to improve overall predictive performance these methods operationalise the stein principle by shrinking heterogeneous estimates towards a common centre thereby reducing variance at the cost of a controlled increase in bias so here s the bottom line bias and precision are not the same and they rarely get along think of lars and milton the former was a broken clock that was correct twice a day the latter a model of consistency in the wrong direction stein s paradox then drops the hammer sometimes the smartest move is to sacrifice a little accuracy for a lot of stability good statisticians know this great policymakers act on it share on facebook opens in new window facebook share on x opens in new window x share on bluesky opens in new window bluesky audioholic summer research 22 jun 2026 at 16 16 posted in varia leave a comment when summer arrives we audiophiles will have plenty of time to enjoy beautiful music on our systems but yours truly just like john maynard prefers champagne over beer to accompany the music share on facebook opens in new window facebook share on x opens in new window x share on bluesky opens in new window bluesky ett välförtjänt bottenrekord 21 jun 2026 at 09 06 posted in politics society leave a comment på en pressträff i mars meddelade l ledaren simona mohamsson att hon var beredd ge sverigedemokraterna ministerposter ett mer flagrant svek mot partiets liberala arv är svårt att finna och har så klart bidragit till verkliga liberalers fanflykt från partiet samma partiledare meddelade i i förra månaden att hon vill göra sverige till ett skatteparadis och fördubbla antalet miljardärer till år 2037 och detta grodors plums och ankors plask ska man behöva höra år 2026 år 1991 genomförde sverige det som sedan dess har kallats för århundradets skattereform denna reform innebar en genomgripande omstrukturering av det svenska skattesystemet vilket resulterade i en betydande sänkning av den totala skattebördan bolagsskatten som i slutet av 1980 talet låg på omkring 60 procent sänktes stegvis och ligger idag på cirka 21 procent sverige idag har den näst högsta förmögenhetskoncentrationen i eu och flera samtidiga rapporter visar att fler än 700 000 svenskar lever i fattigdom detta innebär en fördubbling sedan 2021 och motsvarar nästan 7 av befolkningen och så har mohamsson mage att i årets i särklass löjligaste skatteutspel tala om att vi behöver sänka skatterna och fördubbla antalet miljardärer liberalernas låga opinionssiffror är en direkt konsekvens av partiets egna handlingar inte minst mohamssons beslut att öppna för att ge sverigedemokraterna ministerposter har med rätta uppfattats som ett svek mot det liberala hjärtat i partiet att partiet nu uppnår bottennoteringar på omkring 1 procent är en logisk följd av ett parti som förlorat både sin ideologiska kompass och sitt förtroende hos väljarna share on facebook opens in new window facebook share on x opens in new window x share on bluesky opens in new window bluesky arbetslösheten inte statsskulden är problemet 20 jun 2026 at 16 14 posted in economics politics society 1 comment när finanspolitiska rådet för några månader sedan kritiserade regeringen för att inte ha följt sina egna rampolitiska ekonomiska regler kunde en del politiker uppenbarligen inte låta bli att ta tillfället i akt och i populistisk anda ondgöra sig över att våra barn och barnbarn kommer att få betala dyrt för bristande prioriteringar idag tyvärr kan man bara ta sig för pannan när man tar del av denna kritik det här är inte rocket science i grund och botten handlar det om något så enkelt som att göra klart för sig att det är skillnad på skuld och skuld även om det på makroplanet av nödvändighet är så att skulder och tillgångar balanserar varandra så är det inte oväsentligt vem som har tillgångarna och vem som har skulderna länge har man varit motvillig att öka de offentliga skulderna eftersom ekonomiska kriser i mångt och mycket fortfarande uppfattas som förorsakade av för mycket skulder men det är här fördelningen av skulder kommer in om staten i en lågkonjunktur lånar pengar för att bygga ut järnvägar skola och hälsovård så är ju de samhälleliga kostnaderna för detta minimala eftersom resurserna annars legat oanvända när hjulen väl börjar snurra kan både de offentliga och de privata skulderna betalas av i stället för att värna om statsfinanserna bör man se till att värna om samhällets framtid problemet med en statsskuld är oftast inte att den är för stor utan för liten vad många politiker och mediala så kallade experter inte verkar vilja förstå är att det finns en avgörande skillnad mellan privata och offentliga skulder om en individ försöker spara och dra ner på sina skulder så kan det mycket väl vara rationellt men om alla försöker göra det blir följden att den aggregerade efterfrågan sjunker och arbetslösheten riskerar att öka en enskild individ måste alltid betala sina skulder men en stat kan alltid betala tillbaka sina gamla skulder med nya skulder staten är inte en individ statliga skulder är inte som privata skulder en stats skulder är väsentligen en skuld till sig själv till dess medborgare en statsskuld är varken bra eller dålig den ska vara ett medel att uppnå två övergripande makroekonomiska mål full sysselsättning och prisstabilitet vad som är heligt är inte att ha en balanserad budget eller att hålla nere statsskulden om idén om sunda statsfinanser leder till ökad arbetslöshet och instabila priser borde det vara självklart att den överges den svenska utlandsskulden och den konsoliderade statsskulden är historiskt låga med tanke på de stora utmaningar som sverige står inför är fortsatt tal om ansvar för statsbudgeten minst sagt oansvarigt budgetunderskott är inte sveriges problem idag att fortsatt prata om att spara i ladorna sms lån och en tömd statskassa är bara ren dumhet för ett par år sedan kom regeringen och socialdemokraterna överens om att slopa överskottsmålet i det finanspolitiska ramverket och ersätta det med ett balans mål för att möjliggöra stora infrastruktursatsningar och få fart på ekonomin det var bra men långt ifrån tillräckligt det enda vettiga i dagens situation är så klart att man skulle ha ett underskotts mål och möjliggöra ännu större nödvändiga investeringar i välfärd och underhåll av vår infrastruktur och att nu låta skuldankaret ligga kvar på 35 är fel väg att gå med de problem svensk ekonomi brottas med idag inte minst den höga arbetslösheten duger inga sådana harhjärtade halvmesyrer share on facebook opens in new window facebook share on x opens in new window x share on bluesky opens in new window bluesky how credible is the credibility revolution in econometrics 17 jun 2026 at 16 32 posted in statistics econometrics leave a comment the so called credibility revolution in econometrics rests on the non parametric and robust nature of its inferences which are seen as independent of incredible or at best doubtful economic theories such approaches including natural experiments and regression discontinuity designs like well designed rcts often do carry conviction over their domain of validity but as is often the case they estimate an ate that is valid only in the limited circumstances under which it was obtained an aspect of the familiar trade off between getting a result that is likely to be accurate in itself versus getting one that is likely to be useful as evidence for other claims put differently the special requirements of rcts regression discontinuity methods and instrumental variables often give us an estimate of a local magnitude that is not what we originally set out to measure credibility is fine but it would be better if it did not so often involve a shift away from what we want to measure to some other quantity that is dictated by the design indeed if we focus on design we run the risk of prioritizing method over substance and of ranking results not by what we learn about the world but according to a hierarchy of method which is one of our main targets economics is about a great deal more than estimating average treatment effects it is not epidemiology and the design analysis framework will not make economics more credible but turn it into the kind of alchemy that turns gold into lead not the reverse angus deaton nancy cartwright especially when it comes to questions of causality randomisation is nowadays considered something of a gold standard everything has to be evidence based and the evidence must come from randomised experiments funding bodies demand it journals prefer it policymakers trust it but just like econometric modelling randomisation is basically a deductive method given the assumptions such as manipulability transitivity separability additivity linearity and so forth these methods deliver deductive inferences the problem of course is that we will never completely know when the assumptions are correct and although randomisation may contribute to controlling for confounding it does not guarantee it genuine randomness presupposes infinite experimentation or at least a well defined superpopulation and a perfectly executed randomisation protocol yet we know that all real experimentation is finite in finite samples randomisation only ensures balance on average across hypothetical repetitions for any given actual trial substantial imbalances may remain and even if randomisation helps to establish average causal effects it says nothing about individual effects unless homogeneity is added to the list of assumptions which defeats the whole point of allowing for heterogeneity real target systems are seldo...
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