Considere a estimativa da função linear !$ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + u !$, cujos parâmetros tenham sido estimados pelo Método dos Mínimos Quadrados Ordinários. Julgue as afirmativas:

Item 4 - Se !$ V ( u | x_1, x_2 ) = θ_0 !$, então serão tendenciosos os estimadores de mínimos quadrados da variância de !$ \hat { \beta}_0 !$, !$ \hat { \beta}_1 !$ e !$ \hat { \beta}_2 !$.

Oct 27th 2016

IF THE Democratic Party were a business, investors would mutter that it has a succession crisis. Its presidential nominee is 69 years old, and its leaders in Congress—Representative Nancy Pelosi and Senator Harry Reid—are both 76. That pin-up of the campus left, Senator Bernie Sanders, is 75. The young thruster set to lead Senate Democrats after January, Charles Schumer of New York, is 65. Nor is the galaxy of Democrats outside Washington thick with dazzling stars: after several bruising elections, the party currently holds just 18 out of 50 governors’ mansions.

Talk to thoughtful Democrats about the future and one name inspires more hope than most: Kamala Harris, the attorney-general of California and, barring a Wash3ington sceptics may dismiss Ms Harris as a typical Californian progressive. It is true that her campaign ads boast of suing big banks for fraud. She also has a distinctly paternalist streak. Greeting an eight year old in his classroom, the attorney-general solemnly coachesmeteor-strike between now and November 8th, that state’s next member of the Senate. Insiders noticed when Ms Harris, 52, was endorsed by President Barack Obama, even though, under a run-off election system used in California, her opponent is a long-serving Democratic congresswoman, Loretta Sanchez.

Ms Sanchez has ascribed this snub to race solidarity between her opponent and the president, sniffing: “She is African-American, he is too.” In fact, Ms Harris and Mr Obama share bonds more subtle than similarly complex life-stories (the attorney-general’s parents, an Indian-born cancer researcher and a Jamaican economist, met at the University of California, Berkeley, and divorced when she was young). Both began political careers in places where success required coalition-building across party lines: Mr Obama in the fusty, cronyish Illinois state Senate, and Ms Harris in the lock-’em-up world of elected public prosecutors, starting as a district attorney for San Francisco, before becoming head of law enforcement across California in 2010.

A recent weekday found Ms Harris at John Muir Elementary School in San Francisco. As happy playground shrieks drifted through the windows, she faced TV cameras to unveil her fourth annual report on chronic school truancy. A populist firebrand would not have lacked for material. Surrounded by Victorian houses snapped up by tech millionaires, stoking local resentments, John Muir serves mostly poor families from other, less gentrified neighbourhoods. Ms Harris began studying truancy after learning that 94% of San Francisco’s murder victims under 25 were high-school dropouts. Research showed that three-quarters of young children who often miss days at kindergarten later fail California’s maths and reading tests in third grade. Pupils who fail those tests are in turn four times likelier to drop out of high school, and those who drop out are eight times likelier to end up in jail. Chronic truancy is much more common among black children, moreover. Yet as she explained her findings, the attorney-general did not thunder about racial injustice or inequality. Instead she noted that high-school dropouts cost the state more than $46bn a year in public-safety and public-health spending. Letting children miss school offers taxpayers a poor “return on investment” and deprives California of a skilled workforce, Ms Harris argued. It stops government being “efficient and effective”.

That technocratic tone does not surprise a long-standing ally, Lateefah Simon. When the pair first met, Ms Harris was a young city lawyer, working on sex-trafficking cases. Ms Simon was just out of her teens, a radical activist working with troubled young women, and, she recalls proudly, “known for bringing hundreds of young girls into police commission meetings, shutting them down.” Ms Harris finally advised her that systems change under pressure from the outside and the inside: “Kamala said to me, you can’t always win with a bullhorn.” When Ms Harris became district attorney she hired Ms Simon to run a programme for low-level, non-violent drug offenders. Though strikingly cheap, it drew national attention for preventing 90% of its graduates from reoffending. Ms Simon explains how Ms Harris would tell youngsters their chances of going to jail or dying if they did not change course. Then she would offer help with everything from housing to remedial education and apprenticeships—even dentistry cadged from a local university, after she read research linking job prospects to bad teeth. Ms Simon calls her old boss both “data-driven” and tough: “If you hurt a woman, she wants you in jail.”

More than a decade later, Ms Harris still puts her faith in data, as she cites crises that Republicans and Democrats alike know need to be addressed, in fields as diverse as criminal justice, immigration, the costs of higher education or the drugs epidemic that is as cruel a scourge in conservative rural states as it is in inner cities. Over a stop for iced coffees on the campaign trail, she says transparency is the key to building trust among people, and then between communities and government. To that end in 2015 her department began releasing torrents of statistics about arrests and deaths in custody across California. Nor is keeping the trust of the police forgotten: Ms Harris’s department publicises data on law-enforcement officers killed or assaulted on duty.

The case for the prosecutor

Washington sceptics may dismiss Ms Harris as a typical Californian progressive. It is true that her campaign ads boast of suing big banks for fraud. She also has a distinctly paternalist streak. Greeting an eight year old in his classroom, the attorney-general solemnly coaches him: “We shake hands and look each other in the eyes.” Asked by a little girl about favourite foods, Ms Harris replies: “I like French fries, but I love spinach.”

But Ms Harris is a prosecutor to her core, who approaches voters as she would 12 jurors of different backgrounds: “You have to point to the facts.” Contemplating a country where millions feel displaced by change, she yearns to see another approach to politics tried: “to give people an image of what the future looks like, and to paint that image in a way that they can see themselves in it.” Fierce, charming and eloquent, Ms Harris may be a big part of the Democratic Party’s future too.