Scott Sumner offers this explanation, by way of Larry Summers, on how unemployment insurance influences the unemployment rate:
In a study using state data on registrants in Aid to Families with Dependent Children and food stamp programs, my colleague Kim Clark and I found that the work-registration requirement actually increased measured unemployment by about 0.5 to 0.8 percentage points. If this same relationship holds in 2005, this requirement increases the measure of unemployment by 750,000 to 1.2 million people. Without the condition that they look for work, many of these people would not be counted as unemployed. Similarly, unemployment insurance increases the measure of unemployment by inducing people to say that they are job hunting in order to collect benefits.
The second way government assistance programs contribute to long-term unemployment is by providing an incentive, and the means, not to work. Each unemployed person has a “reservation wage”—the minimum wage he or she insists on getting before accepting a job. Unemployment insurance and other social assistance programs increase that reservation wage, causing an unemployed person to remain unemployed longer.
So UI a) brings more of the unemployed to the attention of government statisticians, and b) creates an incentive not to work. Sumner mentions reforming the system, such as through personal accounts. I assume he means Individual Unemployment Accounts:
The unemployment compensation system in the United States is out of date and in trouble. The system has four fundamental problems: (1) during recessions, it often cannot meet its financial obligations without federal aid or deficit spending; (2) it is out of step with the structural and cultural realities of the modern workforce; (3) it encourages layoffs and unemployment; and (4) it operates in isolation from other programs related to employment and financial security. We propose an alternative unemployment policy based on the individual unemployment account (IUA). The IUA would be a mandatory and portable individual trust to which the employer and employee contributed. It shifts control and responsibility from the employer and the state government to the employer and the employee, and it is compatible with the realities of a twenty-first-century economy. We begin by providing an overview of how the current unemployment insurance system works and discussing its problems. We then describe an alternative unemployment policy based on IUAs and discuss the benefits of such a policy.