## EFFICIENT UNEMPLOYMENT INSURANCE: A Model of Job Search 2

Depending on workers’ application decisions, there may be more competition for some jobs than others. To capture this, we let qj be the ratio of workers who apply for jobs at firms offering wage Wj to the number firms posting that wage. We refer to this as the job’s expected queue length, an endogenous measure of the extent of competition for jobs offering Wj. We assume that a worker applying to wage wj is hired with probability //(fy), where ^ : E+ Uoo —> [0,1] is decreasing and continuously differentiable; if many workers apply for one type of job, each has a low employment probability website.

Symmetrically, the probability that firm j hires a worker is r](qj), where 77 : 1R+ U 00 —» [0,1] is increasing and continuously differentiable.2 This implies that holding constant the number of workers applying for a given wage, if more firms post that wage, each has a lower hiring probability. We impose the boundary conditions т/(0) = д(оо) == 0 and 77(00) = /x(0) = 1.
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## EFFICIENT UNEMPLOYMENT INSURANCE: A Model of Job Search

Preferences and Technology

There is a continuum 1 of identical workers, each with the von Neumann-Morgenstern utility function u(c) over final consumption, и is twice continuously differentiable, strictly increasing, and weakly concave. All workers are endowed with initial wealth Л0, which they may either store or invest in a mutual fund. The absence of aggregate risk ensures that the mutual fund’s gross rate of return is equal to the return from storage, R = 1. Worker z’s consumption is therefore equal to his assets A0, minus lump-sum taxes r, plus net income from wages or unemployment benefits y,-, so his utility is

u(A + yi),

where A = A0 — r is after-tax assets. In most of the paper, we will think of UI as provided by the government and financed by taxes, but it could also be provided by a private insurance firm or the worker’s family.
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## EFFICIENT UNEMPLOYMENT INSURANCE: Introduction 3

The result that UI is welfare improving is also related to the implicit contract literature developed by Azariadis (1975), Bailey (1974), and Gordon (1974). In this literature, firms provide insurance to risk-averse workers by increasing employment above the first-best level. Introducing UI would make workers more willing to take the job loss risk and improve welfare. There are, however, important differences between this story and our’s further.

First, endogenous job composition (capital-labor ratios) and free entry play key a role in our model, and imply that UI not only increases ex ante welfare but also raises the level of output and improves the composition of jobs. In the standard implicit contract model, UI reduces output, and there are no implications about job composition. Second, our result is derived in a general equilibrium search model, which has two advantages: (i) the source of the inefficiencies are fully specified, and we show that when frictions disappear, the economy is efficient and there is no room for UI; (ii) firms cannot improve upon the decentralized equilibrium, which contrasts with the implicit contract setting where firms can increase their profits by introducing severance payments.
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## EFFICIENT UNEMPLOYMENT INSURANCE: Introduction 2

A feature of our model is that despite the dynamic nature of the decisions, the analysis can be carried out in a static model. We prove this by fully analyzing a dynamic model of search with precautionary savings, and establishing that all the qualitative results are the same as in a static model. Since the equilibrium of the static model is equivalent to the solution of a constrained maximization problem and can be analyzed diagrammatically, it can easily be used for other applications.
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## EFFICIENT UNEMPLOYMENT INSURANCE: Introduction

We develop a general equilibrium model of search and matching with risk-averse agents and incomplete insurance. Firms make irreversible investments and post wages. Workers optimally search among posted wages. There is an unavoidable risk for workers in this frictional economy as they may suffer unemployment. When workers are more risk-averse, wages and unemployment decrease, and firms invest less. The reason is that risk-averse workers wish to avoid the risk of unemployment, and in response, the labor market offers its own version of insurance, an equilibrium with higher employment but lower wages. In a frictional market, when the unemployment risk of workers is reduced, the vacancy risk of firms increases, implying lower utilization of their ex ante investment. Anticipating this, firms reduce their capital-labor ratio review.

UI encourages workers to apply to high wage jobs with high unemployment risk. The impact of UI on worker and firm behavior is driven by a form of moral hazard. Because the insurers cannot directly control workers’ actions, the increased utility of unemployment induces them to search for higher wage jobs. Firms respond by creating high wage jobs, with greater unemployment risk and greater capital-labor ratios, enabling workers to seek riskier opportunities.
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## THE PORTFOLIO FLOWS: Conclusions

We have used a new source of high frequency data on international portfolio flows to learn about how inflows behave and how they interact with returns. Our findings can be summarized as follows:

1. International portfolio inflows are slightly positively correlated across countries, and are more strongly correlated within regions. The correlation of flows in most regions, and particularly within Asia, rises strongly during the Asian crisis subsample, but not during the Mexican crisis subsample.

2. Inflows and outflows are highly persistent. The persistence is complex in the sense that a shock to inflows today is associated with slightly greater inflows over a long period of time.

3. There is very strong trend following in international inflows. The majority of the co-movement of flows and returns at quarterly or monthly intervals is actually due to returns predicting future flows.
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## THE PORTFOLIO FLOWS: The Interaction Between Flows and Returns 5

Table 9 reports our estimates of the structural parameters, a, b, c, e. Note that the magnitude of coefficient e is affected by the fraction of true inflows that are captured by our data. If State Street clients’ share of total inflow into developed countries is half of their share into emerging markets, then we would expect the developed countries’ coefficient to be twice as large. In any case, our estimates of e are positive and statistically significant.

The estimate for the world suggests that a positive shock to inflows equal to 1 basis point of capitalization results in a contemporaneous increase in prices of 68 basis points. The corresponding coefficient for developed countries is 90 basis points. Of course, if these State Street’s clients account for a fifth of total inflows, then the semi-elasticity is one fifth as big. Even so, this would still be a larger sensitivity to prices than has been previously estimated for flows into US mutual funds.

The estimates of с are universally negative, with all but one being statistically significant at the 5% level. Note that a negative estimate of с (combined with the positive coefficient e) suggests that temporary inflows result in a temporary price increases. However, this does not mean that inflows forecast returns negatively—inflows are strongly persistent as we have seen, so that it is unlikely that inflows today will subside fully tomorrow. Thus, the information content in inflows—which we have seen to be positive in emerging markets—is a result of fact the current inflows predict future inflows, and future inflows drive up future prices.
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## THE PORTFOLIO FLOWS: The Interaction Between Flows and Returns 4

This model can be summarized in the following way:

and ^fand XT are decay coefficients to be estimated. £fand Sr represent are the unexpected inflow and shocks to returns; a and b are respective persistence and trend following parameters for order flow, e describes the price impact of unexpected order flow on return, and с represents the extent to which price pressure offsets the information content of inflows. Our structural model can be thought of as a restricted (and over identified) version of the following reduced form model add comment:

where the distributed lag is the same as in the structural model. Parameters 71,t and K2l show the incremental predictability of lagged flows for future flows and returns, respectively. Similarly, TC,2 and 7I22 show the incremental predictability of lagged returns for future flows and returns.
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## THE PORTFOLIO FLOWS: The Interaction Between Flows and Returns 3

Pursuing this line of thinking one step further, we investigate the covariances of idiosyncratic (country specific) portion of flows from equation (1). This is the portion of flows that the Brennan and Cao local-information story emphasizes. Table 6 shows that country specific flows differ from regional factors in several important ways. First, the country-specific flows affect prices less than the regional factor does.

Estimated CVRs are smaller and less statistically significant than those reported in Tables 5. Second, with a few exceptions, country-specific flows seem unrelated to past returns. Third, idiosyncratic flows have only modest predictive power—positive or negative—for future returns. Overall, the results suggest that idiosyncratic flows behave according to our simplest null hypothesis: that flows are relatively uncorrelated with each other and with returns. This is directly at odds with the Brennan and Cao story, which implies a strong correlation between idiosyncratic flows and local returns.

Tables 7 and 8 are analogous to Tables 5 and 6, except that they focuses on excess currency (not equity) returns. Table 7 results are similar to Table 5 in that flows predict currency returns in emerging markets, but not in developed markets.
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## THE PORTFOLIO FLOWS: The Interaction Between Flows and Returns 2

Table 5 presents the decomposition of the quarterly covariance of flows and equity returns at the regional level. The first column reports the actual CKR-statistic with к set equal to 60 (quarterly decomposition.) For the purposes of inference, the variance of the СКЯ-statistic and its components is estimated from the heteroscedasticity-consistent variances of the daily p estimates add comment.

The first point to note about the tables is that they show clearly the benefit of using daily data instead of monthly or quarterly data. As we can see from Table 5, Panel B, contemporaneous covariance, accounts for at most 13% of measured quarterly covariance. We can see that only a third of the quarterly covariance between flows and equity returns can be attributed to the window period from -5 days to +5 days.

Table 5 also shows the decomposition of the lag and lead effects. For both developed markets and emerging markets, it is clear that most of the CKK-statistic is due to component (a). As mentioned earlier, the size and significance of component (a) tell a simple story of investor “trend chasing” behavior. In other words, positive local stock market returns result in future local inflows.
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