Shopping Externalities and Self Fulfilling Unemployment Fluctuations*

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Table 4: Robustness: steady-state unemployment rates and price statistics for combinationsof and RHome production technology for BJ goods (R)10.00 13.33 16.67 20.00Panel A: Steady-state unemployment ratesWeight on BJ goods ()0.80 5.3, 13.9, 100 5.3, 13.2, 100 5.3, 12.8, 100 5.3, 12.5, 1000.87 5.3, 11.9, 100 5.3, 11.3, 100 5.3, 10.9, 100 5.3, 10.7, 1000.93 5.3, 10.2, 100 5.3, 9.7, 100 5.3, 9.3, 100 5.3, 9.1, 1001.00 5.3, 8.8, 100 5.3, 8.3, 100 5.3, 8.0, 100 5.3, 7.8, 100Panel B: Price statistics (see notes)Weight on BJ goods ()0.80 0.23, 1.2, 0.99 0.31, 1.35, 0.99 0.4, 1.5, 0.98 0.49, 1.65, 0.980.87 0.24, 1.3, 0.99 0.33, 1.47, 0.98 0.42, 1.63, 0.98 0.51, 1.79, 0.980.93 0.25, 1.4, 0.99 0.34, 1.58, 0.98 0.43, 1.75, 0.98 0.53, 1.93, 0.981.00 0.26, 1.5, 0.99 0.36, 1.69, 0.98 0.45, 1.88, 0.98 0.54, 2.07, 0.98Notes: In Panel B, the numbers in each cell refer to the coe¢ cient of variation of prices, the ratio of themaximum price to minimum price, and the price paid by unemployed relative to employed.parameters. We …nd that, in the region where the elasticity of the UE rate or is relativelyhigh or the pro…t margin is relatively low, the model admits three steady states. In thisregion, the unemployment rate associated with the intermediate steady state is decreasingin the elasticity of UE and increasing in the …rm’s pro…t margin. These …ndings are intuitivebecause the u-nullcline becomes more curved as we increase the elasticity of the UE rate, andthe J-nullcline becomes ‡atter as we increase the pro…t margin. It is only in the region wherethe elasticity of the UE rate is relatively low and the pro…t margin of the …rm is relativelyhigh that the model admits a unique steady state. Moreover, this region shrinks as weincrease the targeted di¤erence in either expenditures or shopping time between employedand unemployed workers.6 ConclusionsIn this paper, we analyzed a model economy with frictional labor and product markets.Matching frictions in the labor market generate equilibrium unemployment and income differencesbetween employed and unemployed workers. Search frictions in the product marketlead to an equilibrium price distribution for identical goods and, because of di¤erences inthe amount of time available for shopping, to di¤erences in the price paid by employed46
Table 5: Robustness: steady-state unemployment rates and price statistics for combinationsof targets for elasticity of UE rate with respect to and …rms’pro…t marginFirms’pro…t margin1.05 1.1 1.15 1.2Panel A: Steady-state unemployment ratesUE elasticity0.45 5.3, 20.7, 70.3 5.3 5.3 5.30.55 5.3, 12.6, 92.4 5.3, 23.1, 78.1 5.3, 48.8, 100 5.30.65 5.3, 8.3, 100 5.3, 13.2, 100 5.3, 18.8, 94.9 5.3, 25.9, 85.60.75 5.3, 5.7, 100 5.3, 8.2, 100 5.3, 10.7, 100 5.3, 13.4, 100Panel B: Price statistics (see notes)UE elasticity0.45 0.37, 1.72, 0.98 0.41, 1.72, 0.98 0.44, 1.72, 0.98 0.48, 1.72, 0.980.55 0.37, 1.72, 0.98 0.41, 1.72, 0.98 0.44, 1.72, 0.98 0.48, 1.72, 0.980.65 0.37, 1.72, 0.98 0.41, 1.72, 0.98 0.44, 1.72, 0.98 0.48, 1.72, 0.980.75 0.37, 1.72, 0.98 0.41, 1.72, 0.98 0.44, 1.72, 0.98 0.48, 1.72, 0.98Notes: In Panel B, the numbers in each cell refer to the coe¢ cient of variation of prices, the ratio of themaximum price to minimum price, and the price paid by unemployed relative to employed.and unemployed workers. In this economy, a …rm hiring an additional worker creates positiveshopping externalities on other …rms, because employed buyers have more income tospend and less time to search for low prices than unemployed buyers. We proved that, ifthese shopping externalities are strong enough, the employment decisions of di¤erent …rmsbecome strategic complements and multiple rational expectations equilibria emerge.We calibrated the model and showed that the empirical di¤erences in expenditure andshopping time between employed and unemployed workers are large enough to generatemultiplicity and, hence, to open the door for non-fundamental shocks based on changes inagents’expectations about long-run unemployment. Finally, we formally introduced nonfundamentalshocks into the model by de…ning a notion of Regime Swithcing Equilibrium.We showed that a negative shocks to the agents’ expectations (i.e., a switch from an optimisticto a pessimistic regime) generates ‡uctuations in unemployment, vacancies, laborproductivity and in the value of the stock market that look qualitatively and quantitativelysimilar to those observed in the US economy during the Great Recession.Much work remains to be done. First, our paper is silent about the welfare properties ofdi¤erent equilibria. Equilibria with a higher vacancy rate may be better than equilibria witha lower vacancy rate because they lead to lower unemployment and more output. On theother hand, equilibria with a higher vacancy rate may be worse than equilibria with a lower47
Page 2: 1 IntroductionWe propose a novel th
Page 5 and 6: claims). However, they certainly in
Page 7 and 8: the evidence brought forward that
Page 9 and 10: function with boundary conditions (
Page 11 and 12: are given byS t (p) = ((u t )) u t(
Page 13 and 14: The …rm and the worker bargain ov
Page 15 and 16: the paper, which is mainly devoted
Page 17 and 18: espect to u as (1 +S 0 (u) =u )(1
Page 19 and 20: a seller meets a buyer is constant.
Page 21 and 22: The eigenvalues, the determinant an
Page 23 and 24: to denote the set of J’s such tha
Page 25: JJů = 0ů = 0E1E1J1sJ1sE2J3sE2J3sE
Page 28 and 29: understand that regime switches can
Page 30 and 31: De…nition 3. An i-j Regime Switch
Page 32 and 33: 5 Sentiments and the Great Recessio
Page 34 and 35: Table 1: Calibration targetsLabor M
Page 36 and 37: …ndings in Sorensen (2000) and Mo
Page 38 and 39: An increase in unemployment of 1 pe
Page 40 and 41: 11.51110.5109.5Mean posted priceMea
Page 42 and 43: with the pessimistic regime. The de
Page 44 and 45: etween employed and unemployed work
Page 48 and 49: vacancy rate because they are assoc
Page 50 and 51: [22] Heller, W. 1986. “Coordinati
Page 52 and 53: AppendixA Proof of Lemma 1Consider
Page 54 and 55: Claim 5. The only F (p) that satis
Page 56 and 57: where the parameters 0 and 1 are
Page 58: After substituting (C5) into (C6),

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