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Does Unemployment Matter for Lottery Sales and their Persistence? A New Estimation Approach

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Abstract

This paper employs the panel smooth transition autoregressive model to evaluate the threshold effect of unemployment rate on lottery sales and their persistence. To perform the empirical estimation, we use the panel data of lottery sales in 42 US states during the period of January 2003–December 2011. Thus, we have 4536 observations. The empirical results find that the effect of unemployment on lottery sales is nonlinear, heterogeneous, and time-varying, depending on the unemployment rates in different regimes. A rise (decrease) in unemployment will lead to a higher (lower) persistence effect of lottery sales. However, reducing unemployment rate is not a practical instrument for state governments to stabilize lottery markets. For the sellers of lottery tickets, designing new lottery products is a more efficient method for stimulating current lottery sales than anticipating the improvement in the unemployment rate.

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Notes

  1. See Johnston (2011). U.S. lotteries and the state taxman. Reuters, July, 15.

  2. A typical research design to measure the persistence of the dependent variable is to estimate the regression model \(Y_{it} = \alpha_{0} + \alpha_{1} Y_{it - 1} + \varepsilon_{it} ,\) where α1 is the estimated persistence of the dependent variable (Dichev and Tang 2008). That is, the estimated coefficient of the one-period lagged depend variable is considered as the persistence effect. In practice, j-period lagged depend variable, j = 1, 2, …, n, may influence the depend variable. Thus, we include more lagged terms of dependent variable to evaluate the persistence effect. Regarding this kind of definition in the persistence effect, see Cheng and Wu (2013).

  3. The cases of m = 1 and m = 2 correspond to a logistic PSTR model and a logistic quadratic PSTR specification, respectively.

  4. It is easy to extend the PSTR model to more than two regimes. For more details, see González et al. (2005).

  5. For more details on the testing of no remaining non-linearity, see González et al. (2005).

  6. This study excludes the remaining 8 states due to unavailable data.

  7. The estimation results are available upon request.

  8. Following the proposition of González et al. (2005) and the followers, this paper allows the number of location parameters (m) to be either one or two.

  9. While these two cases have at least two transition functions, one of the thresholds locates outside the sample range. That is an unreasonable result.

  10. We only display the results of the optimal estimation model; however, the remaining estimation results are available upon request.

  11. A conventional linear estimation model must pass the misspecification tests, including the tests of no serial correlation, homoscedasticity, linearity, normality, no perfect multicollinearity, and parameter time invariance. However, the testing results in this study show that the PSTAR model is an optimal one. That is, the PSTAR model rejects the linearity of model and supports time-varying parameters. As to the first two tests, they have been verified by the stationarity test. In addition, the estimation result in the stepwise regression has excluded the problem of multicollinearity. Finally, a large sample (4536 observations) used in the empirical estimation makes the estimators with asymptotic normal distributions.

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Correspondence to Po-Chin Wu.

Appendix

Appendix

See Tables 4, 5.

Table 5 Panel unit root test

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Wu, PC., Liu, SY. & Wang, KB. Does Unemployment Matter for Lottery Sales and their Persistence? A New Estimation Approach. Soc Indic Res 130, 581–592 (2017). https://doi.org/10.1007/s11205-015-1183-3

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