## 1. Introduction

## 2. Background on the Difference-in-Differences Estimator

^{T}is the outcome of the treated group and Y

^{C}the control group (Meyer 1995, p. 155). The subscripts 0 and 1 indicate, respectively, the outcomes before and after the treatment. Equation (1) shows clearly why the method is referred to as a difference-in-differences estimator; it is literally the difference between two differences.

## 3. Summarizing the Fair Use Study

We posit that flexible fair use in copyright law has two additional effects in the economy beyond those posited by traditional fair use analyses. Flexible fair use exemptions may: (1) increase the growth rate of private copying technology industries; and (2) increase the growth rate of copyright markets. We test this hypothesis using a differences-in-differences methodology that is applied to the 2005 fair use amendments to the Singapore Copyright Act and test its implications on private copying technology and copyright sectors in Singapore.

_{t}= β

_{0}+ β

_{1}t + e

_{t}

_{t}is the value-added figure and t is a time indicator (t = 1, 2, …, 6). Using the estimated β

_{0}and β

_{1}coefficients from Equation (2), the authors compute the value of y in the final period (y

_{12}, six years later in the year 2010, ignoring the data from 2005 through 2009), and this prediction serves as the pre-treatment value (or untreated value) of y (or ${Y}_{0}^{T}$ from Equation (1)). For example, data from the Private Copying group produces the “prediction” equation:

_{t}= 0.06338 − 0.00388t

## 4. The Empirical Analysis

#### 4.1. Multiple Treatments

#### 4.2. Hypothesis Testing and Sample Sizes

#### 4.3. Dimension Problems

#### 4.4. The Parallel Paths Assumption

#### 4.5. Additional Issues

_{t}− y

_{t}

_{−1}). Without data from 1998, this produces a missing value for year 1999, which reduces the sample size from 12 years to 11 years. Looking at Table A5, however, rather than excluding 1999 from the data as a missing value, the authors have inserted “0” as a data point for that year. The regression results from Table A4 indicate there are 12 observations in the regression, which implies that the “0” observation for 1999 was, in fact, included in the estimation (I was able to replicate the results to confirm this error).

## 5. A Standard Estimation Technique

_{it}= δD

_{it}+ βX

_{it}+ λ

_{t}+ μ

_{i}+ ε

_{it},

_{it}is the outcome for observation i at time t, D

_{it}is a dummy variable that equals 1 if the observation is treated in year t (0 otherwise), X

_{it}is a vector of control variables that vary by observation and time, μ

_{i}is a fixed effect for each observation i, λ

_{t}is a time effect common to all observations in time t, and ε

_{it}is the econometric disturbance term that is assumed to be distributed independently of all μ and λ (Angrist and Krueger 1999, p. 1294). The δ and β

_{1}are also estimated parameters. This model is a two-way fixed effects model (that is, there are dummy variables for each series and each time period). These dummy variables address the dimension problem and account for broader economic shocks (Angrist and Krueger 1999, pp. 1293–99).

_{it}falls out of Equation (4). The data is measured as “value added” of various sectors in the economy, which I label v

_{it}. Thus, Equation (4) can be simplified to:

_{it}= δD

_{it}+ λ

_{t}+ μ

_{i}+ ε

_{it},

_{it}is a dummy variable equal to 1 for the Private Copying or Copyright groups beginning in year 2005 (0 otherwise). The regression is a two-way (SSIC, time) fixed effects regression with a dummy variable that equals 1 for the treatment groups during the treatment period (2005 to 2010). Standard errors are clustered on the SSICs, as is recommended in the literature (Bertrand et al. 2004).

^{2}of the regression is 0.05 and the F-statistic is 4.34 (prob < 0.01). The estimated treatment effect (δ) for the Private Copying group is 0.00074 with a t-statistic of 0.30 (prob = 0.77); the effect is not statistically different from zero. The null hypothesis of “no change” in the Private Copying group’s outcomes before and after 2005 cannot be rejected. For the Copyright group, the estimated treatment effect (δ) is equal to 0.00034 with a t-statistic of 0.81; the effect is not statistically different from zero (prob = 0.43). The null hypothesis of “no change” in the Copyright group’s outcomes before and after 2005 cannot be rejected. Thus, the modifications to Singapore’s copyright law are found to have had no effect on the economic outcomes that Ghafele and Gibert deemed of interest.4

## 6. What if the Results Were Right?

## 7. Conclusions

## Funding

## Conflicts of Interest

## References

- Angrist, Joshua D., and Alan B. Krueger. 1999. Empirical Strategies in Labor Economics. In Handbook of Labor Economics. Edited by Orley Ashenfelter and David Card. Amsterdam: Elsevier Science, vol. 3A. [Google Scholar]
- Angrist, Joshua D., and Jörn-Steffen Pischke. 2008. Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton: Princeton University Press. [Google Scholar]
- Aufderheide, Patricia, and Peter Jaszi. 2011. Reclaiming Fair Use. Chicago: Chicago University Press. [Google Scholar]
- Autor, David H. 2003. Outsourcing at Will: The Contribution of Unjust Dismissal Doctrine to the Growth of Employment Outsourcing. Journal of Labor Economics 21: 1–42. [Google Scholar] [CrossRef][Green Version]
- Barker, George Robert. 2013. Agreed Use and Fair Use: The Economic Effects of Fair Use and Other Copyright Exceptions in the Digital Age. Unpublished Working Paper. Available online: http://ssrn.com/abstract=2298618 or http://dx.doi.org/10.2139/ssrn.2298618 (accessed on 9 July 2013).
- Barker, George R., and Ivan Png. 2013. ALRC Inquiry into Copyright and the Digital Economy Submission in response to Discussion Paper 79: Unreliable Evidence on Fair Use. Submission Received by the Australian Law Reform Commission, Copyright and the Digital Economy (DP 79). Available online: https://www.alrc.gov.au/sites/default/files/subs/507._g_r_barker__prof_i__png.pdf (accessed on 14 September 2018).
- Bertrand, Marianne, Esther Duflo, and Sendhil Mullainathan. 2004. How Much Should We Trust Differences-In-Differences Estimates? Quarterly Journal of Economics 119: 249–75. [Google Scholar] [CrossRef]
- Blank, Rebecca M., and David J. Kappos. 2012. Intellectual Property and the U.S. Economy: Industries in Focus. U.S. Patent & Trademark Office. Available online: http://www.uspto.gov/sites/default/files/news/publications/IP_Report_March_2012.pdf (accessed on 14 September 2018).
- Card, David. 1990. The Impact of the Mariel Boatlift on the Miami Labor Market. Industrial and Labor Relations Review 13: 245–57. [Google Scholar] [CrossRef]
- Galiani, Sebastian, Paul Gertler, and Ernesto Schargrodsky. 2005. Water for Life: The Impact of the Privatization of Water Services on Child Mortality. Journal of Political Economy 113: 83–123. [Google Scholar] [CrossRef]
- Ghafele, Roya, and Benjamin Gibert. 2014. A Counterfactual Impact Analysis of Fair Use Policy on Copyright Related Industries in Singapore. Laws 3: 327–52. [Google Scholar] [CrossRef][Green Version]
- Imbens, Guido W., and Jeffrey M. Wooldridge. 2009. Recent Developments in the Econometrics of Program Evaluation. Journal of Economic Literature 47: 5–86. [Google Scholar] [CrossRef][Green Version]
- Intellectual Office of Singapore. 2016. Asking Permission and Using Copyright. Available online: http://www.ipos.gov.sg/AboutIP/TypesofIPWhatisIntellectualProperty/Whatiscopyright/Askingpermissionandusingcopyright.aspx (accessed on 22 January 2016).
- Lechner, Michael. 2011. The Estimation of Causal Effects by Difference-in-Difference Methods. Foundations and Trends
^{®}in Econometrics 4: 165–224. [Google Scholar] [CrossRef] - Leval, Pierre N. 1990. Toward a Fair Use Standard. Harvard Law Review 103: 1105–36. Available online: http://www.pijip.org/wp-content/uploads/2015/11/103HarvLRev.pdf (accessed on 14 September 2018).
- Mann, Colin. 2014. Singapore Proposes Copyright Amendments. Advanced Television. April 9. Available online: http://advanced-television.com/2014/04/09/singapore-proposes-copyright-amendments/ (accessed on 14 September 2018).
- Meyer, Breed D. 1995. Natural and Quasi-Experiments in Economics. Journal of Business & Economic Statistics 13: 151–61. [Google Scholar]
- Stanford University Library. 2016. What is Fair Use? Available online: http://fairuse.stanford.edu/overview/fair-use/what-is-fair-use (accessed on 22 January 2016).
- TBO. 2014. Singapore Passes Copyright Amendment. Trademarks & Brands Online. Available online: http://www.trademarksandbrandsonline.com/news/singapore-passes-copyright-amendment-4011 (accessed on 14 September 2018).
- WIPO. 2005a. Trade Marks Act (Singapore), Chapter 332, Revised Edition 2005. Available online: http://www.wipo.int/wipolex/en/text.jsp?file_id=187981 (accessed on 14 September 2018).
- WIPO. 2005b. Patents Act (Singapore), Chapter 221, Revised Edition 2005. Available online: http://www.wipo.int/wipolex/en/details.jsp?id=5296 (accessed on 14 September 2018).
- WIPO. 2006. Copyright Act (Singapore), Chapter 63, Revised Edition 2006. Available online: http://www.wipo.int/wipolex/en/text.jsp?file_id=187737 (accessed on 14 September 2018).

1 | An alternative interpretation of the results is that the analysis shows a huge forecast error for the Private Copying group and small errors for the Copyright and Control groups. |

2 | A possible case where both the treated and control groups receive the treatment but the control group remains valid (possibly) is if the control group is genetically immune from the disease being treated (or the treatment itself). Even so, the control group would be suspect. |

3 | Each series is mean-centered (on unity) for illustration purposes. |

4 | Given problems with the data, control group, and the parallel paths assumption, I do not contend that these findings are actually valid. Rather, if I take Ghafele and Gibert’s general approach and apply proper statistical test, no effect is found. |

Industry Group | 2010 Actual | 2010 Predicted | Diff. | Impact (Adj. for Control) |
---|---|---|---|---|

Private Copying | 5.02% | 1.68% | 3.34% | 3.33% |

Copyright | 0.55% | 0.78% | −0.23% | −0.25% |

Control | 0.44% | 0.43% | 0.01% | … |

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