This thesis addresses a long-standing puzzle in empirical econometrics: Does the size distribution of income matter in the aggregate consumption function? Current opinion on whether distribution matters is divided. There is also a lack of consensus (among those who believe distribution effects exist) on the nature of such effects; that is, whether a decrease or an increase in income inequality is needed to stimulate aggregate demand. In this thesis, the previous or existing tests are challenged on the grounds that they do not properly take into account the causal link between the variability of the marginal, not the average, propensity to consume (with respect to the income level) and the existence of distribution effects. This particular link is taken care of, however, if one tests for the linearity (in income) of the micro relation underlying one's aggregate consumption function. The rejection of the linearity hypothesis will establish the existence of distribution effects. Ex post, if the nonlinear relation is such that the marginal propensity to consume declines with income, it also follows that an equalization in the income distribution produces greater aggregate consumption. The theoretical contribution of this thesis lies in the clarification of these issues. On the empirical side, this thesis cautions against the casual use of the term "distribution effects". In the current income-current expenditure framework of the Keynesians, it refers to "the effect of a redistribution of real disposable income" on aggregate real consumers' expenditure. In the Permanent Income Hypothesis framework, however, it could mean either "the effect of a redistribution of real disposable income" or "the effect of a redistribution of real permanent income" on aggregate real consumption. In this thesis, the distributions of real disposable income and real permanent income are alternatively assumed to follow the lognormal density, and two conclusions are empirically determined: I. The distribution of real disposable income matters in the current income-current expenditure framework---this result is statistically significant at a 10% level after the correction for serial correlation and simultaneity bias. In particular, the estimates indicate that the marginal propensity to consume declines with the level of real disposable income and, hence, a decrease in inequality would stimulate aggregate demand. II. The elasticity of consumption out of real permanent income is unity; therefore, the distribution of real permanent income does not matter in the Permanent Income Hypothesis framework---this result is statistically. significant at all conventional levels of significance both before and after the correction for serial correlation. Both findings are based on aggregative time-series data for Canada. The consumer unit in this thesis is an individual income-recipient, and the data period is 1947-1976. Maximum-likelihood procedures have been used in the estimation, with proper allowance for across-parameter constraints. In the event of correction for serial correlation, the autocorrelation coefficient is constrained to the open-interval (+1,-1). The results are also double-checked by examining many avenues that might affect the nature of the outcomes. Another contribution of this study is the compilation of data on the distribution of pre-tax personal income (in current dollars) in Canada under the lognormality hypothesis. The parameters of this distribution are determined using the minimum chi-square method. Estimates of the variance (of logarithms of income) parameter show a slight increase in income inequality over the period 1946 to 1976. The data on this parameter are used to approximate the variance of logarithms for the distribution of real disposable income (while establishing result I) and also the same for the distribution of real permanent income (while establishing the result II). / Thesis / Doctor of Philosophy (PhD)

The growing interest in the Internet of Things (IoT) has led to predictions claiming that by 2020 we can expect to be surrounded by 50 billion Internet connected devices. With more entry points to a network, adversaries can potentially use IoT devices as a stepping stone for attacking other devices connected to the network or the network itself. Information security relies on cryptographic primitives that, in turn, depend on secret keys. Furthermore, the issue of Intellectual property (IP) theft in the field of Integrated circuit (IC) design can be tackled with the help of unique device identifiers. Physical unclonable functions (PUFs) provide a tamper-resilient solution for secure key storage and fingerprinting hardware. PUFs use intrinsic manufacturing differences of ICs to assign unique identities to hardware. Arbiter PUFs utilise the differences in delays of identically designed paths, giving rise to an unpredictable response unique to a given IC. This thesis explores the statistical properties of Boolean functions induced by arbiter PUFs. In particular, this empirical study looks into the distribution of induced functions. The data gathered shows that only 3% of all possible 4-variable functions can be induced by a single 4 stage arbiter PUF. Furthermore, some individual functions are more than 5 times more likely than others. Hence, the distribution is non-uniform. We also evaluate alternate PUF designs, improving the coverage vastly, resulting in one particular implementation inducing all 65,536 4-variable functions. We hypothesise the need for n XORed PUFs to induce all 22n possible n-variable Boolean functions.